PROCEEDINGS

OF THE

AMERICAI^ ACADEMY

OF

ARTS AND SCIENCES.

Vol. XL VII.

FROM MAY 1911, TO MAY 1912.

BOSTON:

PUBLISHED BY THE ACADEMY

1912

5anii)crsttg ^xtssx
John Wilson and Son, Cambridge, U.S.A.

a JT r 6-

CONTENTS.

Page
I. An Investigation of the Errors in Cooling Cuives and Methods
for Avoiding these Errors; Also a New Form of Crucible.
By H. C. Hayes 1

II. Determination of the Altitude of Aeroplanes. By R. W.

WiLLSON 23

III. The Nature of Volcanic Action. By R. A. Daly .... 45

IV. The Pegmatites of the Riebeckite-Aegirite Granite of Quincy,

Alass., U.S.A.; Their Structure, Minerals, and Origin. By

C. H. Warren and C. Palache 123

V. The Transition Temperatures of Sodium Chromate as Convenient
Fixed Points in Thermometry. By T. W. Richards and
G. L. Kelley 169

VI. (/.) On the Classification of Certain>Eupatoricae ; {II.) Revision
of the Genus Barroetea; (III) On some Hitherto Undescribed
or Misplaced Composite. By B. L. Robinson 189

VII. Calanoid Copepoda from the Bermuda Islands. By C. O.

ESTERLY 217

VIII. The von Waltenhofen Phenomenon in Soft Iron Rings. By

L. A. Babbitt 227

IX. A New Method of Impact Excitation of Undamped Oscillations
and their Analysis by means of Braum Tube Oscillographs. By
E. L. Chaffee 265

X. The Wave Potential of a Circular Line of Sources. By A. (J.

Webster 313

XI. The Measurement of Hydrostatic Pressures up to 20,000 Kilo-
grams per Square Centimeter. By P. W. Bridg.man . . . 319

IV CONTENTS.

Page
XII. Mercury, Liquid and Solid, Under Pressure. By P. VV.

Bkidgman 345

XIII. Water, in the Liquid and Five Solid Forms, under Pressure. By

P. W. Bridgmax '. 439

XIV. On an Electromagnetic Theory of Gravitation. By D. L.

Webster 559

XV. yl Revision of the Atomic Weight of Phosphorus. By G. P.

Baxter, C. J. Moore and A. C. Boylston 583

XVI. Polycerella Znobofryon. By W. M. Smallwood .... 607

XVII. The Anomalous Magnetization of Iron and Steel. By B. O.

Peirce 631

XVIII. Pyrosulphuryl Chloride and Chlorsulphonic Acid. By C. R.

Sanger and E. R. Riegel 671

XTX. The Fall of a Meteoiite. By E. Thomson 719

XX. An Algebra of Plane Projective Geometry. By H. B. Phillips

and C. L. E. Moore 735

XXI. On Electrical Properties of Crystals. (7.) Stratification and
Capacity of Carborundum. By G. W. Pierce and R. D.
Evans 791

XXII. Records of Meetings 825

Biographical Notices:

Frederick Irving Knight. By Francis H. Williams . . . 867
Thomas Wentworth Higginson. By Andrew MacFarland

Davis 868

Officers and Committees for 1912-13 883

List of Fellows and Foreign Honorary Members .... 885

Statutes and Standing Votes 899

Rumford Premium 913

Index 915

Proceedings of the American Academy of Arts and Sciences.
Vol. XLVII. No. 1. — Mat, 1911.

CONTRIBUTIONS FROM THE JEFFERSON PHYSICAL
LABORATORY, HARVARD UNIVERSITY.

AN INVESTIGATION OF THE ERRORS IN COOLING

CURVES AND METHODS FOR AVOIDING THESE

ERRORS; ALSO A NEW FORM OF CRUCIBLE.

By Harvey C. Hayes.

With Six Plates.

Inyestiqations on Light and Heat pcblished with Aid from the Rumford Fund.

CONTRIBUTIONS FROM THE JEFFERSON PHYSICAL
LABORATORY, HARVARD UNIVERSITY.

AN INVESTIGATION OF THE ERRORS IN COOLING CURVES

AND METHODS FOR AVOIDING THESE ERRORS;

ALSO A NEW FORM OF CRUCIBLE.

By Harvey C. Hayes.

Presented by John Trowbridge, Februarj- 8, 1611. Received December 29, 1910.

Two main difficulties are encountered by one who attempts to make
an accurate study of the physical properties of alloys. The first diffi-
culty is the preparation of an alloy which shall contain only the desired
elements in its make-up. Foreign elements may enter the alloy through
lack of purity in the component metals (and the difficulty of getting
chemically pure metals is never appreciated until one has attempted
it), also impurities are almost sure to get into the alloy from the
crucible. The chemist can, with sufficient pains, prepare pure samples
of nearly all the metals ; but thus far science has not produced a
crucible that will keep them pure while melting them into an alloy.
Impurities from this source have been a hindrance to the study of
alloys, especially a study of their magnetic properties, and have been
a cause for more or less error in the work that has thus far been done.

Roberts- Austen, in his classic experiment, showed that solids diffuse,
even at comparatively low temperatures. This makes doubtful the
possibility of finding a crucible that will not diffuse somewhat into
the alloy at such a temperature as the melting point of most metals.
One solid that does not seem to diffuse into metals, and apparently
the only one that does not, is quicklime. A block of lime with a hol-
low scooped out ofttimes serves the chemist for a crucible, for all that
he requires of a crucible is that it shall hold together long enough to
melt a small portion of metal and then slowly cool. But for the study
of alloys such a crucible will not suffice, as it is often necessary to chill
the melt. A block of lime will not stand such treatment ; and even if
it would, the lime is so poor a conductor of heat that it would be im-
possible to chill an alloy through the comparatively thick walls of such
a crucible.

4 PROCEEDINGS OF THE AMERICAN ACADEMY.

The crucible. — The ideal crucible for work on allo> s would be one
made from thin metal, if we could find some metal that would not
diffuse, for we could then readily study the effects of chilling, as the
crucible would be a good heat conductor. But since all metals diffuse,
even in the solid state, we cannot hope for such a crucible. The best
substitute would be one made from thin metal and lined with a thin
coating of lime.

The need for such a crucible has been felt by all who have attempted
to make anything like an accurate study of alloys, and attempts have
been made to perfect one, but until now without success. The author
has finally succeeded in lining a steel crucible with a thin coating of
lime. These linings are fairly durable so long as they are kept free
from moisture, but if left in a damp place the lime slacks and cracks
off. With a lining two tenths of a millimeter in thickness I have made
seventeen melts, each time chilling in an ice-bath, and at the end of
this time the lining was almost intact.

These linings are made from a mixture of finely powdered quick-
lime and calcium nitrate, about four parts by weight of the lime to one
by weight of the nitrate. Care must be taken that the powders are
thoroughly mixed. Such a mixture fuses to solid lime when sufficient
heat is applied to drive off all the nitric acid.

This last fact is not new. It is often made use of in the chemical
department of Harvard University for preparing small boat- shaped
crucibles suitable for melting small portions of metal. But one meets
with considerable difficulty in keeping the powder in place on the steep
sides of the crucible while it is being fused.

The method finally employed is to use a cylindrical-shaped crucible.
This is clamped, open end outward, in the chuck of a high-speed lathe
and then set spinning. The mixed powder is then carefully blown
inside the crucible where the centrifugal force holds it firmly on the
sides in the form of an even coating. The spinning crucible is then
heated with a blast lamp until all the acid is driven off. It is then
removed from the lathe, set in an upright position, and the bottom
sprinkled with a coating of the powder. This is finally fused on, the
force of gravity keeping the powder in place.

By this method it is possible to give the crucible a very even coating
of almost any desired thickness, though the first attempts are usually
discouraging. I have found it possible to chill an alloy very satisfac-
torily through these thin linings.

For work on weakly magnetic alloys, especially for such as fuse above
eight hundred degrees centigrade, a factor of safety is added by using
for the crucible some weakly magnetic metal such as platinum, as traces

HAYES. — ERRORS IN COOLING CURVES. O

of the crucible might diffuse through the thin porous linings : but
with linings two millimeters or more in thickness there can be little
or no danger from this source.

The perfection of this crucible now makes it possible to prepare an
alloy of definite constitution, and this removes one of the main diffi-
culties in the study of alloys.

Investigation of the Errors in Cooling Curves.

More information concerning an alloy can be had from its cooling
curve than from any other one source, providing the cooling curve is
accurate ; and more information can be had from the temperature-time
curve than from any other of the various forms. The difficulty of get-
ting such curves is not great providing the cooling is slow ; but when
one attempts to take a curve for rapid cooling or chilling numerous
difficulties arise. The remainder of this paper is devoted to a con-
sideration of these difficulties, the errors that as a result have crept
into some of the work on metals, and methods for overcoming these
difficulties.

The errors. — The difficulties that arise when one attempts to take
a cooling curve where the cooling is rapid, and the errors that arise
therefrom, are due to temperature lag and lag in the galvanometer.
Temperature lag takes place through the protection tube, through
imperfect contact between the tube and the enclosed thermo-couple,
and finally through the couple itself. Lag in the galvanometer is a
function of the period of this instrument, probably nearly proportional
to the period. This lag, which for simplicity will be called the elec-
trical lag, can be almost entirely eliminated by using an Einthoven
form of galvanometer (a fine conducting filament suspended in a strong
magnetic field), for here the inertia of the moving parts is reduced to
a minimum, and the period can be made very short without great loss
of sensitiveness. By thus eliminating the electrical lag, I have been
able to study the temperature lag in its various phases. The work has
been carried out in much the following order :

a. Lag due to all three causes, — tube lag, contact lag, and lag in
the junction.

b. Contact lag and lag in the junction.

c. Lag in the junction itself

Method. — The apparatus used in this work, which is described in
detail farther on, consisted essentially of an Einthoven galvanometer
with a commutator arrangement, such that this instrument could be
thrown in series with either of two thermo-couples. These couples

6 PKOCEEDINGS OF THE AJVIEKICAN ACADEMY.

were made of copper against constantan, and were so arranged that one
gave the temperature just outside the protection tube, while the other
gave the temperature from the inside after the usual manner.

Arrangement of thermo-couples. — The arrangement of these junc-
tions was as follows : A cylindrical copper block five inches long and
three inches in diameter had two holes, each three inches deep, drilled
symmetrically in one end. A constantan wire was fused to the bottom
of one hole, thus forming a junction with the copper block as one ele-
ment. This couple gave at all times the temperature of that portion
of the block which formed the bottom of the hole. Moreover, since the
two holes were symmetrically placed and the cooling was made symmet-
rical, this junction gave the temperature at the bottom of the other
hole.

In this second hole an ordinary protection tube was placed with
a copper-constantan junction inside. The protection tube was sur-
rounded with a thin film of lead, so that the tube experienced the same
external conditions that are met with in taking the cooling curve of a
molten metal or alloy. A protection tube open at the end was placed
in the hole first mentioned, so that the heat capacity of the two holes
should be the same.

Because of its short period — less than one fiftieth of a second — it
was possible to alternate the galvanometer rapidly between the two
thermo-couples. For most work, however, an alternation of about once
a second was found satisfactory.

The cold junction of each couple was kept at the temperature of
melting ice, so the deflection of the fiber in the galvanometer was
always proportional to the temperature of the hot junction of the
couple with which it was in series. This deflection was photographed
on a sensitive film which was rotated on the drum of a chronograph.
In this way it was possible to photograph on the same film the two
curves, one giving the temperature just outside the protection tube,
and the other giving the temperature inside the tube, according to the
usual manner. These curves were traced by a succession of fine dots,
but the alternations were so rapid that in the case of slow cooling the
curves appear as an unbroken line. These curves had millivolts for
ordinates and time for abscissae, and the apparatus was so arranged
that these coordinates were photographed on the film. The difference
in height between the two curves at any instant was evidently a meas-
ure of the temperature lag due to all three causes, — tube lag, contact
lag, and lag in the junction ; but thus far there was nothing to indi-
cate what part of this lag was due to each of the three causes.

The curves of the annexed plates, reproduced from the actual photo-

HAYES. — ERRORS IN COOLING CURVES. 7

graphs, show this lag for both quartz and porcelain protection tubes
for different rates of cooling. These curves are reduced to one fifth
the original size. The highest temperature in each case was about 550
degrees centigrade.

tSimilariti; of the thermo-couples and calibration. — Curve 1, Plate 1,
which traverses the sheet four times, due to four revolutions of the
drum, was taken at a very slow rate of cooling, the time of exposure
being about four hours. In place of the ordinary protection tube closed
at the end, the tube used in this case was open at the lower end except
for a thin film of mica. Here the temperature lag between the two
junctions must have been practically zero, because of the slow rate of
cooling and because of the thinness of the film separating them. The
curve, which is in reality double, shows that the two couples were
practically identical throughout the temperature range covered.

A calibration curve for one of these couples was obtained by taking
the melting points of pure tin, lead, zinc, and aluminum, also the
boiling point of water. These results are given in Table I.

TABLE I.

Temperature.
Deg. Centigrade.

Millivolta
(obs.).

Millivolts
(calc).

Boiling water

100

3.85

3.85

Melting tin

232

9.70

9.65

Melting lead

327

14.15

14.19

Melting zinc

419

19.40

19.34

Melting aluminum 657 33.70 33.70

The third column, marked Millivolts (calc), was obtained by apply-
ing the well-known formula connecting temperature and electromotive
force,

E=ae + be\

Here B is the e. m. £ in millivolts and e is in degrees centigrade.
Substituting in this equation the values of B and G, as found for boiling
water and melting Al, the values of a and b were found to be 0.0362
and 0.0000229 respectively ; and since the variation between the ob-
served and calculated results lies within the limit of error, the curve

E= 0.0362 8 + 0.0000229 e^

has been taken as the calibration curve for the two junctions.

Referring to this formula, it is comparatively easy to find the differ-
ence in temperature between the two junctions at any instant during
the cooling. Let L\ be the e. m. f of the junction within the protection

8 PEOCEEDINGS OF THE AMERICAN ACADEMY.

tube, and ©i be the temperature of that junction. Let E2 and Q^ be
the e. m. f. and temperature respectively of the other junction at the
same instant. Then

(01 - 62) = (a/4 bE^ + a' - a/4 hE^ + a=^)/2 h,

the maximum temperature lag through quartz and porcelain protection
tubes for different rates of cooling, is given in Table II. This is
computed from the curves of the accompanying plate (Plates 1 to 6).

'

TABLE II.

Quartz.
Data of T
Curve No. -^^S'

Porcelain.
Data of y
Curve No. -^^S"

Time Coordinates.
One Division equals

2 Plate 1

13 deg.

2a Plate 2

49 deg.

30 sec.

3 Plate 2

45 "

3a Plate 2

118 "

15 "

4 Plate 3

80 "

4a Plate 3

190 "

10 "

5 Plate 3

179 "

5a Plate 4

355 "

5 "

6 Plate 4

270 "

6a Plate 4

480 "

3 "

No simjyle relatioti between the two curves. — These results show that
the error in the cooling curve as usually taken (i. e. by means of a
thermo-couple placed inside a protection tube) is large, especially if the
rate of cooling is at all large. The question then arises : Is it possible
to find a relation between the correct curve and the incorrect curve
such that the correct curve can be obtained from the incorrect one,
i. e. from the curve taken. Curve 8 (Plate 5) enables us to answer
this question.

In taking this curve, time coordinates of which were three seconds
for one space, the copper block was first dipped for an instant to a
depth of two inches in ice-water, then removed, then redipped, then
removed, etc. The lower line, which is very irregular, as we should
expect, is the correct cooling curve. The upper one is the curve ob-
tained by the ordinary method, a junction inside a protection tube.
The relation between the two curves is far from simple, and any for-
mula giving this relation must needs be complicated. Thus far no
formula has been found.

Incorrect curve may give correct temperature of transformation. —
Much of the information, however, that comes from a cooling curve can
be had from a curve that is not absolutely correct ; for this information
comes from the irregularities of the curve, not from the regular parts.
In general, any change in the constitution of a metal is accompanied
by a liberation or absorption of heat, thereby causing a kink in the

HAYES. — ERRORS IN COOLING CURVES. y

cooling curve. How erroneous can the cooling curve be and still give
the temperature of transformation with considerable accuracy 1

For simplicit}^, let us take the case of finding the melting point of a
pure metal. In this case the cooling curve for that portion of time in
which transformation takes place is a straight line parallel to the time
axis. In Figure 1 let the line abc'd represent the true cooling curve,
while line abc represents the cooling curve if no transformation takes

place. Let the line ah'c'd' represent the cooling curve given by the
couple inside the protection tube, and the line ah'e the corresponding
curve if no transformation takes place. Then the temperature lag at the
beginning of transformation is 02 — 0i, and the corresponding time lag
is ti — ^1. The time through which transformation takes place is
tfi — t\i while Gi — 00 is the number of degrees through which the melt
would cool if no transformation takes place.
It will be seen that

®2 ®1 — "7777 ■ 2 (^2 *\h

(IT

lf/0

if we assume that — ™ is the averate rate of cooling during the period

required for 0 to drop to the temperature of transformation, and that

r/0.,

-TTyl is the rate of cooling at the beginning of transformation. Also,

J/(0i-0o)-6'=il/X,

where M is the mass in grams of the melt, H is the average specific
heat, and L is the latent heat of melting. But

10 PROCEEDINGS OF THE AMERICAN ACADEMY.

_ dQi

do .

approximately, where -pJ, is the actual rate of cooling at the beginning

of transformation. Therefore

For safety,

2 (^1 - U) < T,

otherwise the irregularity in 62 will lie wholly above the temperature
of transformation.
Therefore, for safety,

do.

2

1

dT dT

dQ d.Q

For slow cooling -^ = -j— approximately. Then

For rapid cooling -7^ > -7^ throughout most of the temperature

range covered, and our formula becomes

L

62 — Gi « ^,

which is meaningless.

For slow cooling, then, the cooling curve will give us the correct
temperature of the melting point, providing the temperature lag is less
than the ratio between the latent heat of melting and the average
specific heat of the metal during the transformation. This value for
the specific heat is about equal to the average between the specific
heats corresponding to the liquid and solid states, and therefore in
general more than the specific heat of the solid. This ratio always
gives a fairly large value for 63 — Gi, so we may be fairly sure of
obtaining the correct temperature of melting, even though the temper-
ature lag is considerable.

In general an incwrect curve gives incorrect data. — However, in
the case of many transformations, such as a change of allotropy, the
latent heat of transformation is small, so the ratio L/S is small, and

HAYES. — ERRORS IN COOLING CURVES. H

the value of ©a — ©i must be small if the transformation temperature
is to be given with accuracy. This requires that the cooling curve
must be nearly correct. Yet Curve 3 shows that for comparatively
slow cooling the temperature lag is 45 degrees for quartz protection
tubes, and much more for porcelain tubes. The conclusion follows that
the ordinary method for taking cooling curves fails to give with
accuracy the temperature of such transformations as involve slight
absorption or evolution of heat.

Ordinary method of correcting for temperature lag. — This error due
to temperature lag has been long recognized, and the following method
employed to correct it. Both a cooling and a heating curve is taken.
The cooling curve gives a temperature above, while the heating curve
gives a temperature below the temperature of transformation. Assum-
ing that the rate of change of temperature is constant, and that the lag
is proportional to the rate of change of temperature, then the correct
temperature c^n be obtained as follows :

Let e,. be the transformation temperature given by the cooling curve,
e, " " " " " " heating "

a " rate of cooling, assumed uniform,
b " " heating,

k " temperature lag for unit rate of cooling,
© " correct temperature of transformation.

«

" k

Then ©« = © + ^a

G/, = © — kb

© — ©,._ a
©-©/. ~ " b'

Therefore e = — —7 e, + — ^ ©^.

a + 0 a + b

This method erroneous. — The value of this formula dejiends upon
the correctness of the two assumptions upon which it is based. The
rate of change of temperature can be regarded as fairly constant over
a considerable period of time when the cooling is slow. The accuracy
of the second assumption — that the temperature lag is proportional
to the rate of change of temperature — can be tested by the aid of
Curves 1' and 2 (Plate 1), for we can readily find the temperature lag
at any time, and also the rate of cooling, and hence the value for k.

12 PROCEEDINGS OF THE AMERICAN ACADEMY.

On each of these two curves three points were chosen, and the value
of 02 — ©1, -jj,, and k computed with the following results (Table III):

TABLE III.

Cv/rve 1', Plate 1.

oint.

©2 - ©,.

d®
dT

h.

1

5.25 degrees

0.373

13.9

2

3.06 "

0.201

15.2

3

2.12 •'

0.128

16.8

Curve

2, Plate 1.

1

11.2 degrees

0.622

18.0

2

8.34 "

0.422

19.7

3

5.88 "

0.268

21.6

Difference.

1.3
1.6

1.7
1.9

These results show that the lag is not proportional to the rate of
cooling, but that the value of k increases as the value of dQ/dT
decreases, and that this change in k is nearly linear. This increase in
the value of k cannot be accounted for by the fact that the rate of
cooling to the point at which the value of k was computed had not
been constant but had been decreasing, so that in each case the lag was
more than it would have been had the rate of cooling been constant
and of the value at the point in question. The lag would be greater
in proportion for the higher points as the decrease in the rate of cooling
is greater for the portion of the curves before those points.

The true cause for this variation in the value for k does not concern
us here. The fact is that the second assumption is not correct, and,
unless the heating and cooling curves have the same slope, the formula
does not give the correct value for e. Moreover, a comparison of the
results obtained from Curves 1' and 2 shows that even under these last
named conditions the formula is not trustworthy. Curve l' gives a lag
of 5.25 degrees centigrade for a rate of cooling of 0.373 degrees per
second, while Curve 2 gives a lag of 5.88 degrees centigrade for a rate
of cooling of only 0.268 degrees per second.

Contact lag is variable. — These curves were taken with the same
quartz protection tube and the same thermo-couples, and the discrep-
ancy is not due to variation in the thermo-couples, as they were tested
after each curve and found to have remained constant. The variation
was apparently due to change in the contact lag, and this variation is

HAYES. — EREORS IN COOLING CURVES.

13

Fig. 2,.

liable to occur between any two curves, as, for instance, between the
heating and cooling curves used in determining e.

If so much variation can be due to change in the contact lag, it
would seem that this lag must be great, perhaps furnishing a large
part of the entire lag. A consideration of the ordinary form of thermo-
j unction should lead one to suspect this, even though the results ob-
tained from Curves l' and 2 had not disclosed the fact.

The two elements forming the couple are usually fused together in
the form of a bead nearly spherical in shape. Under the most favor-
able conditions this bead rests on the bottom of
the protection tube, though ofttimes it takes a
position as shown in Figure 2. In either case the
contact between the tube and bead is imperfect.
In the first case we have a point, or, at most, a
very small surface of contact, and in the second
case no contact at all. In the first case the j unc-
tion can lose its heat by conduction and radiation,
though mostly by radiation ; and in the second
case its heat must leave wholly by radiation. In
either case it would seem that the contact lag must
be large, and that it would vary with the position
of the junction in the tube.

ConUict lag is gr('<it. — To test out the lag due to imperfect contact
between tube and junction, a protection tube open at the bottom was
used. This allowed the bead of the junction to rest directly on the
coi)per. Here the lag was due to imperfect contact and lag in the
couple itself The lag in the couple was very small, as the material
of the couple was a good heat conductor, and because the heat capacity
of the couple was small. Several curves were taken with this arrange-
ment of the couples, and in each case the lag was nearly as great as
that given by the ordinary arrangement with the same rate of cooling.
Curve 10, Plate 6, is a typical example. Here the rate of cooling was
the same as that employed in Curves 4 and 4a.

It is to be noticed that the lag is nearly a» great as that registered
in Curve 4. This lag is not all due to imperfect contact and lag in
the junction, for a thin film of oxide always formed on the surface of
the copper, even when the surface was polished before the experiment ;
and this oxide is a poor heat conductor. However, the experiment
gives conclusive proof that the contact lag is great.

Means for reducing this lag. — The only way to reduce this lag is to
use a ditferent form of junction. The lag can be materially reduced
by pounding the bead down to a thin sheet and fitting it to the bottom

14 PROCEEDINGS OF THE AMEEICAN ACADEMY.

of the tube ; but even then the contact lag forms a large part of the total
lag. A much better form of couple is one in which the tube forms one
element, with the other element fused to the inside bottom of this tube.

Such a couple has been patented by C. B. Thwing, and is made by
James G. Biddle, Philadelphia. This form of junction, as marketed,
has the outer element and tube made thick and heavy, in order to pro-
long the life of the junction which comes in direct contact with the
molten metal. The junction is useless for accurate work on alloys, as
it contaminates the melt ; but the form of the junction is correct since
the tube lag is made small, the tube being a good heat conductor, and
the contact lag is entirely eliminated.

Improved form of thermo-couple. — The author makes use of a couple
of this form, but places a thin coating of lime on the outside of the
tube to avoid contamination. The metal tube which forms one element
of the junction is made very thin, thus reducing the lag in the couple
itself The tubes are deposited electrolytically on a wax form ; the
wire leading from the tube, and the second element leading from the
bottom of the tube, having been placed in position on the wax form.
These wires are thus sealed to the tube by the process of deposition.
In this manner the couples can be made nearly any desired size.

The temperature lag in these junctions is reduced to a minimum.
The lime coating can be made very thin, thus causing little lag through
the protection tube. The contact lag is small and constant, since the
whole surface of the couple is in close contact with the lime coating.
Finally the lag in the junction itself is nearly zero, as the heat capacity
of the j unction is nearly zero.

Comparison of old and improved form. — Curve 11, Plate 5, really
two separate curves on the same sheet, gives a comparison of the lag
due to the two junctions. The curve on the left was taken under the
most favorable conditions applicable to the ordinary method. The
protection tube was made of thin quartz, and the j unction rested on
the bottom of the tube. The curve on the right shows the correspond-
ing lag when the tube-form of couple is used. Here the apparent lag
is more than the actual lag, as the tube couple gave a higher e. m. f
than the couple of which the copper block formed one element. The
rate of cooling was the same for both curves, and was obtained by
immersing the copper block in oil.

In all the curves taken, the protection tube was surrounded with a
thin film of lead ; yet the cooling curves, except faintly in Curve 1',
give no indication of the freezing point of the lead. This point, how-
ever, is plainly shown in the cooling curve taken with the tube-form of
couple, even though the rate of cooling was high.

HAYES.

ERRORS m COOLING CURVES.

15

The faxjt that the heat liberated by the freezing lead causes no irregu-
larity in the cooling curves taken by the ordinary method, leads one to
believe that not only does that method fail to give the temperature of
transformation with accuracy, but it may fail to give any indication of
the existence of a transformation. On the other hand the possibilities
of the tube-form of couple are great. These possibilities are not fully
shown by Curve 11, as the junction was fairly heavy and the lime

Fig. 3.

coating much thicker than necessary. With a refined couple this lag
can be greatly reduced.

The cooling employed in taking Curve 11 was about the same that
is employed in the oil-tempering of steel. At this rate of cooling a
refined couple would give very little lag, and should give curves suf-
ficiently accurate to throw considerable light on the processes of chil-
ling and tempering.

Against the correcting /or temperature lig hy means of heating curve.
— A study of alloys in the light of Gibb's " Phase Rule " leads one
to believe that their characteristics depend greiitly on their past his-
tory. Having prepared an alh^y, it is doubtful if its ])roperties will be
the same after it has been remelted. It is then highly desirable that

16

PROCEEDINGS OF THE AMERICAN ACADEMY.

the cooling curve be correct as first taken. The usual method requires
the taking of the heating curve, i. e. the remelting of the alloy, in
order that we may apply an incorrect formula to give us the tempera-
ture of such transformations as are registered on these insensitive
curves. This method is cumbersome and, unless the rate of cooling is
very slow, is inaccurate. And when we have taken the heating and
cooling curves and found the so-called temperature of transformation,
it is a question as to what alloy the data belongs.

The tube-form of couple makes it possible to take an accurate cool-
ing curve for slow rates of cooling, and even such rates as are employed

Fig. 4.

in tempering can be taken with a fair degree of accuracy. Thus the
second main difficulty in the study of alloys is largely removed.

Description of the Apparatus.

The recording device. — Figures 3 and 4 represent a top and side
view, respectively, of the recording part of the apparatus. A simplified
form of Einthoven galvanometer G, in circuit with a thermo-couple,
gives the difference in temperature between the hot and cold junction.
An ordinary projecting lantern J throws a beam of light through S2
and illuminates the filament /of the galvanometer. By means of the
lenses /, the light from the filament is focussed on the drum r of a
chronograph. The screen S carries a narrow slit parallel to the axis
of the drum, and thus allows only a spot of light to reach the sensitive
film F which is fastened about the drum. A variation in the tempera-
ture of the hot junction causes the spot of light to move along the
drum in a direction parallel to its axis. If such a movement takes
place while the drum rotates, a curve is photographed on the film, the
coordinates of which are temperature and time.

HAYES. — ERRORS m COOLING CURVES. 17

Placing the time coordinates. — The chronograph is so arranged
that it can be run with either of two motors 1 or 2 (Figure 4). One-
tenth horse power A. C. motors are used for this work, as they give to
the drum a more uniform rotation than the ordinary clockwork arrange-
ment. Motor 2 is connected to a variable gear, such that the time of
rotation for the drum can be varied from forty seconds to two hours.
This motor is used to turn the drum whenever a cooling curve is being
photographed, the gearing always being so adjusted that the drum
rotates about once while the cooling takes place. Box T contains an
arrangement for throwing a periodic flash through Si of the galva-
nometer. This light finally passes through the slit in the screen and
gives a fine white line on the film. If the drum rotates uniformly and
the flashes occur at the end of equal periods of time, and if at the
same time a curve is traced by the spot of light coming from the fila-
ment, we should have, upon developing the film, a temperature vs.
time curve with the time coordinates drawn.

Flaring the e. m. f. coordinates. — By means of the double switch R
a potentiometer P can be thrown into circuit with the galvanometer,
and this instrument can then be made to register millivolts. This
arrangement makes it possible to place electromotive force coordinates,
on the film. First rotate the drum with no e. m. f. through the gal-
vanometer. The spot of light then traces the zero line on the film.
Then repeat this operation for each millivolt, or whatever increment
of e. m. f. is desired, until the range of e. m. f. covered by the thermo-
couple is passed. For this work motor 2 is used, as the gearing here is
such that the drum rotates about once in ten seconds.

In order that these coordinates should have the same intensity as
the curve, the time of exposure should be the same. This causes a
great loss of time, as the period of rotation for the drum is more than
one hour when the cooling is slow. This waste of time is avoided by
widening the slit S while these coordinates are being made. By making
the slit one millimeter wide, the time required for recording one coordi-
nate line is about ten seconds. Thus the total time required for add-
ing the e. m. f coordinates to one of the curves of this paper is about
ten minutes. This method for adding the e. m. f. coordinates amounts
to calibrating the galvanometer for each curve, so that the results are
largely insured against variation in the galvanometer.

This recording apparatus is essentially the same as that devised by
Einthoven and described at length in Annalen der Physik, Ut(>3, Vierte
Folge, Band 12. It is without doubt the best form thus far devised for
recording rapid cooling, but the expense of the apparatus has tended to
prohibit its general use. It therefore seems desirable to describe briefly

VOL. XLVII. — 2

18

PROCEEDINGS OF THE AMERICAN ACADEMY.

the simplified form used in this work. Only ordinary ingenuity is re-
quired for its construction, and the cost is comparatively small.

The galvanometer. — Figure 5 shows the construction of the galva-
nometer. The magnetic field is furnished by eight cast-iron ring mag-
nets, arranged in two sections of four. One section is placed above the
focussing lenses 1, and the other section directly beneath this. A thin
brass chamber fitted between the jaws of the compound magnet carries

the filament, a platinum fiber
about one ten-thousandths of an
inch in diameter. These three
pieces, with some simple device for
varying the tension on the fiber,
completes the galvanometer.

Periodic flashes fo7- giving time
coordinates. — Figures 6 and 7
show in some detail the mechan-
ism employed for giving periodic
flashes. Two rachet wheels, each
carrying sixty teeth, are fastened
rigidly to an axle (Figure 7). A
double electromagnet m attracts
the armature a and causes the
clutch X to turn the axle. Clutch
y is so adjusted that the rotation
is allowed to proceed only a dis-
tance of one tooth. So long as
the current continues through m
the axle is held firmly in position ; but whenever this current is broken
the armature is pulled back by spring s so that clutch x falls behind
another tooth. Upon making the circuit again, the axle is again ro-
tated a distance of one tooth. A relay operated by a separate circuit
is so connected into the circuit which traverses the magnet m, that
when its armature is back the circuit is made through m. The relay is
operated by a circuit that is made for an instant once a second, a sec-
onds pendulum being used for accomplishing this. Thus the circuit m
is broken for an instant once a second, and the axle, therefore, is
rotated one division every second.

A thin aluminium disk twenty centimeters in diameter is clamped
to the end of the axle by means of a thum-screw. Narrow slits are cut
radially into the edge of the disc as shown in Figure 7. This disc is
interposed between a Nernst glower and slit Si of the galvanometer.
Figure 4. An iron screen i before the glower allows only a narrow

Fig. 5.

HAYES. — ERRORS IN COOUNG CURVES.

19

beam of light to fall upon the disc ; and whenever a slit in the disc
moves across this beam of light a momentary Hash passes into Si. By
var}'ing the number of slits in the disc, the period between flashes can
be made nearly any length between one second and one minute.

Fig. 6.

Fig. 7.

Fig. 8.

The Heating Part of the Apparatus.

The copper block and thermo-couples. — The heating part of the ap-
paratus may be briefly described with the aid of Figures S and 9.
Figure H repre.sents the cross-section of a copper cylinder five inches
lung and three inches in diameter. Two holes, each three inches deep,
are synmietrically drilled in the top of the cylinder. These holes have
a diameter nearly one millimeter greater than the diameter of the pro-
tection tube tu be experimented upon. A protection tube is placed in
each of the holes in order that the heat capacity may be the same for
each. One of these tubes is closed at the lower end and the other one
left open. Within the closed tube an ordinary copper-coustantan

20

PROCEEDINGS OF THE AMERICAN ACADEMY.

junction is placed, and a constantan wire is passed through the open
tube and fused to the copper block. A copper wire w is fused to the
top of the copper block, and protected from the hot gases of the furnace
by means of a short porcelain tube. The space between the closed
tube and the copper block is filled with lead. Thus the closed tube

Fig. 9.

experiences the same conditions that are met with in taking an ordinary
cooling curve for a molten metal or alloy.

The commutator. — The commutator arrangement, by means of
which the two thermo-j unctions are alternately thrown in series with
the galvanometer, is shown in c. Figure 3. It might be added that
several curves could be photographed on the film by simply changing
the form of the commutator. The alternations were about once a
second throughout this work, but the period of the galvanometer was
only one fiftieth of a second, and the damping very rapid, so that as
many as five alternations per second could be made. This means that

H.\TES. — ERRORS IN COOLING CURVES. 21

at least ten such curves could be placed on the same film, and even a
greater number when the rate of cooling is slow.

Copper-constantan couples were used throughout this work, princi-
pally for the reason that it made possible the use of a copper block.
Several reasons made it desirable to use copper. The copper has no
transition points in the temperature range covered, so the cooling
curves would have no irregularities due to such transitions. Copper
being an excellent heat conductor, the temperature at the bottom of the
two holes will be nearly the same, even if there are some slight irregu-
larities in the cooling at the surface. Copper and lead is one of the
few combinations of metals that do not alloy more or less readily.
Lastly, copper against constantan makes a thermo-couple that gives a
high thermo-electromotive force.

Validity of the method employed for determining the lag through the
protection tube, etc. — Since the validity of this whole paper depends
on the condition that the temperature at the bottom of the two holes
shall be the same at all times, numerous tests were made to see if this
condition were fulfilled. To test this condition, a constantan wire was
fused to the bottom of each hole in the block, and the two curves giv-
ing the temperature at the bottom of each of the two holes were taken
for various rates of cooling. These curves overlapped in nearly all
cases, the variation scarcely ever being more than the width of the line.
Curve 14, Plate 6, gives such a set of curves for rapid cooling. The
curves show the temperature variation between the two junctions at its
greatest. On this curve, one space on the time axis represents three
seconds.

It might be urged that a large portion of the lag recorded in all
cases was due to lag through the lead film which surrounded the tube.
Curve 13 (Plate 6), a curve resulting from an accident, offsets this argu-
ment. Just after the cooling had started, the tube broke and allowed
the lead to come in contact with the junction. This break occurred
when the temperature of the block was only a little above the melting-
point of the lead. After the experiment was over, the bead of the
junction was found about half imbedded in the lead. The cooling here
was rapid, having been caused by dipping the copper block in ice-water.
The irregularities in the curve, and probably the breaking of the tube,
were caused by the water boiling over on the top of the block. Despite
this, however, the curves coincide throughout most of their length.
This proves conclusively that there was little lag through the lead
film.

Furnace and cooling hath arrangement. — Figure 9 shows the
arrangement for heating and cooling the copper block. Because of

22 PROCEEDINGS OF THE AMERICAN ACADEMY.

the presence of the thermo-couples it was difficult to move the block
from the furnace to the cooling bath. This difficulty was avoided by-
counterpoising the furnace and bath so that either could be brought
to the block. The cooling bath was arranged to slide up and down,
being guided in this movement by two vertical rods. The depth to
which the block was submerged was regulated by fastening a clamp on
one of the guiding rods. The furnace was counterpoised on an arm which
could turn about a single guiding rod and thus be brought beneath
the block. With this arrangement, the block could be transferred from
the furnace to the bath as quickly as it could if the block were mov-
able. The cold junction of both couples were kept at the temperature
of melting ice by means of an ice-bath /, Figure 9.

Variation in the rate of cooling. — Variation in the rate of cooling
was provided as follows: For rapid cooling, the block of copper was
surrounded by ice-water to within one centimeter of the top. For the
next slower rate the block was dipped in warm water to a depth of one
centimeter. The next slower rate was obtained by surrounding the
block with oil. A still slower rate was given by setting the copper
block on a block of iron that was surrounded by water. The next
slower rate was given by allowing the block to cool in air. Finally,
the slowest rate was obtained by allowing the block to cool in the
furnace. The rate of cooling was thus varied from about half a minute
to over two hours.

Need for the research recorded in this paper became apparent to the
author upon attempting to study the magnetic properties of some
weakly magnetic alloys. The two difficulties which the paper dis-
cusses were at once encountered, and had to be overcome before the
work could proceed. These difficulties have been largely overcome, and
the road noAv seems to be fairly clear to a large and much neglected
field of research.

Jefferson Physical Laboratory
Cambridge, Mass.

Hayes. — Errors in Cooling Curves.

Plate I.

Prog. Amer. Acad. Arts and Sciences. Vol. XLVIi

I

Hayes.— Errors in Cooling Curves.

PU\TE 2.

m

Proc. Amer. Acad. Arts and Sciences. Vol. XLVII.

Hayes. — Errors in Cooling Curves.

Plate 3.

Proc. Amer. Acad. Arts and Sciences. Vol. XLVII.

Hayes.— Errors in Cooling Clrves.

Plate 4.

Proc. Amer. Acad. Arts and Sciences. Vol. XLVII.

Hayes.— Errors in Cooling Curves.

Plate 5.

Proc. Amer. Acad. Arts and Sciences. Vol. XLVII.

Hayes.— Errors in Cooling Curves

Plme 6.

Proc. Amer. Acad. Arts and Sciences. Vol. .XLVII.

I

Proceedings of the American Academy of Arts and Sciences.
Vol. XLVII. No. 2. — May, 1911.

DETERMINATION OF THE ALTITUDE OF AEROPLANES.

By Robert W. Willson.

With Two Plates. \

DETERMINATION OF THE ALTITUDE OF AEROPLANES.

Bt Robert W. Willson.
Presented February 8, 1911. Received December 31, 1910.

The object of this paper is to add something to the discussion of a
somewhat novel problem which has arisen as a result of certain devel-
opments in the art of aviation during the past year.

Up to the time of the aviation meet at Los Angeles in February,
1910, no greater height had been recorded in the flight of a "heavier
than air " machine than about fifteen hundred feet. At that meet
Faulhan, in a Bleriot machine, reached a height of 4165 feet, the
height being determined by triangulation. The reading of his aneroid
was 46U0 feet.

At the Montreal meeting, in June, Walter E. Brookins attained an
altitude of 3523 feet, determined by triangulation, his baroscope read-
ing 200 or 300 feet higher ; and at Atlantic City, in July, the same
aviator raised the record to 6175 feet, as determined by a triangulation
similar to that of the first method described in the following pages.
The height by barograph was 6200 feet.

When the project of an aviation meeting at Cambridge was being
discussed, the writer agreed to be responsible for the accurate meas-
ure of altitudes ; and the results obtained and the methods used form
the subject of this paper. At that time no official accounts of the
e.xperience at other places in making such measurements had been
published, but it was agreed that it would be acceptable to the aviators
that they should attempt to reach their greatest altitudes when in a
vertical plane passing through the starting line of the course, and as
nearly as possible at a point over the grandstand. It was also agreed
that only one machine should be under observation at any time. Under
these conditions the arrangements now to be described were planned.
The accompanying map (Plate 1) of the S([uantum peninsula and the
surrounding country will serve to make the situation clear. The map
shows the positions of the two base lines, and gives the ground plan
of the flight of Brookins on September 8.

First Method, — The Field B.\se.

A measured base of 5000 feet was established on the line NS reaching
from the extreme northern limit of the course, across the field, passing

26 PROCEEDINGS OF THE AMERICAN ACADEMY.

above the center of the grandstand, and terminating at a point just
beyond the boulevard recently built by the Metropolitan Park Com-
mission. The north and south direction was chosen in order that the
observations might not be interfered with by the sun at the times of
day most favorable for flight. It was expected that the aviators would
cross this line near its center on each coil of the ascending spiral, and
that the greatest height attained at such a crossing would be taken as
the height of record.

At each end of the field base was placed a sextant mounted on a
stand (Plate 2), with its plane in the vertical plane of the base line,
and the line of sight pointed toward the grandstand, which was nearly
midway between the stations. A target placed in the line of sight at
a sufficient distance from each sextant served as a substitute for the
horizon line, and when the image of the aeroplane was brought to coin-
cide with the target, as it crossed the plane of reference, the altitude
was read directly from the vernier of the sextant. The height of the
northern station was eighteen feet and of the southern station twenty-
six feet above mean low water ; it is sufficiently accurate to assume
that the sextants were in the same horizontal plane twenty-two feet
above mean low water and nine feet above the center of the field.

After some experiments the target was given the form shown in
Plate 2. The central lozenge was one foot square and the extreme
horizontal length four feet. The wings served to make an approximate
setting as the aeroplane approached the plane from either side. The
horizon mirror of the sextant was replaced by a larger mirror extending
about three inches from the sextant plane, the silvering being removed
from a strip one eighth of an inch wide perpendicular to the plane of the
sextant. Through this opening the target could be seen by the naked
eye placed somewhat to the left of the telescope, and the aeroplane
could thus be picked up and followed and an approximate setting
made some time before coming to the reference plane. At the critical
moment the eye was placed at the telescope and the image of the aero-
plane made to cross the center of the lozenge of the target. The use
of a light blue shade between the index and horizon glass greatly facil-
itated the observation by cutting off the glare of the sky. The clamp
of the index was replaced by a roller turned by a good-sized milled
head, and forming a very convenient " quick slow motion." A "finding
plane " of a size corresponding to the new horizon glass was attached
to the index glass and carried a level perpendicular to the plane of
the sextant, by means of which that plane might be made vertical.
These three modifications are all plainly shown in Plate 2.

The observers were connected with each other and with the commit-

WILLSON. — ALTITUDE OF AEROPLANE FLIGHTS.

27

tee room at the grandstand by a telephone line devoted to this use
alone. A chart, shown about one eighth size (Figure 1), was at hand
from which the height corresponding to simultaneous observations of
the altitude at either end of the base could be read off.

The abscissas and ordinates represent the angles iVand /S' respec-
tively, and the curves give the values of ^ for each 100 feet, computed
from the above formula. The scale was one quarter of an inch for
each degree of X° or *S'°, and on this scale it was not difficult to read
with an error of less than ten feet up to altitudes of 15,000 feet.

00
80

70

GO
50
40
30
20
10

0

1 ■ ■

\

\ \

\\

N^

1^

N

/

\

\

\ \

V\

^

^

^

\

\:

^

^

^

.>

^

\

><
/

^ V

\N

^

%^

\

\

/

X

X

^\

^

X^^N

^

v^V

\.

\

/

)\.

■^

"~-

">-,

"^

S

\

p<

^~-

—

"~~~-

' -

/

■ —

10

•20

30 40

50

GO

70 80 00 100 110 120

Figure 1. Chart for determining approximate altitude from sextant obser-
vations.

This chart was not used, as was expected, to give out the altitude a
few seconds after each crossing, since the committee deemed it wiser
not to make any announcements of altitudes till the end of the day.

The Distant B.\se.

As a check on the observation at the field, and in order to give data-
for a closer investigation of all the circumstances of the flight, a second
base was occupied lying nearly east and west, about two and a half
miles south of the aviation field. Satisfactory stations were found, one

28 PROCEEDINGS OF THE AMERICAN ACADEMY.

on Forbes Hill in Quincy, at a height of 128 feet above the aviation
field (141 feet above mean low water), and the other on the estate of
Mrs. E. M. Carey, in Milton, at a height of 71 feet. The length of
the base line (QM upon the map, Plate 1) was 6236 feet. The stations
were visible to each other, and, although the grandstand was visible
from neither, aeroplanes could be observed as soon as they had risen
to the height of 50 or 75 feet.

The position of the base was selected so that observations could not
at any time be interfered with by the sun, and that the angle of eleva-
tion could be measured without an eye prism up to an altitude of more
than 15,000 feet above the center of the field.

The distance from the field was not so great that it was necessary
to read the angles with great accuracy, while it was sufficiently great
to reduce materially the difficulty in following the rapidly moving
aeroplanes, so that it was possible to observe quickly and accurately
both horizontal and vertical angles without a finding device.

The instruments used were a special theodolite by C. L. Berger
reading horizontal angles to 10" and vertical angles to 20", and a Buif
mining transit reading both horizontal and vertical angles to 20".
Both instruments had full vertical circles, and inverting eyepieces
magnifying about thirty diameters.

Through the kindness of Mr. Carl Keller, the New England Telephone
Company connected the two end stations and the central station at the
field during the entire period of the meet.

It was thus possible to insure simultaneous observations at the two
stations in both coordinates. That they were practically simultaneous
is clearly shown by the tables which follow, in which the approximate
times are given as noted at each station. Where the times differ it is
almost always possible to make an exact agreement by altering one or
both by a single second, so that the mean of the times would rarely be
in error by that amount.

The error of the observers' watches was found by a telephone com-
parison with the official chronometer on the field immediately before
each flight.

By combination of the observations we were able not only to compute
the altitudes of the aeroplanes at intervals of forty seconds or less, but
also to locate their corresponding positions as projected vertically on
the ground plane, and thus to plot so many points of the spiral both
in ascent and descent as to form an interesting and useful record of all
the details of the flight.

It may here be remarked that the use of this method seems prefer-
able to any that requires the aviator to attain his maximum height at a

WILLSON. — ALTITUDE OF AEROPLANE FUGHTS.

29

given point or line. If thus restricted, the Bldriot monoplane espe-
cially is at a disadvantage, as its construction renders it extremely
dilHcult for the operator to see the ground at points anywhere near
directly beneath him. The discussion of his ascending spiral, checked
by observations of his descent, fixes his highest point c^uite accurately
without placing any burden upon the aviator himself. (In reference
to this point, see the flight of Grahame- White discussed on p. 42.)

The character of the results obtained may best be shown by the
records of some of the flights and the methods of discussing them
which follow.

To illustrate the whole process, we may take the observations of tho
flight of Brookins, September 12, the last day when any considerable
flight was made, and at a time when the observers had had several
days of practice. No great altitude was reached, but the flight was in
many respects typical, and exemplifies some of the advantages of the
two methods used, as controlling and checking each other.

TABLE I.

Flight of Brookins, Sept. 12, 1910, as Measured by Sextants. Base
Line, Distance between Stations, 5000 feet. Sextants 9 feet above
Course.

North Station.

South Station.

No.

Direction.

Time.

Vert.
Angle.

Time.

Vert.
Angle.

Computed.

Chart.

1

2
3

4
5
6

7

1st, E
2nd, W
2nd, E
3rd, W
3rd, E
4th, W
4th, E

5'^ 58"" 30'

6 6 55
10 45

12 35

13 10
13 35

17° 7'
obtuse '
39 28
24 4
47 50
71 8
42 24

5" 58"" 35«

6 0 49

7 4

10 53

39

17

45

13° 57'

8 56
25 50
60 26
31 15
20 34
20 12

697 ft.

1533
1791
1967
1672
1338

694 ft.

1529
1799
1964
1664
1314

* Too IiirKo to bo moasurod by tho soxtant.

If the angular altitudes at the two stations are X° and .S"" res])ec-
tively, and the length of the field base r>()<K) feet, the altitude in feet,
fi, given in column 7, is computed by the expression

30 PROCEEDINGS OF THE AMERICAN ACADEMY.

5000

h =

COti\"+ COt>S'"

The values given in column 8 were read directly from the chart
referred to above on page 27. A correction of 9 feet has been added to
each value, as the sextant base was higher than the middle of the field
by that amount.

Only four crossings were well observed in the ascent and two in the
descending spiral. The second observation, however, though incom-
plete, served a purpose, as will appear later. Not only the altitudes,
but the projections of the crossing points on the ground line are given
by the observations, since the distances of the projection from the north
and south stations are h cot N and h cot S respectively, and six points
in the spiral are thus fixed, making, with the start and finish, eight
points in all thus completely determined.

Observations at the Distant Base.

As compared with the eight determinations made by the sextants,
twenty-one simultaneous observations were made at the Quincy-Milton
base. These are shown in detail in Table II. For purposes of com-
parison the results of the sextant observations are inserted, unnum-
bered but in chronological order.

The values of the altitudes in columns 5 and 9 are computed as
follows :

Let h be the height of the aeroplane above the center of the field,
C, the length of the base line, 6236 feet,
q = 128, and m = 11 feet, the heights of Q and M above the

center of the field,
a and /?, the horizontal angles between the aeroplane and base

line at Q and M respectively,
A and B, the angular altitude of the aeroplane at Q and M

respectively.

Then k = Ctan A sin /? cosec (a + f3) + g,

= Ctan B sin a cosec (a -f /?) -f m.

All effects due to the curvature of the earth and refraction are neg-
lected as being less than the errors of measurement which were expected
to occur. The accuracy actually attained would seem, however, to
justify the application of such corrections.

WILLSON. — ALTITUDE OF AEROPLANE FUGHTS.

31

TABLE II.

Flight of Brookins, Sept. 12, 1910, as Measured by Transits. B.\se
Line, Distance between Stations, 6236 feet. Course 13 feet above
Mea.n Low Water.

(^riNCY Station

Milton Statio.n

1

IK

i^;lit a

50ve Course 12S ft.

Height above Course 71 ft. 1

No.
1

Time.

Vert.
Angle.

Hor.
Angle.-

Alt.

Time.

Vert.
Angle.

Hor.
Angle.

Alt.

5" 57"" 31'

1''54'

70° 35'

576 ft.

5" 57'" 30«

2° 17'

82° 10'

583ft.

2

58

12

2 18

74 30

649

58

13

2 36

77 31

653

58

32

by sextants

687

3

58

43

2° 33'

77° 50'

700

58

40

2 47

74 19

705

4

59

24

2 45

S3 3

769

59

22

2 51

70 47

770

5

6 0

20

2 39

77 59

861

6 0

20

[2 53]

79 15

805'

0

49

by sextants

940

6

2

2

3° 24'

67° 53'

1052

2

00

[3 54]

88 29

1054

7

3

8

4 4

65 6

1169

3

10

4 49

89 42

1190

8

3

53

4 44

67 13

1274

3

51

5 23

86 4

1270

9

4

42

5 22

65 31

135S

4

42

6 10

86 7

1362

10

5

13

5 42

63 12

1402

5

13

6 40

87 35

1404

11

5

55

6 13

62 58

1431

5

53

7 16

85 43

1434

12

6

32

6 17

70 48

1482

6

32

6 50

79 19

1488

7

0

by sextants

1524

13

7

3

6° 1'

76° 40'

1518

7

2

6 17

76 1

1.527

14

7

42

5 45

83 45

1.56")

7

41

5 44

71 44

1.571

15

8

15

5 57

87 53

1597

8

15

5 45

67 55

1002

16

9

16

6 38

86 56

1633

9

15

6 21

66 47

1030

17

10

2

7 24

83 14

1693

10

0

7 10

68 4

1()93

18

10

40

8 10

79 59

17.59

10

38

8 1

69 10

1758

10

49

by sextants

1782

19

11

41

9° 14'

72° 12'

1889

11

40

9 37

74 10

1887

20

12

25

8 7

73 25

1949

12

23

8 34

78 2

1955

12

37

by sextants

1958

21

13
13
13

11
14
40

6° 4' 1 75° .58'
by sextants
by sextants
alighted

1674
1663
1311

13

10

6 22

79 8

1674

14

40

* In the cas

e of ob.servations 5 and 6

the vertical

angles

as read (

>(T at

M

ilton h

ave (

3ach been decreased by

1°. This c

orrectic

m is jus

tifie<l

n<

t only

by t h

e agrocincnt thus l)roiiKli

about

hetw

ecn the

two .stat

ions,

1)1

it by the so:

ttant oh.servat ion at 6" 0

m 4,js ^,

hich.

as is s

lown on

paf?c

34

, indicates u

in altitude of 940 feet.

32 PROCEEDINGS OF THE AMERICAN ACADEMY.

To find the horizontal distances Dq and D^ from Q and M, we have,
with Httle extra work and from the same data of computation,

i)j = CsinyScosec (a + ft) and D^ = Csinacosec(a + /3),

and by use of these two distances the points are easily plotted with
reference to the base line. It is sufficiently accurate, however, and
more convenient, to determine the points graphically by drawing lines
at the proper angles with the base by means of a protractor and
straight edge, and marking their intersection as the position of the
aeroplane.

The computations were quickly made on mimeographed forms fol-
lowing the scheme shown on page 33, which gives the original computa-
tions for observations 5 and 6 of Table II, using, of course, the
uncorrected data. The discrepancy of these results pointed out at once
the faulty observations.

The general agreement of the values at the two stations seems to
show that the height is fixed by each observation with an error of less
than five feet ; but observations 5 and 6 at Quincy and Milton, as
computed from the recorded data, show differences too large to be
ascribed to error of observation. The sextant observation at 6*^ 0™ 49^,
although the angle was too great to be measured at the north sextant
station (the spiral being far out beyond the course), still shows that
the observations at the Quincy station give the correct value, and
there seems to be good reason for assuming that the vertical angles
were read 1° too large in each case at the Milton station. It appears
in the discussion of all the flights that the error most frequently made
was in reading the vertical angles. In the whole series of observations
but two errors are indicated in the reading of the horizontal angles,
one of which will be referred to later.

Time-Altitude Curves.

By plotting the successive values of k, given in Table II as abscissas,
with the corresponding times as ordinates, we have the curve given
below. Figure 2 (right), the slope of which gives the rate of ascent in
feet per minute. The points corresponding to transit observations are
indicated by circles, the sextant observations by crosses. The rate of
ascent is about 100 feet per minute, and the descent nearly ten times
as rapid.

WILLSON.

ALTITUDE OF AEROPL.VNE FUGHTS.

33

o .2

^1

■ C 5 :3

o o • *^

2 ». I, 11

1-1 O O" B

o

X

>o

1-

^^

CO

c;

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X

C5

00

CO

t^

o

E

o

o

n*

CO

CO

CO

1-1

(N

CO

c^

o

CO

CO

OS

CS

^H

o

1^

t^

CI

C5

CO

o

a

o

CO

00

ci

d

CO

a

"^

a

oa.

O

05

a

S

s

s

ft

.^

+

a

§
-w

•3

+

1

1

-si

^'

tc

•-^

"

n

CO

00

»f5

00

CO

•^

GO

CI

05

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o

CI

C5

00

CS

CO

CI

CI

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g

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(M

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00

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1— (

o

o

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05

00

CO

I-H

CO

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d

o
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3a.

+
a

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to

da.

+
a

o
CO

/ — V

o

1

bC

_o

1

o

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en

O

CO

IC

00

r-l

r^

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(M

00

OS

C5

t^

CO

CO

CO

1-

t-

-r

e

o

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-r

1-H

o

CI

CS

o

«-H

o

CO

o

r-t

Cl

f-H

i-H

o

o

CO

i^

00

o

■>*

q

e
o

CO

00

OS

d

CO

«

=q

«

aa.
+

bC

a

d

+

S

1

£

-se

H

a

^

=3

"A

1

1

^

;«

-<

8

I

-r

CO

QC

1-H

CI

V

CO

CO

—*

1— t

00

CO

CI

o

o

o

■f

Oi

Z

CO

CO

OS

l^

i-<

00

Q

CO

^^

T— (

-^

CI

Cl

O

Q

Ci

CO

i-H

o\

o

1^

1^

CO

CS

f

00

Z3

--0

1-

1— (

CO

CC

OS

d

ci

o

^

oa.

<c

o

-^

<Ja.

^

'S

ex

&<

■«

H

+

o

.S

CO

+
a

(J

1

i

1

VOL. XLVII.

34

PROCEEDINGS OF THE AMERICAN AC.\DEMT.

Representation of the Spiral.

From the observations of Table II we may plot the ground plan of
the spiral described in the ascent, and, with somewhat less certainty,
that of the much more rapid descent. Each of the sextant observa-
tions, too, fixes a point on the spiral, although taken alone they would
give little information as to the actual path of the aviator.

!e500

sooo-

3CJS

,,000-^

o«

1500 '

* \

::t^

cP'

c^'

.oP

1000 ■

500'

#

f) 10

l.J

20

30

6 O

10

Figure 2. Time-altitude curves of Grahame- White (left) and of Brookins
(right), September 12.

In Figure 3 are plotted the points as thus determined, each being
numbered to correspond with the observation of Table II on which it
depends. The points of crossing the base line are determined by the
sextant observations of Table I.

The elevation of the path, as shown in the lower half of the figure,
is determined by combining the altitudes from Table I and II with the
projections of the observed points of the spiral above.

It is noteworthy that the spiral serves to give with some accuracy
the height at the point of the crossing at 6^ 0™ 49^ where the angle
was too great to be measured at the north end of the base. The figure
shows that the projection of that point, which is marked by the dot
between points 5 and 6 of the spiral, is about 900 feet north of that
station, or 5900 feet from the south station, at which the vertical angle
was measured as 8° 56'. This gives a height of 940 feet (assuming the
elevation of the station as 13 feet), and a little further investigation
shows that the angle at the north station was about 134°, and confirm.s
the record of the observer that it was not measurable, as the sextant
reads only to 128°. The error in position of the projected point is

WILLSOX. — ALTITUDE OF AEROPL.YNE FLIGHTS.

35

probably less than 150 feet, corresponding to an uncertainty of about
24 feet in the deduced height and S" in the angular altitude at the
north station.

In order that an intelligent judgment may be formed of the general
accuracy attained, of the nature and frequency of erroneous observa-
tions, which must always occur in such a series, of the possibility of

200O

1000

Fir.ruK 3. S|)iral of Brookins, September 12, plotted from observutions of
Tublea 1 Mid 11.

36

PROCEEDINGS OF THE AMERICAN ACADEMY.

correcting such observations, and the effect of rejecting them, three
additional sets are given in Tables III, IV, and V. The first is that
of Brookins on September 10, in which he reached the greatest altitude
of the meet, with three discordant observations, one of which has been
corrected, apparently with reason, by altering the vertical angle at the
Quincy station by 1°. The others would be brought into line by
changes of lo' and 30' in the vertical angles at Milton station, but no
outside evidence is furnished by the sextants or spiral to justify such
a change. In both cases the spiral, Figure 5, indicates that the hori-
zontal angles were probably correctly recorded.

.woo

4.500

40O0

a.'ioo

oooo

2.-iOO

2000

1.500

lOOU

000

0?°

OO 1

c

o

I
1
1

1

1

o'

\

1

a'

I
o

0

t

1

D"'

. o

1

I
1

t
1

?

/
/

O

-o'

-I

.-°

\
\
I

1

0

\
\

\

/

1
1
\

1
o

\

1

1

i^-'

»

\

1
\

\

\
1

I

1
\
A

;jo a."> 10

n ()

JO 15 ;io

Figure 4. Flights of September 10: Brookins (Wright biplane), Grahame-
White (Farman biplane).

The second flight, that of Brookins on September 8, shows two cor-
rections of vertical angle and one change of the time of observation at
Quincy, three vertical angles unrecorded at Milton, and one observa-
tion marked worthless, the result from which differs 17 feet from that
at Quincy. This was on the second occasion of making observations.

WILLSON. — ALTITUDE OF AEROPLANE FLIGHTS.

37

and naturally contains more errors and uncertainties, but in no case is
the height uncertain by so much as five feet.

TABLE III.

Flight of Brookins, Sept. 10, 1910. Wright Biplane. Base Llve 6236
FEET, Course 13 feet above Mean Low Water.

QuiNcv Station.

Milton Station.

H

eight above Course 128 ft

Height above Course 71 ft. 1

No.

Time.

Vert.
Angle.

Hor.

Angle.

Altitude.

Time.

Vert.
Angle.

Hor.
Angle.

Altitude.

1

5° SS'" 37*

3° 54'

68° 59'

1220 ft.

5'* 38™ 40«

4° 24'

88° 7'

1222 ft.

2

40

22

5 47

68 28

1511

40

30

6 28

84 30

1518

3

41

40

[71 56

80 41

1910^

41

44

7 55

71 44

1919

4

42

41

7 44

90 59

2005

42

45

7 8

64 54

1981

5

43

42

7 12

90 20

2019

43

46

6 51

67 6

2023

6

54

13

11 12

69 49

3432

54

19

12 10

88 15

34.50

7

55

11

11 53

82 51

3514

55

15

11 49

75 9

3527

8

57

10

15 3

85 36

3713

57

15

14 19

68 35

3715

9

57

52

15 43

82 34

3753

57

55

15 11

70 19

3753

10

58

35

16 16

79 5

3803

58

40

16 16

72 42

3849

11

59

41

16 50

73 42

3858

59

45

17 20

76 48

3865

12

6 0

35

16 36

69 31

3874

0

40

17 43

81 7

3877

13

1

00

15 13

66 1

3986

2

0

10 48

87 55

3986

14

2

37

14 21

71 21

4039

2

36

15 18

84 41

40.50

15

3

15

14 29

80 20

4092

3

20

14 29

76 24

4091

16

4

5

16 .52

81 48

4201

4

10

16 27

72 0

4199

17

4

.')0

17 .52

74 43

4295

4

55

18 17

77 13

4295

18

5

30

17 58

68 8

4338

5

34

19 23

83 22

4339

19

6

22

17 23

60 27

4419

6

26

20 3

92 31

4427

20

7

14

15 36

58 32

4472

7

19

18 12

98 5

4478

21

8

2

14 33

63 25

4496

8

6

16 21

94 55

4503

22

9

2

14 24

73 2

4530

9

7

15 14

85 42

4.549

23

9

39

14 48

78 48

4.569

9

42

15 3

79 47

4576

24

10

20

15 29

85 33

4616

10

25

15 5

72 52

4()26

25

11

9

17 41

87 2

4646

11

14

16 46

68 45

4645

26

12

2

18 59

76 43

4719

12

6

19 13

76 17

4731

27

13

39

13 45

68 5

3974

13

42

14 30

88 33

3844

28

14

24

11 21

81 10

3356

14

28

11 24

76 40

3364

29

16

34

7 18

67 52

1789

16

38

8 8

83 35

1799

30

17

24

4 41

65 55

1375

17

28

5 23

89 54

1381

' Vprt

. angle at Q h

ia.s boon

changod

"rom the re(

corded value of 6° 56'.

The third llight, Figure 2 Qeft), is that of Grahame-White on Septem-
ber 1 2, immediately preceding that of Brookins. The seventh observation
shows a corrected vertical angle at Milton, and the twelfth a correction
of the horizontal angle at the same station, — one of two instances de-

38

PROCEEDINGS OF THE AMERICAN ACADEMY.

5000

4000

Figure 5. Spiral of Brookins, September 10, plotted from observations of
Table III.

WILLSON. — ALTITUDE OF AEROPLANE FLIGHTS.

39

TABLE IV.

FuGHT OF Brookins, Sept. 8, 1910, Wright Biplane. Base Line, 6236
FEET. Course 13 feet above IMe.vn Low Water.

QcijjCT Station.

Milton Station.

Height above Course 128 ft.

Height above Course 71 ft. 1

No.
1

Time.

Vert.
Angle.

Hor.
Angle.

Altitude.

Time.

Vert.
Angle.

Hor.
Angle.

Altitude.

5tt 3sm 418

2° 29'

73° 2'

774 ft.

5n ggm ^-^a

2° 48'

82° 26 '

774 ft.

2

39

55

3 42

76 25

973

39 54

[3 55]

76 0

9671

3

41

1

4 21

84 35

1156

41 1

4 19

69 46

1154

4

42

9

4 13

75 17

1319

42 12

4 32

82 14

1322

5

43

37

5 23

77 49

1506

43 36

5 36

77 34

1506

6

48

2

5 26

73 30

1499

48 0

5 54

81 11

1516 2

7

49

44

7 11

81 2

1732

49 46

7 8

71 19

1732

8

50

59

8 31

76 4

1888

51 1

8 40

73 22

1SS5

9

[52]

13

5 48

80 35

1505'

52 7

5 52

73 17

1506

10

54

28

6 10

80 53

1782

54 27

6 16

75 51

1783

11

55

35

7 3

77 3

1880

55 35

7 17

77 30

1879

12

56

28

8 1

78 7

1959

56 26

74 22

13

57

19

9 22

79 26

2068

57 16

'9' 15

70 34

2068 '

14

58

8

10 41

76 10

2148

58 6

10 39

70 32

2145

15

59

35

8 56

76 18

2254

59 35

9 12

77 13

2255

16

6 0

23

9 17

86 3

2363

6 0 24

8 53

68 52

2365

17

1

32

10 36 95 34

2456

1 31

9 22

58 59

2454

IS

2

33

12 27 100 24

2528

2 31

10 21

52 31

2532

1<)

5

11

[17 42] 186 51'

2766*

5 6

14 56

54 59

2759

20

6

28

[16 38] 69 35

2886 *

6 27

17 4

70 47

2884

21

7

36

14 31 ,60 20

2992

7 35

16 52

85 28

2994

22

8

51

12 10 , 55 16

3102

8 51

14 50

98 9

3104

23

9

41

11 12 ,62 2

3130

9 41

93 44

24

11

56

13 35 87 15

3237

11 54

12 44

[66 23]

32406

25

12

56

14 46 ,98 4

3237

12 55

12 42

55 57

3247

2()

16

21

22 19 125 42

3419

16 16

14 44

30 49

3413

27

17

33

26 23 111 3

3598

17 33

36 44

28

18

46

23 32 90 3

3565

18 46

19 ' '5

51 39

3552"

29

20

14

18 17 75 54

3647

20 4

18 6

70 35

3651

30

22

36

14 52 |86 33

3708

22 36

14 6

68 3

3715

31

23

45

15 21 '78 25

3791

23 46

15 23

74 47

3799

32

24

51

15 28 1 71 28

3831

24 51

16 21

81 7

3837

33

26

23

12 59 91 41

3170

26 26

11 51

63 20

3168

> \'ort

. angle has been inrr

eased 1° for Station M.

2 Marked worthless by ohs

erver at M. Clouds between

5 and 6

.

* Time at Station Q haw he

en decrea.sed by 1"*.

* 5° h

a.s l)een added to ear

1 of the vertieal angles.

» 10'

ha.s been added to ]

lor. Angle at Station M (.sii

iral sug

nested

th

is rhango and sextant also

it 6'' 12'" O-'roiifirms it).

40

PROCEEDINGS OF THE AMERICAN ACADEMY.

tected in the whole series ; it was not indicated by comparison with the
Quincy values, as there is close agreement with either value of the
horizontal angle, but the spiral showed that the horizontal angle must
be in error by about 10°, and a sextant observation at almost the same
instant corroborates the value of the height given in the table.

TABLE V.

Flight of Gr ah ame- White, Sept. 12, 1910. Farman Biplane, Base Line
6236 feet, Course 13 feet above Mean Low Water.

Q01NCY Station.

Milton Station.

Height above Course 128 ft.

Height above Course 71 ft.

No.
1

Time.

Vert.
Angle.

Hor.
Angle.

Altitude.

Time.

Vert.
Angle.

Hor.
Angle.

Altitude.

S*"

13"

15^

2° 25'

79° 51'

792 ft.

5" 13=

'15^

2° 37'

77° 23'

796 ft.

2

5

16

12

4 17

64 6

1114

5 16

13

5 2

87 39

1115

3

5

16

52

4 51

70 36

1163

5 16

51

5 21

79 14

1167

4

5

17

44

4 42

83 22

1206

5 17

42

4 42

70 4

1210

5

5

18

30

4 11

86 3

1301

5 18

30

4 12

72 13

1307

6

5

19

24

3 59

78 23

1336

5 19

18

4 13

80 50

1340

7

5

20

19

4 22

70 23

1369

5 20

18

[4]i 51

87 5

1372

8

5

21

2

4 51

65 34

1501

5 21

2

5 38

91 47

1525

9

5

21

43

5 27

62 51

1538

5 21

44

6 22

92 13

1540

10

5

22

22

6 13

61 14

1582

5 22

21

7 21

90 55

1581

11

5

23

10

7 14

66 6

1673

5 23

9

8 9

81 49

1682

12

5

23

55

8 4

78 33

1687

5 23

54

8 1

[69]224

1693

13

5

25

23

6 13

86 14

1813

5 25

21

6 6

71 19

1811

14

5

26

20

6 5

77 20

1873

5 26

19

6 21

80 36

1873

15

5

26

52

5 56

72 6

1854

5 26

50

6 26

85 54

1857

16

5

27

28

6 9

67 14

1851

5 27

25

6 58

89 49

1873

17

5

28

3

6 40

63 29

1910

5 28

2

7 40

92 24

1909

18

5

28

55

8 0

63 51

1981

5 28

55

9 10

87 56

1981

19

5

29

31

8 54

71 59

2020

5 29

30

9 29

77 44

2029

20

5

30

17

8 32

83 49

2111

5 30

18

8 20

69 53

2121

21

5

31

8

7 17

78 35

2104

5 31

8

7 31

78 10

2114

22

5

31

43

7 12

72 23

2093

7 42

84 7

2086

23

5

32

20

6 7

67 47

1687

5 32

'20

6 50

86 52

1687

24

5

33

14

3 27

66 5

859

5 33

14

4 0

83 12

851

1

Ver1

. anj

?le at M

ilton recorded 5°

51'.

2

Hor

. ang

^le recor

ded at Milton w

IS 70°

24'.

Spiral proves it to be

69°

24' £

inds(

3xtant 0

aservation at aim

ost same ins

>tant corroborates this.

It has been thought worth while to give these observations in detail
for those especially interested in the problem. It is evident that there
is much information in the tables and curves to which we have not

■v^^LLsox. — altitude of aeropl.\ne flights.

41

referred ; for example, rate of ascent per minute, gradient with and
against the wind, etc. The reader who wishes to study them more
minutely may tlierefore msh to plot them on a scale suiHciently large
for his purpose. To make use of the sextant as well as the transit
observations in plotting the spirals, it is necessary to know the relative
position of the two bases. The north end of the field base is distant
15,000 feet and 14,700 feet from Q and 'Si respectively. The south
end of the field base is 10,050 feet from Q and 11,005 feet from M.

In regard to these tables we notice that there is apparently a small
systematic ditierence between heights as observed at Q and M. This
was at first suspected to be due to error in level of the two stations, but
was not the same at all times. It was not due to difference in time ot
observation at the two stations, for although the setting at Milton was
always a fraction of a second later, this could only give rise to a differ-
ence of about one foot at most. It may have been partly due to
difference in levelling of instruments, and perhaps partly to neglect of
refraction and curvature of the earth in the computation.

asort

3000

2.J00

80OO

I50f)

1000

500

1

P

/

,-*■ ■*

I

c

p

*

/

/

1

/

1

*

:

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A .'

/

/

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1

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^ *

,K

/

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U 1

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U 2

5

i(

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a b

FiarRE 0. Time-altitude curve. (Left) flight of Johnstone, September 7
(Wright hii)iane); (right) flight of Gruhame-Whitc (Bld-riot monoplane), and
fligiit of Brookins (Wright biplane).

The time-altitude curves have been plotted for all the flights of the
meet which have any special interest. Those of Brookins, Johnstone,
and Grahame-White on September 7 are i)lotted in Figure (>. They
show the typical rate of ascent of the Wright biplane, about 100 feet
per minute, in direct comparison with the BK'riot which was in the air
at the same time and rising mure than 200 feet per minute.

42 PROCEEDINGS OF THE AMERICAN ACADEMY,

Figure 4, plotted from Table III, represents the highest flight of the
meet, that of Brookins on September 10, at an average rate of about
100 feet per minute. From 5'* 43™ to 5" 57™ the transits were tempora-
rily assigned to Grahame-White in a Farman biplane, who was far off
the course to the southeast and could not be frequently observed by
the sextants, while the latter instruments were sufficient for the obser-
vations of Brookins, who was describing large but regular circles above
the field. At 5^* 52™ Grahame-White was cut off" from view at Milton
by a large tree which lay farther off" the course than it was supposed
that any aviator would go in an altitude attempt, and the transits
were turned back upon Brookins.

The single sextant observation of Grahame- White's descent, however,
combined with the fact that his usual rate on the beginning of the
downward spiral was at least 800 feet per minute, enables us to fill out
the dotted part of the curve, and conclude that he reached a height of
approximately 2200 feet. A comparison of all the curves shows that
if the highest point of the ascent is not actually observed by the tran-
sits, it may always be closely fixed by the intersection of the upper
portions of the curves of ascent and descent.

The spiral of Brookins in this flight is shown in Figure 5. In the
long interval between points 5 and 6, when the transits were turned
upon Grahame-White, the general curve of the spiral, however, is
plainly shown by the sextant observations, although the aviator
changed the direction in which he was circling the course, apparently
in order to make his crossings against the wind.

Figure 7 shows the time-altitude curve of Brookins on September 8,
when he was lost to sight in a light cloud for five minutes at an alti-
tude of 1500 feet, climbed another 500 feet and disappeared a second
time, when he stopped his engine, descending to the 1 500 foot level
again out of the cloud, and then taking a somewhat diff"erent line of
flight, ascended without further difficulties to a height of nearly 4000
feet. The conditions were such that the early part of the spiral was
not well determined, and it does not seem worth while to reproduce it
here. The main features are shown on the ground plan which is shown
on the map of Plate 1. The very discordant sextant observations at
5^ 19™ and 5^ 22™, shown in Figure 7, are unexplained. The former
was made with the machine about 1000 feet south of the southern
station, nearly overhead, and moving in a course nearly parallel to
the line, so that the vertical angle was changing very rapidly, and the
observation difllicult.

No such cause can be assigned for the second error, and it is perhaps
more probable that both were caused by some accidental disturbance

■WTLLSON. — ALTITUDE OF AEROPLANE FLIGHTS.

43

of the vertical plane of the sextant which affected the two observations
alike. No other discrepancy approaching this in amount occurred in
in the whole course of the observations.

4um>

-o'

0-=

,o-o''

.o'- -

I
o

o'

1
\

d'

'

Ofyvi .

/

o
o'

<

9
' o

^

1
1

F

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ouu

V

5

33 i

0 *

5 0

6 3

3 «

0

1

» J

"> 2

ti :,^

:- ;iu

33

Figure 7. Time-altitude curve: Brookins (Wright biplane), September S.

It remains to make grateful acknowledgment of the skill of the
observers and of the interest of many others, without which this
work would have been impossible ; especially of the assistance of
Mr. William Hunt in the observations and reductions, and in drawing
the curves which illustrate this paper.

Students' Astronomical Labor.\tory,
Harvard University.

WiLLSON. -Altitude of Aeroplane Flights.

Plate 1.

- 1-,

Proc. Amer. Acad. Arts and Sciences. Vol. XLVII.

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Proceedings of the American Academy of Arts and Sciences.
Vol. XLVII. No. 3. — June, 1911.

THE NATURE OF VOLCANIC ACTION.

By Reginald A. Daly.

With Five Plates.

THE NATURE OF VOLCANIC ACTION.
By Reginald A. Daly.

Presented April 12, 1911. Received February 23. 1911.

Contents.

Page

The Problem 48

Abyssal Injection 50

Conditions of Abyssal Injection 52

The Substratum 54

Some Direct Consequences of Abj'ssal Injection 55

Genetic Classification of Volcanic Gases 57

Phases of Volcanic Action 58

Fissure Eruptions 58

Eruption through Local Foundering 60

Blue Hills, IMa.ssachusett3 62

Glen Coe, Scotland 62

Yellowstone National Park 63

Central Eruptions , 67

Opening and Localization of the Vent 67

Enlarged Fissures 67

Diatremes 69

Plutonic Cupolas 69

Continuance of Activity ; Analj'sis of Conditions at Kilauea ... 71

Rate of Heat-loss through Conduction into Walls 71

Rate of Heat-lo.ss through Radiation at the Crater . . . .v. . 72

Methods of Heat Transfer 73

Two-ph;i.so Convection 76

Lava Fountains 82

Cooling by rising Juvenile Gas 84

The Volcanic Furnace 85

Summary of the Heat Problem of an Active Central Vent. . . 90
Revival of Activity at the End of a Dormant Period ; Periodicity

of Volcanoes 92

Small Size of Central Vents 97

Explosive Types ; Phrcatic and Magmatic 100

Magmatic DifTcrcntiation at Central Vents 102

Progr&s.s in E.xplosivcncss at the Greater Vents 105

Lava Outflow at Central Vents 106

The two Types of Lava Flows 107

48 PROCEEDINGS OF THE AMERICAN AC.U)EMY.

Page

Vulcanism originating in Satellitic Injections 108

Kilauea the Vent of a Satellitic Injection 109

An Icelandic Example 116

Tertiary and Older Vents from Satellitic Injections ; Suabian

and Scottish Examples 117

A Necessary Division of Central Vents 118

General Summary 119

The Problem.

Volcanic action is the working of the extrusive mechanism which
brings to the earth's surface rock-matter or free gas, initially at the
temperature of incandescence. The mechanism involves the localiza-
tion, opening, and shaping of the vent ; the persistence of a vent as
an open channel during seconds, days, years, centuries, or milleniums ;
the conditions for lava outflow, for gas and vapor outflow, and for the
separation of gas or vapor from lava ; the conditions leading to the
periodicity of eruption at central vents ; and those leading to chemical
variations in the erupted magma.

Since the days of the Greek philosophers thousands of memoirs have
touched upon this complex problem of terrestrial dynamics, but geolo-
gists are still looking for a generally acceptable solution. Within the
last ten or twelve years the variety of new suggestions affecting the
very core of volcanic theory has been, perhaps, as great as that of any
previous decade. In the varying chemical affinities of water and silica
for the bases of rock-matter at different temperatures, Arrhenius finds an
essential condition of all vulcanism. He therefore attempts to support
the time-honored hypothesis that the vapor of meteoric or marine water
absorbed in plutonic magma is the prime motor in eruptions. ^ On the
other hand, Brun holds that water is quite unessential to eruption of
the first order, and he believes he can prove his thesis by actual
analysis of the volcanic emanations.^ Again, Chamberlin explains
vulcanism as due to the extrusion of magmatic tongues, which, by tidal
stresses, are slowly kneaded out of the deep interior of the otherwise
solid earth.3 In entire contrast to that hypothesis, Dutton has come
to the belief that the indications are that most of the volcanic erup-
tions originate at depths between one mile and two and a half miles.*

1 S. Arrhenius, Geol. Foren. i Stockholm Forhandl., 22, 395-419 (1900).

* A. Bnm, Archives des sciences physiques et naturelles, Geneva, fevrier,
1909; f6vrier, 1908; novembre, 1906. Le Globe, octobre, 1907.

3 T. C. Chamberlin and R. D. Salisbury, Geology, 1, 632 (1906), and 2,
104 (1906).

* C. E. Dutton, Volcanos and Radioactivity, 1906, p. 5 (Paper read before
the National Academy of Sciences, April 17, 1906), published at Englewood,
N.J.

DALY. — THE NATURE OF VOLC.VNIC ACTION. 49

Without further noting the divergences of recent views, it is clear that
volcanic theory is in a disorganized state.

There is one patent reason for this conflict of opinion. The Ve-
suvian " steam-engine " and the geyser-like Stromboli have dominated
European thought. Though living in a wilderness of waters, the bril-
liant Englishman in Hawaii, W. L. Green, concluded that water is not
an essential agent in vulcanism, for he had lived many years meditat-
ing on the dry, or nearly dry, emanation from Kilauea.* Arrhenius, a
physical chemist ; Moissan, a synthetic chemist ; Brun, an analytic
chemist ; Mallet, a civil engineer ; von Buch, a Wernerian geologist ;
von Humboldt, a Wernerian who traveled greatly ; Scrope, who built
his philosophy on observations in the limited European field : Stiibel,
a specialist in the giant volcanoes of Ecuador ; Tschermak, a mineralo-
gist ; Daubree, an experimental geologist ; Dutton, master of geological
reconnaissance — each of these, and every other leader in volcanic
study has been forced to think in terms of his intellectual environment.
Each investigator has approached the many-sided problem with special
training and experience, and many vulcanologists have shared the
racial subjectivity which finds explosions, earth -.shaking, and other
surface events humanly so important as largely to control inductions
on the theoretical side. During the last half-century the discovery and
study of thousands of plutonic igneous masses have promoted the view
that vulcanism is a subsidiary effect of intrusion. This thesis is em-
phasized and illustrated in the following pages, wherein the attempt
is made to show its agreement with the essential facts known about
volcanoes, ancient and modern.

A general working theory of vulcanism is here outlined. It has
taken its full form directly as a result of the writer's studies in the
Hawaiian Islands during 1909, but many of the chief conclusions are
founded on his field-work in plutonic geology as well as in the geology
of many ancient volcanic formations. The effort has been made to
cover the more important literature of vulcanism, and as yet no facts
therein stated seem to the writer to be irreconcilable with the theory,
which, on the other hand, finds strong support in the great body of
recorded facts. Many of the essential points in the following argu-

" "Water in a rainy di.strict gets to the hot rocks in all sorts of ways, about
which there need be little mystery. All this steam seems to have no further
connection with the forces concerned in the action of the lav;i.s in Kilauea,
tliiin the vapors which arise from the body of a hard-worked horse, when a
shower of rain ha.s fallen on him, have with the force he exerts in drawing his
load." — W. L. Green, Vestiges of the Molten Globe, Part 11., p. S2, Hono-
lulu, 1887.

VOL. XLVII. — 4

50 PROCEEDINGS OF THE AMERICAN ACADEMY.

ment are by no means new. The principal reason for adding this paper
to the already overburdened literature on volcanoes is that it attempts
to coordinate the accepted principles of vulcanology with each other
and with the truths of plutonic geology. AVhether or not the actual
result is to meet with favor among geologists, the writer feels certain
that the synthetic ideal in vulcanological study has not been actively
pursued in anything like its just measure. That this pursuit necessa-
rily involves some speculation concerning the earth's interior is not a
valid objection to the undertaking. The earth's interior is no more
invisible than is the interior of a molecule. The sanction for modern
chemistry has become as strong as it is because philosophical chemists
have speculated about the invisible, intangible, and unweighable.
Similarly, to be more productive than it is, geology must become more
speculative. In this there is danger if the hypothesis is founded only
on the facts met with in the individual worker's experience ; there is
little danger, but great promise of fruit, if the speculation is synthetic
and regards all the published facts.

During the preparation of this paper the writer has been greatly
aided by discussion of many points with his colleagues. Professor
W. C. Bray, T. A. Jaggar, Jr., G. N. Lewis, and A. A. Noyes of the
IMassachusetts Institute of Technology, and also with Professor H. N.
Davis, Professor L. S. Marks and Dr. P. W. Bridgman of Harvard Uni-
versity, and Professor A. C. Lane of Tufts College. To these gentlemen
the writer's sincere thanks are due ; he alone, however, must bear the
responsibility for the form and substance of the paper. He wishes
further to express special thanks to the Director and chemists of the
United States Geological Survey, who have supplied two of the chemical
analyses noted in the text ; to Mr. H. E. Wilson, of Hilea, Hawaii,
who has furnished one of the photographs here reproduced ; and to
Mr. Walter E. Wall, Government Surveyor of Hawaii, who has ex-
tended many courtesies to the writer, and gave him permission to copy
many manuscript maps used in the assembling of some of the facts on
which this paper is based.

Abyssal Injection.

Surveys on each of the continental plateaus have already shown that
the average rock of the plateau's basement (pre-Cambrian terrane) is,
chemically speaking, of granitic composition, with a silica-percentage
notfar from 70. Notwithstanding the vast erosions of many geological
periods, this terrane is, in places, known to extend downward several
kilometers even at the present time, and it is a reasonable inference,
contradicted by no fact yet discovered, that the acid complex has, gen-

DALY. — THE NATURE OF VOLCANIC ACTION.

51

erally, a minimum depth of many kilometers. Upon its back each of
these acid continental plateaus carries a sedimentary pellicle, locally
increased to the imposing thickness of geosynclinal prisms. (See
Figure 1.)

Figure 1. Diagrammatic section of the earth-shells, showing abyssal injec-
tion and accompanying central eruption. The broken lines below the cone
represent a geosynclinal prism merging into sediments of more usual thickness.
Solid black represents solidified matter of the basaltic substratum, the broad
horizontal band indicating the part of the .substratum crystallized since an
early pre-Cambrian period. Heavy dots represent fluid matter of the substra-
tum, in i)o.sition after the aby.ssal injection has i)artly crv.stallized (along its
walls). Scale given by height of cone, assumed as projecting o kilometers
above the plain of sediments.

Mo.st volcanic rock is of basaltic or andesitic composition, and it is
clear that such material has not been derived from the mere li(juefac-
tion of the basement terrane, or of the sedimentary veneer, or of both
together. The great bulk of the world's lava is exotic. It has peue-
trtiteil the ba.sement terrane and the .sedimentary .shell without absorb-
ing these in large proportion. We thus seem driven to believe in
ahj/ssiil/iasure.i, opened in the earth's outermost shells for the pas.sage
of the molten rock.

By analogy such abyssal injection may be assumed as the preliminary
stage of Pacific vulcanism, although there is much to be said for the
view that the primary acid earth-shell is lacking, or else is very thin,

52 PROCEEDINGS OF THE AMERICAN ACADEMY.

over most of the area covered by that ocean. For example, geodetic
results seem to suggest that the Pacific sediments rest, more or less
directly, on a terrane whose average density is nearer the density of
crystallized basalt than that of granite or common gneiss.

In the case of the greater lava-fields, the abyssal fissures have been
prolonged, as true fissures, to the surface ; there a leading condition of
extrusion is probably the simple hydrostatic adjustment of magma to
a breaking earth-crust. Most central eruptions have occurred in locali-
ties where emitting fissures are not visible. In emphasizing this fact
some geologists have been disposed to deny that fissuring of the crust
is a prerequisite of vulcanism. Their reasoning is strong so far as the
actual opening of many vents is concerned, and one result has been to
sharpen the eyes of vulcanologists as to field relations. But we may
agree with Supan that " one should not throw out the baby with his
bath-water." Though a vent, for the last few hundreds or thousands
of meters, may have been opened by explosion or by other means than
simple fissuring, a fair study of geological maps shows the existence
of strong abyssal fissures beneath most of the volcanic piles which
are not visibly located on surface fissures. Obviously, an immediate
tendency of volcanic action is to cover such feeding fissures. Yet their
existence is to be inferred from the group alignment of the greater
cones. Such is, of course, the traditional explanation of groups like
those of the American Cordilleras, of the Hawaiian series, the Samoan
series, or the Antillean series. Some clusters of vents show no definite
alignment ; instances like the " embryo " volcanoes of Suabia will be
discussed on later pages.

We may, therefore, assume abyssal fissuring and magmatic injection
to be the essential prelimi?iary to vulcanism, as it is, indeed, to all
igneous action. Probably most vulcanologists have made the same
assumption, but the literature of vulcanism nowhere contains a full
statement of some of the chief theoretical consequences of the assump-
tion. Some authors, either expressly or tacitly, refuse to believe in
the principle, but their arguments against it have never been sufficiently
supported by the facts of structural and areal geology. The matter is
so fundamental that it has here been duly stated ; it may savor of
a truism to many working geologists.

Conditions of Abyssal Injection.

The principle may be accepted, though the circumstances permitting
of injection at depths of ten, twenty, or more kilometers are not yet
completely understood. This much more difficult subject has been

DALY. — THE NATURE OF VOLCANIC ACTION. 53

speculatively considered by the writer in a paper published in 1906.*
Therein the general result of the work of Reade, Davison, Fisher, and
G. H. Darwin, on the stresses produced in the earth through cooling,
was assumed as true. A superficial shell of compression is separated
from a much thicker underlying shell of tension, by a level of no strain.
The tensions of the lower shell and the failure of complete "compres-
sive extension " in that shell furnish the conditions favoring magmatic
intrusion into the shell. The writer's earlier statement (page 204 of
the paper referred to), that laterally-confined rock-matter grows vastly
more rigid with increase of pressure, has been recently corroborated in
striking fashion by Adams and Bridgman in their respective high-pres-
sure experiments. Adams shows that, with lateral support at high
pressure, the normally weak mineral, fluorite, became less plastic than
hard steel at ordinary pressure.'' P. W. Bridgman (verbal communica-
tion) has proved that under external hydrostatic pressure amounting to
24,11(10 atmospheres, the cavity of a sealed glass tube is not closed, even
after prolonged application of such enormous force. In an actual test, a
tube, having undergone a hydrostatic pressure of 24,000 atmospheres
— corresponding to the weight of more than eighty kilometers of
the earth's crust — for a period of three hours, was removed from the
press and was found to have undergone no sensible change in size
or form. These experiments seem to sustain the view that at least
the upper, cooler part of the shell in which tension is developed on
account of the cooling of the earth, is not kept fully and continuously
condensed by the weight of the overlying shell. On the contrary, the
shell of tension may be capable of considerable condensation, which
awaits, as well as permits of, the periodic injection of liquid matter
from the substratum. This is also the conclusion of Lane, expressed
in his highly suggestive paper on the " Geologic Activity of the Earth's
originally absorbed Gases," where he has considered the mechanics of
abyssal fissuring.*

In general, the injections must find difficulty in passing beyond the
level of no strain, which is only a few kilometers below the surface of
the planet. In the cases where the magma does succeed in penetrating
the shell of compression, volcanic action ensues.

Since the speculation is not vital to the argument of the present
paper, it will not be further reviewed. It may be noted that the same

• R. A. Duly, Al)yMs;il Igneous Injection ;ls aCiiusal Condition and ;id an
Effect of Mountain-building. Am(;r. .Jour. Science, 22, l'Jo-21G (,1'JUlj).
» r. D. Adam.s, Jour. Gcol., 18, 500 (1910).
» A. C. Lane, Bull. Geol. Soc. America, 6, 2G9 (1894).

54 PROCEEDINGS OF THE AMERICAN ACADEMY.

general conception has been independently stated by H. J. Johnston-
Lavis, one of the world's most experienced students of volcanoes. Only
quite recently has the writer found that he had been anticipated by
Johnston-Lavis in the root idea, as expressed in brief notes published
in the Geological Magazine.® It is a source of genuine satisfaction to
find a fellow adventurer in an almost pathless field of investigation,
and, yet more, to find in that companion a distinguished specialist.

The Substratum.

Similarly, the writer has found that he has been anticipated in the
view that the heat-bringer in all Paleozoic and later igneous action is
a general basaltic substratum underlying the shell of tension. 1° The
essential point was stated by Cotta on page 78 of his " Geologische
Fragen," published in Freiberg in 1858, and by W. Lowthian Green on
page 61 of his "Vestiges of the Molten Globe," Part II, published in

^ 17, 246 and 344 (1890). A fuller statement by the same author appears
in the Geological Magazine, 36, 433 (1909).

" Cf. R. A. Daly, Amer. Jour. Science, 15, 294 (1903).

The writer is clearly conscious that this assumption of an uncrystallized
general substratum conflicts with the planetesimal hypothesis of the ecarth's
origin, as stated by Chamberlin. Wliatever be the mode of assemblage for the
earth's materials originally, it is extremely difficult to accept the view that, when
the planet approached its present size, it could have avoided a stage where it
was molten all over the surface. Lunn's temperature-depth curve (Chamberlin
and Salisbury's "Geology," 2d ed., 1, 564, 1906) for the earth, computed
on the accretion hypothesis, shows temperatures of from 10,000° to 20,000° C.
in the interior. Since, on the hypothesis, the mode of accretion afforded a
very heterogeneous mass at the beginning, there must have been a gravitative
readjustment of the materials rendered fluid by the high temperature of the
interior. The less dense matter, rising from great depth, would bring to the
surface a large proportion of its enormous heat-content, ultimately fusing a
surface shell of great depth. In other words, the earth-furnace imagined by
Chamberlin and Lunn would melt its own walls.

Another serious objection to the hypothesis that the earth has been largely
solid (crystalline) throughout its history is the fact that each of the planets,
Jui)iter, Saturn, Uranus, and Neptune, has a density appropriate to a gaseous
condition and to very liigh temperature even in the surface shell. Again, if the
moon were never fluid at the surface, its matter has been fluid very close to
that surface; every square meter of its visible surface seems to have wit-
nessed igneous action. So far, the published statement of the planetesimal
hypothesis has not discussed the earth's history in terms of the facts known
about its fellow members in the solar system. Since both the gas-nobula and
planetesimal-nebula hypotheses seem to demand an incandescent, molten
stage for the earth, the present writer is inclined to doubt that the geologist,
for most of his thinking, needs a decision as to the truth of either hypothesis.
That is a matter for cosmogony and astrophysics.

DALY. — THE NATURE OF VOLCANIC ACTION. 55

Honolulu in 1887. Each of these books first became accessible to the
writer in I'JOy. It is certainly a pity that the second part of Green's
work is not more generally known. The book is almost as remarkable
a contribution to the philo.sophy of vulcanism as Part I, on the Tetra-
hedral Theory of the Earth, is important in cosmogonic philosophy.
With the advance of geologic exploration, the arguments for a univer-
sal basaltic substratum are to-day more convincing than ever. For the
sake of brevity these arguments will not here be fully presented, though
some of them are mentioned in the sequel.

It will further be assumed that the known temperature gradient may
roughly indicate the depth (estimated at 40 kilometers) at which the
basaltic substratum is actually or potentially fluid. Many writers have
independently arrived at nearly ec^uivalent estimates for this depth.
At such depth the internal friction may be so increased by the pressure
that the substratum almost perfectly resists deformation by the quickly
acting tidal forces.^^ This assumption in no way excludes the possi-
bility that the substratum basalt is a true, non-crystalline fluid, and
that a powerful force, slowly applied (on the principle of stress ditt'er-
ences), could force this highly viscous fluid into the solid crust. As
the fluid rises, its viscosity must fall directly with the lessened ])ressure,
from a possible initial value of perhaps many millions of millions of
times that of water to that of less than fifty times the viscosity of
water, when the fluid reaches the earth's surface.*'

SoAiE Direct Consequences of Abyssal Injection.

The estimate of 40 kilometers for the average depth of the surface
of the substratum may be wide of the mark, but it will serve as
the numerical basis for a statement of certain immediate effects of
injection. 13

" Ilorglotz h:i.s rofently conclu(lo(l that a planot stratified according to den-
sity must resi.st tidal deformation Ix-tter than would the homoRene<ius planet
a.s.sumed by lA)rd Kelvin. G. Ilerglotz, Zeit. fur Math. u. I'liy.-*. 62, 27.1
(190.5).

" Reeker computes the viseoaity of a Hawaiian lava flow (whicli w.a.s by
no means the most fluid already ob.served) as no more than sixty times that
of water. G. V. Becker, Amer. Jour, of Science, 3, 29 (1X97).

" Perhaps the surface of the substratum is !us deep within the earth .as the
limiting depth of i.sostatic compensation. In the .second of his notable
memoirs concerning the figure of the earth and isostiusy, Havford .states that
thf most probalde value of this limiting depfli, for the I'nited States and
a<ijarent area.s, is 122 kilometers, if it be jussumcd that the isostatic compen-
sation is uniformly di.stributed with respect to dejjth. See |)age 77 of hia
"Sui)plementary Investigation in 1909 of the Figure of the Earth and Isoa-

56 PROCEEDINGS OF THE AMERICAN ACADEMY.

First, basaltic magma, rising from such depth nearly to the earth's
surface, must undergo an average expansion ranging between 1.5 and 6
percent.** A small part of this expansional energy may be directly
available for opening fissures in the shell of compression, with conse-
quent extrusion at the surface or development of laccolithic or other
bodies within that shell.

Secondly, some superheat might be expected in each thick abyssal
injection, at levels where the pressure is much less than the 11,000
atmospheres of the original substratum level. The conditions for the
superheat have been briefly discussed in a previous paper. ^^ Super-
heat in large abyssal injections means power of assimilating the wall
rocks either marginally, or through magmatic stoping (forming syntec-
tic magmas) ; the batholithic type of intrusion results. Thin abyssal
injections, rapidly chilled, are relatively or absolutely incapable of such
solution of foreign material ; those injections form the other great class,
typified by ordinary dikes. Each of these types is capable of developing
offshoots of the laccolithic, chonolithic, or sheet order, so that satellitic
injections of primary basalt or of syntectic matter are formed. This
simple but necessary division into assimilating and non-assimilating
injections is of first-class importance in volcanic theory, and underlies
the reasoning of the present paper.

Thirdly, magma which has been forced from the substratum level to
levels where the pressure is 10,000 atmospheres less, must have com-
pletely altered conditions of equilibrium for the juvenile gases. These
include hydrogen, sulphur gas, carbon monoxide, carbon dioxide, chlo-
rine, nitrogen, and other gases, elementary or in combination. The
theory of physical chemistry indicates that the dissolved volatile con-
stituents must, in such a case, slowly diffuse upward, in order to re-
establish equilibrium. There is thus a tendency to saturate and then
supersaturate the upper part of the magma with juvenile gases ; if by
the mere change of pressure the magma is supersaturated with one or
more of the gases, bubbles must form and these must slowly rise. If

tasy," Coast and Geodetic Survey, Washington, 1910. If the top of the
liquid (non-crystallized) basaltic substratum were at a depth as great as 122
kilometers, this change in premises would make no essential difference in the
argument of the present paper. It may be noted that John Milne (Nature, 86,
124 (1911)), using Rizzo's results in studying the velocity of the earthquake
waves which were recently so disastrous at Messina, has estimated the thickness
of the earth's " crust " to be 44 kilometers.

" See Amer. Jour. Science, 22, 201 (1906).

^•^ Amer. Jour. Science, 26, 33 (1908). Cf. J. Joly, Radioactivity and Geol-
ogy, London, 1909, pp. 103-109, where there is an important discussion of
one phase of this subject.

DALY. — THE NATURE OF VOLCANIC ACTION. 57

the injected boily is tightly roofed, the gases continue to rise until the
growing gas-tension at the upper levels stops dill'usion.

Genetic Classification of Volcanic Gases.

It will conduce to clearness if a brief statement is here made as to
the absolute necessity of distinguishing the different classes of volatile
materials which are associated with igneous activity. These fluids are
either magmatic ox phreat'tcA^ Phreatic fluids are of atmospheric or
oceanic origin, and include indoi^e waters, and also those which Lane
has called connate (contemporaneous) waters, because trapped in sedi-
ments at the time of their deposition. As indicated by Suess, explo-
sions due to the heating of phreatic fluids by intrusive magma have
occurred without the ejection of true lava, either fluent or pyroclastic.

Magmatic fluids are those actually dissolved in magma or emanating
therefrom. Those of primary origin and reaching the earth's surface
for the first time are of the juvenile class. The magmatic fluids of
secondary origin, that is, those absorbed from country-rock formations,
have been called resurgent^'' Resurgent fluids may enter the magma
either as constituents of assimilated country-rock or by independent
solution.

Although only magmatic fluids are important in the present connec-
tion, it is useful to review, in tabular form, the whole group of gases
and vapors which are engaged in volcanic and subvolcanic activities.

^Juvenile ■<
Magmatic fluids

(volcanic ; in-
ternal).

^Resurgent

^Emanations directly from abyssal injec-
tion.
Emanations from primary solid abyssal

country -rock.
fVadose and connate fluids absorbed in

the syntectic process.
Vadose fluids absorbed independently of
^ rock assimilation.
Phreatic fluids (subvolcanic ; ( Vadose.
external) ( Connate.

The resurgent fluids may possibly do something toward keeping a
ventoi)en, but their volatilization means the partial lowering of tempera-
ture in the magma, so that their abundance in a conduit inii)Iie.s

" Cf. E. Suoss, Da.s Antlitz rlcr Erdo, Bd. .3, 2to Il-ilfto, Wicn and U'ipzig,
V.\m, p. f)."!.

" R. A. Daly, Amer. Journ. Science, 26, 48 (1908).

58 PROCEEDINGS OF THE AMERICAN ACADEMY.

a certain " damping of the fires " already accomplished. In basaltic
volcanoes assimilation of the normal, acid crust-rocks has evidently
not been important; at such vents the juvenile emanations are clearly
in control from beginning to end of each volcano's history. This
statement does not conflict with the fact that resurgent water, either
vadose or connate with sediments, is often responsible for the explo-
sions at basaltic and other volcanoes. The clearing-out of the explosion
funnel, which is always shallow and superficial, is not so vital to con-
tinued activity as the preservation of fluidity in the magma of the
conduit.

Phases of Volcanic Action.

According to the views expressed in modern text-books of geology,
the emission of incandescent matter at the earth's surface takes place
either in the form of fissure eruptions or in the form of central erup-
tions. The writer believes that a third method should be entertained
as a possibility, namely, by the partial or complete foundering of bath-
olithic roofs. The relation of each of these three phases to abyssal and
satellitic injection may now be sketched.

Fissure Eruptions (Massive Eruptions, Plateau Eruptions).

The regional or greater lava-floods known to have emanated from
simple fissures in their underlying terranes range in date from the
pre-Cambrian to the present. Without exception they are, chemically,
of basaltic composition. As we have seen, such magma must be exotic.
It is a type of lava (extrusive magma) to which a secondary origin
cannot be theoretically attributed. Its abundance, its occurrence in
every continental and oceanic area, and its field relations to the other
chemical t}^es of magma, all point to the derivation of the plateau
basalt from a general substratum. Each flow thus represents an eff"u-
sion from an abyssally injected body which has not been modified by
assimilation of the earth's acid shell or of the sedimentary veneer. But
the very low original slopes of the flows (very often inclined at less
than one degree to the horizontal plane) and their correlative great
lengths, show that the basalt of fissure eruptions is notably super-
heated. Such temperature is appropriate to assimilation.

That solution of pre-Cambrian gneisses or of other rocks has gener-
ally not taken place in sensible amount during fissure eruption must
have either of two meanings. It may mean that the various abyssal
injections underlying such a lava-field are narrow, with widths to be
measured in meters or tens of meters, but not in thousands of meters ;
or the failure to assimilate may be due to special rapidity of injection

DALY. — THE NATURE OF VOLC.VXIC ACTION. 59

with simultaneous extrusion, for solution of foreign rock must take con-
siderable time. The observed average size of the feeding channels
(dikes) in the great lava-fields of the western United States, of North-
western Europe, of India, and elsewhere, corresponds with the furmer
conclusion. The Icelandic How of 17S3 and the nature of the individ-
ual basaltic flows in every prehistoric lava-field, show or suggest that
each extrusion has been rapid. The controlling condition for the lack
of assimilation is probably the narrowness of the abyssal injections, at
least in the part traversing the sedimentary and acid shells of the earth.

The effusion of a basaltic flood is usually ascribed to the mere squeez-
ing out of the magma from beneath a cracked and sinking earth-crust.
Yet some force may also be available from the expansion of the sub-
stratum material as it rises to levels of enormously lessened pressure.
This expansion is of two kinds ; — that of the lava regarded as bubble-
free, and that of the gases separated from it in bubble form. If the
expansive energy of the liquid proper is not all expended in driving
asunder the walls of the injected body, some of that great force is
available for extrusion. As magma nears the surface, the separation
of the dissolved gas must still further increase the volume and tend to
cause outflow at the surface. The relative importance of these three
conditions for extrusion is by no means apparent, though the writer be-
lieves that the expansional energy of the injected liquid should have
more attention than it has had in general treatises on igneous action.

The fact that the great bulk of visible igneous rock is intrusive, and
the related fact that most of the larger Paleozoic and later injections
have not extended to the surface, suggest that the upper part of the
earth's cru.st has long been comparatively difiicidt of penetration by
abyssal magma. It seems fair to hold that a leading cause of this rel-
ative impenetrability is the state of compression in the outermost shell
of the crust. This compressive stress is relieved b}' an orogenic i)ar-
oxysm. After each paroxysm, tensions in the same shell are produced
by the cooling of the rocks which had been heated by shearing. For
a double reason, therefore, fissure eruptions should be more numerous
and of greater volume in periods subse(iuent to strong mountain-build-
ing. This expectation is fairly matched by the facts of geological his-
tory, as shown in the accompanying table.

Locality. Date of Fiiwure Fruption. PreccdinK OroRcnic roriod.

Ijake Superior Keweenawan. Clo.se of the Animikie.

Distri«;t.

Rocky Mts. at Middle Cambrian (?) Eariy Middle Cambrian (?)

4'.»th Parallel.

60

PROCEEDINGS OF THE AMERICAN ACADEMY.

Locality.

British Islands.
Appalachian IMts.
Deccan, India.

Great Rift,

Africa.
Washington State,
K. W. Scotland.
Iceland.

Washington State.
Great Rift,

Africa.
Great Basin,

U. S. A.
Snake River,

Idaho.
Hauran, Syria.
Iceland.

Dale of Fissure Eruption. Preceding Orogenic Period.

Carboniferous. Devonian.

Triassic. Close of Paleozoic.

Cretaceous (or early Late Triassic (also later? ).

Tertiary ?).
Cretaceous (Kaptian " " " "

series).
Eocene (Teanaway basalt). Close of Laramie.
Oligocene (Lower Miocene). ?

Miocene. 1

Miocene (Yakima basalt). Close of Eocene.
Miocene (1) Tertiary (Alps, etc.).

Pliocene.

Pliocene.

Miocene.

Late Miocene.

Pliocene. Tertiary.

Pleistocene and Recenj;. Tertiary.

Eruption through Local Foundering.

Narrow abyssal injections, like the average dike located near the
earth's surface, will not be expected to show evidences of extensive
assimilation of wall-rock, except at levels deeper than those which can
be exposed by crustal deformation and erosion. If the width of the
injection falls below a certain critical value, the magma is chilled too
rapidly to permit of marginal solution or of stoping. If the width ex-
ceeds that critical value, the molten or magmatic period is prolonged
and absorption of the country-rock by both methods may become im-
portant. Other conditions being alike, the critical width where the
injection cuts the gneissic pre-Cambrian shell is doubtless somewhat
greater than it is where the injection cuts the more hydrous, average
sedimentary terrane. But in all cases, the minimum width for abyssal
injections which have absorbed large masses of foreign rock, is to
be measured in hundreds of meters, if not in kilometers. Abyssal in-
jections of greater volume are believed by the writer to work their way
upward, for hundreds or thousands of meters, by absorption of the
country-rock. The molar-contact absorption may be directly solu-
tional, or directly mechanical, i. e., by stoping (followed by solution of
the sunken blocks in depth). The evidence for assimilation, either
marginal or abyssal, is generally masked by that drastic differentiation

DALY. — THE NATURE OF VOLCANIC ACTION. Gl

which is to be expected in large bodies of syntectic magma. This, in
brief, seems to be the essence of batholithic intrusion. A batholith is
an abyssal injection originally endowed with sufficient thermal energy
(size) to enlarge its chamber through incorporating roof and wall rocks.
The lower and greater part of its chamber is formed by simple dike-
like injection along a widening abys.sal tissure. The upper part, which
is generally the only part exposed by erosion, has been opened by the
activity of the magma itself The average batholith, at exposed levels,
is granitic because granite represents the stable and least dense dilVer-
entiate of the average syntectic.

The integrity of the batholith's roof is evidently threatened in two
ways. It is thinned during the process of absorption of the roof-rock
by the molten magma. The latter might work its way to the surface
through piecemeal stoping, which might continue until a large area
of the batholithic roof has disappeared. On the other hand, it is also
possible that part or all of the roof should, under special conditions,
founder en nuisse in the less dense magma. In either case true vol-
canic action is produced. Such wholesale or piecemeal foundering
would not fairly be called simple fissure eruption, though it might be
accompanied by lava floods emitted from fractures in the roof- rock
surrounding the foundered area. The level surface of the lava in the
area of foundering would, in form, resemble a plateau (fissure) eruption,
but the lava would here be generally liparitic rather than basaltic, as
in the great majority of plateau eruptions. Moreover, the liparite
would form a continuous mass merging downwards into granite, and
thus not a series of superposed distinct flows. According to the topog-
raphy, the lava of the foundered area might flood valleys outside that
area. If the hydrostatic adjustment were accomplished in stages,
it would cause successive, superposed flows in the valleys. (See
Figure 2.)

Needless to say, the field evidences do not favor the idea of founder-
ing in the case of many, perhaps most. Paleozoic and later batholiths.
These bodies must be regarded as truly plutonic, according to the or-
thodox creed. Yet it is expedient to entert^iin the hypothesis in ex-
planation of the field relations of some pre-Cambrian batholiths as well
as those of a few younger masses.

In the first })lacc, the evidence «jf local foundering in the past is in
special danger uf being obliterated. The glas.sy or scoriaceous phase
of the " batholith " will nece.s.sarily be eroded away before the granitic
phase can bo exposed, 'i'ho liparitic phase need extend to a depth of
no more than a few iiundred meters, where it would rapidly merge into
the holocrystalline phase. Therefore, comparatively little time would

62

PROCEEDINGS OF THE AMERICAN ACADEMY.

be required to remove the original surface phase. The geologist
studying the erosion surface might have no inkling that the " batholith "
had not been completely covered by a roof of country-rock. The
former existence of a roof cannot be assumed simply because a " batho-
lith " has a holocrystalline structure.

^ooc/gc/ /4/-)9c

/^,-ff£f (y/ Hoof rocM W/f/r o^normo/

. . , / A /her/no/ Orac/te/?/

PHA3^ Of

Figure 2. Ideal section of a district of batholithic foundering. Length
of section assumed, for example, as 60 kilometers.

Blue Hills, Massachisetts.

The relations of the granite, quartz porphyry, and aporhyolite of the
Blue Hills complex, near Boston, Massachusetts, to each other and to
the Cambrian slate which forms the country-rock of the intrusive,
suggest at least that the batholithic roof was very thin. Crosby de-
scribes two large areas of the aporhyolite (felsite) with the characters
of both intrusive and effusive magma. He favors the view that these
bodies are very thick surface flows of the ordinary tj'pe, though he
states the alternative view that the aporhyolite represents the intru-
sive, latest phase of the batholithic magma. ^^ The present writer
believes that, in this case, the hypothesis of partial roof-foundering is
worthy of a competitive place in a full discussion. The belief is founded
on actual acquaintance with only a limited part of the observable field
relations, and it is offered merely as a preliminary suggestion.

Glen Coe, Scotland.

The noteworthy paper of Clough, ]\Iaufe, and Bailey on " The
Cauldron-subsidence of Glen Coe," illustrates a case where part of a

^* W. O. Crosby, The Blue Hills Complex. Occasional Papers of the Bos-
ton Society of Natural History, 4, 385 (1900).

DALY. — THE NATURE OF VOLCANIC ACTION. 63

batholith's roof has sunk along peripheral faults. As the sinking pro-
gressed, the luagiua was squeezed up, following the faults on nearly
every side of the sunken area. If the faulting had progressed still
further, it seems inevitable that foundering would have occurred. In
fact, the authors give a synthetic diagram which imjtlies foundering on
an enormous scale, though in no instance is the sinking crust-block
shown as having extended to the earth's surface.**

Yellowstone Xational Pai-k.

The possibility that foundering has played a part in comparatively
recent vulcanism, first became clear to the writer on a journey in the
Yellowstone Park. (See Figure 8.) The great rhyolite plateiiu, the
largest known on the earth, is cut by canyons reaching 600 meters in
depth. The canyon- walls of the Madison and Bechler rivers show
that, for nearly or (juite this depth and for very great areas, the rhyo-
lite is massive and is not divisible into a number of distinct Hows, as is
characteristic of fissure eruptions and central eruptions. The rhyulite
extends downward, below the river-levels, to unknown depths. 2° Does
it merge, directly beneath, into the true granite of a batholith ?

Part I of the government survey Monograph is, unfortunately, not
yet published, and Part II states the field relations of the rhyolite in
too little detail that one can now assemble the facts bearing on this
problem. A few points may be noted to indicate the general need of
including foundering among the multiple hypotheses relative to the
mode of extrusion represented in the rhyolite plateau.

1. Few geologists will doubt that this lava is the effusive equivalent
of a salic granite. The enormous volume of the rhyolite implies a
plutonic feeder of batholithic proportions, especially if we grant that all
Tertiary granite (or rhyolite) is a direct or indirect product of assimi-
lation. The solution of enough of the jire-Cambrian terrane and of the
locally thin, overlying sediments to yield, after differentiation, these
thousands of cubic kilometers of rhy<jlite, could oidy tiike place in a
very large plutonic chamber. General and independent theory sug-
gests, therefore, that a portion of the Yellowstone Park area is under-
lain by a granite batholith, which, like the rhyolite, is of Pliocene age,
and is one of the youngest bathoHths on record.

2. The scale of the extrusion, \is topography, and topographic rela-

" C. T. Clough, H. B. Maufc, and E. B. Bailey, Quart. Joum. Geol. Soc,
66. f,70 '1000).

" J. I'. Iddinga, Monograj)!! 32, Tart 2, U. S. Gcul. Sur\-cy, 1899, pp. .'JW.
and 375.

64

PROCEEDINGS OF THE AMERICAN ACADEMY.

Figure 3. Sketch map of region embracing the Yellowstone Park (sho^sTi by-
rectangle on the 110th meridian); after Iddings. Small circles represent an-
desitic pyroclastics and flows of Eocene and Miocene age (central eruptions).
Horizontal lines (map in usual orientation) represent Pliocene rhj'olite of the
Park (eruption chiefly by foundering). Vertical lines represent the Pliocene
Snake River basalt (fissure eruption).

DALY. — THE NATURE OF VOLCANIC ACTION. G5

tions, and the relative insignificance of pjToclastic phases, are all
opposed to the view that the rhyolite issued from one or more vents of
the ordinary central-eruption kind. The unprecedented thickness of
the lava in a single, extended mass — more than G< )0 meters thick for
hundreds, if not thousands, of Sfjuare kilometers together — is tiuite
unparalleled in masses known to have been emitted during true hssure
eruption. Moreover, Iddings points out that rhyolite dikes (feeding
fissures) are almost entirely lacking in the Park. 21 The superposition
of distinct rhyolite flows in the regions surrounding the main rhyolite
body may be explained as due to successive outHows from the area of
foundering. Thus, so far as the facts of the field declare against the
central-eruption and fissure-eruption h^'potheses, they appear to favor
some other explanation. As yet the writer has conceived uo other
except that of foundering.

3. The geysers of the Park are practically confined to the area
covereil by the Pliocene rhyolite. In a similar way the other two great
geyser-fields of the world, in Iceland and New Zealand, are located in
regions where magma of liparitic (granitic) composition has been
poured out at the earth's surface. The " fossil " geysers, described
by Freeh in the Kremnitz district of Hungary, are confined to areas of
highly acid lavas.22 Following the general argument outlined above,
the liparitic lava in each of these four districts has been differentiated
from one or more relatively and absolutely large magma chambers,
i. e., in abyssal injections big enough to assimilate acid rocks in
notable amount.

According to Holmes, the Yellowstone geysers were in operation long
before the Pleistocene period and have been active ever since.^^ By an
ingenious method Schlundt and Moore have calculated that about
'2(),(H)() years have elapsed since the Glacial period in the Park. 2* This
figure agrees well with other recent estimates of post-Glacial time.
Twenty thousand years is clearly much less than the total tiuie during
which the geyser activity has been sustained in the Park. Competent
observers agree that the geyser waters are wholly or chiefly of meteoric
origin. The thermal energy required to superheat this cold water to
explosion-points during so many millenniums must be enormous.
Th(jugh the spring waters are radioactive, the heat set free by radio-
activity is not to be considered as of any direct importance in the

»» MonoKraph :}2, Part 2, U. S. Gcol. Survey, 1S*)9, p. 3S1.
" V. Freeh, .\u3 der Natur, Vol. 1, Heft S, lOO.').

»» W. H. Holmes, 12th Ann. Report, U. S. Geol. and Goor. Survey of the
Territories, Part 2, ls.s:{, p. 2i).

" H. Schlundt and II. B. Moore, IJull. 305, U. 8. Gcol. Survey, lOOl), p. 31.

VOL. XLVII. — 5

CG PROCEEDINGS OF THE AMERICAN ACADEMY.

problem. The thermal energy is clearly derived from magma. The
small amount of water ejected in the average geyser eruption, when
compared with the observed diameter of the geyser's throat below its
funnel, shows that the level of superheating is, on the average, not
more than a few hundred meters below the surface. The heat can
hardly be regarded as that residual from a Pliocene lava-flow even
600 meters thick. The specific heat of water is from three to five
times greater than that of rock-matter between the temperatures of
100°C. and 1000°C.

Allowing for radiation above and conduction below the lava flow ;
considering also that the rhyolite was erupted tens of thousands of
years ago, that the rhyolite is comparatively permeable for the chilling
rain-water, and that the visible abstraction of heat from the rhyolite
by the springs is continuous and rapid, — one must doubt the hypothe-
sis that the original heat of even such a thick flow can be responsible
for the present activity of the geysers. The hypothesis suffers, too,
from the difiiculty that it does not explain the high temperatures of
the Mammoth Springs. These emerge from a Mesozoic terrane which
lost its rhyolite cover (a sheet formed by lateral outflow from the main
area of extrusion) in pre-Glacial times. The same point may be urged
in the case of other hot springs, such as those in the bottom of the
Grand Canyon of the Yellowstone. At each of these localities the heat
is passing upwards through the relatively thin roof, composed of the
country-rock of the batholith.

It would, therefore, seem just to refer the geyser temperatures to
one or more great subterranean masses (batholiths) extending, nearly
or quite continuously, 120 kilometers from north to south and 30 to 50
kilometers from east to west. Heat will pass upward from such a
batholith either by simple conduction through the roof-rock or by
gaseous transfer. The analyses of the spring-waters suggest that some
magmatic gas has been added to the ascending meteoric water, which
may have attained its high temperature to a certain extent from the
hot gas.28 But this cause seems quantitatively insufficient to keep
the geysers working at their observed speed, and simple conduction
through the rock is more likely to be the essential cause.

In whichever way the heat is applied to the water, it seems clear
that the actual batholith must be at or near the surface in each geyser
area. The shallowness of the zone of superheating shows a very steep

2' The peculiarly intense alteration of the rhyolite is, in part, explicable
on the assumption that the magmatic gases (specially abundant in the upper
part of every batholith) have slowly passed out through the rhyolite shell
after that shell had solidified.

DALY. — THE NATURE OF VOLCANIC ACTION. 67

thermal gradient. That fact is inconsi.stent with the a-ssumption of a
thick roof over the granite batholith, and it must be remembered that
the batholith has been cooling for a length of time sulficient to permit
of the excavation of Goo-meter canyons in massive rhyolite.

A brief study of the geysers thus lends much probability to these *
conclusions . first, that over thousands of S(|uare kilometers, the batho-
lithic roof was e.xtremely thin when the rhyolite plateau was formed ;
and secondly, that this thin roof was, in places, swallowed up, Briefly
put, the rhyolite of the plateau is locally bottomless, in the sense that
it passes downward into a typical granite batholith. The formation
of the rhyolite plateau means a kind of vulcanism which evidently
needs to be distinguished from fissure eruption and from ordinary
crater eruption.

Central Eruptions.

The larger part of volcanic literature deals with the activities at cone
and crater. Extensive and intensive as these studies have been, the
number of memoirs treating of all the essential problems of central
eruptions is very small. Yet every general theory of volcanic action
must undergo the test of such a thorough questionnaire. This applies
to the hypothesis that all vulcanism is a result of the abyssal injection
of primary basalt. The following argument will be clearer if a prelim-
inary list of the specific problems relating to central eruptions be
reviewed. The list includes : —

1. The localization and opening of the vent.

2. The persistence of a principal vent for many thousands of years.
8. The intermittent character of the eruptivity, including (a) the

alternation of active and dormant phases, and {!>) the pulsatory or
gey.ser-like ([uality of eruption during the active stage.

4. The origin of the heat which, by radiation in active craters, is
lost in stupendous quantities.

.0. The normal evolution of a vent as illustrated in (ii) e.xplosiveness,
and (A) the nature of the lava emitted.

6. The mechanism of lava outflow at central vents.

These tests of our hypothesis will be briefly considered, nearly in the
order given.

Opening and Ijtx'alization of the Vent.

Evhirged fi!fmre.<<. — The events of 1 7H8 at the famous Laki fissure of
Icelaiul illustrate the close relation between some central eruptions and
the ])ronounced fracturing of the surface rocks of the earth. Kor much
or all of its length the master cra<'k was doubtless connected with atyp-
ical, narrow, abyssal injection. Many hills of the cone-and-crater type

68 PROCEEDINGS OF THE AMERICAN ACADEMY.

were built along the fissure, which emitted floods of basalt on the
greatest scale recorded by man. Escape of lava from the abyssal in-
jection was evidently much easier at some points along the visible fis-
sure than at others. The case is analogous to the formation of the
" Dewey craters " (cinder-cones) on the Mauna Loa lateral fissure
opened in 1899, and of scores of similar accumulations on the flanks of
Mauna Loa, Etna, etc. Dutton^^ gives this explanation for some of
the necks occurring in the well known Mount Taylor district of New
Mexico. In all such instances certain poitits in the fissure-lines are
favored in the eruptivity, while the remainder of each fissure was
either never opened clear to the surface, or else was rapidly sealed up
by congealing lava.

The continuance of eruption at any point depends on victory in the
strwjgle with cold. That victory in its turn depends in part on a suffi-
cient width of vent to permit of a column of lava which is not chilled too
greatly by conduction into the wall-rock. Since erupting fissures are
never more than a few meters in width at the surface, it seems neces-
sary to postulate a widening of each fissure where it carries cone and
crater of prolonged activity. The widening may be conceived to de-
pend on four different factors : solution and mechanical removal of
wall-rock by emanating lavas ; melting and explosive abrasion of the
wall-rock by magmatic gas emitted through the lava column. It is not
important here to decide on the relative efficiency of these processes in
merel}' enlarging the original fissure to full vent size. Their relative
efficiency becomes of fundamental significance in the problem of the
persistence of eruptivity at a central vent. In the following discussion
of this topic it is concluded that the vent is kept hot, and therefore
active, because of the emanation of free juvenile gas rising from great
depth — a process which may be styled "gas-fluxing." Since a great
enlargement of an original fissure, below the bottom of any possible ex-
plosion funnel, demands much time, it would follow that most of the
enlargement is due to gas-fluxing. Gaseous explosion and erosion of
the walls by emanating lava might be more eff'ective in the widening
of smaller and more short-lived vents.

It is an easy step from the observed case where central eruptions
are developed on fissures of lava-flooding, to the case of the formation
of central vents on surface fissures from which no true fissure-eruption
has ever taken place. Such a crack may be too narrow to permit the
extrusion of gas-free lava, which, through quick chilling, seals the fis-
sure, and yet the crack may be wide enough to allow passage of the

*• Sixth Annual Report of the United States Geological Survey, 1885,
p. 172.

DALY. — THE NATURE OF VOLCANIC ACTION. 69

juvenile gases from an underljnng abyssal injection. Entering the
crack under pressure and therefore at high temperature, these gases
must tend to enlarge it by slow fusion of the wall-rock. The pro-
cess may or may not be supplemented by the opening of an explosion
funnel at the surface. As the vent is enlarged by gas-flu.xing the
magma rises within it, and, kept tiuid by the emanating gas, permits of
further upward blowpiping.

This mechanism implies that the original surface fissure may not be
discernilile by the geologist. It may correspond to no vertical or hori-
zontal disi)lacement, and at the surface itself be no wider than an ordi-
nary master joint or fault fracture. Enlarging slowly downward, such
a fissure might be charged with accumulating gases so far as ultimately
to cause an explosion. Since the gases must tend to accumulate about
one or more points along the fissure, the explosion form will be that of
a vertical tube surmounted by a funnel. The resulting vent is a dia-
treme, the formation of which was so successfully imitated by Daubree.
This type of diatremes is, then, located on a surface fissure, which may
or may not be continuous with the abyssal fissure of the primary in-
jection. These considerations show the difiiculty of disproving the ex-
istence of through-going crustal fissures beneath central vents.

JJiiitremeK. — Daubree's experiments suggest, however, that some
volcanic diatremes may be formed in homogeneous, unfissured rock,
and a second type, a pure explosion form, should be recognized in a
full classification of vents,

A diatreme of either kind may be enlarged by the continued passage
of the blowpiping gases, by the mechanical erosion of the walls by out-
flowing lava, or by the piecemeal stoping of the walls by the lava
column.

Plutonic Cu]X)las. — Lastly, a complete genetic scheme should recog-
nize a process of vent-opening which is neither explosion, nor the enlarge-
ment of through-going fissures. Most of the greater abyssal injections
are strictly intrusive and do not occasion the outflow of magma at the
earth s surface. Those of batholithic size show, in the field, clear evi-
dence of having actually worked their way up the last few hundred
meters or last few kilometers, before the respective magmas have solid-
ified. The process is one of absorjjtion of the roof-rock, and is ckvirly
distinct from that of mere injection, either abyssal or satellitii*. Both
stoping and marginal assimilation are most rapid at the hottest parts
of the contact Itetween magma and country-rock. At the roof, the
juvenile gases tend to accumulate in any cupola-like irregularities in
the roof. These gases rise from the interior of the magma, i)erhaps
from great depth. Because of the pressure reigning even at the roof

70 PROCEEDINGS OF THE AMERICAN ACADEMY.

of the plutonic body, the gases must have high temperature, which
increases as the gas-tension increases. The total mass of the gas
accumulated at a cupola at any one time may be small, but it may
serve to determine a more rapid incorporation of the roof-rock at the
cupola than in the area of roof surrounding the cupola. It is obvious
also that some roof-rocks are more easily absorbed by a given magma
than are other rocks.

Figure 4. Ideal section showing formation of volcanic vent through the
differential rise of assimilating magma.

The rise of batholithic magma is, therefore, differential. Partly
because of gas control its attack on the roof is most efficient at points,
rather than along lines or in large areas. (Figure 4.) This deduction
seems well matched by the field fact that round intrusive bosses or
small stocks are characteristic cupola forms on large batholiths. Some
of these bosses have been proved to have very steep contact-surfaces
and, in shape, as in their cross-cutting relations, closely simulate vol-
canic necks. It is evident that every such cupola increases as well as
localizes the danger of true volcanic action. Blowpiping fusion or pure
explosion may destroy the relatively thin roof above the cupola. The
resulting vent is, then, of composite origin. Its upper part is like the
two simple types of central vents already described. Its lower part is
neither diatreme nor blowpiped hole, but represents the work of all the
agencies of magmatic assimilation in depth. This composite type of

DALY. — THE NATURE OF VOLCANIC ACTION. 71

vent illustrates the close connection between volcanic and plutonic
geology.

The original location of each first-rank vent is thus explained by the
roof- topography of the underlying magma chamber. Some one of the
cupola-like oll'shoots of the lluid magma, where it i)enetrates the solid
rock above, must become a place for the accumulation of the rising
gases. A vent once formed at the top of the cupola, it must tend to
persist as a vent throughout the period of magmatic tluidity. Other
vents from the same chamber may be opened, but must have shorter
lives, because of the drawing away of the juvenile gases toward the
more favored vent. (See Figure 7.)

Continuance of Acti city at Central Vents: Analysis
of Conditions at Kilauea.

Left to itself, the lava column of a vent must soon freeze and activ-
ity must cease. Long-continued activity is conditional on victory in
the struggle with cold. How is the victory attained ? How is the heat
of the underlying magma chamber transferred to the narrow vent?
Hawaiian vents supply data on this fundamental question. Though
Kilauea may be the vent of a satellitic injection (see p. 109), the mech-
anism is doubtless the same as for a vent over a main abyssal injection.

Rate of Ihut-hi^.'i through Conduction into the IValls. — It is possible
to obtain a rough idea of the enormous rate at which heat is given out,
by conduction and radiation, at Kilauea. (Plate L) Actual calcula-
tion will show that radiation is much more responsible for the loss of
heat than is conduction into the wall-rocks of the vent. To make this
point clear it will be assumed that the cross-section of the conduit is
throughout as large as the area of the lava lake, though very probably
the lake represents a strongly flaring part of the lava column. (See
Figure 6.) The conditions of the lake in 190'.), when it was studied
by the writer, are assumed. The area of the lake (and therewith the
cross-section of the lava column) is considered as circular, with radius
of loo meters. This is more than the superficial extent of the lake in
1909 but less than its average extent since 1.S20. The cylindrical pipe
with the uniform cross-section is assumed to extend to a depth of two
kilometers, where it opens out into the great feeding chamber.

Let the temperature of the magma be assumed as 1200° C. ; and
let the average original temperature of the rocks now forming the
conduit walls be assumed as 40''C. Two hundred and fifty years after
the conduit was first opened and henceforth occupied by lava at the
uniform temperature of 1200°C., the rate of flow of heat through the
wails would be nearly uniform; and 12 meters from the contact of

72 PROCEEDINGS OF THE AMERICAN ACADEMY.

the molten lava the temperature of the wall-rock would be about
1115° C.27 This estimate is based on the assumption that the dif-
fusivity for heat in rock at high temperature has the value given by
Kelvin. That value is certainly too high, but the temperature stated
for a point 12 meters from the contact would in any case be reached
after some centuries following the establishment of the lava column.
An idea of the heat loss by conduction may now be obtained. The
equation for heat flow is :

q = kA- — -^-t,

X

where k is the coefficient of conductivity, A the area of the surface
traversed, a- the thickness of the plate traversed, t the time, T and Ti
the steady temperatures of the two sides of the plate. In this case we
may use C. G. S. units, with k 0.005 (certainly too high a value for
these temperatures), t one second, x 1200, and J. 2 7rr X 200,000. We
have

q = .005 X 2 X 3.14+ X 10,000 X 200,000 X ^^^^~ |^^^ x 1
= approximately 4,450,000 gram calories.

The result expresses the approximate amount of heat lost by con-
duction into the wall-rock during each second.

Hate of Heat Loss through Radiation at the Crater. — Siegl has
recently supplied a datum required for estimating the heat lost by
radiation from the surface of the lava lake. The general equation is

log >Sf = log c-f clog r,

in which S represents the number of calories radiated per second, T is
the absolute temperature stated in degrees centigrade, and c and e are
constants. For basalt Siegl has found that c = (10)"^^ X 0.589, and
c z= 4.083.28 His experiments show that the equation holds for basalt
up to 472° absolute. It is very probable that it may be applied, with
relatively small, or at least non-significant, error, to basalt at the higher
temperatures and under the conditions of radiation represented at
Kilauea. Such extrapolation gives the following results :

27 R. A. Daly, Amor. Jour. Science, 26, 23 (1908).

*^ K. Siegl, Sitzungsber. Akad. Wissen. Wien, Math.-Naturw. Klasse, Bd.
116, 1203 (1907).

DALY.

— THE

NATURE OF

VOLCANIC

ACTION,

fC.

T° abs.

S.

450

723

0.277

727

10(K)

1.044

1000

1273

2..S()()

1200

1473

5.082

73

In 1909 the present writer used a Ft^ry pjTometer to determine the
average temperature of the non-incandescent scum which regularly
covered at lea.st two thirds of the lava lake. The average temperature
for this part was estimated to be about 450° C. ; the corresponding heat
loss is computed to be 0.277 cal. per square centimeter per .second.

At the best points of observation in 1909, the area of the hottest
lava was not large enough to cover the " black spot " of the pyrometer
for a time long enough to give a reading for its full temperature. It
was clear, however, from the behavior of the galvanometer needle dur-
ing the brief exposures of the very hot lava in the "Old Faithful
fountains," that its temperature was well above lOOO" (J. Froui the
color the temperature of the hottest lava visible in the lake was esti-
mated to be somewhat over 1200° C. The third of the lake relatively
free from scum was estimated to have an average temperature of
1000° C, corresponding to a heat loss of 2.8 calories per square centi-
meter per second.

With radius of 100 meters the circular lake would lose in heat about
375,000,000 calories per second. The actual lake of 1909 probably
lo.st more than 230,000,000 calories per second.

We may conclude that heat was then being lost by radiation more
than fifty times faster than by conduction into the walls of the
Kilauean pipe, if it be assumed as two kilometers deep. It would .seem
that radiation at the crater must be the dominant one of these two
phases of heat loss in any strongly active volcano.

Mi'thoih of Ilmt Tnin^jh: — ^The upward transfer of lu'at into a
volcanic j)ipe might conceivably take place in five dilferent ways :
(1) by explosive removal of nuiterial from the ui)per part of the vent,
followed by ni)rise of magma from the still Huid chamber; (2) by sim-
ple overflow of magma at the lip of the crater ; (3) by thermal convec-
tion in the lava column ; (4) by a process which may be called, for
convenience, "two-pha.se convection " ; and (5) by the jiassago of free
juvenile ga.s throiKjh the lava column, thus bringing al»yssal heat to
the upper j)art of the vent.

The first and .second proce.s.ses have obviously played no essential
nMes in keeping up the heat supply in Kilauca siuco 1823, when do-
tailed records of its activity began.

74 PROCEEDINGS OF THE AMERICAN ACADEMY.

Mere thermal convection can hardly be regarded as an essential
factor in postponing the solidification of a lava column. In this
matter the analogy with water heated from below should be applied
only with due attention to quantitative values. The degree of super-
heat in the actual well-established vents is not indefinitely high ; it is
doubtless no more than 200° or 300^ C. If convection be lively enough
to keep the column molten, the maximum thermal-density differences
within the vent itself should certainly be less than those corresponding
to a difference of 100°. A temperature change of 100° C. means a
density change in magma of less than one half of one per cent.^s The
density change in water as it passes from 4° C. to 100° C, or vice
versa, is about 4.3 per cent. With a density difference about one
tenth that of water in the same temperature interval, and with that
difference distributed through kilometers of depth instead of through
decimeters, as in the ordinary convective experiment with water, the
convective potential in the lava column is evidently of a very low order.
Moreover, the speed of the convection depends on the viscosity of the
magma, which through chilling and through pressure is doubtless, on
the average, hundreds or thousands of times more viscous than water.
It follows that in resistance to be overcome, as in working potential,
heat convection must be incomparably less rapid in a volcanic conduit
than in artificially heated water.

For example, let us suppose that at the depth of two kilometers the
conduit passes into the feeding magma chamber ; that there the tem-
perature is 1300° C, while the temperature at the surface is 1200° C, ;
that the average kinetic viscosity of the conduit lava is as low as that
of a liquid 100 times more viscous than water ; that the thermal con-
vection in the conduit is to be compared in rapidity with that obtain-
ing in water heated from 4° to 100° in a wide tube one meter high.
The maximum convective gradient for the water system may be ex-
pressed as

4.3 (per cent expansion) _ , q

1 (meter, thickness)
The gradient in the lava column is approximately
0.5 (per cent expansion) _ ^^^j,.
2000 (meters)

The maximum speed of convection in the water of the imagined ex-

/ 43 \

periment is, then, I - X 100= 11,720,000 or more times greater

y^.UOU^O J

than that of the lava in the conduit.

" According to Barus, as quoted in Amer. Jour. Science, 26, 26 (1908).

DALY. — THE NATURE OF VOLCANIC ACTION'. 4 O

It seems certain that such slow transfer of magma could not keep
the temperature of surface lava of the lake at anything like the ob-
served point. On the average, every square centimeter of the lake's
surface in 1009 radiated about one calory i)cr second or 86 400 cala.

?~e e r j-oo

FiorRE 5. Sketch map (after J. M. LydRate) of Halemaumau in July,
1909. .\rrow3 indicatf the general trend of currents in tlie lava lake during
that month. The i>ositii>n.s of "Old Faithful" and of the more important
caves eroded by the licpiid lava in the "Black Ledge" are shown. Tigurea
Bhow depths below the " Rest House."

per day. Taking .35 as the mean specific heat of basalt (1200°-1 300°),
this implies a daily heat loss corresponding to a temperature fall of
loO°C. in a vertical column of lava more than 2400 meters deep, and
one square centimeter in area at its upper surface. Evidently, other
and much more effective agencies must be at work to keep Kilauea
active, year in and year out.

76 PROCEEDINGS OF THE AMERICAN ACADEMY.

Trro-phase Convection. — However, there is a different and very
powerful kind of convection constantly illustrated in Halemaumau
when that lake is in full activity. (Figure 5.) The persistent stream-
ing of the lava into the caves, characteristically developed at the shore
cliffs of the lake, is evidently due to surface gradients. In general,
the "scum " stands higher in the central part of the lake than it does
in the caves and in the channels leading to the caves. The " scum "
or thin crust of the lake prevents or retards the escape of the mag-
matic gases, which accumulate beneath it and form a kind of froth, or
emulsion of lava and gas, of relatively low density. The tendency is,
thus, to raise the crust in one or more areas. In each cave, because of
reflection from its roof, and perhaps also because of special heating
through actual combustion of sulphur, hydrogen, and other gases, the
crust is rapidly and completely fused. The escape of the gases is
there facilitated and the surface of the lava is correspondingly lowered.
The surface slopes are, therefore, steepest in the channels leading to
the caves, and streaming at the rate of two to five kilometers an hour
may be observed in the channels. Elsewhere the surface slopes are
lower and streaming is less rapid. The caves are not outletting tun-
nels, as so often stated, but each is closed at a distance of a few meters
from its entrance. The lava which has streamed into the cave must
return to the main part of the lake. Only one way of return is possi-
ble, that by a backward sub-surface current. Having lost its dilating
gas and grown rapidly denser, the heavy lava sinks and flows toward
the center of the lake. Similarly, the ever-changing surface slopes in
other parts of the lake compel vertical currents and vortices of the
most complex design. (Figure 6.) This type of magmatic movement
may be called " two-phase convection." ^o It depends on the presence
of a liquid " phase " and a gas " phase " in the lava.

If vesiculation of the liquid magma is possible in great depth, two-
phase convection may cause a relatively speedy transfer of hot magma
to the surface. How effective this process can be is worthy of some-
what detailed statement. The imposing change in magmatic density,
which is effected by very slight increase in vesiculation, will first be
indicated. The speed at which individual bubbles rise will then be
estimated, and, finally, a rough quantitative idea of the convection
enforced by the development of gas bubbles in depth will be obtained.

The specimens of Hawaiian pahoehoe lava collected by the writer

'° The term "two-phase," so convenient in describing this type of convec-
tion, was suggested to the writer by Dr. W. C. Bray, of the Massachusetts
Institute of Technology.

DALY,

THE NATURE OF VOLCANIC ACTION.

i t

contain, on the average, at least 200 vesicles per cubic centimeter of
the lava. The vesicles of the surface layers are roughly spherical and
average no more than 2 mm. in diameter, though, of course, the range
of diameters is very great. For convenience, let a spherical mass of
hydrogen, having the radius of 1 mm. at one atmosphere of pressure
and at 1200° C, be called the "standard bubble " for basalt. Extra-
polating on Amagat's pressure-volume curves for hydrogen at 1200'^C.,

S/acA

FiOTRE 6. Diagrammatic section of Halemaumau, illustrating two-phase
convection, erosion of caves, and vortical action. The lava " scum " is ropre-
senterl by the heavy black line at the lake surface. Length of section about
300 meters. Vertical scale specially exaggerated in drawing the " scum "
line.

the volumes and radii for the standard bubble at high pressures may
be calculated within a margin of error which is probably very small.
Examples are shown in the following table :

Ar'proximato depths in rnag-
niatic column (inetcra).

PrcMure in
atmospheres.

Volume
(cra.»).

Radius
(cm.).

730

200

0.00011')

0.030

3r,.oo

1000

.000025

.018

7300

2000

.000014

.015

Gas-free ba.salt at r200°C. and one atmosphere has a specific gravity
of about 2.75. On account of the slight compressibility of rock-matter,
that value may be assumed as typical for gas-free basaltic magma at
I)res.snres up to several thousand atmos])heres. If such magma become
charged with 200 standard bubbles per cubic centimeter, at 200,
loon, and 2000 atmospheres, the specific gravity falls to the following
approximate values (Col. 1) :

78 PROCEEDINGS OF THE AMERICAN ACADEMY.

Pressure. Specific Gravity.

1. 2.

200 2.688 2.7495

1000 2.736 2.74975

2000 2.742 2-74997

A single standard bubble replacing the liquid in each cubic centi-
meter of gas-free basalt would lower the specific gravity to the amounts
shown, again approximately, in Col. 2.

This last table illustrates possible ranges of buoyancies induced by
vesiculation at the three depths chosen. The actual buoyancy attained
may often be much higher. It will be seen that the buoyancy pro-
duced by only a small extra vesiculation of a local mass of magma
must occasion a rapid uprise of that mass.

The bubbles themselves, as independent bodies, must rise with com-
parative slowness. The experiments of H. S. Allen have shown that
small spherical bubbles, rising in a liquid, attain their terminal velo-
city according to the formula previously deduced by Stokes for the
rise of light solid spheres of very small radius. ^^

Let r represent the radius of a bubble ; d' , its density ; d, the density
of the surrounding magma ; v, the coefficient of viscosity of the magma ;
g, the acceleration of gravity ; and x, the terminal velocity of the rising
bubble, that is, the velocity when the motion is steady. The Stokes
formula applies if the product dxr is small compared with v. This is
clearly true for the standard bubble in liquid basalt with the viscosi-
ties appropriate to pressures of 200 to 2000 atmospheres. We have, then,

o 2/^^ -A

Computing the values of x when the magmatic viscosity is assumed
to be constant and only 100 times that of water at 15° C. (0.0115) or
1.15 in C. G. S. units, we have, at the three illustrative pressures :

Depth
(meters).

Pressure
(ats.).

Terminal Velocity (x).
Cm. per Second. Meters per Hour.

730

200

0.47 16.9

3650

1000

.17 6.1

7300

2000

.12 4.2

31 H. S. Allen, Phil. ]\Iag., 50, 323 and 519 (1900). G. G. Stokes, Cam-
bridge Phil. Trans., 9 (2), 8 (1850).

DALY. — THE NATURE OF VOLCANIC ACTION. tV

Since experiment shows that the viscosity of a liquid rises rapidly
with pressure, it is instructive to assume higher values of v for the
greater pressures. If v be taken again arbitrarily as 500 and 10,000
times that of water for magma under the pressures of 1000 atmospheres
and 2000 atmospheres, respectively, we have for x these values :

Pressure vianr^aifu- ' Terminal Velocity (i) .

(ats.). viscosiiy. Cm. per Second. Meters per Hour.

200 1.15 0.47 16.9

1000 5.75 .034 1.2

2000 115.00 .0012 .04

In all cases smaller bubbles would rise more slowly, x varying
directly as the sc^uare of the radius.

Two important conclusions may be drawn from these computations.
Gas bubbles of the " standard " mass or of smaller mass must rise from
the deeper levels of an abyssal injection with extreme slowness. In
view of the high magmatic viscosity and great pressure in depth, it is
conceivable that it may take thousands of years for a " standard "
bubble to rise from a depth of, say, ten kilometers to the earth's
surface. This suggests one reason why gaseous emanation is so pro-
longed at central vents.

Secondly, from the slowness with which bubbles rise, it is clear that
a swarm of bubbles, which for any reason have been aggregated locally
in .'special abundance, would be dispersed into the surrounding, less
vesiculated magma with great slowness. The local mass of magma
thus specially vesiculated would be less dense than the average magma
and, as a unit, would rise toward the crater. It now remains to indicate
that a very moderate amount of extra vesiculation must cause such a
two-phase mass to rise with comparatively great velocity.

Of course, this case has not been investigated experiment^illy ; an
indirect method must be used in its discussion and the result can at
present hardly be other than (jualitative.

( )nce again to make the mental picture clearer, it is well to assume
certain conditions arbitrarily. As an example, let the swarm-tilled
mass be spherical ; let the reigning pressures and nuigniatic viscosity bo
as in the foregoing cases ; let the surrounding magma have a density of
2.75 ; and let the extra vesiculation be to the extent of 50 " stundurd "
bubbles per cubic centimeter on the average. The corresponding den-
sities of the sphere are .shown in the second column of the following
table :

80 PROCEEDINGS OF THE AMERICAN ACADEMY.

Pressure (ats.).

Sp. Gr.

d-d'.

V (assumed).

R (cm.),

200

2.734

0.016

1.15

0.52

1000

2.746

.004

5.75

2.40

2000

2.748

.002

115.00

22.25

For solid spheres rising in the magma we may compute the " critical
radius " (/{), that is, the radius of the largest sphere which would obey
the law of the Stokes formula. The values for I?, as stated in the fifth
column, have been found with the help of Allen's formula : ^^

9 v^

2 gd (d - d')'

The terminal velocities of the solid spheres having the critical radii
would be, for the corresponding values of R, v, and (d — d'), as follows :

d-d'.

r.

R (cm.).

Terminal Velocity.
Cm. per Sec. Meters per Hour,

0.016

1.15

0.52

0.82 29.5

0 004

5.75

2.40

.87 31.4

0.002

115.00

22.25

1.88 67.6

The figures show that even for small solid spheres the velocities are
considerable. With increase of radius the terminal velocities would at
first increase very fast, and then more slowly. However, since the
resistance to the motion would, for large spheres, vary with the square
of the velocity, neither the Stokes formula nor any other yet developed
can declare the actual velocity for large solid spheres moving in the
magma.

Nevertheless, Allen's formula for large spheres is of distinct help in
guiding one to a proper appreciation of the case. It reads :

,,„ 1 4 7r d — d

^ =k-s-^"-d-^

where ^ is a constant for a given liquid-solid system. ^^ Jt follows that
the terminal velocity here varies directly as the square root of the
radius and as the square root of the difference of the two densities.
Referring to the table showing terminal velocities for solid spheres with
critical radii, it seems clear that, in any of the three cases, spheres of

M H. S. Allen, Phi). Mag., 60, 324 (1900).
33 H. S. Allen, Phil. Mag., 50, 532 (1900).

DALY. — THE NATURE OF VOLCANIC ACTION. 81

corresponding density and of radii of 10 or more meters would rise at
the rate of at least 10 centimeters per second or 3G0 meters per hour.

This analogy of solid spheres seems to afford some help in our
imagining the course of a specially vesiculated mass of lic^uid magma.
The rough quantitative estimate just made for large solid spheres can-
not be directly applied to this case. On account of the possibility of
internal movements in the rising mass of liquid magma, its speed of
uprise will not be quite the same as that of a solid mass of the same
shape, size, and density. Yet the correction to be applied is probably
small.

As such a mass approaches the surface, through a column of rapidly
decreasing viscosity and with a constant increase of buoyancy because of
expansion of the contained bubbles, the velocity must greatly increase.
However much a given mass of magma might lose buoyancy through
the loss of its larger, more swiftly rising bubbles, the total effect must
be to generate a powerful upward current in the magmatic column.

In spite of the lack uf the necessary, full experimental data, our
general conclusion seems to be as follows. Experiment does show that
the rise of individual gas bubbles in magma will be very slow. ?seither
experiment nor theory can as yet declare the actual speed of the rise
of a ma.ss of specially vesiculated magma, but the analogy of solid
spheres moving under gravity in a liquid enforces the belief that the
more buoyant magma will move rapidly if its volume is of the order of
thou.sands of cubic meters. A.ssuming such differential vesiculation in
great depth, and assuming also a mechanism by which the gas of risen
magma is dissipated (as in a volcanic vent), two-phase convection
must stir the magma column to great depth and with considerable
rapidity. Such a process must be incomj)arably more rapid than that
of thermal convection under volcanic conditions. The transfer of heat
may readily be conceived as able to supply the radiation loss in the
crater for long periods of time.

The basal assumption, that vesiculation occurs at great depth in a
volcanic conduit, is necessarily ditlicult to test by the facts of liold geol-
ogy. During its solidification an intrusive body is likely to be cleansed of
its bubbles, "which ri.se, and the gas so collected at the roof is .slowly di.s-
sipated into the country-rock. This may be the explanation of the lack
of vesiculation in most dikes, sheets, laccoliths, and V)atholiths. In gen-
eral, the rock of a lava neck maybe similarly freed from bublilcs during
the relatively long period of crystallization. Nevertheless, ca.ses are
not wanting where bubbles are known to have been tra])])i'd in basalt at
depths greater than 300 meters. The basalt of the West Maui neck,
illustrated in Figure 10, is charged with many minute vesicles at a

VOL. XLVII. — 6

82 PROCEEDINGS OF THE AMERICAN ACADEMY.

depth at least 300 meters below the original top of this lava column.
Ransome (in Bulletin 303 of the United States Geological Survey,
1907, p. 68) states that the bottom of a single 320-raeter flow of basalt
at Eldorado Canyon, Nevada, is vesicular. These and other known
examples seem to strengthen the belief that bubbles may form in
magma at the depth of several kilometers.

It is important to note that two-phase convection has two distinct,
though related causes. Principal stress has hitherto been laid on dif-
ferential vesiculation in depth, whereby a mass of magma becomes more
buoyant than the enclosing magma and rises. Just as inevitably, the
magma which is freed of gas at the crater, must sink and stir the
column to great depth. Even if the column is not vesiculated at all,
this second mode of convection is likely to be effective in the vertical
transfer of the magma. As a rule, the density of a liquid is lowered by
the absorption of hydrogen, nitrogen, oxygen, or other relatively light
gas. This is very probably true of natural mixtures of juvenile gases
when dissolved in magma. As these gases stream or diffuse from all
azimuths in the feeding chamber toward the base of the narrow con-
duit, they are there concentrated. Thus, the magma in the conduit, at
its lower levels, attains a density less than that of the average magma
of the feeding chamber, and, a fortiori, less than that of the gas-freed
magma descending from the crater level. This is another kind of den-
sity convection depending on the relative concentration of juvenile gas.
For lack of experimental data, it is now impossible to estimate the
efficiency of this species of convection. It may be a powerful ally of
two-phase convection proper. For example, it is conceivable that the
upward movement of magma is begun in the conduit because of the
concentration of gas in solution and not in bubble phase. Then, as
the magma rises to levels of smaller pressure, the gas begins to separate
out in bubbles and enforces true two-phase convection of ever-increas-
ing speed. In view of these various modes of gas-control, the vertical
stirring of the magma column may, perhaps, be more safely described
as, in general, a gas-concentration convection. Yet, the actually ob-
served fact is that, at the crater, the gaseous phase does separate, in
bubble form, from the liquid phase, and the writer has preferred
to emphasize this empirical fact in adopting the name "two-phase
convection."

Lava Fountains. — Herein the writer believes that we have an essen-
tial part of the explanation of " Old Faithful," the site of the greater
periodic "fountains " of Kilauea. (Plate II. B.) That circular area,
about twenty meters in 1909, has represented the true axis of the lava
column for many years, and seems to have been the main source of

DALY. — THE NATURE OF VOLCANIC ACTION. S3

magmatic heat throughout the known history of Kilauea. In 1909, at
average intervals of about thirty-hve seconds, the surface of the lava
lake in this area was domed up to maximum heights of a few meters.
These fountains are not due to the rise and explosion of great gas
bubbles, the collapse of which could have been readily observed. No
appreciable amount of gas or va{)or was given off at the moment of
doming or immediately afterwards. The outbursts are best explained,
in part, on the principle illustrated in the upspringing of a log of light
wood freed at the bottom of a lake. Through its momentum the log
may jump clear out of the lake. In i)art, the outbursts of " Old Faith-
ful " are due to true explosive dilation of the gas bubbles in the "log."
The latter process is doubtless the chief cause of the smaller " foun-
tains " playing over the surface of Ilalemaumau, and of those which
played over the surface of Dana Lake or New Lake twenty-five years
ago. The draining of each of these two lakes has shown that it was
saucer-shaped and very shallow over most of its area, and the writer
believes this is true of Ilalemaumau to-day. (Compare Plate III.)
The depth is generally much too small to allow of such momentum
in magmatic " logs " that they might leap to the heights actually
observed.

The site of "Old Faithful" is, thus, the place where the juvenile
gases rise from the depths in two-phase mixture with liquid lava.
With the collapse of each dome, the gas-charged magma finds its level
and runs under the semi-solid or solid " scum " on the lake surface.
(Figure Ct.) There the gas is slowly freed and accumulates beneath
the "scum " until the tension produces a true explosion, that is, one
of the many smaller " fountiiins " so constantly appearing on the lake.

The incessant streaming in Ilalemaumau, the nature of the " Old
Faithful fountains," and the ceaseless vortical motion in the lake, as
well as the similar phenomena in the active Mokuaweoweo, are so
many direct evidences of two-])hase convection, which calculation shows
must be rajiid, j)rovided slight variations in vesicularity occur in tiie
depths of the lava column. Though it is not possible to prove abso-
lutely that the Kilauean column is vesiculated in depth, itcertiiinlyisso
at the surface to a remarkable degree. At many jxiints, the lower j)art
of the wall of Halcniaiiinau was found, in 1!MI9, to be covered with
thin ctjatings of black glass which represented splashes of lava from
the adjacent lake. This lava almost instantly " froze " to the wall.
In every ca.se it was extremely porous, so as to be (piite spongy in
appearance. The vesiculation was almost if Jiot (piito complete be-
fore the " sjila-sh " struck thn wall, and it is sini))lest to supi)ose that
the surface lava of the lake is a froth. There is no known reason why

84 PROCEEDINGS OF THE AMERICAN ACADEMY.

vesicalation should be the rule at one atmosphere of pressure and non-
existent at one hundred or one thousand atmospheres ; it is all a ques-
tion of the degree of saturation with gas. The two-phase convection
hypothesis rests on this unproved assumption, but its merit is great, as
it explains the essential facts of circulation in Halemaumau. The hy-
pothesis also explains the periodicity of " Old Faithful." Throughout
the years 1908 and 1909 its geyser-like uprush occurred, on the
average, once every 35 seconds or thereabouts. This pulsatory effect
is expected as a result of the mechanism of two-phase convection.

Cooling by Rising Juvenile Gas. — As a fifth hypothesis it might be
conceived that the heat is kept up in the lake through the rise of
bubbles oi free juvenile gas from the magma chamber, the bubbles
arriving at the surface with some excess of temperature above that re-
quired to give the lava of the lake its observed fluidity. But the
feeble explosiveness of the emanating gas at Kilauea shows that any
unit mass of it, arriving at the surface, is already nearly expanded to the
volume appropriate to one atmosphere of pressure, and therefore that
the gas is in nearly perfect thermal equilibrium with the enclosing lava
at the surface. Such bubbles, as they rise and expand, must thereby
tend to cool the magma.

The cooling effect is very great, as may be shown by the following
calculation. In an adiabatic expansion of a perfect gas: let T' be the
initial absolute temperature, and T the final absolute temperature ; let
p be the initial pressure, and }) the final pressure; and let y{= 1.4)
be the ratio of the specific heat of the gas at constant pressure to its
specific heat at constant volume. Then

r _ (py-^

T ~\p] '

At about 37 meters below the lake surface the pressure is 10 atmos-
pheres. If the bubble, after expanding adiabatieally, is to arrive at
the surface at a temperature of 1200°C., it must have at the depth of
37 meters a temperature of about 3700°C. (assuming no dissociation of
the gas). Evidently the free-moving gases have a cooling effect on
the upper part of the lava column. That this effect is actually small
is, of course, due to the small mass of gas emitted in a unit of time and
to the fact that y is much less than 1.4 for the actual (not "perfect ")
gases while rising through the deeper levels. IMoreover, it has been
noted that the rise of a bubble must be exceedingly slow if its mass is
anything like that in the average vesicle of frozen lava. So slow is
the transfer that the rapid heat wastage at Halemaumau cannot pos-
sibly be compensated by any residual superheat in the emanating gas.

DALY. — THE XATURE OF VOLCANIC ACTION'. 85

On the other hand, the thermal conditions are different in craters
floored with highly viscous lava. There the emanating ga.ses com-
monly issue at pressures of more than one atmosphere, and they are
thus kept hot and endowed with some fluxing power. The small blow-
holes in Kilauea, as in most other basaltic districts, have long been
kept open through this action. It is quite possible that such hot-
blasting is operative on a greater scale in larger openings like the crater
of Stromboli. Yet even at Stromboli that cannot be the chief method
of heat transfer from the depths, and again no other method than that
of two-phase convection seems competent to keep the lower and greater
part of the lava column fluid. At Kilauea, at the wonderful Mokua-
weoweo (the vent of a main abyssal injection), at Matavanu in Savaii,
we seem compelled to exclude all other agencies for heat transfer except
this type of convection. The same explanation seems to apply also to
Vesuvius and Stromboli, for their craters in times of strong activity
have been observed at close quarters and, like Halemaumau, they show
lava " fountains " and other features of this convection.

The Volcanic Furnace. — So far, no assumption has been made
that the hejTt transferred to the top of the volcanic conduit is other than
primary in origin, that is, heat due to the initial temperature of the
parent abyssal injection. Such is the orthodox view of volcanic heat.
The rough estimate made in the discussion of thermal convection sug-
gests the difficulty of understanding how the mere primary heat suf-
fices to explain the long life of many volcanoes.

It may well be questioned, however, that all the heat at a volcanic
vent is primary.^* That due to the radioactivity of magma during
the fluid stage of an abyssal injection is too small in amount to afiect
the rate of heat loss to any sensible degree. More promising is the
idea that heat-producing chemical reactions in the conduit may have
powerful effect. Since the day when Sir Humphry Davy renounced
his own explanation of magmatic heat as due to the oxidation of alka-
line metals contacting with water, most volcanic theories have regarded
magma as inert so far as exothermic reactions are concerned. On the
other hand, recent studies of gaseous emanations from active volcanoes
and from artificially heated rocks and meteorites clearly suggest the
po.ssibility of such reactions.

Analysis of any i)erfectly fresh igneous rock shows the presence of
water to a considerable i)ercentage by weight. This is true of in-
trusive gabbros and diabase as well as of ba.saltic lavas. Must of

" Cf. G. Tschcmiak, SitzunRsbcr. .\kjul. WisM. Wicn, 76. ltJ2 (1.S77), where
a brief statcracut is given, showiug u dear uuticipatiuu uf this hypothesis.

86 PROCEEDINGS OF THE AMERICAN ACADEMY.

the non-hygroscopic water determined in the analysis of quite unal-
tered gabbro or basalt may be as much a primary constituent as the
silica or the alumina. We must believe that hydrogen and oxygen, in
the proportion characteristic of water, are present in primary basaltic
magma. It does not follow that, under volcanic conditions, these ele-
ments will issue from the vent in combination as water. In his able
monograph on " The Gases in Rocks," R. T. Chamberlin indicates the
general reaction to be expected in the Kilauean or other basaltic magma
chamber. He writes :

" The effect of pressure on chemical equilibrium is to favor the for-
mation of that system which occupies the smaller volume, but if there
is no change in volume, in passing from one system to the other, the
increase of pressure presumably has no influence on equilibrium. In
the reaction

3FeO -f H2O ^ FesOi + H2

considered as a thermochemical equation, the number of gaseous mole-
cules, and hence the volume of gas, always remains the same, so that it
is not likely that this action will be influenced by change -of pressure.
A rise of temperature favors the formation of that system which ab-
sorbs heat when it is formed. A comparison of the amount of heat
liberated by oxidizing three molecules of FeO to Fe304 and one mole-
cule of Ha to H2O shows that, in the former case, 73,700 calories are
evolved, and in the latter, 58,300 ; that is, 3Fe() + H2O — >- FcsOi +
H2 + 15,400 calories. As heat is evolved in this process, a rise of
temperature would accelerate the reaction in this direction less than in
the reverse. In other words, the higher the temperature, the more
would the formation of ferrous oxide and water be favored as compared
with the conditions at lower temperatures.

"Because of this, there is much reason to suppose that, at the
depths where lavas originate, hydrogen and oxygen exist combined as
water, since up to temperatures of 2000° C, the dissociation of water
takes place only to a limited extent. If a state of equilibrium between
hydrogen, water, and the iron compounds were established in the
heated interior where a magma originated, as soon as it commenced its
way upward and began to lose heat the condition of equilibrium
would be destroyed. With the falling temperature the tendency to re-
establish equilibrium would favor the formation of that system which
was produced with the liberation of heat, i. e., magnetic oxide and free
hydrogen. In ascending lavas which are losing heat, the tendency,
therefore, is to produce hydrogen and magnetite, or ferroso-ferric com-
pounds. This is doubtless an important source for the hydrogen which

DALY. — THE NATL'RE OF VOLCAXIC ACTIOX.

87

is so copiously exhaled during a volcanic eruption. At the same time
this process aocnunts for the widespread occurrence of magnetite in
igneous rocks." '*

The abundant animal life of Cambrian and later time implies that
the earth's atmosphere has long had a very low cuntent of carlxtn diu-x-
ide. The amount of this o.xitle which has been locked up in the car-
bonate rocks since the beginning of the Cambrian period is so enormous

Figure 7. Ideal longitudinal section of an abyssal injection, showing the
relation of vulcanism to the secular rise (arrow.s) of juvenile gas. The middle
vent is artive because it originates at the highest point (cupola) in the in-
jected body. The other vents are extinct because of this advantage of the
middle vent. Solid black represents the already crystallized material of the
injection. Cross-lined area is the countr>'-rock. Length of section about 100
kilometers.

that mo.st of it, or all of it, mu.st be considered as of juvenile origin.
Yet more clearly than in the case of water, carbon dioxide must be
regarded as a ])rimary constituent of earth magma. Under the same
conditions as those described by Chamberlin, ferrous iron is oxidized to
magnetite by carbon dioxide, yielding carbon monoxide and G<H)(> cal-
ories ])er gram molecule.

The list of the juvenile gases and vapors also includes nitrogen,
chlorine, sulphur, and hyilrocarbon.s. These and other volatile sub-

" n. T. Chamberlin, The r,a.ses in Rocks, Publication No. IOC), Carnegie
Institution of Wiushington, 1908, p. 00.

88

PROCEEDINGS OF THE AMERICAN ACADEMY.

stances, including hydrogen and carbon monoxide, stream from all
azimuths in the magma chamber to the lower end of the conduit. The

pipe has always a very much
smaller cross-section than the feed-
ing chamber, implying some con-
centration of the volatile matter.
(Figures 7 and 8.) At conduit
temperatures this ever-varying
mixture of gases must, according
to practically infinite probability,
be in unstable chemical equililib-
rium ; under the conditions new
equilibria are attained with the
evolution of heat.

The relative proportions of each
gas must, in general, be different
from that in the primary magma
before it was injected. Concentra-
tion of the gases means, according
S U B 3 T R AT U M ^^ ^^® ^^^^ ^^ mass-action, the de-

Figures. Ideal cross-section through velopment of new compounds. As
middle cone shown in Figure 7, to same *^^® pressure is less m the conduit
scale. than in the underlying chamber,

the viscosity of the magma is less,
the gas bubbles are larger, and the speed of possible reactions is thereby
increased.

Of course, the actual amount of heat evolved during the chemical
rearrangements in the conduit cannot be estimated, but a glance at the
following tables (showing some examples) must assure one that the
heat product from the complex system may be of a high order. 36

Heats of Formation.

Calories per

Calories per

Calorios per

Gram-molecule.

Gram-molecule.

Gram-iiiolc'cule.

[HCl] +22,000

[SO2]

-f71,080

[CaCl^]

+ 190,300

.H/)" 58,300

[CO2]

96,960

[K0CI2]

211,220

[HsS] 5,400

[SO3]

103,240

'NaoCi;

195,380

.HsN] 11,890

T^Os'

369,900

'FeCU]

82,050

;H4C] 21,750

[FeS]

24,000

.CO] 29,000

[CaF^]

238,800

^* The values for the heats of formation and reaction are taken from the
works of Thomsen, Muir and Wilson, Xernst, and others. In some cases
more recent experiments give slightly different values.

DALY. — THE NATURE OF VOLCANIC ACTION. 89

Heats of Reaction.

CH4 + '2i).i = CO, + "iUjO +195,200 cals.
COs + Hj = CO + \U) + 9,iKS0 cals.
3Fe() + 11,0 = FcsO* 4- Ha + l.'),4()() cals.
3FeO + CO2 = l"Vs04 + (JO + (5,000 cals.
Nils + HCl = XH4CI + 42,500 cals.37
CO + 0 = CO2 + G.S,040 cals.

In addition, there is the possibility that a large supply of energy was
potentialized at the high temperatures of the primitive earth and that
this energy becomes converted into magmatic heat under the conditions
of a volcanic vent. Becker has suggested this in the case of uranium. 3*
Arrhenius has [troposed the hypothesis that the heat of the sun is
supplied principally through the break-up of endothennic compounds.^^
Warren has .shown that, at high pressure and temperature, steam is
partially converted into the strongly endothermic ozone and hytlrogen
peroxide. **• Lines indicating cyanogen are found in the spectra of
some stars and comets, and Arrhenius attributes the nitrogen of the
air largely to the dissociation of volcanic cyanogen. In the formation
of a gram-molecule of this gas, 05,700 calories are potentialized. The
dissociation of chlorine involves the absorption of 113,000 calories.*^
Dissociation of other gaseous elements means heat absorption of the
same order of magnitude. When ferric oxide and iron sulphide react
to form ferrous oxide and sulphur dioxide, 80,(540 calories are ab-sorbed.
When carbon and carbon dioxide react to produce carbon monoxide,
3.s,soo calories are absorbed. When steam and C react to form carbon
monoxide and free hydrogen, 28,900 calories are absorbed.

In addition to the heat evolved by the di.ssociation of endothermic
compounds, another source of great energy is to be found in the com-
bination of the freed, "nascent" elements with other constituents of

" Though ammonium chloride may not be able to form within the mufoiia
column of a volcanic conduit, it docs form at the surface, where (he loss of
heat chiefly occurs. Similarly, an)m<jnia may form from its elements in the
relatively cool cru.st of the lava lake in a crater, also producing heat at the
zone of radiation.

" G. V. Becker, Bull. Geol. Soc. America, 19, 11(5 (1908). The final yield
of radium is about 2,000 millions of calories per gram, or nearly 250,(XX) timea
the tlirrmal valu<' of a gram of carbon burnt in oxygi-n.

" S, Arrhenius, Worlds in the Mailing, New York, 91 (1908).

*" H. N. Warren, Chem. News, 77, 192 (1S9S). When one gram of oxygen
is c()nvert<'d into one gram of ozone, 7.")() calories are alisorbed.

" M. Pier, Zeit. fiir phys. Chemie, 62, i'.S.') (HtOS). Kkliolm has suggested
that the formation of "elements" may partly explain solar energy.

90 PROCEEDINGS OF THE AMERICAN ACADEMY.

the magma. The powerful thermal effect of interaction between hydro-
gen or oxygen and the carbon or nitrogen atoms of cyanogen hardly
needs quantitative statement to show its value.

In this connection it may be noted that the total melting heat of
ordinary rock-matter (measured from 0°C.) is only 400 to 450 cals. per
gram, and that the latent heat is only about 90 cals. per gram.

Such examples emphasize the value of the conception that abyssal
injection, entailing a sharp change of pressure and a slower change of
temperature in primary magma, may set free a vast amount of energy
which is available for conserving the melting temperature in a lava
conduit. Very great superheat is, however, prevented by two-phase
convection, which tends to keep the volcanic furnace and the surface
lava at nearly the same temperature.

The whole system, as imagined, is somewhat analogous to a modern
hot-water plant with an almost perfectly lagged vertical pipe running
up from the furnace. Or, again, the generation of heat in the conduit
is analogous to that in the gas-mixture of a blowpipe. In the first
case (two-phase convention) the rising gas is a passive agent in the
upward transfer of heat ; in the second case (chemical changes) the
gas is a positive heater. For a double reason juvenile gas has fluxing
power in the vent.

Summary on the Heat Problem of an Active Central Vent. — A vol-
cano of the central-eruption type, like all others, depends on antecedent
abyssal injection of magma into the earth's crust, furnishing a magma
chamber whence the vent may draw its supply of energy.

Three possibilities are open : (1) The primary magma may have
been initially saturated with juvenile gas at the original pressure of
10,000 atmospheres or more. (2) Only the upper part of the magma
may be saturated ^\•ith gas because of the change of pressure resulting
from the injection. (3) Or the magma may not be saturated immedi-
ately after injection, even at the pressure of one atmosphere.

In the first case, bubbles must form throughout the chamber at all
levels above the original depth of the magma. In the second case,
bubbles must form at all levels above the lowest one where saturation
has been developed by change of pressure. In the third case, bubbles
will form only after other causes than mere change of pressure have
operated. At least three such causes are conceivable. (a) The
upper part of the magma chamber might become supersaturated
through the upward molecular diffusion of gases, whereby these are
concentrated. This is a reasonable expectation on the general princi-
ples of physical chemistry, though experimental or other proofs are
lacking, (b) The slow crystallization of the magma might be accom-

DALY.— THE NATURE OF VOLCANIC ACTION. 91

panied by the ejection of gas, as it is actually seen to emanate dur-
ing the crystallization of artificial slags. That process might cause
local supersaturation in the still liquid magma, with the forma-
tion of bubbles, (e) Chemical reactions in the magma, such as the
generation of hydrogen from dissolved primary water vapor — a reaction
to be expected witli a slight fall of temperature — might produce gases
insoluble in the magma at the pressure reigning at the place of the
reaction.

Among so many possibilities, it seems legitimate to assume the gen-
eration of free gas in the main magma chamber. Irrespective of their
origin, the bubbles must rise with great slowness through the magma
chamber, because, first, they are of small size ; and, secondly, because
the viscosity of magma under great pressures must be relatively high.
Even in the case of supersaturation in all parts of the new abyssal in-
jection, the entire freeing of the bubbles may occupy many thousands
of years.

As the bubbles rise, the gas tends to be concentrated in the volcanic
conduit. There the laws of mass-action and of the degradation of
energy seem to enforce exothermic reactions of the gaseous constituents
among themselves and with the elements of the liquid magma. It is
most probable that the heat so generated is very great when compared
to the mass of matter participating in the reactions. The conduit is
thus a furnace where the potential energy of the accumulating gases
is converted into heat energy.

Other sources of heat which aid in prolonging the activity of the
volcano are: (a) the conversion of the potential energy of the liiju id
components of the magmatic system when thrown out of chemical
equilibrium by the change of pressure and subsequent lowering of
temperature ; (b) the liberation of latent heat in the slow crystalliza-
tion at the walls of the magma chamber ; and (c) some degree of
initial superheat in the magma, perhaps of the order of 1<)()° or '2i)()°
Centigrade.

Since the loss of heat at an active vent is chiefly due to radiation
at the crater, the continuance of activity is controlled by the efficiency
of the mechanism by which the heat of the main chamber and the heat
chemically generated in the conduit are transferred to the earth's sur-
face. Field observations at Ivilauea and elsewhere, along with a priori
deduction.s, have suggested the general dominance of two-phase con-
vection (or, more generally, convection due to systematic, local changes
in gas-concentrati(jn) in making this transfer.

Juvenile gas is thus conceived to act in a two-fold cai)!U'ity — as a
positive heater and as the agent enforcing convection. Its net eflect

92 PROCEEDINGS OF THE AMERICAN ACADEMY.

is to keep fluid the top part of the lava column during the volcano's
activity. The conception as a whole may therefore be called the gas-
fluxing hypothesis. For vents occupied by highly fluid lava this
hypothesis as just stated seems to suffice. For craters floored with
more viscous lava, the emanating gas issues under more or less high
pressure and may function as a melting blast, making more perfect the
analogy with an artificial blowpipe.

Revival of Activity at the End of a Dormant Period.

One of the leading problems in vulcauism relates to the periodicity
of central eruptions. This also seems to find explanation on the gas-
fluxing hypothesis. We have seen that the accumulation of gas
bubbles in the conduit must be a very slow process. So long as tho
vent is open, the escape of the gas from the magma is specially facili-
tated. That is true, not because the pressure on the main part of the
lava column is less than in times of dormancy, but because of the rapid
freeing of gas into the open air, with the consequent rapid production
of heavy, gas-freed lava which sinks and thus hastens the two-phase
convection. The tendency is, therefore, sooner or later to exhaust the
gas concentrated at the lower end of the conduit. With sufficient re-
moval of the heat-producing and heat-transferring agent, the forces of
cold temporarily win in the never-ceasing struggle and the lava solidi-
fies at the surface ; a plug of greater or less thickness is formed. The
crater may become temporarily so dead that even solfataric action
ceases and a forest may flourish within the crater, as has been the case
with Vesuvius.

On account of the small horizontal dimensions of the average vent,
the consolidation of such a lava plug may be completed in a few years.
This new rock is characteristically tough ; when cooled, it is the
strongest rock in the average volcanic cone. In the text-books on
dynamical geology and in special vulcanological memoirs, the removal
of the plug is usually stated to be due to simple explosion of the gases
accumulating below it. Yet it is obvious that in the normal cone,
which is largely built of loose ash deposits of very low tensile strength,
the weakest place in the pile is on its flank and not at the main central
plug. By the orthodox view, therefore, the new crater, the main one
for the succeeding period of activity, should have a different location
from that of the earlier main crater. The fact is, that, in very
many cases, the main vent is located at the same place through
the many diff'erent periods of activity of the greater cones. The
beautiful symmetry of a Fujiyama or of a Mayon is the result. The
removal of the plug at the close of a dormant period is clearly not the

DALY. — THE NATURE OF VOLCANIC ACTION.

93

mere mechanical result of explosion. There must be a preliminary
weakening of the plug, and apparently the only cause for that weaken-
ing is to be found in the fluxing by juvenile gas.

First we may consider the case where the terrestrial forces keep the
liquid column supported in the conduit. With the formation of the
plug, the loss of heat falls to a very low rate as compared with that
ruling in the active period. Until the plug is removed, nearly all the

CRATELR

FioritE 9. Section of upper part of a dormant cone, showing some progress
in Ras-fluxing. Broken line iu middle of vent shows original depth of the solid
plug.

loss is due to conduction and is very slow. Two-phase convection is
slowed down, but the rise of bubbles does not cease nor does the vol-
canic furnace cease working, since a' renewed concentration of juvenile
gas is begun. To that positive source of heat in the conduit is to be
added the heat developed by the compression of the gas as it accumu-
lates beneath the plug and as it is sijueezed by any upthrusting of the
magmatic column due to crustal movement. Gradually the lowest part
of the plug becomes lic^uefied, preferably along its vertical axis, where
the heat inherited from the last active period preserves the line of max-
imum temperature in the whole upi)er ])art of the volcano. The relicjue-
fied lava sinks into the column, dissolving some of the accumulating
gas, so that heat of solution is })robably to be added to the other sup-
plies which tend to threaten the existence of the plug. Hence, at least
three processes cooperate in fusing the plug ; these are : heat of chemical
reaction, heat of gas compression, and heat of gas solution. As the
])lug is thus weakened, the gas-tension increases and activity is renewed
by (jne or more major explosions, shattering the remaining part of the
plug. (Figure 9.)

94 PROCEEDINGS OF THE AMERICAN ACADEMY.

Though full experimental data for the testing of these conclusions
are not yet in hand, it is not difficult to see that the fluxing power of
even small masses of juvenile gas is great under these conditions. If
chemical reactions supply any large fraction of the heat lost by radia-
tion in the active period, they must raise the temperature of the lava
column under conditions of dormancy. This involves a slow melting
of the country-rock, and especially the plug.

In most cases dormancy is ended by explosions so powerful as to
show pressures under the plugs of even higher order than the pres-
sures in the greatest modern cannon at the moment of discharge. These
pressures run Avell over 2,000 atmospheres. If a given plug, when frozen
to maximum thickness, is 1000 meters deep, the initial pressure on the
gas first collecting beneath it would be about 270 atmospheres.
Amagat's experiments furnish the data from which the temperature
effect of the adiabatic compression of the typical gases, carbon dioxide
and hydrogen, may be approximately computed.

At the request of the writer Professor H. N. Davis has kindly de-
duced the thermodynamic equation for these two cases. If T^ is the
initial temperature ; J", the final temperature ; po, the initial pressure ;
and ^?, the final pressure, we have

= ^« &

in which n is an exponent approximately determined from Amagat's
curves. If the initial temperature and pressure are, respectively,
1273°C. absolute and 270 atmospheres, and the final pressure is 2700 at-
mospheres, the average value of n for carbon dioxide is about 0.17 ; and,
for hydrogen, n probably lies between 0.26 and 0.31. For carbon diox-
ide the computed value of 7" is 1880° absolute, and for hydrogen 2300°
to 2600° absolute. This adiabatic compression of carbon dioxide
would develop heat to the amount of about 200 calories per gram.
Similar compression of pure hydrogen would develop an amount of
heat ranging from 3000 to 4000 calories per gram. The compression of
the gaseous mixture actually formed under volcanic plugs would pro-
duce heat to amounts intermediate between those calculated for carbon
dioxide and for hydrogen. Since hydrogen is one of the most abundant
constituents of the mixture, it is possible that adiabatic compression
of the mixture, under the conditions above described, would produce
at least 1000 calories per gram of gas. Since the latent heat of holo-
crystalline igneous rock is about 90 calories (Vogt), this heat of com-
pression could fuse more than 10 grams of rock per gram of gas.

DALY. — THE NATURE OF VOLCANIC ACTION. 95

Calculation further shows that if the compression of a considerable
volume of gas be isothermal, other conditions being as above assumed
for the adiabatic compression, the heat produced is of the same large
order of magnitude.

As the lower part of the plug is fused, the liquid sinks through the
gas-rich part of the magma column, so that the fluxing gas is always
in immediate contact with the solid rock. Since the solid plug retains
a relatively high temperature inherited from the last active period,
and since the vertical axis of the plug is the hottest part of the vol-
canic cone at all levels above the top of the lava column, it is clear
that fluxing will be most rapid along the axis.

Again, a local development of heat is to be expected as the re-fused
rock, which had been largely freed of gas in the last active period,
begins to absorb the gases collecting in the conduit. Nothing is known
as to the solution heat of any j uvenile gas as it is absorbed in a nat-
ural magma. In each case it is practically certain to be positive and
it may be important in amount. The data for the same gases when
dissolved in water have some value in the way of analogy. The follow-
ing table is taken from Thomsen's Thermochemistry:

Vapor or gaa

Heat of solution

dissolved in water.

For 1 gram

-mol.

For 1 gram.

NHs

8,430 cals.

496 cals,

SOo

7,700

120

CI2

4,870

69

COo

5,880

134

us

4,560

134

HCl

17,315

475

"When hydrogen dissolves in water, heat to the amount of about 800
cals. per gram of the gas is evolved. *2

In this whole problem it must be remembered that hydrogen forms
a relatively large part of juvenile gas-mixtures. This gas has the high-
est specific heat of all substances yet measured, and its heat of solution
in water is also very high. Its efficiency in melting a volcanic plug
may perhaps be greater than that of the other gases and vapors put
together.

In view of all the conditions, it seems correct to hold that the ac-
cumulation of gas beneath a solid volcanic plug develops a special kind
of local furnace. The energy here transformed into heat is both pt)ten-
tial and mechanical. In part, it is heat of solution ; in large part, it

*' G. N. Lewis, verbal communication.

96 PROCEEDINGS OF THE AMERICAN ACADEMY.

may be due to chemical reactions ; in part, it is due to the condensa-
tion of free gas constantly increasing in mass, within a closed chamber.
The increase in mass is assumed to be due to the exclusion of gas in the
crj'stallization at the walls of the abyssal injection, and perhaps to
other molecular transformations within the magma chamber.

If the lava column is not kept supported, but withdraws for a time
from the plug, the compression-melting of the plug must await suf-
ficient accumulation of gas from beneath or the return of the fluid lava
(because of general strains in the earth's crust or for other reasons) into
the conduit. The mechanism is, however, the same as in the case just
discussed, and the base of the plug is gradually melted.

The re-fused magma must become graduall}'' more and more charged
with gas. How much gas per unit weight of rock would be required
to fuse an average plug is obviously now impossible to declare, but the
maximum quantity of gas in solution may not need to be more than
two or three per cent of the total weight of the magma in the actual
conduit. The astounding explosive energy of newly awakened vol-
canoes, as shown in the vast heights to which fine ejecta are thrown
and by the excessive comminution of the respective plugs, seem to in-
dicate saturation of the magmas to an even higher degree. The " evis-
ceration " of some cones has possibly been due to the concentration of
juvenile gases beneath plugs not yet sufiiciently fluxed to permit of a
reopening of the former vents by more moderate explosions. In neither
case, however, is it probable that pure explosion could restore activity
to the dormant volcanoes. Here again, as in the continuance of ac-
tivity after the vent is opened, the problem is one of heat supply.

Another cause for dormancy is to be found in the sudden emptying of
a lava-filled conduit by escape through a lateral fissure, forming satel-
litic intrusion, or distant surface flow, or both at once. This is a com-
mon event at both Kilauea and Mauna Loa. A multiple eff'ect is
produced. A large volume of specially concentrated juvenile gas is
taken out of the vent, just so far diminishing the motive power and
heat supply in that vent. As observed at Kilauea, the level of the
conduit lava may not be restored to its former height for months or
years. During that time the upper part of the conduit wall is cooling,
and, through decrepitation and initial weakness, large masses fall from
the wall and choke the vent. A resumption of activity at the surface
must be delayed by these processes.

In the present argument we need not dwell on the fact that, if the
volcanic mechanism is nicely balanced, a minute effect, like tidal strain,
may pull the trigger and renew activity, for which the essential con-
ditions have been long preparing. However, it seems clear that cos-

DALY. — THE NATURE OF VOLCANHC ACTION. 97

mical stresses do not seriously deform an abyssal injection durin",' its
lifetime as the feeder of a central vent. During such a period, which
may be thousands of years in length but seldom or never millions of
years in length, crustal readjustments must be minute, for even the
greatest lava flows that could have been thus squeezed out at central
vents are always very small in relative measure. The last-mentioned
fact and the persistent recurrence of eruption at the main vent appear
to forbid the h}'pothesis that renewal of activity at central vents is due
to renewal of injection along new abyssal fissures. It would be highly
improbable that the vent of a second injection would coincide with that
of the first injection ; and on the other hand, the great crustal disturb-
ance accompanying the second injection should normally cause first-
class lava floods at the initial vent, instead of the comparatively
insignificant flows actually observed at central vents. Difficult as
the problem is, the change from donnancy to activity does not, in
general, seem to call for anything so drastic as a strong deformation
of the earth's crust in its entire thickness.

In conclusion, the gas-fluxing hypothesis appears to be worthy of a
leading place among those which can be constructed to account for the
stubborn persistence in the revival of activity at a vent like Mokua-
weoweo, Vesuvius, or Etna.

Small Size of Central Vents.

The gas-fluxing hj^pothesis accounts for other general features of
central eruptions. The small cross-sections of the vents at Kilauea,
Hualalai, Mauna Loa, and even at Mokuaweoweo, as everywhere else
in the world, are all of the order of size expected if the fluidity of each
lava column is due to the slow passage of relatively minute masses of
gas through those vents.

The writer is not able to agree with J. D. Dana, that the conduits
beneath Kilauea and Mauna Loa are nearly equivalent in horizontal
section to the great sinks (" calderas ") in which the lava lakes are sit-
uated. Each of those sinks measures roughly five kilometers by three
kilometers. The periodic rise and fall of the floor of the Kilauean sink
(the only one carefully studied) can be explained on the assumption
that its conduit has a much smaller cross-section. The " New Lake "
after five years of activity, was emptied in 1 SSfi, and was proved to have
had a depth of only a few meters. It was a saucer-shaped sheet of lava
resting on solid rock. (Compare Plate III.) When the present Ilale-
maumau is emptied, the lava runs out through a very narrow hole appar-
ently less than thirty meters wide, and leaves a broad, funnel-shaped
cavity. The action is like that of water running out of a domestic sink

VOL. XLVII. — 7

98 PROCEEDINGS OF THE AMERICAN ACADEMY.

with centrally placed discharge : in both cases vortical motion is observed
in the rapidly escaping liquid. *3 Similarly, the vast Kilauean lake of
1820 to 1860 is best interpreted as a true lake with solid floor, except
for the narrow pipe which has always supplied the heat at this volcano.
That pipe is probably the same pipe into which Halemaumau at times
discharges its lava and from which the gas issues, to make the foun-
tains of " Old Faithful." All the Kilauean lakes have represented over-
floivs from that vent or from a few, more temporary, narrow pipes. The
fluidity of the lake has, in each case, been preserved for years by the
process above outlined for the existing lake.

Whatever adverse criticism of this conclusion regarding Kilauea may
succeed, it is certain that the whole area of either of the Hawaiian
sinks cannot be directly taken to represent the size of the conduits.
The surface areas of other lava columns active in historic time are all
very much smaller. It is doubtful that any one of them, just below
the floor of the flaring crater, has been as much as one kilometer.
J. D. Dana computed the volume of the 1852 floor from Mauna Loa,
which appears to have emptied the conduit to a depth of 2,500 feet, as
estimated from the difference of level of the summit lake and of the
point of discharge. The result was 10,560,000,000 cubic feet.** This
corresponds to the volume in a cylindrical conduit about 2,300 feet or
700 meters in diameter. Similar calculations from other lateral out-
flows seem to give a mean diameter for the conduit of the same order
of magnitude. Such a lateral fissure once opened, it would seem highly
probable that the conduit would be emptied almost entirely by the simple
outflow of the lava through the fissure ; discharge into " subterranean
cavities," would be unlikely. Moreover, it is possible that some of
the 1852 lava represents a temporary rise of magma in the conduit,
so that only part of the estimated volume of the flow can be used in
calculating the average diameter of the Mauna Loa conduit. Thus,
the calculation made according to the method outlined, strengthens
the suspicion that the lava column of the world's vastest volcano is
but a comparatively narrow pipe, perhaps much less than 600 meters
in average diameter.

All of the ancient central vents now exposed as " necks " after pro-
longed denudation, are relatively small. (Compare Figure 10.) The
average diameter of the pipes recorded in geological literature is well
under 500 meters. The largest of the hundreds of deeply eroded lava
necks in the Mount Taylor region of New Mexico is said to be not more

*3 C. H. Hitchcock, Hawaii and its Volcanoes, Honolulu, 1909, p. 254.
** J. D. Dana, Characteristics of Volcanoes, New York, 1891, p. 210.

DALY. — THE NATURE OF VOLCANIC ACTION.

99

than 450 meters in diameter. The size of the lava conduit is often
not shown by the maps of many volcanic "necks." For example, the
largest Scottish " necks " described by Geikie are chiefly composed of
pyroclastic materials and may represent erosion sections through explo-
sion funnels with their characteristic flare. Without even allowing for

PLAN OF NECK

Figure 10. Section and ground plan of b;isalt-lava neck in a lateral gorge of
the lao valley in West Maui, illustrating the cylindrical form due to gas-
fluxing. This w;us one of th(,' subsidiary vents on the flanks of the great We^t
Maui cone. There is no trace of faulting in the ash-and-flow series and it is
possible that this neck represents the local enlargement (by gas-flu\ing) of
one of the dike fi-ssures now visible in the canyon. Nearly natural scale;
major diameter of the neck about 50 meters.

that uncertainty, the writer believes that the conduits of central erup-
tions, measured below the explosion zone, have an average diameter
of much less than one kilometer. The term "conduit" here means,
of course, the pipe above the primary abyssal injection. The main
magma chamber may be indefinitely greater in horizontal section.

We may conchide that the conduits of central eruptions are always
small and of the order of magnitude appropriate to the gas-tluxuig

100 PROCEEDINGS OF THE AMERICAN ACADEMY.

h3^potliesis. On any other hypothesis it is hard to explain the fact
that the pipes of moderately large cones are about as large as those of
the very greatest cones. In all cases there seems to be a limital size
and that is controlled by the available heat supply along the axis of
the vent. The size is small because the (indirect) fusing power of ema-
nating gas must be strictly limited. Moreover, the cylindrical shape
of each typical pipe is a solutional or fluxing form. (Figure 10.)

Explosive types : Magmatic and Pkreatic.

The foregoing genetic statement for the Hawaiian vents has been
sketched in terms of a quite general process and it is necessary to
glance at the relation of the hypothesis to the explosive type of
central eruption.

Volatile matter occurring in the rocks of the contact-shell about any
intrusive magma must show increased tension. If the intrusion is
large and near enough to the earth's surface, this tension may lead to
explosion in the roof of the igneous body. In case no incandescent
matter is extruded, the explosion is not volcanic according to our defi-
nition of that term (p. 48). Following Suess, it may be called pkreatic.
A similar explosion may happen as a result of the slow conduction of
heat from the conduit of a long dormant volcanic cone. Such a cone
is normally porous. Rain-water, snow-water, or sea-water is trapped
in the vesicular flows and loose tuffs, as these are in turn buried during
the original growth of the cone. The circulation of vadose water is also
facilitated by this special porosity.

The suggestion of Suess that the remarkable explosion at the famous
Kieskessel was of phreatic origin has been supported by the detailed
studies of Branco and others. ^^ Purely geological studies had indicated
the presence of a large laccolithic mass beneath the great Ries depres-
sion. That conclusion has been brilliantly supported by the magnetic
studies of Haussmann in the region. The local disturbances of the
needle in dip and azimuth can be explained, according to Haussmann,
only by the assumption of one or more large subterranean bodies of
basic rock. 46 In the Rieskessel itself the upper surface of the basic
rock is calculated to be no more than two kilometers deep. Outside
the depression, its average depth was estimated at five kilometers.
Since the visible floor of the Ries is the granite of the " Grundgebirge,"

" W. Branco, Abhand. kon. preuss. Akad. Wiss. Berlin, 1902, p. 14.

** K. Haussmann, Abhand. kon. preusa. Akad. Wiss. Berlin, 1904, Abt. IV,
p. 137. Sauer has suggested that the liparite of the Kieskessel tuffs is due to
the melting of the intruded granite by the basic magma. See W. Branco and
F. Fraas, Abhand. kon. preuss. Akad. Wiss. Berlin, 1901, p. 54.

DALY. — THE NATURE OF VOLCANIC ACTION, 101

the basic mass or masses can only be interpreted as due to injection.
Branco dates the intrusion of the Ries " laccoHth " in the mid-Miocene.
The overlying granite and its Mesozoic sedimentary veneer were domed
.y the injection and the top of the dome was largely destroyed by a
phreatic explosion. It was followed by the appearance of a little
liparitic tuft' erupted at a few points in the newly formed basin, but the
explosion itself was non-volcanic.

According to Sekiya and Kikuchi, the great explosion of 18S8 at
Bandai-San was absolutely unaccompanied by the extrusion of lava.*^
A priest living on the mountain survived the explosion. He reported
the vapors surrounding him to have been respirable, and the Japanese
geologists conclude from all available data that the catastrophe was a
steam explosion. There were no signs that juvenile gases formed an
important part of the volatile mixture. This " eruption " of Bandai-
San seems, therefore, to be an excellent example of a phreatic explo-
sion on a true volcanic cone.

Phreatic eruption means steam-explosion without magmatic extru-
sion. Kilauea represents magmatic extrusion without steam-explosion.
Between these two extremes of terrestrial activity stands the type
representing the vast majority of active and extinct central eruptions.
In the non-volcanic or pseudo-volcanic activity of Bandai-San in 1888,
as in a Kilauea or a Vesuvius, true igneous injection is a pre-requisite.
The gases given off at Kilauea form a nearly pure juvenile mixture
with characteristic high temperature. The gases given oft" at Vesu-
vius form a mixture of juvenile, resurgent, and vadose volatile matter.
A type of the resurgent gas is the carbon dioxide set free in the de-
monstrable assimilation of Mesozoic limestone and dolomite in the
Vesuvian lava column. The gas and vapor given oif at Bandai-San in
1888 was apparently almost purely vadose or meteoric in origin.

True volcanoes of the central-eruption type must vary enormously
in the relative and absolute proportions of juvenile, resurgent, and
vadose fluids composing their emanations. As the resurgent and
vadose fluids are volatilized, heat is lost and the viscosity of the
lava column rises. Assimilation of foreign rock in depth must lower
the temperature, and in the end, increase the viscosity and also the
average violence of explosions. In addition, magmatic dilTerentiation
generally brings the more silicious and more viscous pole to the ujiper
part of the lava column, and aids in the preparation of explosive
conditions.

For these and other reasons, volcanoes of the central-eruption tyi)e

*' S. Sekiya and J. Kikuchi, Jour. Coll. Science, Tokio, 1889, p. lOG.

102 PROCEEDINGS OF THE AMERICAN ACADEMY.

have always had a great variety in dynamic habit and in the character
of their ejectamenta. Yet, in every one of them, the essential problem
is the same ; it refers to the mechanism by which heat is kept supplied
to the narrow, thread-like vents for long periods. To that problem, the
questions as to how sea-water or vadose water is absorbed by under-
ground magma, as to the dominance or subdominance of steam-explo-
sion at individual vents, and as to the physical differences in the
emanating lavas, are subsidiary. The problem of the Hawaiian vents
is, from this point of view, the problem of all vulcanism reduced to its
lowest terms. Here the gas-fluxing h}'j)othesis seems satisfactory. In
most other volcanic regions, where thick sediments are cut by the feed-
ing magma, or where heavy snows or rains wet the cones and, through
seepage, cause steam-explosions, the control by juvenile gas may be
obscured to the eye of the observer, but it still remains, in every case,
the true cause of continued activity. Kilauea and Mokuaweoweo, like
Matavanu and the vents in Reunion, teach us that steam-explosion is
an adventitious feature of vulcanism. Except abyssal injection itself,
the only indispensable process in central vents is quiet exhalation.
jXeither explosive drilling of the vent, nor ejection of lava, nor the
contacting of meteoric or marine water with hot lava is indispensable.
Each of these three processes is an expected effect of the slow emana-
tion of juvenile gas from main abyssal injections or from their satel-
litic offshoots.

Magmatic Differentiation at Central Vents.

The chemical variation exhibited in the lavas or pyroclastic materials
successively ejected at the normal vent offers a problem of special im-
portance. Volume for volume, this variability is much more striking
than it is in the average large intrusive body — stock, batholith, lac-
colith, or sheet. At present many petrologists favor the pure-differen-
tiation theory, which regards the splitting magma as primary, and
finds no place for notable assimilation of wall-rocks by the primary
magma. The writer believes that this question can only be cleared up
by an attentive study of the world's plutonic masses, and that, in the
nature of the case, its answer is not to be found at central vents. Field
and chemical relations point indubitably to the fact that wholesale as
similation has occurred in the subjacent bodies classed as stocks and
batholiths. Because of assimilation these masses generally have not
the basaltic composition of the primary abyssal injection. The visible
granite, diorite, or syenite represents the frozen top of an abyssal in-
jection which is there a more or less differentiated syntectic. The
lower part of each injection, approaching the substratum level, is prob-

DALY. — THE NATURE OF VOLCANIC ACTION'. 103

ably basaltic and little modified in composition from its original con-
dition. The syntectic-differentiation theory is so strong that the writer
is disposed to prophesy its ultimate victory in the competition among
explanations of the igneous magmas and rocks,

Since the lava column of every volcanic vent is an offshoot from an
abyssal injection, the lava may represent either the primary basalt, or
one of its differentiates, or syntectic material, or a differentiate from
syntectic material. The rapid chemical variations in the extrusive
magma at the average central vent shows that the conditions are here

N

ZONE. OF C\NOLR CONES

3/ope o/^

'auno loc? ^,,^-<z:ONE OF A A lava^

:ONE OF PAHO^HO^ LA\/A

FiGfKB 11. Diagrammatic projection of Maana Kea, illiLstrating the field
character of the rocks encountered in cUmbing from sea-level to thesununit at
4213 meters above sea. Length of section 55 kilometers. Vertical scale twice
the natural.

specially favorable for differentiation. Two of these conditions are
implied in the essential meclianism of central eruption. The upward
passage of juvenile and resurgent gases in great relative abundance,
lowers the " point " of .solidification of the magma, increases the fluidity,
and probably in still other ways aids in magmatic splitting. Secondly,
the alternation of active and dormant periods means that the top of the
lava column passes repeatedly through the narroAv range of tempera-
ture Cjust above the crystallization point), where differentiation is most
likely to take place.** High superheat is opposed to magmatic splitting.

Each of the.se conditions affects only a small volume of magma at
any one time ; if lava representing either pole of the differentiation i.s
alone extruded, the volume of that flow must be relatively small. New
magma rises in the vent. It may be mixed with that representing the
other pole of the differentiation just accomplished. The mixture may
be extruded, or it may itself be differentiated before the next outflow.
Through absorption of foreign rock the new lava may have a composi-
tion unlike that originally differentiated.

It seems inevitable, therefore, that, at the restless volcanic vent, the
ever-changing conditions must make a cone which is chemiciilly heter-

*' Int rusivc masses normally pass through this temperature range only once
before dolidificatiun.

104 PROCEEDINGS OF THE AMERICAN ACADEMY.

ogeneous to an extent not matched in the usual plutonic mass. Stand-
ard examples have been described at Electric Peak and Sepulchre
Mountain in the Yellowstone Park ; at the Lipari Island vents ; at
Tonopah, Nevada ; at the Kaiserstuhl in Baden, etc.

The extinct Mauna Kea in Hawaii (alt. 4213 meters) affords a good
illustration of a lava column which has not contacted with important
sedimentary masses. In this case magmatic differentiation seems to
have played the most important role, though its heavy winter snow-
cap may have furnished a special condition for explosiveness in the
last stage of the cone's activity. (Figure 11.) The broad base of
this volcano, visible in the long sea-clififonthe north side of the island,
is essentially composed of olivine basalt of the fluent pahoehoe type.
From about the 1500-meter contour to the 3500-meter contour, the
slopes are chiefly underlain by flows of a much less femic basalt, with
some interbedded ash and breccia. Above the 3500-meter contour the
mass is very largely pyroclastic, and the leading petrographic types
are trachydolerite and andesitic basalt or basic augite andesite. (Plate
IV, B.) The following analyses show the march of the differentiation :

1

2

3

SiOa

49.19

49.73

50.92

TiOa

1.72

3.05

2.55

Al^Oa

14.02

16.39

17.59

Fe.Os

5.62

7.58

3.80

FeO

8.68

3.98

6.69

MnO

.54

.23

.20

MgO

6.42

4.06

3.90

CaO

9.10

7.17

6.97

Na^O

3.24

4.12

4.28

K^O

1.04

1.93

1.86

H.O- 1
H.0+ \

.u{

.81
.54

.35
.79

P2O,

.28

.84

.40

CO2

None

None

NiO

.04

<(

Cr^Os

None

((

BaO

.03

SrO

None

ZrO^

.03

s

None

SOs

((

100.59

100.53

100.30

Seer.

2.911

2.761

DALY. — THE NATURE OF VOLCANIC ACTION. 105

1. Average analysis of twenty olivine basalts from Hawaii, repre-
senting closely the composition of the basement of Mauna Kea.

2. Andesitic basalt, flow at ll,()()()-foot contour, Manna Kea.

3. Trachydolerite, flow at 13,000-foot contour, Mauna Kea.
Analyses 2 and 3 by G. Steiger in the laboratory of the United

States Geological Survey.

Progress in Explosiveness at the Greater Vents.

The explosive effect at central vents is a function of the magmatic
viscosity and of gas tension, which means gas concentration.

Though the presence of much gas tends to lower the viscosity,
temperature is obviously in dominant control over that property of
magma. The initial store of heat in the abyssal injection is normally
lost through radiation in the crater, through conduction at the roof
and walls of the whole magma chamber, through assimilation of
country-rock, and possibly through the absorption of vadose water. As
the whole mass cools, the juvenile gas emanates with ever lowering
temperature and the lava of the volcanic conduit must have a slow
decrease of average temperature.

Magmatic diflerentiation must tend to affect the viscosity of the
upper zone of lava, the exploding zone, in the same sense. The more
acid differentiate usually rises toward the top of the vent. Though
differentiation may be roughly cyclical, the successive splitting tends
to make a secular increase of acidity in the upper zone of the conduit
magma. Hence, irrespective of temperature, there is an increase of
viscosity in the magma zone where explosions originate. The case of
^launa Kea, just described, is an example of the partial control by
magmatic differentiation over explosiveness. As the viscosity rises,
the escape of magmatic gases is more diflicult ; the resulting tension is
periodically relieved by explosions. Here also the action is cyclical,
but there is, on the average, a slow increase in the amount of gas
trapped before each explosion.

Again, the amount of volatile matter entering the magma column,
either through assimilation of sediments or through the direct absorp-
tion of meteoric water, tends to increase with process of time. And,
with the gi-owth of a great, generally porous cone, the chance fir
phreatic explosion at or near the crater is favored.

All of these factors vork fot/ctl/rr to produce maxinnim explosivenc-s
at central vents which are long-lived i)ecause fed from great abyssal
injections. The maximum normally appears in an advanced stage in
the evolution of a first-class volcanic cone, though necessarily some

106

PROCEEDINGS OF THE AMERICAN ACADEMY.

time before complete extinction. Short-lived vents, opened above
satellitic and therefore relatively small injections, will, of course, have
no such tendency to great systematic change in explosiveness.

Lava Outfloiv at Central Vents.

A noteworthy feature of all central eruptions is the relatively insig-
nificant size of their individual lava flows. Thoroddsen has estimated
the volume of the celebrated fissure eruption of Skaptar Jokull in
Iceland at 12,3-2() millions of cubic meters. He gives the volume of
one prehistoric flow as 43,160 millions of cubic meters; of a second,
500,000 millions of cubic meters. In striking contrast are the follow-
ing examples of the larger recorded flows at volcanic cones.

Locality.

Date.

volume in minions
of cubic meters.

Authority.

Semeroe, Java

1885

300

De Lapparent.

Etna

1669

980

von Waltershausen

((

1852

420

«(

((

1865

92

{(

((

1879

57

«

]\Iauna Loa, Hawaii

1852

299

J. D. Dana.

u

((

1855

455

C. H. Hitchcock.

<(

«

1880-1

413

(( u

(C

((

1907

153

E. D. Baldwin.

Geological investigation shows that the flows from the central vents
of Paleozoic and later periods have been of the same order of magni-
tude as the flows of the human period. With very few exceptions or
none at all, these larger flows have issued from lateral fissures in the
cones, and a large part of the volume of each flow is readily explained
as the lava drained out, hydrostatically, from the upper part of each
conduit. Without recorded exception all overflows at the main cra-
ters are incomparably smaller than those noted in the foregoing table.
Therefore, the ascensive force in central conduits is either slight, or, if
powerful, is applied for short periods.

The smallness of individual overflows clearly suggests that the
magma chambers >vhich continue to feed central vents are very sel-
dom deformed by important movements of the earth's crust. If the
magma in the chamber were diastrophically pinched, we should expect,
at times, relatively enormous lava-floods from central vents. Some
authors hold, on the contrary, that the growth of a great cone sometimes
occasions subsidence, so that crustal movement may be a consequence
rather than a direct cause of lava overflow at central vents.

DALY. — THE NATURE OF VOLCANTC ACTION. 107

"Without entering further into this subject, it will here suffice to
mention the principal causes for lava outtlow as deduced from the
abyssal-injection premise. These are:

1. Very minute deformation of the feeding magma chamber.

2. The effervescence of lava, due to the periodic accumulation
of magmatic gases in the vent. These gases may be juvenile or
resurgent.

8. The assimilation of country-rock in depth, leading, probably, to
increase of volume.

4. The increase of volume through heating in the conduit " furnace "
— a process specially like to occur during the dormant period when
the vent is temporarily plugged.

These causes may co-operate, but at basaltic volcanoes the third is
clearly subordinate.

The Two Types of Lava Flows.

A preliminary study of the Hawaiian lavas, wilh respect to their
field habit, has led the writer to suspect significant gas-control even in
this detail of vulcanism. On the average the vesiculation of pahoehoe
or ropy lava was found to be more evenly developed than in the aa or
block lava. The contrast is illustrated in Plate V. The rather uni-
formly disseminated vesicles of pahoehoe are of relatively small and
relatively uniform size, and tend to have spherical form. The irregu-
larly distributed vesicles of aa lava are generally larger, though more
variable in size; much fewer in number, and of less total volume per
unit volume of rock ; and more irregular in shape. These facts indi-
cate a more uniform distribution of gas in the pahoehoe than in the
aa t}'pe. The aa vesicle, which is often thousands of times bigger than
the average pahoehoe vesicle, has undoubtedly grown through the
coalescence of many bubbles of gas. Such growth must in very high
degree (see page 78) favor the escape of the gas into the air, and we
may regard these large vesicles as representing so much gas trapped in
the freezing lava. Before solidification had set in, gas must have es-
caped from every aa flow in large volume. In fact, observers of the
two types in actual movement agree that the gas emanation from flow-
ing aa lava is much more abundant than that from flowing pahoehoe.*^

The difference of field habit in fluent lava and block lava is thus
explained, with some show of probability, by the relative abundance of

*» Cf. J. D. Dana, Characteristics of Volcanoes, New Yorlc, 1891, p. 242,

JudKf Hitchcock describes a typical Hawaiian aa flow as advaricititi "witli no
explosions, but a tremendous roaring, like ten thousand bhidt-furnaccs all at
work at once."

108 PROCEEDINGS OF THE AMERICAN ACADEMY.

volatile matter and, still more, by the evenness of its distribution.
For both reasons pahoehoe lava is certain to be less viscous than is aa
lava, other conditions being the same ; the pahoehoe moves, as it were,
on molecular and vesicular "ball-bearings."

The fact that many flows, fpom the very points of emission, are al-
together of the one type, while others are throughout of the other t}^e,
shows that the differences of gas-distribution are developed in the vent.
The problem as to exactly what circumstances there control the gas-
distribution has not yet been solved. Slight differences in temperature,
or differences in the advance toward solidification (with gas expulsion)
may be the effective cause. The writer has observed a tendency for
the phenocrysts of aa lava to be of larger average size than those
in pahoehoe lava which gives practically the same oxide proportions
in ordinary chemical analysis (volatile matter other than water neg-
lected) ; but he is as yet not prepared to regard this as an established
rule.

Vulcanism Originating in Satellitic Injections.

We have so far considered central vents as, in general, direct off-
shoots of main abyssal injections. The latter have been described:
as dike-like, though often of great widths ; as extending upwards from
the primary substratum, nearly or quite to the earth's surface for some
such vertical distance as forty kilometers. Batholiths have been in-
terpreted as chemically modified abyssal injections of the primary basalt.
Plutonic stocks and bosses represent cupolas in batholithic roofs. Stocks,
bosses, and batholiths compose the group of "subjacent" intrusive
bodies. ^'^ Laccoliths, sheets, and ordinary dikes are individualized
bodies, satellitic with respect to their feeding abyssal injections, and
like the latter, owe their intrusion to a simple parting of the invaded
rock-formations. Irregular bodies intruded in the same fashion have
been called " chonoliths " : they form a fourth class of "satellitic
injections." ^^

All satellitic injections soon lose thermal and hydrostatic connection
with their respective abyssal injections. All laccoliths and chonoliths,
like most sheets and some dikes, have solid floors during most of their
magmatic activity. If a satellitic injection is of large size, its content of
heat energy and of gas may suffice to open one or more vents to the
earth's surface, according to the methods already described. Volcanic
action is thus initiated which differs in some respects from that due to
direct emanations from a main abyssal injection.

" R. A. Daly, Journal of Geology, 13, 508 (1905).
»i Cf. Journal of Geology, 13, 498 (1905).

DALY. — THE NATURE OF VOLCANIC ACTION. 109

The importance of this fact is manifold. Its recognition aids in our
understanding: the short Hfe of many volcanoes of the central t3'pe ;
the lack of lava flows at many of them ; the independent activity of
neighboring vents ; the chemical dissimilarity of the lavas from neigh-
boring vents ; the quite common clustering of many small vents in a
region which shows no trace, or but few traces, of the alignment of its
volcanoes ; and the frequent evidence of surface deformation in such
regions. The evidences for this type of vulcanism are indirect, but
they are numerous ; taken together, they form a combination of no
mean strength.

In the first place, an excellent analogy to the vents from satellitic
injections can be observed in nature. The blow-holes and driblet cones
formed on the surface of the deep lava flows of Etna, Reunion, Hawaii,
Savaii, etc., are continued in their brief activity because of the thermo-
gaseous energy of lava quite removed from the parent vent. The blow-
holes occasionally opened in the dome-shaped "bulges" or "tumuli "
formed on the pahoehoe of Hawaii or Reunion are particularly instruc-
tive, for such tumuli, when just formed, represent small laccoliths of
still fluid lava capped by recently frozen lava-crust.

To the weight of analogy is to be added that of a priori reasoning.
According to almost any of the extant theories of igneous action, vul-
canism originating in magmatic satellites should be expected. Many
satellitic injections of great size have been exposed by erosion ; it would
be a matter for distinct surprise if none of them ever perforated its
roof.

Field observation must naturally make the compelling test of the
principle. Have we any active example ? Can we find traces of it in
denuded regions where erosion enables us to study the anatomy of vol-
canoes 1 Each method of applying the field test has its own difiiculty.
In the first case the satellitic injection is inaccessible and can only be
located through inference ; in the second case it is but rarely that de-
nudation could expose the injected mass without destroying the conduit
above. Yet the writer believes that the field inferences seem to support
the principle.

The case of Kilauea, as an illustration, will be presented in some
detail ; the conception was first clearly attained by the writer during
his field-work at that volcano in 1 ;»()!).

Kihiuea, the Vent of a Stitellitir Injection. — A glance at the govern-
ment map of the island of Hawaii shows the reader that the contour
lines are peculiarly shaped in the southeast quarter of the island. (Fig-
ure 12.) From a low depression a few kilometers west of Kilauea to
Cape Kumukahi, a distance of fifty kilometers, the lines are rather

Figure 12. Redrawn Government map of southeastern Hawaii.

Heights in feet.

DALY. — THE NATURE OF VOLC.YNIC ACTION. Ill

strongly convex to the eastward. They there portray a long arch-
shaped spur running out from Mauna Loa. From sea-level at the cape,
the crest-line of the spur rises at the average rate of about twenty
meters per kilometer, or 1 in 50. At Kilauea the spur is plateau -like,
and immediately to the westward of the Kilauean "sink" there is a
faint downward slope to the west. This arrangement of slopes does
not mean that Kilauea is a crater surrounding a cone. It is rather a
large pit or "sink" in the side of ]\Iauna Loa (Plate II, A). Along
the Kau coast, southwest of Kilauea, the Mauna Loa slope varies from
1 in 10 to 1 in 15, averaging about 1 in 12.

The broad spur is capable of two interpretations. It has either been
built up by the specially prolonged extrusion of lava in this region, or
it is due to local deformation of the general Mauna Loa slope, as if by
deep-seated intrusion of the laccolithic type.

There is no sign that Kilauea has ever overflowed the outer walls of
its great sink. The writer tried, in the field, to answer that question
definitely by plotting the attitudes of the festoons of " ropes " on the
pahoehoe flows forming the surrounding surface, but was defeated,
through the failure to find a sufficient amount of that surface not
covered by ash deposits. In any case, however, the general topography
shows that no significant part of the spur could have been built up by
overflows from this vent. Lava seems never to have issued from most
of the many pit-craters situated on the back of the spur, and the total
effect of activity of that kind at the other craters in the whole Puna
district may have been a vanishing quantity so far as the development
of the arch is concerned.

On the other hand, it is evident that lava flows from the upper
slopes of Mauna Loa could not have constructed the spur in its present
form. Such flows as do run down the southeast flank of the main vol-
cano are deflected by the arch and run either northeastwardly toward
Hilo, or southwardly into southern Kau. Finally, the spur does not
apjjear to owe its principal volume to a succession of fissure eruptions
along its a.xis. The flow of 1840 may be an exception tending to prove
the rule. It represented a subterranean discliarge of the magma
chamber of which Kilauea is still the active vent. The formation of
that chamber is really the point at issue. The injection of its magna
might have followed or directly caused the formation of the spur; in
either case extrusion of lava from the chamber is a wholly subsidiary
and unessential fact. Furtlier field work is necessary to determine how
far the surface of the spur has been rai.sed by local eruptions like that
of 1H40.

The alternative explanation of the spur-arch regards it as a mass of

112 PROCEEDINGS OF THE AMERICAN ACADEMY.

Mauna Loa lava uplifted by a geologically recent intrusion of magma
which is still fluid. The form of the arch suggests a laccolithic body.
Though there is, perhaps, no possibility of proving it, this hypothesis
has high value in giving a new explanation for the general indepen-
dence in the activity of Mokuaweoweo and Halemaumau. The feed-
ing channels of a typical laccolith are always narrow. They must
freeze quickly and the satellitic injection loses hydrostatic connection
with its parent abyssal injection. The latter may most simply be re-
garded as that underlying Mokuaweoweo now and during the building

:> ^

MAUNA LOA "^ "o

- 'S

•Seo /et^e/

(C

Figure 13. Diagrammatic section to illustrate the hypothesis that the
Kilauean vent is fed from a large, still partly fluid laccolith injected into the
side of Mauna Loa. The broken line represents the now sealed channel through
which the laccolithic magma was injected; its course merely conjectural.
Natural scale.

of most or all of the island of Hawaii. In other words, the postulated
laccolith is an offshoot from the main Pacific fissure which located the
Hawaiian archipelago. (Figure 13.)

The remaining evidences favoring this hypothesis may be briefly
listed.

1. The many pit-craters in the eastern Kau district and in the Puna
district, including Kilauea, Kilauea Iki, Keanakakoi, Mokaopuohi, etc.,
are almost unique features in the whole island. (Plate IV, A.) Some
of the pits on Hualalai are of similar form and their mode of origin
may possibly be connected with another satellitic injection beneath
that western cone. The pit-craters of Kau and Puna are not arranged
in lines, as if located on master fissures, but are irregularly grouped
in clusters. The field evidences show that most, perhaps all, of them
have not been opened by explosion, and also that most of them have
not emitted lava. The extinct ones, like the active Halemaumau,
have been kept open by fusing gases. Their lives have been brief,
because dependent upon temporary concentration of juvenile gases
at the various points. In origin they are analogous to the clustered
blow-holes on the crust of the Kilauean lake between 1820 and 1840.

2. The Kilauean records show that, from 1820 to 1911, that crater

DALY. — TUE NATURE OF VOLCANIC ACTION. 113

has been decreasing in its activity with fair regularity. The very rapid
rate of decline suggests a relatively small feeding chamber.

3. The iuiperfect observations so far made seem to show that the lava
fountains of Mokuaweoweo more nearly a])proach brilliant-white heat
than do those of Kilauea in the hottest state of its present eruption.
The difference of temperature may be as much as 200°C.'*2 Assuming
that the magma of the Kilauean laccolith originally had the higher of
these temperatures, the cooling would be of the order expected if the
laccolith were of good size and not more than a few thousand years old.

If the average slope of Mauna Loa, before the laccolith was injected,
was one in twelve, as now in southern Kau (obviously an uncertain
assumption), a minimum estimate of the volume of the laccolith may
be made. The top of the broad arch just east of Kilauea must have
been raised at least 1000 meters, which is, therefore, the minimum
thickness of the laccolith in that large area. The average thickness,
as shown by the surface deformation, would be at least 500 meters and
the area at least 500 square kilometers. The corresponding volume
of the laccolith is 250 cubic kilometers. A body of magma of that
size and endowed originally with the high temperature demonstrated
at Mokuaweoweo, might, in part, remain fluid for 2000 years. There
is nothing to indicate that Kilauea is so old.

Clearly little stress is due any such computation of the size. It can
give only an order of magnitude. The magmatic body may be much
larger, and it may have a form not ideally laccolithic.

4. Kilauea is the largest, the last, and most persistent of all the pit-
craters for some good reason. The shape of the arch on which it stands
suggests that it overlies the highest point in the roof of the laccolith,
where the fluxing gases would naturally accumulate in largest quantity
and where they would finally tend to emanate from the magma cham-
ber. The smaller, extinct craters may easily represent so many points
where irregularities in the roof, lower down, temporarily caused local
accumulations of the gases.

5. Like the pit-craters, important systems of earthquake cracks like
those of 1868 southwest of Kilauea, are concentrated in the Kau-Puna

'' Quite recently Dr. Tempest Anderson has recorded that, even in day-
light, the lava of the active Matavanu lava lake in Samoa was, at the time of
his vi.sit in 1909, of brilliant-white incandescence (Quart. Jour. Geol. Soc.
London, 66, 1)27 and (J.J2, 1910). This indicates a temperature little, if any-
thiuR, short of 1400° C. The color of the hottest lava at the "Old Faithful"
fountains of Kilauea of the same year was, in the daytime, a brijiht orange,
corresjjonding to a temperature not far from 1200° C. The intensity of tiie
heat at Matavanu has been, for years, of the order represented in the great
eruptions of Mauna Loa.
VOL. XLVII. — 8

114

PROCEEDINGS OF THE AMERICAN ACADEMY.

region of the island. (Figure 14.) This fact is explicable on the
laccolithic hypothesis for the origin of Kilauea, since the roof of such
a body must evidently be in danger of Assuring and of moderate
dislocation.

Figure 14. Redraft of the Government MS. map (1907) of part of south-
ern Hawaii, showing fault-scarps and "earthquake" fissures. The long; soarp
in the south ranges up to 500 meters in height. Contour interval, 200 feet.

6. An obvious test of the hypothesis consists in the search for direct
evidences of uplift in the laccolithic area. No notices of strongly ele-
vated shore-lines in this region have been published. In view of the
considerable number of good observers who have traversed this part of

DALY. — THE NATURE OF VOLCAXIC ACTION. 115

the coastal belt, it is probable that neither old strands nor coral de-
posits are here to be found at any notable heights above sea-level.
However, that fact, however fully demonstrated, could not invalidate
the laccolithic h}-pothesis. Highly Huid laccoliths like that at Shonkin
Sag do not disturb the strata into which they are thrust, to a greater dis-
tance from the edge of each laccolith than that equal to one-twentieth or
one-tenth of the laccolith's horizontal diameter. Even for more viscous
intrusions, like that at the classic Mt. Hillers in the Henry Mountains,
this distance is less than one-tifth of the diameter. There is no sure
reason for thinking that the edge of the Kilauea laccolith was near
enough to the seashore of the pre-intrusion period to displace the coast-
line materially. It is also important to observe that a fault runs
roughly parallel to the longer axis of the great arch for a distance of
about thirty-five kilometers. It is located from three to five kilometers
inside the shore-line. Its downthrow throughout is on the seaward
side, and the amount of throw varies from about 100 meters to 500
meters or more. (See Figures 12 and 14.)

The maximum displacement is registered in a remarkable cliff south
of Kilauea. (Figure 14.) This greatest of all the pure fault-scarps
in the island finds its own explanation, if we correlate the displacement
with the upthrust incidental to the laccolithic injection.

7. The generally accepted hypothesis that Kilauea is a primary vent
like ^lokuaweoweo, entirely fails to explain the fact that we have no
certain trace of a lava outflow over the wall of Kilauea. It places no
difficulty in the way of the h}'pothesis here outlined.

8. Nevertheless, it is significant that, while Kilauea is less violent
in its eruption than Mokuaweoweo, the lower vent is the more ooncinu-
ously active. The latter contrast finds simple explanation on the
laccolithic hypothesi.s, which implies that the magma chamber of
Kilauea, below the cylindrical vent, is much nearer the earth's surface
than is the vaster magma chamber feeding the long pipe of Mokuaweo-
weo. The lodger pipe is evidently liable to the more ready discharge
by eruption through lateral fissures, and the space voided by such a
discharge must, on the average, be greater than that voided in a dis-
charge of Kilauea. A minute subsidence of the laccolith's nearly flat
roof after a major discharge at Kilauea would be much more rapid than
a similar settling of the thick roof over the main, probably narrower
and more fissure-like chamber beneath Mokuaweoweo.

9. Finally, the laccolith ha.s been imagined with the help of an ac-
tual example. Under the Uwekahuna triangulation stiition in the wall
of the Kilauean sink, the writer found a small, but typical laccolith
which arches the basaltic flows above it, aud rests on older flat-lying

116

PROCEEDINGS OF THE AMERICAN ACADEMY.

flows. (Figure 15.) This body, shown in complete section, is only about
150 meters long by 18 meters in thickness in the middle, thickest part.
Its roof, still essentially unaffected by erosion, is little more than
140 meters thick. The rock of this small body is holocrystalline, wehr-
litic in chemical composition, but having enough plagioclase to place it
among the ultrabasic olivine gabbros. The body shows chilled contact
phases and its injected origin cannot be questioned. We have here.

To/> o/ lA/esf IVa// of /f/'/<yc/ecf

>

Figure 15. Diagrammatic view of wall of Kilauea at the Uwekahuna sta-
tion, showing ultra-basic porphyritic gabbro injected into older volcanic lay-
ers. The "laccolith," arching the ash-beds above it, is about 150 meters in
length. About natural scale.

barring volcanic perforation of the roof, a true homologue of the laccolith
postulated to explain the peculiar history and relations of Kilauea.

In summary, we note the convergence of several independent lines of
argument in favor of the suggested hypothesis. It seems justifiable to
class Kilauea tentatively as the living vent of a still liquid satellitic
injection. We may also conclude that it is unsafe to deny, simply
because of the hydrostatic independence of the two active Hawaiian
lava columns, that a primary fluid substratum of basaltic composition
underlies the whole island.

A n Icelandic Example. — Reck has suggested that the crater of the
Hrossaborg in central Iceland is a gas-exploded opening (diatreme) in

DALY. — THE NATURE OF VOLCANIC ACTION. 117

the roof of a laccolith. The injection is of comparatively late date,
presumably Recent or Quaternary. *3

We may now briefly note other probable examples of the opening of
vents above satellitic injections. Testimony to its existence in former
geological periods and in other regions tends to strengthen belief in
the hy])othesis as imagined in this Hawaiian study.

Tertiary and OUer Vents from i>atellitic Injections. Suahian and
Scottish Examples. — As a result of his extraordinarily thorough study
of the mid-Miocene eruptions in Suabia, Branco concluded that the
Urach region is underlain by a " kuchenformige Masse," or laccolith.
In ground-plan its estimated diameters range between thirty and
forty-tive kilometers. Its position coincides with that of a very low,
but broad doming of the Jurassic strata in the Bavarian Alb, as
determined by Regelmann. Through secular erosion, the frontal
escarpment of the Alb has retreated at least twenty-three kilometers
since the volcanic epoch.

On the top of the Alb plateau are thirty-eight tuff vents ; in the
escarpment are thirty-five more, and in the " Vorland," or region
traversed by the escarpment in its southward retreat, there are fifty-
four tutf vents and five basaltic vents. Xo lava flows occurred on the
Alb, and the few lava necks have become visible because of denudation
in the "Vorland." Though the explosion funnels are still more or less
intact on the Alb, the largest of them, the Randeck "Maar," does not
exceed one kilometer in diameter. The average diameter of the 132
vents is far less. The evidence is clear as to the short life of each of
these vent.s, which Branco has made the world type of "volcanic
embryos." Their brief, almost wholly explosive activities, their distri-
bution in a cluster without reference to master fractures, and the dome-
like warping of the Jurassic beds in this region, all declare the justice
of Branco's laccolithic hypothesis. Furthermore, his discussion of ^lan-
delsloh's 340-meter boring at Neuff'en shows that the temperature
gradient in at least one part of the Urach region is abnormally high,
about ten meters per degree Centigrade. Branco regards the abnor-
mal gradient as due to the wave of heat still being conducted from the
mid-Miocene injection. This suggestion is by no means extreme and
it clearly tends to support his laccolithic hj^iothesis."* (See also p. 100.)

The peculiar abundance of small tuff-necks of Permian age in ])art3
of Scotland is subject to a similar tentative explanation. Various
memoirs of A. Geikie have made these vents famous as types of true

" H. Reck, Moniitshcr. deut. rcoI. Gcs. No. 4, I'.tlO, p. 2!«.
" W. Hranco, Schwabcn's 12."^ Vulkim-Embrj'oncn, Stuttgart, 1894. Cf.
E. Sut-as, Du3 ^Vntlitz dcr Erdc, Bd. 3, 2tc Uiilfe, 1909, p. 055.

118 PROCEEDINGS OF THE AMERICAN ACADEMY.

necks. In Fifeshire, eighty of them have been counted in an area
measuring eighteen kilometers by ten kilometers. In western Ayrshire,
sixty vents are found in an area measuring sixty by thirty kilometers,
and, of those vents, twenty are necks occurring within an area of thirty-
five square kilometers. In the great majority of cases, Geikie and his
collaborators have been unable to find any connection between the
positions of the necks and lines of dislocation. The Carboniferous
strata have suffered sieve-like perforation like that of the Jurassic beds
in Suabia. In each of the Scottish districts, the lower part of the very
thick Carboniferous sedimentary series carries numerous thick sills of
dolerite. These sills are mapped as chiefly Carboniferous in date, but
Geikie thinks that some of the Fifeshire sills at least are Permian.
The steady association of tuff-neck and sill in the Scottish shires
scarcely looks accidental.

Gas emanations from the magma forming these actual intrusives or
similar ones occurring in the underlying pre-Carboniferous formations,
together with the possible emanation of gas from the heated country-
rock, would seem to be competent to explain most of the tuff- necks.
Explosive drilling (diatremes) and gas-fluxing might in turn dominate
in the opening of the vents. The total activity must be small, because
each gas-emitting or lava-emitting chamber was small.

The list of districts where the writer suspects secondary vulcanism
includes also the area of necks in Noss Sound, Shetland. ^^ These are
small and the volcanic throats are filled with a coarse agglomerate
of sandstone and shale. Peach and Home infer that the vents never
emitted any streams of lava.^® The eruptivity is referred to the Lower
Old Red Sandstone period. The date may be nearly the same as that
of the injection or the thick sills and dikes which abound in the Noss
Sound region.

A Necessary Division of Central Vents. — It is obviously difficult to
devise field criteria which shall infallibly distinguish central eruptions
respectively originating in main abyssal injections and in satelhtic in-
jections. Long and strong activity, large outflow of lava, and align-
ment in chains will generally characterize the central vents of abyssal
injections. Brief activity, small output of lava, cluster grouping, and
traces of surface deformation in the region are the expected features
of the central vents of satellitic injections. As one or more of these
features is absent or is obscured, the classification is hard to apply.

'^ A. Geikie, Quart. Jour. Geol. Soc. London. Presidential Address, 48,
95 (1892).

" B. N. Peach and J. Home, Trans. Roy. Soc. Edinburgh, 32, 359 (1884),
and 28, 418 (1878).

DALY. — THE NATURE OF VOLCANIC ACTION. 119

The chief object of the foregoing discussion has been, however, not
to propose a division directly useful in field work, so much as to erect
a fence over which speculation about the earth's interior cannot pass.
The best way to check mischievous speculation is to advance bene-
ficent speculation, founded on all the known facts. For example, the
bold statement that there can be no magmatic substratum beneath
a district bearing two simultaneously active lava columns of ditfering
heights can no longer be made without an investigation of their nature
as " principal " vents (abyssal injections) or " subordinate " vents
(satellitic injections). The formal classification is of positive use in
recognizing a mechanism by which the petrographic contrast of the
lavas from neighboring vents may have originated. If two of these are
opened above different satellitic injections, the chances are good that
the magmatic histories of the injections will be different ; their emanat-
ing lavas would diverge in chemical type according to the progress
respectively made in the formation of syntectic and differentiated
magmas.

Some " subordinate " vents are monogenetic in Stiibel's sense, and
there are a few analogies between the system of vulcanism here sug-
gested and that elaborated by the illustrious German. But the writer
cannot agree with Stiibel's principal conclusion as to the motor power
in vulcanism, and entirely fails to find geologic or petrologic evidence
for the existence of his " Panzerdecke."

General Summ.\ry.

The general h}T)othesis briefly outlined in the present paper assumes,
by sanction of the facts of general geology, that the earth is exteriorly
composed of successive shells of density increasing with depth. Be-
neath the interrupted sedimentary shell is a continuous solid "gran-
itic " shell, and still deeper, an eruptible basaltic shell or substratum.
All igneous action, since an early pre-Cambrian period, is the result of
the mechanical intrusion of the substratum basalt into the overlying
shell. This fundamental process is specifically called " abyssal injic-
tion." It is not a hypothetical process, but one which is clearly ap-
parent in the chemistry and field relations of igneous rocks. The
conditions leading to abyssal injection form a subject of great theoret-
ical difficulty, but the discovery of the e.xact medianism is not essen-
tial to the jjresented explanation of volcanoes. Nor is it necessary to
decide on the degree of viscosity characterizing the basaltic substratum,
although it is pointed out, once again, that the observed small amount
of deformation of this planet under cosmical stresses does not prove

120 PROCEEDINGS OF THE AMERICAN ACADEMY.

that the substratum is crystallized. The central thesis of this paper
is that all vulcanism is a consequence of abyssal injection, or in other
words, that from the date of the oldest known pre-Cambrian lavas,
every volcanic vent has been opened because of a preliminary mechani-
cal intrusion of molten basalt into the acid earth-shell.

Emphasis is laid on the absolute necessity of classifying the gases
and vapors which do important work at volcanic vents. These are
either magmatic or phreatic in origin. The magmatic volatile fluids
are subdivided into juvenile and " resurgent " ; the j^hreatic fluids into
vadme and connate. Each of these classes may be important in the
djiiamics of volcanic explosion ; on the other hand, the juvenile mag-
matic gases are assuredly the most important in keeping a volcanic
vent alive.

Besides fissure eruptions and central eruptions, the writer recognizes
a class of vents not usually considered in treatises on vulcanism. This
third kind of volcanic action maybe caWed foundering e7'uptio?i ; the
hypothesis is presented that some batholiths have swallowed up parts
of their roofs, thus directly exposing a large area of each batholith to
the sky.

This paper is chiefly concerned with the problem of central eruptions.
They are of two main classes. In the ^' jmncipal " class, each vent
represents emanations from a main abyssal injection ; in the other,
^'^subordinate," class, each vent originates over a magmatic body (lac-
colith, sheet, etc.) which is satellitic with respect to a main abyssal
injection. Of these two classes, " principal " volcanoes must, on the
average, be the more intense in activity, of longer life, more productive
of lava-flows, and more clearly related to crustal fissures. The facts
of the field suggest that Kilauea is a " subordinate " volcano. Terti-
ary and Paleozoic examples are probably represented in Suabia and
Scotland. The localization of central vents and their very common
aligiunent are explained by the principle of abyssal injection. Lack
of alignment in a group of vents is suggestive of their " subordinate "
origin. In the nature of the case, " subordinate " vents must, in their
activities, show a high degree of independence of one another and of
neighboring " principal " vents.

Continued eruption at a central vent is a heat problem. The pri-
mary heat of its abyssal injection is not the only source of thermal
supply. A leading place in the theory should be kept for the sujiply
due to chemical reactions among the primary constituents of the in-
jected magma. Abyssal injection means an enormous change in the
pressure conditions of the magma. As a result, the juvenile gases rise
toward the top of the magma chamber. They are concentrated in the

DALY. — THE NATURE OF VOLCANIC ACTION. 121

actual volcanic pipe and, according to the law of mass-action, exother-
mic reactions on a large scale are to be expected. The possibility that
energy was potentialized in the primitive basaltic substratmn by the
formation of dissolved eudothermic compounds, like cyanogen, ozone,
hydrogen peroxide, etc., is indicated. In consequence of changes in
pressure and temperature, due to injection, the dissociation of those
compounds and the formation of new, stable compounds formed partly
or wholly from their elements, give a double source of heat in the mag-
matic column. The heats of formation for the probable reactions are so
great that small masses of juvenile gas might furnish a relatively large
supply of heat. Though it is at present impossible to estimate the
fraction of the total volcanic heat due to chemical reactions, a working
philosophy of vulcanism should give due regard to the hypothesis that
a central vent is a true furnace.

Using Siegl's recent results from experiments, the writer has calcu-
lated the approximate rate of heat loss through radiation at an active
crater. The loss by radiation occurs, in general, at a much faster rate
than the heat loss by conduction into the walls of the vent for a depth
of many kilometers. The methods of the transfer of heat from the
depths are discussed.

The principle of " two-phase convection " is concluded to be essential
to the maintenance of prolonged activity at central vents. This con-
ception is illustrated by the analogy of solid spheres moving, under
gravity, in viscous fluids.

Explanation is offered for the dormancy and related periodicity of
certain vents ; for the typical shape of such a vent, and for its com-
paratively small size. These features, when coupled with long persis-
tence in activity, are chiefly dependent on two-phase convection.
Since the latter process is, in its turn, dependent on the rise of gases
in the magma chamber, this general conception of central eruptions is
called the gai^-fiuxlng hijjfotke!^'is.

The petrographic variety of lavas is to be largely explained on prin-
ciples which have been demonstrated in plutonic geology. The lavas
emitted at central vents may be : primary basalt ; differentiates of pure
primary basalt ; syntectic magmas, i. e. those produced by the solution
of foreign rock in primary basalt ; or differentiates of syntectic mag-
mas. The petrographic diversity in the lavas of neighboring volcanoes
becomes better understood through the recognition of the two ("prin-
cipal " and "subordinate ") classes of central vents.

The explosiveness of volcanoes is a necessary step in tiie march of
events following abyssal injection. The inciting cause is to be sought
in the tension of resurgent gas as well as of juvenile gas. Progress in

122 PROCEEDINGS OF THE AMERICAN ACADEMY.

magmatic differentiation tends to favor explosiveness to an important
degree. Magmatic and phreatic explosions must be distinguished if
the tangle of vulcanological facts is to be unravelled. Though the
rise of hot magma into rocks charged with vadose or connate water
does often cause explosion, the steam-pressure produced by such
volatilized water can no more be regarded as the cause of vulcanism
than is the boiling of a kettle the cause of the heat in the stove.
The formation of the magma column, extending through the earth's
" granitic " and sedimentary shells to the surface, is the crucial prob-
lem. It is obviously a mere matter of detail whether or not the coun-
try-rocks at the upper end of the magmatic column are wet and
therefore explosive.

The facts of volcanic geology seem, therefore, to co-operate with the
facts of plutonic geology in showing that the essential process in igne-
ous action on this planet is the rise of basaltic magma from the uni-
versal substratum along abyssal fissures in the earth's acid shell. The
whole group of conceptions emphasized in this paper may be summar-
ized in the name " substratum-Injection hypothesis."

Massachusetts Institute of Technology,
Boston, Massachusetts.

PLATE I.

A. Panoramic photograph of Halemaumau on January 13, 1910, with
Rlauna Loa in the background. The nearly circular lake was about 200 me-
ters in diameter; its surface was estimated to be about 25 meters below the
rim of the crater. Copjright by E. Moses, Hilo.

B. Panoramic photograph of Halemaumau on February 20, 1910. Lake
level fallen about 30 meters below the surface of the "black ledge" in the
foreground. Copyright by E. Moses, Hilo.

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PLATE II.

A. Halemaumau, the crater in the Kilauean sink, taken from the Uweka-
huna triangulation station by H. E. Wilson, Aug. 29, 1908. Diameter of
erater about 500 meters.

B. The lava lake at Kilauea, taken at night (July, 1909) with an exposure
of somewhat less than one quarter of a second, showing an outburst of " Old
Faithful," an intensely luminous cave in the background, and a few of the
brighter cracks in the " scum " on the lake.

Daly.— The Nature of Volcanic Action.

Plate II, A.

hm

Plate II, B

Proc. Amer. Acad. Arts and Sciences. Vol. XLVII.

PLATE III.

The largest of the Puna pit-craters in Hawaii. The plain is a frozen lava
lake, the bottom of which is indicated by the inked line. Beneath that mas-
sive lava is old talus material, exposed in the fault-scarp of the foreground,
which shows a maximum thickness of 60 meters for the lava prism. The con-
duit which fed this lake was probably at the deep hole overlooked by the fault
cliff of the middle foreground. The lava plain is about one kilometer in
length.

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PLATE IV.

A. One of the small pit-craters of the Puna district of Hawaii. It is a pipe
fluxed through the old, flat-lying lava of the Mauna Loa (fluent) type. The
crater is about 175 meters in diameter.

B. Cinder cones from 100 to 200 meters or more in height, from summit of
the highest cinder cone on Mauna Kea, looking northeast.

Daly. — The Nature of Vet

\r~ A /"■ T'r* •

Plate IV, A

Plate IV, B

Proc. Amer. Acad. Arts and Sciences. Vol. XLVII.

I

PLATE V.

A. Typical pahoehoe lava of Hawaii. About four-fifths natural size.

B. A common phase of the aa lava of Hawaii. About four-fifths natural

size.

Daly —The Nature of Volcanic Action

Plate V, A

Plate V, B

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Proc. amer. ACAD. Arts ano bciENCEs. vol. XLVll.

Proceedings of the American Academy of Arts and Sciences.
Vol. XLVII. No. 4. — July, 1911.

THE PEGMATITES OF THE RIEBEC KIT E-AEGI RITE

GRAMTE OF QilSCY, MASS., U. S. A.; THEIR

STRUCTURE, MINERALS, AXD ORIGIN .

By Chables H. Warren and Charles Palache.

With Three Plates.

THE PEGMATITES OF THE RIEBECKITE-AEGIRITE

GRANITE OF QUINCY, MASS., U. S. A. ; THEIR

STRUCTURE, MINER.\LS, AND ORIGIN.

Bt Chakles H. Warhen and Charles Palache.

Table of Contents.

Introductory 125

Part I. The Enclosing Granite 120

Occurrences of Pegmatite in the Area 127

Pegmatite-pipe of the Ballou Quarry, North Common Hill, Quincy , . 129
Pegmatite-pipes of the Fallon Quarry, " " " " 132

Discussion Relating to the Chemical Composition, Sequence of Crj'staliz-

ation, and Mode of Origin of the Pegmatite-Pipea 143

Part II. Special notes of the minerals of the Quincy-granite pegmatites ;

quartz; the feldspars; inclusions in the feldspars; riebeckite; crocidolite

and the needle-like hornblende; aegirite; parisite; ilmenite; octahedrite;

fluorite ; calcite ; wulfenite 147

Introductory.

The general geologic features of the area of riebeckite-aegirite rocks
which have an exten.sive development a few miles south of Boston in
the city of Quincy, and to the west of Quincy, in what is known as the
Blue Hill reservation, have been brought most fully to the attention of
geologists by Professor W. 0. Crosby in a well-known memoir. ^ Taken
as a whole the igneous rocks of this area form an intrusive mass of
rudely elliptical outline measuring some H miles in length by 2 to 3
in breadth. They are intru.sive into Cambrian strata and are quite
certainly precarboniferous. They consist essentially of granite, exten-
sive developments of granite-porphjTy and quartz-alkali-feldspar-por-
pbyry, the two last forming a cover over the granite ; nielano and
leucocratic ditTerentiation products ; and large masses of apo-rhyolite,
intrusive through the other rocks. On account of the economic im-
portance of the Quincy granite it has received considerable attention
from petrographers, and of it alone we have a somewhat full petro-
graphical description.* Of the other rocks of the area, we have as yet

^ The IJlue Hill Complex, Boston Soc. Nat. Historv, Occas. Papers, Vol. 4.

« See particularly T. X. Dale, Bull. U. S. Geol. Sur., No. 351. Dr. Dale,
besides giving a description of the granite, gives abo the more important
references to the literature of this region.

126 PROCEEDINGS OF THE AMERICAN ACADEMY.

no adequate petrographical description ; but work is now in progress
which it is hoped may soon make good this deficiency.

Pegmatitic developments, so common in many granites, were almost
unknown in the Quincy granite until some few years ago a mass of
pegmatite was discovered in one of the quarries and later two other
pegmatites were exposed in another quarry. These pegmatites possess
so many features of unusual interest, structurally and mineralogically,
both in themselves and in their relations to the enclosing granite, that
it has been thought well to publish a detailed description of them ; and
with this task the present paper is concerned.

Part I. The Enclosing Granite.
Before taking up the detailed description of the pegmatites it will be
appropriate to give a very brief summary of the important characters
of the enclosing granite. In texture it is equi-granular, hypauto-
morphic to xenomorphic and of medium to coarse grain. Mineralogi-
cally it consists of albite-microcline perthite, quartz, riebeckite with
related alkali -hornblendes as yet not exactly determined, and aegirite,
with zircon, ilmenite or magnetite, and fluorite as the chief accessories.
The characteristics of the various minerals including their textural
relations to each other, are quite similar to those of the main part of
the pegmatites and it will be unnecessary to go into a detailed descrip-
tion of them here. It may be remarked that the rock shows evidence
of having suffered from movements, the minerals being sometimes con-
siderably disturbed or even crushed and recrystallized. The granite
enclosing the Ballon and Fallon quarry pegmatites is practically
identical with that in the adjoining Hard wick quarry of which Dr.
H. S. Washington has given us a chemical analysis ^ which is here
reproduced.

SiOa

73.93

TiO.

.18

AI2O3

12.29

Fe^Os

2.91

FeO

1.55

MnO

trace

MgO

.04

CaO

.31

Na^O

4.66

K,0

4.63

H,0

.41

100.91

3 Am. Jour. Sci., 6, 181 (1898).

WARREX AND PALACHE. — QUIXCY PEGMATITES. 127

For a rock so high in silica the iron is notably high ; the alkalies are
also high, particularly the soda, and account for the abundant soda-
iron amphibole and pyroxene present in the rock. MgO and CaO are
very low. At least one third of the lime is present as calcite.

Occurrences of Pegmatite in the Quincy-Blue Hill Area.

Up to the present time the following pegmatites have been noted in
the area : 1st. Crossing the top of Rattlesnake Hill (eas^cent^al part
of the area) in a nearly E. W. direction, is a narrow, dike-like vein of
pegmatite. It has been traced for about 60 feet and varies from H to
10 inches in width. Structurally it is somewhat similar to the pegmatite
pijies to be described beyond, having on both margins a zone of fine
graphic-granite succeeded toward the center by rather coarse feldspar
and quartz containing riebeckite. The center contains a few small
crystal pockets and occasional masses of quartz. Another smaller and
less regular vein of similar character occurs nearby.

2nd. On the low hill lying south of North Common Hill, Quincy, and
just east of the railroad near Pine Hill on the top near its southern
brow, are several veins and irregular spots of pegmatitic character.
The granite near the top and on the steep southern slope of the hill
is capped by a fine-grained granitic rock with a strong tendency toward
a porphyritic texture. It dips gently to the south. It is in sharp
contact with the granite and along the contact is frequently a rather
abundant and coarse-grained development of riebeckite crystals. A
few feet north, and underneath the contact in the granite, is an irregular
streak of fine-grained granitic rock which contains streaks of much
coarser quartz, feldspar, and riebeckite. Its width will average in the
neighborhood of two feet and its length, while considerable, cannot be
closely determined. While this may be a dike it may also be a detached
piece of the overlying fine-grained rock. Its exact nature has not yet
been determined. The granite in several places near the contact shows
a local coarsening of the grain forming pegmatitic spots made conspic-
uous by presence of long black riebeckite crystals. Several vein or
dike-like streaks of coarse texture also intersect the granite here. The
smaller ones vary from one to about four inches in thickness, and are
more or less irregular in course, and of only a few feet or yards in
length. They consist essentially of feldspar, the usual microcline-
microperthite albite, riebeckite, and (juartz, and are for the most part
considerably coarser in grain than the granite, but also contain a vari-
able amount of fine granitic material. This sometimes forms a streak
along the margin and again has an irregular distribution through the

128 PROCEEDINGS OF THE AMERICAN ACADEMY.

coarser material. The largest vein lies some ten yards north of the
contact mentioned and has been traced for at least 75 yards in a nearly
E. W. direction. The maximum width of this vein is about 12
inches. Along its strike, at least to the east, in which direction it is
best exposed, it tapers to two or three inches in width. Its contacts
are well defined, but are in the nature of a sudden coarsening of the
granite. Its structure is symmetrical and indicates successive stages
of formation. First come bands of coarse material 2 to 5 inches in
width. This consists essentially of microperthite, albite, quartz, and
riebeckite. The riebeckite is very conspicuous, suggesting tourmaline
at first sight, and is the most abundant mineral present. While many
of the riebeckite prisms are of small size, the average will measure from
1 to 1 i cm. thick and perhaps 5 cm. long. Many crystals are much
larger, measuring 1 to 1^ cm. thick and 10 to 12 cm. long. There is a
strong suggestion that there was originally an orientation of these
normal to the walls, although they now lie at random and occasionally
parallel to them. Although they frequently include feldspar grains,
sometimes arranged symmetrically to their own structure, and are
deeply indented (or corroded) about the margins, they nevertheless
commonly show a fairly good crystal cross-section consisting of w, 110
and h, 010. They are commonly fractured and the fractures are filled
with fine-grained quartz and feldspar. This band is succeeded by a
narrow gray streak of much finer grained (1 to 2 mm.) which in turn
is followed by a narrow (1-2 cm.) streak of a light brown color, of
somewhat coarser grain than the preceding. In the gray streak the
riebeckite crystals lie irregularly or, if an)i;hing, show a tendency to
stand normal to the contact. In the central streak there is a marked
orientation parallel to the contact. The microscope shows that this
portion of the vein was probably undergoing movement during the
process of crystallization. The larger grains are much disturbed in
structure, broken, crushed, recrystallized particularly about the margins,
and are surrounded by very fine material consisting largely of albite or
quartz grains with shreds and particles of riebeckite. Fluorite, ilmenite
(or magnetite) and zircon are accessories. There has been considerable
kaolinization, and ferruginous decomposition products and carbonates
are often present. Except for the tendency of the riebeckite to develop
rough prismatic outlines in the prism zone, the minerals are xeno-
m Orphic. Aegirite is entirely wanting. It may be noted that the
enclosing granite here shows very little aegirite.

These pegmatitic developments are entirely different in character
from those to be described later and certainly have a somewhat differ-
ent origin. While no positive conclusion has yet been reached regard-

WARREX AND PALACHE. — QUIXCV PEGMATITES. 129

ing them, they are believed to be closely connected in their manner of
origin with the seams and veinlets occurring elsewhere in the granite
which are rich in riebeckite. The formation of these appears to be
connected with a period of movement attendeti by fracturing of the
granite and followed by a heading up of the fractures with granitic
material. (See general discu.s.sion at the end of Part I.)

3rd. Three masses of pegmatite, pipe-like in form, one located in
Hallou's and the other two in Fallon's quarry, both (juarries being clo.se
together on the south central jxjrtion of N(jrth Common Hill, (^uincy.
These pipes are, up to date, the only im])ortant pegmatites of the
Quincy area and are the special subject of this paper.

Occasional small patches of coarser texture than the granite occur in
several places in the area. Quite recently several have been found a
little to the east of the Balluu (juarry and just west of the Hardwick
quarry. They are interesting because of a considerable content of
molybdenite segregated about their margins.

The Pegmatite of the Ballou Quarry, North Common Hill,

QUINCY.

The pegmatite in the Ballou ([uarry was first brought to the atten-
tion of mineralogists in l.s'.io, at which time it was examined by Dr.
Palache. In 1 *.>(»« a short description of it was published by Dr. Dale
(Bull. r. S. (i. S., No. 45:1 p. 4'J). Several handsome .sj)ecimens were
cut from it and polished by Mr. F. Wesley Fuller of West Quincy, one
of the finest, a complete section, now in the mineralogical collection of
Harvard University, being reproduced in Plate 1, Figure 12.

The pegmatite was encountered at a depth of something like KK) feet,
and its downward extension, covered by slide material, still remains
in the bottom of the i^uarry. Its position is nearly vertical. Some
twenty feet of it have been removed, and while its depth is of course
largely conjectural, it seems .safe to assume that it is at least 40 or 50 feet.
Its form is that of a pipe, in places nearly cylindrical and again rudely
lenticular in cross-section with small, irregular branches. It is always
concentric in structure and sometimes shows an indistinct radial
arrangement of its minerals from the margin inward. Its three shells
or zones, although (juite irregular in outline and width and intimately
blended where they i)ass int<j one another, are nevertheless fairly dis-
tinct ; likewise the contiict with the granite is blended although the
change fnjm one to the other is sudden. The outer zone is chartlc-
terized by being considerably darker in color than the granite about
it. It is much heavier on one side of the pipe than the other. Its

130 PROCEEDINGS OF THE .AJMERICAN ACADEMY.

width is here from 2 to 5 inches and it is marked toward the granite
by a greater segregation of dark constituents, chiefly rather slender
aegirite or riebeckite crystals. These are arranged to some extent
parallel to the margin. The same sort of segregation marks also
the inner margin. Between these, the rock in texture and composi-
tion resembles closely the granite except that the riebeckite and
aegirite are considerably more abundant and the mineral grains are all
of larger size. The proportion of aegirite to riebeckite is also greater
than in the granite. On one side of the pipe the dark margin is
less prominent, the whole zone having practically shrunk to an irreg-
ular streak of granitic material in which the dark constituents are very
abundant, particularly aegirite.

As a rule the next zone is an irregular one, 1 to 2 inches wide, of fine
graphic-granite, containing a few prisms of riebeckite and aegirite. It
is the least clearly defined of the zones and passes almost imperceptibly
into the main part of the pegmatite. In places the graphic-granite
seems to be almost or quite wanting and its place is occupied either
by the coarse pegmatite or by a fine-grained mixture of microperthite,
quartz, aegirite and a little riebeckite. The main portion consists
essentially of a pegmatite or coarse-grained, aegirite granite, carrying
some riebeckite, abundant accessory zircon, fluorite, ilmenite, and
smaller amounts of other minerals including parisite. The feldspars
are an albite-microcline-microperthite of a pale greenish color except
where reddish from iron stains. Toward the center where they are
the largest, they measure as much as 2 by 2.5 cm. They contain
aegirite and riebeckite microlites and black inclusions, also the minute
cavities common to all the feldspar of the granite and pegmatites.
The quartz, in amount the next mineral present, is without crystal
form. Its grains are, except near the center, on the average smaller
than the feldspar and of a grayish to white semi-translucent variety.
Toward the center the quartz is coarser and more abundant, and at
intervals along the length of the pipe, it forms masses two inches or
more in thickness and several inches long. In fact the quartz forms
a more or less well-defined central core. The aegirite, besides occurring
in the form of many small, light-green grains and prisms, forms also
abundant, large prismatic individuals of a more or less composite
character. These frequently measure 1 cm. in width and 2 or 3 cm. in
length, are dark green in color, and form a very striking characteristic
of the polished specimens. Riebeckite forms occasional large crystals
always more or less completely enclosed by a parallel growth of aegirite.
Riebeckite is also usually intergrown in the aegirite crystals and com-
monly forms a sort of a central core in many of the crystals. These

WARREX AND PAL-\CUE. — QUINCY PEGMATITES. 131

should in fact be properly termed aegirite-riebeckite crystals. They
often contain granular masses of dark purple tiuorit© mixed with zircon,
ilmenite, and quartz, besides decomposition products, chiefly ferrugi-
nous in character, which are apt to discolor that portion of the crystal
in which they occur. With the coarser material of this zone is
more or less fine-grained material. This corresponds to the more
abundant fine material to be noted later in connection with the descrip-
tion of the Fallon quarry pegmatites, and consists largely of quartz,
microcline, aegirite, zircon, tluorite, ilmenite, a few grains of a nearly
colorless, isotropic mineral of very high refractive index thought to
be beckelite (see later), besides various secondary products. The
larger feldspar grains lying about these fine-grained, zircon -rich areas,
are particularly apt to contain small, slender prismoid crystals of
albite which are probably later crystallizations, and are connected
with pneumatolitic processes. Parts of this fine-grained material are
very rich in zircon, and ilmenite (and hematite ?). Alteration develops
in this material (see later) a red or brownish-red stain which produces
in the rock the appearance of metallic spot^. Occasional crystals of
zircon attain macroscopic size and are well developed crystallographi-
cally. Thin sections of these zircon-rich portions show an interesting
relationship between the quartz and zircon. There is a marked ten-
dency on the part of the zircon to form granular intergrowths with
quartz. In some instances relatively large zircon grains showing
simultaneous extinctions are found enclosed in a (juartz grain. In
most ca.ses, however, both minerals are granular. The zircon tends
to form closely packed aggregates ; the grains may have a parallel
orientation, although they are often separate and show a more or less
well-defined crystal outline. The quartz also shows a tendency to
a parallel arrangement of its grains. The (juartz-zircon intergrowths
are commonly bounded as a whole by a crystal outline, apparently
that of a zircon crystal having a short prism with the unit pjTamid
termination. This outline is usually marked by a string of small
zircon grains. The quartz surrounding these areas has fi-e(iuently a
distinct orientation of its crystals per])endicular to the boundaries of
the area, a feature that, indeed, may be obscurely visible in the hand
specimen. The areas often penetrate adjoining feldspar grains and
are closely associated with aegirite. Fluorite, ilmenite, and ferrugi-
nous alteration products are also quite abundantly mixed with the
zircon and fpiartz. These zircon-cjuartz groujjs evidently belong to
the i)neumatolitic i)erio(l and represent, it is believed, zircon crystals
which subsequent to their formation sufiered more or le.ss recrystal-
lization, replacement by ({uartz, and perhaps granulation. Figure

132 PROCEEDINGS OF THE AMERICAN ACADEMY.

14, Plate 2, is a microphotograph of some of these zircon-quartz
groups.

Mr. Dale * states that these spots consist of magnetite, titanite,
epidote, zircon, allanite, fluorite, aegirite and quartz. So far as the
present investigation has shown the iron oxide is practically all
ilmenite, nor has titanite or epidote been identified in the material
at our disposal. Two or three minute, dark reddish grains with a
highly resinous lustre have been noted macroscopically, and are not
improbably allanite, though this has not been positively ascertained on
account of the very meagre amount. Ilmenite and hematite besides
the mode of occurrence noted, occur frequently in the form of tabular
crystals lying along the sides, or between the cleavages of the feldspars
and in the aegirite. The parisite has been observed to occur in crystals,
a millimeter in diameter closely associated with aegirite crystals, quartz
and fluorite, and clearly belongs, as in the other pegmatites, to the last
stage of crystallization of the pipes, and is apparently pneumatolitic in
origin. It may be noted that small amounts of galena, sphalerite,
chalcopyrite, molybdenite occur in small grains here and there through
the pegmatite. For other details relating to the minerals see the later
description of the large pipe of the Fallon quarry and the special
descriptions beyond.

The Fallon Quarry Pegmatites.

The first pegmatite discovered in the Fallon quarry outcropped at
the surface on the south rim of the quarry, where a small remnant of
it still remains. From this point the pegmatite, having a similar pipe-
like form, and quite similar otherwise to the pegmatite in the Ballou
quarry, dipped down into the granite to the north at an angle of about
45°. Following this course, it extended to a depth of about 75 feet
(vert.) and then terminated. There is now no trace of it in the bottom
of the quarry, but many fragments of it, still remaining on the dump,
show clearly its structure and composition.

The second and far more interesting pegmatite follows the same
general direction but appears to have flatter dip, and lies below and to
the south of the first. The uppermost part yet exposed appears in
the southern wall of the quarry about fifty feet below the surface.
Here it resembles the first pipe except that it is larger. Along its
downward extension, it increases in size, becomes rudely elliptical in
cross-section, the major axis being vertical, and contains centrally
toward its lower end a remarkable pocket. A few feet below the
pocket the pegmatite terminates rather abruptly. Its total length as

* Bull. U. S. Geol. Sur., No. 354, p. 50.

WARRE.V AND PALACHE. — QUI.VCY PEGMATITES.

133

now exposed is about 20 feet. The indications are that it may extend
upward into the granite toward the south for some distance.

Figure 1.

Sketch of cross-section of upper portion of the large Fallon quarry pipe.

A, outer dark colored zone 2 to 5 inches wide, finer in grain than the granite,
richer in dark silicates; both margins richer in dark silicates than the middle,
and with an arrangement of minerals parallel to the margins, a, offset in the
band.

B, zone of graphic-granite 2 to 4 inches wide. An intergrowth of microcline-
albite microperthite (GO per cent) and quartz (30 per cent) with a few scat-
tered i)risms of riebeckite. Passes almost imperceptibly into the next zone.

C, principal zone of unequal, but prevailingly coarse-grained granite or
pegmatite; contain.^ a streak of grai)hic-granite (crossed) and numerous large
crystals of riebeckite-aegirite. ci, concentration of fine zircon, quartz, aegirite
rich material next to quartz center, c^, quartz bleb (2 or 3 inches) with
penetrating aegirite prisms.

D, c<'ntral mass of quartz, grayish-white and massive, penetrated by radiat-
ing acgirito groups and large aegirite-ricbcckite cr\'stals along margins (dn)
and containing centrally masses of sulphids with fluorite (di). One foot wide
by two high, roughly.

Compare with Figure 13, Plate 1.

The concentric structure of this ma-ss is marked as in the other pij)e3,
but little if any radial structure can be seen. The section expo.sed in
the quarry wall shows that in its general characteristics it is closely

134 PROCEEDINGS OF THE AMERICAN ACADEMY.

similar to the Ballou pipe. Figure 1 is a sketch of this section and
with its legend will serve to give a general idea of the character
and arrangement of its parts. It should be noted that the demarka-
tion between the zones is not usually as sharp as those in the figure.
Figure 13, Plate 1, a photograph, gives also an idea of its structure
and appearance.

The dark marginal zone (A in the figure) is here somewhat finer in
grain than the granite and much darker in color. There is a distinct
arrangement of its minerals parallel to the margins which are also
characterized by a greater abundance of dark silicates with which are
numerous small grains of black oxides and chalcopyrite. The zone is
particularly dark, fine grained, and sharply defined about the upper
side of the pipe and in one place is sharply offset. Except in its finer
grain, the parallel arrangement of its minerals and the greater propor-
tion of dark minerals, particularly aegirite, which occurs to the ex-
clusion of the riebeckite in some of the slides examined, the rock of
this zone appears in thin section under the microscope to be much like
the granite ; the textural relations of the minerals are the same and
their composition appears to be identical.

The zone of graphic-granite (B of Figure 1) seems to be practically
continuous just inside the dark band above described and with a width
of from 2 to 4 inches passes almost imperceptibly into the main zone
of coarse granite or pegmatite within.

In the graphic-granite, individual cleavage surfaces of the feldspar
will perhaps average two to three cm. on a side. Their long direction
stands generally perpendicular to the margin. In this occurs, some-
times quite plentifully, riebeckite crystals somewhat intergrown with
aegirite. The feldspar is a microcline-albite-microperthite. As de-
termined by a Rosival measurement made on two extra-large thin
sections it makes up approximately 60 per cent of the intergrowth.
The albite appears to be slightly in excess of the microcline and always
acts as the host. It strongly predominates about the margins of the
crystals and quite generally forms practically the outside of the per-
thite crystals. The feldspar contains the same microliths of aegirite
and riebeckite, the black specks and cavities, as do those of the granite.
The contacts of the feldspars (largely the albite member) and the
quartz are mutually indented and show what has been described by
Pirsson^ as the " interdented " texture. Minute rounded grains of
quartz are common just within the feldspar along the contacts, and
suggest chains of tiny islands in appearance. The quartz contains

0 Am. J. Sci., 23, 272, 1907.

WARREN AND PALACHE. — QUIXCT PEGMATITES. 13')

minute black inclusions and fluid cavities often with moveable bubbles.
The extinction of the (juartz is usually (juite uniform, there being little
indication here of strains or crushing. The riebeckite forms rather
flat, elongated prisms (1 to 5 mm. broad by 10 to o(» mm. long), but
without terminations, the ends being always frayed or continued with
aegirite. Aegirite with the exception of the growths on the riebeckite
and the microlites in the feldspars is rather sparingly present in this
graphic-granite zone.

The zone just described passes almost imperceptibly into the next
and principal zone (C in Figure 1) whose leading characteristic is per-
haps its irregularity of grain. Running through this material in a direc-
tion parallel to the outer margin is a narrow strip of graphic-granite
(crossed in figure). It consists essentially of greenish-white crystals
of albite-microcline-microperthite ; irregular grains of semi-transparent,
grayish quartz, long black riebeckite prisms, often much intergrown
and practically always surrounded and terminated on the ends by
aegirite ; aegirite prisms and grains ; filling in the spaces between the
larger grains is a considerable amount of fine-grained material. This
may be light green in color when aegirite is abundant, but more com-
monly is brownish or brownish red. Occasional small crystal pockets
occur in this zone, and in these parisite, fluorite, ilmenite, and second-
ary riebeckite have been noted. Parisite grains have also been found
closely associated with aegirite and quartz, particularly near the quartz
center. The fine material forms a more or less continuous network
through the zone and in places forms patches of a centimeter or more
across. Toward the central quartz zone the fine material seems to in-
crease in amount and immediately about the quartz it constitutes
almost a distinct zone itself.

Under the micro.scope the fine material is seen to consist of variable
amounts of quartz, microcline with a little microperthite and albite,
aegirite, zircon and ilmenite, magnetite (?), calcite and certain poorly
defined decomposition products. The quartz and feldspar occupy
spaces of about equal size, but under crossed nicols the feldspar breaks
up into a mosaic of small equi-dimensional grains. The quartz shows
an undulatory extinction. The aegirite is abundant in the shajie of
irregular grains lying fur the most part in the (juartz areas or between
the (juartz grains and the microcline. Many of the smaller grains lie
grouped in such a manner as to suggest that they were once ])art8 of a
single crystal. Zircon is very abundant, particularly in quartz-rich
portions of the fine material, and while some of the grains will meas-
ure 1 to 2 or perhaps 3 mm. on a side and exhibit well-developed
short prisms capped by unit pyramid.s, the majority are small and ap-

13G PROCEEDINGS OF THE AMERICAN ACADEMY.

pear at least in thin section to lack sharp crystalline form. The larger
grains commonly show a fine zonal structure ; the small ones are
usually clustered, sometimes with parallel orientation and sometimes
without, but in the latter case forming a mass often suggesting a
larger crystal in outline as in the Ballou pegmatite. The zircon
also lies almost wholly in the quartz or between it and the feldspar.
Only a few grains have been noted in the microcline. Ilmenite and
perhaps magnetite (?) are abundant with the zircon and by their
alteration furnish the brownish or reddish-brown stain which often
gives these colors the surrounding grains. Calcite is also present
here, and is apt to be closely associated with the clusters of zircon,
frequently embedding them. Closely associated with the calcite and
the stained areas, sometimes quite abundantly, are several other prod-
ucts evidently secondary. One resembles chlorite. Another com-
pact yellowish material has not been identified. The zones in the
zircon crystals, particularly the outer zone, are often filled almost to
opacity by a fine light brown to red, dusty product. In spots the
smaller zircons are also more or less filled with it. What this product
is has not been determined.

The feldspar of the coarser-grained portion is the same microcline-
albite-microperthite as that in the granite. Its color is usually a pale
greenish-white, although it is sometimes reddish from the alteration of
small plates of ilmenite or hematite which occur along the cleavage
planes. The crystals are rudely rectangular in outline but always
with xenomorphic outlines towards the other minerals. In size they
vary greatly, ranging from grains 3 or 4 mm. on a side to ones 1.5 by
2 cm., rarely larger. The average probably lies about midway between
these figures. As in the granite, the albite strongly predominates
about the outside of the grains. Smaller, relatively long and narrow
shreds of albite lie in or along the margins and to some extent within
the body of the crystals. The usual included microlites of aegirite
and riebeckite as well as the minute black particles and cavities are
present. A little kaolinization has taken place in portions of the
])egmatite.

Aegirite and riebeckite are both abundant. Taking the zone as a
whole the former is the most plentiful. The riebeckite forms elongate
crystals ranging in size fi"om small grains up to large and very con-
spicuous crystals, 1 to 2 cm. in diameter and 5 to even 15 cm. in
length. The larger crystals are more abundant towards the center
and may extend out into the quartz center. Although indented by
the feldspar and often including grains of it, the riebeckite, especially
in the larger crystals, shows a tendency to develop a crystal cross-

WARREX AND PAL.\CHE. — QUINCT PEGMATITES. 137

section made up of the forms 110 and 010. Terminal planes are
wliolly wanting. Without exception the riebeckite is intergrown with
aegirite. Commonly in parallel position, though again without definite
orientation (c axis in common), the aegirite may occur (^uite at ran-
dom in the body of the riebeckite, but it is most abundant about the
outside, particularly on the ends, forming an almost or quite continu-
ous shell about the riebeckite. Indeed the ends of the riebeckite crys-
tals are usually continued as a solid mass of aegirite. The aegirite
may almost wholly replace the other mineral, there being only a core
or a few shreds of riebeckite visible. Besides this mode of occurrence
the aegirite is found scattered throughout the coarser parts of the rock
and as noted, abundantly in the finer material — and as inclusions in
the feldspar. The habit of the aegirite is distinctly toward a delicate
columnar structure parallel to the vertical axis, and when broken the
fracture is usually splintery. Often there is a marked radial arrange-
ment of the prisms or groups of prisms. This habit is especially com-
mon along the contact with the quartz center where clusters of some
size occur, the tapering aegirites extending out into the quartz. Occa-
sional separate crystals may be seen lying in the massive quartz 3 or
4 mm. in thickness and several centimeters long. In general through-
out this zone the main part of the aegirite, although clearly more
closely connected with the quartz in period of formation than with
any other mineral, appears to have to some extent preceded it, since a
tendency toward automorphic outlines is commonly observed with
reference to the quartz. Its color is prevailingly grass-green.

A commonly noted feature of the aegirite-riebeckite crystals is the
occurrence in their midst of spots consisting of dark purple tiuorite
grains, associated with ilmenite, zircon, calcite. These are often stained
with ferruginous products.

The central (quartz (D of figure) is massive in character, semi-trans-
lucent and of a grayish or grayish-white color. Like the rest of the
quartz it contains minute inclusions and cavities often with bubbles-
Masses of granular galena and sphalerite, one nearly as large as a man's
fist, also similar sized pieces of a very dark purple fiuorite occur in
places through the center of the quartz. Some of these were associated
with blue crocidolite like that found in the large pockets.

On the other and western side of the pipe, the succession of zones is
essentially the same except that they are not quite so wide.

Through the lower and thicker i)art of the pegmatite containing the
large central pocket the section differs somewhat from that given above,
is less regular, and shows sudden changes in character difiicult to de-
scribe. Going from east to west through its thickest jwirt we meet

138

PROCEEDINGS OF THE AMERICAN ACADEMY.

Figure 2.

Cross-section through the lower portion of the large Fallon quarry pipe at
a point where the central pocket has its maximum development. The ver-
tical dimension is about 10 ft., the horizontal about 6 ft.

A, dark marginal zone, similar in character to that described for Figure 1,
but as a whole somewhat less sharply defined, and, in its lower portions,
merging almost imperceptibly into the granite without.

B, main zone of the pipe showing a more or less well defined outer band
of graphic-granite with streaks and patches of the same in other parts, but
in the main consisting of an inequi-granular but prevailingly coarse mixture
of microcline-albite microperthite, quartz, large, scattered aegirite-riebeckite
crystals, aegirite, zircon, etc. Occasional quartz blebs and small crystal
pockets are also present.

C, zone consisting of a porous, inequi-granular mixture of microcline and
aegirite. This becomes exceedingly open in texture as the walls of the central
pocket are approached and exhibits beautifully free crystallizations of aegirite
and microcline on which are implanted crystals of parisite, octahedrite, and
ilmenite.

D, microlitic cavity more or less completely filled with quartz crystals, free
and attached, fluorite octahedra, fragments of all portions of the surrounding
pegmatite, except the dark margin, and the whole embedded in a closely
felted mass of beautifully fibrous, grayish-blue crocidolite.

WARREN AND PAL.\CUE. — QULNCY PEGMATITES. 139

first the dark margiual band (Zone A, Figure 2) here wider than fur-
ther south, less sharply defined, coarser, and at the lower end merging
almost imperceptibly into the surrounding granite.

As in the previous section this zone is succeeded by graphic-granite
and uneven though rather coarse granite or pegmatite forming together
a zone about 2 feet in width in its eastern and thickest portion, but
much narrower on the western side as shown in the figure (B, Figure 2).
It will be noted that in the figure a continuous band of graphic-granite
(crossed) has been indicated just inside the dark margin ; also another
strip within the zone running parallel to the boundary. This misrep-
resents the actual facts to some extent. The graphic-granite is not,
so near as could be told, entirely continuous, but is replaced at times,
either by the coarse pegmatite, or by a finer, granular rock carrying
rounded quartz grains and relatively long, slender riebeckite crystals.
Occasionally streaks of large feldspar crystals lie in this latter material
with an arrangement rudely parallel to the margins of the zone. These
variations seemed particularly strong on the western side of the pipe,
but the exact extent, however, of the graphic-granite, etc., was exceed-
ingly difficult to trace accurately and no attempt to do so has been
made in the figure. As elsewhere, the gradation of the graphic-granite
into the main rock of the pipe is almost imperceptible. The texture
and mineral composition of the main part of this zone is practically
identical with that of zone B of Figure 1, previously described.

Along a somewhat irregular surface this zone changes rather abruptly
both as to texture and mineral composition into the next zone (C of
Figure 2). This latter varies considerably in thickness and consists of
numerous, relatively large, rudely rectangular crystals of microcline
(range of size, 4 or 5 mm. by 2 or 3 cm.) with xenomorphic borders,
embedded in a groundmass consisting essentially of microcline and
aegirite, quite fine in grain and highly porous in texture. In this
groundmass the microcline usually predominates in amount although
frequently the aegirite equals or exceeds it. Quartz, while present in
the form of small grains in the groundmass, is hardly more than an
accessory. As the walls of the central pocket are approached this
rock becomes essentially a mass of rather loosely cohering, white or
cream-colored microcline crystals and very abundant, dark green to
almost black aegirite prisms and needles, the whole filled with small
ramifying pockets into which the free ends of the crystals project.
Although much of this material is rather course (centimeter) grained
there is also a large amount of fine material. The feldspar crystals,
although somewhat kaolinized in ])laces, are as a whole remarkably
fre.sh. Some crystals are deeply pitted by solvent action and where

140 PROCEEDINGS OF THE AMERICAN ACADEMY.

freely exposed, show a secondary growth of clear microcline substance.
These later growths contain abundant inclusions of minute aegirite and
riebeckite microliths, sometimes being literally crowded with them.
The central part of the crystals appear to be rather freer from inclu-
sions than the run of feldspar in the pegmatites. The aegirite occurs
crowded in between the feldspars and projects in thickly clustered
groups into the free spaces. Its crystals are of all sizes from mere
slivers up to crystals 1 cm. broad, 4 cm. thick, and 3, 4 or 10 cm.
long. The crystals show a strong tendency toward a composite sub-
radial grouping and great irregularities of development. The larger
crystals, to even a greater extent than the feldspar, show evidence of
a strong solvent action, some of them being largely eaten away or
completely honeycombed. Implanted on the surfaces of the feldspar
and original aegirite crystallizations are many beautiful, light green
patches of very minute, thickly clustered aegirite crystals of later
growth. Occasional quartz crystals occur in the pockets or are em-
bedded in the feldspar and aegirite near the walls of the main central
pocket.

Implanted on the surfaces of the feldspar and aegirite, particularly
in the pockets, are also : many slender, often richly terminated crystals
of the rare mineral jyarisite, often including or closely associated
with minute crystals of aegirite ; small quartz crystals ; minute, beauti-
fully crystallized, black octahedrites, occurring as single crystals, in
twinned couplets and in clusters ; ilmenite, in the form of minute flat
plates or in rosettes of black or grayish black color. Both the ilmenite
and octahedrite are often abundant in the cavities formed by solution
in the larger aegirite crystals. On the surfaces of the feldspar and
closely associated with the parisite, there is sometimes to be seen a
pale pink or buff coating of a material composed of tiny clusters of
exceedingly minute, feebly translucent grains. The identity of this
coating has not been determined, but it is thought to be zeolitic in
character. Some of the aegirite and feldspar is also coated with a thin,
blackish-red or brown film of iron and manganese oxides.

Inside the zonejust described is a remarkable pocket (D in Figure 2)
which is unquestionably miarolitic in character. Although a consider-
able portion had been removed when the pipe was first examined by the
writers, the evidence collected shows that it was almost certainly a
single continuous cavity of somewhat irregular contours with a maximum
width of about 2 feet, narrowing upward along its strike and broader
below than above. Its greatest depth vertically, as observed, was
about 3 feet. It was continuous with the central mass of quartz exposed
above in the quarry wall. It may be noted here, as indicated by the

WARREN AND PAL.\CIIE. — QriNCY PEGMATITES. 141

figure, that the position of the pocket is not exactly central since
the zones on the eastern side are considerably thicker than those on the
west which measure each only a few inches.

The Ctntrnl I'nckit. — The contents of the large central cavity were
most unusual in character and consisted essentially of : quartz crystals
of all sizes from exceedingly minute individuals up to great crystals, K)
cm. thick and 30 cm. long ; rock fragments of all portions of the peg-
matite except the dark marginal zone of sizes ranging from that of a
walnut up to that of a man's head ; tluorite octahedra, sometimes of
large size ; and a thickly felted mass of a delicate, grayish-blue cro-
cidolite filled with minute hair-like crystals of riebeckite. The crocido-
lite embeds, more or less completely, the quartz and rock fragments.

Many of the quartz crystals, particularly the larger ones, were at-
tached to the walls and included the microcline and aegirite crystals of
the pocket lining. Others, and possibly the greater number, were
wholly enclosed in, and enclose, the crocidolite, or were attached to the
fragments. In fact, the crocidolite is literally crowded with quartz
crystals, most of them quite small. Much of the quartz has been
strongly attacked by solvent action, the crystals being deeply etched,
pitted, and in some instances a good part of a crystal has been dissolved
away. Some of the »|uartz is coated with the same black or brownish
material noted on the aegirite crystals of the pocket lining. The
minerals of the fragments show abundant evidence of solvent action
and a later second growth. The riebeckite crystals in particular are
often deei)ly honeycombed and in the cavities thus formed are later
crystallizations of hair-like riebeckite, ilmenite, quartz, and tluorite.
Some of the broken surfaces of the fragments have received a later
growth of quartz parallel to the original quartz crystals of the fragment.
The hair-like riebeckite, often suspending minute, pierced (juartz crys-
tals, frequently form beautiful clusters on the free surfaces of the frag-
ments or in small cavities. Crystals of parisite are implanted in the
same way on the fragments. Embedded in the crocidolite are casts
of original fluorite octahedra sometimes partially filled with a mass of
riebeckite fibers and crocidolite originally contained in the tluorite.
The casts are generally discolored or partially filled by brown wax-like
material. The large riebeckite crystals of the coarse granite or peg-
matite bordering the upper portion of the central pocket also show
strong corosion. Here the usual lining of microcline and aegirite ap-
pears to have been either very thin, or more probably was broken off,
since many fragments of coarser pegmatite with aegirite and microcline
cr}'stal8 attached to one side are found among the fragments in the
pocket.

142 PROCEEDINGS OF THE AMERICAN ACADEMY.

Below and somewhat to the east of the central pocket (not shown in
the figure) and apparently continuous with the aegirite-microcline rock
surrounding the pocket, is a considerable mass of a fine-grained, light
greenish-white rock of quite unusual character. The microscope re-
solves it into : quartz, microcline, and albite, a little microperthite,
accessory zircon, ilmenite, calcite, fluorite, rarely parisite and probably
the rare-earth silicate, beckelite. The albite forms perthitic inter-
growths with the microcline only to a small extent, but occurs abun-
dantly in the form of slender, simply twinned crystals elongated
parallel to the edge 001 AOIO. In width they rarely exceed 0.06 mm.,
while the length varies from 4 to 20 times the width. These lie
clustered around the microcline grains or between them and the quartz,
often parallel to the margin and again projecting at random into them.
They also occur quite thickly scattered through the microcline crystals,
less commonly in the quartz. Their relation to the aegirite crystals is
like that of plagioclase to augite in the diabases. Where the albite
crystals lie together in parallel or sub-parallel position, their side lines
are straight, but where they cross one another, or where they touch or
penetrate microcline, quartz, or aegirite, the boundaries are sinuous and
curiously irregular. The aegirite also includes, or is indented by the
microcline.

The zircon is abundant for an accessory and lies mostly in the quartz.
It exhibits much the same features as the zircon in the fine-grained
portions of the main zone. The same is true of the calcite and ilmenite
and the same alteration products are associated with them.

Associated with the zircon in the quartz is a small amount of a min-
eral whose properties are as follows : — color, pale yellow to almost
colorless ; habit, usually in rounded grains, but occasionally in sharp
octahedra ; cleavage, occasional, as prominent cracks, thought to be
cubical ; index of refraction, very high ; isotropic. Unless this be
some new species, its properties, as enumerated, point to its being the
rare mineral, beckelite, a silicate of calcium and the cerium earths, dis-
covered and described by J. Morozewiez from Balka Wali-Tarama,
where it occurred in a dike-like apophysis of mariaupolite. The
apophysis consisted of a sugar-grained groundmass of albite con-
taining phenocrysts of nephelite and magnetite. (See Rosenbusch,
Mikroscopische Physiographie, 1905 Ed., p. 395.) The occurrence of
the parisite, also a calcium, cerium-earth mineral, in the pegmatite
perhaps supports the identification of this mineral as beckelite.

An estimate of the percentages of the main constituents by the
Rosival method, in this case only approximate, gave: quartz 26.1 per
cent, microcline 22.5 per cent, albite 35.0 per cent, aegirite 14.2

WARREN AND PAL.\CI1E. — QUINCY PEGMATITES. 143

per cent, reuiaiiuler 2.2 per cent. This shows that the comi)osition of
this rock does not probably ilepart very far from that of the j^ranite,
although texturally so radically ditVerent. Figure K) Plate III, is a
uiicrophotograph of a thin section uf the rock and will illustrate its
main features.

To what extent the texture of this rock may be original, and to what
extent due to recrystallization under pneumatolitic conditions it is dif-
ficult to say. If original, we have a striking example of the strong
contrasts of texture which may occur in a portion of a rock-magma
rich in mineralizers, but not otherwise, so far as can be determined,
very different in chemical composition. If a product of recrystallization,
we see that there has been an almost complete separation of the potash
and soda feldspars with the consetiuent destruction of the microperthite
structure, as well as other minor changes.

Chemical Composition, Se(4Uence of Cryst.a.llization, Origin.

Without an exact knowledge of the chemical composition of the peg-
matites as a whole, a thing almost impossible to obtain, it is of course
not possible to discuss with as much certainty as we could wish, the
relationships that exist between the pegmatites and the granite. A
careful consideration of the mineral composition of the two leads,
however, to the conclusion that the pegmatites are decidedly richer
than the granite in quartz, aegirite, zircon, tluorite, the rare earth
mineral, parisite, and meta,llic sulphides. The central pocket in the
Fallon quarry pipe, which was undoubtedly originally filled with water
or water vapor, leads to the conclusion that the material from which
the pegmatite formed was also richer in water or water vapor, a con-
clusion in keeping with the usual idea regarding pegmatites. Of the
constituents present in the pegmatite in excessive amounts over those
in the granite magma, the water or water vapor and the fluorine appear
to be the only ones competent to have exerted an influence strong
enough to have brought about any considerable variations in the tex-
ture of the two rocks. And after all it appears to be true in the pres-
ent case, as has been suggested for other pegmatites,® that the main
difference between the pegmatite and its granite is irregularity of tex-
ture in the former accomjjanied in jiart at least by a considerably
greater coarseness of grain. In the present wise there is also a re-
markable zonal arrangement of parts as a further distinguishing mark.

The textural relations of the minerals in the pegmatites are, up to a
certain point, identical with the granite, and sliow that a striking

• Ba-stin, Jour, of Cleol., vol. IS, No. 4, I'JIO.

144 PROCEEDINGS OF THE AMERICAN ACADEMY.

characteristic of both is the great overlapping of the periods of
crystalHzation of the minerals. In fact, if we take into consideration
the small included crystals of aegirite and riebeckite in the feldspar
and consider them as original crystallizations from the magma, we are
forced to conclude that all of the minerals have been growing during
the entire period of the solidification of the rock. This overlapping of
the crystallization periods appears to be a characteristic of rocks
of this type.^ If, on the other hand, we disregard the small in-
cluded aegirite, and riebeckites, it seems clear that the feld-
spar and riebeckite were first to individualize from the magma. If
aegirite be an original mineral, and there appears no adequate reason
to think otherwise, its period of growth must have begun well back in
that of the original riebeckite and extended beyond it. In portions of
the pegmatites and granite where aegirite predominates, or where
riebeckite is wanting, the aegirite appears to some extent contempo-
raneous with the feldspar but the greater pert is distinctly later.
Throughout the granite and the massive parts of the pegmatites, the
aegirite is closely associated with the development of the quartz as is
also the zircon. It has been generally noted in riebeckite rocks that
zircon has crystallized from first to last. In the present case, the
mineral does occur in the feldspar and riebeckite, but the bulk of it is
characteristically associated with the quartz, indicating a preference to
a late development.

Murgoci, in discussing the origin of riebeckite, in the article pre-
viously alluded to, assigns a role of the utmost importance to mineral-
izers and variations of pressure as factors controlling the formation of
riebeckite and aegirite in rocks of the Quincy type. He advances the
idea that the question as to whether riebeckite or aegirite develops in
a magma of this kind, depends entirely on variations in the pressure
and the amount of mineralizers " (Fl, Na, Ti, Zr, etc.)" obtaining, or
present at any given point in the crystallizing magma. Mineralizers
are, doubtless, a leading characteristic of such magmas, and were cer-
tainly present in the Quincy-rock magma, but the evidence thus far
available does not seem sufficient to guarantee to these mineralizers
so critical a rule. In fact the evidence gleaned from the present in-
vestigation, while it does not in any way deny to mineralizers an im-
portant role in the crystallization of the rock, seems to argue against
the hypothesis referred to. The two minerals are not dimorphous, for
they differ sharply in chemical composition. The aegirite for example,
contains, 31.86 per cent of Fe203 and 0.87 per cent FeO ; the riebeckite

' Murgoci, Am. Jour. Sci., 33, 133 (1905).

WARREX A\D PALACHE. — QUIN'CY PEGMATITES. 145

contains 14.")1 per cent of Fe2()8 and 21.43 per cent of FeO. Or the
aegirite contains 22.98 per cent of iron, the riebeckite, 26.S1 per cent, a
difference of 3.<s8 per cent. There is an even greater diff"erence in the
soda content, not to mention minor dilVerences. To convert one into
the other calls upon the mineraHzers and pressure, besides oxidizing or
reducing a considerable amount of iron, to actually aff'ect a consider-
able change in the chemical composition. It seems more reasonable to
assume that the development of one or the other of these minerals
depends primarily upon the relative concentrations at a given point of
the various constituents which go to form the minerals.

The separation, whether by actual crystallization or by some process
of molecular segregation prior to actual crystallization, of the feldspar
and a part at least of the riebeckite from the magma, had the effect of
greiitly increasing the concentration of the more volatile or li(iuid con-
stitutents, such as water, tiuorine, also silica, the aegirite radical, zircon,
etc., in the residual portions of the magma. The habit which the
minerals crystallizing from such portions of the magma might or may
have assumed, also the habit of the main part of the feldspar and
riebeckite, has been somewhat modified by movements in the rock,
either during the later stages of crystallization or subsequently, or
both. This is indicated by the straining and granulation of the quartz ;
the deorientation of the portions of the feldspar, particularly the mar-
ginal portions ; the development (recrystallization) of the smaller albite
crystals about and between the larger grains ; the frayed, granular,
broken or otherwise irregular character of the last formed riebeckite
and aegirite. Evidence of strong movements, accompanied by solvent
and crystallizing action, are to be seen in the presence of the frag-
ments in the large central pocket of the Fallon pipe, in the solution
and recrystallization recorded there, and in the many seams, now
sealed with relatively coarse riebeckite, feldspar, etc., which cross the
granite in many places ; also in the small quartz veins cutting the
granite in some of the quarries. There is also abundant outside evi-
dence that the granite has passed through profound periods of dynamic
disturbance since intrusion. It was during some period or periods of
movement^ accompanied perhaps by an increase of temperature and
possibly by a recurrence of pneumatolitic activity, that the development
of the greater number of the minute cavities and the crystallizations of
aegirite and riebeckite in the feldspar is thought to have taken place.
Their location is generally in positions most favorable to the jjonetra-
tion of solutions, viz. — along the boundaries of twinning or i)erthite
lamellae, or along cleavage directions. Other crystalliziitions of like
origin but varying habit lie about the borders of the aegirite-ricbeckite

146 PROCEEDINGS OF THE AMERICAN ACADEMY.

individuals, between the grains of broken quartz and in minute fracture
zones. By admitting this mode of origin for these crystallizations we
are at least relieved of the difficulty of explaining how the aegirite,
with an undoubted tendency to develop in the main at a late period
with or just preceding the quartz, should also have been the first se-
cretion from the magma. It simplifies the sequence of crystallization.
Future study of the porphyries, etc., associated with the granite will
doubtless throw further light on this question.

The zonal structure of the pegmatites and the mineral composition
of each shows that there was a progressive segregation of mineral-
forming compounds. In each zone, however, we notice essentially the
same sequence of crystallization as in the granite, as if such zone had
to some extent at least crystallized as an individual unit.

Following out these considerations relative to the crystallization of
the granite magma, etc, we may, perhaps, find a clue to the mode of
the formation of the pegmatite masses. The earlier compounds which
separated from the magma resulted in a gradual concentration of the
more volatile and liquid constituents and of the elements or radicals
which tend to accompany them. These, becoming segregated at certain
points, determined by unknown local factors, tended to escape by
rising through the surrounding material. In so doing they became
elongated in form by reason of the drag exerted on their margins by
the more viscous material enclosing them. Hence the pipe-like form.
This idea of movement in the pegmatitic material finds support in
the presence of the fluidal structure noted as characteristic of
parts of the dark marginal zone. This structure also suggests
that the band belongs perhaps as much to the granite as to the
pegmatite proper, as does also its texture, mineral composition, and
gradual merging into the granite through portions of its extent. The
pipe in the Ballou quarry is far below even the present surface of the
granite, nor is there any indication anywhere that these pegmatites
ever succeeded in reaching the surface. They appear to have been
imprisoned in the granite by its solidification.

While the exact process of formation of the zonal structure cannot be
accounted for with certainty with our present knowledge of the factors
determining rock differentiation and crystallization, the hypothesis
which seems to the writers to be best in accord with the observed facts
is as follows : — In the case of each pipe the entire mass of pegmatitic
material from which they developed having segregated from the gi-anite
magma as above outlined, it retained by reason of its different compo-
sition (greater per cent of water, etc.) its liquidity and power for further
differentiation, etc., and perhaps retained them even after the enclosing

WARREX AND PALACUE. — QUIXCY PEGMATITES. 147

magma had solidified. Further differentiation into more or less clearly
defined and well characterized zones then took place within this
material, possibly by a process of fractional crystallization, althou{,'h we
are inclined to believe that the differentiation preceded actual crystal-
lization and that each zone crystallized as an individual. This process
resulted in still further concentration of the silica, water, fluorine, rare-
earths, etc., toward the center of the mass resulting finally in the
(juartz centers, and, in the case of the large Fallon ([uarry pipe, of a
free space or pocket filled with a watery solution.

It may be noted here that the graphic-granite zone with its 60 per
cent feldspar and 40 per cent quartz seems to depart rather widely from
the proportions of these minerals supposed by Vogt and others to be
nearly constant and to represent a eutectic mixture. The graphic-
granite does not, so far as we can see, correspond either in its mineral
composition or in its structural relations to the rest of the pegma-
tite, to a eutectic mixture of the minerals of the pegmatite. lu
fact, not only in the present case, but in graphic-granites in general,
there appear to the writers to be serious, if not fatal, objections to their
being regarded as eutectic mixtures. The idea is at present little
more than an interesting speculation suggested by a resemblance in the
texture to that of known eutectics among metals and a crude approxi-
mation in a number of cases to a constancy in chemical composition.

At some time subsei^uent to the solidification of the pegmatite as a
whole, but while there was still liquid in the pocket containing Huorine
and some dissolved mineral matter, movements took place in the
granite which were sufiicieut to fracture the i)egmatite, fragments of
which fell into the pocket. This was followed by the period of resolu-
tion and recrystallization already noted as occurring in the pocket and
its lining and believed to have been contemporaneous with a similar
process in the massive pegmatite and the granite as well.

It is possible that some portion of the crocidolite formation may have
taken place at a later period i)erhaps even subseciuent to the formation
of the present system of joint cracks in the granite. As Dale has
jxiinted out and others ob.served, the joint cracks are commonly filled
with riebeckitic crystallizations, often crocidolitic in character.

P.\RT II. Special Notes on the Minerals of the Pegmatites.

Qiotrfz. — Crystallized (juartz is an abundant constituent of the cen-
tral pocket of the Fallon pegmatite, individual crystals reaching a length
of 30 cm. They are either smoky through included black needles of
riebeckite, pale blue from inclusions of crocidolite, or quite colorless.

148 PROCEEDINGS OF THE AMERICAN ACADEMY.

The smoky and blue crystals are invariably of simple quartz type, prism
largely developed with positive and negative rhombohedrons ; in the
crocidolite the crystals are doubly terminated. Most of these crystals
are deeply etched by solutions which have in some cases dissolved away
the whole termination leaving a ragged pitted fragment ; only occasion-
ally has the etching been of a sort to leave solution planes and such as
were seen were too rough to be measurable.

The colorless quartz crystals are of a later generation, are small and
complexly developed, the following forms having been observed ou the
one crystal measured :

m(lOTO), r(lOTl), z(OlTl), [(4.011), e(50ol), s(ll2l), x(j1(J1),
u(31il), (21S1), (53S3), (8.5.T3. 5), (3252).

The crystal measured was a right-handed one ; left-handed crystals
were equally abundant and both types are commonly twinned on the
"Dauphind law."

One very interesting phase of the development of quartz crystals is
seen on the surfaces of fractured masses of graphic-granite which have
evidently remained after fracture in a solution capable of supplying
silica. The quartz of the graphic-granite has grown outward into the
surrounding free space, the crystals parallel over considerable areas and
with good lustre and a smoky or bluish color but much etched. Some
similar but less abundant growth of feldspar and riebeckite could also
be observed on the same fragments. Almost always these fragments of
regenerated pegmatite are cemented by finely felted crocidolite and the
quartz is only revealed when the adhering fibres are removed by
vigorous scrubbing with a stiff brush.

The quartz in the central portion and in the massive parts of the
pegmatite all contains strings and sheets of inclusions other than rie-
beckite, etc. These are either minute black particles or cavities. In
the more freely developed quartz crystals of the pocket the fluid cavi-
ties and black inclusions do not seem to be as abundant and often there
are almost none at all. The cavities are exactly similar to those in the
granite except that they probably reach a larger size on the average.
In shape they are round, elliptical, pear-shaped or irregular ; rarely they
have been noted with a dihexahedral shape. The cavities commonly
contain bubbles which can often be made to move from side to side by
turning the stage of the microscope in an inclined position. The largest
cavity noted measured 0.02 mm. and the bubble 0.005 mm. Many cav-
ities may be seen from .001 to 0.010 mm. in diameter, while the bubbles
will in general range from one fifth to one third of the diameter of their
cavity. The cavities are often discolored with a ferruginous stain.

WARREN AND PALACHE. — QUINCY PEGMATITES. 149

The quartz of the massive part of the pegmatites is relatively or wholly
free from the minute microlith.s of aegirite and riebeekite so abundant
in the feldspar. It appears to have been the last mineral to develop in
the normal crystalliiuition of the pegmatite as well as in the granite,
and also to have been the last mineral to cease its growth in the sec-
ondary deposition which took place in the pocket.

The Ftkhjxirs. — MicrocUne in well formed crystals of orthoclase
habit makes up the greater part of the porous material near the great
central pocket. The crystals range from a diameter of two and a
half cm. downwards to mere crystiil specks ; they are, however, very
constant in habit presenting a remarkably cuboid form due to the
dominant development of the base, clinopinacoid, and orthodome ; prism
and unit pyramid, the only other forms found, being very subonlinate
in size. The faces are smooth and give fairly good reflections of the
goniometer signal. The albite twinning, shown by microscopic study
to be universally present is not apparent on the exterior of the crys-
tals ; its presence makes the crystals sensibly monoclinic, however,
and the measurements obtained approximate to those of orthoclase.
Well formed Baveno twins are seen in a few specimens but most of
the crystals are in clusters without apparent definite relation of the
constituent individuals. The color of the microcline is white to pale
ivory yellow. On faces of the prism, there is often a secondary
coating of colorless glassy feldspar in parallel position to the main
crystal which the microscope shows to be also microcline although its
appearance strongly suggested the growths of albite so common on
orthoclase from numerous localities.

Orientated sections, cut from the freely developed crystals of the
pocket lining and from some of the larger crystals of zone C, show that
the micnjcline is twinned after the albite law only and thus lacks the
grating structure characteristic of microcline in general. In basal
sections the twinning is .seen to be very finely j)olysynthetic. The in-
dividual lamellae appear as short strips slightly elongated parallel to
010. Their boundaries are as a rule not sharp. The two sets of
lamellae extinguish symmetrically on either side of the trace of the
twinning plane at an angle of Hi degrees (average of 12 measuromonts).
The clearer growths of later age are in parallel position to the older
crystal and in them the twinning lamellae are often longer and more
sharply defined. In the small microclines throughout the finer grained
portions of the j)ipe the twinning is usually more .sharply defined. The
extinction in oio .sections was found from the average of ten measure-
ments to be ;'» degrees. Figure 17, Plate 3, is u microphotograpli, in
polarized light, of a basal section of one of the microcline crystals from

150 PROCEEDINGS OF THE AMERICAN ACADEMY.

the pocket, and Figure 16, Plate 3, one of an approximately basal
section of a small microcline crystal in a thin section from some of the
fine-grained portion of zone C. In these figures one set of lamellae
are seen extinguished. Although there is some kaolinization, the cry-
stals are as a whole quite fresh.

The microcline of the microperthite throughout the massive parts of
the pegmatites, as well as in the enclosing granite, is also quite fresh.
The relative amounts of microcline and albite appear to be fairly con-
stant, the latter being slightly greater in amount particularly about the
margins, and hence appears as the host. The microcline strips as seen in
010 sections appear as narrow bands with somewhat irregular outlines.
They have the usual orientation, steeply inclined to the vertical axis, usu-
ally extend with fair continuity and variable width nearly across the
width of the crystal, pinching out at or near the border. In basal sections
they are commonly quite irregular in outline although they preserve
in a general way a course across the crystal parallel to the ortho-axis.
The twinning in the microcline, when present, is nearly always after the
albite law only, "gitter" structure being rare. In many crystals the
microcline strips show twinning throughout, in others a portion only of
the strips show the twinning, while again a part of one strip will be
twinned but not the remainder. There is a close similarity between
the microperthite of the Quincy granite and its pegmatites and that of
certain dike-rocks (aegirite-gorudite) from Norway. Brogger, Becke and
Kloos 8 in writing of these dike-rocks from the neighborhood of Lan-
gesundfiord, Laurvik, Fredriksvarn, Lovo, etc., note that the predomi-
nant microperthite is a microcline — plagioclase intergrowth in which
the microcline has the relations that orthoclase usually does. The
microcline departs from the usual habit of granitic microcline in that
the lack of the gitter-structure is altogether characteristic, the mineral
being often untwinned, or again twinned after the albite law only.
Microcline showing this particular habit of twinning has been termed
moir(^-microcline by Brogger to distinguish it from the more common
"gitter-microcline." The general shape of the perthite lamellae and
their manner of arrangement appears also to be much the same as in
the Quincy rocks.

The albite throughout seems to have a composition not more basic
than Ab 95 An 5. Some measurements on the smaller separate individu-
als indicate that some of it may be nearer an albite oligoclase. The al-
bite of the microperthite is characterized by its freshness and relative
freedom from included black particles and cavities. As already noted

8 Zs. f. Kr., 16, 54 et seq. (1890).

MARREX AND PAL.VCI1E. — QUIXCY PEGMATITES. 151

it usually strongly predominates about the outside of the grains, often
forming the entire margin. It is generally very finely twinned, rather
high magnifications being required for its clear definition. The twin-
ning lamellae are usually broader and stronger in the marginal parts.
Thealbite about the margins is often extended out into adjoining feld-
spar and (juartz grains, and these parts are sometimes deorientated.
Separate small crystals of albite, usually elongate in habit and finely
twinned, are commonly found about the larger feldspar grains. These
often penetrate into the adjoining crystals sometimes with sharp cr3'stal
terminations, particularly with reference to the quartz. With them are
quartz and microcline and these smaller, interstitial grains in places
form almost a groundmass for the larger crystals.

The peculiar relations of the albite to the microcline, quartz, and
aegirite in the fine-grained rock lying below the central pocket in the
Fallon pegmatite has already been described. It is especially note-
worthy that albite is lacking in innermost portions of this pegmatite
except in this fine-grained rock, and that here it is not in perthitic
intergrowth except to a slight extent.

Inclusions in the Fell spar. — The feldspar of the pegmatite as well
as the granite is remarkable for its inclusions. There appears to be
a strong tendency toward regularity in their arrangement. Thus in
sections they may be seen arranged roughly parallel to the twinning
plane, the direction taken by the perthite strips, or to cleavage direc-
tions ; again they ai)pear to he wholly without definite arrangement.
Aegirite and riebeckite microlites are both usually quite numerous,
but their relative proportions vary considerably. It has often been
observed that they are apt to be more abundant in the immediate
neighborhood of large crystals of aegirite-riebeckite, and that they
may in such ca.ses even have an orientation exactly parallel to the
large crystal. The riebeckite has the form of minute shreds or
rods rarely exceeding 0.02 mm. in width and usually many times as
long as wiile. They sometimes form clusters. Strings of small crystals
of riebeckite also occur along fractures in the feldspar. In optical char-
acter they correspond to riebeckite. Their prevailing color is a rather
light to dark blue, often more or less smuky. The aegirite microlites
vary much in size from grains whose dimensions are mciisured in
thou.sandths to those measured by a few hundredths of a millimeter.
Usually with a distinct elongation parallel to the vertical axis, they are
often curiiiusly irregular in habit. Sometimes j)articles of ditVeront
sizes and .^hapes are arranged in strings following some defniite direc-
tion through the feldsjtar. In color they are pale yellowish-green, or
yellow to almost colorless when in very small grains, a is always

152 PKOCEEDINGS OF THE AMERICAN ACADEMY.

parallel to the elongation and the extinction is very small. These
have apparently been called epidote by Dale ^ and do suggest that min-
eral in appearance as does much of the coarser aegirite of the pegma-
tites. Epidote is, so far as observed, altogether wanting, a fact quite
in keeping with the chemical character of the pegmatite.

The minute black particles, like occasional larger black grains, are
probably mostly ilmenite or magnetite ; some are hematite. They fre-
quently give rise to slight reddish stains in their immediate surround-
ings. They are more common in the microcline than in the albite.
Minute cavities are also abundant in the feldspar. These may be
round, elliptical, almost rectangular, or amoeba-like in shape. Though
sometimes partially filled with black, reddish or yellowish stains, they
do not seem to have now any other filling.

RiebecMte. — Macroscopically the riebeckite is characterized by a
black or bluish-black color, often rendered greenish by the associated
aegirite. The crystals of riebeckite are prismatic, showing only outlines
of the unit prism and occasionally a face of the clinopinacoid. Termi-
nal faces were not observed. Measurements of the prismatic cleavage
angle made on two fragments yielded identical values of 55° 5', an
angle considerably larger than that of common hornblende which is 55°
49'. A rather feeble tendency to part parallel to the base seems to be
present. With the exception of the inclusions in the feldspar and some
of the smaller crystals, the riebeckite is always intergrown with aegirite
to a greater or less extent in the manner previously described. Where
the riebeckite comes in contact with the feldspar and quartz, the two
are always to some extent intergrown and as already noted small shreds
or grains of riebeckite often lie near the contact sometimes with the
same orientation as the larger grain. Again shreds grow out from the
edge as if they were secondary growths. The riebeckite also usually
contains abundant black particles and larger black oxide grains, pre-
sumably ilmenite. Occasional grains of feldspar, fluorite, and zircon are
also included, and patches of carbonates, fluorite, ore grains, and zircon
are often seen.

The deep color and strong absorption of the mineral makes the deter-
mination of its optical properties with any precision very difficult.
This difficulty is increased by the fact that it has been found impossi-
ble after many trials to obtain entirely satisfactory sections of the min-
eral across the cleavage owing to its extreme brittleness. By the study
of finely crushed material and thin sections the following characters
have been made out :

' Loc. cit., p. 49.

WARREN AND PALACHE. — QUINCY PEGMATITES. 153

Ray near c'=a Ray // to b = c Ray near a = b

For sections 0.03 mm. For 0.03 mm. thick- For thickness un-

or under, deep blue to ness, very dark smoky der 0.03 mm., yellow,

bluish smoky green. For green to almost black. For 0.03 and over,

over 0.03 mm. nearly or brownish yellow with

quite black. a greenish shade.

Absorption a < c much greater than 6. For many sections inter-
mediate in position between the front and side pinacoids, a peculiar
dull, grayish blue (some might call this a drab or even see a violet tone
of color) is seen. This is particularly true of thin cleavage fragments.
In many sections parallel to the clinopinacoid it has been observed
that the distribution of color is not uniform, the blue being seen in
streaks parallel to the cleavage, or lying along lines crossing the cleav-
age, suggesting in appearance minute cracks along which there has
been some slight chemical change. In such cases the remainder of the
section had a dull green color. In the riebeckite from the pegmatites
at least, such variation in color does not appear to be connected with
any significant change in the chemical composition. Tests with the
sensitive tint on very thin cleavage fragments show always a negative
elongation. The extinction in 010 sections does not exceed 4 or 5 de-
grees, measured on the prismatic cleavage. Its accurate determination
is rendered difficult by the strong natural color and strong dispersion
of the mineral. A single section perpendicular to the prismatic axis
was obtained sufficiently thin to yield, in convergent light, using a
powerful illumination, a faint biaxial interference figure. The hyper-
bolae move well out of the field on rotation of the preparation, indicat-
ing a large axial angle. The axial plane bisects the acute angle of the
cleavages. This is substantiated by the interference figure obtained
from the 010 section which is clearly that of an obtuse bisectrix with
the axial-plane lying parallel to the cleavage direction. The hyper-
bolae in figures from this section are faintly colored red and blue ; also
interference brushes obtained from random sections are strongly colored
red or blue indicating a strong dispersion, the exact character of which
has not been made out. From the above it appears that the axial
plane in this rieheckitelies perpendicular to b, 010, an tmusual relation
for a hornblende, while the acute bisectrix lies inclined by not over 4
or 5 degrees to c\ and is negative. A determination of the index of
refraction for the yellow ray b, by the immersion method, gave a value
of 1.695 (sodium).

Chemical Composition. — Material for a chemical analysis was ob-
tained from a single large crystal which appeared exceptionally free

154 PROCEEDINGS OF THE AxMERICAN ACADEMY.

TABLE

I.

Nos.

1

2

3 4

5

6 7 8 9 10

Spec. Gr.

3.39

, ,

3.433

• • •• •• <• *.

Si02

51.79

50.01

49.30 49.83

49.65

45.4 52.11 51.89 52.13 51.03

TiOo

1.28

1.43

4.0

Al.,63

.68

.75^

1.34

.. 1.01

Fe.,03

14.51

28.30

30.72 14.87

17.66

16.8 20.62 19.22 19.53 17.88

FeO

21.43

9.87

7.97 18.86

19.55

22.0 16.75 17.53 21.25 21.19

MnO

1.15

.63

1.75

,. ,. ,, ^, ^,

CaO

1.28

1.32

2.75

3.16

4.2 .. .40 ..

MgO

.10

.34

.41

0.6 1.77 2.43 .22 .09

NaaO

6.15

8.79

(By diff. 8.331

7.61

6.7 (6.16) 7.71 6.26 6.41

KoO

1.10

.72

19.26 1.44

, ,

15 ..

F

.20

. ,

• • • < • • . •

H.,0-115°C.

.10

'. '. .20

• • •• .. .*

H.,0+115°C.

1.30

1.67-

'■ .. 1.58 2.362 3.9523.642

Totals ]

L01.26

99.98

97.87 100.64

99.7 .. 101.69 99.74100.24

LessO = 2F

.09

101.17»

1 Including Li20.

2 Total No. 5 and probably 8-9-10 are loss on ignition.

^ The total is too high, a fault most difficult to avoid in the laboratory
where it was made. In the summer when the windows have to be open the
dust from innumerable trains and the street causes small increments, chiefly
silica, to accumulate. — C. H. W.

* ZrOs.

No. 1. Riebeckite, from pegmatite, Fallon Quarry, North Common Hill,
Quincy, Mass., U. S. A. Analysis by Warren.

2. Riebeckite, Island of Socotra. Analysis by Sauer, Z. D. G. G., 40,

138 (1888).

3. Riebeckite, Island of Socotra. Analysis by Sauer, ibid.

4. Riebeckite, Colorado, U. S. A. Analysis by Koenig, Zs. Kr., 1, 430

(1877).

5. Riebeckite, Cape Ann, Massachusetts, U. S. A. Analysis by Dr. J. F.

McGregory. Quoted by Rosenbusch, Mikr. Phys., p. 341, from
private correspondence.

6. Riebeckite, Red Hill, New Hampshire, U. S. A. From Paisanite,

Pirsson and Washington, Am. J. Sci., 33, 439 (1907). Calculated
from the rock analysis.

7. Crocidolite, South Africa. Analysis by DoeUer, Zs. Kr., 4, 40 (1879).

8. Crocidolite, South Africa. Anah'sis by Renard and Klement, Bull.

Ac. Belg., 8, 530.

9. Crocidolite, Cumberland, Rhode Island, U. S. A, Analysis by Chester

and Cairns, Am. J. Sci., 34, 108 (1887).
10. The Same as No. 8.

WARREN AND PALACHE. — QUINCY PEGMATITES. 155

from impurities. This was broken up and carefully picked over by
hand under a powerful glass. When examined under the microscbpe
it appeared agreeably free from alteration and included grains, except
some inevitable black dust and a few black oxide particles as well as a
trace of aegirite and microcline. The average of closely agreeing dupli-
cates is given in column 1, Table I. For comparison a number of
analyses of riebeckite and crocidolite of similar composition from other
localities are reproduced in columns 2-10. Several others have been
omitted because their large content of MgO and CaO excludes them
from a close comparison with the present type.

The Quincy mineral differs rather sharply from the Socotra variety
in the relative proportions of ferric and ferrous iron, the latter being
much higher in ferric and lower in ferrous oxide. The Colorado and
Cape Ann varieties (this last is from an alkaline stock similar in many
respects to the Quincy stock and distant from it some forty miles) are
much closer in this respec'., as is also that from Red Hill, although
this contains a notable quantity of CaO. The crocidolite analyses
(7-9) show a rather closer relationship to the Quincy mineral. The
alkalies of the Socotra and Colorado minerals are also notably higher
than those of the Quincy riebeckite which, however, is nearer to the val-
ues for these oxides in the case of the Cape Ann and Red Hill mineral
and in all of the crocidolites. The water percentages are not satisfac-
tory, and at least in the case of crocidolite undoubtedly represent in part
hydroscopic water. Fluorine is probably present in all. With correc-
tions made in the waters and fluorine the agreement in the analyses
would probably be closer. For further comparison the molecular ratios
derived from the above analyses are given in Table H.

TABLE II.

Nos. 1 2345678 9 10

SiO, 0.863 0.833 0.822 0.830 0.820 0.756 0.868 0.865 0.869 0.850

FejOs + 0.097 .177 0.192 0.093 0.123 0.105 0.137 0.120 0.122 0.111

a little AI2O3

TiOj 0.015 .. .. 0.017

RO, chiefly

FeO 0.337 0.176 0.168 0.278 0.326 0.391 0.262 0.296 0.299 0.300

NasO -f- a little KjO

0.111 0.148(0.150)20.149 0.123 0.108(0.098)20.125 0.101 0.103
H2O +F 0.0821 0.089' .. 0.0833 0.128^0.2173 0.200

1 H2O above 115°. 2 By difference.

3 Total, probably loss on ignition and therefore high.

If the TiOa is deducted, with a proportionate amount of FeO to form
ilmenite, the ratios for the Quincy riebeckite (No. 1) may be appor-

156 PROCEEDINGS OF THE AMERICAN ACADEMY.

tioned as follows : — NaaFejSiiOia, 0.582 ; R^Sii O12 ; 0.834 ; SiOj left,
0.058. This may also be expressed by the ratio, Si02 : R2O8 :
(RO + R2O + H2O + F) = 8 : 0.90 : 4.76. The excess of silica is
considerable. What the cause is, is not clear. It may be due to im-
purity of the material analyzed. The potash seems rather high and
may be in error. The presence of even a little feldspar or quartz in the
sample would easily produce the apparent excess of silica as calculated.
In the cases of several of the other analyses it is necessary, in order to
make them correspond to the metasilicate formulae, to assume the
presence of a molecule, Il"Fe2Si40i2 on account of the excess of Fe203.
In any case, the ratios lack sharpness and are far from satisfactory. It
seems highly probable, however, that if the fluorine and water were
correctly determined, and the precise role which they play known
(whether they are a part of the chemical molecules or are merely held
in solid solution or both), also probably some minor changes made in the
figures for some of the other constituents, the molecular ratios of these
amphiboles would show satisfactory agreement and the formulae
would correspond quite closely to, the simple metasilicate molecules.
Table III shows the molecular ratios apportioned among the molecules
mentioned above ; also the percentages of the molecule Na2FeaSi40i2
for each of the minerals whose analyses have been given.

TABLE III.

12345678 9 10

Na2Fe:Si40i2 0.582 0.888 0.900 0.558 0.738 0.630 0.588 0.720 0.606 0.618

RFe2Si40i2 .. 0.174 0.252 0.234 .. 0.126 0.048

(R. R2)4Si40i2 0.834 0.294 0.252 0.668 0.838 0.785 0.612 0.85S 0.812 0.984

Rem'nderSiOz 0.058 0.022 0.072 0.134 0.087 .. 0.014 0.044 0.025 0.086
Per cent of

Na2Fe2Si40i2 42 68 69 43 57 44 45 55 47 47

The Quincy mineral (1), that from Colorado (4), from Cape Ann
(5), from Red Hill (6), and one of the crocidolites (8) show perhaps the
greatest similarity, although there is considerable divergence among
even these. In every one but No. 6 there is an excess of Si02. The
amount of the Na2Fe2Si40i2 radical varies from 69 per cent for the Soco-
tra mineral to 42 per cent for the Quincy variety. Six numbers, 1, 4, 6,
7, 8, 9, fall below the average which is 51.7. Statements in the literature
regarding the composition of riebeckite and crocidolite are to the effect
that they consist essentially of the radical Na2Fe2Si40i2 with varying
amounts of R4Si40i3 and analogous molecules. While the former mole-
cule is certainly essential, the above data indicate that we are not
justified in considering it the predominant molecule.

WARREN AND PALACHE. — QUINCT PEGMATITES. 157

Crocldolite and the Slender Blue or Black Amphibole Crystals of the
Pocket. — As seen under the microscope the crocidolite appears as a
tangled felt of the most exceedingly minute fibers, pale blue to almost
colorless, a lies with the elongation, the extinction is apparently
small, and the index of refraction for the ray vibrating perpen-
dicular to their length seems to be the same, as near as can be told,
as the yellow ray of the riebeckite. If the crocidolite be immersed
in water the fibers straighten out in a most remarkable manner. The
crocidolite is shot through and through with the slender black am-
phibole crystals and tiny quartz crystals. It is therefore impossible
to get pure material for analysis. Some carefully picked material,
freed from quartz, so far as possible, by hand, was analyzed for ferrous
iron and was found to contain 17.8 FeO. This figure must be much
under the true value, since considerable quartz weighed out with the
crocidolite must have been dissolved during the decomposition with
hydro-fluoric acid, and the content of hydroscopic water is undoubt-
edly large. Making allowances for these, the value for the ferrous iron
is probably close to that found in the riebeckite.

The blue or black amphibole crystals occurring in the crocidolite, in
pockets, and on exposed surfaces of the pegmatite fi'agments have the
form of elongated, relatively flat prisms, deeply striated parallel to
the elongation (parallel c') but not so far as observed, terminated with
definite planes.

The smallest of the crystals will measure in thickness but little
more than the larger crocidolite fibers. The width may in general be
said to run from 0.04 to 0.003 mm., although the larger crystals may
sometimes be observed as wide as 1.5 mm. The thickness will vary from
about one fourth to one tenth of the width. The majority of the crystals
as they lie on the flat side are opaque except at the very edges. The
pleochrism and absorption are the same as for the riebeckite and the
index of refraction for the yellowish colored ray appears to be also the
same.

Both the crocidolite and the minute prisms are believed to be near
to or identical with the riebeckite in chemical composition,

Aeg trite. — The aegirite of the central pocket is also prismatic in
development, sometimes, and especially in the smaller crystals, showing
distinct and measurable terminations. There is, however, even in the
best crystals much facetting and curvature of part of the terminal
planes, especially in those highly inclined to the vertical axis. The
faces of the prism zone are generally plane and measurements of suf-
ficient accuracy were obtained to make it clear that these crystals may
be referred satisfiactorily to the axial elements of aegirite as described

158 PROCEEDINGS OF THE AMERICAN ACADEMY.

by Brogger. As a rule the smaller the crystal the better the quality
of its faces ; the best ones were minute needles of clear green color.
Larger crystals are dark green to blackish gi-een in color and often occur
in subparallel groups, sheafe or rosette forms ; many show fractures
more or less healed or extreme bending.

Twinning on the orthopinacoid is common in larger crystals but is
invariably associated with rounding and irregularity of the terminal
planes to a degree that entirely precludes measurement.

The basal plane was not observed. The form series as a whole is
much more like that of augite than like that described as typical for
either aegirite or acmite. None of the forms supposed by Brogger to
be peculiar to those species were discovered. On this account and be-
cause several of the forms determined have not been recorded for
aegirite, since, moreover, this aegirite is shown by the analysis to be
nearer to the theoretical aegirite molecule Na2Fe2Si40i2 than any pre-
viously described, it was deemed advisable to calculate the angles of
the forms found on the basis of the axial ratio derived from these
measurements, and they are accordingly presented in the following
table together with the observed angles.

The axial ratio calculated from fifty faces of six forms on eight
crystals gives the values of the first line below, with which may be
compared the ratios of aegirite and acmite as determined by Brogger.

a b 0 P

Aegirite, Quincy 1.1044 : 1 : 0.G043 72° 27'

Aegirite, Norway, Brogger 1.0975 : 1 : 0.6009 73 09

Acmite, " " 1.0996 : 1 : 0.6012 73 11

Table of Angles of Aegirite, Quinct.

po = .5572 qo = .5762 e == .3015 ^ m = 72°27' ^^ ^^

Calculated. Measured. Limits. ' Faces, ity."

<t> p <t> P 4> P

a 100 90°00'90°00' 89°57' 90°00' 89°37'-90°04' 5 poor

b 010 00 00 90 00 00 37 90 00 1 poor

mllO 43 35 90 00 43 33 90 00 43 00 -43 55 27 good

f 310 70 42 90 00 70 26 90 00 69 56 -70 56 5 poor

u ni 55 50 47 06 55 54 47 08 55 17 -56 16 46°54'-47°31 11 good

s 111 -23 15 33 20 -23 40 33 24 1 fair

w 331 48 21 69 52 48 29 69 50 47 45 -49 13 69 36 -70 00 4 poor

A 331 -37 47 66 27 -37 46 66 42 1 poor

5 r)51 46 31 77 10 44 46 77 57 44 02 -45 31 77 30 -78 25 2 v. poor

T Tl2 -5 32 16 53 - 5 51 16 50 5 16 -6 19 16 40 -16 57 5 good

8 311 -66 44 56 50 -66 40 56 45 66 37 -66 44 2 v. poor

d 131 26 09 63 39 26 40 63 48 26 19 -26 52 63 34 -64 03 3 good

WARREN AND PALACHE. — QUINCY PEGMATITES.

159

The forms w(331), (551), (112), and d(131) are new to aegirite
although all are known on augite. The habit of the Quincy aegirite
crystal is shown by Figures 3 and 4.

The general mode of occurrence of aegirite in the massive parts of the
pegmatites has been previously described and may be briefly summarized
here as follows : — It is in almost constant association with the riebeck-
ite, either intergrown with it in the body of the crystal, or more com-

f

1

r

■ r

771

I

a

f

^ '

--

. \

m

^-L

Figure 3.

Figure 4.

monly about the margins, particularly the ends where it is usually very
strongly developed. The vertical axis is commonly parallel to that of the
riebeckite, though frequently there is no relation between the positions
of the two. This relation to the riebeckite and its common occurrence
with quartz indicates a strong preference for the late stages of crystal-
lization. Its dominant habit is toward a decided prismatic elongation
with a parallel or sub-parallel grouping of separate prisms, as has been
noted with regard to crystals in the pockets. When in quartz good
prismatic outlines are often noted, but terminations were rarely ob-
served in the sections examined. Macroscopically, the color varies
from a light, slightly yellowish green to dark, or even blackish green.
In thin sections the color is seen to vary greatly even in a single and
otherwise optically homogeneous fragment. The usual color is:

a = Pale to deep green, sometimes with a slight bluish caste :
rarely almost colorless, particularly in one part of a crystal.
b = Pale yellowish green to almost colorless.
c = Pale yellow to pale yellowish green : almost colorless.

160 PROCEEDINGS OF THE AMERICAN ACADEMY.

In many crystals the whole or a part possess a hrownish-yellow or
even reddish-yellow color. This is often most pronounced about black
oxide (ilmenite) grains and is believed to be due to a pigment stain of
ferruginous character. There at least appears to be no regularity in
the distribution of the brownish and reddish colorations, a makes
an angle of 6° with c', and other optical properties are the usual ones
for this mineral. Twins parallel to a, 100 are common. A careful
examination of aegirite from various portions of the diflFerent pegma-
tites indicates that it is identical in chemical composition throughout.

Chemical Composition. — The almost universal contamination of the
aegirite with other minerals made the obtaining of suitable material
for chemical analysis very difficult. By means of magnetic and heavy
solution separations combined with hand picking under the microscope
about three grams of material was finally obtained which showed as
impurities only a little ilmenite and a trace of octahedrite and quartz.

The analysis made in duplicate averaged as follows :

Aegirite, Fallon Quarry, North Common Hill, Quincy, Mass., U. S. A.
Analyst Warren.

Per cent. Molecular Ratios.

SiOz 51.73 0.862 0.862

TiOi 0.64 0.008 0.008

AI2O3 1.91 0.018 0.217

FeA 31.86 0.199

FeO 0.87 0.012

MnO 0.60 0.008

CaO 0.87 0.015 0.226

MgO 0.14 0.003

NaaO 11.43 0.184

K2O 0.40 0.004

H2O 0.20

F none

Total 100.65

Specific gravity at 25° C. 3.499.

Although a portion of the TiOa was probably present as TiOa (octa-
hedrite) most of it is combined with RO as ilmenite, and after deduct-
ing the TiOa and the proportionate amount of RO as ilmenite, the
combined ratios are, SiOs =0.838, RaOs = 0.217, RO + R20= 0.218 ;
or very nearly SiOa : R2O8 : RO + R2O = 4:1:1. This is almost ex-
actly the ratio of the compound (R"2R) Fe2Si40i2. So far as known to
the writers the ferrous iron is lower in this aegirite than in any hitherto
analyzed, and the composition approaches very closely to the theoretical

WARREN AND PALACHE. — QUINCY PEGMATITES.

161

composition of the compound Na2Fe2Si40i2 which is Si02 52 per cent
Fe203 34.6 per cent, Na20 13.4 per cent.

Parisite. — The occurrence of the rare fluo-carbonate of calcium and
the cerium earths, parisite, as a pneumatolitic mineral in the Quincy
pegmatites is a new and interesting one. A closely related mineral,
synchisite, associated with the barium-parisite, cordylite, has been
described by Nordenskiold ^^ and Flink ; ^^ it occurs
at Narsasuk, Greenland, implanted on feldspar and
aegirite or in cavities in pegmatite, an occurrence
identical with that at Quincy.

Parisite has been found both in the Ballou pegma-
tite where it occurs only as grains in the massive
rock, and in the Fallon pegmatite pipes where it is
relatively abundant in all parts of the pipe where
open spaces are present, implanted on the surfaces
of the microcline and aegirite crystals. It also is
found to some extent on the fragments in the central
pocket. The crystals of parisite are generally sharply
formed and of prismatic habit, ranging from ex-
tremely slender columns as much as one cm. long to
short, stout, prismatic individuals scarcely longer
than broad. The color is clear amber yellow in fresh
crystals, dull yellow to brown and opaque when
altered as it not unfrequently is. Such altered
crystals show a perfect basal cleavage and pearly Figure 5.
lustre on the base, both of which properties are entirely absent in fresh
material. The same dependence of cleavage upon chemical alteration
was found to exist upon parisite from Muso, the type locality, so that
cleavage is undoubtedly a secondary property in this mineral.

The crystals are invariably striated horizontally and show infinite
variety in the detail of individual development. They are either tri-
gonal or hexagonal in cross-section ; in the former case steep rhom-
bohedrons being dominant, in the latter second-order pyramids. In
neither case are actual prism planes more than rudimentary, the
pseudoprisms being bounded by oscillatory combination of the steeply
inclined rhombohedron or pyramid faces. The termination is gen-
erally a large and brilliant lustrous face of the pinacoid ; sometimes,
however, the relative size of this plane is much reduced by the presence
of low rhombohedrons and second-order pyramids which either slightly
truncate the edges between base and pseudoprism or may be developed

" G. For. Forh., 16, 338 (1894).

" Bull. G. Inst. Upsala, 5, 81 (1901) ; Med. om. Gronland, 14, 236 (1898).

162

PROCEEDINGS OF THE AMERICAN ACADEMY.

to such a degree as to give a pointed trigonal or pyamidal termination.
Many crystals were measured and a very complex form series was found
to be present, full details of which are to be found elsewhere. ^^ jt may
suffice to state here that parisite was found to be undoubtedly rhom-
bohedral in symmetry and to be referable to axes having the ratio
= 1 : 1.2912. The forms of most prominent occurrence are the

a

base and second-order prism, c(OOOl), a(ll20),

"

C

-f_

H

/

i J

~lJ

k

\

t J

17

r

IV

w \

Figure 6.

Figure 7.

second-order pyramids, (ll53), (5.5.TU.12), (44H9), r(22i3), (4453),
positive rhombohedrons, (4.0.1.15), (20^5), (50o4), k(202l), s(3o5l),

(10.0.T0.3), (50ol), (60^1),
negative rhombohedrons, (0.3.3.10), (0.9.^.25), (022l), (0552), (0331),

(04il), (06^1),
scalenohedron (4.2.1^.11),

Figures 5, 6, and 7 show typical combinations.

The relation of the position here adopted for the crystals of parisite
to" that formerly used (as in Dana, System, p. 290) maybe stated thus :
the former second-order pyramid series corresponds to the rhombohe-
drons of the new position; the former unit pyramid p(loTl) receives
the new symbol p(ll2l), the former second-order pyramid g(ll23)
becomes the new positive unit rhombohedron g(lOTl).

Optical Properties of Parisite. — As seen under the microscope, very
small crystals or fragments are a very pale yellow to almost colorless
and show a barely perceptible dichroism. For crystals \ mm. thick the

" Am. J. Sci., 31, 533 (1911). Zeitschr. fiir Kryst., 49 (1911).

WARREN AND PALACHE. — QUINCY PEGMATITES. 163

o> ray is bright yellow, often with a brownish tone ; the e ray is golden
yellow. The absorption is w > c slight. For crystals 1 mm. thick the
dichroism and absorption is but slightly greater. Upon alteration the
crystals become filled with a dusty product, are less transparent, and
often exhibit a brownish or brownish-red stain of varying intensity.

The indices of refraction were determined by the immersion method
using a barium-mercuric-iodide solution. The determinations were
made on a number of perfectly clear, small crystals chosen on account
of the uniform development of their prism zones ; also upon one larger
crystal (l^mm. in diam.) terminated by a perfect basal plane which
made it possible to orientate the crystal and cut a section parallel to
the prismatic axis. An attempt was made to measure the indices
directly upon this crystal by means of the Abbe refractometer but with-
out success owing to the small size of the section and its low degree of
transparency. The fine striations parallel to the edge between the
base and the prism stand out very sharply under the microscope and
make it possible to orientate the crystals with great accuracy on the
microscope stage. The values obtained with sodium light are given
below, also those heretofore given for parisite as determined by
Senarmont and those for synchisite according to Flink.

Parisite, Quincy. Parisite, Muso.
Warren. Senarmont.

Synchisite, Greenland,
Flink.

6=1.757 1.670

1.7701

w= 1.676 (± 0.002) 1.569

1.6742

0) = 0.081 0.103

0.0959

The Montana parisite, also crystals from Muso valley taken from the
mineral collection of Harvard University were tested by the immersion
method and their indices were found to correspond to the values given
for the Quincy mineral. The older values given for the Muso mineral
appear to be quite wrong. The ordinary rays for parisite and synchi-
site are almost identical. The extraordinary rays appear to differ by
0.0131. While the extraordinary ray for the Quincy mineral is prob-
ably not as accurately determined as the value for the ordinary,
the error can hardly be as great as 0.0131, and the difference between
the two minerals for this constant may be a real one.

Chemical Composition of Parisite. — About a kilo of fine-grained
material recovered from the fragile lining of the central pockets was
carefully washed and fractioned by means of screens, an electro magnet,
and heavy solutions until a fraction was obtained weighing about ten
grams and consisting largely of parisite mixed with more or less aegirite,
octahedrite, feldspar, and quartz. From this about three grams of clear

164 PROCEEDINGS OF THE AMERICAN ACADEMY.

yellow or amber colored crystals were separated by hand-picking under
a powerful lens. Aside from a slight stain in a few crystals the only
impurities visible under the microscope were minute adhering grains of
octahedrite and aegirite hardly amounting to more than a trace.

The result of the chemical analysis made on these crystals is as
follows :

Parisite,

Quincy,

Mass.

Analysist Warren.

CO2

24.16

SrO

tr.

Fluor.

6.56

NaaO

.30

CeaOg

30.94

K2O

.20

(La, Di)203

27.31

H2O

tr.

Yt^Os

tr.

Gangue

1.02

FeoOs

.32

102.21

CaO

]1.40

less 0 =
Total

2F

2.76
99.45

Spec. G. 4.320

The molecular ratios derived from the above analysis are : — CO2 :
F : II2O3 : CaO = 0.549 : 0.345 : 0.178 : 0.205. This may be written,
CO2 : F : R3O3 : CaO = 3 : 1.88 : 0.97 : 1.11 which equals very nearly
3:2: 1 : 1. This ratio leads to the formula (R"F)2 Ca(C03)3,
which is the same as that derived for the mineral by Penfield and
Warren ^^ from analyses of the mineral from the original locality, Muso
valley, U. S. of Colombia and a locality in Ravalli Co., Montana. The
chemical composition throughout of the Quincy mineral is very close
to that of the parisite from the other localities mentioned. The for-
mula also agrees with that derived for the barium -bearing mineral from
Greenland. Synchisite, although identical with parisite in its crys-
tallographic and essentially so in its optical constants and in the ele-
ments present, contains, according to the analysis of Flink, one more
molecule of calcium carbonate, the formula for the synchisite being
(R"F)2Ca2(C03)4. It is true that the two minerals differ perhaps
slightly in specific gravity and in the value for the extraordinary ray.
The relationship deserves further investigation.

For a more complete discussion of the relationship of these minerals
and the crystallography of the parisite, see a paper by Palache and
Warren.^*

Ilmenite. — Ilmenite occurs in moderate abundance in both the
Ballon and Fallon pegmatites. It appears to have been of rather late

" Am. J. Sci. 8, 21 (1899).

" Zeits. f. Kryst., 49 (1911), and Am. J. Sci., 31, 533 (1911).

WARREN" AND PALACHE. — QUINCY PEGMATITES.

165

Figure 8.

formation and is particularly associated with aegirite, as embedded
xenomorphic plates, and groups of tiny crystals implanted on crevices
of fractured aegirite crystals (Ballou quarry), and as clusters of
larger crystals upon the walls of cavities left by the destruction of
such crystals by magmatic resorption (Fallon quarry). The crystals
are small, not exceeding

a diameter of 2 mm. and |f-~~->__ C

are always very thin
tabular in habit. A dull
black coating of manga-
nese oxide commonly
gives them a lustreless
appearance, but in two specimens brilliant crystals were obtained which,
despite minute size, gave good measurements on the goniometer.
Octahedrite is almost always sparingly present with ilmenite.

The forms observed are as follows: c(OOOl), m(lOTO), a(ll2o),
5(2130),* ^ (10T9), u(10T4), f (2025), r(lOTl), f(0. 7.7.20), e(0lT2),
A(04?5),* s(022l), X(05o2),* g(0.3.3.11),* k(0.3.3.10),* 7r(ll23),
n(2243). (* New forms.)

The crystals from Ballou quarry showed the forms c, m, a, 8, r, and tt,

the prism zone being well de-
veloped and the base large and
very brilliant. The prism is
new to ilmenite. Figure 8.

Crystals from Fallon quarry
are dominantly rhombohedral,
prism faces being reduced to mere lines. The crystals measured
showed the following combinations :

1. c, 8, r, f, e, s, n.

2. c, m, 0, i, r, k. '

3. c, m, 6, r, u, e, k, tt, n.

4. c, m, 6, r, n.

5. c, 0, $, r, e, g, A, \, n.

6. c, m, 6, i, r, e, A, k, n.

7. c, u, r.

As shown in Figure 9, flat positive rhombohedrons are largely de-
veloped on these crystals, recalling the description of one (the common)
phase of " Crichtonite " from Oisans by Descloizeaux.^^ That author
considered the rhombohedrons which he measured, (10T5)and (10T9)

Figure 9.

" Mineralogie, 2, 222 (1893).

IGG PROCEEDINGS OF THE AMERICAN ACADEMY.

and (l.n.T.ll) as negative but left the determination of sign doubtful.
The second of these forms is common to all the crystals from Fallon
quarry and is certainly positive, so both the others should be likewise
so considered. Several negative rhombohedrons new to ilmenite were
observed and are based on the following data :

Form. Calculated. Measured . No. Face limits of p.

(f> p <f> p

g (0.3.5.11) 30 00' 23° 34' 30 00' 23^46' 3 23° 28' to 24° 05'
k (0. .3.5. 10) " 25 37 " 25 34 1
A (0445) " 51 59 " 51 57 2 51 53 to 52 00

\ (05o2) 30 00' 75 57 30 00' 76 06 1

Limits of <^
8 (2l50) 10 53 90 00 10 30 90 00 4 10° 36' to 11° 34

The presence on one crystal of the form f, observed before only by
Solly on a Binnenthal crystal, confirms this form. All the forms pres-
ent gave angles agreeing very closely with the values calculated from
the axial ratio of Koksharow as used by Dana.

Chemical tests on the ilmenite from both quarries revealed strong
qualitative reactions for manganese ; an analysis would be interesting
but it was not possible to separate enough of the fresh mineral for this
purpose.

Octahedrite. — Octahedrite is found chiefly in the large central pocket
of the Fallon pegmatite, generally in close association with aegirite and
often formed posterior to the alteration of that mineral since it is not
infrequently seen on the walls of hollow casts of aegirite crystals asso-
ciated with fluorite and ilmenite. Isolated crystals were also found
implanted on feldspar crystals. The crystals of octahedrite are small,
of a deep black color and of very brilliant lustre. They show only the
forms c(OOl), m(llO), p(lll), k(112), and z(113), the two last the least
common. These crystals are marked by two peculiarities ; they are in
large part of prismatic habit with the first-order prism dominant, a habit
not before described for this mineral and causing the crystals to be at
first mistaken for zircon ; and they occur in cruciform twin groups with
the form (101) as twin plane. The twins are sometimes complete inter-
penetrations of two equal crystals as shown in the figure ; sometimes
but one end of each is developed ; again a larger crystal has a much
smaller one in twin relation to it. The groups are exquisitely sharp
and leave no doubt as to the definiteness of the twinning since the two
upper faces of the unit pyramid of each crystal and the two lower,
parallel and opposite faces to these reflect the signal simultaneously in

WARREN AND PALACHE. — QUINCY PEGMATITES.

167

pairs ; thus the faces of (101) which are in zone with these unit pyramid
faces must be parallel to the twin plane.

This twin law has been observed but once before on this mineral, on
crystals from the titaniferous calcite-quartz veins of Somerville, Mass.^^
There twins were extremely rare, while here they are sufficiently
numerous to be considered characteristic for the locality. Combina-
tions of prism and unit pyramid are far the most common among these
crystals. A few, however, show the base as a tiny facet and in a few

in

m,

Figure 10.

Figure 11.

the flatter pyramids k or z replace the acute summit of the common form.
Figures 10 and 11 illustrate the habit of the octahedrite crystals.

Fluorite. — Mention has been made in preceding pages of the distri-
bution of fluorite throughout all parts of the pegmatite masses. It is
generally in small grains but near the central pocket, especially in that
part where crocidolite was abundant the fluorite individuals were larger,
one mass showing cleavage faces nine inches across having been found.
Where wholly embedded in crocidolite the fluorite crystals are automor-
phic, octahedrons up to one inch in diameter thus occurring ; they
are dull and somewhat rounded, the color a deep purple like all the
fluorite of this locality, but occasionally there is a surface layer of

*' On Octahedrite, Brookite, and Titanite from Somerville, Mass., C.
Palache, Rosenbusch Festschrift, 1906, 311.

168 PROCEEDINGS OF THE AMERICAN ACADEMY.

bluish green color due to included fibers of the blue crocidolite. The
hollow casts left by the solution of such crystals have already been
described.

In one or two cavities in the Fallon pegmatite there were seen tiny
cubes of fluorite implanted on quartz, and in another such pocket,
peculiar in containing also crystals of calcite, the cube was modified
by two hexoctahedrons which appear to be new to fluorite. The
measurements and derived symbols of these forms follow :

Calculated. Measured. Limits. Readines.

4> P 'P P </> P

( 3.10.16 m°A2' 33°07' 15°45' 33''20'

< 3.16.10 10 38 58 26 10 36 58 33 10°30'- 10°42' 58°30'- 58°36' 2
(10.16.3 32 00 80 58 32 04 81 05 31 52 - 32 16 80 50 - 81 20 4

( 259 21 48 30 54 21 01 31 15 20 45 - 21 18 31 11 - 31 19 2

< 295 12 32 61 32 12 32 61 25 12 27 - 12 37 61 23 - 61 26 2
( 592 29 03 79 00

Calcite. — Certain small pockets in the Fallon pegmatite were filled
by a final deposit of calcite. In one or two cases the calcite supplied
was insufficient to wholly fill the open space and in these cavities
calcite crystals were found showing the somewhat unusual combination
of prism and base only, m(lOTO) and c(OOOl).

Wulfenite. — Thin coatings of light yellow color as well as tiny
crystals of Wulfenite were found on smoky quartz in the crocidolite
pocket. The crystals are in part model-perfect combinations of first-
order pyramid with third-order prism, n( 111) and f(320), see Figure 6,
p. 990, Dana, System, in part cube-like combinations of a prism and
the base. The amount of wulfenite is very small and its presence is
easily accounted for by the association in the same region of the
pegmatite of molybdenite and galena.

EXPLANATION OF PLATES
PLATE L

Figure 12. Section of Ballou Pipe.

The photograph shows a block cut from the pipe through its center
about parallel to its axis (face marked A) and also across the axis (side
marked B). The diameter is a httle more than three feet. The concentra-
tion of dark sihcates about the margin is very strong. The graphic-granite
zone can hardly be distinguished from the main zone of pegmatite. The
long dark prisms, more abundant toward the center, are of aegirite-riebeckite.
The dark gray center is largely quartz. An indistinct radial structure may
be seen.

Figure 13.

This is a part section across a portion of one of the Fallon quarry
pipes. It was cut from a loose block and its exact location cannot be told.
The height of the block is about three feet, but as the section is cut some-
what obliquely the actual width of the zones is less than that shown by the
figure. D is a piece of the quartz center. C is the zone of coarse pegmatite
with its large aegirite-riebeckite prisms. B shows the graphic-granite band,
here very strongly developed. A is the marginal zone with a slight con-
centration of dark silicates along the inner margin. This band here is very
similar to the granite and probably merges gradually into it.

Compare with Figure 1, page 133.

Q

O

OQ

LU
I-
<

—I
Q.

■■.eVi:^!::V

n

6

>

X

o
>

o

z

o

LU
Of

<

!:^

<

<

Q

<

<

o
o

q;
Q.

CM
6

EXPLANATION OF PLATES
PLATE IL

Figure 14.

Microphotograph of quartz-zircon groups in the fine-grained portions of
the pegmatite pipe in the Ballou quarry. In the lower right-hand quadrant
one of these aggregates is seen with a well developed crystal outline. In this,
the dark areas are zircon, the white, quartz. The surrounding material is
quartz. Other groups above and to the left.

Crossed-nicols. Magnification about 120 diameters.

Figure 15.

Microphotograph of fine-grained rock lying just below and slightly east of
the large pocket in the Fallon quarry pegmatite. Shows small lath-shaped
albite crystals scattered through, and lying about, microcline grains. The
smooth areas are quartz. Just between the two lower quartz grains is one
of aegirite, also penetrated by the albite.

Crossed-nicols. Magnification about 120 diameters.

Warren and Palache.— Quincy Pegmatites.

Plate II

Fig. 14.

Fig. 15.
Proc. Amer. Acad. Arts and Sciences Vol. XLVII.

EXPLANATION OF PLATES.
PLATE III.

Figure 16.

Microphotograph of a small microcline crystal in the finer-grained portion
of the main pegmatite zone. The section is approximately parallel to the
base and shows twinning after the albitc law only. One set of lamellae are
in the position of extinction between crossed-nicols. Magnification about
150 diameters.

Figure 17.

Microphotograph of a basal section of microcline, cut from a freely de-
veloped crystal from the pocket. Shows twinning after the albite law only.
One set of lamellae are shown in the position of extinction between crossed-
nicols. Magnification about 350 diameters.

Warren and Palache.— Quincy Pegmatite<?.

Plate 111.

Fig. 16.

Fig. 17.
Proc. Amer. Acad. Arts and Sciences. Vol. XLVII.

Proceedings of the American Academy of Arts and Sciences.
Vol. XLVII. No. 5. — July, 1911.

CONTRIBUTIONS FROM THE CHEMICAL LABORATORY
OF HARVARD COLLEGE.

THE TRANSITION TEMPERATURES OF SODIUM

CHROMATE AS CONVENIENT FIXED

POINTS IN THERMOMETRY,

By Theodore W. Richards and George Leslie Kelley.

Investigations on Light and Heat published with Aid fbom the Rumford Fund.

CONTRIBUTIONS FROM THE CHEMICAL LABORATORY
OF HARVARD COLLEGE.

THE TRANSITION TEMPERATURES OF SODIUM CHROMATE
AS CONVENIENT FIXED POINTS IN THERMOMETRY.

By Theodore William Richabds and George Leslie Kelley.

Preeented April 12, 1911. Received April 4, 1911

Introduction.

In previous papers^ from this laboratory it has been shown that the
transition temperature of a crystallized salt is in some cases so easily
observed and so constantly maintained as to form a convenient fixed
point of reference for the scale of temperature. The cases of sodium
sulphate (32.383°) and bromide (50.674°) and manganese chloride
(58.089°) have been studied in detail and found to be very satisfactory
in these respects.

Among other substances suggested for this purpose, sodium chromate
is especially inviting because two of its transition temperatures are
near 20'', a temperature at which it is frequently desirable to verify
thermometers.

The outcome of the work on this salt described in the present paper
was entirely satisfactory, and gives promise of great practical usefulness
to those who are interested in exact thermometric measurement.
Nevertheless, the problem was not so simple as it had at first appeared.
The wealth of variety exhibited by the hydrates proved at first to be
an embarrassment of riches, and led to some preliminary confusion,
which has been happily reduced to order. Moreover, the salt is some-

^T. W. Richards, Am. J. Sci. (4), 6, 201 (1898); Richards and Churchill,
These Proceedings, 34. 277 (1899); Richards and Wells, These Proceed-
ings, 41, 435 (1906); Ibid., 38, 431 (1902); Richards and Wrede, These Pro-
ceedings, 43, 343 (1907). These five papers are all to be found in full in the
Zeitschr. fiir phys. Chem., the references being respectively 26, 690 (1898) ;
28, 313 (1899) ; 43, 465 (1903) ; 61, 313 (1908). The work on manganese
chloride was finished by Dr. Wrede and one of us at the University of Berlin.

172 PROCEEDENGS OF THE AAIERICAN ACADEMY.

what less easy to purify than the sulphate, and when it is impure,
a given percentage of impurity causes a larger error in the transition
temperature than in the case of the sulphate. This is largely because
the transition is from the dekahydrate to tetra- or hexahydrate, instead
of to anhydrous salt, so that the amount of solution formed to dissolve
the impurities is less, and therefore the concentration of the impurity
in the solution is greater. Another difficulty arises from the fact that
chromic acid is a weak acid, and hence its salts are easily capable of
absorbing acid impurities. This was shown experimentally by passing
pure carbon dioxide into the solution. Large volumes of the gas were
absorbed, and the solution became perceptibly orange because of the
formation of the dichromate. Boiling expels the gas but slowly,
because the hydrolysis increases with rise of temperature. Indeed,
a boiling solution of the purest salt is so much hydrolyzed as to be red
in color and to react strongly with phenolphthalein. Probably the
passing of pure air, or boiling at low temperature for a long time in
a partial vacuum, would be needed to displace all of the carbon dioxide,
and even this might not serve. Of course the solution of the salt ab-
sorbs hydrochloric acid and other strong acid vapors yet more easily ;
and even the dry salt, which is unaffected by carbon dioxide, is attacked
by stronger substances.

Theoretically the tendency of the solution to hydrolyze offers no ob-
jection to the use of the salt as a means of fixing a definite point on
the thermometer scale, because the Phase Rule, which determines the
definiteness of the points, does not consider the state in which the sub-
stance exists in any of the phases. The feeble nature of chromic acid
is annoying and objectionable only for the practical reason that it makes
the preparation and preservation of the pure salt more difficult. When
the salt has once been prepared in the pure state, it must be carefully
guarded in order to preserve its purity.

These difficulties, however, all disappear when the experimenter is
forewarned against them ; for easily effected precautions are capable
of surmounting them all.

Preparation of Pure Sodium Chromate.

Several methods of further purification of sodium chromate were
tried. Crystallization as the dekahydrate is of no avail as a means of
ridding the crystals of their most usual impurity, the sulphate, because
this is isomorphous with the chromate. Indeed the sulphate tends into
the crystals, leaving the mother liquor somewhat purer than before the
crystallization. The tetrahydrate is but little more satisfactory as a

RICHARDS. — TRANSITION TEMPERATURES OF SODIUM CHROMATE. 173

means of accomplishing the purification ; ten successive crystalHzations
having failed to yield a pure salt. Moreover, inconvenience arises from
the fact that it is stable under the solution only between 26° and G2.8°,
and because its solubility has only a comparatively small temperature
coefficient, the yields are small.

Attempts to prepare the salt by recrystallizing chromic anhydride
were likewise abandoned as unprofitable. The best chromic anhydride
obtainable was found to contain much sulphate, which w^as very slow
to leave during the particularly wasteful process of its crystallization.
In one case twelve successive crystallizations of a kilogram of chromic
anhydride gave only a few grams of product which still contained
traces of sulphur. These unsuccessful methods are recounted only
to save other experimenters the trouble of attempting the same
processes.

Another method which is distinctly better than the preceding is per-
haps worthy of more detailed discussion, although a still better and
much simpler procedure was afterwards devised.

The sulphate can be quickly eliminated by relying upon the very
different solubilities of silver chromate and sulphate. If a chromate is
slowly precipitated by silver nitrate in dilute solution, using not quite
enough of the precipitate to remove the chromate wholly from the solu-
tion, the precipitate contains very little sulphate. The chromate of
silver is then thoroughly washed, and easily converted into sodium
chromate by treatment with a solution of pure sodium chloride. The
presence of an excess of precipitated silver chromate ensures the absence
of all but the merest traces of chloride in the solution, if time has been
allowed for the attainment of equilibrium. If greater purity is desired,
the chromate may be reprecipitated by silver nitrate, and again treated
with pure common salt. The very appreciable quantity of silver which
the solution of sodium chromate still contains is easily precipitated by
copper wire or gauze, and the cupric chromate, being easily soluble, is
quickly eliminated upon crystallizing the sodium chromate as dekahy-
drate. It is idle to attempt to get rid of the silver chromate by crystal-
lization, since its solubility is affected about as much proportionally by
temperature as that of sodium chromate is. After the silver has been
removed, five crystallizations were enough to remove all the copper and
other impurities, and a specimen of sodium chromate was obtained
which gave every evidence of being pure.

Yet another available method, the most satisfactory one of all, de-
pends upon the fact that sodium bichromate may be easily and quickly
freed from sulphate by recrystallization. The bichromate is very solu-
ble, and possesses a moderately great change of solubility with the tern-

174 PROCEEDINGS OF THE AMERICAN ACADEMY.

perature ; 100 parts of water dissolve 162 parts of the dry salt at 100°
and 109 parts at 15°. ^ Since, however, the salt crystallizes with two
molecules of water, the actual loss on crystallization is less than would
appear from a superficial inspection of these figures. The weight of
the crystals separated fi-om a saturated solution between these two tem-
peratures from 162 grams of anhydrous salt dissolved in 100 grams of
water is easily calculated fi-om the equation :

Na^CrA ^ ^109

when a? = 87 grams. Thus more than half the salt is easily recovered
from each crystallization, and if use is made of a wider range of tem-
perature, permitted by the high saturated boiling point (139° with
solubility 210 parts to 100 of water) a still larger yield may be obtained.
Since the solubility diminishes but slightly below 15°, further cooling
is not profitable. Thus the crystallization of this salt is convenient and
efficient ; and since sodium bichromate is not isomorphous with the cor-
responding salts either of potassium or of sulphuric acid (the most prob-
able and insidious impurities) crystallization forms an admirable means
of purification. The elimination of the sulphuric acid requires only
three or four crystallizations if the crystals are separated centrifugally.
A large excess of chromic acid causes unnecessary loss, because of the very
great solubility of the trichromate,^ but a small excess is convenient,
because the elimination of the dark brownish tint of the trichromate
from the mother liquor is a convenient guide as to the purity of the
salt.

The crystallized, pure bichromate was treated with somewhat less than
the calculated amount of pure sodium carbonate, and with the help of
the excess of bichromate the carbon dioxide was easily removed by
boiling the solution during an hour. From a neutral solution all the
carbon dioxide cannot be expelled. The sodium carbonate for this
purpose should be prepared by repeatedly crystallizing the purest soda
of commerce in porcelain, or better in platinum dishes, until sulphates
and chlorides are certainly absent.

The sodium chromate containing a small amount of sodium bichro-
mate, prepared as described above, was neutralized with the help of
phenolphthalein by means of a solution of pure sodium hydroxide,
made from sodium by allowing this metal to stand in a platinum dish
in a desiccator over a dilute solution of the hydroxide.

« Stanley, Chem. News, 54, 194 (1886). 3 Ibid.

RICHARDS. — TRANSITION TEMPERATURES OF SODIUM CHROMATE. 175

Some time was spent in determining the conditions under which
phenolphthalein gives satisfactory results in the presence of pure
sodium chromate. Schreinemakers * states that the chromate is neu-
tral to phenolphthalein and recommends the use of this indicator in
analyzing solutions of chromates for excess of either hydroxyl or
chromate ion. In our experiments it appeared that the solubility
of the indicator in very concentrated sodium chromate solutions is too
small under ordinary conditions to permit of a visible reaction with the
low concentration of ionized hydroxyl which must exist there. This is
especially true when alcoholic phenolphthalein is dropped into a satu-
rated solution of the chromate. In this case the indicator seems to be
precipitated by the salt in such form as to dissolve only very slowly on
subsequent dilution. This difficulty was avoided by diluting the indi-
cator with pure water in the first place. On the other hand, a dilute
solution of the salt is easily shown to be appreciably hydrolyzed, the
color of phenolphthalein being distinctly visible superposed on the yel-
low of the salt. Increasing temperature of course causes increasing
hydrolysis ; in boiling solutions of the purest very concentrated sodium
chromate the hydrolysis is sufficiently great to cause a distinctly
reddish tint.

As an outcome of these experiments the neutralization was conducted
in concentrated solutions of sodium chromate at room temperature, the
indicator in dilute solution being added to the separate test portions.
To the main solution sodium hydroxide was added until the phenol-
phthalein just began to show its color in the separate test, and then
sodium dichromate until the color just disappeared. This solution
may have contained a constant and very slight excess of dichromate,
but this substance is easily removed by subsequent crystallization,
being heteromorphous as regards sodium chromate.

The neutral salt prepared in this way may be further purified by
crystallizing either as the dekahydrate, hexahydrate, or tetrahydrate.
The first named phase, Na2Cr04 • IOH2O is to be preferred on account of
economy of material, except as a means of eliminating sodium sulphate.

To crystallize the salt with four molecules of water the temperature
of the solution must be kept above 26° ; but at 20° 100 parts of water
dissolve 86 parts of sodium chromate, whereas at 0°C. 100 parts of
water dissolve only about .32 parts of sodium chromate in equilibrium
with dekahydrate ; hence arises one reason for the greater economy in
crystallizing the dekahydrate at the lower temperatures. Moreover, a
greater rate of purification from every common impurity except sodium

* Zeitschr. f. Phys. Chem., 56, 72 (1906).

176 PROCEEDINGS OF THE AMERICAN ACADEMY.

sulphate is possible by this method than from the other hydrates. Six
or seven crystallizations as the tetrahydrate give only the same degree
of purity as three or four crystallizations as the dekahydrate.

The dekahydrates of sodium sulphate and chromate are isomorphous,
as already stated ; hence the sulphate must be previously removed by
crystallizing the dichromate in the manner already described.

Crystallization of the pure chromate is best carried out at 5° in plat-
inum vessels ; and centrifugal drainage, as usual, greatly increases its
efficiency as a means of purification. After three or sometimes four
crystallizations the sodium chromate was found to give a transition
temperature which could not be raised by further crystallization. This
is, of course, the criterion to be used in deciding how long to continue
the purifying operations. The difficulties attending the purification of
this substance are no greater than those attending the purification of
sodium sulphate, provided that isomorphous substances are absent.
The mother liquors may be made to yield at least two more crops
of crystals ; their evaporation for this purpose is free from danger only
when the platinum vessels employed are so constructed as to prevent
the entrance of carbon dioxide. The yield of pure sodium chromate
may be nearly fifty per cent of the amount corresponding to the pure
sodium bichromate employed. Pure sodium chromate must be preserved
in a desiccator, containing a small amount of a solution of sodium hy-
droxide solution to absorb carbon dioxide. If the salt is to be kept for
any length of time it should be placed in platinumVessels. The tetrahy-
drate is the most convenient form in which to preserve the salt for long
periods, as it is permanent under usual conditions.

The Hydrates of Sodium Chromate.

The dekahydrate, Na2Cr04 • IOH2O, isomorphous with common
Glauber's salt, is so well known that description is unnecessary. It is
easily obtained in large crystals by inoculating a cold supersaturated
solution of the former salt with a crystal of the latter. In order to
avoid the suspicion of contamination with sulphate, inoculation was
carried out successively on several watch glasses, the first being touched
with sulphate, the second with chromate taken from the opposite side
of the first, and so on, the bulk of the material being inoculated with
pure chromate from the last watch glass. Whenever the temperature
of the laboratory rose above 20° this procedure was necessary, because
at this temperature all of the chromate in the laboratory suffered
change into the tetra- or hexahydrate, and so none remained where-
with to start the crystallization of a new specimen. Like sodium sul-
phate, the chromate has a wide range of metastability of supersaturation,

RICHARDS. — TRANSITION TEMPERATURES OF SODIUM CHROMATE. 177

and like it, the chromate is efflorescent in the dry air of the steam-
heated ^ laboratory. In order to make sure of the composition of the
salt, a specimen which had been dried as much as possible without visi-
ble efflorescence was analyzed. 0.8316 gram of the salt lost on dehydra-
tion 0.4358 gram of water, or 52.43 per cent. The theoretical per-
centage is 52.70, hence there can be no doubt as to the formula
NaAOi-lOHzO.e

^^he hexahydrate, Na2Cr04 • 6H2O has only a very small range of
stability, as will be seen from an examination of the diagram on page
1 78. The preparation of this hydrate was first described by Salkowski."^
At temperatures below 19.53°, especially in contact with its solution, it
tends to pass into the dekahydrate modification, and above 26°, into
tetrahydrate. Inasmuch as the temperatures within which it is stable
are those most frequently found in the laboratory, it is the phase most
frequently met with. When the dekahydrate warms to 19.53° or the
tetrahydrate cools to 26° particles of hexahydrate in the atmosphere
induce the crystallization of this form so readily that it is often difficult
to prevent the appearance of this phase. In two analyses, 1.4152
grams and 1.7786 grams of the salt lost respectively 0.5705 gram and
0.7122 gram of water on drying at 180° to constant weight. These
results correspond to 40.3 and 39.4 per cent of water respectively, and
since the first sample was somewhat moist and thfe second was slightly
effloresced, there can be no doubt that the substance was really
Na2Cr()4 • eHzO, a salt possessing theoretically 40.0 per cent of water.
The material gives a transition point at about 25.9° (hydrogen scale),
being converted into tetrahydrate at that temperature.

The tetrahydrate, Na2Cr04 • 4H2O, is stable in contact with its solution
only at temperatures above 26° and below 62.8° ±. Even in the dry
air of a steam-heated room it shows no evidence of efflorescence ; there-
fore its aqueous vapor tension must be very low. This hydrate is formed
when a hot concentrated solution of sodium chromate is allowed to cool
to a temperature above 26°, and the needle-shaped crystals melt at
about 62.8°. Occasionally other crystals of a hydrate or anhydride sep-
arate from the solution above 62.8". Because the hydration of the latter
crystals at low temperatures is slow, enough water should be added to
a very hot solution to keep the salt dissolved until the temperature 62.8°

* Kopp's ascribing deliquescence to the salt must have been due to his
working in a very moist atmosphere.

• These analyses, as well as those of the hexa- and tetrahydrate given further
on, were kindly made by J. B. Churchill under the direction of one of us.

' Salkowski, Ber., 34, 1947 (1901). The salt had been made and analyzed
previously by Richards and Churchill, but no description had been published.

178

PROCEEDINGS OF THE AMERICAN ACADEMY.

has been reached by the cooling material. Two analysis of the tetra-
hydrate showed 30.74 and 30.76 per cent of water, sufficiently close
to the theoretical value 30.72. On cooling a solution saturated at
63°, it frequently happens that no crystals appear, although upon
adding a crystal of the tetrahydrate crystallization at once occurs.

90

S

|4

80

70

60

30

15' 20= 25°

Temperature

In the accompanying figure the solubilities ^ of sodium chromate in
contact with its various hydrates have been plotted for temperatures
in the neighborhood of room temperature. Evidently three transitions
are possible within a small range. The dekahydrate undergoes transi-
tion to the hexahydrate and solution at 19.53°, or into tetrahydrate
and solution at 19.99°,^ depending on which of these last-named
hydrates is present. A similar transition from hexahydrate to
tetrahydrate and solution occurs at 25.9° ±.

8 Mylius and Funk, Ber. d. ch. Ges., 33, 3689 (1901); also Salkowski, ibid.,
34, 1948 (1901). These are recorded in Landolt and Bornstein Tabellen (1905),
page 5.57.

^ This is probably the point found by J. L. R. Morgan as approximately
19.92°, Zeit. anorg. Chem., 55, 263 (1907).

RICHARDS. — TRANSITION TEMPERATURES OF SODIUM CHROMATE. 179

To bring about the transition at 19.90°, it is necessary to superheat
the dekahydrate past the lower transition point, 19.53°. Not many
other instances of this sort have been carefully studied. Walker and
Fyffe^^ have examined the solubility of Ba(C2H302)2 • 3H2O (which un-
dergoes a transition into the monohydrate and solution at 24.7°) as far
as 26.1°, 1.4° above its transition point; and the solubility of a
Ni (103)2 -21120 has been studied by Meusser^^up to 50°, 13° above
the temperature of its transition into the anhydride and solution. ^^

The addition of a foreign substance not isomorphous with the deka-
hydrate lowers the transition point as usual.^*^ The addition of sodium
chloride was found some time since by C. A. Bigelow and one of us to
lower the transition temperatures (19.53) about the expected amount.
This result was not published at the time, but has since been confirmed
by J. L. R. Morgan. 14

A much more interesting effect is observed with isomorphous hy-
drates. For example, successive additions of sodium sulphate to the
solution of chromate gave successive elevations of the transition tem-
perature, even when the crystals contained no sodium sulphate. ^^
These elevations were roughly proportional to the amount added. The
experiments were not carried on with a view to determining the limits
of this change, but an elevation of about 4° was found in some in-
stances. The temperatures at first obtained were variable ; but on
vigorously stirring in an environment 0.5° warmer than the mixed
hydrates, equilibrium was apparently reached after five minutes, and
often remained undisturbed for fifteen minutes or longer. This raising
of the transition point involves an interesting extension of the range
of stability of the dekahydrate.

So far as we can find this phenomenon of the raising of the transition
temperature of hydrated crystals by the presence of isomorphous hy-
drated crystals is here described for the first time. It deserves and
shall receive here in the near future more thorough investigation.

" Walker and Fyffe, Journal Chem. Soc, 83, 180 (1903).

" Meusser, Berichte, 34, 2440 (1901).

*^ See also Berthoud, Sur I'impossibilit^ de surchauffer un solide. Journal
de chim. Phys., 8, 377 (1910).

" Lowenherz, Zeit. phys. Chem., 4, 349 (1889).

" Morgan, Zeit. anorg. Chem., 55, 263 (1907) ; 56, 168 (1907).

^^ This fact was first observed by Churchill and one of us about ten 5''ear3
ago, but has not been published until now. The value 19.6° (which made no
pretensions to great accuracy) assigned to the lowest transition point of
sodium chromate at that time was undoubtedly too high from this cause,
because the salt was made from ordinary chromic anhydride. These Pro-
ceedings, 34, 277 (1899).

180 PROCEEDINGS OF THE AMERICAN ACADEMY.

The relative composition of crystals and mother liquor was evidently
worthy of study. A solution of sodium chromate containing a consid-
erable amount of sodium sulphate was cooled to 10° to crystallize. The
crystals were drained in a centrifuge, washed with a little cold water,
and again centrifuged. 7.05 grams of this solution contained 0.432
gram of sodium sulphate and 1.707 grams of the chromate, whereas
2.25 grams of the hydrated crystals contained 0.425 gram of the sul-
phate and 0.515 gram of the chromate. The solubility of the chromate
at 10° is roughly speaking 50 parts in 100 of water and of the sulphate
9 parts in 100 of water. The distribution of the dissolved substances
between their solution and mixed crystals is thus seen to be in the
same sense as their respective solubilities at the temperature of crys-
tallization. The sulphate decidedly tends towards the crystals, the
chromate towards the mother liquors.

As has been elsewhere pointed out, Salkowski was the first to observe
that the curve of solubility of the hexahydrate cuts those of the deka-
and tetrahydrates at about 19.5° and 26° respectively. Mylius and
Funk ^^ earlier observed that the transition from the dekahydrate to the
anhydride is accomplished through the intermediate tetrahydrate, which
is stable between 20° and 65". Salkowski,^^ commenting upon their
work in view of his later discovery of the hexahydrate, says that this
statement must be extended to include the hexahydrate for its few de-
•grees of stability. The statement of Salkowski must now be extended
to include the fact that the transition from dekahydrate to the anhy-
dride may be through the hexa- and tetrahydrates, or in the absence
of the hexahydrate, this transition may be through the tetrahydrate
alone, as originally stated by Mylius and Funk.

We have confirmed the statement of Salkowski that the temperature
of the transition from the hexahydrate to the tetrahydrate is in the
neighborhood of 26°, but owing to lack of time we have been unable to
determine this point with exactness.

The exact determination of the two lower transition points, for use
in precise thermometry, will now be described.

The Apparatus.

The apparatus employed was like that employed in determining the
transition temperature of sodium sulphate.^^ It was essentially similar

" Abhandlung der Physik. Techn. Reichsanstalt, III, 449 (1900).

^■f Loc. cit. ; this fact had also been observed but not published by Richards
and Churchill before that time.

" Richards and Wells, Zeit. phya. Chem., 43, 465 (1903) ; These
Proceedings, 38, 43 (1902).

RICHARDS. — TRANSITION TEMPERATURES OF SODIUM CHROiL\.TE. 181

to Beckmann's well-known freezing point apparatus, consisting of two
large test-tubes, one within the other, immersed for nine-tenths of their
length in a roomy, transparent water bath. The inner test-tube, which
contained the mixed hydrate, was 3.3 cm. wide and 16 cm. long (in-
ternal measurements) and had a capacity of 120 cc. The outer tube
was large enough to allow a small air space between the two vessels at
every point except the top, where the inner vessel was insulated from
the outer one by a narrow rubber ring. This ring held the inner tube
in place, preventing heat conductance through the glass to the material,
and excluded the outer air from the space between the two tubes.
Thus all the heat obtained by the melting material came to it from the
outer bath through the confined air-jacket, which is an absolutely
necessary provision if accuracy is sought.

The inner large test-tube containing the sodium chromate was closed
at the top by a rubber stopper, carefully freed from loosely adhering
matter which might contaminate the materials. It was pierced by two
holes, through which short glass tubes were passed. One of these tubes
was of the same length as the thickness of the stopper, and served to
hold the stirrer ; while the other reached 0. 7 cm. above the stopper and
below to within 1 cm. of the sodium chromate, and served to admit and
support the thermometer. To the upper end of the latter tube a short
length of stout rubber tubing was attached, the object of which was to
hold the thermometer in place at any desired level. A water jacket
around the thermometer is necessary only when the temperature of the
room is several degrees distant from 20° ; because a correction for the
protruding column can be applied with sufficient accuracy when the
temperature difference is small.

The stirrer was made of a piece of platinum wire 15 cm. in length, at
one end bent into the shape of a ring, at the other end sealed into
a glass tube which served as a handle.

The thermometers were three in number. The first, an excellent
Beckmann thermometer, the scale of which was divided into hundredths
of a degree, was used for the preliminary experiments, where the con-
stancy of the transition temperature of successive fractions was the main
issue. Two Baudin thermometers, 15200 and 15276, standardized with
the greatest care at the Bureau International des Poids et Mesures,
were used in the final determination of the points on the hydrogen
scale. These thermometers have been previously described ; ^^ their
scales are divided into tenths of a degree, and readings within (>.(»01°
were made by means of a Geneva cathetometer, observing the marks not

" Richards and Wells, These Proceedings, 38, 43 (1902) ; Zeit. phys.
Chem., 43, 465 (1902).

182 PROCEEDINGS OF THE AJVIERICAN ACADEMY.

only in the usual way, but also through the glass behind the mercury.
The freezing-points were taken both before and not long after the tran-
sition temperatures, and during the intervening time the instruments
were carefully protected from large temperature changes.

The Temperature of the Transition from NazCrOi- lOffzO
to Na^CrOi ■ QH^O.

When moist crystals of the dekahydrate are melted without the ad-
dition of the solid hexahydrate, the temperatures obtained are variable
and generally low. This is undoubtedly due to the fact that the water
of crystallization, together with the water adhering to the crystals, is
enough to dissolve the sodic chromate completely, thus preventing the
formation of solid hexahydrate.

In order to avoid this difficulty, it was found best to heat about one
fifth of the moist hexahydrate in a quartz or platinum vessel to 60°,
thus driving off perhaps a third of the water of crystallization. The
cooled product yielded solid Na2Cr04 • 4H2O and its solution. This was
added to the remainder of the Na2Cr04 • lOHoO, after which the whole
mass was warmed to 28° C. in the test-tube in which the determination
was to be made. The proportion of Na2Cr04 • 4H2O to Na2Cr( \ • IOH2O
should be such that at this temperature the whole is in solution. The
solution was then cooled by dipping the test-tube into a beaker con-
taining water at 20°. When the temperature of the solution had
fallen to 25°, a crystal of Na2Cr04 • 6H2O was added ; it produced
copious crystallization. On further cooling to 19° or slightly lower
a crystal of dekahydrate was added, and still more heat was taken
from the mixture, with stirring, until the mixture of the two solid
phases and solution of sodium chromate was plastic.

The temperature of the water bath was kept one or two tenths of a
degree higher than the equilibrium point (19.5°) and the room tem-
perature also was kept not far away. This latter condition was not very
essential, because with one of our thermometers the stem exposure was
6.5° and with the other only 0.5°.

In a preliminary set of readings, corrected in the usual way for cali-
bration, for internal and external pressure, for error in the fundamental
interval, for the corrected ice-point, for the exposed column, and to the
hydrogen scale, the following values were found : —

Preliminary determination by thermometer 15200 19.518°
" " " 15276 19.525°

19.522°

RICHARDS. — TRANSITION TEMPERATURES OF SODIUM CHROMATE. 183

The Beckmann thermometer in this mixture indicated 0-580°. Upon
crystallizing the material once more, and separating the mother liquor
by centrifugal action, the crystals still gave exactly the same transition
point, 0.580°, — the atmospheric pressure having remained essentially
constant. Therefore it was clear that the material was as pure as it
could be obtained by crystallization, and the final estimation was
made.

The individual readings were corrected for stem exposure, and all
averaged to give the observed value used in calculating the tempera-
ture referred to the hydrogen scale. The ice-points, which are the
most uncertain part of this determination, were taken as the averages
of four separate fairly concordant sets of readings, two of which were
made some time before the determinations, and two immediately after-
wards. As the thermometers are old and well seasoned, this procedure
seemed likely to furnish the best result.

Thermometer 15200,

Reading in salt (cor.) 19.804° In ice + .201°

Correction, calibration

" internal pressure

Corrected reading in ice

Correction, fundamental int.

Correction to hydrogen scale

Thermometer 15276
Reading in salt (cor.)
Cor. calibration
" internal pressure

Corrected reading in ice

Cor. fundamental interval

Cor. to hydrogen scale

Total average of two final readings

The average of the two preliminary readings was 19.522° -f .004^,
a result as near as could be expected to the final value, considering the

- .026

+

.002

+ .027

+

.009

19.805°

+

.212°

- .212

19.593°

+ .014

19.607°

- .084

19.523°

19.750°

In ice

.143°

- .025

—

.001

+ .039

+

.012

19.764°

+

.154°

- .154

19.610°

+ .001

19.611°

-.084

19.527°

19.525 ± 0.002°

184 PROCEEDINGS OF THE AMERICAN ACADEMY.

range of error of each. The value of 19.525°, the result of the final
determination above, may be accepted for the present as the most
l)robable figure. ^^

TJie Temperature of the Transition from Na ^Cr 0 i. 10 H^O
to Na^CrOiAH^O.

This mixture of hydrates is somewhat more difficult to prepare than
the mixture of deka- and hexahydrates. From a study of the diagram
on page 178 it appears that the tetrahydrate is metastable with respect
to the hexahydrate between the temperatures 19.53° and 25.9 ±. The
difficulty is to exclude the hexahydrate during the cooling of the tetra-
hydrate and solution from 26° to 19.99°, the transition point of the
deka- to the tetrahydrate. ^^ Even after the dekahydrate has appeared,
and has in part relieved the supersaturation, care must be taken to ex-
clude the intermediate hydrate. At 19.99° both dekahydrate and
tetrahydrate are metastable with respect to the hexahydrate. If to a
mixture of the two former a crystal of the latter be added, a depression
and irregularity in the temperature occurs, and the temperature
gradually falls to that of the lower transition point. ^^

The mixture of hydrates is prepared (within the test-tube in which
the transition temperature is to be determined) by a method closely
resembling that described for preparing the mixture of dekahydrate and
hexahydrate. To the dekahydrate is added such a quantity of tetra-
hydrate that nearly all the solid will be in solution at 28°. By heat-
ing the mixture to this temperature, one may feel certain that none of
the hexahydrate is present. The tube is then closed by a clean stop-
per through which the handle of a stirrer passes. The stopper serves
to protect the contents from accidental inoculation by hexahydrate.
When the solution has been cooled to about 19°, it is inoculated with
some freshly prepared dekahydrate, which must be free from hexahy-
drate. Further gradual subtraction of heat, with constant stirring,
gives a mixture of the desired plastic consistency.

The material used in the preliminary determination of this transition
point was the same as that used in the preliminary determination of

2" Over one third of an atmosphere's pressure is necessary to alter this
temperature by as much as 0.001°. (SeeTammann, "Krys. and Schmelzen,"
262 (Leipzig, 190.3).)

2^ Gernez's supposed disintegration of Na2Cr04.4H20 in the presence of the
IOH2O salt (Compt. Rend., 149, 77 (1910), would not affect this point, if,
as Gernez reasonably supposes, this disintegration is due simply to the for-
mation of the dekahydrate from included water within the salt, and not to
the formation of a hydrate with less than 4H2O.

RICHARDS. — TRANSITION TEMPERATURES OF SODIUM CHROMATE. 185

the equilibrium temperature of the mixed deka- and hexahydrates.
With the Beckmann thermometer the new point was 1.039°. On the
Baudin thermometers all individual rea;dings were corrected for stem
exposure and averaged as before.

Preliminary reading by Thermometer 15200 19.984°

15276 19.990°

The average 19.987°

The material used in the final observations was the same as that
used for the previous final work, after conversion into a mixture of
deka- and tetrahydrate. With the Beckmann thermometer it gave the
transition point 1.039, the same as that given by the salt used in the
preliminary tests j ust recorded.

Final Determination I.

Thermometer 15200

Reading in salt (cor.)

20.269° In ice

.201°

Cor. calibration

- .028

+

.002

Cor. internal pressure

+ .027

+

.009

20.268°

.212°

Corrected reading in ice

- .212
20.056°

Cor. fundamental interval

+ .014
20.070°

Correction to hydrogen scale

- .085

19.985°

Final Determination II.

Thermometer 15276
Reading in salt (cor.)
Cor. calibration
Cor. internal pressure

20.209° In ice .143°
— .022 - .001
+ .039 + .012

20.226° 0.154'

Corrected reading in ice — -154

20.072°
Cor. fundamental interval + .001

20.073°
Cor. to hydrogen scale — .085

19.988°
Total average of two final readings 19.987° ± 0.002

186 PROCEEDINGS OF THE AMERICAN ACADEMY.

It is interesting to note that the difference between the two transi-
tion temperatures is given as almost exactly the same quantity by the
final readings of the two thermometers.

Difference by thermometer 15200 = 0.462°
" " 15276 = 0.461°

This of course gives a means of calibrating the Beckmann ther-
mometer, which gave 0.459° for the interval — evidently the marks
were a trifle too far apart on the latter instrument.

The close parallelism of the results with the two Baudin thermome-
ters seems to indicate that the most probable cause of error in such
work is not due to mistake in observing either of the transition temper-
atures, but rather to the difficulty of determining the ice-point. There
can be no question that either of the sodium chromate equilibrium-
temperatures is a far better means of fixing the scale of a thermometer
to be used near room temperature than is the freezing point of water.

The Temperature of the Transition from NazCrO^ ■ QH^O
to Na^CrO^ ■ 4.H^0.

The material used in this determination was sodium chromate ob-
tained from the mother liquors of previous preparations, purified by
recrystallization as dekahydrate until the temperature of transition
from the dekahydrate to the hexahydrate as shown by the Beckmann
thermometer was 0.580. A supersaturated solution of this pure salt
at 25° was inoculated with hexahydrate and further cooled with stirring
to 18°, the dekahydrate being scrupulously excluded. The plentiful
crystals of hexahydrate were then centrifuged to remove the excess of
mother liquor, and in order to make certain that none of the dekahy-
drate was present, the crystals were allowed to stand in a bath at 25°
for an hour. No change occurred in the appearance of the material.
Just before taking the transition temperature a few crystals of the
tetrahydrate were added.

Whether on account of the interference of other unknown hydrates, or
of the comparatively small heat of this transition, or of the unavoidable
haste in which the experiments had to be conducted, much less constant
results were obtained in this case than in the preceding. It appeared
that the equilibrium temperature of the hexa- and tetrahydrates was
not far from 25.90° on the hydrogen scale ; but this figure is subject to
further revision.

This point is worthy of further investigation, for it is exceedingly

RICHARDS. — TRANSITION TEMPERATURES OF SODIUM CHROMATE. 187

convenient, taken together with the other points given by this same
salt, as a means of calibrating a Beckmann thermometer. The interval
between the dekahydrate-tetrahydrate point (19.987) and the higher
transition temperature is almost 6°, the usual length of a Beckmann
thermometer. By adding a degree to the scale, which could easily be
done in future, the lowest transition temperature of sodium chromate
also could be brought within the scope of the instrument. To be able
to verify a thermometer over its whole length, and at the same time to
evaluate accurately the interval 0.462 on one part of the scale, all with
the single purified salt, is indeed a highly desirable circumstance.

Of course the determination of the several points as given in this
paper must be looked upon as merely preliminary, because time per-
mitted the study of these temperatures on only two thermometers.
The average of the readings of many thermometers should ultimately
be taken. Nevertheless we believe that the averages given in this
paper are sufficiently exact to be a great boon to those desiring to verify
thermometers about the temperature of the room.

It is a pleasure to acknowledge the usefulness of a grant made many
years ago by the Rumford Fund, of the American Academy of Arts
and Sciences, for this purpose. Much of the material used in the
investigation was purchased with its aid.

Summary,

1. The great advantage of sodium chromate as a means of verifying
thermometers at three fixed temperatures in the neighborhood of 20°
is emphasized.

2. A method for the easy preparation of pure sodium chromate has
been elaborated.

3. The existence of three hydrates of sodium chromate; namely, the
deka-, hexa- and tetrahydrates has been confirmed.

4. The accurate estimation of the point of conversion of each of
these hydrates into each of the other two has been shown to be easily
feasible.

5. The addition of heteromorphous substances lowers the transition
points as usual.

6. The addition of sodium sulphate (which gives an isomorphous
dekahydrate) raises the temperature of the dekahydrate-hexahydrate
e(iuilibrium. This is perhaps the first observation of this type of
phenomenon.

7. The temperature of the dekahydrate-hexahydrate transition is
found to be approximately 19.525°, on the international hydrogen
scale.

188 PROCEEDINGS OF THE AJMEEICAN ACADEMY.

8. The temperature of the dekahydrate-tetrahydrate transition is
found to be approximately 19.987*^, on this scale.

9. The temperature of the hexahydrate-tetrahydrate transition is
found to be approximately 25.90°, on this scale.

10. All these points, especially the last, are to receive further
investigation at Harvard in the near future.

Proceedings of the American Academy of Arts and Sciences.
Vol. XL VII. No. 6. — July, 1911.

CONTRIBUTIONS FROM THE GRAY HERBARIUM
OF HARVARD UNIVERSITY.

New Series. — No. XXXIX.

By B. L. Robinson.

I. On the Classification of certain Etipatorieae.
II. Revision of the Genus Barroetea.
III. On some hitherto undescribed or misplaced Compositae.

CONTRIBUTIONS FROM THE GRAY HERBARIUM OF HARVARD
UNIVERSITY. — NEW SERIES, NO. XXXIX.

By B. L. Robinson.

Presented March 8, 1911. Received May 4, 1911.

I. ON THE CLASSIFICATION OF CERTAIN EUPATORIEAE

Ageratum Gaumeri, sp. no v., annuum erectum 4 dm. vel ultra alti-
tudine copiose ramosum modice pubescens ; caule tereti gracili medul-
loso ; ramis oppositis adscendentibus foliosis ; foliis ovatis acuminatis
crebre et regulariter crenato-serratis tenuibus 3.5-6 cm. longis 2.5-4
cm. latis utrinque viridibus basi integris rotundatis vix ad insertionem
petioli acuminatis, petiolo 1.5-2.2 cm. longo ; inflorescentia perlaxa in
ramulis singulis racemiformi, pedicellis 2-4 (usque ad 6) cm. longis
unicapitulatis cum bracteolis 1-4 filiformibus minimis munitis ; capi-
tulis oblate subsphaericis 7-9 mm. diametro ; involucri squamis linear-
ibus attenuatis costatis glabriusculis subaequalibus ; disco conico ;
corollis limbum versus caeruleis ; styli ramis longe exsertis pulcherrime
caeruleis ; achaeniis nigrescentibus 5-angulatis vix in angulis obscure
hispidulis 1.2 mm. longis ; pappi squamis 5, aliis saepissime breviori-
bus muticis, aliis in aristam longam desinentibus et achaeniam longi-
tudine subaequantibus. — Ageratum intermedium Millsp. Field. Col.
Mus. Pub. Bot. Ser. iii. 90 (1904), not Hemsl. — Izamal, Yucatan, Dr.
G. F. Gaumer, no. 395 (type, in Gray Herb.). From tbe species here
described A. iyitermed'mm Hemsl. differs in having stems of a decidedly
firmer texture, presumably perennial and of a more spreading habit.
The leaves are smaller and the heads are borne in rather compact 2-5-
headed long-peduncled cymes. Finally the pappus is much shorter.
From the common and somewhat variable annual species A. conyzoides
L., the plant here described differs much in habit, in its more finely
serrate leaves, greater smoothness, and especially in its loose open in-
florescence, which on the individual branches becomes somewhat
racemiform,

Ageratum Peckii, sp. nov., annuum erectum fastigiatim ramosum
5 dm. altum foliosissimum glabrum ; radice fibrosa ; caule subtereti basin
versus crassiusculo nodoso, internodiis inferioribus brevibus, superiori-

192 PROCEEDINGS OF THE AMERICAN ACADEMY.

bus gradatim longioribus gracilioribus atropurpureis folia longitudine
superantibus ; foliis lineari-oblongis integris 2.5-4.5 cm. longis 2.5-6
mm. latis obtusiusculis vel vix acutis basi subsessilibus vel petioliforme
angustatis ; cymis inaequaliter trichotomis, ramis lateralibus quam ter-
minali multo longioribus usque ad 8 cm. longitudine; cymulis parvis
1-2.5 cm. diametro 3-7-capitulatis ; bracteis subulatis; pedicellis 2-10
mm. longis bracteolatis ; capitulis 3.5-4 mm. diametro ; involucri
squamis ca. 20 glabris anguste lanceolati-linearibus acutissimis pler-
umque 2-costatis ; corollis glabris purpureis ; achaeniis nigris acute 5-
angulatis 1 mm. longis glabris ; pappi squamis 5 lanceolatis scariosis
apice setiferis 2 mm. longis. — British Honduras, in sandy open ground,
on pine ridge near Manatee Lagoon, 25 July, 1905, Prof. Morton E.
Peck, no. 80 (type, in Gray Herb.). A very distinct annual species with
glabrous narrow entire leaves, commonly proliferous in the axils.

Ageratum radicans, sp. nov., glabrum prostratum ramosum ad
nodos et etiam hinc inde inter eos radicans ; caule teretiusculo brunneo
vel stramineo-brunneo ; internodiis 3-8 cm. longis ; foliis oppositis an-
guste elliptico-oblongis integerrimis glabris 3-nerviis supra viridibus et
cum nerviis impressis subtus pallidioribus impunctatis 4-8 cm. longis
5-15 mm. latis apice obtusiusculis basi petioliforme angustatis ; in-
florescentiis longe pedunculatis contractis cymosis paucicapitulatis ;
capitulis breviter pedicellatis 8-10 mm. diametro ; involucri squamis
anguste lanceolatis acutissimis plerumque 2-costatis subaequalibus
(paucis exterioribus parvis exceptis) maturitate patentibus; flosculis
glabris ; corollis limbum versus purpurascentibus ; achaeniis acute 5-
augulatis ca. 1.2 mm. longis ; pappi squamis 5 albis plus minusve erosis
vel laceratis apice cum seta munitis ca. 2.2 mm. longis. — British
Honduras, in fresh water pond near Manatee Lagoon, 4 August, 1905,
Prof. Morton E. Peck, no. 99 (type, in Gray Herb.). This species, in
technical characters exceedingly near A. Peckii, differs much in its
prostrate and repent habit, its very much larger leaves, and slightly
larger heads, flowers, and achenes.

Podophania dissecta (Hook. & Am.), comb. nov. Phania ? dis-
secta Hook. & Am. Bot. Beech. 433 (1841). Eupatoriumdissectum (Hook.
& Arn.) Benth. Bot. Sulph. 113 (1844). Podophania Ghiesbreghtiana
Baill. Bull. Soc. Linn. Par. i. 268 (1880). Repeated efforts to discover
any distinctions between the types of Hooker & Arnott and of Baillon
have failed to disclose any difference, the floral characters, foliage, and
even pubescence appearing to be identical.

HoFMEiSTERiA FASCicuLATA (Benth.) Walp., var. pubescens (Wats.),
comb. nov. H. jnihescensy^aXs,. Proc. Am. Acad. xxiv. 54 (1889). The
glandular pubescence, although, when copious, as in the original speci-

ROBINSON.

ON CERTAIN EUPATORIEAE. 193

men upon which Dr. Watson founded his species, becoming a striking
feature, seems to be accompanied by no other differential character
and is, as shown by later collections, by no means constant.

Trichogonia capitata (Rusby), comb. nov. Eiipatorium capitatum
Rusby, Bull. N. Y. Bot. Gard. iv. 380 (1907). An examination of a
cotj'pe of this species {Bang, no. 2114) in the Gray Herbarium shows
not only that it has the general habit and foliage as in Trichogonia,
but possesses the plumose pappus characteristic of that genus, to which
accordingly it should be referred.

EuPATORiUM BETONiciFOLiUM Mill., var. integrifolium (Gray), comb,
nov. E. Hartwegi Benth. PL Hartw. 19 (1839). Coelestinia Hartiregi
(Benth.) Walp. Rep. ii. 545 (1843). ConocUnium betonicum DC., var. ?
integrifoUum Gray, PI. Wright, i, 88 (1852). Eiipatorium betonicum
(DC.) HemsL, var. subintegrum Gray, Syn. Fl. i. pt. 2, 102 (1884).
ConocUnium integrifolium (Gray) Small, Fl. S. E. U. S. 1170, 1338
(1903). Eiipatorium betonicum, var. intregrifoUum (Gray) Small,
11. cc.

EuPATORiUM COELESTINUM L., var. SALINUM Griseb. Cat. PI. Cub. 146
(1866). This plant (Wright's no. 2811 from Cuba) though a marked
form is described somewhat misleadingly thus : " forma foliis acute
dentatis." The teeth of the leaves are in fact by no means acute,
being in most instances actually rounded at the tip ; but what fur-
nishes the really striking difference between this form and the typical
E. coelestinum is the fact that the leaves are considerably more deeply
and somewhat doubly toothed. The blades also are of a more deltoid
outline.

Eupatorium frustratum, sp. nov., perenne 3-9 dm. altum a basi
paulo lignescenti ramosum, radice fibrosa, ramis teretibus striatis
viridibus patente vel crispe puberulis adscendentibus, internodiis lon-
giusculis folia multo superantibus ; foliis oppositis petiolatis ovatis
vel eis ramulorum lanceolato-ovatis) 3-nerviis crenato-serratis obtus-
iusculis 1.5-3.2 cm. longis 0.8-2.2 cm. latis utrinque breviter pubes-
centibus ; inflorescentia iterum atque iterum cymoso-furcata, axe
principali in capitulo quasi abortive terminante (unde nomen) ; capit-
ulis ovoideo-cylindricis 1 cm. longis 5 mm. diametro, involucri squamis
multiseriatim imbricatis arete appressis viridi-striatis apice rotundatis
valde deciduis, receptaculo elevato crassiusculo cylindrico 1.5 mm. alto
minute papillose ; flosculis caeruleis ; achaeniis olivaceis minute in
faciebus sursum strigillosis. — Ooclinium rigidum Chapm. Bot. Gaz. iii.
6 (1878), not DC. Eupatorium heteroclinium Gray, Syn. Fl. i. pt. 2,
95 (1884), not Griseb. Osmia heteroclina Small, Fl. S. E. U. S. 1164
(1903), excl. syn. — South Florida: coral soil. Lignum Vitae Key,

VOL. XLVII. — 13

f

194 PROCEEDINGS OF THE AMERICAN ACADEMY.

^4. //. Curtiss, no. 1195* (t}^e, in Gray Herb.); Key West, Blodgett;
Jew Fish Key, Chapman; rich thicket, Key Largo, June, 1880, A. H.
Curtiss, no. 171 ; Upper Metacumbe, 11 April, 1892, J. H. Simpson, no.
565. This species, long identified with the Jamaican E. heteroclinium
Griseb., differs in having decidedly smaller heads, shorter leaves of a
more deltoid contour, more obtuse involucral scales, olivaceous instead
of dark violet-brown achenes which are strigillose instead of smooth on
their faces, and in other minor characters. Were these plants of
Florida and Jamaica really identical, it would certainly be strange that
their range did not include Cuba.

EuPATORiUM GLABRATUM HBK. Nov. Gen. et Spec. iv. 127 (1820).
To the synonymy of this species should be added E. xalapense HBK. 1. c.
128 (1820), and E. gonocladum DC. Prod. v. 171 (1836). The greater
part of recently collected material of this affinity has been referred to E.
glahratum, while E. xalapense and E. gonocladum have remained ob-
scure. After examining at the herbarium of the Museum of Natural
History in Paris original material of E. glahratum and E. xalapense,
and at the De Candollean herbarium in Geneva the exceedingly frag-
mentary type of E. gonocladum, the writer has failed to detect any sig-
nificant difference. Of the two earlier names, the more commonly used
E. glahratum happily has priority of position.

Eupatorium iodostylum, sp. nov., fruticosum ; ramis teretibus
flexuosis brunneo-griseis plus minusve striatulis glabratis; ramulis
foliosis crispe vel patente purpureo-puberulis, pilis sub lente monili-
formibus ; foliis oppositis oblongo-lanceolatis undulate et subremote
serratis tenuibus basi anguste acuminatis ad apicem verum subobtusum
gradatim angustatis 10-16 cm. longis 3-3.6 cm. latis utrinque sparse
obscureque pubescentibus penninerviis supra austere viridibus subtus
vix pallidioribus ; petiolo 1.8-2.8 cm. longo patente pubescenti ; corym-
bis terminalibus erectis pedunculatis alternirameis multicapitulatis
6-10 cm. diametro convexis vel planiusculis ; bracteis linearibus 1-2
cm. longis ; ramulis inflorescentiae crispe purpurascenti-puberulis ; ped-
icellis anthesi 5 fructu saepius ad 10 mm. longitudine ; capitulis 26-34-
floris graciliter campanu latis anthesi ca. 1 1 mm. altis 7-9 mm. diametro ;
involucri squamis ca. triseriatis linearibus ciliolatis laxe imbricatis, ex-
terioribus herbaceis attenuatis 4-8 mm. longis, interioribus ca. 1 cm.
longis perangustis tenuibus subscariosis acutis striatulis ; corollis gra-
ciliter tubulosis 5-6 mm. longis apicem versus pulcherrime roseo-
purpureis a basi ad apicem levissime ampliatis, faucibus nullis, limbi
dentibus 5 deltoideis 0.8 mm. longis, antheris distinctis anguste
oblongis apice appendiculatis basi integris ; styli ramis longe exsertis
filiformibus laete violaceis ; achaeniis 3 mm. longis argute 5-costato-

ROBINSON. — ON CERTAIN EUPATORIEAE. 195

angulatis glabris basin versus attenuatis ; pappi setis gracillimis albis
25-30 coroUam subaequantibus. — Limestone rocks, Trinidad Moun-
tains, Santa Clara, Cuba, Arroyo Cimarron, altitude 470 m., N. L. &
E. G. Britton, 5 March, 1910 (type, in Gray Herb.).

Eupatorium (§ Imbricata) pluriseriatum, sp. nov., fruticosum
inflorescentia excepta glaberrimum ; ramis arcuatis pallide griseo-
brunnescentibus subteretibus lucidulis; ramulis purpurascentibus stri-
atulis ; foliis oppositis graciliter petiolatis ovatis firmiusculis longe
falcatim attenuato-acuminatis denticulatis 9-12 cm. longis 4.5-5.5 cm.
latis utrinque laete viridibus basi rotundatis sed ad insertionem petioli
ca. 2.7 cm. longi in eo plus minusve acuminato-decurrentibus ; panicula
corymbosa oppositiramea multicapitulata densiuscula, axe et ramulis
puberulis ; capitulis (infeliciter immaturis) cylindraceis ca. 8 mm. altis

4 mm. diametro 7-10-floris breviter pedicellatis vel in apicibus ramu-
lorum subsessilibus et fasciculatim aggregatis ; involucri squamis valde
iuaequalibus multiseriatim imbricatis glabris subscariosis viridi-stria-
tulis fimbriati-ciliolatis, apice rotundatis, margine saepius brunne-
scentibus quasi ustis, a receptaculo cylindrico truncato caducis ; corollis
glabris graciliter tubulosis quam achaenis etiam glabris multo longi-
oribus ; pappi setis tenuibus corollas subaequantibus sursum minute
scabratis. — On bank ; Aguacate, altitude 750-850 m., Trinidad Moun-
tains, Santa Clara, Cuba, 10-11 March, 1910, N. L. Britton S Percy
Wilson, no. 5407 (type, in Gray Herb.).

Eupatorium urticaefolium Reichard, var. tomentellum, var, nov.,
formae typicae habitu statura foliis etc. simile ; caule ab apice usque
infra mediam partem dense breviterque crispe griseo-tomentello ; foliis
plerumque subtus tomentellis. — Madison, Wisconsin, 28 August, 1893,
Judge J. B. Churchill (type) ; Mt. Carmel, Illinois, 1875, Dr. D.
Schneck (Gray Herb.) ; edge of maple forest, Marquette, Michigan, 12
August, 1901, Bronson Barhw (Gray Herb.). This variety differs
from E. urticaefolium, var. vilUcaule Fernald of the middle Atlantic
States in having a very much shorter closer non-viscid indumentum.

Mikania cristata, sp. nov., robusta scandens ; caulibus angulato-
striatis puberulo-tomentellis, internodiis usque ad 1.7 dm. longis;
foliis oppositis longe petiolatis late ovatis profunde cordatis acumi-
natis firmiusculis integriusculis utrinque breviter velutino-tomentosis
a basi 3-5(-9)-nerviis ; petiolis robustis recurvatis tortis anguineis ca.

5 cm. longis basin versus crassioribus, eis ejusdem jugi membrana
stipulari margine appendicibus caudiformibus conspicue cristata con-
nexis ; capitulis 4-flori8 corymbosis ca. 9 mm. longis breviter pedicil-
latis, corymbis oppositis pedunculatis ca. 1 dm. diametro, pedunculis
(4-6 cm. longis) et inflorescentiae ramulis valde compressis ; involucri

196 PROCEEDINGS OF THE AAIERICAN ACADEMY.

squamis oblongis obtiisiusculis ca. 6 mm. longis, exterioribus dorse
puberulis ; corollae tubo cylindrico curvato glabro 3 mm. longo, fauci-
bus nuUis, limbi dentibus 5 oblongo-linearibus patentibus 1.8 mm.
longis obtusiusculis ; acbaeniis glabris 5-costato-angulatis deorsum
attenuatis 3.6 mm. longis ; pappi setis ca. 50 rufis 4.5 mm. longis
laevibus. — Bushy places, La Palma, Costa Rica, September, 1898,
altitude 1459 m., Ad. Tonduz, no. 12,583 (type, in U. S. Nat. Mus.,
fragm. in Gray Herb.). A species well marked by the conspicuously
crested stipular appendages.

Mikania hexagona sp. nov., fruticosa robusta scandens ; caulibus
lignosis tortis acute et subalato-hexagonis atrobrunneis cavis 1 cm.
diametro, internodiis longissimis (3 dm. et ultra) ; ramis oppositis
alato-hexagonis praecipue in angulis tomentellis ; foliis late ovatis
acuminatis integris 1 dm. longis 7 cm. latis basi rotundatis in petiolum
2.5 cm. longum plus minusve cuneatum decurrentibus paulo supra
basin 7-nervatisutrinque scabro-puberulis viridibus infra paulo pallidi-
doribus, superioribus et floralibus multo minoribus subsessilibus ; inflor-
escentiis composite corymbosis ca. 2 dm. diametro densiusculis ; brac-
teis herbaceis ovato-lanceolatis acuminatis tenuibus, ultimis involucri
squamas saepe aequantibus dorso obscure puberlis ; pedicellis gracilibus
3-5 mm. longis ; involucri squamis anguste lanceolato-oblongis acumi-
natis tenuibus pallide viridibus glabriusculis ; corollis 5 mm. longis
glabris, tuboproprio 2.5 mm. longo gracili firmiusculo, faucibus benedis-
tinctis campanulatis vix 1 mm. altis, dentibus limbi oblongis crispis ca.
2 mm. longis saepe conniventibus ; achaeniis 5-angulatis ca. 4 mm. longis
deorsum decrescentibus ; pappi setis ca. 70 ca. 5 mm. longis rufescen-
tibus ; styli ramis filiformibus nee clavellatis 4 mm. longis. — Near
Tovar, Venezuela, 1854-55, altitude 1700 m., A. Fendler, no. 626
(type, in Gray Herb.). A species seemingly well marked by its very
robust hexagonal stem with acute narrowly wing-margined angles.

Mikania leucophylla (Rusby), comb. nov. Willoughbya leuco-
philJa Rusby, Bull. N. Y. Bot. Gard. iv. 382 (1907).

Mikania longiflora (Rusby), comb. nov. Willoughbya longijiora
Rusby, Bull. N. Y. Bot. Gard. iv. 382 (1907).

Mikania myricaefolia (Bojer) DC. Prod. v. 188 (1836). Triris
myricaefolia Bojer in litt. ex DC. 1. c. Examination of the tj-pe of
this plant of Madagascar, kindly permitted by Mr. Casimir de Candolle,
showed that it has alternate thickish leaves narrowed at the base to
short but slender petioles, heads (all in bud) nearly cylindrical, invo-
lucral scales 6 to 7, and florets 10 to 11. Although from the very
immature heads it is impossible to ascertain satisfactorily the style
characters or other details regarding the florets, it is nevertheless cer-

ROBINSON. — ON CERTAIN EUPATORIEAE. 197

tain from the number of involucral scales and of the florets in the head
that the plant is not a 3Iikania, nor from its habit and alternate leaves
does it seem likely that it belongs in the tribe of the Eupatorieae.

Mikania paezensis, sp. no v., scandens ; caule et ramulis striatis
a tomento brevi fusco vel atropurpureo etiam fere nigrescenti tectis ;
foliis longiuscule petiolatis oppositis ovatis acutis crenato-denticulatis
supra bullato-rugosis pubescentibus subtus pallidioribus tomentosis basi
sinu patenti cordatis ca. 4.5 cm. longis ca. 3.5 cm. latis ; petiolo tomen-
toso 3-3.5 cm. longo; corymbis ad 7 cm. longe pedunculatis 6-10 cm.
diametro planiusculis tomentellis, bracteis foliaceis reductis 0.8-1.6 cm.
longis ovatis petiolatis, pedicellis gracilibus 4-6 mm. longis ; capitulis
ca. 12 mm. longis; involucri squamis lanceolato-oblongis acutiusculis
dorso fusco-tomentellis 8-9 mm. longis ; corollis 5-6 mm. longis, tubo
gracili, faucibus campanulatis, limbi dentibus 5 latissime triangularibus
erectiusculis apicem versus tomentellis ; achaeniis 5 mm. longis atro-
brunneis glabris deorsum decrescentibus argute 5-costato-angulatis ;
costis albidis minutissime scabratis. — Las Escaleretas, Moras Valley,
Rio Paez basin, Tierra Adentro, State of Cauca, Colombia, altitude
2500-3000 m., February, 1906, Pittier, no. 1336 (type, in U. S. Nat.
Mus., fragm. in Gray Herb.). Notwithstanding its constantly 5-angled
achenes this species seems to be suspiciously near the plant described
below as Kanhnia violascens. The two differ sufficiently in leaf-form,
indumentum, length of peduncles, size of heads, etc., to be satisfactory
as species, but in placing them in different genera (though their tech-
nical characters appear to require it) there seems to be some
artificiality.

Mikania parviflora (Aubl.) Karst. Deutsche Fl. 1061 (1883);
Urb. ex Hieron. in Engl. Bot. Jahrb. xxviii. 579 (1901). Eupatorium
parviflorum Aubl. Fl. Guian. ii. 797, t. 315 (1775). — To the synonymy
of this widely distributed and moderately variable species should be
added, in the opinion of the writer, the following : Mikania olivacea
Klatt, Bull. Soc. Bot. Belg. xxxi. 195 (1892); Rob. & Greenm. Proc.
Am. Acad, xxxii. 12 (1896), and Wilhughbya Hieronymi Rusby, Bull.
N. Y. Bot. Gard. iv. 383 (1907). As thus interpreted, this species
ranges from Costa Rica to Guiana and Bolivia.

Mikania sulcata (Hook. & Am.), comb. nov. Eupatoritim mlcatnm
Hook. & Am. Comp. Bot. Mag. i. 243 (1835). Mikania j?en!<temon-
oides DC. Prod. v. 189 (1836). M. pentstemonoides Bak. in Mart. Fl.
Bras. vi. pt. 2, 221 (1876).

Mikania sulcata (Hook. & Am.) Robinson, var. ambigua (DC),
comb, nov. M. ambigua DC. Prod. v. 187 (1836). M. pentstemonoides,
var. ambigua (DC.) Bak. in Mart Fl. Bras. vi. pt. 2, 221 (1876).

198 PROCEEDINGS OF THE AMERICAN ACADEMY.

Mikania ternata (Vell.)> comb. nov. Cacalia ternata Veil. Fl. Flum.
(text) 336 (1825), viii. t. 56 (1827). Mikania dentata Spreng. Syst.
iii. 422 (1826) presumably, but scarcely of Schlecht. Linnaea, xi. 12
(1837), which notwithstanding the sign of affirmation employed by
Schlechtendal can from character hardly have related to the plant
described by Sprengel. M. apiifolia DC. Prod. v. 202 (1836).

Kanimia corymbiifolia, sp. nov., herbacea perennis erecta rigi-
dula glaberrima 6-7 dm. alta usque ad inflorescentiam corymbosam
simplici, internodiis infimis brevibus (2-15 mm. solum longis), supre-
mis usque ad 6 cm. longitudine ; foliis oppositis erectis appressis linear-
ibus crassiusculis rigidulis integerrimis 3-nerviis obtusis sessilibus 4-7
cm. longis 1-3 mm. latis superioribus gradatim minoribus ; inflorescentia
trichotoma 3-11 cm. lata planiuscula 4-20-capitulata ; bracteis anguste
linearibus plus minusve alternis 8-12 mm. longis ; capitulis (quoque
cum bracteola unica arete suffulto) 1.3 cm. altis 4-floris erectis ; involucri
squamis ovato-oblongis crassiusculis acutiusculis 2-3 mm. latis ; cor-
ollis 7 mm. longis, tubo gracili 3 mm. longo, faucibus brevissimis,
limbi dentibus lineari-oblongis ; achaeniis immaturis 4.5 mm. longis
summa parte 10-costato-angulatis ; pappi setis ca. 44 rufis 6 mm.
longis scabridis. — Moist meadows near a brook in the Serradao near
Cuyab^, Mattogrosso, Brazil, February, 1889, R. Pilger, no. 220 of Dr.
Hermann Meyer's second Brazilian journey. Type in the herbarium
of the Royal Botanical Gardens, Berlin ; fragments and tracing in the
Gray Herbarium. A species markedly distinct in habit from its con-
geners, resembling in its thickish firm ribbed narrow leaves some spe-
cies of the African genus Corymbium.

Kanimia violascens, sp. nov., scandens ubique a hirsutia densa
sordida violascenti tecta ; caule flexuoso torto multi-angulato, inter-
nodiis 6-9 cm. longis ; foliis oppositis petiolatis ovalibus grosse ere-
natis profunde cum sinu angusto cordatis ca. 4 cm. longis ca. 3.5 cm.
latis apice rotundatis crassiusculis bullato-rugosis ; petiolo 1.5-2 cm.
longo ; corymbis trichotomis axillaribus erectis ad 2 cm. longe peduncu-
latis cum bracteis foliaceis suborbicularibus munitis ; bracteolis parvis
ovalibus ; pedicellis 4-8 mm. longis ; capitulis 1.2-1.5 cm. altis 4-floris ;
involucri squamis oblongis apicem versus carinatis plus minusve at-
tenuatis sordide villoso-tomentosis ca. 9 mm. longis ; corollis 7 mm.
longis, tubo gracili glabro 4 mm. longo, faucibus campanulatis glabris ;
dentibus limbi 5 deltoideis erectiusculis apicem versus hispidulis ; achae-
niis 5.5 mm. longis nigris basin versus decrescentibus, costis plerumque
7-8 (rariter in eodem capitulo achaenio uno vel altero 5-costato) albidis
minutissime scabridis, pappi setis ca. 75 rufidulis corollam aequanti-
bus ; styli ramis gracillimis filiformibus longe exsertis et recurvatis

ROBINSON. — ON CERTAIN EUPATORIEAE. 199

antheris linearibus apice cum appendice ovata obtusa scariosa munitis.
— Alto del Tabano among the Andes of the southern Cordillera of Co-
lombia, altitude about 3500 m,, 4 May, 1876, E. Andre, no. 3123
(tj^pe, in Gray Herb.).

Brickellia amplexicaulis, sp. no v., herbacea vel fruticulosa 1.3-1.8
dm. alta ; caulibus teretibus medullosis saepe purpureis copiose et pa-
tente glandulari-pubescentibus ; foliis oppositis oblongis vel saepius
ovato-oblongis crenato-serratis vel -dentatis basi arete sessilibus late
cordato-amplexicaulibus ad apicem obtusiusculum angustatis 8-13 cm.
longis 2.5-5.8 cm. latis utrinque pubescentibus subtus paulo pallidior-
ibus saepe indumento densiori tectis pinuativenatis et a loco 1-1.5 cm.
supra basin 3-nerviis ; inflorescentia elongata laxe paniculata folioso-
bracteata ; pedicellis ad 5 cm. longis filiformibus patente adscendentibus ;
capitulis 1.2-1.5 mm. altis ca. 13-floris; involucri squamis angustis
tenuibus attenuatis valde inaequalibus viridibus vel saepe purpuras-
centibus vel etiam atropurpureis saltim exterioribus patente ciliolatis ;
corollis 9 mm. longis gracillimis exacte tubulatis glabris, faucibus nul-
lis, limbi dentibus brevissimis erectis ; styli ramis erectis nigrescenti-
bus modice clavellatis ; achaeniis breviter sed dense hirsutulis ; pappi
setis 50-60 laete albis quam corolla distincte brevioribus. — B. Wisli-
zeni var. Gray, PI. Wright, ii. 71 (1853). B. Wislizeni, wax. panicu-
lata Gray ace to Pringle, PI. Mex. (1885), nomen nudum. — Sonora :
near Santa Cruz, 1851, Charles Wright, no. 1136 (type, in Gray
Herb.) ; Huchuerachi, 4 December, 1890, Hartman, no. 325 ; Oakridge
Pass, Hartman, no. 333. Chihuahua : rocky hills near the city of
Chihuahua, 8 October, 1885, Pringle, no. 609 ; Sierra en Media, 28
September, 1899, E. W. Nelson, nos. 6475 and 6491 ; near Batopilas,
3-4 October, 1898, E. A. Goldman, no. 204. Sinaloa : Cerro Colo-
rado, 3 November, 1904, Brandegee. — This species, though somewhat
variable in the breadth and toothing of the leaves, seems to be constant
and readily recognizable as to essentials. It is readily distinguished
from B. Wislizeni by its smaller decidedly fewer- flowered heads,
looser inflorescence, and larger leaves.

Var. lanceolata (Gray), comb, nov., foliis quam eis formae typicae
multo angustioribus lanceolato-oblongis minus amplexicaulibus ca. 6 cm.
longis 1.2-1.5 cm. latis. — B. Wislizeni Gray, var. lanceolata Gray,
Syn. Fl. i. pt. 2, 107 (1884). — San Francisco Mountains, near Clifton,
Arizona, 1 November, 1880, E. L. Greene (type, in Gray Herb.).

Brickellia brasiliensis (Spreng.), comb. nov. Eupatorium brasili-
ense Spreng. Syst. iii. 417 (1826) ; DC. Prod. v. 182. Clavigera pini-
folia Gardn. in Hook. Lond. Jour. Bot. v. 461 (1846). Brickellia
pinifolia Gray, PI. Wright, i. 84 (1852) ; Bak. in Mart. Fl. Bras. vi. pt.

200 PROCEEDINGS OF THE AMERICAN ACADEIkf?-.

2, 372 (excl. syn. Carphephorus coridi/olius DC, which is clearly dis-
tinct). Mikania ericoides Mart, ex Bak. 1. c. (1876).

Brickellia coridifolia (DC), comb. nov. Carphephorus coridi-
foUns DC. Prod. vii. 267 (1838). This species, resting solely upon
the original material collected on the Serro do Frio, Minas Geraes,
Brazil, in 1833, Vautier, no. 314, was placed by DeCandolle in the
genus Carphepho)-us doubtless because he found the receptacle chaffy
at least to some extent. Dissection of a head from a cotype in the
Gray Herbarium shows the receptacle to be chiefly free from chaff.
At only one point two narrow scales, like the inner ones of the invo-
lucre, were crowded in among the flowers, and formed, as it were, a sort of
re-entrant part of the involucre. In all other respects the plant agrees
technically with Brickellia. Mr. J. G. Baker, in treating the Eupatorieae
for the Flora Brasiliensis, doubtfully reduces the species to a synonym
of Brickellia pinifolia (Gardn.) Gray — a species above reduced to
B. brasiliensis (Spreng.) Robinson — but the plant, when compared
with B. brasiliensis is obviously distinct. The involucral scales for
instance are very different, being in C. cordifolius nearly twice as long
as in B. brasiliensis. They are furthermore much more attenuate, dis-
tinctly 3-ribbed, and dorsally glandular-puberulent, while in B. brasili-
ensis they are glabrous and minutely many-striate. In involucre the
plant agrees much better with Brickellia than with the North Amer-
ican genus Carphephorus. Moreover, the limb of the corolla is very
short as in Brickellia instead of being rather deeply cleft as in Carphe-
phorus. The afiinities of the species appear to be with B. brasiliensis,
though without doubt the plant is specifically distinct. The species
being little known it seems worth while to put on record the traits
brought out by recent examination. Capitulis 8-floris turbinato-cam-
panulatis 1.2 cm. altis ca. 1 cm. diametro ; involucri squamis lanceo-
latis vel anguste oblongis acutis dorso convexis tomentellis striatulis
ca. 3-seriatis valde inaequalibus ; receptaculo parvo piano cum paleis
paucissimis marginalibus irregulariter munito ; pappi setis ca. 30
barbellatis corollas aequantibus ; corollis 7-8 mm. longis vix sursum
ampliatis, dentibus limbi 5, 0.5 mm. longis ; styli ramis clavellatis ;
antheris anguste oblongis vix connatis apice breviter et late appen-
diculatis basi integris ; achaeniis immaturis 2 mm. longis papillo-
sis deorsum decrescentibus 5-costato-angulatis cum nerviis obscuris
intermediis.

Brickellia diffusa (Vahl) Gray, PI. Wright, i. 86 (1852). Fupa-
torum dijusum Vahl, Symb. Bot. iii. 94 (1 794). To the synonymy of this
species should be added Eupatorium trichosanthum A. Rich. Fl. Cub.
Fanerog. ii. 41 (1853), the type of which was recently examined by

ROBINSON. — ON CERTAIN EUPATORIEAE. 201

the writer in the herbarium of the Museum of Natural History at
Paris.

Brickellia scoparia (DC.) Gray, var. subauriculata, var. nov.,
foliis basin versus paulo ampliatis ad 7 mm. latitudine subauriculatis,
auriculis brevissimis rotundatis, margine revolutis. — Hills of Zacatecas,
Mexico, 25 October, 1888, Pringle, no. 1766 (type, in Gray Herb.);
also en route from San Luis Potosi to Tampico, December, 1878, to
February, 1879, Palmer, no. 1077. The hitherto unpublished herba-
rium name of this variety has been on some plant-labels attributed to
Dr. Gray, but this seems to have been an error. So far as can be as-
certained from the material and records at the Gray Herbarium, Dr.
Gray regarded Palmer's no. 1077 as typical B. corymbosa, and the
Pringle plant was not collected until after Dr. Gray's death. Under
these circumstances it seems undesirable, as it is unnecessary, to em-
ploy a parenthetical authority in this case.

Kuhnia adenolepis, sp. nov., perennis, caulibus saepe 2 gracilibus
e caudice lignescenti oriuntibus erectis summa parte minutissime pube-
rulis 6-8 dm. altis teretibus obscure striatulis purpureis ; foliis alternis,
infimis ante anthesin delapsis, intermediis anguste lanceolatis integer-
rimis louge attenuatis 6-7 cm. longis 7 mm. latis saepe falc9.tis paten-
tibus utrinque viridibus glabris puncticulatis basi 3-nerviis ; foliis
superioribus gradatim minoribus, eis ramorum floriferum parvis line-
aribus ; capitulis paucis 2-3 in ramis gracilibus elongatis bractiferis
solitariis terminalibus erectis vel leviter nutantibus 12-13 mm. diame-
tro 18 mm. altis ca. 10-r2-floris ; involucri squamis viridibus albido-
striatis multiseriatim imbricatis, saltim exterioribus cum gland ulis
nigresceutibus subsessilibus eleganter ciliolatis ; corollis gracilibus
apicem versus atropurpurascentibus, dentibus limbi brevissimis sub-
erectis ; styli ramis nigresceutibus clavellatis conspicue exsertis ; pappi
setis valde plumosis leviter fulvescentibus. — Chapala Mountains, near
Guadalajara, Mexico, 13 December, 1889, C. G. Pringle, no. 2933
(type, in Gray Herb.). A species of graceful habit and seemingly
unique in its curiously glandular-ciliolate involucral bracts.

LiATRis TENUIFOLIA Nutt., var. laevigata (Nutt.), comb, nov., quam
forma typica conspicue robustior ; foliis 4-8 mm. latis coriaceis; capitulis
saepe sed non semper paulo majoribusetiam ad 9 mm. longitudine. —
L. laevigata Nutt. Trans. Am. Phil. Soc. vii. 285 (1840). L. tenuifolia
Nutt. /5 Torr. & Gray, Fl. ii. 70 (1841). Lacinaria laevigata (Nutt.)
Small, Fl. S. E. U. S. 1175 (1903). Laciniaria laevigata (Nutt.) Small,
1. c. 1339. — To this variety may be referred Mr. Nash's nos. 1669 and
2599 from Eustis, Florida, while Prof. Hitchcock's no. 154 from Marco,
Florida, represents a transition to the more slender typical form. It is

202 PROCEEDINGS OF THE AMERICAN ACADEMY.

believed that few persons will be disposed to follow the older authors
in uniting without distinction of name plants so conspicuously different
in their foliage as L. tenuifolia and L. laevigata, yet on the other hand
intergradation seems to be demonstrated and there are no differences
of much taxonomic significance. To maintain the larger plant as a
distinct species on the sole ground of its greater robustness, seems as
undesirable as to suppress it altogether.

II. REVISION OF THE GENUS BARROETEA.

BARROETEA Gray. (Clarissimo G. Barroeta doctori medicinae
et professori scholae metallorum ad oppidum mexicanum San Luis
Potosi dictum institutae ob amicitiam suam cum collectoribus botanicis
doctoribus Parryo et Palmero petito eorum dedicata.) — Capitula medi-
ocria 17-35-flora; involucri campanulati vel turbinati squamis valde
inaequalibus appresse imbricatis tenuibus costato-lineatis saepius at-
tenuatis raro obtusis vel apice rotundatis mucronulatisque ; receptaculo
piano nudo. Corollae tubulatae glabrae pallidae ad insertionem fil-
amentorum plus minusve constrictae, faucibus vix uUis, limbo breviter
5-dentato. Antherae distinctae vel levissime connatae, apice in appen-
dicem latam obtusissimam productae, basi rotundatae integrae. Styli
rami clavellati vel apud speciem unicam valde sursum incrassati, paulo
exserti. Achaenia valde obcompressa anguste oblonga, margine sursum
scabrata vel ciliolata, in facie exteriori vel uninervia vel conspicue uni-
costata, in facie interiori 2-3-nervia vel -costata. — Proc. Am, Acad. xv.
29 (1879), xvii. 206 (1882) ; Hemsl. Biol. Cent. -Am. Bot. ii. 102 (1881);
Hoffm. in Engl. & Prantl, Nat. Pflanzenf. iv. Abt. 5, 142 (1890).
Barroetia Hook. f. & Jacks. Ind. Kew. i. 276 (1893) ; Dalla Torre &
Harms, Gen. Siphon. 528 (1905). — Herbae graciles annuae vel pe-
rennes nonnunquam basi paulo lignescentes saepius ramosae foliosae
crispe puberulae vel tomentellae rarius glanduliferae. Folia vel omnia
opposita vel superiora alterna ovata petiolata vel sessilia crenati-
vel argute serrati-dentata, apice et dentibus saltim posticis in appen-
dices setiformes desinentibus. Capitula saepius in panicula laxiuscula
foliaceo-bracteata disposita.

Genus Brickelliae arete affineet eaehabitu, involucro, etc. simillimum
differt dentibus foliorum setiferis et praesertim achaeniis valde obcom-
pressis 5-6-costatis.

Species hucusque cognitae 7 omnes mexicanae praecipue montanae et
calciphilae locos umbrosos praeferentes, una (n. 1) excepta inter se
arctissime affines characteribus quamquam saepe obviis tamen incertis
et minus constantibus diagnoscendae.

ROBINSON. — GENUS BARROETEA. 203

Clavis specierum.

a. Pubescentia pedicelli glandulifera. Corolla achaenio distincte brevior.

1. B. glutinosa.

a. Pubescentia pedicelli non glandulifera. Corolla achaenium subaequans

vel eo longior, b.

b. Folia arete sessilia, c.

c. Capitula nutantia, involucri squamis subscariosis exterioribus cum

ceteris contiguis 2. B. Pavonii.

c. Capitula erecta, involucri squamis majus herbaceis exterioribus sub-

remotis 3. ^. sessilifolia.

h. Folia saltim caulina petiolata, d.

d. Achaenia obscure in faciebus nervata, e.

e. Folia argute et grosse dentata, dentibus omnibus longiuscule setigeris.
Capitula 17-23-flora 4. B. setosa.

e. Folia crenato-dentata, dentibus breviter setigeris vel setis ad apicem

et dentes 1-3 posticos restrictis. Capitula 30-35-flora.

5. B. subuligera.

d. Achaenia prominule et conspicue in faciebus 1-3-costata, /.

/. Inflorescentiae saltim secundariae conspicue dichotomae capitula

saepe in dichotomis gerentes ; pedicelli capitula longitudine

aequantes vel superantes 6. B. laxiflora.

f. Capitula subsessilia in ramis elongatis paniculae. 7. B. brevipes.

1. B. GLUTINOSA Brandegee, annua subsimplex vel pauclramea 1-2
dm. alta undique breviter denseque glandulo-puberula ; caule subtereti
purpurascenti ; foliis ovatis duplice crenato-serratis omnino esetosis
tenuibus utrinqiie viridibus subtus vix pallidioribus supra minute papil-
losis subtus resinoso-atomiferis 1-2 cm. longis 8-15 mm. latis basi sub-
truncatis vel subcordatis, petiolis 1-1.5 cm. longis ; capitulis 1-5 in
pedunculis axillaribus 4-50 mm. longis erectis vel leviter nutantibus
ca. 25-floris ; involucri campanulati 9 mm. alti squamis obtusis mucron-
ulatisque oblongo-lanceolatis atropurpureis ; corollis 3-6 mm. longis
sursum in fauces subdistinctos ampliatis ; styli ramis sursum valde in-
crassatis ; achaeniis 4 mm. longis griseis vix costatis scabridis, pappi
setis laete albis sursum scabridis achaenio brevioribus. — Zoe, v. 262
(1908). — In umbrosis montium Cerros dictorum prope San Luis Tul-
titlanpa, Puebla, Mexico, Purpus, n. 2625. Species generis ob statu-
ram minorem, indumentum purpureum glanduliferum, capitula pauca,
styli ramos apice crassissimos distinctissima.

2. B. Pavonii Gray, herbacea ramosa ; foliis ovatis basi subcordatis
vel subtruncatis tenuibus subduplice crenato-serratis ca. 3 cm. longis
2 cm. latis utrinque pubescentibus supra viridibus subtus pallidioribus,
apice et dentibus paucis posticis setuliferis ; capitulis laxe paniculatis
9 mm. altis ca. 15-floris in apice pedicelli gracilis 1 cm. longi nutanti-
bus ; involucri squamis anguste lanceolato-linearibus acutis subglabris

204 PKOCEEDINGS OF THE AMERICAN ACADEMY.

margine tenuissimis scariosis ; corolla achaenium subaequanti ; costis
achaenii nigrescentis sursum hispidulis, intervallis glabris. — Proc. Am.
Acad. xvii. 206 (1882). Eupatorium setiferum et E. ciispidatum herb.
Pavonii ex Grayo, 1. c. — Mexico, hb. Pa v. nunc hb. Boiss. Species ut
videtnr nunquam iterum lecta.

3. B. SESSiLiFOLiA Greenman, caule erecto tereti crispe pubescenti
6 dm. alto superne oppositirameo ; foliis arete sessilibus late ovatis basi
subtruncatis duplice serratis acutis supra laete viridibus subtus paulo
pallidioribus 2.5-4.5 cm. longis 1.4-3.5 cm. latis utrinque pubescentibus,
dentibus apiceque setuliferis ; panicula diffusa ; capitulis graciliter et
longiuscule pedicellatis ca. 17-floris; involucri squamis anguste lance-
olatis attenuatis viridibus albicostatis, margine scariosa; corolla 4.8
mm. longa ad insertionem filamentorum obscure constricta, superne
non ampliata ; styli ramis leviter clavellatis ; achaeniis nigrescentibus
3.5 mm. longis in facie* interior! 1- obverse plernmque 3-costatis. —
Proc. Am. Acad. xl. 35 (1904). — In collibus calcareis prope pagum
Yautepec, Morelos, Mexico, Pringle, n. 9865 ; in rupibus calcareis
convallis praeruptae Iguala, Guerrero, altitudine 915 m., Pringle, n.
10,322 ; et prope urbem Acapulco, Palmer, n. 625 (expeditionis Oct.
1894-Mar. 1895 factae).

4. B. SETOSA Gray, herba a basi decumbenti suberecta gracilis ca.
6 dm. alta ; caule tereti rubescenti minute crispeque puberulo opposi-
tirameo ; foliis ovatis argute serrato-dentatis 1.2-3 cm. longis 8-15
mm. latis membranaceis utrinque viridibus tenuiter puberulis, petiolis
4 mm. longis ; capitulis ca. 20-floris in axillis foliorum superiorum ped-
icellatis vel numerosioribus et in panicula plus minusve diffusa dispos-
itis 5 involucri squamis anguste oblongo-lanceolatis attenuatis saepe
purpurascentibus ; corolla et pappi setis achaenium superantibus ;
achaeniis facie interiori planiusculis obscure 1-nervatis dorso 2-nerva-
tis. — Proc. Am. Acad. xv. 29 (1879); Hemsl. Biol. Cent.-Am. Bot.
ii. 102 (1881). Barroetia setosa (Gray) Hook, f & Jacks. Ind. Kew.
i. 276 (1895). — San Luis Potosi, altitudine 1830-2440 m., Parr^/ &
Palmer, n. 353 ; in collibus calcareis prope pagum Cardenas, San Luis
Potosi, Pringle, nn. 3319, 3320.

5. B. suBULiGERA (Schauer) Gray, perennis saepe basi suffrutescens ;
caulibus 1 vel saepe pluribus teretibus suberectis laxe ramosis fere a
basi foliatis 4-8 dm. altis crispe tomentellis vel puberulis ; foliis del-
toideo-ovatis crenato- serratis utrinque pubescentibus vel puberulis 1-3
cm. longis 9-18 mm. latis, apice saepe obtusiusculo et dentibus saltim
1-3 posticis vel saepe omnibus cum setis munitis ; capitulis ca. 30-
floris 1 cm. altis ; involucri squamis linearibus vel lineari-lanceolatis
attenuatis plerumque viridibus ; coroUis gracilibus 5.5-7 mm. longis ad

ROBINSON. — GENUS BARROETEA. 205

insertionem filamentorum constrictis, faucibus vix ullis, limbi dentibus
brevissimis ; achaeniis 3-3.8 mm. longjs, faciebus planiusculis vix ner-
vatis. — Proc. Am. Acad. xv. 29 (1879); Hemsl. Biol. Cent-Am. Bot.
ii. 102 (1881). Bulhostylis subuligera Schauer, Linnaea, xix. 718
(1847). Eupatorium ? subidigerum (Schauer) Gray, PL Wright, i. 86
(1852) ex Hemsl. 1. c. sed combinatio a Grayo non expressim facta est.
Barroetia subuligera (Schauer) Hook. f. & Jacks. Ind. Kew. i. 276
(1895). — In reipublicae mexicanae late distributa. Hidalgo: ad
Zimapan, Asckenborn, n. 260 (specimen typicum, hb. Berol., fragmentis
a cl. Eichlero benevolente missis in hb. Grayano etiam conservatis).
Chihuahua : in montibus Santa Eulalia, Pringle, n. 346 ; in convalle
praerupta Bachimba, Pringle, n. 111. Coahuila : adSoledad, Palmer,
n. 452 (armo 1880) ; prope Torreon, Palmer, n. 483 (anno 1898).
Zacatecas : prope Arroyo Cedros, Kirkwood, n. 35. Durango : ad
Mapimi, Palmer, n. 519 (anno 1898).

Var. LATiSQUAMA Grecnman, foliis majoribus usque ad 5 cm. longis
3.5 cm. latis ; capitulis paulo majoribus 30-35-floris ; involucri squamis
anguste lanceolati-oblongis purpurascentibus obtusis vel apice rotun-
datis et mucronulatis. — Proc. Am. Acad. xl. 35 (1904). — In collibus
prope Etzatlan, Jalisco, Pringle, n. 8773.

6. B. LAXiFLORA Brandegee, annua crispe puberula diffuse oppos-
itiramea, ramis patente adscendentibus gracilibus ; foliis late ovatis
vel deltoideo-ovatis tenuibus grosse crenatis vel plus minusve argute
dentatis utrinque tenuiter pubescentibus vel glabriusculis basi truncatis
vel late cordatis ad insertionem petioli saepe breviter cuneatis apice
saepe obtuso et dentibus plerisque posticis cum setis munitis ; foliis
caulinis 4-6 cm. longis 3-5 cm. latis graciliter ad 2.5 cm. longe petio-
latis, ramealibus multo minoribus nunc ovato-oblongis nunc triangu-
lari-lanceolatis 3-5 mm. longe petiolatis ; capitulis graciliter saepius
longiuscule pedicellatis 9 mm. altis 4.5 mm. diametro ca. 23-floris ; in-
volucri squamis anguste lanceolatis vel linearibus attenuatis viridibus
albo-striatis, interioribus ad 7 mm. longitudine; corollis achaenia
longitudine subaequantibus tubulosis sine faucibus ullis distinctis ;
achaeniis in facie interiori 1-costatis in facie exteriori 2-costatis in cos-
tis et etiam saepe inter eas sursum hispidulis. — Univ. Calif. Publ.
Bot. iv. 93 (1910). — PuEBLA : Coxcatlan, Purpus, n. 4128. Oaxaca :
in convalle praerupta Tomellin dicta, altitudine 915 m., Pringle, n.
5968 ; Cuicatlan, altitudine 550-600 m., Pringle, n. 5799, E. W. Nel-
son, n. 1868. SiNALOA : prope Culiacan, Schaffner, Brandegee. Ala-
mos : Palmer, n. 677 (anno 1890).

7. B. brevipes, sp. nov., oppositiramea ; caule tereti purpurascenti
crispe pubescenti, internodiis folia multo superantibus; ramis elon-

206 PROCEEDINGS OF THE AAIERICAN ACADEMY.

gatis plus minusve flexuosis; foliis triangulari-ovatis late cordatis cre-
nato-serratis apice et dentibus 1-3 latere utroque basin versus setigeris
supra viridibus sparse pubescentibus subtus paulo pallidioribus in venis
villosulis, caulinis ca. 3 cm. longis 2.5 cm. latis graciliter (praecipue
iuferioribus) petiolatis, ramealibus 1-2.5 cm. longis subsessillibus ; cap-
itulisca. 18-21-florisnumerosisbrevissime pedicellatis vel subsessilibus
in ramis paniculae longis flexuosis spiciformibus bracteatis interrupte dis-
positis; involucri squamis viridibus albo-costatis lanceolato-linearibus
valde inaequalibus vix subuligeris, interioribus ca. 1 cm. longis ; cor-
ollis gracillime tubulosis 4.3 mm. longis; achaeniis atrobrunneis valde
compressis lineari-oblongis 3.6 mm. longis; pappi setis ca. 18 albis
corollas aequantibus. — Oaxaca : secundum viam ad Cuicatlan alti-
tudine 2075-2380 m., 3 Oct. 1894, E. W. Nelson, n. 1520 (specimen
typicum in herb. Grayano conservatum). Species capitiilis subsessil-
ibus facile diagnoscenda.

III. ON SOME HITHERTO UNDESCRIBED OR MISPLACED

COMPOSITAE.

Microglossa mespilifolia (Less.), comb, nov. Aster mespilifoliiis
Less. Syn. Conip. 180 (1832). Nidorella mespilifolia (Less.) DC. Prod,
v. 321 (1836). Microglossa mesplloides Benth. & Hook. f. Gen. ii.
282 (1873), without express combination and with obvious clerical
error as to the specific name; Hook. f. & Jacks. Ind. Kew. ii. 229
(1895).

Psiadia Boivini (Klatt), comb, nov, Pluchea Boivlni Klatt, Ann.
Sci. Nat. ser. 5, xviii. 369 (1873). As suspected by Cordemoy, Fl. de
rile de la Reunion, 526 (1895), this species proves on examination of
Dr. Klatt's type (now in the Gray Herbarium) to have the characters
of a Psiadia and not of a Pluchea. The anthers, for instance, are en-
tire and rounded at the base and not caudate. Whether or not Cor-
demoy's Psiadia Frappieri may prove a synonym is a point which
cannot be determined from description alone. In any event, however,
the earlier specific name of Klatt would have to prevail.

Pluchea rubelliflora (F. v. Muell.), comb. nov. Eyrea ruhelUfiora
F. v. Muell. Linnaea, xxv. 403 (1852-53). Pluchea EyreaY. v. Muell-
Rep. Babb. Exp. 11, 12 (1858); Benth. Fl. Austral, iii. 528(1866).
— The restoration of von Mueller's earlier specific name becomes neces-
sary under the International Rules of Nomenclature.

Rutidosis multiflora (Nees), comb. nov. Styloiicerus multlflorus
Nees in Lehm. PI. Preiss. ii. 244 (1846-47). Pumllo argyrolepis
Schlecht. Linnaea, xxi. 448 (1848). Actinopappus perpusillus Hook. f.

KOBINSON. — ON CERTAIN COMPOSITAE. 207

aud A. Drummondii Gray in Hook. Jour. Bot. and Kew. Misc. iv. 22G
(1852). PumiloPreissii Sonder, Linnaea, xxv. 487 (1852-53). Rutidosis
Pum'ilo Benth. Fl. Austral, iii. 595 (1866), It is obvious that Ben-
tham's specific name Pumilo, though long current, cannot stand under
the International Rules, since it is antedated by several other names.
Of the various designations under which the plant has been described,
Nees's Stijloncerus multiflorus bears the earliest date. It was pub-
Kshed in the second fascicle of the second volume of Lehmann's Plantae
Preissianae, and the preface of this volume, which included three fas-
cicles, was dated November, 1847. Meisner under date of July, 1848,
speaks (Flora, 1848, p. 4'J6) of the second and third fascicles of the sec-
ond volume of Lehmann's work as just issued, an expression, which at
least so far as it concerns the second fascicle presumably means some-
time during the spring or early summer of 1848. Schlechtendal's
Pumilo argyrolepis was also published in 1848, a circumstance raising
no small doubt as to the relative priority of these names. Yet it is to
be noted that on a preceding page of his paper (Linnaea, xxi. 444)
Schlechtendal refers to an article in the issue of the Botanische Zeit-
ung, dated 26 May, 1848, proving that Schlechtendal's own publica-
tion must have been distinctly later. Indeed, it is shown therein that
in the meantime added plants had been found by one of his corres-
pondents, had been sent for identification, were studied, described, and
the descriptions had reached print, all of which is not likely to have
happened between the end of May and July, when as stated by Meisner
fascicles 2 and 3 of the second volume of the Plantae Preissianae
had already been issued (at what previous date we do not know).
There is certainly nothing to show that the paper of Schlechtendal
preceded that of Nees. In default of such evidence, precedence may
be determined by the second clause of Article 39 of the International
Rules, which reads: "In the absence of proof to the contrary the date
placed on the work containing the name or combination of names is
regarded as correct." This, in the case of Nees's Styloncerus multi-
florus is, as we have seen, " 1846-47," while with Schlechtendal's
Pumilo argyrolepis it is 1848.

Origin and Identity of Pharetranthus. The genus Pharetran-
thus Klatt, published in Flora, Ixviii. 203 (1885), was founded on
specimens collected by Hugh Cuming (no. 2454). These were sup-
posed to have come from the Philippine Islands both by Klatt, who
described them, and by Schultz Bipontinus, who seems to have made
a preliminary examination of them. The genus was tentatively placed
in Coreoj)sis by 0. Hoffmann in Engl. & Prantl, Nat. Pflanzenf iv. Ab.
5, 243 (1890), an opinion which he later— 1. c. iv. Ab. 5, 390 (1894),

208 PROCEEDINGS OF THE AMERICAN ACADEMY.

and Nachtr. zu iv. Ab. 5, 325 (1897) — revised by referring Phare-
tranthus Klatt to Fetrobium R. Br. While the name Petrohium R,
Br. must, according to the International Rules of Nomenclature, give
way to the earlier and adequately published name of Laxmannia Forst.
& Forst. f , the identity of Pliaretranthus, supposedly of the Philippine
Islands, with this peculiar monotypic genus, of the island of St. Helena,
presents a taxonomic and geographic problem which seems never to
have been discussed. Such an identity is certainly improbable on
phytogeographic grounds, especially in the case of a species wholly
unknown from intermediate localities. Dr. Klatt's type of his Phare-
tranthus ferrugineus is preserved in the Gray Herbarium, and in fact
appears to be identical with Lawmannia Forst. & Forst. f , the " White-
wood Cabbage-tree " of St. Helena. Examination of accessible works
on the Philippine flora, including Mr. Elmer's recent enumeration of
the Compositae of the Philippine Islands, fails to show any record of
the species in question. Under these circumstances it seems highly
probable that there was some confusion of labels or other slip or error
in attributing the plant of Cuming to the Philippine Archipelago. In
this connection it is to be noted with interest that on his return voy-
age Hugh Cuming stopped at St. Helena, where it is more than likely
that he obtained the material upon which Dr. Klatt later founded his
genus Pharetranthus. At all events such an origin would appear to
be a permissible assumption or at least a justifiable working hypothesis
until the plant can be re-discovered in the Philippine Islands if this
ever happens. The synonymy of the species in question is as follows :

Laxmannia arborea Forst. & Forst. f Char. Gen. 94, t. 47 (1776).
Spilatitkes arborea (Forst. & Forst. f.) Forst. f. Com. Hort. Goett. ix. 67
(1787). Spilanthes tetrandra Roxb. in Beatson's Tracts, 301 (1816),
which was the sterile plant, and Bidens arborea Roxb. 1. c. (1816),
which was the corresponding fertile plant. Petrobium R. Br. Trans.
Linn. Soc. xii. 113 (1816). P. arboreum R. Br. ex DC. Prod. v. 502
(1836). Drimyphyllum Helenianum Burch. ex DC. 1. c (1836). Phare-
tranthus ferrugineus Klatt, Flora, Ixviii. 204 (1885).

Tragoceras Schiedeanum Less. Linnaea, ix. 269 (1834). To the
synonomy of this species should be added Baltimora monocephala Klatt,
Ann. k. k. Naturh. Hofmus. Wien, ix. 360 (1894), a species founded
upon a specimen collected by Knechtel at Chapultepec, Mexico, and
now in the Gray Herbarium. The identity appears first to have been
noted by Dr. J. M. Greenman, but seems not to have been hitherto
recorded in print.

Monactis subdeltoidea, sp. nov., fruticosa ramosa ; ramis flexuosis
crassiusculis subteretibus vix striato-angulatis brunnescentibus tomeu-

ROBINSON. — ON CERTAIN COMPOSITAE. 209

tellis, indumento e pilis multicellularibus tenuissimis plus minusve
inter se implexis composito ; foliis alternis subdeltoideo-ovatis acutis
nee acuminatis basi subtruncatis glandulari-denticulatis (glandulis inter
se 3-5 mm. distantibus) supra tenuiter sed densiuscule pubescentibus
subtus molliter tomentosis canescentibus, lamina 5-6 cm. longis 3-3.5
cm. latis paulo supra basin 3-nervata; petiolo cuneato-alato ca. 1.2 cm.
longo ad insertionem laminae usque ad 7 mm. latitudine expanse ;
inflorescentia planiuscula multicapitulata, bracteis lanceolatis subses-
silibus ; capitulis radiatis 7 mm. altis, disco ca. 7 mm. diametro ; in-
volucri campanulati squamis sub-triseriatim imbricatis arete appressis
ovato-oblongis obtusis sordide lanoso-tomentosis ; flosculis radialibus
ca. 6 Q , ligulis late oblongis vel ellipticis apice brevissime 3-dentatis 5-7
mm. longis 3-3.6 mm. latis laete flavis, tubo ea. 1.5 mm. longo plus
minusve piloso ; flosculis disci ca. 25 $ , corollis flavidis, tubo 1.5 mm.
longo faueibus subeylindricis 2 mm. longis, limbi dentibus 5 breviter
triangularibus ; acliaeniis immaturis prismaticis 2.7 mm. longis omniuo
ealvis glabriuseulis. — ■ On banks of the Maehangara River, near Quito,
Ecuador, 2750 m. altitude, 21 January, 1856 ; W. Jameson, no. 162
(type, in Gray Herb.). From the original 31. Jlaverioides HBK. of
Venezuela, as well as from the recent M. Jelskii Hieron. of Peru, the
present species differs in its many-flowered heads, the disk-flowers
being about 25, while in M. Jlaverioides they are said to be 5-10 and
in M. Jelskii they are 6-7. Furthermore, the form of the leaf in the
Ecuadorean plant is very different from either of the other species, the
blade being more nearly deltoid with a truncate base somewhat sharply
distinguishable from the cuneately winged petiole.

Montanoa tehuacana, sp. nov., frutieosa vel arboreseens 3-5 m.
alta ramosa ; ramis plerisque oppositis divergentibus areuato-adscen-
dentibus foliosis leviter striatis tenuissime puberulis juventate brunneis
deinde griseis ; foliis oppositis, supra pallide viridibus scabris et cum
pilis brevissimis basi incrassatis munitis, subtus caneseenti-tomentellis
reticulato-venosis, inferioribus 2 dm. longis 1.6 dm. latis patente trilo-
batis, lobis lateralibus latis crenato-angulatis, lobo terminali variabili
vel obtuso vel acuto vel etiam acuminato in eodem specimine, petiolo
usque ad 8 cm. longo in parte superiori euneato-alato ; foliis superiori-
bus, i. e. ramulorum floriferum obovato-oblongis firmiusculis obtusis
supra rugosis ca. 4 cm. longis ca. 1.5 cm. latis obsolete erenulato-
serratis basi brevissime petiolatis et (supra petiolum) eordato-biau-
rieulatis, aurieulis rotundatis ; capitulis laxe corymbosis graeiliter
pedicellatis ea. 3 cm. diametro (ligulis inclusis) ; involucri squamis
ovato-lanceolatis anthesi ca. 6 mm. longis griseo-tomentellis ; paleis
a basi late ovata membranacea pallida in apicem longum spinosum

VOL. XL VII. — 14

210 PROCEEDINGS OF THE AMERICAN ACADEMY.

patentem abrupte contractis. — Tufa bluffs near Tehuacan, Puebla,
Mexico, 1680 m. altitude, 7 August, 1901, C. G. Pringle, no. 8585
(type, in Gray Herb.) ; in the vicinity of San Luis Tultitlanapa, Puebla,
near Oaxaca, August, 1908, C. A. Purpus, no. 3105 (Gray Herb.) and
no. 3104 (Gray Herb.). The last-mentioned specimen has the upper
leaves closely sessile instead of being provided with the usual very short
wingless petioles beneath the auricles, but the plant is otherwise so
closely identical that it must be inferred that this variation is merely
formal and trifling. The affinity of the species is clearly with M.
Pringlel Robinson & Greenman, Proc. Am. Acad, xxxiv. 512 (1899),
which, however, has leaves of quite a different type of serration and the
involucral bracts of a peculiar obovate-spatulate form.

Lepidesmia squarrosa Klatt, Bull. Herb. Boiss. iv. 479, t. 7(1896).
This species, the type of a newly distinguished as yet monotypic genus,
was founded upon a plant collected in dry places at Caimanera, Cuba,
by von Eggers, May, 1889 (no. 5439). Dr. Klatt was inclined to regard
his genus as being of the Eujyatorieae Ageratinae and very nearly re-
lated to Asche?ibomia. Hoffmann in Engl. & Prantl, Nat. Pflanzenf.
Nachtr. 321, 322 places Lepidesmia next Ageratum and distinguishes
it from that genus chiefly by the more imbricated involucral scales.
However, even a cursory inspection of the type of Lepidesmia, as repre-
sented by fragments in the herbarium of the late Dr. Klatt, led the
writer to believe that the plant could not belong among the Eupatorieae,
and a careful dissection has shown that the style-branches, instead of
having the clavate unappendaged form found in the Eupatorieae, are
divided into a basal rather short thickish and somewhat compressed
portion surmounted by a rather elongated attenuate and papillose ap-
pendage in the manner of many Heliantheae. In fact, it seems proba-
ble that the genus should be placed near Isocarpha R. Br. In habit,
as well as in technical characters, it is not very unlike /. oppo-
sitifolia R. Br., which also possesses opposite leaves, which are lan-
ceolate and subsessile, glomerate heads with subscarious involucre and
chaffy receptacle. However, the distinct pappus, much smaller heads,
and flattish receptacle furnish ample generic distinctions.

losTEPHANE TRiLOBATA Hemsl. Biol. Cent. -Am. Bot. ii. 169 (1881).
With this species the following appear to be identical : Budbeckia
chrysantka (Sch. Bip.) Klatt, Leopoldina, xxiii. 143 (1887), page 3 of
reprint, and Echinacea chrysantha Sch. Bip. ace. to Klatt, 1. c. (1887),
page 4 of reprint. The species of Schultz Bipontinus seems never to
have been described until taken up and transferred to Rudbeclia by
Klatt. It rested upon Liebmann's no. 575, collected at Cubre de
Estepa, Mexico. In the herbarium of the late Dr. Klatt, a collection

ROBINSOX. — ON CERTAIN COMPOSITAE. 211

now incorporated in the Gray Herbarium, there is a single head and an
excellent sketch of Klatt's type, both of which clearly show the species
to have been an lostephane, identical so far as can be seen with the
earlier /. trilohata of Hemsley. Here also should be placed, as it ap-
pears, the recently published Gymnolomia scaposa Brandegee, Univ.
Calif. Publ. Bot. iv. 93 (1910).

Perymenium Peckii, sp. nov., fruticosum gracile 3-9 m. altum in
plantis adjacentibus se suffulciens quasi scandens ; caule tetragono
scabro in speciminibus siccatis 4-sulcato brunneo, internodiis 4-5 cm.
longis ; foliis oppositis lanceolatis tenuibus graciliter petiolatis acumi-
natis obscure et remote serrulatis 3-nerviis basi rotundato-subacutis
5 cm. longis 1.5 cm. latis supra viridibus minute et adpresse pilosis
subtus distincte pallidioribus molliter pabescentibus fere tomentosis
non solum in nerviis sed etiam inter eas ; petiolo 7-9 mm. longo ;
panicula oppositiramea ovoidea foliaceo-bracteata 1.3 dm. longa 1 dm.
diametro, ramis curvato-adscendentibus, corymbulis ca. 2 cm. diametro
5-7-capitulatis, pedicellis gracilibus 2-8 mm. longis; capitulis ca. 5-
radiatis 6 mm. altis ; involucri ovoidei squamis inaequalibus late ovatis
obtusis strigillosis ; ligulis albidis apice profunde 2-3-dentatis vel etiam
-lobatis ca. 4 mm. longis fertilibus ; flosculis disci ca. 15 ; achaeniis
valde immaturis compressis oblanceolatis ; pappi aristis ca. 10 valde
inaequalibus stramineis scabridis. — In openings in the forest, British
Honduras, Prof. Morton E. Peck, no. 284 (type, in Gray Herb.). This
species is most nearly related to P. miavcephalum Sch. Bip., which,
however, has longer bright yellow ligules nearly entire at the tip, and
leaves of a very different pubescence, the lower surface being nearly
smooth except along the strigillose nerves.

Verbesina caracasana Robinson & Greenman, Proc. Am. Acad,
xxxiv. 559 (1899). This species, hitherto known only from Venezuela,
may be recorded from Colombia, where it was collected in Santa Marta,
November, 1898-1901, altitude 460 m., by H. H. Smith, no. 510 (Gray
Herb.). Mr. Smith's specimen examined is immature (still in bud),
but shows clear identity with the Venezuelan plant. It was distrib-
uted as F. dlversifolia DC, a species which has alternate leaves and
many other differences.

Verbesina Columbiana, sp. nov., ubique griseo-puberula verisi-
militer herbacea alta robusta ; caule teretiusculo exalato striato-angu-
lato medulloso ; foliis alternis pinnatifidis 2-3 dm. longis 1.2-1.7 dm.
latis utrinque griseo-viridibus dense et scabriuscule puberulis, lobis
ca. 7, oblongis vel oblongo-lanceolatis acuminatis serrulatis 1-7 cm.
longis 0.7-2.5 cm. latis; petiolo 6-8 cm. longo bialato 1.5-1.7 cm.
latitudine basi biauriculato ; inflorescentia composite corymbosa plana

212 PROCEEDINGS OF THE AMERICAN ACADEMY.

2.5 dm. diametro multicapitulata griseo-tomentella, pedicellis filiformi-
bus 6-8 mm. longis ; capitulis ovoideo-subglobosis ca. 38-floris
anthesi ca. 5 mm. diametro ; involucri squamis oblongis acutis vel acu-
minatis pallidis dorso molliter piiberulis, extimis multo brevioribus
apice obtusiusculis vel etiam rotundatis crassiusculis nigrescentibus ;
flosculis liguliferis ca. 5 pistilliferis, ligulis albis subquadratis 3-dentatis
2.5 mm. longis, tubo 2 mm. longo tomentello ; corollis disci 3.5 mm.
longis, tubo et faucibus tomentellis ; acheniis obovatis late bialatis, facie-
bus plus minusve in media parte carinatis sursum scabridis vel tnber-
culatis, pappi aristis 2 subaequalibus. — Santa Marta, Colombia,
December, 1898-1901, altitude 75 m., H. H. Smith, no. 671 (type, in
Gray Herb.) ; also from tbe banks of the Magdalena River, Quematido,
Colombia, 5 December, 1875, Andre, no. 222 (Gray Herb.). The latter
specimen is said to have been herbaceous and 3-5 m. high. Mr. Smith's
plant was distributed as V, gigantea Jacq., but it differs from that spe-
cies of the Antilles in having heads about 38-flowered instead of about
20-flowered, in having broadly winged achenes, and in details of foliage
and involucre. The related Y. myriocephala Sch. Bip. of Mexico also
has smaller subcylindric about 20-flowered heads and narrowly winged
achenes.

Verbesina costaricencis, sp. nov., herbacea vel basi lignescenti
alta ; caule teretiusculo leviter striato-angulato glabro exalato purpur-
ascenti glaucescenti medulloso ; foliis alternis magnis longipetiolatis
profunde pinnatifidis 1.5-2 dm. longis 1—1.4 dm. latis supra dense
scabro-pubescentibus atroviridibus subtus pallidioribus molliter pubes-
centi-tomentellis, lobis ca. 11 lanceolato-oblongis acuminatis obsolete
subremoteque serrulatis 7-10 cm. longis 2-3.5 cm. latis, rhachi alato
1-1.3 cm. lato, sinubus rotundatis ; corymbis compositis terminalibus
planiusculis multicapitulatis 1.5 dm. diametro basi foliaceo-bracteatis ;
capitulis obovoideis discoideis 8 mm. altis 5 mm. diametro ; involucri
squamis exterioribus valde inaequalibus anguste oblongis apice sub-
herbaceis nigrescentibus rotundatis vel vix mucronulatis 1-4 mm.
longis interioribus subaequalibus ca. 6 mm. longis tenuibus diaphanis
acutiusculis glabriusculis margine erosis ; flosculis liguliferis nullis, eis
disci ca. 21 ; corollis 3.6 mm. longis, tubo proprio plus minusve con-
stricto strigilloso brevi, faucibus cylindricis tubo duplo longioribus, limbi
dentibus oblongo-lanceolatis ; achaeniis compressis oblanceolatis sur-
sum hispidulis basin versus attenuatis tenuiter costatis marginatis vix
alatis ; pappi aristis saepius 3 achaenium subaequantibus duabus inter
se continguis in angulo interiori, tertia eis opposita. — V. nicaraguen-
sh .7. D. Sm. Enum. PI. Guat. v. 44 (1899), not Benth. — Rio Virilla,
San Jos^, Costa Rica, altitude 1100 m., December, 1895, Ad. Tonduz*

ROBINSON. — ON CERTAIN COMPOSITAE. 213

110. 9833 herb. nat. Cost. (= no. 7068 distrib. J. D. Srn.). This plant
is clearly distinct from V. nicaraguensis Benth., which has 8-10-rayed
heads, widely winged achenes, and a different leaf-contour.

Verbesina gigantoides, sp. no v., robusta alta ; caule crasso ter-
etiusculo purpurascenti glaberrimo plus minusve pruinoso intus cum
medulla alba constipato ; foliis alternis pinnatifidis longe petiolatis
firmiusculis supra glaberrimis lucidulis plus minusve ruguloso-bullatis
subtus olivaceis molliter pubescentibus 2-3 dm. longis 1-2.5 dm.
latis, rhachi alata ca. 2 cm. lata, lobis ca. 11 lanceolatis caudato-atten-
uatis saepe falcatis integerrimis vel obscure undulatis 8-15 cm. longis
2.5-4 cm. latis, infimis reflexis; sinubus rotundatis; petiolo tereti-
usculo purpurascenti glaberrimo omnino exalato ; panicula ampla valde
convexa pubescenti ; bracteolis lineari-filiformibus ; pedicellis 3-6 mm.
longis ; capitulis numerosissimis 5 mm. diametro 7 mm. altis ca. 20-
floris ; involucri squamis obovato- vel oblanceolato-oblongis abrupte
acutiusculis margine ciliata excepta glabriusculis ; flosculis liguliferis
ca. 4-5 pistilliferis ; ligulis albis oblongis 3.5 mm. longis apice leviter
3-dentatis ; flosculis disci ca. 15, corolla albida subcylindrica, tubo
pubescenti, limbi dentibus 5 oblongo-lanceolatis ; antheris linearibus
nigrescentibus vix connatis ; achaeniis 3.5 mm. longis pyriformibus
auguste alatis deorsum valde attenuatis, alis ciliato-laceris, pappi aristis
2 subaequalibus ca. 2 mm. longis. — V. gigantea Robinson & Green-
man, Proc. Am. Acad, xxxiv. 561 (1899), in part, not Jacq. — From
near Yajalon, Chiapas, Mexico, 21 November, 1895, E. W. Nelson, no.
3423 (type, in Gray Herb.). This is one of several habitally similar
plants, which have been in a preliminary way referred to V. gigantea
Jacq. Happily, through the careful definition and segregation of the
West Indian species by Prof. Urban, Symb. Ant. v. 264-265 (1907), it
has become possible to interpret more definitely the continental forms
of this group.

Verbesina leucactinota, sp. nov., perennis verisimiliter herbacea
robusta alta griseo-tomentella ; caule subtereti leviter striate exalato ;
foliis alternis pinnatifidis supra viridibus scabriusculo-puberulis subtus
molliter griseo-tomentellis 2 dm. vel ultra longitudine 1.3 dm. latis
saepius 9-lobis ; lobis lanceolatis 4-7 cm. longis attenuatis 1..3-2.3 cm.
latis, sinubus rotundatis ; petiolo late bialato basicum auriculis magnis
amplexicauli sed alis in caule non decurrentibus ; inflorescentia panicu-
lata magna valde convexa ; bracteis foliaceis anguste lanceolato-ob-
longis acutis integris 4-8 cm. longis ca. 1 cm. latis basi biauriculatis ;
capitulis ca. 27-floris conspicue radiatis ; flosculis liguliferis ca. 5 ; li-
gulis ellipticis albis breviter apice 3-dentatis 4 mm. longis ; corollis
disci albidis 3 mm. longis ; antheris nigrescentibus conspicue exsertis ;

214 PROCEEDINGS OF THE AMERICAN ACADEMY.

achaeniis valde immaturis oblanceolatis ; pappi aristis 2 subaequalibus
achaenium subaequantibus. — V. diversifoUa Britton, Bull. Torr. Bot.
Club, xix. 150 (1892), not DC. — Coripati, Yungas, Bolivia, April,
1894, Bajig, no. 2135 (type, in Gray Herb.). Tbough doubtfully re-
ferred to V. diversifoUa DC. by Robinson & Greenman, Proc. Am.
Acad, xxxiv. 562 (1899), this plant with wingless stem and about 9-
lobed leaves now seems clearly distinct from that Brazilian species. It
is nearer V. gigantea Jacq., from which, however, it differs in its more
numerous rays, more strongly auriculate petioles, harsher pubescence,
and in many other details. From V. columbiana, here described, it
differs in its smaller less numerously flowered heads, more developed
rays, etc. It is also near V. myriocephala Sch. Bip. of Mexico, but
differs in its more convex inflorescence, scabrous-puberulent stem, nar-
row elongate and entire bracts, etc.

Verbesina (§ Lipactinia) oligantha, sp. nov., fruticosa 2-3 m.
alta ; caule teretiusculo exalato griseo scabrido-puberulo aetate lenti-
cellis parvis late ellipticis brunneis aspero ; foliis oppositis rhomboideo-
ovatis 1.2-1.6 dm. longis 5-7 cm. latis acuminatis serratis basi cuneatis
integris utrinque viridibus scaberrime puberulis, nerviis lateralibus
prineipibus 3-4 plus minusve ex eodem loco (2-3 cm. supra basin)
oriuntibus, ceteris remotioribus et pinnatim locatis ; petiolo 1-1.5 cm.
longo crispe et scabride puberulo ; cymis compositis planis multicap-
itulatis densiusculis basi foliaceo-bracteatis, pedicellis filiformibus
erectiusculis 1-7 mm. longis; capitulis 12 mm. altis 4 mm. diametro
saepissime 7-floris ; involucri squamis valde inaequalibus, exterioribus
multo brevioribus ovatis 2-3 mm. longis interioribus oblongis abrupte
acuminatis 6 mm. longis flosculos amplectentibus ; coroUis omnibus tu-
bulosis flavis ; achaeniis valde compressis oblanceolatis olivaceis in facie-
bus paulo pubescentibus apicem versus angulo interiori anguste alatis,
— In granitic soil, Jimalcota, Mexico, altitude 300 m., 18 November,
1898, E. Langkisse, no. 644 (type, in Giay Herb.). It is clear that this
species is closely related to V. paucijlma Hemsl. but it differs mark-
edly in its' less conspicuous but more scabrous pubescence, its broadly
rhomboic-ovate leaves, and in its less herbaceous much smoother
involucre.

Calyptocarpus blepharolepis, sp. nov., annuus prostratus multi-
caulis et fere a basi patente oppositirameus ; caulibus ramisque gracilibus
teretibus striatulis flexuosis cum pilis albis hirsutulo-pubescentibus
plerumque bis bifurcatis ; internodiis saepe longissimis ; foliis oppos-
itis petiolatis spatulato-obovatis integris apice rotundatis mucronulatis
utrinque cum pilis albis basi incrassatis strigosis 2-2.5 cm. longis
1.1-1.4 cm. latis subtus distincte pallidioribus, petiolis I cm. longis hir-

ROBINSON. — ON CERTAIN COMPOSITAE. 215

sutis ; capitibus in bifiircis arete sessilibus 1.4 cm. diametro multifloris ;
involucri squamis oblongis biseriatim imbricatis subaequalibus abrupte
acuminatis dorso glabriusculis leviter striatis margine conspicue albo-
ciliatis ; flosculis liguliferis ca. 8, ligulis brevissimis ovatis crassiusculiS'
albidis viridi-striatulis vix 1.5 mm. longis pistilliferis, acbaenio striatulo
glabriusculo exalato apice longiuscuie divaricatim 3-aculeato ; pappi
aculeis ca. 3 mm. longis; disci tlosculis numerosis, achaeniis murica-
tis. — Tensaw, Alabama, 18 August, 1904, ^S. 31. Tracy, no. 8946
(type, in Gray Herb.). This plant, distributed as Cah/ptrocarpus tam-
picanus Small, differs markedly from that species in its spatulate-
obovate leaves, larger closely sessile heads, and especially in its involucral
scales. These are dorsally nearly glabrous but on the edges conspicu-
ously ciliate, while in Calyptoca7'pus vialis Less. {Oligogpie tampicana
DC, Cahiptroca7-pus tampicana Small) the condition is reversed, that is
to say the involucral scales are dorsally strigose-pubescent but the
margin nearly or quite free from ciliation. The discovery of a second
and clearly distinct species of the hitherto monotypic Cabjptocarpus is
of interest. From the weedlike nature and wide distribution of its
Texano-Mexican congener, there must be some doubt whether the
plant here described will prove really indigenous in its Alabama habitat,
or whether it may not ultimately be found to be an introduction from
some other region.

Balduina angustif olia (Pursh), comb. nov. Buphthalmum angusti-
follum Pursh, Fl. ii. 564 (1814). Actinospermum angustifoUum (Pursh)
Torr. & Gray, Fl. ii. 389 (1842). The distinctions by which some recent
efforts have been made to separate the genera ActlnOspermum and
Balduina do not appear to the writer to be of generic validity.
The genera being united, priority of specific name requires the new
combination here proposed.

Senecio fimbrillifer (Cass.), comb. nov. Eupatorium auriculatum
Lam. Encyc. ii. 411 (1786), a specific name not available because of
Senecio auriculatus Burm. f. Fl. Ind. 181 (1768). Eupatorium scandens
Link, Enum. ii. 307 (1822) according to Lessing, Syn. Comp. 392 (1832),
this name also not available because of the now valid homonym Senecio
scandens Buch.-Ham. ex D. Don, Prod. Fl. Nepal. 178 (1825). Cacalia
fimhrillifera Cass. Diet, xlviii. 460 (1827). Senecio deltoideus Less.
Syn. Comp. 392 (1832). Mikania auriculata Willd, Sp. PI. iii. 1745
(1804).

Senecio pyrifolius (Bojer), comb. nov. Trixis pyrifolia Bojer ex DC.
Prod. V. 195 (1836). MiTcania pyrifolia DC. 1. c. ; Klatt in Engl. Bot.
Jahrb. xii. Beibl. 27, p. 22 (1890). Senecio curvatus Bak. Jour. Linn
Soc. XX. 190 (1883). The identity of Mikania pyrifolia (Bojer) DC-

216 PROCEEDINGS OF THE AMERICAN ACADEMY.

and the much later Senecio curvatus Bak. was recently noticed by the
writer on successively examining the types preserved in the DeCandol-
lean and Kew herbaria respectively. The identity appears to have been
previously inferred by Dr. F. W. Klatt, for after determining Hilde-
brandt's no. 3626 as Mikania injrifolia in Engl. Bot. Jahrb. xii. Beibl.
27, p. 22 (1890), he later cites the same number as Senecio cm-vatus
Bak. in Ann. k. k. Naturh. Hofinus. Wien, vii. 299 (1892). Although
the name Senecio pyrifollus was used in manuscript by von Martius
for a Brazilian species, it was published only as a synonym of
Senecio ellipticus DC. Prod. vi. 420 (1837) by Baker in Mart. Fl. Bras,
vi. pt. 3, 318 (1884). This use of the name, especially as unaccom-
panied by independent description and therefore incapable of revival,
seems in no way to preclude the new combination here made for the
plant of Madagascar.

Saussurea baicalensis (Adams), comb. nov. Liatris haicalensis
Adams, M^m. Soc Nat. Mosc. v. 115 (1817). Carpi ephor us haica-
lensis DC. Prod. V. 132 (1836). Saussurea pycnocephala Ledeb. Ic.
Fl. Ross. i. 15, t. 59 (1829), Fl. Alt. iv. 14 (1833), & Fl. Ross. ii. 661
(1845-46), which see for detailed synonymy. As Adams's original de-
scription of this species is excellent and detailed there seems no reason
why according to present nomenclatorial rules the earliest though long-
neglected specific name should not be restored as indicated above. The
association of the species with Liatris, to which it has considerable
habital resemblance, was not unnatural at a time when the relatively
obscure tribal distinctions of the Compositae were unknown.

Proceedings of the American Academy of Arts and Sciences.
Vol. XLVII. No. 7. — July, 1911.

CALANOID COPEPODA FROM THE BERMUDA ISLANDS.

By Calvin O. Esterly.

With Four Plates.

CALANOID COPEPODA FROM THE BERMUDA ISLANDS.^

By Calvin 0. Esterlt.

Presented by E. L. Mark, May 10, 1911. Received May 12, 1911.

The copepods mentioned in this paper were collected during June,
July, and August, 1907. A small " open " plankton net was used, and
both vertical and horizontal (surface) towings were made, but there is
no special significance in vertical collecting with a non-closing net.
Most of the collections were made close to Agar's Island. In addition,
four hauls were made about two miles north of North Rock, three of
these being vertical from about twelve fathoms.

The calanoid copepods are represented in Bermuda by five genera,
one of which is new, and six species of which four are new. The list
is as follows : Acartia bermudensis n. sp., Acartia spinata n. sp., Cal-
anopia am&ricana Dahl, Clausocalanus furcatus Brady, Lampoidopus
marJci n. gen., n. sp., Pseudocyclops magnus n. sp. I have given here
very brief characterizations of the species previously described by
others, as a basis for comparison with similar forms from other locali-
ties, and drawings of certain parts have been included for the same
purpose. New forms are described and illustrated more fully.

Lampoidopus^ marki' n. gen., n. sp.

Plate 1, Figure 4 ; Plate 2, Figures 13, 14, 20, 21 ; Plate 3, Figures 25, 26,
28, 29, 30, 31, 34 ; Plate 4, Figures 35, 38, 42.

The head and posterior margin of the last thoracic segment are
smoothly rounded in both sexes (Plate , Figure 4 ; Plate 2, Figures 14,
21). There are five segments in the cephalothorax of both male and
female, the head being fused with the first segment of the thorax. The
rostrum is present and consists of a fleshy rounded plate, which at its

^ Contributions from the Bermuda Biological Station for Research, No. 21.

2 Aa/i7rds, torch, eldos, like, irovs, foot, in allusion to the fancied resemblance
of the last two joints of the outer ramus of the left fifth foot to the conven-
tional representation of the flames of a torch (see Plate 3, Figure 34).

^ The species is named for my teacher, Dr. E. L. Mark.

220 PROCEEDINGS OF THE AMERICAN ACADEMY.

base occupies nearly the entire distance between the bases of the
anterior antennae (Plate 2, Figures 20, 21).

The abdomen of the female is 3-segmented, the genital segment being
as long as the other two ; the second segment is a little longer than
the third (Plate 1, Figure 4 ; Plate 2, Figure 13). The abdomen of
the male (Plate 2, Figure 14) is apparently 4-segmented. The four
segments are of about equal lengths. The furcal rami in both sexes
are about three and one half times as long as broad.

The anterior antennae reach to the end of the furca. Both antennae
in the female are 25-jointed. The right one in the male is a grasping
organ (Plate 4, Figure 35) and is 23-jointed ; the left is 25-jointed.
The terminal portion of the grasping antenna is 4-jointed.

The other cephalic appendages are alike in the sexes. The posterior
antennae have the inner ramus shorter than the outer ; the former is
2-jointed and the latter 8-jointed. The blade of the mandible (Plate
3, Figure 26) is well developed and has numerous rather fine teeth of
irregular form on the cutting edge. The outer ramus is 4-jointed, the
first three joints having each one bristle, the fourth joint having two ;
the inner ramus is 2-jointed, the first joint carrying three bristles and
the second carrying eleven, as shown in Plate 3, Figure 31. The
maxilla (Plate 3, Figure 25) has the rami and lobes well developed.
The "outer border lobe" bears a group of three small bristles and a
group of seven that are much larger. The outer ramus carries bristles
of about equal sizes ; the inner ramus has fourteen bristles altogether,
disposed, as shown, in two groups of three bristles each and two of four
bristles each. The masticatory lobe has ten of the very heavy spinose
bristles and three delicate smooth bristles. The second lobe of the
inner margin has five bristles, the third has four, and the second basal
has five. The anterior maxilliped is rather short and broad (Plate 3,
Figure 28). There are seven lobes on the inner margin ; the number
of bristles on the lobes in order is 6, 3, 3, 3, 4, 2, 4. The posterior
maxilliped (Plate 4, Figure 38) is slender and weakly developed ; it is
7 -jointed, the endopodite containing five joints. The endopodite is as
long as the second basal ; the greatest breadth of the first basal is twice
that of the second. The first basal has the bristles on the inner mar-
gin disposed in four groups, consisting of 1, 2, 4, and 3, respectively,
beginning at the base. The joints of the inner ramus have the follow-
ing number of bristles on the inner margin, beginning with the first
joint : 4, 4, 3, 4, 4.

The four anterior pairs of swimming feet are alike in the sexes. Both
rami in all the pairs are 3-jointed, and the first basal in all has one
inner marginal bristle.

ESTERLY. — CALANOID COPEPODA FROM THE BERMUDA ISLANDS. 221

Table I, which follows, shows the number of bristles or thorns on the
joints of the rami of the first four pairs of feet. The abbreviations are
as follows : Se., a bristle or thorn on the outer margin ; JSi, a similar
structure on the inner margin of any joint ; St., a bristle on the distal
end of a terminal joint.

TABLE I.

Pair.

Joint.

Outer Ramus.

Inner Ramus.

Se.

Si.

St.

Se.

St.

St.

I.

II.

III.

IV.

1

2
3
1
2
3
1
2
3
1
2
3

1

3
2

3

5

0
0

1
0
0

1

0
0

1

0
0

1

0
0

1

0
0
2
0
0
2
0
0
2

1

2
4

1
2
5
1

2
3

1
1
4

0
0
1
0
0

1

0
0
0
0
0

The fifth pair of feet shows most marked peculiarities. These feet
are symmetrical in the male. Each inner ramus is 1 -jointed, that of
the right foot being club-shaped (Plate 3, Figure 30), that of the left
foot (Plate 3, Figure 34) shorter and broader. The outer ramus of the
right foot is 2-jointed, that of the left foot 3-jointed with the terminal
joint peculiarly modified (Plate 3, Figure 3t). It is split up into three
or four parts, or slender processes, one of which branches and carries a
very delicate lamellar structure that ends distally in fine hair-like
divisions. The figure gives a better idea of the structure of this foot
than is possible in a description. The end joint of the outer ramus of
the left foot is of the same structure in all the specimens I have
examined.

The right and left fifth feet of the female are symmetrical ; the inner
ramus is 2-jointed, the outer 3-jointed (Plate 3, Figure 29). A pecul-
iarity is the attachment of the terminal joint of the outer ramus at
the middle of the inner margin of the second joint.

The average length of the males is 1.05 mm., of the females 1 mm.

The color of both sexes is brownish buff; the pigment is generally
distributed through the body and appendages.

222 PROCEEDINGS OF THE AMERICAN ACADEMY.

The only place where I found this copepod was in a cave in the
small ledge-like island across from the bathing place at Agar's Island
(see the map in Mark, : 09, p. 2). The cave is a small one and is at the
south-west end of the ledge. I have never seen a specimen of Lampoi-
dopus that was taken anywhere else and it is my belief that the ani-
mals are not found outside the cave, at least, not any distance from it.
Collections were not made in the water between Agar's Island and the
ledge, but there were some from the ship channel, and this is rather
close to the place where the cave is located in the ledge. The animals
were very abundant in the cave ; young in all stages of development
as well as adults were taken. The only haul was made at high tide.
A small net was fastened to the end of a pole and swept through the
water inside the cave.

The most interesting thing connected with the finding of this co-
pepod is that, so far as I know, the small cave is the only place near
Agar's Island where the "hat" or "shade " coral {Agaricia fragilis) is
found. Furthermore the coloration of the copepod is strikingly like
that of the coral, the same brownish tint characterizing both. It is my
belief that this is an example of protective coloration. If so it offers a
new case among Copepoda especially, and plankton animals generally.

According to Steuer (: 10, p. 282), complete lack of color, and hya-
linity, is the best adaptation to a plankton life. Blue and violet are
adaptive to the blue water of warm seas, and red, brown-red or dark vio-
let belong to the abyssal zooplankton, Steuer also states (p. 283) that
creeping or swimming animals from the Sargasso Sea are characterized by
brown or green shades. Taking these general observations into con-
sideration with the circumscribed distribution of Lampoidopus, and the
fact that the other copepods obtained are transparent and colorless or
else bluish, it seems reasonable to regard the color of Lampoidopus as
protective. It is certainly suggestive of this that these little copepods
should have a coloration that is unusual in the group as a whole, that
their distribution should be so limited, and that at the same time their
colors should be so similar to that of the corals. I did not make col-
lections in other caves, but it would be interesting to know if these
copepods are found elsewhere and, if so, whether they are found gen-
erally with Agaricia.

Calanopia americana Dahl.

Plate 2, Figures 12, 15; Plate 3, Figures 27, 32; Plate 4, Figure 39.

These copepods are very abundant around Agar's Island and very
rare in the locality of North Rock. They may be easily recognized by
their comparatively large size, the pointed posterior borders of the thorax

ESTERLY. — CALANOID COPEPODA FROM THE BERMUDA ISLANDS. 223

(Plate 2, Figure 15), and the heavy, grasping antenna (the right) of the
male (Plate 3, Figure 32). The cephalothorax is twice as long in the
mid-dorsal line as its greatest breadth (Plate 2, Figure 12). The ros-
trum (Plate 2, Figure 15) is very stout, and bifid, in both sexes. So
far as the figures of Dahl ('94, Taf. 1, Fig. 23-26) are concerned, this
seems to be the same species, though identification from his figures
is not easy.

The length of the male is 1.2-1.3 mm., that of the female 1.4 mm.

The eye-spot is red ; most specimens are otherwise colorless and
transparent, but a few have red pigment in the mouth region, along
the flanks and ventral surface of the body, and in the bases of the
appendages.

Clausocalanus furcatus Brady.

Plate 1, Figures 2, 7, 9; Plate 2, Figure 11; Plate 3, Figure 33; Plate 4, Fig-
ures 36, 40, 44.

These copepods are small, but easily recognized by the heavy, bifid
rostrum (Plate 1, Figures 7, 9). The distal border of the second basal
in the third and fourth pairs of feet is toothed in a way that is char-
acteristic of the genus (Plate 3, Figure 33). I think there is little
doubt of the correctness of the identification of this species, though
the proportions of the abdominal segments in the male (Plate 2, Figure
11), or in the female, do not agree precisely with other accounts (Gies-
brecht und Schmeil, '98, p. 27 ; Scott, : 02, p. 403).

The animals are colorless and very transparent. The length of the
males averages 0.8 mm., that of the females 1.14 mm. This species
was much more abundant at North Rock than in any other place where
collections were made.

Pseudocyclops magnus n- sp.
Plate 1, Figures 6, 8 ; Plate 3, Figure 23; Plate 4, Figure 41.

The head and posterior borders of the last thoracic segment are
smoothly rounded (Plate 1, Figures 6, 8), and the rostrum is stout.
The anterior antennae of the female (Plate 3, Figure 23) are 17-
jointed and about one-fifth as long as the entire body. The inner
ramus of the fifth foot (Plate 4, Figure 41) is 2-jointed, the first and
second joints (of the original three) being fused ; the end joint carries
a stout, feathered bristle.

It is fairly safe to say that this form is new, though I found but one
specimen, a female. The fifth foot differs from that of the species de-
scribed before, and the size (length 1.1 mm.) is greater than that of
F. obtusatus, the largest of the hitherto described species.

224 PROCEEDINGS OF THE AMERICAN ACADEMY.

The animal was colorless and transparent, with a red eye-spot. It
was taken in a haul at Agar's Island.

Acartia spinata n. sp.

Plate 1, Figures 3, 5; Plate 2, Figures 16, 19; Plate 3, Figure 24; Plate 4,
Figures 37, 45.

The forehead is smoothly rounded in each sex, as are the posterior
margins of the last thoracic segment ; these margins are provided, in
both the male and female, with heavy spines disposed in two sets (Plate
2, Figures 16, 19). The posterior borders of the abdominal segments and
likewise the furca are spinose on the dorsal side, and in the male (Fig-
ure 16) there are little spines on the sides of the second segment. The
length of the cephalothorax along the mid-dorsal line is 3^ times its
greatest width (Plate 1, Figure 3). The genital segment of the female
is about as long as the rest of the abdomen including the furca, and
the second and third abdominal segments are of about equal lengths.
In the male the genital segment is about one-third the length of the
second segment, which is twice the length of the third. Rostral fila-
ments are present (Plate 1, Figure 5).

The anterior antennae reach back in the females to the end of the
anal segment, and in the males about to the posterior border of the
third thoracic segment. The second joint of the antenna in the female
(Plate 4, Figure 45) has a prominent spine on the ventral surface, and
the third joint has a similar spine on the anterior margin at the base
of the joint. That feature will distinguish this species from the other
species (bermudensis) described here.

The fifth feet in each sex are of the usual form for the genus, but
exhibit specific characters. Those of the male are shown in Plate 3,
Figure 24 ; those of the female in Plate 4, Figure 37.

The males average 1.13 mm. in length, the females 1.18 mm.

The animals have a faint bluish tinge in the body when alive, while the
eye is very dark blue, this being a noticeable feature of the species.
These copepods are very abundant at North Rock and rather uncom-
mon elsewhere, though taken about Agar's Island. The species belongs
to the hifilosa-totisa-gieshrechti group, but differs from all the other
species in ways that are distinctive.

Acartia bermudensis n. sp-

Plate 1, Figure 1 ; Plate 2, Figures 10, 17, 18 ; Plate 3, Figure 22 ; Plate 4,
Figure 43.

The females may be easily distinguished from those of the preceding
species by the absence of spines on the anterior antennae. Another

ESTEELY. — CALANOID COPEPODA FROM THE BERMUDA ISLANDS. 225

point is the character of the spines on the posterior border of the last
thoracic segment; in bennudensis (Plate 2, Figure 17) these are much
smaller, shorter and more numerous than in spinata (Figure 16). In
the males of bermud^nsis the ventral group of spines on the border of
the last thoracic segment is replaced by hairs (Plate 2, Figure 18). The
distribution of spines and hairs on the abdominal segments is shown in
Figures 17 and 18 of Plate 2.

This species lacks the rostral filaments. In the females the anterior
antennae reach back to the end of the genital segment, in the males to
the posterior border of the third thoracic segment.

The genital segment in the females is almost as long as the rest of
the abdomen (Plate 2, Figures 10, 17), and the furca is about a third
longer than wide. In the male the genital segment (Plate 2, Figure 18)
is three-fifths as long as the second segment ; the second is a little
longer than the third and three times as long as the fourth. The
length of the cephalothorax along the mid-dorsal line is three times its
greatest width (Plate 1, Figure 1).

The fifth feet show specific characters. In the female (Plate 4,
Figure 43) the middle joint of the fifth foot carries a blunt flap-like
process on the inner margin, which reminds one of an inner ramus.
The fifth feet of the male are shown in Plate 3, Figure 22.

This Acartia was common in hauls around Agar's Island, while spin-
ata is quite rare in that locality ; the reverse is the case in collections
taken from the vicinity of North Rock. A. bermudensis belongs to the
clausi-discaudata group.

The males average .9.3 mm. in length, the females .86 mm. The
animals are transparent and practically colorless.

Occidental College,
Los Angeles, California.

Bibliography.
Brady, G. S.

'83. Report on the Copepoda collected by H. M. S. "Challenger''
during the years 1873-76. Challenger Reports, vol. 8 (Part
xxiii), 142 pp., 55 pis.

Breemen, P. J. van

: 08. Copepoden. Nordisches Plankton, Siebente Lieferung, viii -f
264 pp., 251 Fig.

Dahl, F.

'94. Die Copepodenfauna des unteren Amazonas. Ber. Naturf. Gesell.
Freiburg, Bd. 8, pp. 10-23, Taf. 1.

226 PROCEEDINGS OF THE AMERICAN ACADEMY.

Giesbrecht, W.

'92. Systematik und Faunistik der pelagischen Copepoden des Golfes
von Neapel, etc. Fauna und Flora des Golfes von Neapel.
Monogr. 19, Text ix + 831 pp., Atlas 54 Taf.

Giesbrecht, W., und Schmeil, O.

'98. Copcpoda. I. Gymnoplea. Das Tierreich (Schulze), Lief. 6.
Berlin, 1898, xvi + 169 pp., 31 Fig.

Mark, E. L.

; 09. The new Bermuda biological station for research. Proc. Seventh
Internal . Zo5l. Congress, Boston, 1907. Also, Contributions
from the Bermuda Biological Station for Research, No. 17,
Nov. 1909, 6 pp.

Sars, G. O.

: 01-03. An account of the Crustacea of Norway with short descriptions
and figures of all the species, vol. 4 (Copepoda Calanoida)
pp. 1-171, pis. 1-102 and suppl. pis. 1-6.

Scott, Andrew.

:02. On some Red Sea and Indian Copepoda. Proceed, and Trans.
Liverpool Biol. Soc, vol. 16, pp. 397-428, 3 pis.

Steuer, Adolf.

: 10. Planktonkunde. Pp. xv +[723, 365 Abbildungen im Texte und 1
Tafel. Leipzig und Berlin, Verlag von B. G. Teubner.

Wolfenden, R. N.

: 04. Notes on the Copepoda of the North Atlantic Sea and the Faroe
Channel. Jour. Mar. Biol. Assoc, vol. 7 (n. s.), pp. 110-146,
pi. 9.

PLATE 1.

Figure 1. Acartia bermudensis n. sp. Female, cephalothorax and part
of abdomen, dorsal, x 113.

Figure 2. Clausocalanus furcatus Brady. Female, cephalothorax and
part of abdomen, dorsal, x 113.

Figure 3. Acartia spinata n. sp. Female, cephalothorax and part of
abdomen dorsal, x 113.

Figure 4. Lampoidopus marki n. gen., n. sp. Female, lateral, x 80.

Figure 5. Acartia spinata n. sp. Female, forehead from below, x 245.

Figure 6. Pseudocyclops magnus n. sp. Female, last two thoracic seg-
ments and abdomen, lateral, x 266.

Figure 7. Clausocalanus furcatus Brady. Female, forehead to show
rostrum, lateral, x 266.

Figure 8. Pseudocyclops magnus n. sp. Female, forehead showing ros-
trum, lateral, x 266.

Figure 9. Clausocalanus furcatus Brady. Female, lateral, x 93.

Esterly.-Calanoid Copepods Bermuda

Plate I.

C. O. E. DEL. pf^Qt^^ Af^ER, Acad. Arts and Sciences. Vol. XLVl

PLATE 2.

Figure 10. Acartia bermudensis n. sp. Female, abdomen and part of last

thoracic segment, dorsal, x 200.
Figure 11. Clausocalanus furcatur Brady. Male, abdomen and part of

last thoracic segment (on left side), dorsal, x 183.
Figure 12. Calanopia americana Dahl. Female, cephalothorax and part

of genital segment, dorsal, x 85.
Figure 13. Lampoidopus marki n. gen., n. sp. Female, abdomen and part

of last thoracic segment, dorsal, x 200.
Figure 14. Lampoidopus marki n. gen., n. sp. Male, abdomen and last

two thoracic segments, lateral, x 183.
Figure 15. Calanopia americana Dahl. Male, lateral, x 60.
Figure 16. Acartia spinata n. sp. Male, last thoracic segment and abdomen

lateral, x 170.
Figure 17. Acartia bermudensis n. sp. Female, last thoracic segment and

abdomen, lateral, x 390.
Figure 18. Acartia bermudensis n. sp. Male, last thoracic segment and

abdomen, lateral, x 200.
Figure 19. Acartia spinata n. sp. Female, part of last thoracic segment,

and the abdomen, lateral, x 200.
Figure 20. Lampoidopus marki n. gen., n. sp. Male, forehead showing

rostrum, ventral, x 183.
Figure 21. Lampoidopus marki n. sp., n. gen. Female, anterior half of

head, lateral, x 200.

ESTERLY. — CALANOID COPEPODS BERMUDA

Plate 2.

C. 0. E. DEL.

Proc. Amer. Acad. Arts and Sciences. Vol. XLVll.

PLATE 3.

Figure 22. Acartia bermudensis n. sp. Male, fifth pair of feet, x 352.
Figure 23. Pseudocyclops magnus n. sp. Female, anterior antenna, x 375.
Figure 24. Acartia spinata n. sp. Male, fifth pair of feet, x 375.
Figure 25. Lampoidopus mark! n. gen., n. sp. Female, maxilla, x 352.
Figure 26. Lampoidopus marki n. gen., n. sp. Female, mandibular blade.

X 352.
Figure 27. Calanopia americana Dahl. Male, two terminal joints of right

fifth .foot. X 375.
Figure 28. Lampoidopus marki n. gen., n. sp. Female, anterior maxilliped.

X 352.
Figure 29. Lampoidopus marki n. gen., n. sp. Female, fifth foot, x 352.
Figure 30. Lampoidopus marki n. gen., n. sp. Male, right fifth foot; outer

ramus at left of figure, x 352.
Figure 31. Lampoidopus marki n. gen., n. sp. Female, rami of mandible.

X 3.52.
Figure 32. Calanopia americana Dahl. Male, the grasping portion of right

anterior antenna, x 325.
Figure 33. Clausocalanus furcatus Brady. Female, second basal, first and

second joints of the outer ramus, and the inner ramus of the

third foot, x 352.
Figure 34. Lampoidopus marki n. gen., n. sp. Male, left fifth foot; outer

ramus at left of figure, x 352.

ESTERLY. — CALANOID COPEPODS BERMUDA.

Plate 3.

E.O. E. DEL.

Proc. Amer. Acad. Arts and Sciences. Vol. XLVM.

PLATE 4.

Figure 35. Lampoidopus marki n. gen., n. sp. Male, geniculating part of
right anterior antenna, x 470.

Figure 36. Clausocalanus furcatus Brady. Male, right foot of fifth pair.
X 470.

Figure 37. Acartia spinata n. sp. Female, fifth foot. The bristle on the
outer margin of the second joint is not shown entire, x 500.

Figure 38. Lampoidopus marki n. gen., n. sp. Female, posterior maxilliped.
The bristles are not shown, x 113.

Figure 39. Calanopia americana Dahl. Female, fifth foot, x 500.

Figure 40. Clausocalanus furcatus Brady. iVIale, left foot of fifth pair.
X 470.

Figure 41. Pseudoeyclops magnus n. sp. Female, fifth foot, x 500.

Figure 42. Lampoidopus marki n. gen., n. sp. Female, first foot, x 470.

Figure 43. Acartia bermudensis n. sp. Female, fifth foot, x 500.

Figure 44. Clausocalanus furcatus Brady. Female, fifth pair of feet, x 470.

Figure 45. Acartia spinata n. sp. Female, first five joints of anterior an-
tenna from below, x 93.

ESTERLY. — CALANOID COPEPODS BERMUDA.

Plate 4.

Proc. Amer. Acad. Arts and Sciences. Vol. XLVII

Proceedings of the American Academy of Arts and Sciences.
Vol. XLVII. No. 8. — November, 1911.

CONTRIBUTIONS FROM THE JEFFERSON PHYSICAL
LABORATORY, HARVARD UNIVERSITY.

THE VON WALTENHOFEN PHENOMENON IN SOFT

IRON RINGS.

\

By Louis A. Babbitt.

With a Plate.

CONTRIBUTIONS FROM THE JEFFERSON PHYSICAL
LABORATORY, HARVARD UNIVERSITY.

THE VON WALTENHOFEN PHENOMENON IN SOFT

mON RINGS.

Presented by B. O. Peirce, May 10. Received July 11, 1911.

By Louis A. Babbitt.

The purposes of the investigation described in this paper were two :
first, to determine how the manner of growth of a magnetizing field of
given final intensity about a mass of finely-divided iron affects the
change which the field produces in the magnetic condition of this iron ;
second, to harmonize the results found by previous observers in the
same field of inquiry.

About fifty years ago von Waltenhofen ^ observed that when the field
in a solenoid used to magnetize a soft iron rod was suddenly reduced to
zero by breaking the circuit, the remanent magnetism of the iron was,
under certain circumstances, opposite in direction to that induced by
the field just applied. This result, interpreted by means of Weber's
theory of elementary magnets possessing inertia, led almost immedi-
ately to the conclusion that the magnetic condition of the mass of iron
is affected by the manner in which the magnetizing field is built up. If,
for example, the field were changed continuously in the same direction,
in one instance by two steps and in the other by one, firom one given
value to another, the one-step method should produce, according to
Weber's hypothesis, the greater magnetic change in the iron ; for the
greater velocity acquired by the elementary magnets under this method
would cause them to rotate through a greater angle, and shoWi^a greater
flux change in the metal. Similarly, a high electromotive force applied
to the magnetizing circuit should, through the more rapid magnetiza-
tion produced, give a larger magnetic change than a low voltage would,
even though the final value of the current is the same in both cases.

From a commercial, as well as from a scientific point of view, this
phenomenon is important. The calculations which precede electrical

* Pogg. Ann., 120, 650. Winkelmann, Hand, der Physik, 5, 214.

230 PROCEEDINGS OF THE AMERICAN ACADEMY.

construction are often based upon hysteresis diagrams or magnetization
curves, which are supposed to show the magnetic characteristics of
different specimens of iron and steel under given excitations, and, if the
forms of these figures depend very much upon the manner of applica-
tion of the excitations, it is essential that the observations be made
under conditions approximately the same as those under which the iron
will have to do its work. It is important, therefore, that the engineer
should know how closely the test conditions and the working condi-
tions must correspond, and a number of investigators have studied the
subject.

At the outset the subject may be divided into two parts : first, the
magnetization of large solid masses of iron ; second, the magnetization
of finely laminated iron.

For the former it is almost unanimously agreed that, if the change
in the magnetizing field is always the same in direction, in going from
one value of the magnetic field to another, the manner in which
that change is produced affects the total change of flux in the iron.
Fromme,2 Lehman,^ Gumlich and Schmidt,* Heyse,^ Rilcker ® and
B. 0. Peirce "^ have obtained results with various shapes of iron, such
as toroids, ellipsoids and rods, which show this difference in the flux
change to a greater or less extent. Rilcker, for instance, found that
in the case of soft iron it might amount to 30 per cent of the total
flux change. For hard material the percentage was smaller.

In some early experiments I used a large, massive cast iron magnet
weighing about 1500 kilogrammes. Its general shape is shown in Fig-
ure 1. The base is of rectangular cross-section, 40 cm. by 20 cm., 101
cm. long and 80 cm. high ; the arms are cylinders of steel 25 cm. in
diameter and are capped by rectangular pole pieces 4.5 cm. thick and
580 cm. in area. Four coils having a total of 2823 turns and a
resistance of 12.4 ohms served for the magnetization.

The time required for the current to reach a constant value in such
a system is very appreciable. Two to three minutes was not at all
unusual. Such long, slow flux changes taking place in the iron could
not be measured accurately by the long-period galvanometer ^ that had
been constructed for this sort of work. However, it was found that

2 Wied. Ann., 43, 181 (1891); 44, 138 (1891).

3 Ibid., 48, 422 (1893).

* Elektroteknische Zeitschrift, 21, 1900.

5 Inaug. Diss. Halle, p. 33, 1901.

6 Inaug. Diss. Halle, 1905.

' These Proceedings, 43, 155 (1907).
8 These Proceedings, 44, 1908. '

BABBITT. — THE VON WALTENHOFEN PHENOMENON.

231

a slight modification of the usual procedure in step-by-step ballistic
measurements would give consistent results. Instead of keeping the
secondary circuit closed during the whole flux change corresponding
to a given step of the primary current, advantage was taken of the slow
movement of the amperemeter and, when the current had attained a
certain value in the primary, the secondary was broken. The flux
change up to that point was recorded with more or less accuracy.

Figure 1.

The iron was then carried on around its hysteresis curve, and, when the
primary current had reached the same value that it had at the instant
when the secondary was broken, the secondary circuit was again closed,
and it remained closed during the completion of the step of the pri-
mary current, thus giving a ballistic efl"ect which measured the change
of magnetic flux during the second part of the step in question. If
two minutes are required for the complete flux change and a galvan-
ometer with a period of five minutes be used, a division of the one step
into four parts instead of two as just described will give a result having
a probable error not greater than 0.4 of one per cent. The sum of the
four throws will give the total flux change in that step. The applica-
tion of this method to the various steps of an hysteresis curve will
give results of any desired degree of accuracy up to the limit of the
instrument. In fact, numerous tests showed that after the iron had
been carried through a cycle a large number of times two successive
cycles obtained in this way were equivalent both as a whole and in
their corresponding steps to within one half of one per cent.

The three curves A, C, and D of Figure 2, corresponding to 4, 28 and
56 steps respectively, were obtained in the manner just described. The
maximum value of the magnetizing current and consequently the maxi-

232

PROCEEDINGS OF THE AMERICAN ACADEMY.

mum H is the same for all three. In each case the iron was carried
around its hysteresis cycle a large number of times. No demagnetiza-
tion was attempted ; the change from one curve to another consisted
merely in the change of the number of steps.

The maximum value of B was approximately 6000. The vertical
ordinate is in terms of throws of the galvanometer. If one half the
throw for a complete reversal of the maximum H be taken as 833,

the maximum values of B for the
three curves would be represented
by 824, 770, and 692; that is, for
the introduction of four steps in-
stead of one into the hysteresis
curve, the maximum value of B
has fallen 1 per cent, for 28 steps
7.6 per cent, and for 56 steps 17.4
per cent.

For massive iron therefore it is
undoubtedly true that a change in
the number of steps of magnetization
has a certain measurable effect on
the final magnetic condition of the
iron.

In such masses of iron the eddy
currents can in no wise be neglected.
There is nothing to show that the
phenomena may not be accounted
for by their action as well as by
some inherent property of the iron
itself; or indeed by both of these causes existing side by side. For
more definite conclusions it is necessary to eliminate one of the fac-
tors. The former yields the more readily.

It has been shown that in the case of a long cylinder the reduction
of the eddy currents^ can be carried to any desired point by a sufficient
lamination of the iron, and a toroid, if the radius of the ring be large
enough in proportion to that of the solid mass, presents a form approx-
imating that of a cylinder. While a mathematical demonstration will
not be attempted, I think it safe to regard lamination as playing in
my toroid the same role as in a cylinder, and by the elimination of
eddy currents offering a means for deciding to what we are to attribute
the effect of variation in the methods of magnetization.

B

^A

y.

^

L^-Tv r

^^

K

-«

/ "

J

{/

y

/i

{/

/

f

A

y

i

i

f

1

_H

0

1

I

/

A

f

/

/

/,

/

If

/

^'//

y

''I'

^

'/

L

7^

1^

-^

y

l^-^

Figure 2.

These Proceedings, 43, 161-182 (1907).

BABBITT. — THE VON WALTENHOFEN PHENOMENON.

233

Along this Hue three investigators have worked Fromme ^^ studied
the difference in the magnetic condition of bundles of iron wires accord-
ing as they were in the magnetizing solenoid when the current was
applied or were put in afterward. To be sure, he found a difference ;
but since part of his process included handling the bundles while under
the influence of the field it seems to me that we should not accept his

Tsmmm
TPSmmssm

CP

III II 1 1 II hO — I

A [^

nAMM^

RG ^

Figure 3.

results as conclusive. The jarring ii and straining of the wires due to
the handling might account for them. Rlicker ^^ took hysteresis curves
consisting of various numbers of steps for a small toroid of soft iron
wire and observed a decrease in the maximum flux through the iron as
the number of steps was increased. For his specimen this decrease was
the most pronounced when the induction per square centimeter, B,
was about 4000 and amounted then to 6 per cent of the total induc-
tion. B. 0. Peirce ^^ compared step-by-step hysteresis curves of a
toroid which had a finely divided core, with similar curves calculated
from the manner of growth of the current in the magnetizing coil ; an
oscillograph supplied the necessary current-curves. Beyond the prob-
able errors of this method he could detect no difference between the
two sets of curves.

At present, therefore, we have two diametrically opposed conclusions
supported by experiment.

" Wied. Ann., 4, 76 (1878).
" Inaug. Diss. Halle, 1905.

" Ibid., 5, 345 (1878).

" These Proceedings, 43 (1907).

234 PROCEEDINGS OF THE AMERICAN ACADEMY.

The shape of the iron is an important consideration. That all un-
necessary difficulties might be avoided, such as would be introduced by
the poles of a broken magnetic circuit, the toroid was chosen, for my
work, as the simplest and consequently the most suitable form.

The arrangement of the apparatus is briefly as follows. The primary
of the toroid, TP, Figure 3, to be investigated, is connected in series
with an amperemeter, A, a set of resistance gaps, K.G, into which any
desired resistance coil could be introduced, a rheostat, R, a reversing
switch, 0, and a set of ten storage cells. The double switch, N,
allowed me to change from the primary of the toroid to the primary
of the calibrating solenoid, CP. The switch, M, was for the purpose of
introducing a resistance, K, approximately equal to that of the primary
of the toroid, when it was desirable to reduce the field in it to zero
without breaking for any length of time the flow of current from the
battery. This device kept the current more nearly constant than
would have been otherwise possible. The secondary circuit consisted
of the ballistic galvanometer, BG, in series with the secondary of the
toroid, TS, the secondary of the calibrating solenoid, CS, and the
switch, L. This last permitted me to throw the galvanometer into
the damping circuit. The flux changes produced in the iron core were
measured by the throw of the ballistic galvanometer.

Description of the Apparatus.

The usual form of ballistic galvanometer with a period of aljout 15
seconds is not suited for this work. The total flux change in the
toroid is not completed before the coil has swung considerably out of
its zero position ; and consequently the angular rotation of the coil
is no longer proportional to that flux change. For my purposes I con-
structed an instrument similar to one used by Professor Peirce.**

The coil of the galvanometer, which was of the Ayrton-Mather type,
was loaded by two brass balls to increase its moment of inertia. The
whole was suspended by steel gimp ; the current was conducted to
and from the coil, of which the ends were soldered to the two vertical
wires, by spirals of copper gimp similarly attached.

The increase in the inertia of the suspended system due to the two
brass balls increased the period of the galvanometer in this instance
to 65 seconds. As it was found by experiment that, if the secondary
circuit were closed one half a second after the primary circuit, there
was no perceptible deflection of the galvanometer, the period was re-

" These Proceedings, 44, 283 (1909).

BABBITT. — THE VON WALTENHOFEN PHENOMENON. 235

garded as sufficiently great to register within the accuracy of the in-
strument the flux change that took place.

The throw was read by means of a telescope and scale ; the dis-
tance of the latter from the mirror was 86 cm. Since the total possi-
ble deflection on either side of the zero amounted to 23 or 24 cm., it
was necessary either to compare angles calculated from the deflec-
tion or to compute the angles for one set of deflections, add them, and
determine the single deflection corresponding thereto. In other words,
for throws of more than ten centimeters it was not admissible to regard
the deflection as proportional to the flux change in the toroid.

The calibration by means of the standardizing solenoids showed that
the throw could be obtained consistently, for any given quantity of
electricity sent through the instrument, to within 0.1 mm. Thus for
throws greater than 10 cm. 0.1 per cent and often 0.05 per cent was
the accuracy attained. For such agreement three things were abso-
lutely essential : the suspended system must be at rest before the
throw commenced ; the throw must be taken always in the same direc-
tion ; the coil, in coming back, must never swing more than a few
millimeters beyond its zero position. If it did go far beyond, the zero
point was changed and the next deflection or two were not quite what
they should be ; usually too large. In this connection, too, it was ob-
served that the first two and sometimes three throws taken in the day's
work were in general larger than those that followed by a fraction of a
millimeter ; they were always thrown out of each set of results as
doubtful. Although the care of complying with all the conditions
made it necessary to spend from three to six hours in taking the data
for any one of the curves presented later the accuracy of the results
seemed to make it worth while.

One more peculiarity came out during the investigation. When the
current in the primary of the calibrating solenoid was simply broken,
instead of reversed as usual, and the deflection for the reversal calcu-
lated from the resulting throw, this was in general a few tenths of a
millimeter greater than an observed deflection for a reversal. The
diff'erence appeared only when the total reversal gave a throw of more
than 12 or 14 cm. It seemed as if somewhere in the secondary circuit
there must be a slight leakage produced by the higher voltage of the
complete reversal. In order to be sure of the amount of this differ-
ence a full reversal was taken in the''calibrating test before each day's
work as nearly as possible equal in throw to that produced by the re-
versal of the field to be used on the toroid during the day ; then the
throw was observed when the same current was broken, and the error
calculated. It was hoped that the conditions in the secondary circuit

236 PROCEEDINGS OF THE AMERICAN ACADEMY.

■when the current in the solenoid was reversed would be sufficiently
like those existing when the field of the toroid was reversed to give
the same leakage. As a matter of fact, the difference between the cal-
culated and observed reversals for the solenoid were throughout so
nearly equal to the corresponding difference when a reversal consisting
of a number of steps was compared with a complete reversal of the field
in the iron, that in all probability the conditions were approximately
the same and the leakage likewise. Unfortunately this leakage was not
taken into account at first because of the other greater inaccuracies
then occurring in the work ; it is applied, therefore, only to the work
done on coils I and III, not to 11.

The amperemeter was supplied with a number of shunts so that the
constancy of the current could always be determined to within 0. 1 per
cent, and as a general rule more closely than that. It did not appear
to be necessary to measure so exactly the true value of the current
used ; and no attempt was made to do so. However, it was given by
the instrument within 0.5 per cent.

The resistances in the primary circuit were made of constantan wire
set in enamel. For the moderate currents used, seldom over two am-
peres, their rise in temperature did not have any appreciable effect.

The primary and secondary solenoids used in calibrating the ballis-
tic galvanometer were both carefully made. The primary consisted of
5526 turns of No. 18 B. & S. annunciator wire wound on a brass tube
split longitudinally. The total length of the coil was 176.2 cm. The
secondary consisted of 538 turns of well insulated wire wound on a
wooden core. The primary was attached to the wall vertically at a
distance of 15 feet from the galvanometer ; inside it and equidistant
from either end was hung the secondary. This arrangement being
always constant allowed the testing of the galvanometer at the begin-
ning and end of the day's work, and showed immediately whether any
change had occurred.

Except for soldered joints the secondary was throughout a copper
circuit. Thus all trouble Irom thermoelectric currents was eliminated.

Three toroids were used which for convenience we may designate as
I, II and III. The second was the first to be experimented on, but the
meaning of its data will be clearer if discussed after the more extensive
investigation with toroid I.

The core of I was made out of carefully annealed soft wire. After
the winding, the wires were insulated from each other by soaking the
whole in shellac and drying it. A layer of paper covered the core ;
on it was wound a single layer of secondary divided into four parts.
A second layer of paper, the first layer of the primary, a third layer of

BABBITT. — THE VON WALTENHOFEN PHENOMENON. 237

paper, and the second layer of the primary, followed in the order given.
Care was taken to make the winding as uniform as possible. The data
for the toroid are as follows:

Average diameter of the iron wire of the core 0.0254 cm.

Number of turns of iron wire in the core 600

Weight of iron in the core 98.23 gm.

Area of cross-section of the iron in the core 0.303 sq. cm.

Average radius of the iron ring 5.6 cm.

Secondary, 4 coils, No. 26, double silk insulation.

Coil A 50 turns.

Coil B 75 turns.

Coil C 100 turns.

CoilD 340 turns.

Primary, 2 layers

First layer 164 turns

Second layer 157 turns

The core II consisted of iron wire not so well annealed as that of I.
Insulation was obtained by dipping the wound core into hot paraffine.
The primary and secondary were put on with the same precautions as
to paper insulation and the uniformity of winding as in the case of
toroid I. The data for II are:

Average diameter of the iron wire of the core 0.0285 cm.

Number of turns of iron wire in the core 500

Weight of iron in the ring 88.1 gm.

Area of cross-section of the iron ring 0.318 sq. cm.

Average radius of the iron ring 5.55 cm.

Secondary, 4 coils, No. 26, double silk insulation,

Coil A 157 turns.

CoilB 146 turns.

Coil C 154 turns.

CoilD .•* . 131 turns.

Primary, 2 layers.

First layer 160 turns.

Second layer 160 turns.

The core of III ^^ weighing 55 lbs. consisted of wire approximately
one third of a millimeter in diameter. Insulation ' of the iron was
effected by means of paraffine. The larger wire used for both primary
and secondary afforded by its double insulation complete freedom from
any appreciable leakage.

^^ The same core was used by B. 0. Peirce: These Proceedings, 43, 5
(1907).

238 PROCEEDINGS OF THE AMERICAN ACADEMY.

The demagnetization of toroids I and II was carried out in one of
two ways. In one process the toroid was left with its primary in the
primary circuit, Figure 3. By means of the reversing switch the field
was reversed and after each reversal decreased by the addition of resis-
tance from the rheostat and the gaps provided for that purpose. When
the current had been reduced to about 0.1 of an ampere the toroid was
disconnected and attached to the secondary of an alternating current
transformer. This was movable and could be pulled along a track
away from the primary which was connected to the 110-volt, 60-cycle
lighting circuit. The further demagnetization was carried out in this
manner.

The second method consisted of the introduction into the primary
circuit, Figure 3, of a piece of apparatus designed to reverse the cur-
rent automatically. The main features were a motor and four rods
joined to the motor through gears and cranks. The cranks lowered
the rods by pairs into mercury cups beneath. With one pair of rods
in contact with the mercury, and with the proper electrical connections
from the toroid to the rods, and from the mercury cups to the battery,
the current flowed in one direction through the toroid ; when the
motor was turned until these two rods were raised and the other
pair were in contact, the current flowed in the opposite direction. The
running of the motor together with the introduction of resistance into
the main circuit resulted in the demagnetization of the toroids. By
keeping the amperemeter in the circuit it was possible to regulate the
demagnetizing current so that it should never be above that already
applied to the toroid. This is a distinct advantage over the first
method, in that the history of the iron is better known and the effect
of its previous magnetic history more easily determined. With the
motor running so as to give three or four reversals of the field in the
toroid per second, the resistance was introduced gradually from the
rheostat and gaps until the current was not above 0.0003 ampere.
The time given to one demagnetization by this device was between
two and three hours.

The Investigation of Toroid I.

The primary and secondary of the toroid were connected with their
respective circuits as shown in Figure 3. If M and the other switches
be set so that the current flows through K, and if, after the core has
been demagnetized, M be thrown over, the throw of the calibrated gal-
vanometer will give means of calculating the B induced in the iron.
Let the current be reversed by 0 while the secondary circuit is broken

BABBITT. —THE VON WALTENHOFEN PHENOMENON. 239

at L ; make the secondary again at L and reverse 0. The B calcu-
lated from this last throw will be in general different from the first B.
If one repeats the process, amounting to carrying the iron around the
hysteresis cycle, a sufficient number of times, it will be found that the
value of B will become constant or at any rate very nearly so. Instead
of computing B it will be just as satisfactory to compare directly the
throws of the galvanometer. This will be done throughout the work.

Any one of the complete reversals just described will be referred to
as a 1-step reversal. A 3-step reversal will consist of the following
process. With a maximum of the flux in one direction at the start, the
current is broken by throwing over M and thus putting K in the cir-
cuit. After the introduction of resistance and the reversal of 0, M is
thrown back to the primary of the toroid. Finally the resistance just
introduced is cut out, by moving a rheostat arm, if it be in the rheostat,
or by short-circuiting a coil, if it be in one of the gaps. For each of
these three steps the flux change is recorded as a throw of the galvano-
meter. The angular displacement of the coil can be computed and
from the sum of these angles the corresponding single throw in centi-
meters. By correcting for leakage one has the single throw that can
be used as a basis for comparison. A 7-step reversal would consist of
seven steps between the two flux maxima, and so on.

The result of carrying out such an operation is to go from one mag-
netic condition to another in a given number of steps. If the initial
conditions be twice the same and the final inducing field twice the
same, but the number of steps in one case diff'erent from that in the
other, there are at hand the means for determining, by comparing the
corresponding single throws of the galvanometer, what effect the num-
ber of steps has on a magnetic change. To satisfy the second of the
two conditions is a comparatively easy matter. The first is more
troublesome. However, if the iron be carried through a large number
of hysteresis cycles, until the maximum B for the cycle is constant,
a number of observations taken for 1-step reversals and then a number
for 3-step reversals, it is certain that for the first 3-step reversal the
initial conditions were the same as for the last 1-step reversal. Fur-
thermore, if the following 3-step reversals give the same result as did
the first 3-step reversal, it is fairly safe to assume that there has been
no change in the iron after the first 3-step cycle. For two low values
of H, 2.35 and 3.46, this process was carried out; the corresponding
maxima for B were 820 and 1394.

In the first case, after the ballistic galvanometer was found to be
working with its usual accuracy (0.1 per cent), the iron was carried
through twenty-five 3-step reversals with a maximum field of 2.35.

240

PROCEEDINGS OF THE AMERICAN ACADEMY.

The following observations were taken for the 26th and 28th reversals
one 3-step reversal coming between the two. No measurements are
here recorded for the odd-numbered reversals, which were, of course,
in the opposite direction to the even-numbered ones.

Rev.

Amp. Read.

Ball. Galv.

i^orresponaing
Single Throw.

26th

8.90
0.00

4.12

0.00
5.94

4.07

>- 10.53

5.94
8.90

2.31

Rev.

Amp. Read.

Ball. Galv.

Corresponding
Single Throw.

28th

8.90
0.00

4.12

0.00
5.94

4.07 y 10.55

5.94
8.90

2.33

The 29th to the 82d were 1-step reversals. Of these the 30th, 32d,
80th and 82d are recorded.

Rev.

30th
32d

80th
82d

Amp. Read.

8.90
8.90

8.90
8.90

Ball. Galv.

10.55
10.54

10.51
10.51

Average Throw.

10.55
10.51

The difference between the average of the twenty-seven even-num-
bered reversals, 30th-82d, and the average of the first two recorded
1-step reversals, 10.55, is 0.1 per cent. The flux change per reversal
has decreased slightly, from 10.55 to 10.51, during the course of the
3-step reversals. That this is characteristic of the specimen during
its early magnetic history will appear from the data following.

In this case the maximum value of H is 3.46, of B 1394. Thirty
3-step reversals were taken and then the 31st and 33d observed.

BABBITT. — THE VON WALTENHOFEN PHENOMENON.

241

Rev.

Amp. Read.

Ball. Galv.

Corresponding
Single Throw.

31st

13.27
0.00

6.45

0.00
8.26

8.40

^

23.06

8.26
13.27

7.75

Rev.

Amp. Read.

Ball. Galv.

Corresponding
Single Throw.

33d

13.27
0.00

5.89

0.00
8.26

7.95

>

23.06

8.26
13.27

8.75 ;

A set of 1-step reversals followed the 33d, out of whicli four are
recorded.

Av. Throw for
Galv. Read. 13.27.

\ 22.99

22.58

Rev.

Amp. Read.

Ball. Galv

35th
37th

13.27
13.26

23.01
22.94

87th
89th

13.26
13.26

22.56
22.59

Here the 1-step reversals give a smaller " throw," indicating a smaller
flux change, than the 3-step reversals, but it is to be noted that the
first 1-step reversal gave a throw very nearly as large as that given by
the 3-step reversals, though the general tendency of the 1-step reversals
was to reduce the throw.

A demagnetization and reversal of the order of steps, that is, putting
the series of 1-step reversals first, yielded the following. Three of the
first 55 reversals are recorded.

Rev.

51st

53d

55th

Amp. Read.

13.26
13.26
13.25

Ball. Galv.

22.53
22.,57
22.56

Average Throw.
22.55

Of the 52 3-step reversals that followed the 1-step two are recorded.

VOL. XLVII. — 16

242

PROCEEDINGS OF THE AMERICAN ACADEMY.

Rev.
105th

Amp. Read.

13.25
0.00

Ball. Galv.
6.40

Corresponding
Single Throw.

0.00
8.26

8.32

>

22.50

8.26
13.26

7.34

107th

13.26
0.00

5.91

0.00
8.26

7.94

>-

22.50

8.26
13.27

8.22

Y^

I

\

o

\

\

cc

I
1-

^

^

V

_i

\

<

\

N

220

^

■^

.

' —

■ — ■

■at^i

_

o

REVERSALS

100

X

200

Figure 4. Set II: B 6000: first magnetization; all 1-step reversals except
the 196th and the 198th, which are 3-step.

Again there is a very slight fall in the maximum B as the number of
reversals increases. The 3-step and 1-step processes yield the same
results to within 5 parts in 2250.

From these three sets of data it is evident that the effect of the
method of magnetization is, in so far as the number of steps is con-
cerned and these tests are carried, of no consequence. In the worst
case the difference between the total flux change for 1-step and 3-step
reversals is one third of one per cent, and in the best one tenth of one
per cent.

It is important to note that such a statement applies only when
the iron has reached such a state that it passes repeatedly through

BABBITT. — THE VON WALTENHOFEN PHENOMENON.

243

practically the same hysteresis cycle. For the first eight or ten rever-
sals the cycle is changing rapidly and it may well be that, with the
iron in that condition, the number of steps taken in going from one
value of H to another does effect the final value of B. As it is of in-
terest to settle this question too, the method of investigation must be
changed somewhat.

Instead of reversing the
field a large number of times
before observing the throw of
the galvanometer, let the
throw be observed when the
field is first applied and there-
after for every reversal. If
the first throw be regarded
as the zero reversal and be
doubled in order to make it
comparable with the others, a
throw-reversal curve may be
plotted as shown in Figure 4.
Now, with due care that the
demagnetizing current shall
not rise above the magnetiz-
ing current just used, let the
toroid be demagnetized by the
motor attachment. Another
throw-reversal curve taken
exactly as before wiU show
the manner in which the
iron approaches a constant
maximum of B on the second Figure 5. Set II: B 6000: fourth mag-
magnetization. A set of such netization; all are 1-step reversals except
curves giving the behavior of *^^ ^^^ ^^"^ ^^^ ^^*^' ^^'"^^ ^'^ ^-step.
the iron on the first, fourth

fifth, sixth, seventh, and eighth magnetizations are those of Figures 4,
5, 6, 7, 8, and 9 respectively.

It is evident that no two of the curves are exactly alike. The first
shows a sharp fall of the maximum B as the field is reversed. On the
other hand the second shows a rather rapid rise, as do the remainder.
Even so, it is not possible to pick out the same reversal on any two
consecutive curves and expect them to register the same flux change
except by chance. This is true when the curves examined consist
entirely of 1-step reversals up to and including the reversal in question.

r

'i-^

. Y ^

Y

r

r-<

r^

y-

~"

^

) '

^

y

210 -

/

/

w

^

o
cc

I

<

o

OArt

200

190

1

0

1

0

RE

:v

Ef

=JS

A

LS

3

0

X

244

PROCEEDINGS OF THE AMERICAN ACADEMY.

It is, therefore, out of the question to expect any consistency in results
obtained by comparing reversals if a process of demagnetization inter-
venes. If 1-step reversals on two successive curves are not comparable
and, so far as can be seen, follow no exact law, it is not logical to obtain
a hysteresis curve of a given number of steps, demagnetize the iron,
obtain a second curve of a different number of steps, and, because the

maximum B of one curve
is greater than that of
another, declare that the
number of steps affects the
magnetic condition of the
iron.

This variation in mag-
netic condition is due, I
suppose, to the past history
which theoretically can
never be twice exactly the
same. It may depend on
the previous magnetiza-
tions or demagnetizations
or on both. No complete
distinction between the
effect of the two is possi-
ble, but some few things
appear to be true. The
remarkable drop in the first
curve and rise in the second
followed by the more rapid
rise in the later curves seem
to show the result of pre-
vious magnetic history, in
particular, the previous
magnetizations. For as the number of magnetizations increases, the
curves assume more and more the same general form. The variations
in the number of reversals required for any particular magnetization
to reach a constant state, even after the form of the curve remains
unchanged, leads one to suspect that the demagnetization plays an
important part. If the iron be treated on each occasion with the
same magnetic field, the process of demagnetization is practically the
only variable. In it the number of reversals for any given magnetic
field and sometimes the number of steps used varied considerably.
There is no reason for supposing that a change in the demagnetizing

Y

210

>

>-*

\~-i

__^

^

»_,

r- <)

J

r

/

r^

)

f

05
O

I

/

r-

<

200

<

)

o

i.

I

R

EV

IRi

)AL

S

2

0

X

Figure 6. Set II: B6000: fifth magnetiza-
tion; O indicates 1-step reversals; X 3-step
reversals.

BABBITT. — THE VON WALTENHOFEN PHENOMENON.

245

process would not affect the iioii- magnetic condition. This is the
initial condition for the next magnetization and, if not twice the same,
might well be the cause of the variations observed in the early part
of the magnetization-reversal curves. It seems to be the more prob-
able cause, inasmuch as the previous magnetizations were pretty nearly
alike and would be expected to give less haphazard variations thaa
•were actually observed. If
the demagnetizing process
for any given maximum of
B, or at any rate that part
of it which affected appre-
ciably the non-magnetic
condition of the iron, were
carried out always in the
same manner, I am in-
clined to believe that in
most cases the sixth or
seventh magnetization-
reversal curves would be
duplicated by those that
followed. However, it
seems to be impossible to
obtain a second time the
magnetic condition exhib-
ited, for a given maximum
of B, by any point of the
first few curves. The same
value of B might be ob-
tained, but that does not
mean the same magnetic
condition ; for the next
reversal in the two cases
would yield distinctly different values of B.

The tedious process of making each demagnetization the same was
not suited to the apparatus at hand and would require a large amount
of time and trouble. Furthermore, the relative effect of the various
parts of the demagnetizing process on the non-magnetic condition is
practically unknown. These two facts eliminated for the present a
continuation of the work by the comparison of any two curves separated
by a process of demagnetization. Even such knowledge as I have indi-
cated would be of no avail for the first few curves of a set, where it is
probably impossible to duplicate any point of the magnetic condition.

y-

■w-^

T—

— T

r^

^

v

^

)

210 -

^^

M

^

T^

/

t

;

r

^"

/

cc

T

H

-J

o

200

190

< )

of

1

0

F

EN

/E

=iS

AL

S

3

0

X

Figure 7. Set II: B 6000: sixth magneti-
zation; O indicates 1-step reversals; X 3-step
reversals.

246

PROCEEDINGS OF THE AMERICAN ACADEMY.

The only method applicable was the following. In taking any one
of the magnetization-reversal curves by 1-step reversals, for instance
curve 7 (Figure 8), the observer introduced at one or two places, as at
the fourth and fourteenth reversals, a reversal consisting of a larger
number of steps. If the curve be plotted from 1-step reversals only
and, after it has been drawn, the other reversals marked in their

proper places, some con-
clusion as to the effect of
the latter can be estab-
lished. The case in which
the iron has attained a
constant cyclic change has
been discussed ; it is evi-
dent that for that condi-
tion this method will
decide at once whether or
not the number of steps
has any effect. If the iron
is still in the stage of
variation, the early part
of the curve, one cannot
be so sure. However, if
there is no abrupt change
in the direction in going
from the 1-step reversal
just before the 3-step to
that just following, and
if the 3-step lies to within
the expected error on the
curve, it seems highly
probable that the number
of steps is immaterial. If
the general shape of the
curve in that region is about like that in the corresponding regions of
the curves preceding and following, where the region consists wholly of
1-step reversals, the probability is correspondingly increased. Of course,
no such similarity as this exists for the first three curves of a set with
moderate flux density.

The method of attack that has been outlined was carried out for
approximately the following values of B per square centimeter, 3000,
6000, 7400, 10,100, 13,500, and 19,300, in the order named, and the
data obtained have been plotted, in six sets, giving the curves shown.

Y

210

■ J

r-

» — «

r-^

)

(

^

y^

) — «

^

^

/

CO

/

o

I
i

/

J

)

<

/

'

200

d

A

t

i

J

RF

VF

^SA

IS

2

0

X

Figure 8. Set II: B 6000: seventh mag-
netization; O indicates 1-step reversals; X 3-
Btep reversals.

BABBITT. — THE VON WALTENHOFEN PHENOMENON.

247

There is no object in introducing all of the data ; but as a typical ex-
ample I select the fourth magnetization curve for B = 7400, Figure
13, and give both the data and method of treatment in full.

Y

i-«

(^

) ,

»— 1

— 1

^M

)

2i0

i

r-«

r^

>-<

r*

H

)

j/

>

/

f

>
O

/

h-

_l

< -

o

1

1

onn -

1

1

1

< 1

_ 1

or"

11

3

R

EV

EF

iSi

^L

s

3

0

X

Figure 9. Set II: B 6000: eighth magnetization: O indicates 1-step re-
versals; X 3-step reversals.

Typical Set of Data.

The toroid has been demagnetized by the motor reverser. The
process occupied alaout three hours and ended when the current had
been reduced to 0.0003 amp.

The temperature of the room at the beginning was 18.5° C.

Test op Ballistic Galvanometer.

Reading of
Amperemeter.

Throw on Re-
vereLng Current.

Reading of
Amperemeter.

Throw on Open-
ing Circuit.

7.16

16.77

7.15

8.29

7.16

16.78

7.16

8.31

7.16

16.76

248

PROCEEDINGS OF THE AMERICAN ACADEMY.

Average observed throw for reversal of current 7.16 is 16.78. The
average calculated throw for the reversal of the current 7.16 is 16.77.
These two values were so close that it was assumed that in this in-
stance there was no leakage.

Data for Magnetization-Reversal Curve.

No. of
Rev.

Reading of
Amperemeter.

Throw of Ball.
Galv. in cm.

No. of Steps
in Reversal.

0

13.63

7.53

1

2d

13.63

16.61

1

4th

13.63

16.68

1

No. of
Rev.

Reading of
Amperemeter.

Throw of Ball.
Galv. in cm.

No. of Steps
in Reversal.

6th

13.63 to 0.00

1.70

5

0.00 to 6.09

2.475

6.09 to 7.91

2.95

7.91 to 11.04

7.02

11.04 to 13.68

2.375

8th

13.68

16.87

1

10th

13.67

16.90

1

12th

13.67

16.92

1

18th

13.67

16.94

1

,20th

13.67 to 0.00

1.69

5

0.00 to 6.09

2.465

6.09 to 7.91

2.95

9.91 to 11.03

7.265

11.03 to 13.67

2.385

22d

13.67 to 0.00

1.67

6

0.00 to 6.09

2.47

6.09 to 7.92

2.94

7.92 to 11.04

7.32

11.04 to 13.67

2.37

24th

13.67

16.97

All odd numbered reversals were 1-step reversals.

The toroid was demagnetized and the galvanometer tested again.

Test of Ballistic Galvanometer.

Reading of
Am peremeter.

7.18

Throw on
Reversing Current.

16.81

Reading of
Amperemeter.

7.18

Throw on
Opening Circuit.

8.35

BABBITT. — THE VON WALTENHOFEN PHENOMENON.

249

The temperature of the room at the end was 18.3° C

The temperature of the room dropped gradually during the course

of the work. However, as three hours were required for the completion

of one such set of data, the

change was very gradual, and

owing to the care taken to

keep windows, doors, and

heating appliances un-
changed during that period

and for some time before it,

the rate of the drop was

practically constant. This

would prevent anything more 250

than a gradual change in the

iron or the galvanometer and

could not be regarded as

the cause for any sudden

variation in the curve.

The galvanometer, as us-
ual, showed that it could be

relied on to give an accuracy of 0.1 of a per cent. The difference

between a throw for a reversal, 16.77, calculated from breaking the

primary circuit of the testing solenoid, and the observed throw for a

Y

255

CO

\

0

V

\

I
1-

N

<^

<

\

S,

0

V

\

\

X.

^

"^

"^

«

30

100

REVERSALS

Figure 10. Set I: B 3000: first mag-
netization; O indicates 1-step reversal.

Y

238

0
oc

I

- •

1

1

/

y

1
1

^

\

s>

<
0

235

1
1
1
1

■^

-XL

"^

i

0

2

0

REN

/ER

SA

LS

IC

)0

X

Figure 11. Set I: B 3000: third magnetization; all 3-step reversals.

reversal, 16.78, shows that there is in this case practically no correction
for leakage. In fact the leakage seemed to occur only when most of the
secondary of the toroid was in use. If one were not willing to make

250

PROCEEDINGS OF THE AMERICAN ACADEMY.

this correction on the ground that it might not be the same for the
reversal of the solenoid as for the reversal of toroid, one would find
occasionally the reversals consisting of the larger number of steps
giving a slightly greater flux change than the 1-step reversals. I have
made the correction wherever it entered.

Y

^

,

,

,

,

— ^

'r

2oU

>

i

y

(n

/

o

/

/

/

X

1-

/

_J
<

/

o

220

Figure 12.
reversals.

5 REVERSALS 10 15 X.

Set I: B 3000: tenth magnetization; O indicates 1-step

The throw, 7.5.3, due to the first application of the field was ex-
pressed in terms of degrees, doubled and changed again to a throw in
centimeters in order that it might be on the same scale as the reversals.
It is plotted as the zero reversal.

The 6th, 22d, and 24th are 5-step reversals. For each separate step
of each of these the angular displacement of the coil was calculated.
The five angles of any one reversal were added and turned again into
centimeters throw of the galvanometer. A curve, Figure 13, was
plotted from the 1-step reversals; millimeters were plotted throughout
instead of centimeters. The 5-step reversals were added after the
curve had been drawn in order that any variation might appear more
plainly.

All the curves of the following six sets were obtained by the same
method.

BABBITT. — THE VON WALTENHOFEN PHENOMENON.

251

Discussion of the Curves.

Throughout, the reversals consisting of more than one step fall, with
very few exceptions, to within 0.1 of a per cent on the 1-step curves.
The exceptions occur where they are to be expected, namely, where
there would be, with 1-step reversals only, fairly sharp changes in the
direction of the curves.

A difference between the
first magnetization-reversal
curves and those that follow
for the same maximum of B
appears in each set. It is
most noticeable for moderate
values of B, from 4000 to
6000. In this region the
first two or three curves of a
set are of a decidedly differ-
ent character ; the fall in the
induction as represented by
the first seems to be charac-
teristic, as does the rise and
fall in the second and third
magnetizations. The curves
for the higher inductions
show the rise and fall in the
first curve and not a fall
starting immediately. For
any maximum of the induc-
tion the last curves of a set
take on the same general
shape — a sharp rise to a
constant maximum value.

The point brought out earlier becomes still more prominent and con-
clusive. It is that a comparison of the correspondingly numbered re-
versals on any two successive curves cannot be relied on for definite or
decisive conclusions as to the effect of various processes of magnetiza-
tion or production of the hysteresis cycle. It may be that if one chose
those parts of the curves which indicated a constant value of B, the
comparison would be of some value ; but even here there is room for
doubt.

Y

.

t (

(

r^

^—

"^

o

^ -^

y

c

^

y

I

/

.i

<

160

0

i

\-

i

J

RE

VEI

^SA

LS

2

0

X

Figure 13. Set III: B 7400: fourth
magnetization; O indicates 1-step reversals;
X 5-step reversals.

252

PROCEEDINGS OE THE AMERICAN ACADEMY.

The Investigation of Toroid II.

Coil II occupied the same position with respect to the circuit, (Fig-
ure 3,) as did coil I ; the secondary was in series with the ballistic gal-
vanometer and the secondary of the calibrating coil, the primary in
series with the amperemeter, rheostats, and storage cells.

The method of demagnetization was that first used, the reversing
switch (Figure 3), and the alternating current transformer. Certain

features of the latter are
important. The secondary
could not be drawn con-
tinuously away from the
primary without reducing
the demagnetizing fields
more rapidly than was
deemed advisable. Hence it
was moved a short distance
and allowed to rest a few
seconds. This reduced the
field by steps and in such a
manner that both the total
number of steps and the
number of reversals in each
step were not regulated even
roughly. Consequently no
two magnetizations were ex-
actly alike or approximately
alike. In other words, the
history of the iron just
previous to what we have
regarded as the initial con-
dition, was subject to varia-
tion. It would be strange
if the initial condition were not afiected by this variation. In that
case the result of the first application of the field to the iron after one
demagnetization might well differ from that obtained by the first
application after the next demagnetization.

The work on this coil was done before that on coil I, but as the
results can be discussed more readily by reference to the more exten-
sive data on the latter it was thought best to treat them in this order.
The objection to any extended investigation with coil II lay in a weak
consequent pole discovered at one point in the ring. The difficulties

Y"

s

\

s

c N

s

^

' T

^>.

h-<

-<

»-.

-_

^

— <

inn

(0

$

o

»-

<

o

170 -

()

0

<

>

1

0

F

^E'

•E

RS

>Al

-S

X

Figure 14. Set IV: B 10,100: first mag-
netization; O indicates 1-step reversals; x
5-step reversals.

BABBITT. — THE VON WALTENHOFEN PHENOMENON.

253

in the way of experimentation were sufficiently great without unneces-
sary additions, the effect of which was unknown ; thus immediately
after the discovery, core II was discarded and core I made.

The first two sets of data given below were taken in the following
manner. The iron was demagnetized and the galvanometer tested.
Then the magnetizing field was applied in one or more steps, as
is indicated. A repetition of
this process yielded the data
under discussion. It is to be
observed that the flux change
recorded is that taking place
when the iron is carried from
zero magnetization to the first
peak of the hysteresis curve.

First Set of Data.
The iron was demagnetized

Test op Galvanometer.

iperemeter
Reading.

Ballistic
Throw.

13.80

21.54

13.81

21.60

13.81

21.59

The iron was demagnetized iqc
by transformer and the field
built up in one step :

Y
180

,^

^

)

:

1

=— 1)

i

r

1

CO

1

^

1

tr

1

•

»-

1

1

o

/

1

170

1

1

1

1

1

1

/

1

/

1

*

iRn

J

Amperemeter
Reading.

1.220

Ballistic
Throw.

20.76

2 REVERSALS 6 X

Figure 15. Set IV: B 10,100: second
magnetization; .Q indicates 1-step reversals;
X 5-step reversals.

The iron was demagnetized and the field built up in one step :

Amperemeter Reading.
1.220

Ballistic Throw.

20.76

The iron was demagnetized and the field built up in two steps

Amperemeter Reading.
0.641
1.221

Ballistic Throw,
23.92
6.67

The iron was demagnetized and the field built up in two steps :

254

PROCEEDINGS OF THE AMERICAN ACADEMY.

Y

^-<

k^

'^

-

")

: — (

160

to

o
a.

X

•

t-

^

150

Amperemeter
Reading.

0.641
1.221

Ballistic
Throw.

13.94
6.65

Test of Galvanometer.

Amperemeter
Reading.

13.77
13.77

Ballistic
Throw.

21.46
21.44

10

B 13,500: first
magnetization; O indicates 1-step reversals;
X 5-step reversals.

REVERSALS 5
Figure 16. Set V:

The ballistic galvanometer
showed a change of about
seven parts in 2150 during
the work. The average 1 -step
reversal calculated from the
two 2-step reversals is 20.85.
The current and so the field
is slightly greater than for
the 1-step reversals. How-
ever, it is doubtful if this would account for the difference between
20.76 and 20.85 with the flux B, at 13,000 as here. Probably the
leakage due to the higher potential produced by the 1-step reversal and
not taken into account for
this core would make up the
difference. At any rate one
can be sure that for this par-
ticular core at this particular
value of B the flux change
due to two steps is not less
than that due to one.

Second Set of Data.

The iron was demagnetized
by the transformer.

Test of Ballistic Galvan-

ometer.

Amperemeter
Reading.

13.85
13.85

Ballistic
Throw.

21.76
21.75

Y

icn

,'■<

K^

^•"^

-S

i

I

<

100

j

0

2

! F

iEVEF

ISAL£

> 1

0

X

Figure 17. Set V: B 13,500: second
magnetization; O indicates 1-step rever-
sals;- X 5-step reversals.

The iron was demagnetized by the transformer and the field built up
in one step :

BABBITT. — THE VON WALTENHOFEN PHENOMENON.

255

Amperemeter Reading.
1.218

Ballistic Throw.
20.81

A repetition of the process yielded the following :

Amperemeter Reading. Ballistic Throw.

1.219 20.82

The iron was demagnet-
ized by the transformer.

Test of Ballistic Galvan-
ometer.

Amperemeter
Reading.

13.78

Ballistic
Throw.

21.54

The iron was demagnet-
ized by the transformer and
the field built up in two 200
steps :

Amperemeter
Reading.

Ballistic
Throw.

0.640

13.94

1.220

6.64

The iron was

demagnet-

ized by the transformer and

the field built

up in two

steps :

Amperemeter
Reading.

Ballistic
Throw.

0.640

13.96

1.219

6.58

o

cc

I

<

1901

REVERSALS

10

Figure 18. Set VI: B 19,300: first mag-
netization; O indicates 1-step reversals; X
6-step reversals.

The iron was demagnetized by the transformer.

Test op Ballistic Galvanometer.

Ballistic Throw.
21.48

The iron was demagnetized by the transformer and the field built
up in three steps :

Amperemeter Reading. Ballistic Throw.
0.484 8.44

0.757 7.55

1.219 4.45

Amperemeter Reading.

13.75

256 PROCEEDINGS OF THE AMERICAN ACADEinr.

The iron was demagnetized by the transformer and the field built
up in three steps :

Amperemeter Reading. Ballistic Throw.

0.484 8.68

0.757 7.41

1.219 4.41

The galvanometer varied more than usual during the first two tests.
If their average be taken to be used for the 1-step building-up inter-
vening, the correction to be applied to 20.81 is about 0.05. That is, to
make the 1-step building-up comparable to the 2-step and 3-step that
follow there must be added 0.05 giving 20.86. The two 2-step processes
give as the average calculated single deflection 20.81 ; the two 3-step
processes 20.82. As before we have no data by which the leakage cor-
rection may be determined. However, the 2-step and 3-step processes
to which it probably would not apply agree very closely. The 1-step
process gives a flux change higher than the other two, but this may be
due to the early variation of the galvanometer which would produce
just that error in case the leakage correction were zero.

The maximum flux, B, was about 13,000.

Out of the many attempts made to obtain similar data for lower
values of B, the two given above were the only ones of any value. As
a sample of the results usually obtained I off"er the following.

The iron was demagnetized by the transformer.

Test of Ballistic Galvanometer.

Amperemeter Reading. Ballistic Throw.
14.26 22.22

14.26 22.21

14.25 22.17

The iron was demagnetized by the transformer and the field built
up in one step :

Amperemeter Reading. Ballistic Throw.

11.00 20.71

Four repetitions of the demagnetization and building-up of the cur-
rent gave as four successive results those recorded.

Amperemeter Reading. Ballistic Throw.
11.00 20.81

10.99 20.55

10.98 20.51

10.98 20.76

BABBITT. — THE VON WALTENHOFEN PHENOMENON. 257

The galvanometer was not tested at the end of this set but on the next
day it was found to be the same to within 0.1 of one per cent. The
comparatively wide divergence between the flux changes in the iron as
indicated by the instrument are far greater than any variation in it was
ever found to be. When the 1-step process yields such heterogeneous
results, it is not possible to draw any decided conclusions by comparing
them with 2- or 3-step processes of magnetization. Taking an average
in a case like this introduces an average error of 1^ per cent at the
start. Consequently all such data were discarded.

One magnetization differs from the next only in the effects produced
by the previous history of the iron. We may divide that into two
parts : (1), the previous magnetizations, (2), the previous demagnetiza-
tions. If the variations were due to the former, we should expect at
least that there would be a continuous change and not the jumps back
and forth which were often more pronounced and numerous than those
recorded above. In other words, a continuous rise or fall in the flux
induced would not be unexpected ; but an alternation of the two, giving
wavy curves no two of which can be superposed for the same maximum
fields, leads one to suspect that some disturbing element enters which is
more potent than the previous magnetization.

The demagnetization seems to be that element. Only by chance is
it twice the same. In one instance it may consist of 500 reversals with
a maximum field of 3, 260 with a maximum field of 2.8, 800 with a
maximum field of 2.5, and so on ; in the next instance it may consist of
200 reversals with a maximum field of 3.1, 400 with a maximum field
of 2.9, 350 with a maximum field of 2.6, and so on. The motion of the
secondary, which could not be made continuous and of which the various
small distances moved were by no means equal, would give just this sort
of thing. To assume that such a variation in the process should not
have its effect on the non-magnetic condition in which the iron is left
is hardly safe. In fact, the results obtained when ever}'thing except
this process is constant are so variable as to indicate in all probability
that the cause of the variation lies here.

The trouble with this method led to one somewhat similar to that
used on core I. The iron was demagnetized and then carried around
a hysteresis cycle with a constant maximum field for any desired num-
ber of times. It was stopped at some point between the two maximum
fields, brought to a zero inducing field by simply breaking the circuit,
and carried on in the direction in which it was going originally to the
peak of the hysteresis curve in one step. If the flux change is always the
same when the one step is repeated, it is to be inferred that the one-step
replacing a larger number does not have any appreciable effect on the

VOL. XL VII. — 17

258 PROCEEDINGS OF THE AMERICAN ACADEMY.

fourth or fifth hysteresis cycle following, assuming that that is the num-
ber introduced between the two 1-step processes. If in continuing the
work two steps be introduced in place of the one and they are in turn
always the same, the same conclusion can be drawn in regard to their
influence. If finally the flux changes produced by the 1-step and
2-step processes were identically equal, it is evident that, when the
iron is retracing each time the same hysteresis curve, it makes no differ-
ence whether that part of the curve tested be passed over in two steps
or one.

For a maximum flux of 13,000 the following data was obtained in the
manner just described.

The iron was demagnetized.

Test of Ballistic Galvanometer.

Amperemeter Heading. Ballistic Throw.

13.75 21.30

13.77 21.35

The iron was carried through 14.5 hysteresis cycles of forty-four steps
each and back on the last half of the 15th until H was about 1.2.
The field was then. reduced to zero and the flux change observed on
raising it to its full value in one step.

Amperemeter Reading. Balliatic Throw,

1.220 21.89

The iron was carried through 4.5 cycles ; the next half cycle was
treated as above :

Amperemeter Reading. Ballistic Throw.

1.222 21.98

The iron was carried through 4.5 cycles ; the next half cycle was
treated as above :

Amperemeter Reading. Ballistic Throw.

1.223 21.92

The iron was carried through 4.5 cycles ; the next half cycle was
treated as above :

Amperemeter Reading. Ballistic Throw.

1.224 21.96

The iron was carried through 4.5 cycles ; the next half cycle was
treated as above except that two steps replaced the one :

BABBITT. — THE VON WALTENHOFEN PHENOMENON. 259

Amperemeter Reading.

Ballistic Throw.

0.760

17.92

1.223

3.92

After 4.5 more cycles the two steps were repeated in the next half
cycle :

Amperemeter Reading. Ballistic Throw.

0.642 15.82

1.223 5.98

After 4.5 cycles the two steps were repeated in the next half cycle :

Amperemeter Reading. Ballistic Throw.

0.642 15.81

1.223 5.90

The iron was carried through 4.5 cycles ; the next half cycle was
treated as at first — one step used :

Amperemeter Reading. Ballistic Throw.

1.223 22.02

The iron was carried through 4.5 cycles ; the one step was used
in the next half cycle :

Amperemeter Reading. Ballistic Throw.

1.223 22.00

The iron was carried through 4.5 cycles ; the one step was used
in the next half cycle :

Amperemeter Reading. Ballistic Throw.

1.222 22.07

The iron was carried through 4.5 cycles ; the one step was used
in the next half cycle :

Amperemeter Reading. Ballistic Throw.

1.223 22.11

The average of all the 1-step processes except the first gives 22.01.
The calculated 1-step reversal for the first 2-step process is 22.05, for
the second 22.08, for the third 21.99. The average of these three is
22.04. This differs by three parts in 2200 from the average 1-step
process. Since the average error for the latter is five parts in 2200 and
for the former three parts in 2200, this difference is well within the
error arising from other sources, and within | per cent, it is safe to
say that one step and two yield the same results. It will be observed
that in the case of the two steps the dividing point was not the same

260 PROCEEDINGS OF THE AMERICAN ACADEMY.

for all three cases. What variation there was seems to have had no
effect.

An 8-step reversal with a maximum B of 3100 was tried and com-
pared with a 1-step reversal of the same field. The ratio of the former
to the latter was as 914 to 922. By the use of a 10-step reversal and
a maximum B of 8000, it was found that the 1-step reversal corre-
sponding yielded a maximum B about 2 per cent smaller. Such an
unexpected phenomenon led to the testing of the core, excited by
a strong field, by means of iron filings spread on a sheet of paper
directly above it. A slight consequent pole appeared at one spot.
Lack of knowledge of the other factors entering into the work pre-
vented any attempt to determine whether or not such a pole would
affect the building up of the magnetic field. The core was immediately
discarded.

In so far as they were consistent the results obtained from this core
show that the number of steps taken in going from one magnetic con-
dition to another is immaterial, provided the flux change be always in
the same direction. The inconsistent results support my view that
when a process of demagnetization intervenes between two processes of
magnetization one is not at liberty to regard the first eight or ten
hysteresis cycles that may be passed over in the first magnetization as
necessarily equal to the corresponding hysteresis cycles of the succeed-
ing magnetization. In fact, I should hesitate to compare any two sets
of readings if I had demagnetized the specimen between the two.

If one were to take the trouble to go through exactly the same
process in each demagnetization, that is, use exactly the same number
of steps, reverse the field the same number of times, and see to it that
the field maxima were always the same in both order and magnitude
for the corresponding steps, it is presumable that in time one could get
the iron into such a condition that consistent reversal-flux curves similar
to those given for core I would be obtained. Then one would
be justified in comparing the flux change produced by any given
reversal with the corresponding flux change produced after the next
demagnetization. Such a procedure would be extremely laborious.
However, it is not inconceivable that certain parts of the demagnet-
ization have a greater effect than others on the final non-magnetic
condition and that attention to those alone would be sufficient to
assure consistent results. There is an opportunity here for further
research.

BABBITT.

THE VON WALTENHOFEN PHENOMENON.

261

The Investigation of Toroid III.

The amount of iron in toroids I and II and as a consequence
the time required for the building up of the current are, even for
low voltages, comparatively small. Toroid III, on the other hand,
supplies conditions more nearly comparable to the large, solid mag-
netic circuit used at first. With an applied voltage just sufficient to
produce a medium flux den-
sity in the iron, approxi-
mately two seconds would
elapse before the ampere-
meter in the primary circuit,
Figure 3, would come to rest.
To make sure that no small
effects were masked by the
size of I and II, III was
tested in the same maimer.

The circuit. Figure 3, re-
mained unchanged in every
respect save one, the ballistic
galvanometer. The slow flux
change in III required the
use of an instrument having
a much longer period. Re-
course was had to one of the
types used by Professor
Peirce *• ; the new galvan-
ometer constructed differed
from the old in that the balls
supported by the projecting
rods were replaced by an
aluminium disk weighted at
the circumference by a brass ring, Figure 19 (Plate). The period of
this heavy system was approximately five minutes ; and the error intro-
duced when the flux change was continuous and uniform for 20 seconds,
0.7 of one per cent; that is, the observed throw would be 0.993 times
the true throw.

The same care in manipulation that applied to the earlier instru-
ment was necessary here. In fact the task of bringing the suspended

Y

— (

\

\

\

270

\

\

•

\

s.

\

■ ■ [■■-■-

1 1

\

i i
1

o

\

V

X

1-

\

<

i

\,

o

\

s.

\

s.

PRO

\

^

\

<

\

\

^

0

z

1- (

^E\

^ER

SA

LS

1

3

X

Figure 19. The value of B is 3000:
the X indicates 24-step reversals, the O 1-
step reversals.

" These Proceedings, 44 (1909).

262

PROCEEDINGS OF THE AMERICAN ACADEMY.

system absolutely to rest was no small one and yet extremely impor-
tant for accurate measurements.

The data for three curves was obtained with the maximum flux

densities respectively of 800,
7650 and 14,000 per square
centimeter. Since the method
was almost exactly similar to
that employed in the case of
toriods I and II, it seems
worth while to note only the
difference. This lay in the
demagnetization ; for toroid
III it was carried out wholly
by the reversing switch, N
(Figure 3), and the rheostat
or resistance cells, R and
RG.

The accuracy with which
the long-period galvanometer
could be handled was fully as
great as that of the shorter.
The only error introduced lay
in the 0.7 of one per cent;
and this was eliminated to
considerable extent. For

Y

to
o

I
t-

J
<

o

305

\

\

\

\

\

\

\

\

300

\

\

\

L

I—

20

6 REVERSALS

Figure 20. The value of B is 7650: the
X indicates 22-step reversals, the O 1-step
reversals.

a

while about 0.7 of one per
cent of the throw would be
lost when 1-step reversal was
taken, a corresponding loss occurred in the reversals consisting of a
larger number of steps, for the same field reversed. It was found that
a large proportion of these
small steps required about
20 seconds for their com-
pletion ; as a conseijuence
their sum would be less
than the true sum. From
observations as to the time
the two instances and

240

in

239

1 REVERSALS 5 X

Figure 21. The value of B is 14,000: the
X indicates 28-step reversals, the O 1-step
reversals.

the size of the throws I

should regard it as very

probable that at least half

the error was cancelled by this introduction of the same inaccuracy in

the two cases compared.

BABBITT. — THE VON WALTENHOFEN PHENOMENON. 263

The three curves, Figures 19, 20 and 21, show the results of the
investigation.

Evidently the 24-, 22- and 28-step reversals fall very nearly on the
corresponding 1-step curves and are for all practical purposes equal in
their flux change to the 1-step reversals.

Some of the peculiarities that appeared in the early curves of toroids
I and II do not appear in these curves so prominently. However, III
has been magnetized a large number of times in previous investigations
and could not be expected to yield other than the results actually
obtained.

Summary.

The uniformity of the results for all three toroids leads to the con-
clusion that, in the early stages of its magnetic history, the condition
of the iron is constantly changing. During this stage of transition no
given condition can be repeated by any of the ordinary methods of
demagnetization and remagnetization ; but as the mass is subjected
again and again to the magnetizing process it attains more and more
nearly to a condition such that, for all practical purposes, any mag-
netic state may be repeated as often as desired.

The process of demagnetization affects, by the manner in which it is
carried out, the first few hysteresis curves that follow. This effect, in
so far as the present investigation determined its extent, consists in a
change in the maximum induction attained when the maximum field
for the particular curve in question is applied.

The various stages through which the iron passes during its early
magnetic history are the more numerous for the low flux densities and
disappear almost completely as the point of saturation is approached.
It is possible that, if one started with a high flux density and came
down to the lower, another set of phenomena might appear.

The work on the large solid magnet showed conclusively that the
form of the hysteresis curve depended upon the number of steps
employed. The corresponding experimentation on finely divided
masses, both large and small, indicated that the hysteresis cycle was
not affected by the number of steps. Such was found to be the case
in three distinct specimens of iron ; for wherever the curves could be
exactly determined, the points derived from the two methods of pro-
cedure, one by a small number, and the other by a large number of
steps, fell, within 0. 1 of one per cent, on a smooth curve. An obvious
reconciliation of the two results lies in regarding the eddy currents, and
not any inherent property of the iron, as responsible for the observed

264 PROCEEDINGS OF THE AMERICAN ACADEMY.

variations in the hysteresis curve. In other words, whatever variation
exists due to a special property of the iron seems to amount to less
than 0.001 of the total flux change.

In general, therefore, any method of obtaining an hysteresis curve of
finely laminated iron will permit one to forecast its future action. It
is assumed, of course, that we have carried it past the transitional
stage. On the other hand, for solid masses of iron that method should
be employed which corresponds as nearly as possible to the future
working conditions.

The Jefferson Laboratory,
Cambridge, Mass.

Babbitt. — The Von Waltenhofen Phenomenon.

Proc. Amer. Acad. Arts and Sciences. Vol. XLVII

Proceedings of the American Academy of Arts and Sciences.
Vol. XLVII. No. 9. — November, 1911.

CONTRIBUTIONS FROM THE JEFFERSON PHYSICAL
LABORATORY, HARVARD UNIVERSITY.

A NEW METHOD OF IMPACT EXCITATION OF

UNDAMPED OSCILLATIONS AND THEIR ANALYSIS BY

MEANS OF BRAUN TUBE OSCILLOGRAPHS.

By E. Leon Chaffee.

With Seven Plates.

CONTRIBUTIONS FROM THE JEFFERSON PHYSICAL LABORA-
TORY, HARVARD UNIVERSITY

A NEW METHOD OF IMPACT EXCITATION OF UNDAMPED
ELECTRIC OSCILLATIONS AND THEIR ANALYSIS BY
MEANS OF BRAUN TUBE OSCILLOGRAPHS.

By E. Leon Chaffee,

Presented by G. W. Pierce. Received July 11, 1911.

Introduction.

Electrical oscillations are at present of interest chiefly on account
of their practical applications to radio-telegraphy and radio-telephony.
The production and study of very rapid oscillations is also of intense
theoretical interest, and the applications of oscillations in high fre-
quency measurements and in research are of no small importance.

Previous to the last few years practically the only method of produc-
ing oscillations was by means of the disruptive discharge of a condenser
across a comparatively long spark gap between metallic terminals in
air. Under such conditions a train of damped oscillations is produced
at each spark. The duration of these trains is very short in compari-
son with the interval of time between them. It is evident that such an
intermittent and impulsive system is ill adapted to accurate electrical
measurements ; and for use in wireless telegraphy the system is noisy,
inefficient, besides which the necessity of using high potentials in-
creases the danger and the difficulty of insulation. For wireless tele-
phony, where a regular and continuous radiation of power is necessary,
the long spark method is absolutely useless.

In the last few years there have come into extensive use the short
gap or quenched spark method, and the arc methods of producing
electrical oscillations. These methods make use of the characteristics
of very short spark gaps between large parallel metal surfaces, or the
peculiar characteristics of certain forms of arcs. The advantages of
these methods of generating oscillations lie in their greater efficiency,
the absence of noise, the much greater regularity and continuity of the

2G8 PROCEEDINGS OF THE AMERICAN ACADEMY.

resulting oscillations, and the use of low potentials. The trains of
oscillations either follow each other very closely or, as with the arc
method, the oscillations are continuous with no intervals of inactivity.

For the purpose of this article it will be sufficient simply to men-
tion and to classify the short gap and arc methods according to the
characteristics of the resulting oscillations, and to designate the
types by the names of their observers or discoverers. There are
three such types, namely : the Duddell or singing arc oscillations ;
the Poulsen oscillations ; and the Wien oscillations, or the so-called
"Stosserregung."

The Duddell * oscillations are produced when a direct-current
carbon arc in air is shunted by an oscillatory circuit. This method
of producing oscillations is characterized by the fact that the arc
always remains lighted, that is, the condenser current is at every
instant less than the supply or main current. These oscillations are
of small energy and limited in frequency to about 10,000 per second
which fact renders them impracticable for radio-telegraphy.

The Poulsen ^ oscillations are produced by the Poulsen arc, which
is essentially a Duddell arc between a water-cooled copper anode and
a carbon cathode ; this arc takes place in a magnetic field and in an
atmosphere of some hydro-carbon gas. In this case the arc is ex-
tinguished at each oscillation, the condenser current at some instants
being greater than the supply current. The Poulsen oscillations are
much more intense than the Duddell type, and much higher frequencies
can be attained ; the energy, however, grows rapidly less as the fre-
quency is increased. Frequencies of a million or more can be obtained
but with small energy. Although the Poulsen oscillations are used in
wireless signaling they have some disadvantages, such as low efficiency,
and the characteristic change of wave length with changing arc length
and arc current.

Under the head of Wien ^ oscillations fall those produced by the
Lepel * arc, the Peukert ^ arc, etc. The generators for oscillations of
this class consist of two or more very short gaps between large metallic
surfaces separated by paper, or by a thin film of oil, and so mounted as
to exclude the air. The gaps are connected in series and shunted by an
oscillatory circuit similar to the arrangement for the other forms of

1 W. Duddell, Joum. Inst. Elect. Eng., 30, 232 (1900).

* V. Poulsen, British Patent Specifications, 15,599 of 1903.
« Max Wien, Physik. Zeitsch., 11, 76, Feb. 1, 1910.

* Lepel, Electrician (London), 63, pp. 142, 157, 174, 345, 376 (1909); 64,
pp. 153, 386 (1909-10); G. W. Nasmyth, Phys. Rev., 32, No. 1, 103 (1911).

' Peukert arc. Electrician (London), 64, 361, 550.

CHAFFEE. — IMPACT EXCITATION OF ELECTRIC OSCILLATIONS. 269

generators. Loosely coupled to this primary circuit is a secondary
circuit in which are induced the Wien oscillations. At each breaking-
down of the gap a highly damped train of oscillations ensues, which
produces in the secondary circuit the two ordinary coupling waves.
During the interval between the ending of one primary train and the
beginning of the next the secondary circuit oscillates in its own free
period. Thus there are produced oscillations of three periods, the
latter being of the most importance.

All of the above mentioned methods for producing oscillations were
tried without success by the author in an attempt to obtain oscillations
of a frequency of more than 10^ vibrations per second, and of sufficient
regularity, continuity, and intensity for use in another investigation.
After the failure of the then known methods, further experimentation
produced the new oscillation gap and method which are to be studied
in the following contribution. The method in some particulars closely
resembles the Poulsen method, but in electrical action the system is
quite different from any included in the three classes mentioned above.

The oscillations of this new system do not fall in any of the three
classes of oscillations mentioned, but are, as will appear later, inter-
mediate between the Poulsen and Wien types. The oscillations pro-
duced are unlike the Poulsen oscillations in that their period is but
very slightly affected by changes of supply current and not at all by
changes of arc length, and they are sinusoidal in wave form. The
oscillations are different from the Wien type in being continuous, and
having but one period, which is practically the free period of the
circuit in which the oscillations are induced.

It is shown in the following article that this new system produces
oscillations superior to the other systems in regularity, which, with its
simplicity, commends its use in the laboratory and in practice. It is
the only method known by the author for producing intense con-
tinuous oscillations at extremely high fr-equencies. The author has
obtained continuous and practically undamped oscillations of several
amperes at 20 meters wave length, which corresponds to a frequency of
1.5 X 10'' oscillations per second.

The following article is presented in three parts. In Part I it is
proposed to give the general characteristics of the oscillation gap. In
Part II the oscillations are studied more in detail by means of Braun
tube oscillographs, and Part III contains a few practical considerations
and applications of the oscillations.

270

PROCEEDINGS OF THE AMERICAN ACADEMY.

Part I.

The General Characteristics of the Oscillation Gap.

(1) Description of Apparatus.

The gap consists essentially of an aluminum cathode and an anode
of some other metal such as copper or silver, both water or air cooled
and surrounded by an atmosphere of moist hydrogen. The active sur-
faces of the terminals are accurately parallel planes of one or two
square centimeters area, and adjustable as to distance separating

Figure 1. Air-cooled Cu-Al Discharge Gap. ^ natural size.

them, which, for the best results, is about .07 mm. Large terminals
are undesirable on account of the increased electrostatic capacity of
the gap, which must be small in comparison with the main capacity of
the circuit.

For the cathode, aluminum is the only metal which gives at all satis-
factory results, and the gap should be constructed so that the termi-
nals can be occasionally renewed. After the gap has been in operation
for some time the aluminum becomes pitted and covered with a very
hard oxide which is difficult to remove. One electrode was operated,

CHAFFEE. — IMPACT EXCITATION OF ELECTRIC OSCILLATIONS. 271

however, for over one hundred hours with fairly satisfactory results at
the expiration of that time.

Several metals work well as anode, the latter apparently playing
very little part in the action of the gap. It appears, however, that
the denser metals of high cathode drop, such as copper and silver, are
desirable. The anode, with occasional cleaning, will serve indefinitely.

Although the amount of heat produced in the gap is small, some

FiGUKE 2. Details of Water-cooled Cii-Al Gap. f natural size.

method of cooling the terminals is necessary. Air cooling by means
of radiating vanes is to be preferred on account of convenience and
simplicity. Figure 1 gives the details of an air-cooled gap, the right-
hand half in section. At e there is shown the Al electrode which is
held by a taper-fit in the massive terminal t. Opposed to this Al elec-
trode is a similarly shaped copper electrode held by taper-fit in a similar
massive terminal. These terminals are threaded and engage in the
side castings cc, and are provided with blackened metallic radiating
vanes as shown. The side castings are separated by a thin slab of
hard rubber or asbestos board, which has a central circular hole to
serve for the gap chamber h. Rubber handles rr are for use in ad-
justment. The inlet and outlet for the hydrogen are shown at i and o.
The drawing is one half size.

272

PROCEEDINGS OF THE AMERICAN ACADEMY.

A water-cooled gap as shown in Figure 2 was, however, used through-
out this investigation. By reference to the drawing this gap is seen
to consist of two hollow threaded electrodes capped with aluminum
and copper, respectively, and each provided at the outside end with
an inlet and outlet tube for the passage of the cooling water. The
terminals are enclosed in a hard rubber casing provided with a circular

p/wvyw

L

0

<I) — Tmn^

L-0-1

Figure 3. Diagram of Comiections.

glass front. Hard rubber disks attached to the electrodes serve for
adjusting handles. The figure is a reduction in the ratio of 5 to 2.

The general diagram of connections is shown in Figure 3. >S' is a
source of direct current of a few hundred volts, and, in what follows,
530 is to be assumed unless otherwise stated. lo is a D. C. ammeter
which measures the current in the supply circuit. This circuit also
contains the two inductances or choke coils Lo Lo, and a variable re-
sistance 7?o, capable of reducing the current to about 0.2 ampere. In
the following experiments Lo Lo are ordinary A. C. arc-light induct-
ances, and Ro is a resistance, adjustable in one half ampere steps, in
series with a variable copper-sulphate electrolytic resistance. Cx and
C-i. are variable air condensers, G the gap, L^ and L^ the variable
primary and secondary of the closely-coupled oscillation transformer,
and 1.2 a hot-wire ammeter.

(2) Operation of Gap.

The system will start automatically if the distance between the
terminals is not much greater than 0. 1 mm. In appearance the dis-
charge resembles a very minute arc, of an intense reddish-purple color,
absolutely quiet and stationary. The discharge remains at one point
on the electrodes for several minutes until the aluminum is slightly
pitted, when it suddenly shifts to another point. When the discharge
is examined by means of a spectroscope only the primary hydrogen

CHAFFEE. — IMPACT EXCITATION OF ELECTRIC OSCILLATIONS. 273

spectrum appears with an occasional weak flashing-up of a few of the
ahiminum lines. Plate lb gives the discharge spectrum with an
aluminum comparison spectrum. The nature of the discharge will be
considered more in detail in Part II, but it is evident from the figure
that the metals are not vaporized, and the indications are that the
conduction is entirely by gaseous ionization.

140

180

100

80

60

5 40

iij
<

UJ

a:

O

X

20

O.

-<.

O

o

— -

—:-

-^

o

r^

o

r-^

0

.0

4

.0

8

.1

0

.1

4

.18

.22

M.M

LENGTH OF GAP

Figure 4. Effect of Changing Length of Gap.

lo = .335 ampere.
\o = 106 meters.
C\= 112 X 10-5 M./.
C2= 60 X 10-5 m/.

When the secondary oscillations are examined by means of a wave
meter, but one wave with exceedingly sharp tuning is observed. On
account of the steadiness of the oscilliations it is often difficult to set
the wave meter — which makes use of a telephone receiver as the de-
tecting device — without the use of a chopper or interrupter in the
wave meter circuit.

• The change in wave length of the secondary oscillations with chang-
ing supply current is very much less than is observed with the Poulsen
and Lepel generators. This point is, however, more profitably con-
sidered later, after a better understanding of the action of the gap has
been gained.

In order to show the effect on the intensity of the secondary oscilla-
tions of varying the length of the gap, the curve shown in Figure 4
was taken. It is seen that the intensity of the secondary current, as
measured by the hot-wire ammeter, does, to some extent, depend upon
the length of the gap, but not to the extent that might be expected.
At 0.19 mm. the secondary current is a maximum, but at about this

VOL. XLVII. — 18

274 PROCEEDINGS OF THE AMERICAN ACADEMY.

length of the gap the discharge begins to hiss and become unsteady.
For other values of the main current, Ig, the curve would be slightly
different, but, in general, the best results are obtained with a gap
length of from ,04 to .09 mm.

The effect of changing the pressure of the hydrogen was investigated.
Apparently atmospheric pressure gives the most satisfactory results,
although, for decreased pressure, the oscillations are possibly slightly
more intense until the pressure of about 10 or 20 cm. is reached, when
they rapidly become weaker. Increased pressure is decidedly det-
rimental.

Before entering upon an explanation of the curves and results it is
essential that a comprehensive idea of the operation of the system be
had. To this end the following brief review of the events during one
cycle is introduced, the details of which will be considered more at
length later. It is clearest, in tracing the sequence of phenomena, to
begin at the instant after the system has been started, when the poten-
tial of the primary condenser Ci (Figure 3) has attained a value suffi-
cient to break down the high resistance of the gap. The gap resistance
rapidly falls to a very low value as the discharge of condenser (\ and
the main current lot which was previously flowing into Ci and which
remains practically constant on account of the inductances Lq A> rush
across the gap and through the primary coil Xi. This current rush
takes place according to a definite positive loop of current with respect
to time, the shape, amplitude, and duration of which depend upon the
constants of the circuit, the rapidity of absorption of energy by the
secondary circuit, and, to a slight extent, upon the conditions of
the gap and strength of the main current Ig. The condenser Ci is
discharged and charged somewhat in the opposite direction by this
positive current rush. If conditions are right the discharge stops as
soon as /i becomes zero, there being no inverse current. The secondary
receives a certain increment of energy from this discharge, and con-
tinues to oscillate after the primary discharge stops.

This absence of inverse current above referred to is due to the com-
bination of three conditions. First, and most important, is the practi-
cally instantaneous re-establishment of the high initial gap resistance
when the current becomes zero, due probably to the formation of an
insulating oxide film on the aluminum ; second, the higher cathode
drop of the anode metal ; third, the absorption of energy by the sec-
ondary, although rectification usually takes place without this aid.

At the end of the above mentioned current-rush the current through
the gap is zero and the condenser Ci has an inverse charge. Since the
main current must remain constant it is now flowing into Ci, it having

CHAFFEE. — IMPACT EXCITATION OF ELECTRIC OSCILLATIONS. 275

been gradually shifted over to Ci as ii decreased toward zero. The
main current /„ flows into Ci at a practically constant rate, neutraliz-
ing the inverse charge and charging it in the initial direction. The
potential difference of Ci increases uniformly, attaining a much higher
value than exists outside the choke coils.

Impressed across the gap is the potential difference of the condenser
Ci plus the ripples induced in the primary circuit by the secondary
current, these potential ripples serving as a trigger to start the primary
discharge on a second cycle in the proper phase relation with the
secondary oscillation.

It is evident from the above consideration that, on account of the
inductances Lg Lg, the condenser Ci can attain a much higher differ-
ence of potential than that of the source, the magnitude of this
condenser potential being determined by the breaking-down potential
of the gap. It is also clear that, if this breaking-down potential be
assumed approximately constant, the number of discharges of Ci per
second depends upon the main current 7^.

The duration of each primary discharge does not, as has been stated,
depend upon the supply current, so that it is only the duration of the
interval between primary discharges which changes with varying main
current. The secondary continues to oscillate during these intervals
with decreasing amplitude according to the damping of the secondary
circuit. In what follows the number of secondary oscillations to one
primary discharge and charge is spoken of as the " inverse charge
frequency referred to the secondary oscillation " or simply I. C. F.

From what has been said it is clear that the secondary receives
periodic impulses from the primary, the frequency of these impulses
depending upon the main current and the capacity of the primary
condenser. During the intervals of non-activity of the primary circuit
the secondary circuit oscillates in its own free period and with damping
determined solely by the conditions of the secondary circuit, such as
resistance and radiation. The secondary oscillation cannot, then,
strictly be called undamped. The amplitude of the oscillation can,
however, be maintained practically constant by making the primary
impulses occur every two or three secondary oscillations, and, if the
damping in the secondary circuit be small, the resulting oscillations are
then almost perfectly undamped and continuous.

In order that the maximum energy be transferred to the secondary
circuit there are two conditions of syntony, as they may be termed,
to be fulfilled. In the first place the primary discharges must always
occur in the proper phase relation with the secondary oscillation, or,
in other words, the I. C. F. must be a whole number. This is, as has

276 PROCEEDINGS OF THE AMERICAN ACADEMY.

been pointed out, more or less automatically regulated by the reac-
tion of the secondary oscillation on the primary circuit, but not en-
tirely so for low values of I. C. F. The second condition of syntony is
that the shape of the primary wave or current-rush must be such that
the resulting electromotive force impulses in the secondary circuit,
due to the different parts of the primary wave, bear the proper phase
relation to the secondary wave. With a fixed secondary circuit the
first condition can be obtained by varying the main current /o, or the
primary capacity Ci. The second condition of syntony can be estab-
lished by changing the primary inductance Xi.

(3) Observations and Discussion of Results.

The two conditions of syntony are illustrated by the curves of
Figures 5 and 6. In Figure 5 the full line curve gives the variations
of the secondary current, I^, plotted to an arbitrary scale, as the main
current, /«, is varied, and shows maxima and minima of Ii as the first
condition of syntony is more or less perfectly fulfilled. The dotted
disconnected lines give the maximum wave length readings of the wave
meter, excited by the primary discharge, as ordinates plotted to the
variable 7^. The third dot-and-dash curve is the wave meter reading
when the secondary circuit is open. This figure is a fair representation
of several curves taken under different but similar conditions.

In explanation of Figure 5 attention is called to the following facts.
It is evident that if the potential to which the condenser is charged
is practically the same under all conditions, — and experiment shows
that this is approximately the case, — then with a given Ci, the number
of discharges per second in the primary circuit is roughly proportional
to the current /<,. This actual spark fi-equency produces in the wave
meter an effect corresponding to a wave of that frequency. This pri-
mary fundamental wave length, as it will be called, plotted to To would
give a curve of the general shape given by the dot-and-dash line in the
figure. When, however, the secondary circuit is closed the secondary
current exerts an equilibrating influence on the primary discharge,
helping it to occur, as has been stated, at a definite time in relation to
the secondary current, thereby forcing the primary circuit to operate
according to the short horizontal lines. For instance, by reference to
the figure it is seen that, for a supply current of 0.7 ampere, the
unforced primary fundamental wave length is 350 meters. The fre-
quency corresponding to this is about 860,000 per second, which means
that there are that number of primary discharges occurring per second.
When, however, the secondary circuit, having a natural wave length

CHAFFEE.

IMPACT EXCITATION OF ELECTRIC OSCILLATIONS.

Ui

A2 = 95 metres, is closed, conditions are different on account of the
absorption of energy by the secondary circuit, and the primary dis-
charges at a rate corresponding to a wave length of about 280 meters.
This is about three times A2, showing that the I. C. F. is 3. As the
supply current is decreased the primary is forced by the secondary to
discharge at this rate until the current has become so small that the

1000

800

600

400

z

-I

U
>

<

to
cr

UJ

I-
ui

2

200

.6 .8

AMPERES.

Figure 5. Illustration of Syntony to Charge Frequency.

Ao = 95 meters.
Ci = 80 X 10-5 M./.
C2 = 60 X 10-5 ^./.

slower rates corresponding to I. C. F.'s of 4 or 5 are more stable. When
conditions are least forced for these values of I. C. F. a maximum of
secondary current is observed as shown at Ig = 0.46 in the figure. It
is seen that for the steep part of the dot-and-dash curve the I. C. F.
j amps between several successive values. It is also now easy to under-
stand that the maxima of secondary current naturally occur at values
of lo where the I. C. F. is less forced.

The second condition of syntony, namely, the syntony of wave form.

278

PROCEEDINGS OF THE AMERICAN ACADEMY.

is represented iu Figure 6. In this case the hot-wire ammeter reading
was taken in the secondary circuit as an inductance, in series with the
primary of the oscillation transformer, was varied, the abscissa scale
being in turns of the coil. The disconnected curve, marked Xi, repre-
sents the primary fundamental wave length plotted to turns of iuduct-

230

210

O

Z

UJ

190

170

150

>

<

CO

111

UJ

5

130
0 2 4 6 8 10

TURNS OF INDUCTANCE.

Figure 6. Curve showing Syntony to Wave Form.

Ao = 86 meters.
lo = .75 ampere.
Ci = 60 X 10-5 m/.
Cs = 40 X 10-5 M./.

ance. The curve of secondary current shows the marked maximum
when, the I. C. F. remaining constant, the primary discharge loop has
the best duration compared to the period of the secondary oscillation.
The forcing by the secondary oscillation of the primary to discharge
at the frequency corresponding to a wave length of 138 meters is well
shown by the Xj curve.

A very interesting and useful chart, in showing the way in which the
variables change, is shown in Figure 7. This diagram was taken for

CHAFFEE. — IMPACT EXCITATION OF ELECTRIC OSCILLATIONS. 279

1 1

'Z

\

>
a.
<

\

\

a
z
o
o

J
1

\

\

(

X) CD

1/ /

oc

o

o

II

\

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<

1

(O c

tH C

I

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0 CO

1

o

O
1

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>

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o

Figure 7. Experimental Chart.

280 PROCEEDINGS OF THE AMERICAN ACADEMY.

particular values of Zi, L^ aud the coefficient of coupling of the two
circuits, and is not general so far as the scales are concerned. The
shape of the curves is general, however, and, it is hoped, may prove
explanatory of the relations of the many variables.

The curves resembling hyperbolas are each for a constant primary
capacity plotted with main current, /», as abscissae, and fundamental
wave length of the primary discharge frequency as ordinates. The
lower curve, marked " secondary wave length," gives the capacity of the
secondary circuit as abscissae and the resulting syntonic secondary
wave length as ordinates. The other similar curves are got by multi-
plying the ordinates of the last-mentioned curve by 2, 3, 4, etc. The

remaining curve marked r^ = 1.71, needs a word of explanation.

Several measurements were taken of the natural period of the primary
circuit when adjusted to give maximum secondary current, for different
secondary wave lengths, and it was found that this natural primary
period divided by the corresponding secondary period was, in every
case, within one or two per cent of the quantity 1.71. This would be
slightly different for different coefficients of coupling. The curve in
question is the locus of the intersections of the vertical C2 lines and
the C'l curves which fulfill this condition.

The use of the diagram of Figure 7 may be made clearer by the
following. Suppose that the secondary wave length desired is
75 meters. The secondary wave length curve gives 40 X 10~'^ t^.f.

as the secondary capacity, and passing vertically up to the — curve,

A2

it is seen that the primary capacity must be 80 X 10~^ /i./. If, now,
the vertical C^, = 40 line be followed to the intersection of the
3X2 curve, and then horizontally to the same Ci = 80 curve, aud down
to the current axis, one gets the cun-ent /„ = 1.1. This current gives
the discharge frequency, with Cg = 80, corresponding to a wave length
of 225 meters, which is three times the secondary wave length, and
therefore shows that, with that /„, the primary condenser is discharg-
ing every third secondary oscillation. In other words, the I. C. F. is
3. Similarly it is seen that for an I. C. F. of 4 the main current must
be 0.69 amperes ; for I. C. F. equal to 5, Ig must be 0.54 amperes, etc.

Among other things the diagram shows that in general the supply
currents which give the large values of I. C. F. differ but slightly,
which is an advantage for some purposes. It is readily seen that
small values of I. C. F. are impossible to obtain unless the wave length
is short and the supply current very large.

The coupling between the primary and secondary circuits should be

CHAFFEE. — IMPACT EXCITATION OF ELECTRIC OSCILL.A.TIONS. 281

very close. In order to attain this the primary and secondary coils
■were wound parallel on the same frame so that they interlocked. The
diameter of the coils is about 5 inches, and from one to seven or eight
turns were used. Direct coupling is almost as satisfactory as magnetic
coupling, but for regularity and freedom from harmonics the latter is
to be preferred, and was used throughout this experiment. The close-

6

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u

Q. '

< 3

VOt

TS

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*^ "

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t5=-

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c

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o

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200

100

8

4

6

la

14

16

8 10

OHMS

Figure 8. Current Curves, with Changing Resistance.

A = 100 meters.
lo = .55 ampere.
Ci= 175 X 10-5 m/.
C2=86 X 10-5^./.

ness of the coupling, or, what is of more importance, the mutual
inductance between the primary and secondary circuits, should, for the
best results, be adjusted according to the amount of power delivered by
the secondary circuit. The connection between the mutual inductance
and the conditions in the secondary circuit is shown by the curves of
Figures 8, 9 and 10.

In taking the curves of Figure 8, the primary supply current, the
primary capacity, and the secondary wave length were kept the same
in order to maintain constant the two syntony conditions, while a resist-
ance in the secondary circuit was varied for different numbers of turns
on the secondary helix. The primary capacity was 175 X 10"® /*./. ;

282 PROCEEDINGS OF THE AMERICAN ACADEMY.

the supply current was 0.55 ampere, and there were four turns on the
primary helix. The secondary wave length was 100 meters and the
curves 1-5 give the values of h in amperes for the designated number
of turns on the secondary coil, as the resistance in the secondary
circuit was varied from 0 to 16 ohms. On the same diagram appears
the voltage across the gap for the several conditions.

These, and some of the curves shortly to be considered, are plotted
for, or in terms of, turns of secondary helix, the primary helix remain-
ing unchanged. With the apparatus used the mutual inductance
between the two circuits is not exactly proportional to the number of
secondary turns on account of a slight variation in the position of the
coils, but nearly enough so, so that the number of secondary turns can
be considered as proportional to the mutual inductance between the
primary and secondary circuits.

The resistance used in the secondary circuit was an oil-cooled man-
ganin wire resistance, wound non-inductively, and with a wire of such
a diameter that the high frequency resistance is considered to be prac-
tically the same as the ordinary resistance.

It is clear, on examination oiF the current curves of Figure 8, that if
a large current in a circuit of small resistance is desired, the mutual
inductance should be small. If, on the other hand, there is a consider-
able radiation of power from the secondary circuit, or if the circuit con-
tains a large resistance, it is necessary that the mutual inductance be
large.

The reason for this necessary change in mutual inductance to suit
the various conditions is to be sought in the reaction of the secondary
current on the primary circuit. It is probable that the coupling
should be as close as possible consistent with a certain reaction, above
which the primary conditions, such as phase, etc., would be affected to
the extent of causing the power to decrease. Suppose then it be as-
sumed that the permissible reaction on the primary is constant, and
that the current in the secondary is proportional to M, the coefficient
of mutual inductance. Then it follows that the reaction voltage, Ei,
in the primary is

El = const, oc 3II2.

M

But I2 ^ — if the wave length and primary current are constant.
R2

Therefore

^1 oc ^- = const., or M"^ a R^.

CHAFFEE. — IMPACT EXCITATION OF ELECTRIC OSCILLATIONS. 283

If, now, M be assumed proportional to N^ the above expression may
be written,

N^ = KRi, where ^ is a constant.

This is the relation which must probably approximately hold in order
that the reaction of the secondary current on the primary circuit may
not exceed a certain amount, and is, therefore, for a given R2 or radia-

60

40

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20

10

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- EFFICIEN

CY.

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ATTS

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50

40

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UJ

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20

UJ

OS

10

6

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OHMS.

12

14

16

18

Figure 9. Power and Efficiency Curves with Changing Resistance.

A2 = 100 meters.
lo = .55 ampere.
Ci = 175 X 10-5 M./.
C2 = 86 X 10-5 ix.j.

tion coefficient of the secondary circuit, the condition for maximum
power. This will later be shown experimentally to be nearly true.

In Figure 9 is plotted the power, I^R%, in watts dissipated in the
secondary resistance for the conditions represented in Figure 8, from
which the curves of Figure 9 were obtained, and, also, the correspond-
ing efficiencies (dotted lines) exclusive of the power lost in the outside
resistance, Ro, are shown. The heat lost in Ro is omitted in calculat-
ing the efficiencies because, as will be stated later, by a proper choice
of generator this resistance can be left out.

The full line curves of Figure 10 were derived from those of
Figure 8, and are constant secondary current curves plotted to the

284

PROCEEDINGS OF THE AMERICAN ACADEMY.

ratio of secondary to primary turns of helix as ordinates, and secondary
resistance as abscissae. The ordinate scale is, as has been pointed out,
practically proportional to the mutual inductance between the two
circuits, but, for the sake of definite units, is expressed in terms of
turns of helix. The curves were derived by taking the intersections of
the horizontal, 1, 1.5, 2, 3, 4, and 5 ampere coordinate lines with the

1

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36 V^

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FiGUEE 10. Power Curves Derived from Figure 8.

A 2 = 100 meters.
lo = .55 ampere.
Ci = 175 X 10-5 fi.f.
C2 = 86 X 10-5 M./.

secondary current curves of Figure 8, and plotting to the correspond-
ing secondary resistances. The dot-and-dash curve is drawn through
the points of maximum slope of the constant current curves, and is the
locus of the points representing maximum power output. It is ap-
proximately a parabola, expressible in the form

(

j^ 1 <x- It 2, or, since i\ j = 4 = const.,
iVa^ = -ff'i 7?2 where Ki is a constant.

This is the same expression which was previously derived by assuming
the existence of a maximum permissible reaction of the secondary cur-

CHAFFEE. — DIPACT EXCITATION OF ELECTRIC OSCILLATIONS. 285

rent on the primary circuit, and shows that, within the errors of
experiment, the assumption is fairly well borne out.

The remaining dotted curves of Figure 10 are calculated constant-
watt curves, and enable one to tell at once the power being delivered
under any condition represented by the full line curves of the diagram.
Apparently the larger the secondary resistance and the greater the

S4

oc
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a.

|3

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AMPERES.

1.4

16

FiGUEE 11. Power and Efficiency Curves with Changing Current, [/o].

A2 = 100 meters.
Cy = 175 X 10-5 M./.
C2 = 86 X 10-5 M./.

number of turns on the secondary of the helix, the greater would be
the power output, but it will be seen that the distance between the
constant-watt curves rapidly increases, making it necessary to very
much increase R^ and N-^ to give a slightly larger output. Therefore
the curves do show the existence of a limit to the power derivable from
one gap. These curves also show that with a small number of turns
on the secondary helix it is impossible to deliver to the secondary a
large amount of power no matter what the resistance is in the
secondary circuit. It is clear, as has been said before, that the
mutual inductance must be large, and the radiation or resistance large
in order to obtain a large amount of power from the secondary circuit.
The curves of Figure 8 and those of Figures 9 and 10, which were
derived from Figure 8, were taken when the supply current, /o, was

286 PROCEEDINGS OF THE AMERICAN ACADEMY.

maintained constant at .55 amperes, the current which, with a wave
length of 100 meters, gives about the best average efficiency for all
conditions. The curves of Figure 11 show the eflect on the efficiency
of changing the supply current, lo- The secondary wave length was
maintained constant at 100 meters, and there were 4 turns on both the
secondary and primary of the helix. The full line curves show the
variations in current in amperes in the secondary circuit for three
values of secondary resistance, as the main supply current, /<,, is varied
from 0 to 1.5 amperes. The dotted curves give the efficiencies for the
three curves plotted to the right hand scale. The relative magnitudes

of the efficiencies would be slightly different for other values of -^,

but the curves show that for 100 meters wave length in the secondary,
the maximum efficiency is obtained when the gap is operated on a
supply current of from 0.3 to 0.8 ampere, the exact magnitude of the
supply current for maximum efficiency depending on the resistance in
the secondary circuit.

All of the data given above are for a wave length of 100 meters in
the secondary circuit. The shape of the curves would be similar for
other wave lengths but the scales different. If the secondary wave
length were longer the primary condenser would be larger, and the
supply current for maximum efficiency would be greater, but the gap
does not work steadily under any conditions with a supply current
greater than about 1.5 amperes.

In conclusion of Part I, a few words should be said concerning the
variation in frequency of the secondary oscillations as the supply
current is changed. Although this point has not as yet been investi-
gated at all thoroughly, the conclusions drawn from some experiments
and observations show that the frequency of the oscillations increases
slightly, and practically linearly, as the supply current is increased.
This increase is from 1 per cent to 10 or 12 per cent for a change of
supply current from .2 to 2 amperes, and depends upon the adjust-
ments, the percentage increase being greater the closer the coupling,
and the greater the number of primary discharges per second.

It is improbable that this change in frequency with changing supply
current can be attributed, as is done in the case of the Poulsen and
Lepel arcs, to the change in slope of the voltage-current characteristic,
for a change in gap length, which changes the slope of the E-I curve
more than a change in supply current, does not cause a detectable
change in frequency. If there is a change in frequency due to change
of gap lengtli, it is less than 1 per cent for a change of gap length from
.005 to 0.15 mm.

CHAFFEE. — IMPACT EXCITATION OF ELECTRIC OSCILLATIONS. 287

It i3 thought that the variation of frequency with changing supply-
current is due to a wavering or shifting of the period of the secondary
oscillation between a forced condition, when the primary is in action,
and the free period of the secondary circuit, when unaffected by the
primary discharge, this wavering being more often and of a greater
effect on the resultant or average w^ave length the greater the number
of primary discharges per second. The number of primary discharges
is proportional to the supply current, so that according to the above
assumption, the change in frequency would be directly proportional to
the supply current.

The large changes in frequency with changing arc current and arc
length is a serious disadvantage in the use of the Poulsen arc, but
with the system being studied, the change of frequency is so small and
the supply current and arc length remain so very constant that there
is, under all ordinary circumstances, practically no change in frequency.

Part II.

Analysis of Oscillations by Means of Braun Tube'

Oscillographs.

In Part I the general characteristics of the aluminum-cathode oscil-
lation gap were studied, but little idea could be obtained as to the
instantaneous relations of the variables. It is the purpose in Part II to
analyse, by means of the Braun cathode-ray tube, the entire sequence
of events during a complete cycle of changes, and to develop a clearer
idea of the nature of the oscillations and the action of the gap. Before
attacking the problem, however, it is necessary to describe the additional
apparatus made use of in the following experiments :

(1) The Braun Tubes and Accessory Apparatus.

The Braun cathode-ray tube is a most valuable piece of apparatus
for delineating transient electrical phenomena. Its use has been de-
scribed by Braun,® Zenneck,^ and others,^ but a few words from the
author's experience with the use of the Braun tube in connection with
high frequency currents may be of interest.

The Braun tubes used in the following work were imported from
Germany, but it was found necessary to alter them. The aluminum

6 F. Braun, Wied. Ann., 60, 5.52 (1897) ; Elektrot. Ztschr., 19, 201 (1898).
' Zenneck, Ann. d. Physik., 9, 497 (1902).

8 .1. M. Varley, Phil. Mas;., 3, 500 (1902) ; Varley and Murdock, Elec-
trician (London), 55, 335 (1905).

288 PROCEEDINGS OF THE AMERICAN ACADEMY.

or mica diaphragms, which serve to limit the cathode stream to a small
pencil, were replaced by glass diaphragms, sealed into the tubes and
having the shape of a truncated cone. The apertures of the dia-
phragms are from .5 to .7 mm. in diameter, and give a very sharply
defined luminous spot of about 1 to 1.5 mm. diameter on the fluorescent
screen. Figure 12 shows the general form of the tubes and the glass
diaphragms.

-^

f

Figure 12. Braun Tube and Deflecting Coil.

Braun tubes making use of electrostatic deflection of the cathode
beam were also used in parts of the experiment. They are essentially
the same as those just described with the addition of the two electro-
static deflecting plates. These plates are about 8 by 2.5 cm. in
dimensions, and are sealed inside the tubes about 2.5 cm. apart.

Several Braun tubes have been made at the laboratory, and it was
found important that the distance between the cathode and the anode
should not be less than about 15 cm. A very sensitive fluorescent
screen for visual observation is made by dusting very finely powdered
willemite over a piece of mica or glass freshly painted with a thin coat
of water glass, although according to Zenneck a zinc sulphide screen is
to be preferred for photography and was used in this research.

In order that the cathode beam may be homogeneous, that is, have
at all times the same velocity and consequently the same deflection
under a certain force, it is necessary that the potential of the source
causing the discharge be very constant. This restriction, of course,
excludes induction coils and transformers, and practically limits the
desirable sources to either the large static machine or the high potential
battery.

If a static machine is used, one of many plates is necessary in order
to give sufficient intensity to the cathode beam, and if possible the
plates should have no sectors or carriers.

The ideal source of current for a Braun tube is the high-voltage
secondary battery, capable of giving a potential of from 10,000 to
20,000 volts. In order to control the current, should the vacuum
drop, the current from such a plant should pass through two or three

CHAFFEE. — IMPACT EXCITATION OF ELECTRIC OSCILLATIONS. 289

feet of running water in glass tubes. In this investigation the Braun
tubes were operated on Professor Trowbridge's large 20,000 cell battery,
which has proved of the greatest value in this and other work. Usually
not over 20,000 volts were used, that being sufficient, under proper
adjustment of vacuum, to give a very intense and homogeneous
cathode beam.

The proper adjustment of the vacuum is of the utmost importance,
and depends entirely upon conditions. For the greatest intensity of
the spot and, at the same time, the greatest sensitiveness, the pressure
inside the tube should be as high as possible consistent with a clearly
defined spot. After some experience, the appearance of the discharge
about the cathode serves as the best indicator as to the exhaustion.
The best results are usually obtained when the luminous stream from
the center of the cathode is about 1 mm. in diameter, although in
special cases a higher or perhaps a lower exhaustion is desirable. The
vacuum, however, changes when using large currents, making it neces-
sary that the tubes be in connection with a mercury pump. The Gaede
rotary pump was used in this investigation.

If a pump in connection with the tube is not convenient, a vacuum
regulator, containing potassium chlorate or some other substance such
as is used on X-ray bulbs, is suggested for lowering the vacuum when
necessary.

In order to eliminate the deflection of the beam by the earth's mag-
netic field, the tubes are mounted with their axes parallel to the earth's
magnetic force, which mounting gives the tubes an inclination of about
70° with the horizontal. The camera, for photographing the oscillo-
graphs, was directed downward, viewing the upper or front surface of
the fluorescent screen. Plate 1 a, shows the general arrangement of
apparatus.

The deflecting coils, when used with high frequency current, can, of
course, contain no iron. The coils, which were used in this investiga-
tion for the magnetic deflection of the cathode beam, are composed of
from two to sixteen rectangular turns of copper wire, .325 cm. in diam-
eter, half of the turns being on either side of the tube. The turns are
about 7 or 8 cm. in width, and from 10 to 12 cm. in length. A nearly
uniform field within the coil is secured by making the width of the
rectangular turns /y/2 times the distance between the planes of the two
parts of the coil.

When using high irequencies, the difference in potential between
two parts of the same coil, due to inductance, is sufficient to ca.use very
large electrostatic deflections of the cathode beam. This disturbance
is most effectually eliminated by surrounding the tube inside the coil

VOL. XLVII. — 19

290 PROCEEDINGS OF THE AMERICAN ACADEMY.

by a split solenoid of fine insulated copper wire wound on a paper
tube. This device completely shields the cathode beam from electro-
static disturbances, but allows the magnetic forces to pass undiminished.

When the Braun tube is used for alternating currents of commercial
frequencies, or for phenomena taking place in a few hundredths of a
second, the velocity of the luminous spot over the screen is small
enough to give a visible streak of light even if the phenomenon lasts
for only one cycle.

When high frequency currents are used, however, the velocity of de-
flection of the cathode beam is so great that it is necessary that the
luminous spot travel over the same path thousands of times a
second in order that even a visible effect may be observed, and many
more times if a photographic record is to be taken with a reasonable
exposure.

It is then apparent that, if a sequence of instantaneous phenomena
is to be delineated by causing the cathode beam to trace out a pattern
on the fluorescent screen of the Braun tube, the c)'cle of events must
repeat many hundreds of thousands of times a second, and with such
regularity that the spot of light will, each cycle, travel over exactly
the same path.

When using the Braun tube for studying electrical oscillation, this is
usually more or less of a difficult condition to attain on account of the
uncertain and variable action of most forms of discharge gaps. The
gap and system under consideration is, however, so regular and con-
stant that it is not at all difficult to obtain photographs of patterns
representing cyclic changes, many of which recur three million times a
second with practically no variation.

Plates 1-7 are a few of over fifteen dozen photographs taken repre-
senting various conditions, and give unmistakable evidence of the
remarkable regularity and continuity of the oscillations of the Cu-Al
gap. The photographs were taken on Seed's Gilt Edge No. 27 plates,
and exposures of from 3 to 30 seconds were made. The figures are
practically natural size.

(2) The Primary Wave.

The observations for determining the shape and phase, with respect
to the secondary oscillation, of the primary current rush were obtained
by leading the primary and secondary currents each through a 4-turn
deflecting coil about the Braun tube, the two coils making an angle of
90° with each other. The arrangement is diagrammatically shown in
Figure 13, where the letters have the before mentioned significance.

CHAFFEE. — IMPACT EXCITATION OF ELECTRIC OSCILLATIOxVS. 291

There is obtained on the fluorescent screen by this arrangement a per-
fectly definite and well defined pattern, which gives the corresponding
instantaneous values of the primary and secondary currents. Plate 1 c,
is one of many photographs of such a pattern, taken with an exposuie
of about 15 to 30 seconds, and represents the conditions when adjust-
ments are made for maximum energy in the secondary circuit.

Figure 13.

Knowing, as will be adequately proved later, that the secondary
oscillation is sinusoidal, the primary current, plotted to time, and its
phase relation to the secondary current, can readily be derived from
the patterns mentioned above. In c of Plate 1 the vertical distance c/i
to the primary loop above, from any point on the horizontal line dis-
tant (5?2 from the center or undeflected spot, gives the instantaneous
primary current, ii, and the simultaneously secondary current, ?2- A
sine curve of amplitude represented by the secondary deflection is
drawn, and the time coordinate for any corresponding values of i^ and
12 is the time, obtained from the sine curve, at which the current
coordinate is i^- The direction of the spot of light is indicated by the
arrows. The curve marked ij, in Figure 14, shows the development of
two figures, both reduced to the same scale for better comparison.
In in the figure is the secondary current. Seven such developments
were made representing entirely different conditions, but in each case
the phase of A with respect to I2 was practically the same as is shown
in Figure 14, and the shapes of the /i curves differed so slightly that,
to save confusion, they are not reproduced.

Examination of the photograph and of the developments show, as
was stated in Part I, that there is no inverse current. Although the
primary wave appears to have twice the period of the secondary oscil-
lation, if the slope of the curve, or — -^ which is proportional to the

292 PROCEEDINGS OF THE AMERICAN ACADEMY.

resulting induced electromotive force in the secondary circuit, be
plotted, a curve of the same period as /j is obtained. This e. m. f.
curve is shown at A' in Figure 14.

If, now, the ordinates of the e. m. f. curve be multiplied by the corre-
sponding values of the secondary current, a quantity proportional to
the instantaneous rate at which energy is being transferred to the sec-

FlGURE 14.

7i . . . . . Primary Discharge Wave.

I2 Secondary Wave.

E Electromotive Force due to 7i.

W Power Delivered to Secondary Circuit.

ondary is obtained, and if plotted, gives the curve marked TT^ in Figure
14. The portions of the curve below the axis of time are negative,
and represent a return of energy to the primary circuit. The algebraic
sum of the areas under the four loops is proportional to the total
energy permanently delivered to the secondary circuit in one cycle.
It is apparent that very little energy is returned to the primary circuit,
and that the second half of the primary loop gives the greater amount
of energy to the secondary circuit, the first part of the primary dis-
charge being more or less irregular on account of the sudden breaking
down of the high initial gap resistance and the superposed higher
harmonies resulting from the sudden shock to the system.

In Part I it was stated that the primary current loops occur every
two or more secondary oscillations. In this case the primary wave,

CHAFFEE. — IMPACT EXCITATION OF ELECTRIC OSCILLATIONS. 293

considered as an intermittent function, could be analyzed into har-
monics. Instead, however, of analyzing the current wave, the equiva-
lent problem of expanding the resulting e. m. f. wave into harmonics
can easily be done if, as is seen by reference to Figure 14 to be roughly
true, the e. m. f. curve be assumed to be an intermittently repeated
sine cycle.

FiGUKE 15.

Suppose the particular case of a discharge every two secondar}''
oscillations (I. C. F. = 2) be considered in detail Figure 15 indicates
the conditions of the problem. The full line sine curve, marked in
represents the secondary oscillation which has thus far been considered,
or in other words, the primary harmonic of maximum intensity. The
other full line, marked ii, is the primary discharge, and the dotted
line the approximate e. m. f. wave which was referred to above.

The function

7r/2

e = 0

0

77/2

e = ^ sin 2x

is to be developed into a Fourier series of the form

e= ai sina: + a^ sin 1x ■\- a^ sin 3.r +

where any coefficient a^ is given by the expression

am = - \ /M sin mx dx = - \ E sin 2x sin mx dx
rr J 0 IT Jq

The result is expressed below.

e^=: E (.43 sin ^4- .50 sin 2x+ .26 sin 3.r —

.061 sin 5x+ .028 sinT.i- — .017 sin 9.r + . .

294 PROCEEDINGS OF THE AMERICAN ACADEMY.

If the harmonics are to be expressed in terms of time and the period of
the e. m. f. wave, which is the same as the period of the secondary
oscillation, the substitution

2a; = 2irnt or

x= — -— IS to be made.

Then ^2 = ^ (-43 sin 27rl ^j^ + .50 sin 27r«^ + .26 sin 2;r[^ 1^ — .061
sin 27r \^\t + .028 sin 27rl -^ 1^ — .017 sin 27T[^Ji5 + . .j

The results for I. C. F. equal to 3 and 4 are given below.
I. C. F. = 3

es = E(.2l sin 27rr| |i + .33 sin 2^1^ 1^ + .33 sin S'rl^ |^ +

.24sin2Trr ^ U+.lOsin 27r ^ U-.04sin 2it\ ~ \t-. . . j

LC. F. =4

^4 = ^^.12 sin 277 J p + .21 sin 2tt\ ^ K+ -26 sin 2-k\ '^ \t +

.25 sin 2n?it + .20 sin 277 '^ U + .13 sin 27r ^ r + • • • • )

A classification of the harmonics is given in the adjoining table,
where the columns are headed according to the I. C. F.

The coefficients of the various terms in the developments mean very
little, but the existence of most of the harmonics, given in the table,
has been verified by wave meter readings.

A much more beautiful proof of the existence of the harmonics is
presented by Braun tube oscillographs. If, in addition to the arrange-
ment of circuits shown in Figure 13 for obtaining the primary wave
form, another adjustable secondary circuit be used, excited by the
primary current, and having a deflecting coil also about the Braun tube
and parallel to the primary deflecting coil, the pattern observed on the
fluorescent screen is the resultant of the deflections of the first sec-

CHAFFEE. — IMPACT EXCITATION OF ELECTRIC OSCILLATIONS.

295

I. C. F.

1

2

3

4

5

6

7

n

n

TC

n

n

n

n

2

3

4

5

6

7

2n

2?i

2re

2n

2/1

n

3

4

5

6

7

3n

3n

3n

3n

3n

y

n

4

5

6

7

4/1

4rt

4n

4n

3

n

5

6

7

5n

5rt

5n

5n

5n

2~

y

T

w

"6"

7

m

V

'a

6n

6n

6n

o

n

a

4

5

7

u

c3

7n

7n

7n

7n

7n

t^

2

3

4

5

6

n

(S

a

Sn

8n

8«

Sn

Oh

3

5

6

7

9«.

9rt

9/1

9/1

9/1

T

4

5

6

7

lOn

lOn

lOn

lOn

3

4

6

7

lln

lln

Ibi

lln

ll/i

etc.

3

etc.

4

etc.

5

12n
5

etc.

6
etc.

7

ondary current, and, at right angles to it, the sum of the deflections
due to the primary and the second secondary currents. If, now, the
second secondary capacity be varied, there suddenly appears on the
fluorescent screen, as resonance for one of the harmonics of the primary
is obtained, a Lissajou's figure corresponding to the ratio of frequencies
of the two secondary oscillations. In addition to the simple Lissajou's
figure, which is due to the free vibration of the two secondaries, there

296 PEOCEEDINGS OF THE AMERICAN ACADEMY.

appears a less intense irregular loop due to the intermittent primary
discharges.

Plate 1, cuts d and e, and a and h of Plate 2 are photographs of a
few of the patterns obtained by the above described method. The
second secondary circuit was a wave meter with its coil parallel to the
primary deflecting coil, from which it received its impulses. An ex-
amination of the primary loop is often instructive in giving the relation
of the primary discharge to the secondary oscillation. It is seen that
the regular Lissajou's figure may or may not be complete according to
the value of the I. C. F. In h of Plate 2 the ratio of frequencies
is 3 : 1, and the I. C. F. is 3, so that the primary discharges occur once
for every journey of the spot over the pattern, thereby distorting a
part of the Lissajou's figure.

Cuts h-f of Plate 2 are due simply to the deflections of the two
secondary oscillations, the second secondary circuit receiving its im-
pulses from the same primary coil which excited the first secondary
circuit. Some of the photographs shown were purposely taken with a
slight diflierence in phase to show the double line. Cut e of Plate 1
represents the same ratio of frequencies as that of cut a of Plate 2 but
with a considerable shift in phase.

A consideration of cuts d-f of Plate 2 shows that, although the
coupling was close, the secondary currents do not depart from the
sinusoidal form even while the primary impulse occurs. A possible
rough explanation of this non-departure from the sinusoidal form can
be had from a consideration of the shape of the primary wave form
shown in Figure 14. The primary impulse I\ of Figure 14 is seen to be
approximately a cosine curve, of the same period as the free secondary
oscillation, plus a constant, until the maximum current is attained,
when the current decreases in a straight line. But by substitution in
the diflerential equation for an oscillatory circuit, one finds that a
cosine wave plus a constant or linear function of the time satisfies
the conditions of a sine secondary oscillation. The proof of this
proposition is not given here.

The shape of the primary wave form, which has just been considered,
is determined principally by the changes in resistance which take
place in the gap. If there were no change in resistance, and the influ-
ence of the secondary current were negligible, the form of the primary
current rush would be given by the familiar equation

CHAFFEE. — IMPACT EXCITATION OF ELECTRIC OSCILLATIONS. 297

where

2X1 Ci

^"^ ^ = 2zr(7x

Qo is the initial charge in the primary condenser Ci, and Li and Bi are
the inductance and resistance in the primary circuit. The curve,
which represents this equation, is, as is well known, a rise and fall of
current with respect to time, and is aperiodic or oscillatory according
as Ei^ is greater or less than AL-i/Ci. The critical resistance above
which the discharge is non-oscillatory is, for the circuits which were
used in this investigation, of the magnitude of 100 ohms. As will be
seen later, the average resistance of the gap is so low compared to this
quantity that the existence of no inverse current cannot be attributed
solely to the aperiodic nature of a discharge through a high resistance.
Moreover, if the average resistance were high enough to cause the dis-
charge to be aperiodic, the end of the discharge would be asymtotic to
the time axis.

The resistance of the gap very rapidly drops from a very high value
at the start to a low value. Since the resistance is a function of the
current, and very probably a function of the time of which we have no
knowledge, it is impossible to derive any exact mathematical expres-
sion for the current curve. A consideration of the physical aspects
will, however, reveal to some extent the reasons for the shape shown.
If, in the differential equation for the primary circuit.

di
the term ^i is suddenly decreased, it is evident that the term Lx -~

at

will prevent at first a rapid change in current. This, in part, ex-
plains the slow rise of current as shown by the first part of the primary
wave form. As the discharge progresses the resistance becomes lower,
and the current increases, following more closely one of the expo-
nential discharge curves of low resistance. For reasons previously
given, the discharge stops as soon as the current becomes zero.

(3) Ths Resistance of the Gap.

It is interesting, by assuming an approximate expression for the
primary wave form, to calculate the change in resistance of the gap

298 PROCEEDINGS OF THE AMERICAN ACADEMY.

necessarj' to give the observed primarj^ current curve. An examination
of the experimental curves of Figure 14 shows that the first part of the
primary wave can be approximately represented by the expression

?l = /i (1 —cos o) t).

where now /i represents the instantaneous value, and /i the maximum
value of the primary current, and « is 2 tt times the secondary frequency.
Time is reckoned from the beginning of the primary discharge.

The corresponding expression for the secondary wave is found by
measurements of Figure 14 to be

?2 = /2 sin {oi>t+ 115"").

These expressions can now be substituted in the differential equa-
tion for the primary circuit,

r

Jo I

in which R^ is the resistance of the gap, ll^ is the resistance of the
rest of the primary circuit.
Also

^c = /i — lo- (See Figure 13)
whence

Lxl\ ft) sin mt — Mh CO cos (w^ + 11 5°) + {Rx + R^h (1 — cos ai)

{Ii — Io)t _ J ^ma>t _ Qo
C'l ft>6'i Ci

Solving for 74 there results

Qo (Ii-Io)t

Ii( Zico — -— jsin ft)!? + MIoto cos (at + 115°)

/l(l —cos at)

Qo Ii-To

lA Li<o — • yr^ — h .91 31(0 -^ ) sin cot — .42 il/Zz cos at
\ tift) JiJ

^1
if Ri be neglected.

If appropriate values for the constants of this expression be taken,

and Rf, plotted to the current ii, the curve shown by the dotted line of

Figure 16 is obtained.

CHAFFEE. — IMPACT EXCITATION OF ELECTRIC OSCILLATIONS.

299

The change of resistance of the gap can be obtained experimentally
by use of a Braun tube provided with electrostatic deflecting plates.
These electrostatic plates are connected directly across the gap as
shown by Figure 17, causing a deflection perpendicular to that caused

S60

320

280

240

.200

160

120

80

40

\

, \

\

\

■\

._.

. \

\

\

\^

1 \

■\

\

1 \

\

1

\

O

i '

1

\
\ \

\

\

ii

\

\

\

\

\^

G

\

\

\\

1

\

i

s.

\

«
1 >

\

1 1

1 t

\

1

1 \

\

\^

\

sV \

\

-' >

V

A

N-^

V,

t^___

■^-t,.

rrf:

—

_

0

L

2

3

i

I

1

»

3

7

AMPERES.

Figure 16. Resistance Curves of Cu-Al Gap.

G . . . . Glow Discharge.
L . . . . Discharge with Very Long Gap.
S . . . . Discharge with Very Short Gap.
Dotted curve .... Calculated.

by the total current through the gap. In this way a trace of the
voltage-current characteristic curve is obtained from which can be
derived the resistance corresponding to any current.

Cuts a-e of Plate 3 are photographs of E-I characteristic curves as
above described. Cut a represents the conditions for a very long gap.
The path of the spot of light, in tracing this figure, may be understood
from the following. As the condenser charges there is no current

300

PROCEEDINGS OF THE AMERICAN ACADEMY.

through the gap, and hence no current deflection, but the potential of
the condenser increases to a certain value determined by the breaking-
down potential of the gap. This charging is represented in the
photograph by a movement of the luminous spot from A, its undeflected
position, to B, the potential at which the gap breaks down, which in
magnitude, in this case, is equal to about 450 volts. The instant that

— €£^

Figure 17.

the gap breaks down the potential drops, and the current through the
gap increases giving the curve, from B to C, roughly resembling a hyper-
bola. As the current decreases, represented by the line CA in the
photograph, the potential remains practically zero, showing that after
the gap has been once ionized the resistance remains low until the
current becomes zero. The current does not increase in the negative
direction for reasons previously given. During the passage of the
primary current the capacity, Ci, has been completely discharged and
charged in the reverse direction so that, as soon as the current stops,
the full potential of the reversed condenser is brought to bear across
the gap. This is represented by the point Z>. Current is now, however,
flowing into Ci at a constant rate, causing the fluorescent spot to move
along the voltage axis from D to B to begin a new cycle.

The same kind of diagram is shown in cuts b and c of Plate 3 for
shorter gaps. It is evident, as would be expected, that as the gap is
shortened, the B-I curve closes in toward the two axes.

It is also seen that with a very short gap the current increase is
oscillatory. These oscillations are very rapid, having a wave length of
the magnitude of four or five meters, and on account of the extremely
high fi-equency cause the large potential oscillations shown by the
blurred space in cut d of Plate 3.

The reason for these su])erposed higher frequency oscillations is easy
to understand if we consider again the rapid drop in resistance repre-

CH.\FFEE. — IMPACT EXCITATION OF ELECTRIC OSCILLATIONS. 301

sented by the very steep resistance curve for a short gap. A decrease
in resistance means an increased current, but the increase in current
further causes a decrease in resistance. This action promotes an un-
stable condition, and would cause a tremeadously sudden rush of
current if the inductance of the whole circuit did not exert a con-
trolling action. The effect is, however, that the terminals of the gap
and the wires in the immediate vicinity of the gap are suddenly robbed
of electricity, and because of the inductance of these terminal lead
wires, the terminals are charged in the opposite direction. When
the potential of the reversed terminals attains a sufficient value this
momentary current rush stops and reverses. It is evident, without
further consideration, that the conditions are right for the observed
superposed oscillations, these oscillations being more intense at the gap
and extending back with diminishing amplitude into the primary
circuit. This effect will be very apparent in some of the pictures yet
to be considered.

Cut e of Plate 3 is a photograph taken when, on account of the dry-
ness of the hydrogen, practically nothing but a glow discharge could
be obtained. The gap in this particular case was traversed by a high
frequency current. The photograph is introduced only for the small
curved point at the right hand end of the potential deflection, which is
the characteristic of the glow discharge.

Cut /of Plate 3 was taken in the same manner as the pictures just
described except for the addition of a secondary deflection coil parallel
to the primary coil about the tube. In this way there is obtained a
spreading out of the diagram, and a clearer view of the actual path
of the luminescent spot. The helical path from right to left results
from the secondary current oscillation, and superposed primary potential
oscillations due to the influence of the secondary vibrations on the
primary circuit, both occurring during the charging of the primary con-
denser. The abrupt end represents the point at which the gap breaks
down and the spot moves very rapidly, at first, over the primary
discharge loop.

The change in resistance with changing current, derived from these
E-I characteristics, gives curves of the general shape shown by the full
line curves of Figure 16. The curve marked L was derived from cut a
of Plate 3, and represents the change in resistance of a very long gap.
The other two full-line curves are for shorter gaps, and, in the extreme
corner, is suggested the condition for decreasing current which com-
pletes the cyclic resistance changes.

It is seen, on examination of Figure 16, that the dotted curve, derived
from an assumed expression for the primary wave form, agrees well in

302 PROCEEDINGS OF THE AMERICAN ACADEMY.

shape with the experimental curves (heavy lines). The scales of the
curves serve only to give an approximate idea of the magnitudes of the
resistances at different cun-ents, for the position of the curves depends
upon the arc length and undoubtedly upon the period of discharge. It
is -worthy of note that the resistance at zero current is very high, thus
admitting of a high initial charge in the primary condenser before the
gap breaks down. The resistance curves are very steep, being much
steeper than the corresponding curves for the Poulsen arc. It is, in
part, this steepness which adapts the gap to the production of very high
frequency oscillations. The very rapid reestablishment of the high
resistance is also of primary importance in the action of the gap with
high frequencies.

The upper dot-and-dash curve is for the curved point at the end of
the potential deflection in cut e of Plate 3 just mentioned, and repre-
sents the conditions for glow discharge.

(4) The Inverse Charge Frequency (I. C. F.).

Reference has often been made to the I. C. F., the value of which, as
was stated, depends upon the wave length of the secondary oscillation,
the size of the primary condenser (7i, and the value of the supply cur-
rent Iq. In order to show that the I. C. F. has, under most conditions,
a perfectly definite value, and at the same time, to illustrate some other
points concerning the system, the photographs of Plate 4 were taken.

The arrangement of circuits, for the figures under discussion, was as
follows : Two parallel deflecting coils were placed about the Braun
tube, and so situated as to deviate the cathode beam in a direction
perpendicular to the electrostatic deflection. One of these coils was
connected in the primary circuit and the other in the secondary
circuit. The electrostatic deflecting plates were connected to the
terminals of the primary condenser C^.

The oscillograms of Plate 4 represent, therefore, the sum of the
primary and secondary currents by deflections in the vertical direction,
and the potential of Ci, by deflections in the horizontal direction. In
all of the cuts the straight lower portion results fi'om the secondary
oscillation during the charging of Ci, when the gap current is zero.

The explanation of cut h will serve for all of the pictures of Plate 4.
At point A the condenser Ci is charged to a potential sufficient to
jump across the gap. When the primary discharge begins, the spot of
light moves very rapidly at first over the loop A EC. This discharge
starts or maintains the secondary oscillation, so that the vertical deflec-
tion is due to the primary current plus the simultaneous secondary

CHAFFEE. — IMPACT EXCITATION OF ELECTRIC OSCILLATIONS. 303

current. During the discharge the potential of the primary condenser
falls and increases in the opposite direction, so that, at the end of the
discharge, represented at C, the condenser potential is reversed. At
point C the primary discharge is completed. The rest of the diagram
from C to A is due to the secondary oscillation, which causes the
vertical deflection, and the uniformly changing potential of the primary
condenser while charging, which causes the horizontal deflection from

Cto^.

The numher of secondary oscillations taking place during one pri-
mary cycle, and which has been called the I. C. F., is clearly shown by
the photographs. In the case of cut h, the secondary completes one
period during the primary discharge, and three complete secondary
periods during charging from G to A, so that the I. C. P. is 4.

The instant at which the primary discharge begins and ends with
reference to the secondary wave, is shown to be the same as was
derived in the section on the primary wave. The high harmonic
oscillations in the primary which occur, as has been mentioned, after
the high resistance of the gap is broken down, are apparent in the
beaded appearance of the upper loops of the oscillograms.

In cuts a-e of Plate 4 the spot travelled over the patterns in an anti-
clockwise direction. The I. C. P.'s are respectively 3, 4, and 6. In
cuts a and h the undeflected position of the spot is shown, and the
relative magnitudes of the direct and inverse potentials of the primary
condenser can be noted.

The beats, shown in cuts c-f of Plate 4, are due to the interference
of two oscillations in a doubly-periodic secondary system employed in
this case. The second-secondary oscillation is due to the vibration
of an helix, a few turns of which were included in the secondary cir-
cuit. The luminous spot in cut d travelled in a clockwise direction.

(5) Resistance Damping.

In order to obtain an oscillogram of a variable which is a function
of time, it is necessary to use some device which will give a uniform
time axis to the figure. For instance, if it is desired to obtain an
oscillograph of the commercial alternating current, one passes the cur-
rent through the deflecting coil about the Braun tube. There appears
on the screen a straight line, which results from the to-and-fro move-
ments of the luminous spot over the same straight path. In order to
see the current wave developed with respect to time, it is necessary to
observe the line deflection in a revolving mirror, its axis being parallel
to the line deflection. If a photograph is to be taken, it is further

304 PROCEEDINGS OF THE AMERICAN ACADEirT.

necessary to drive the mirror by some synchronous device so that the
image of the developed figure may be stationary on the photographic
plate for a time sufficient to make the exposure. This synchronizing
device is not difficult to arrange when using commercial alternating
currents, but when it is desired to take an oscillogram of a high
frequency current or condenser discharge, it is usually impossible to
make the necessary synchronization. When using high frequency
currents, the velocity of the spot of light on the fluorescent screen is
so great that, in order to obtain a photograph, it is necessary that the
cycle of changes, as shown by the pattern on the screen, be repeated
many hundred thousand times with such regularity and certainty that
the image is always in exactly the same position. The requirements
of both the acting system and the synchronizing device are very
exacting.

The development of the time axis can be most effectually accom-
plished with the system under discussion by the very simple connection
which was used in the last section. The electrostatic plates, which
cause a deflection perpendicular to the current coils, are connected to
the terminals of the primary condenser C i. During the interval be-
tween primary discharges, when the primary condenser is charging, the
primary current is zero, and the main or charging current is almost
perfectly constant on account of the large inductances in the mains.
This uniform charging causes a uniform increase in potential of the
condenser d, and' hence a uniformly developed time axis on the fluor-
escent screen. The oscillations of the secondary, or any effect started
by the primary discharge, is thereby developed, as is shown by the
lower portions of the cuts of Plate 4.

This arrangement for the development of current or potential de-
flection with respect to time is of the greatest use in many ways. Its
application will be illustrated here by showing the damping curves
with oscillations of a frequency of two million or more per second.

Cuts a and h of Plate 5 represent the damping of the secondary
oscillations due to the addition of resistance in the secondary circuit.
The primary capacity and supply current were so adjusted as to give
large values of the I. C. F. in order that as many secondary oscilla-
tions as possible might appear in the damped oscillation trains shown.
The adjustments for the pictures of Plate 6 were so made that each
oscillation train is just completed before the beginning of the next.
The trains, therefore, succeed each other with no intervals of rest. By
adjustments of the supply current or primary capacity it is possible to
lengthen or shorten the interval between the primary discharges, and
by varying the resistance in the secondary circuit the number of oscilla-

CHAFFEE. — IMPACT EXCITATION OF ELECTRIC OSCILLATIONS. 305

tions in one train or the damping can be varied at will. The damping
is evidently exponential in fulfilment of the familiar theory.

Cuts c-f of Plate 5 and cut a of Plate 6 are the results of adding to.
the arrangement of circuits just considered, a second secondary cir-
cuit, excited by the primary discharge and with its deflecting coil
placed parallel to that of the first secondary. There results, therefore,
a doubly-periodic secondary system having two secondary circuits
inductively coupled together. The doubly-periodic secondary oscilla-
tion gives the beats and curious figures shown. Cuts c and d are due
to the addition of two oscillations differing widely in frequency. As
will be seen from the description of the figures, the second oscillation
is m one case over twice and in the other case almost three times the
frequency of the main secondary oscillation.

Cut a of Plate 6 shows beats taken with almost undamped oscilla-
tions. The wave lengths are not recorded but they were probably of
the magnitude of 100 meters.

(6) Damping in a Circuit Containing a Spark Gap.

When the dissipation of energy in an oscillatory circuit is propor-
tional to the square of the current, as is the case in a constant resist-
ance, the damping is exponential. If, however, the resistance is a
function of the current the energy dissipation is no longer proportional
to the square of the current, and the damping no longer exponential.
For instance, the resistance of a spark gap or arc is a function of the
current, the resistance being greater the smaller the current through
the gap.

Richarz and Ziegler* in 1900 observed, in a revolving mirror, the
straight line deflection which is produced in a Braun tube when a con-
denser is rapidly discharged across a spark gap and through the de-
flecting coil. The frequency of the oscillations was very low. On
account of the impossibility of taking a photograph, we have only their
description of the phenomenon as seen in the revolving mirror. In
appearance the figure resembled the backbone of a fish, or, in other
words, a long straight line, due to the undeflected spot, and at intervals
along the line pairs of equally inclined short straight lines, as one
would indicate an arrow point. The short lines were due to the more
intense maximum deflections during a train of oscillations, the separate
oscillations being entirely undiscernible. The results showed that the
damping due to a spark gap is not exponential but approximately
linear.

9 F. Richarz u. W. Ziegler, Ann. d. Phys., 1, 468, 1900.
VOL. XL VII. — 20

306 PROCEEDINGS OF THE AMERICAN ACADEMY.

Zenneck,!" in 1904, obtained further experimental proof of the
approximately linear damping due to a spark gap. He photographed
the line deflection, and by a process of projection from the several
brighter spots, due to the decreasing amplitudes of the oscillations, de-
rived the damping curves. Frequencies up to 1800 per second were
used by him,

Heydweiller,!! in 1906, showed that the results obtained by the
above mentioned experimenters can be deducted theoretically. Hey-
dweiller assumes, in deducing the linear damping, that the gap has a
characteristic expressible in the form.

b

e = a + .

t

where e and ^ are the voltage across and current thi'ongh the gap, re-
spectively, and a and b are constants. He further assumes that b is
negligible, which reduces the conditions to the assumption of a con-
stant voltage across the gap. Solving the differential equation for the
discharge of a condenser across a constant potential gap, he obtained
rectilinear damping.

If a discharge gap be substituted for the secondary resistance in the
arrangement of circuits which was used in the last section for obtain-
ing plain resistance damping, very clear oscillograms can be obtained
of the oscillation trains when the damping is caused by a gap. Al-
though the inherent irregularity of some metallic gaps, when used in
the secondary circuit, causes some irregularity of the oscillographs, yet
good photogi'aphic records can be obtained, as is shown by the cuts of
Plates 6 and 7. In order to obtain a potential sufficient to maintain
the discharge across the secondary gap, it was necessary to use a large

N
primary condenser and supply current, and to make the ratio, -^,

of the secondary to primary turns on the helix large.

Cuts b and c of Plate 6 show two of the pictures first taken, and
illustrate well the linear damping. The gap length was very short ;
the terminals were of aluminum.

Further investigation showed that the oscillation train took on en-
tirely different aspects according as the discharge could be classed
as a pure arc, or a spa?^k discharge. When the discharge is a pure arc,
the separate oscillations are regular and practically sinusoidal, and the
damping is still linear. If the discharge is classed as a spark discharge,

" J. Zcnneck, Ann. d. Phys., 13, S22, 1904.

" R. Heydweiller, Ann. d. Physik., 19, 646, 1906.

CHAFFEE. — IMPACT EXCITATION OF ELECTRIC OSCILLATIONS. 307

although the damping is linear, the separate oscillation loops are
distorted as will appear presently.

Cut d of Plate 6 represents the condition when the discharge ter-
minals of the secondary gap are carbon. The discharge was quiet and
very brilliant, resembling, as indeed it was, the pure carbon arc operat-
ing, however, at a frequency of 5.7 X 10^ oscillations per second.

Figure 18. Form of Spark Gap Damping Curve.

Cut e of Plate 6 gives the appearance of the oscillogram when the
terminals are of aluminum in air. The discharge in this case, as well
as for cuts b and c, was probably a pure arc due to the carbon and
other impurities in the aluminum. In appearance, the discharge was
brilliant and similar to the carbon arc.

Magnesium terminals usually give the pure-arc discharge-form of
damping curve, due probably to the large amount of magnesium vapor
present in the discharge, or possibly to the burning of the magnesium
into the oxide.

Cut/ of Plate 6 and the pictures of Plate 7 represent the appearance
of the spark discharge oscillograms. When the temperature of the

308 PROCEEDINGS OF THE AMERICAN ACADEJIY.

discharge is kept low the conductivity of the gap is not maintained
over the interval of zero current by the presence of incandescent metallic
or carbon vapor, and the high resistance of the gap is partially estab-
lished at each crossing of the axis by the current curve. This necessi-
tates a reionization of the gas at the beginning of each current loop, or
the breaking down of a possible oxide film, thereby distorting the wave
in the neighborhood of the axis, as is shown by the figures.

The general form of the curve for spark damping, which is indicated
in the photographs, was at times momentarily clearly outlined on the
fiuorescent screen and is shown by the drawing of Figure 18. Ap-
parently, in some of the photographs, the loops begin, in point of
time, before the ending of the previous loop. This apparent paradox
is due to the slight shift in the time axis resulting from the reaction
of the strong secondary discharges upon the potential of the primary
condenser.

The oscillogram photographs of spark damping here shown were
taken for aluminum terminals because of the greater regularity of the
discharge between terminals of that metal. Many other metals were
tried, such as copper, cadmium, zinc, etc., and in practically every case
in which the discharge was a spark -discharge, the oscillations took the
same form as is shown in Figure 18.

When one of the terminals is carbon or magnesium, the current loops
on one side of the time axis are of the pure arc form, while those on
the other side are of the spark-discharge form.

If the terminals are dissimilar there is usually evidence of a rectify-
ing effect. Particularly is this so if one terminal is of aluminum and
the other of copper or iron. Cut d of Plate 7 shows this rectification.

The effect of hydrogen on the discharge is indicated by cuts e and
/ of Plate 7, which were taken under the same conditions except for
the H surrounding the gap terminals in the case of cut/ The hydro-
gen serves, in this case, principally to ensure a spark rather than an arc
discharge, and probably increases the damping.

The outward appearance of the discharge is in no way an indication
as to whether the oscillogram takes the arc or spark form. The form
of the oscillogram serves conveniently to differentiate between the
pure arc and the spark discharges, when the terms arc and spark are
applied to discharges operating on alternating currents. The discharge
of the Cu-Al oscillation gap, which has been studied in this investiga-
tion, cannot, according to this definition, be called an arc, but is a
spark discharge.

The photographs here shown of gap damping furnish in no way a
complete discussion of the subject, but are presented to give additional

CHAFFEE. — IMPACT EXCITATION OF ELECTRIC OSCILLATIONS. 309

proof of the existence of linear damping in a circuit containing a spark
gap, and to show that there are two distinct forms of the oscillation
trains according to the nature of the gap.

(7) Xotes Concerning the Mechanism of Conduction in the Cu-Al Gap.

Very little can at present be given concerning the exact nature of
the conduction which takes place in the gap under discussion and the
office of the necessary hydrogen. No oscillations can be obtained un-
less the gap is immersed in some gas rich in hydrogen, but the latter
alone gives by far the best results. In any case the gas must be moist.
As was shown early in Part I, the absence of metallic vapor indicates
that the conduction is probably affected entirely by the ionization of
the surrounding gas. Since, as was also observed, the metal used for
the anode makes little difference in the operation of the gap, and since
aluminum is the only metal which works at all well as cathode, it is
safe to say that it is the aluminum cathode, working in conjunction
with the hydrogen, which gives the characteristic properties of the
oscillation gap which has been partially studied in the foregoing
pages. It might be mentioned here that magnesium acts to some ex-
tent as cathode, but, on account of its low vaporizing point, works very
irregularly and unsatisfactorily. The discharge, in this case, is in-
tensely green showing vaporization.

The fact that moisture in the hydrogen is necessary indicates that
an oxidation of the aluminum plays some part in the operation. The
necessity of an hydrogen atmosphere leads one to believe that perhaps
a reduction of the ever present aluminum oxide film at some time
during the cycle may take place, there pc ^sibly being a cyclic change
of oxidation and reduction of the aluminum determined by the tempera-
ture at various instants during one primary discharge. For instance,
it may be that some action such as follows takes place. At the begin-
ning of the discharge, the thin oxide film makes necessary a high
breaking-down potential in order to start a discharge. As soon, how-
ever, as the discharge is started, H ions are conveyed to the aluminum
cathode, and, since the atmosphere about the terminal is H, reduce the
oxide film. The free surface of the aluminum is thereby exposed, and
the resistance drops to a low value. This reduction would be the
greater the larger the current, and there would result the very rapid
drop in resistance which is shown in the curves of Figure 16. As soon
as the discharge stops the aluminum partially reoxidizes, thereby
reestablishing the initial high resistance.

It is probable that the regularity of the gap is partly due to the fact

310

PROCEEDINGS OF THE AMERICAN ACADEMY.

<

CO
40
20

^

WATTi

jc

\x

^

y^

^

^

■^^F.

/

Ul

30

•25

20

that the discharge takes place for some time at one definite point on
the aluminum, this confinement of the discharge to one place resulting
possibly from the protecting oxide film over the rest of the surface.

Part III.

Practical Considerations and Applications.

(1) Practical Considerations.

From a practical point of view interest centers on the question of
the amount of power obtainable from the system. The gap is not

a high-power generator of
electrical oscillations ; its
advantages lie in simplicity
and regularity. The con-
ditions for maximum power
were considered in Part I,
and it was seen that the
maximum power efficiently
obtained from one gap at
100 meters wave length is
about 40 to 45 watts. It
is probable, although no
extensive tests have yet
been made, that the power
obtainable is greater at longer, wave lengths.

If greater power is required, gaps can profitably be operated in
series. Two gaps work perfectly and three gaps well on 500 volts,
with much increased power output. Four gaps were satisfactorily run
on 1000 volts, but in general there is a slight sacrifice of regularity of
operation as the number of gaps in series is increased.

The amount of power obtained, when gaps are operated in series
with a definite supply current, is not directly proportional to the num-
ber of gaps. When two gaps are operated in series, the power output
is almost twice that from one gap. When more gaps are connected in
series, the gain in power is much less, the greater the number of gaps
the less the gain in power output.

The average voltage across one gap ranges from 90 to 150, but is,
under most conditions, about 100. As the number of gaps in series is
increased, the current being constant, the voltage across the series
is practically proportional to the number of gaps.

The efficiency of the system, when gaps are operated in series,
decreases as the number of gaps is increased.

1

3

GAP5 IN SERIES

Figure 19. Gaps in Series.

CHAFFEE. — IMPACT EXCITATION OF ELECTRIC OSCILLATIONS. 311

The following table and the curves of Figure 19 give an idea of the
result of increasing the number of gaps in series. The values of the
efficiency and power may be somewhat misleading as the adjustments
were not for conditions of maximum power and efficiency. The general
shape of the curves, however, may prove of interest :

No. of Gaps.

lo-

E.

R.

I. R.

Eff.

1

.55

145

15.9

25.5

32.5%

2

.55

260

15.9

39.3

27.5

3

.55

360

15.9

55.0

27.0

4

.55

500

15.9

64.8

23.6

As was stated in Part I, a proper choice of dynamo permits the
omission of the external resistance. The dynamo, for use in this
manner must be characterized by a rapidly falling voltage-current
curve in order that the voltage will increase if the discharge tends to
stop. The high voltage on' open circuit of a generator of this kind also
serves automatically to start the gap or gaps.

(2) Applications.

Various applications of the continuous oscillations might well be
spoken of, but reference will be made to only three, i. e. : the use of the
oscillation system in conjunction with a Braun tube for demonstration ;
the calibration of a wave meter by means of harmonics ; and wireless
telegraphy and telephony.

The simplicity and convenience of the system as a generator of con-
tinuous high frequency oscillations render the apparatus particularly
suitable for demonstration and laboratory use. Especially is the sys-
tem of value when used in connection with a Braun tube, for, with such
an equipment, many of the phenomena of electrical oscillations can be
visualized, such as the damping due to resistance, the damping due to
radiation in an antenna, etc.

As was pointed out in Part II, two secondary circuits of different
periods can be caused to oscillate, the exact ratio of frequencies being
given directly by the resulting Lissajou's figure. If, then, the period
of one of the secondary circuits is fixed and accurately determined in
some manner, the period of the second variable secondary circuit is
given in terms of the first or standard. In this way, with proper ad-
justments, a large number of determined periods can be obtained, and
an accurate calibration of a wave meter made.*^

** Suggested by Professor G. W. Pierce.

312 PROCEEDINGS OF THE AMERICAN ACADEMY.

The system can, of course, be readily used for wireless telegraphy
provided some method such as a chopper be used for making audible
the continuous transmission of power. One gap operating on from .0 to
.8 ampere will undoubtedly transmit up to 70 miles with some advan-
tages over the other systems. In addition to the advantages of high
efficiency, one wave length, etc., is the great gain in simplicity and
regularity, and the advantage of working directly on the commercial
voltages for hours with no attention.

One of the most interesting applications of the aluminum-copper
gap is its successful use in wireless telephony. Professor G. W. Pierce
and the author have given the apparatus a thorough test in connection
with wireless telephony, and have carried on conversations for several
hours at a time between two distant stations with practically perfect
articulation. The remarkable constancy and regularity of the system
as a generator of continuous oscillations has been proved to be of great
value for the wireless transmission of articulate speech. This will
probably be the subject of a later communication.

Jefferson Physical Laboratory,
Harvard University,
Cambridge, Mass.

PLATE 1.

Mounting of Braun Tube.

Spectrum of Gap

with

Aluminum Comparison.

Spectrum.

d.

A.2 = 118 meters.
Ag = 236 meters.
Ratio =1:2.
/. C. F. = 4.

c.

Ig = .73 ampere.
A2 = 110 meters.
I. C. F. = 5.

= 76 meters.

= 114 meters.
Ratio = 2:3.
/. C. F. = 4.

^2

^3

Chaffee. - Impact Excitation of Electric Oscillations.

Plate I.

PROC. Amer. Acad, arts and Sciences. Vol. XLVII.

PLATE 2.

LissAJOu's Figures.

a.

\2 = 80 meters.
A3 = 120 meters.
Ratio 2:3.
/. C. F. = 6.
Iq = .65 ampere.

A2 = 158 meters.
A.3 = 474 meters.
Ratio 1:3.
/. C. F. = 3.
/o = 1 ampere.

A2 = 173 meters.
A3 = 231 meters.
Ratio = 3:4.

A2 = 180 meters.
A3 ^ 300 meters.
Ratio = 3:5.

e.

A2 = 200 meters.
A3 = 250 meters.
Ratio = 4:5.

/.
A2 = 180 meters.
A3 = 315 meters.
Ratio =4:7.

Chaffee. — Impact Excitation of Electric Oscillations.

Plate 2.

Pkoc. Amer. Acad. Arts and Sciences. Vol. XLVI

PLATE 3.

E—I Characteristics.

o. — Very Long Gap.

Iq = -55 ampere.

1 cm. = 4.0 amperes (vertical).

2 cm. = 250 volts (horizontal) .

c, — Short Gap.

lo = .54 ampere.

1 cm. = 1.3 amperes (vertical).

1 cm. 230 volts (horizontal).

Cu-Al gap operating on
oscillator^' current. Characteristic
of Glow Discharge shown at the
end of the potential deflection.

h. — Long Gap.

Ig = 1.0 ampere.

1 cm. = 4.25 amperes (vertical).

1 cm. = 250 volts (horizontal).

d. — Very Short Gap.

Ig = 1.5 amperes.

1 cm. = 4.25 amperes (vertical).

1 cm. = 250 volts (horizontal).

268 meters.
.5 ampere.

Chaffee.— Impact Excitation of Electric Oscillations.

Plate 3.

PROC. AMER. ACAU. ARIS and bCiENCtb, VuL. XLVI

PLATE 4.

a.

As = 185 meters.
/„ = .85 ampere.
Ci = 178 X 10-5 ju./.
I. C. F. = 3.

Iff = .68 ampere.
Ci = 110 X 10-5 M./.
I. C. F. = 4.

c.

X2 = 180 meters.
/fl = .32 ampere.
/. C. F. = 6.

d.

A2 = 78 meters.
7o = .63 ampere.
I. C. F. = 9.

e.

A2 = 88 meters.
/„ = .4 ampere.
Ci = 170 X 10-5 |u./.
7. C. F. = 11.

Ao = 65 meters.
Ig = .5 ampere.
/. C. F. = 7.

Chaffee.- Impact Excitation of Electric Oscillations.

Plate 4.

PftOC. AMER. ACAD. AkIS AND SCIENCES. VOL. XLVII

PLATE 5.
Resistance Damping and Beats,

a.

^2 =
lo =

I. C. F.

5.9 ohms.
112 meters.
.35 ampere.
150 X 10-5 M-/.

12.

A.2 = 400 meters.

154 meters.
325 meters.

X

370 meters.
290 meters.

lo

=

.4 ampere.

\'

=

140 meters.

A.

=

390.

R^

=

6 ohms.

/.

A =215 meters.
A' = 255 meters.

Chaffee. — Impact Excitation of Electric Oscillations.

Plate 5.

e J

Proc. Amer. Acad. Arts and Sciences. Vol. XLVI

PLATE 6.

Gap Damping Oscijllographs.

a.

Beats.

c. — Al-Al in Air.
A = 525 meters.
lo = 1.2 amperes.

e. — Al-Al in Air.
\ = 575 meters.
1„ = 1.5 amperes.
Water cooled.

h.— Al-Al in H.
A -= 520 meters.
/o = 1.2 amperes.

d. — Carbon-Carbon in Air.
A = 525 meters.
/q = 1.4 amperes.

f.— Al-Al in H.
A = 575 meters,
/p = 1.9 amperes.
Water cooled.

Chaffee.— Impact Excitation of Electric Oscillations.

Plate 6.

Proc. Amer. Acad. Arts and Sciences. Vol. XLVII.

PLATE 7.
Gap Damping.

a. — Al-Al in Air.

A = 525.
Water cooled.

c. — Al-Al in H.

A = 525 meters.
Water cooled.

«. — Al-Al Arc in Air.

A = 525 meters.
I„ = 1.3 amperes.

b. — Al-Al in Air.

A = 525 meters.
Water cooled.

d. — Cu-Al in H.
Shows rectification.

Same as Figure 5, except
hydrogen instead of air
surrounded gap.

Chaffee.— Impact Excitation of Electric Oscillations.

Plate 7.

pRoc. Amer. Acad. Arts and Sciences. Vol. XLV

Proceedings of the American Academy of Arts and Sciences.
Vol. XLVII. No. 10. — December, 1911.

THE WAVE POTENTIAL OF A CIRCULAR LINE

OF SOURCES.

By a. G. Webster.

THE WAVE POTENTIAL OF A CIRCULAR LINE

OF SOURCES.

By a. G. Webster.

Presented December 14, 1910. Received October 11, 1911.

The fundamental solution of the wave equation

:t* = ''^■^- (1)

obtained by putting (f> = ue'^"^, so that u satisfies

Aw + K^u = 0, (2)

and representing a source, is m = e^'^''/r (r = distance from source).
Now we have Hankel's formula for an arbitrary function,

F{r) = rXdX Hpdp F(p) J(\p) JiXr), (J= Jo, Bessel's func.) (3)
and putting ^0') = e^'"'/r,

Jnco /^oo

Xd\ I dpei'^PJiXp) J{Xr), (4)

0 «7 0

and since

j;"rfp.<'-/(Ap)=^=L=, (5)

this gives

ei^_ C'^XdX J(\r) ,.

r ~ Jo ^J^~~^^' ^ ^

If we now use r in a different sense as

r^ = a;^ + f, while M"" = x' + f + z%

gikr P'^ /^<»

316 PROCEEDINGS OF THE AMERICAN ACADEMY.

we easily obtain the solution

^_ pg-zVX^=fc'xj'(A?-)(/A.

~T~Jo v^^^^' *

This result was given by Sommerfeld, Ann. der Phys. 1909, Bd. 28,
p. 683.

From this I obtain for a ring of sources of radius a,

M= / \ \ J(Xr) J(Xa)dX, (8)

J 0 A /A 2 _ „2

which reduces to (7) when a = 0, and when k = 0, to

u= I ^'^J{\r) J(Xa) dX, (9)

the well-known expression for the Newtonian potential of a ring ; and
when r = 0, to

uiz)= ^-===Xj{Xa)d\ (10)

J 0 V A^ — K^

which can be shown to be equal to

the correct expression for points on the axis of symmetry.
Now since

J(\r) = - / <i'^"°s«(^(o, (11)

ttJo

we have

^^==X/(Xr)/(A«)a

1 /^=0 fn rn , XflX

= I I I d9d(ae^^ ('■ COS 0. +o cos b)-2 Va^k2 ^ (12)

"■Jo Jo Jo -^/A"^ — K^

We will divide this into two parts, the integrals from 0 to k, and k to x .
Putting now

A = K sin (fi, Vx^ — K^ = IK cos <^, dX = k cos <f) d<f>,

WEBSTER. — WAVE POTENTIAL OF CIRCULAR LINE OF SOURCES. 317
— — I I dddiM I e^" [(>• cos o) +o cos e)ain <t>—z cos -t>] . sin </> o?rf>, (13)

TT Jo Jo Jo

and developing the exponential,

= — 7-/ / dOdijj I ^— {iKKr cos oi + a cos 6) sin (b — z cos (f>'\)^
TT Jo Jo Jo 'Trsl

• sin <^ (Iff).
Developing by the polynomial theorem,

s=oo l-{-m+n=s

TT^ Jo ^ Vo Jo ±, ,^,

s = 0 l,m,n

(iK y (r COS o) sin cftY (a cos 0 sin ^)'" (— z cos 0)"
/! w ! nl

Integrating according to 0 and w, the odd powers vanish, and

A--- X'-s:v(^''^)^^^+"'^+''^^'l-3-5...(2/-lV"l-3-5(2^-l)(-c)''
^ 0 0 0 (20! (2»^)!?i! 2-4-6.. . 2/-2-4-6. . .2m

X / sin<^2a+m)+icos»<^^^^ (14)
"" ~ ' 0 0 0 ^"'^^^'^'"^^\2 • 4 • 6 . . . 20' (2 • 4 • 6 . . . 2^2)^

(- c)"(/ + w^)

-C-^)

CO cc oo

^=-v222.

(^•^)2(Z+m)+n (-/ ^ ^^) I ^2?^2m (_ ^)n

^^^2^+'«(^!)'^(m!)2w!(w+l)(w + 3) . . .[;i + 2(/+;;i)+ 1]'

(10)
In order to obtain the real part we will proceed differently,

B = ^J-z Va-i=7« -~== J(Xr) J(Xa) dX, (17)

318 PROCEEDINGS OF THE AMERICAN ACADEMY.

and putting

X2 _ ^2 ^ ^H\ /"^^ = Kdt,

a/A" - K=^
B = K e-^'t J(^rVl + f) J (KaVl + t^) dt, (18)

which by means of the formula
becomes

^ = k/ > >,-..elz:iH^)'^_^I"\W'll +J')^^^

Jr»oo 00 P = a
0 s = Op=0

~\^P^o.-eo 2^^\j.l(s-p)lY q\{s-q)\Jo' ^*

~" " J^ ^Q^Q 22('+'») (/ ! m ly n\{l + m - n) ! c2'*+i ' ^'^^'^

/=00 TO = 00

; n ^n 2'+™ (/ ! m 1)^ ^^

1 = 0 m = 0 ^ ' n = 0

/ - (/k)"+1 (- zY

\n ! (w + 1

)(/? + 3) . . . [w + 2(/+ 7w)+ 1]
(2w)

+

2'+"* w ! (/ + m

1 \

— n) \ c2'i+i )

Proceedings of the American Academy of Arts and Sciences.
Vol. XLVII. No. 11. — December, 1911.

CONTRIBUTIONS FROM THE JEFFERSON PHYSICAL
LABORATORY, HARVARD UNIVERSITY.

THE MEASUREMENT OF HYDROSTATIC PRESSURES

UP TO 20,000 KILOGRAMS PER

SQUARE CENTIMETER.

By p. W. Bridgman.

CONTRIBUTIONS FROM THE JEFFERSON PHYSICAL
LABORATORY, HARVARD UNIVERSITY.

THE MEASUREMENT OF HYDROSTATIC PRESSURES UP
TO 20,000 KILOGRAMS PER SQUARE CENTIMETER.

By p. W. Bridgman.

Presented by G. W. Pierce, October 11, 1911. Received October 6, 1911.

In these Proceedings, Vol. XLV, Numbers 8 and 9, 1909, two methods
of measuring hydrostatic pressures were described and applied up to
6800 kgm./cm.^ The first method was by means of an absolute gauge
of the freely moving piston type; the second method depended ulti-
mately on the first, and utilized the change in the electrical resistance
of mercury under pressure. The pressure reached with these two
forms of gauge was higher than the highest previous accurately meas-
ured pressures, which extended to only 3000 or 4000 kgm./cm.^ ; but
since the earlier paper, the region of attainable and measurable pres-
sures has been still further extended to over 20,000 kgm., so that a re-
examination of the gauges there proposed became necessary. Both of
the previous methods were found to become inapplicable at pressures
much higher than 6800 kgm., the first because of the yielding of the
steel of the gauge and the second because of the freezing of the mer-
cury. In this paper the modifications of these two methods are de-
scribed with which it has been found possible to reach these higher
pressures. The freely moving piston gauge has been changed in design
so that it has been possible to reach 13,000 kgm., and has been pro-
vided with a different reading device. The second method, involving
the change in resistance of mercury, has been replaced by another
method using the change in resistance of manganin wire. With this
an indicated pressure of 20,670 kgm. has been reached. This paper is
occupied with a discussion of the calibration, the corrections, and the
details of manipulation of these gauges.

The Absolute Gauge.

The novel features of the gauge described in the previous paper
which made it possible to more than double the pressure range of

VOL. XLVII. — 21

322

PROCEEDINGS OF THE AMERICAN ACADEMY.

Amagat were the smallness of the piston exposed to pressure (1/16 inch),
and the fact that the pressure cylinder in which this piston moved was
exposed to pressure on the external as well as on the internal surface,
so that the effect of the increasing pressure was to decrease the inter-
nal bore of the cylinder and
so decrease the leak. The
application of pressure to the
outside of the cylinder was
made through the medium of
the packing.^ The figure
referred to shows that the
disposition of the packing
was such that the cylinder
was exposed externally to
pressure over the lower end,
and to none at all over the
upper. At high pressures the
effect of such an arrangement
is invariably to pinch off the
cylinder, the packing forcing
its way into the cylinder and
separating the upper from the
lower end. Two things are
necessary to produce this
effect : external pressure and
non-support of one of the
ends. The action is similar
to that of a roll of putty
which, when squeezed in the
hand, will ooze out sidewise if the ends of the roll are left free, but may
be prevented by compressing the ends of the roll between the fingers
of the other hand.

In the new form of gauge the two novel features, smallness of piston
and a cylinder exposed to pressure on the outside, have been retained,
but the manner of applying the packing has been so changed as to
avoid the pinching-off effect. The new gauge is shown in Figure 1.
The cylinder AB is placed lower down than in the former gauge, so
that now it is in the part of the metal subjected to hydrostatic pressure
only. The packing, which now takes the form of a cone of soft steel,
D, is placed above the upper end of the cylinder. This new form

Figure 1. The absolute gauge; shows
the cylinder of the gauge and the method of
mounting it in the containing vessel.

1 See Figure 2, p. 205, loc. cit.

BRroGMAN. — MEASUREMENT OF HYDROSTATIC PRESSURES.

323

Nm

rv-^

N/^

B

A

gains at three points. The soft steel packing, which takes the place

of the rubber, does not transmit pressure hydrostatically and so exerts

a smaller pinching-off effect ; the cylinder is made of hardened nickel

steel instead of tool steel, so that it has a higher yield point and more

etfectively resists what pinching-off

eft'ect there is ; and the cylinder itself,

which is the only vital part, is placed

entirely beyond the reach of this effect.

Even in this form, however, the soft

steel packing does flow sufiiciently to

produce the beginning of the effect.

After the application of the maximum

pressure the bore at C showed a very

marked decrease. But since nothing

depends on the size of the bore at C,

no inaccuracy is introduced.

This form gives up one advantage
claimed for the former gauge, namely,
that by changing the area over which
the packing is distributed it becomes
possible to some extent to control the
distortion of the cylinder and so the
leak. But this question of leak proved
of much less importance than was an-
ticipated, it being possible to range
from 0 to 13,500 kgm. without incon-
venient leak at any point. The leak YiGvn^2. The absolute gauge;
does, however, as anticipated, become shows enlarged detaU of the cyhn-
less at higher pressures, partly because der and the piston,
of closing up of the crack, so that some

sort of control of the leak would become necessary if the crack should
ever close up completely. But it has been found possible with the
present form of gauge to provide an effective control of leak by provid-
ing for the highest pressures a piston slightly smaller than normal.
This is evidently easier than to attempt so to design the gauge that
the adaptability for different pressures should be secured by changing
the packing. The need for even this procedure of changing the piston
would probably be slight in practise, for as already stated, one piston
sufficed up to 13,500 kgm., and the gauge itself would probably not
stand much more.

It is evident that the new form given the gauge makes necessary a
recomputation of the correction for distortion. The effect of this distor-

324 PROCEEDINGS OF THE AMERICAN ACADEMY.

tion is to change the effective area of the piston and so to change the
total thrust exerted on the piston by a given hydrostatic pressure.
As previously explained, this correction is calculated mathematically
and is merely a rough approximation. Its justification is that the
correction is in any event exceedingly small, and that no easy experi-
mental method of determining it directly presents itself The cor-
rection is to be made by finding the change in the mean area of the
cylinder and the piston at the lower and the upper ends, and taking
the mean of these two changes. This gives the change in the effective
area of the cross-section as was proved in the former paper.

The stress system on the piston and cylinder is as follows. On the
piston there is the longitudinal thrust produced by the action of
hydrostatic pressure on the end at A, and the equal and opposite
thrust of the equilibrating forces at B. This thrust is uniform
throughout the length of the piston. In addition there is the normal
pressure on the curved surface exerted by the liquid which is slowly
flowing out through the crack between piston and cylinder. At A
this pressure is equal to the total hydrostatic pressure, and regularly
decreases from here outward to zero at B. On the cylinder there is
externally a uniform hydrostatic pressure over nearly the entire length ;
internally the same distribution of pressure as acts on the piston. At
the inner end A the resultant of these two systems of stress is effect-
ively a uniform hydrostatic pressure on both piston and cylinder, under
which both shrink uniformly. If r and R are the radii of piston
and cylinder initially, and / and R' the corresponding values under
pressure, we have evidently :

At the lower end r = r i 1 — ^ j

..= «(i-4).

New effective radius = — ^ = — r— ^ ( 1 — — V

2 2 \ '6 J

Effective area changed by ~-

= — 4X1 f )-^ X p

p is pre

k = compressibility = G X 10

p is pressure in kgm./cm.'^ "j

BRIDGMAN. — MEASUREMENT OF HYDROSTATIC PRESSURES. 325

At the end B, the piston is exposed merely to the thrust p. It will
be assumed that the strain is the same as that under a thrust p uni-
form throughout the entire length.

Then at B ,-' = ^^1+^^

= r (1 + 1.4 X 10-'' X p),

where o- is Poisson's ratio, assumed = 0.28, and E = Young's modulus,
taken as 2 X 10^ kgm./cm.^.

This correction for the distortion of the piston is not open to serious
question, because of the smallness of the diameter compared with the
length. But the calculation of the distortion of the cylinder at the
upper end is open to much more serious question, because the irregular
shape and unknown action of the packing produce an unknown stress
system in the mass of metal about the upper end. In place, then, of
a calculation, the experimental fact was used that in all probability the
crack between piston and cylinder would not completely disappear at
less than 15,000 kgm., since the piston still possessed some freedom of
motion at 13,000. Discussion of this experimental fact is given later.
It will be assumed, then, simply that the distortion is proportional to
the pressure, and that the combined distortion of cylinder and piston
will produce complete closing at 15,000. The initial size of the crack
was determined experimentally, by measuring the piston and the
effective area, to be 0.00035 inch.

This gives at the upper end R' = R {\ — ap).
When the crack closes r' = R'

or r (1 + 1.4 X 10-'^ x jt?) = (r + 0.00035) (1 — ap).

Substituting r=l/16,

we find 0 = 2.3X10"''.

At B R!- R{\- 2.3 x 10"' X />).

Whence / + i^' = r + i? + ^^^ [(1.4 - 2.3) X 10"^ X p\

Effective radius, ^^^^ = ^"t^ (1 " 0-45 X 10"^ X p).

Effective area decreased by 0.90 X 10"'' X p.

The average change of effective area, top and bottom, which is the
correction desired, is therefore — 2.4 X 10"^ X ^.

326 PROCEEDINGS OF THE AMERICAN ACADEMY.

The correction found in this way is to be regarded as an upper limit,
the assumption being made that the crack will close up at 15,000 kgm.
The correction found by this assumption is somewhat doubtful. A
lower limit to the correction can be found by making the assumption
as far removed as possible from that made above, namely, that at the
upper end the cylinder suffers no change of internal radius. The
change of effective area at the upper end is due to enlarging of the pis-
ton alone, therefore, and is evidently 1.4 X 10"'^ X p. In this case
the change in the effective area is 1.3 X 10"' X p. The upper and the
lower limits differ only 1/10 per cent at 10,000 kgm. The correction
applied in the following work was taken as the mean of these two
limits, 1.8 X 10~^ X p, and the observed gauge readings have been in-
creased in this ratio. This happens to be the same as the correction
used for the former gauge.

The experimental evidence used in part of the above approxima-
tions requires brief mention. The calculations given above show a
more rapid closing of the crack at the end B, so that the tendency of
the piston would be to bind at the upper end. This was verified ex-
perimentally by the fact that the upper end of the piston was always
more brightly polished after a little use than the lower end, and that
sticking could be avoided at the higher pressures by making the piston
slightly conical. To accomplish this it was sufficient to make the
upper end 0.0002 inch less in diameter than the lower. The figure
above for the initial width of the crack at the upper end (0.00035 inch)
was obtained by combining with the conicality the measured value for
the effective area to be described later.

In actual use care was necessary to be sure that the sticking was
really due to closing of the crack, and not to viscosity in the fluid
transmitting pressure. In the early experiments, in which the trans-
mitting fluid was molasses and glycerine, almost complete sticking was
found at pressures as low as 7500. That this was not due to closing of
the crack was shown simply by warming the whole apparatus, thus
decreasing the viscosity without materially decreasing the size of the
crack. It was thus possible to reach. 13,000 with very much less sticking
than at 7800 at the lower temperature, and also with much less leak,
showing an actual decrease in the size of the crack at high pressures.
The liquid finally adopted for use in this work was a mixture of glucose
with glycerine and water. Glycerine and water were first mixed in
equal parts, and then the glucose thinned with this mixture to a best
consistency found by experiment. The advantage is that the pressure
effect on viscosity is much less than for the molasses and glycerine mix-
ture, so that a mixture of given consistency will work over twice the
pressure range of the molasses mixture.

BRIDGMAN. — MEASUREMENT OF HYDROSTATIC PRESSURES. 327

The functioning of the gauge at high pressures is therefore prevented
by two effects, — increased viscosity of the liquid, and closing of the
crack. In view of the fact that the gauge still worked at 13,500 when
both these effects were operative, the estimate made above that the
functioning would cease at 15,000 by the closing of the crack only
would seem to be amply low. The maximum value set on the correction
above is probably, therefore, too high.

The calibration of the piston and cylinder at low pressures to de-
termine the effective cross-section was carried out by the method used
in the previous paper. Some such indirect method of calibration was
made necessary by the fact that the dimensions of the small piston are
so small as to make accurate direct measurements of its effective diam-
eter impossible. The method consisted in hanging weights on the piston
to be calibrated and on a larger piston of known area, in such a propor-
tion that the pressure produced by the two pistons should be the same.
This is done most simply by connecting the two freely moving pistons
to the same pressure chamber, keeping the weights on one piston invari-
able, and changing those on the other until neither rises or falls. The
details of the method were the same as that described before, the same
comparison piece of apparatus being used.

The results of the comparison showed an effective diameter for the
piston of 0.06250 inches. The measured diameter was only 0.0623
inches at the larger end and 0.0622 inches at the center, showing a crack
between piston and cylinder 0.0003 inches wide at the center, 0.00025
inches at the lower end, and 0.00035 inches at the upper end, as used in
the calculation above.

In the earlier measurement of high pressures, the thrust was found
by hanging weights directly on the piston, and determining by trial
that weight which produced neither rise nor fall of the piston. This
has the advantage of ideal accuracy, but has several serious disad-
vantages of manipulation. Flexibility of design in the apparatus is
sacrificed because the gauge must be kept vertical. The scale pan and
weights become increasingly cumbersome at high pressures, so that an
assistant is needed. And worst of all, it requires considerable time to
make a reading. This is a fatal objection where the pressure must be
read instantaneously, as in experiments to be described in a following
paper on the freezing of mercury by the method of electrical resistance.

The present gauge was made direct reading and instantaneous by
causing the thrust to produce a measurable deflection in a stiff spring.
The new process is related to the old exactly as weighing with a spring
balance is to weighing with separate weights. The spring balance is
less accurate, but very much more convenient. The accuracy obtain-

328 PROCEEDINGS OF THE AMERICAN ACADEMY.

able with the new device was, however, sufficient for all requirements.
There is an added advantage in that the stroke of the piston over the
entire pressure range may be very much decreased. The stroke of
12 mm. in the previous work was reduced to J. 5 mm. in this form.
This ensures greater strength at the upper end where the piston pro-

FiGURE 3. The springs with which the thrust on the piston is measured.

jects unsupported from the cylinder, and also ensures greater accuracy,
the piston always playing in approximately the same part of the
cylinder.

Several forms of spring were tried. The form finally adopted as
giving the great stiffness desired without inconvenient bulk was that
of a saucer. Two of these saucer-shaped springs were used, placed rim
to rim, and the thrust applied at the center (see Figure 3). This ar-
rangement has the advantage of avoiding all friction when the circum-
ference of the saucer increases under pressure, since here the two
saucers support each other and move together without slipping.

The choice of steel is of great importance. The most suitable of the
many kinds tried was one manufactured by the Halcomb Steel Co. in
the form of sheets.

Much experimentation was necessary before the best dimensions and
the best heat treatment of the springs was found. The sheet from
which the springs were cut was 0.105 inches thick. This was cut into
discs 2 1/2 inches in diameter, with a 1/4-inch hole through the cen-
ter. The disc was then turned on one flat face so as to decrease regu-
larly from 0.105 inches at the center to 0.035 inches at the edge. It
was given the saucer shape in a die while hot, the depression at the
center being about 1/4 inch. The greatest care was necessary in hard-
ening to prevent warping. This was conveniently done by heating to a
bright red heat in a bath of molten lead so as to secure a uniform heat,
and then quenching by plunging edgewise into water. The temper
was drawn by heating to 370° C. in oil. The temperature was impor-
tant : 360° C. was too low. Finally, after tempering, the springs were
ground fiat on the edge to provide a bearing surface against each
other. Warping due to hardening was most distinctly shown by varia-

BRIDGMAN. — MEASUREMENT OF HYDROSTATIC PRESSURE^. 329

tions in the width of the ground strip. A pair of springs so made will
support indefinitely at the center a weight of 1350 pounds without
permanent set. The deflection under this load is 2 or 3 mm. The
actual working pressure did not exceed 650 lbs.

The small motion of the springs was magnified by a simple mirror
device, and observed with a telescope and scale rigidly attached to the
frame holding the springs. The scale distance was only 30 cm., but it
was nevertheless possible to obtain a magnification of over 1500 times
with perfect consistency and freedom from back lash or tremor. The
magnification was doubled by reflecting twice from the moving mirror.
The size of the piston, sensitiveness of the springs, and optical mag-
nification were altogether such that 8 kgm./cm.** on the gauge produced
a deflection of 0.1 mm. at the observing telescope. This gives 1/10
per cent as the accuracy of the pressure readings at 8000 kgm./cm.^ ;
proportionally more at the higher pressures.

All of the parts connecting together the springs and the mirrors were
made of steel. This has the advantage of avoiding any motion of the
mirrors which might be produced by changes of temperature of the sur-
rounding atmosphere. The only temperature effect is that due to the
change in the elastic constants of the steel spring with variations of
temperature. This was so small that no appreciable error is introduced
under the ordinary conditions of use.

Any device for measuring the magnitude of a stress by the deflection
of a spring must be subjected to pretty careful scrutiny before the
measurements can be accepted as accurate, because there are disturbing
effects, such as elastic after-working and hysteresis, which complicate
matters. It was hoped to reduce these eff'ects to a negligible value by
using as the working stress less than half the stress at the elastic limit
as mentioned above. But even with this precaution it seemed desira-
ble to calibrate carefully the springs under working conditions.

In order to facilitate the comparison, the springs, multiplying mech-
anism, and telescope and scale were rigidly connected in one piece.
This could be screwed either to the end of the absolute gauge for the
purpose of measuring the thrust on the piston, or to the calibrating de-
vice. The calibration was eff'ected at first by hanging weights on a
stirrup, but this process, always discontinuous and sometimes as compli-
cated as applying two, removing one, applying two, etc., was so unlike
the process of loading during actual use that another method was seen
to be necessary. Two freely moving pistons were used, as when finding
the area of the 1/16-inch piston, both communicating with a Cailletet
pressure pump of the Socit^td Genevoise. One piston, 1/4 inch in di-
ameter, was the same as that used iu the previous work. Weights were

330 PROCEEDINGS OF THE AMERICAN ACADEMY.

suspended directly from the upper end of this piston. This piston was
kept in constant rotation by a small motor so as to avoid friction. The
other freely moving piston, 5/16 inch in diameter, was in direct hy-
drostatic communication with the 1/4-inch piston, and at its upper
end pressed directly against the springs to be calibrated. (This 5/16-
inch piston could be rotated by hand as occasion required to destroy
friction.) From the weight on the 1/4-inch piston, and the areas of
the 1/4 -inch and the 5/16-inch pistons, the thrust on the springs
could be calculated. The area of the 5/16-inch piston was found in
the same way as that of the 1/16-inch piston. The method has all the
advantages of the discarded method of the direct application of weights,
namely, complete freedom from all elastic effects and hysteresis, and in
addition permits very much more convenient and flexible application
of pressure.

The procedure of the calibration was to place a weight on the 1/4-
inch piston, completely depressing it. The piston was then floated
again by raising the pressure to the equilibrium value with the Cail-
letet pump. The 5/16-inch piston was then rotated to destroy fric-
tion, and the deflection of the spring read. Eleven such steps were
made with increasing and decreasing pressure, making twenty-two
steps in all. The same weights were used in all the calibrations, so
that the results were strictly comparable. The pressure exerted by
the fluid, as given by the gauge of the Geneva pump, was also recorded
as a check. The accuracy of the other readings was so great, however,
that these check readings could never be used.

Calibration with this device was first made to find whether the
gauge had any error of position, since it was generally calibrated verti-
cally, but used horizontally. This could evidently be done very simply
by changing the position of the cylinder with the 5/16-inch piston,
a change in the calibrating procedure which could not be made so
simply when weights were directly applied. The result of the calibi-a-
tion in the horizontal position showed no detectable error due to this
change of position. Of course no such error was to be expected, since
all the parts were very stiff in comparison with their weights.

A second result of the calibration was that the springs show no
elastic after-effects. By this is meant the gradual creep after applica-
tion of a load, and gradual recovery after removal. The effect is
generally most pronounced at the two ends of the pressure range.
These springs, however, showed no tendency to yield viscously under
the maximum stress, and never showed any wandering of the zero after
release of pressure.

A third result of the calibration was that the springs do not follow

BRIDGMAN. — MEASUREMENT OF HYDROSTATIC PRESSURES. 331

the linear law, but are increasingly deflected at the higher pressures.
The change was not large, but perfectly distinct, about 6 per cent less
weight being required to produce a given deflection at 650 lbs. than
initially. This is rather surprising in a substance like this spring
steel, which ordinarily follows the linear law to the elastic limit. The

TABLE I.

Relation between Load and Deflection of Springs without Device

FOR Avoiding Hysteresis.

Load
Kgm.

Mirror Deflection.

Load
Kgm.

Mirror Deflection.

Increasing
Load.

Decreasing
Load.

Increasing
Load.

Decreasing
Load.

00.00

0.00

0.00

95.62

8.52

8.64

16.26

1.42

1.49

112.27

10.06

10.18

33.37

2.94

3.02

128.27

11.55

11.66

49.35

4.35

4.45

143.32

12.97

13.07

65.54

5.81

5.91

160.18

14.57

14.64

81.59

7.24

7.36

173.85

15.90

effect is evidently due here to the change of geometrical shape, the
springs becoming so much flatter under the higher stresses that the
geometrical configuration as such has a lower elastic constant, although
the elastic constant of the material itself is unaltered. It is customary
in the mathematical treatment of the bending of thin rods or plates to
assume that the deflection remains proportional to the stress up to the
elastic limit. This experiment shows that this approximation may
become invalid at considerably less than the elastic limit.

A fourth result was that the gauge does show some hysteresis, a
result which was not expected in. view of the second result. For as a
general rule, hysteresis and elastic after-effects, while not directly
related, occur together, both being evidence of some molecular in-
stability. Table I., giving the difference between the reading under
increasing and decreasing pressure, shows the usual magnitude of
the effect. The first column in the table gives the total load at
each step. The effect is much less than that due to departure from
linearity mentioned above, so that here we have a hysteresis loop
of the unusual shape shown in Figure 4. The lag in similar cases is

332

PROCEEDINGS OF THE AMERICAN ACADEMY.

usually so great that the curvature with decreasing stress is the re-
verse of that with increasing stress, so that the loop has the general
shape of a double convex lens. Furthermore the loop is usually very
nearly symmetrical with respect to the line joining the extremities.
This is the only example of a loop of the above shape known to the

writer. This single example is
sufficient to show that there is
no necessary connection between
hysteresis and departure from the
linear relation between stress and
strain, as might be supposed if
all loops were of the ordinary
type.

This h)\steresis, while compara-
tively small, was nevertheless suf-
ficient to reduce the accuracy
of measurements made with the
gauge far below that desired. A
method of avoiding hysteresis
was therefore adopted. It depends
on the fact, well known for mag-
netism, that if the stress is varied
cyclically by small amounts about
any fixed point, a small hysteresis
loop is described about this point.
The result is that if stress is
relieved from the point A (see
Figure 5) after increasing pressure, the path AB will be described.while
if it is increased from the point C after decreasing pressure, the path
CB is described. Suppose that during increasing pressure the point D
has been reached, or that during decreasing pressure the same stress,
shown at E, has been reached. The difference between the points E
and D represents the error due to hysteresis. To make the readings
at these two points the same, we may evidently apply a small extra
load at D, raising the stress to A, and then remove the extra load, or
at E we may remove a slight portion of the load to C and then reapply
it. The same point B is finally reached, and the pressure readings
have become single valued. The extra load necessary to apply or
remove must be determined by experiment, and would be expected to
vary at different parts of the hysteresis loop.

This extra load was applied in practise by a very simple lever ar-
rangement, by which the springs could be deflected one way or the

STRESS

Figure 4. Shows the unusual na-
ture of the hysteresis cycles described
by the springs.

BRIDGMAN. — MEASUREMENT OF HYDROSTATIC PRESSURES, 333

other before making readings. The following set of readings, picked
at random ft-om a great number, shows how nearly it was possible to
avoid hysteresis by the method. The difference of readings is seldom
more than the possible error of reading. The small extra load applied
or removed before making these readings was constant over the entire
range, being sufficient to produce a deflection
of about 2.0 divisions. It is evidently not
quite enough at the higher pressures and a
.little too much at the lower pressures. The
mean of the two readings nowhere differs from
either reading by more than the errors of
observation, however, and this simpler pro-
cedure was therefore adopted.

The most inconvenient fact disclosed by the
calibration was that the constant of the springs
varies slowly from time to time. Over two or
three days no change whatever is to be noticed,
but in a week or a month there are likely to
be changes beyond the limits of error. The
change is irregular and has no apparent con-
nection with temperature changes. No tem-
perature effect within the limits of working
room temperatures was ever found. The
change is doubtless due to some slow process
of molecular accommodation going on within
the metal itself. At one time the springs
were permanently deformed by a violent explo-
sion, so that the deflection under the same
load was increased in the ratio 16:14. After
this deformation for a month or more the
change with time was more rapid than usual
magnitude of the variation with time. The first set of three, Jan-
uary-April, 1910, was made at intervals during constant use of the
gauge. During this time the gauge constant decreased and then in-
creased again. The explosion referred to above took place on De-
cember 24, 1909. The last two readings, September 6 and 24, 1910,
were made after the springs had been resting for about four months.
The constant is in general higher, but the greatest increase has come
at the middle of the range, so that the relation between stress and
strain is more nearly linear than before. After this prolonged period
of rest, the gauge has remained much more nearly constant than
before.

Figure 5. Detail of a
hysteresis loop, showang
the method of avoiding
the effects of hysteresis in
making the readings with
the springs.

The table shows the

334

PROCEEDINGS OF THE AMERICAN ACADEMY.

TABLE II.

Relation betweex Load and Deflection of Springs with Device for

Avoiding Hysteresis.

Load
Kgm.

Mirror Deflection.

Load
Kgm.

Mirror Deflection.

Increasing
Load.

Decreasing
Load.

Increasing
Load.

Decreasing
Load.

00.00

0.00

0.00

95.62

8.50

8.50

16.26

1.43

1.42

112.27

10.02

10.04

33.37

2.94

2.92

128.27

11.51

11.54

49.35

4.35

4.34

143.32

12.98

12.94

65.54

5.S0

5.79

160.18

14.54

14.54

81.59

7.23

7.23

173.85

15.85

TABLE III.
Shot\t:ng Variation of Springs with Time.

Load
Kgm.

Mirror Deflection.

Jan. 1.

March 30.

April 27.

Sept. 6.

Sept. 21.

16.26

1.65

1.63

1.65

1.66

1.66

33.37

3.37

3.32

3.36

3.38

3.38

49.35

5.00

4.95

4.98

5.02

5.03

65.54

6.68

6.58

6.65

6.70

6.70

81.59

8.37

8.25

8.35

8.39

8.40

95.62

9.86

9.74

9.83

9.88

9.89

112.27

11.66

11.63

11.64

11.69

11.70

128.27

13.42

13.28

13.40

13.44

13.47

143.32

15.09

14.96

15.09

15.14

15.15

160.18

17.00

16.88

17.02

17.05

17.08

173.8.1

18.60

18.52

18.63

18.63

18.65

BRIDGMAN. — MEASUREMENT OF HYDROSTATIC PRESSURES. 335

This change of gauge constant with time demands that frequent
calibration be made. In all the work of the following papers in which
considerable accuracy was desired, such calibrations were made every
few days. It is not much trouble to make this calibration. The
twenty-two readings with increasing and decreasing pressures can be
made in the course of half an hour. When the gauge is so calibrated,
and the procedure for avoiding hysteresis is adopted, the readings are
consistent to the limit of sensitiveness. This has already been stated
to be about 8 kgm./cm.l

The gauge in actual use has shown itself very convenient. The
readings may be made rapidly and immediately after the application
of pressure, since there are no thermal effects such as dissipation of
heat of compression. The temperature effect is so small that it may
be used directly in the room without a thermostat, and the leak is so
slight that it "may be used in entire comfort in measuring many high-
pressure effects. Where applicable, the gauge is more convenient than
the electrical resistance gauge and it has been used whenever possible.

The Manganin Resistance Gauge.

In the earlier paper a method was described for measuring high
pressures by measuring the electrical resistance of pure mercury under
pressure. The method had the advantage of being perfectly repro-
ducible, so that any one could at any time measure pressure without
recourse to the then inconvenient fundamental standard of pressure.
The advantage has been in large part offset by the devising of the
convenient form of absolute gauge described in the first part of this
paper. Moreover, the method becomes inapplicable at somewhat
higher pressures than those reached formerly because of the freez-
ing of the mercury. Thus at 0°, the freezing pressure is about 7500
kgm./cm.^. Aside from this difficulty, which might be avoided by
placing the mercury in a separate vessel, maintained at higher tem-
perature, there are numerous inconveniences of manipulation, as, for
instance, that the mercury must always be kept in an upright position.
But the greatest inconvenience of all is that the glass capillary con-
taining the mercury is always shattered by an explosion, and explosions
become more and more frequent at high pressures.

There are frequently situations, however, where the absolute gauge
becomes unavailable, and where a gauge with some of the properties
of the mercury gauge becomes desirable. For instance, it is often
necessary to secure absolute freedom from leak, and this is obviously
impossible with a freely moving piston as in the absolute gauge.

336 PROCEEDINGS OF THE AMERICAN ACADEMY.

Measurements of compressibility or of change of volume during freez-
ing, as in two following papers, demand this property of freedom from
leak.

The method of pressure measurement adopted here, and which secures
freedom from leak, has already been described by Lisell.* He meas-
ured the effect of pressure on the resistance of manganin wire, and
proposed that the change of resistance be used as a measure of pressure.
Lisell found the effect of pressure between 0 and 4200 atmos to be
linear, and showed that there was no appreciable temperature effect
between 0° and room temperature. But Lisell also showed that diff"er-
ent specimens of manganin show slightly different pressure coefficients,
so that the advantage of reproducibility must be given up. Lately,
Lafay ^ has also measured the pressure effect on manganin up to 3500
kgm. and has found nearly the same pressure coefficient as did Lisell.

The data of this paper show by direct comparison with the absolute
gauge that the manganin is suitable as a pressure gauge over much
wider ranges of pressure. Up to 13,000 kgm. the relation is linear
within the errors of the absolute gauge. It would not have been sur-
prising if this had not been true, in view of the fact that manganin has
a pressure coefficient which is positive instead of negative like that of
all the pure metals. Furthermore, over this pressure range the read-
ings are entirely free from hysteresis or creep. This is opposed to the
work of Lussana,* who found various temporary effects after the appli-
cation of pressure. His results have not been verified by subsequent
observers, however, and the entire absence of the effect here under a
very much wider pressure range would seem to make pretty certain
that there was some obscure source of error in Lussana's work.

The manganin used in this work was of German manufacture. No. 38,
double silk covered, of about 30 ohms to the meter. With change of
temperature it shows a maximum resistance at about 27°. The coils
were of about 100 ohms resistance, the wire being wound non-induc-
tively on itself in the form of a toroid, about 1 cm. in diameter and
5 mm. thick. To protect the wire, the toroid was covered with a wind-
ing of fine silk ribbon, only the ends of the wire being exposed in order
to make connections with the insulating plug. This plug was of the
same design as that shown in the previous paper, except that it was
made of hardened nickel steel instead of tool steel.

' Lisell, Om Tryckets Inflytande pS. det Elektriska Ledningsmotstandet
hos Metaller samt en ny Metod att Mata Hoga Tryck (Diss. Upsala, 1903)
3 Lafay, C. R., 149, 566-569 (1909).
* Lussana, Nuov. Cim., 10, 73-84 (1899); 5, 305-314 (1903).

BRIDGMAX. MEASUREMENT OF HYDROSTATIC PRESSURES. 337

The apparatus for producing and measuring pressure consisted of
two cylinders connected by a tube of nickel steel. In the lower cylin-
der the pressure was produced and measured. The absolute gauge of
the first part of this paper was screwed directly into the side of this
C34inder. The cylinder itself was of Krupp chrome nickel steel, 8 inches
outside diameter, 1 1/8 inches inside diameter. It was placed in a
hydraulic press of 200 tons capacity, and the pressure produced by a
1 1/8-inch piston forced into the cylinder by the ram of the press.
The upper cylinder, also of Krupp chrome nickel steel, 4 1/2 inches
outside and 9/16 inch inside diameter, contained the manganin wire to
be tested. The connecting tube to the lower cylinder passed through
the bottom of the tank of a thermostat, which surrounded the upper
cylinder, and with which the temperature could be kept constant to
0.01°. No such temperature precaution was necessary for the absolute
gauge. The lower cylinder was filled with the mixture of glucose and
glycerine needed to secure tightness of the piston of the absolute gauge,
and the upper cylinder was filled initially with either kerosene or gaso-
lene, in which the manganin coil was directly immersed. The action
of pressure was to compress the kerosene, glucose passing fi-om the
lower cylinder to the lower jmrt of the upper cylinder. The compres-
sion was never sufiicient, however, to bring the glucose into contact
with the manganin. Although kerosene or gasolene are somewhat incon-
venient because of their high compressibility, still their use was made
necessary by the fact that a heavier oil freezes under pressure, so that
it does not transmit pressure hydrostatically to all parts of the wire.
The kerosene is also known to become stiff like vaseline at say 10'^
and 8000 kgm., but the viscosity is not so great as to introduce irregu-
larities. When either kerosene or gasolene is used, the insulating
qualities of the plug are practically perfect without requiring any spe-
cial precautions. The insulation resistance was always over 10 megohms,
which was the limit of the measuring device conveniently at hand.
Formerly, in working with mercury, pressure was transmitted by a
mixture of water and glycerine. It was necessary to specially protect
the separate parts, and even then the insulation resistance was never
greater than several hundred thousand ohms.

The electrical measurements were made by the same null method
and on the same Carey Foster bridge as those described in the former
paper.

In making the calibration and in using the gauge, there is one fact
to be borne in mind which has its analogy in the mercury resistance.
This is the seasoning effect of pressure ; the gauge does not respond
to the first application of pressure in the same way that it does to the

VOL. XLVII. — 22

338

PROCEEDINGS OF THE AMERICAN ACADEMY.

second or subsequent applications ; there is a gradual settling down
to a steady state. In the case of mercury, this was due to the equal-
ization of strains in the containing capillary of glass. In the case of
the manganin, some such process of accommodation must be going on
within the mass of the metal. This is shown principally by drift of the

TABLE IV.
Pressure Coefficient op Resistance of Manganin.

Pressure
Kgm./cm.2.

pRo

Pressure
Kgm. /cm.2.

pRo

1260

2272

9290

2302

2610

2282

8000

2304

3810

2299

&450

2302

5000

2301

4790

2304

6180

2299

3250

2291

7210

2300

1740

2308

8230

2302

1000

2272

zero, but the pressure coefficient may change slightly. The seasoning
process occupies more time for the manganin than for the glass; it
may extend over as much as a month after the first application. It
is hastened by frequent applications of pressure, but may apparently
run to completion in sufficient time after only one application. To
effect the seasoning, it does not seem to be necessary to subject the
coil to the maximum pressure under which it is contemplated using it.
The coil used to the highest pressure reached in this work, 20,500 kgm.,
had been seasoned by the application of not more than 12,000 kgm., yet
it showed no farther change after the application of a pressure 8500
kgm. in excess of the seasoning pressure.

The results obtained with one such well-seasoned coil at 0°
are shown in the table. In making the comparison with the
absolute gauge all the precautions described in the first part of ths
paper were observed. It is seen that within the limits of error of
the pressure readings, the change of resistance is proportional to
pressure.

BRIDGMAN. — MEASUREMENT OF HYDROSTATIC PRESSURES. 339

To show within what limits different pieces from the same spool
of wire give the same results, three coils were made from the ends
and the middle of a length of wire of 70 m. The constants for
the separate coils at 0 were .O523OI, .052307, and .052325, in the
order of the coils, a variation of one per cent. The temperature
effect was found by measuring these same coils again at 50°. These
same three coils gave 2295, 2319, and 2320 respectively. One of
the coils measured at —12° showed no measurable difference between
-12° and 0°.

The maximum pressure to which these calibrations were made varied
somewhat with the temperature, because at the lower temperatures the
mixture of glucose and glycerine used with the absolute gauge became
viscous so rapidly with increasing pressure as to transmit pressure very
slowly. At the low temperatures the pressure was increased until this
limit was reached. The slow flow of glucose from the lower to the
upper cylinder might occupy an hour or more before the equilibrium
was complete. The fact that there was such a process of flow was
definitely shown by the slow fall of pressure in the lower cylinder as
indicated by the absolute gauge, with a simultaneous slow rise of
pressure in the upper cylinder, as indicated by the manganin resistance.
At 0° the maximum reached was in one case 11,000 kgm. This was
probably too high for complete equalization of pressure, for the change
of resistance was 1/2 per cent too low at this maximum. The measure-
ments at 0° were not usually carried as far as this, 9500 being the
more usual limit. Slight differences in the composition of the glucose
mixture made very pronounced differences in the viscosity at high
pressure. At 50° the highest reached was 12,000. Even here the
viscosity was very considerable. On one occasion pressure was pushed
to 13,000 at 50°. There was the same slow equalization of pressure,
extending over about half an hour, as was found at 0°. At the end of
this time the resistance had nearly acquired the value given by a
linear relation, when the experiment was terminated by an explosion.
The final reading below this at 11,500, at which there was also some
viscous yield, completely satisfied the linear relation.

We may conclude, therefore, that over the temperature range 0°-5o°
the pressure resistance relation is linear within 1/10 per cent of the
change of resistance, up to 13,000 kgm. This was proved by actual
experiment at 50° to 12,000, and to 9500 at 0°. The extrapolation to
13,000 at 0° is comparatively slight, and is made all the more probable
by the fact that our usual experience would lead us to expect greater
departure from linearity at higher temperatures, and no such depar-
ture was found.

340 PROCEEDINGS OF THE AMERICAN ACADEMY.

Although different specimens of manganin do not have the same
constant, still it may be worth while comparing the results found here
with those of other observers so as to give an idea of the magnitude
of the variation of the effect. Lafay ^ found 2.16 X 10"' per kgm./cm.^
as the effect on one specimen. Lisell® found for two specimens of an-
nealed wire 2.13 X 10~' and 2.08 X 10~* ; for three specimens of hard
drawn wire results from 2.279 X lO"' to 2.338 X lO"'. The data of
this paper, which are for hard drawn wire, vary from 2.295 X 10~' to
2.325 X 10"^

Four of these manganin resistance gauges have been in almost con-
stant use for over a year. As compared with the mercury gauge they
have had the advantage of greater convenience and ease of manipula-
tion, even over the pressure range within which the mercury remains
fluid. During the work explosions have been of frequent occurrence,
the shock of any one of which would have broken the glass capillary
containing the mercury. It is not necessary to apply elaborate tem-
perature precautions as for the mercury. The only temperature cor-
rection necessary to apply is a small one for the shift of the zero. This
may be determined accurately enough by hanging a thermometer in
the air of the room near the cylinder containing the manganin. At
room temperatures of 20° a change of temperature of 1° demands a
pressure correction of only 5 kgm.

As compared with the absolute gauge of the first part of the paper,
each form has distinct advantages. Where available, the absolute
gauge is more convenient, because it is direct reading and immediate.
But the absolute gauge has the disadvantage of leak, so that often the
manganin gauge becomes absolutely necessary. Futhermore, it has
the disadvantage of being more cumbersome. This means that all
parts of the apparatus in connection with the gauge must be corre-
spondingly enlarged. This is often a fatal disadvantage, entirely apart
from any considerations of expense or convenience, because in order to
reach the highest pressures, the steel parts must be hardened, and it
is not possible to harden large steel cylinders. The upper limit of
pressure attainable will have to be reached with comparatively small
apparatus. The reason for not pushing the absolute gauge to its
limit was not so much fear of destroying the gauge as the fact that
the large 8-inch steel cyHnder containing the gauge was of soft nickel
steel, and that the yield point would have been reached at 15,000 kgm.
This cylinder had been previously seasoned by applying pressures up
to 28,000 kgm., which had the effect of increasing the internal diameter

"* Lafay, loc. cit. • Lisell, loc. cit.

BRIDGMAJ^. — MEASUREMENT OF HYDROSTATIC PRESSURES. 341

from 5/8 inch to 1 1/8 inches, but even this was not sufficient to raise
the limit permanently to over 15,000 kgm.

The compactness of the manganin gauge makes it particularly
adapted for working with the highest pressures where everything
must be in one piece because of the impossibility of making con-
necting tubes. The gauge has been so used in a number of experi-
ments on the freezing of water under pressure. The gauge was
screwed into one end of a large steel cylinder, the plunger was
pushed in from the other end, and the water was in the space be-
tween. The dimensions were kept down so that the entire block,
together with a part of the hydraulic press, could be placed in a
thermostat.

The manganin gauge may be used by extrapolation to measure pres-
sures beyond the reach of the absolute gauge. It has been so used in
investigating the freezing of water up to an indicated pressure of
20,500 kgm., and this limit could without doubt be exceeded. The
limit is not in the manganin itself, but in the hardened steel parts,
which have a tendency to stretch too much at pressures as high or
higher than 20,000 kgm. Of course the use of any standard by extra-
polation is undesirable, but at present any means of measuring these
very high pressures with probable accuracy is welcome. In any event,
the extrapolation from 12,000 to 20,000 is very much less than the
extrapolation from the previous maximum of 4000 to 12,000, which is
here shown by actual experiment to be justified. What is more, it
will be an easy matter to translate high-pressure readings in terms of a
manganin gauge into absolute pressures, if at any time the direct cali-
bration is extended from 13,000 to 20,000, and proves that a linear ex-
trapolation is not sufficiently accurate.

The only serious disadvantage in the manganin gauge as thus far
described, when compared with either the mercury gauge or the abso-
lute gauge, is the fact that it is not readily reproducible, so that each
new coil of wire must be calibrated against an absolute gauge. This
disadvantage may be obviated by the use of fixed pressures of refer-
ence analogous to the melting points of the metals used as points of
reference in thermometry. The linearity of the relation between resist-
ance and pressure having been established by the work of this paper,
it is necessary to know for each coil only the change of resistance cor-
responding to a single known pressure in order to fix completely the
behaviour of the coil.

Such pressures of reference are given very conveniently by the points
of transition between the various kinds of ice and water. For low
pressures such a pressure of reference is given by the pressure of transi-

342 PROCEEDINGS OF THE AMERICAN ACADEMY.

tion from ice I to ice III, using Tammann's "^ notation. This pres-
sure is very nearly independent of temperature between —22° and— 30'^.
This particular transformation has the advantage that the reaction
runs with very great velocity and is accompanied by a comparatively
enormous change of volume, 20 per cent, so that in any piece of appa-
ratus, once given the two phases, the equilibrium pressure is automati-
cally set up almost immediately. This pressure has been found to be
2120 kgm. at —23°. For higher pressures, the transition point at 0°
from water to a liitherto unknown variety of ice, ice VI may be used.
This point has been found by experiment to be 6370 kgm. Equilib-
rium is reached more slowly than for the transition I-III, but for
work at higher pressures the use of this transition point will give a
more accurate calibration. This method of calibration has actually
been used, with satisfactory results, for two other coils than the four
mentioned above.

The calibration of the manganin resistance without the use of an
absolute gauge may of course be effected by comparison with any
other accurately measured pressure phenomenon. For instance, the
calibration may be made by comparing the manganin resistance with the
mercury resistance, the data for which have been already published.

Summary of Results.

Two gauges for high pressures are described in this paper. The
first is an absolute gauge which has been used up to 13,000 kgm.
The construction of the gauge is described, the correction for dis-
tortion is determined, and the reading mechanism is discussed. A
procedure is given for freeing the deflections of the springs with which
the thrust is measured from hysteresis. All of the factors may be de-
termined with sufficient accuracy so that the gauge is accurate to the
limit of accuracy of reading, 1/10 per cent at 8000 kgm./cm.^. The
second gauge is a manganin resistance. This is shown to be suitable
for the purpose, since there is complete freedom from hysteresis and
elastic after-effects. The relation between pressure and resistance is
shown to be linear up to 12,000 kgm., but the gauge has been used by
extrapolation up to 20,500. The accuracy of the readings with this is
at least as great as with the absolute gauge. The relative advantages
for various kinds of experiment of these two forms of gauge are dis-
cussed. Finally, by the use of standard pressures of reference it is

' Tammann, Kristallisieren und Schmelzen, pp. 315-344 (Barth, Leipzig,
1903).

BREDGMAN. — MEASUREMENT OF HYDROSTATIC PRESSURES. 343

shown that a manganin resistance gauge may be calibrated without
direct reference to an absolute gauge.

This investigation was a necessary preliminary to the measurement
of various thermal properties of mercury and water under pressure, the
expenses of which have been partially defrayed by several liberal ap-
propriations from the Rumford Fund of the American Academy of
Arts and Sciences.

Jefferson Physical Laboratory,

Harvard University, Cambridge, Mass.,

October, 1911.

Proceedings of the American Academy of Arts and Sciences.
Vol. XLVII. No. 12. — December, 1911.

CONTRIBUTIONS FROM THE JEFFERSON PHYSICAL
LABORATORY, HARVARD UNIVERSITY.

MERCURY, LIQUID AND SOLID, UNDER PRESSURE.

Bt p. W. Bridgman.

With a Plate.

Investigations on Light and Heat made and pubusheo with Aid fbom the

RuMFORD Fund.

CONTRIBUTIONS FROM THE JEFFERSON PHYSICAL
LABORATORY, HARVARD UNIVERSITY.

MERCURY, LIQUID AND SOLID, UNDER PRESSURE.

By p. W. Bridgman.

Presented by G. W. Pierce, Oct. 11, 1911. Received Oct. 6, 1911.

Introduction.

This paper is an attempt to present for the liquid and solid phases
of a single simple substance, mercury, data corresponding to the data
which have been collected for the gaseous and liquid phases of many-
substances. These latter data are the relations connecting temperature,
pressure, and volume of the gas together with the changes involved
when the gas passes to the liquid state. Out of these data have come
the theories of the molecular structure of gases and vapors, and the
various relations connecting the gaseous with the liquid phase, of
which the theory expressed by the equation of van der Waals is the
best known. The corresponding work for the liquid and solid phases,
that is, the mapping out of the pressure- volume-temperature surface of
the liquid and the determination of the quantities involved in the
change from the liquid to the solid state, has never been done. As a
result, the theory of liquids is entirely undeveloped, and the theory of
the relation between liquid and solid hardly begun. For instance, the
fundamental question as to the existence of a critical point for the
liquid-solid states analogous to that for the vapor-liquid is as yet
unsettled.

The apparent reason for this neglect of the thermodynamic data for
the liquid and solid is merely experimental difficulty. Whereas for a
vapor the critical pressure never exceeds a few hundred atmospheres,
the pressures involved in a corresponding study of the liquid-solid
phases are of the order of tens of thousands of atmospheres. These
pressures are so high as to tax to the utmost the tightness of every
joint and the strength of the steel vessels. In this present work it
has been found possible by a special packing device, which secures ab-
solute freedom from leak, and by the use of the highest grades of steel

348 PROCEEDINGS OF THE AMERICAN ACADEMY.

manufactured, to reach 30,000 and even 40,000 atmos on the first ap-
pHcation of pressure. On subsequent applications rupture may come
at half the first maximum. This subsequent early rupture is due to the
fact that these pressures are greatly in excess of the theoretical limit
of the steel, so that there is a distortion of thennner parts far beyond
the elastic limit and consequent rapid fatigjie. The pressures reached
in this paper are not the greatest attainable because of the questionable
scientific economy of pushing pressures to a value where rupture may
occur at any moment and destroy valuable apparatus and time.

The previous work in this field is wholly below 5000 kgm. The two
principal investigators are Amagat,i who studied the compressibility
and the thermal dilatation of a number of liquids up to 3000 atmos,
without, however, touching on the change of state liquid-solid; and
Tammann,2 who studied the change of state liquid-solid, without
determining the behavior of the liquid, over a range of pressure of usu-
ally about 3000 kgm., but reaching a few times to 4000 and once to
4800. There are no liquids common to the work of both Amagat and
Tammann, so that the complete data are not known for even a single
liquid.

The previous work done on mercury is almost negligible for the
present purpose. Accurate compressibility determinations run only to
500 kgm. (the highest are by Kichards ^), and the effect of pressure
on freezing point has been observed only by Tammann, * who found
results up to 2000 kgm. that are inconsistent among themselves by
30 per cent.

The data of this paper cover a range of 12,000 kgm., and give both
the changes of volume of the liquid with temperature and pressure, and
the thermodynamic data required on the freezing curve. The temper-
ature range corresponding to this wide pressure range is comparatively
small, since at 12,000 kgm. the freezing temperature has been raised to
only 20°, that is, through a range of 60°.

In addition to the data connected more intimately with pressure,
several quantities relating to solid mercury at atmospheric pressure
have incidentally been determined. It has been a surprise to find how
untrustworthy the commonly accepted data for solid mercury are.
Thus the only determination of the latent heat of melting dates back
to 1838, before the value of the melting temperature itself was known
more accurately than within 3°.

1 Amagat, Ann. de Chim. et Phys. (6), 29, 6S-136, 505-574 (1893).
' Tammann, Kristallisieren and Sohmelzen (Barth, Leipzig, 1903).
3 Richards, Pub. Carnegie Inst. Wash., No. 7 (1903), and No. 76 (1907).
* Tammann, loc. cit., p. 248.

BRIDGMAN. — MERCURY UNDER PRESSURE. 349

The experimental material of the paper, with respect to both subject
matter and experimental method, falls naturally into two parts. The
first is concerned with the p-v-t surface of the liquid. To map this the
isothermal compressibility of the liquid was found at two temperatures,
0° and 22°, and combined with the known dilatation at atmospheric
pressure. This is sufficient to cover the region in question, because
the change of dilatation with temperature is slight. The second part is
concerned with the changes taking place on the freezing curve. Ther-
modynamically, the data required are the change of volume on passing
from liquid to solid and the variation of freezing temperature with
pressure. From these the latent heat may be calculated by Clapey-
ron's equation. Two independent methods were used ; one which gave
both the change of volume and the relation between temperature and
pressure on the freezing curve, and another which gave only the freez-
ing curve. In addition still another method was used in determining
the change of volume on freezing at atmospheric pressure.

In the conclusion, the data collected are discussed from the point of
view of their bearing on present theories of the liquid state, and the
change solid-liquid. These data for a single substance cannot j ustify
by any means an attempt at a new theory. This is simply a first step,
indicating in a general way the nature of the effects to be expected
at high pressures. From this point of view there are considerations
both for and against the use of mercury. On the one hand, the com-
pressibility and thermal dilatation of mercury are comparatively small,
so that the change in these quantities under the pressure range em-
ployed is not nearly as great as it would be for many organic liquids ;
but on the other hand, the internal structure of mercury is probably
at least as simple as that of any other known substance, so that in the
liquid state the results are not complicated by entrance of polymeriza-
tion, and on the freezing curve the results are not complicated by the
entrance of allotropic forms, as they are in the case of water, for example.

The discussion of the methods and the possibilities of error has nec-
essarily been somewhat minute and painstaking. It is hoped that this
will be pardoned when it is realized that the field in which these meas-
urements are made has been hitherto practically unworked, and is one
where there are several unusual sources of error to be guarded against.
At the same time it is a field in which, by the exercise of proper pre-
cautions, an accuracy equal to that of the greater number of physi-
cal measurements can be reached. The accuracy of nearly all of the
following measurements is of the order of 1/10 per cent.

350 PROCEEDINGS OF THE AMERICAN ACADEMY.

Contents.

I. Introduction 347

II. The P-V-T Surface of Liquid Mercury 351

a. Nature of the Experimental Problem — Difficulties in Measuring

Comjiressibility at High Pressures 351

h. Description of the New Method 354

Formulae 357

Details of Manipulation 358

Compressibility of the Steel Piezometers 362

Discussion of the Method 362

Hysteresis in the Containing C3'linder 364

The New Values iij) to 10,000 kgm. — Temperature Coefficient 366

Comparison with Other Results 367

c. Data on the Comi)ressibility of Mercury 368

The Method of adjusting the Data 369

Comparison with Other Results 376

d. Discussion of the Results 380

Compressibility as a Function of Pressure and Tempera-
ture 381

Dilatation as a Function of the Pressure 382

Variation with Temperature Imperceptible 380

The Specific Heats • 383

The Adiabatic Compressibility 384

The Heat of Compression 384

Changes of Internal Energy 386

III. The Change of State, Liquid-Solid 387

a. The Thermodynamic Data needed — Methods 387

b. Co-ordinates of the Freezing Curve by Change of Resistance 388

Method and Details of Manipulation 388

Data — Method of Adjusting the Values 393

Incidental Data during Resistance Measurements .... 394

Electrical Resistance of Liquid Mercury imder Pressure 395
Electrical Resistance of Solid Mercury — Change Solid to

Liquid 395

Rough Value for Pressure Coefficient of Resistance of Solid 396
Comparison with Pre\aous Values for the Resistance of

the Solid 397

Resistance of an Amalgam under Pressure 398

c. The Melting Curve by the Change of Volume Method . . . 399

The Method 399

The Apparatus 400

Order of Procedure ^ 401

Detailed Discussion of Possible Errors 402

Leak 402

Elastic After-Effects 402

Elastic Deformation — Calculation of Correction . . . 406

Temperature Corrections 408

Thermal Dilatation of the Transmitting Liquid .... 410

BRIDGIVIAN. — MERCURY UNDER PRESSURE. 351

Change of State of the Transmitting Liquid 413

Measurements of Piston Displacement 413

Pressure Measurements 414

The Data 414

Methods of Computation 416

The Latent Heat — New Value at Atmospheric Pressure . 420

Recomputed Value for the Specific Heat of the SoUd . 422

Rough Value for the Compressibility of the Solid .... 423

d. Change of Volume at Atmospheric Pressure 423

Probable Error in the Previous Results 424

The New Method 424

The New Value 428

Recomputation of Quantities depending on the Value for

the Change of Volume 428

Density of the Sohd 428

Dilatation of the Solid 428

Direct Experimental Evidence on this Point .... 429

e. Subcooling and Superheating 429

IV. Conclusion 431

Bearing on the Theory of Liquids 432

Bearing on the Theory of the Change of State, Liquid-Solid . . 433

Significant Behavior of Latent Heat and Internal Energy . . . 435

V. Summary 437

The P-V-T Surface of Mercury.
The Coynpressibility of Liquid Mercury.

This first section of the paper is devoted to a determination of the
compressibility of mercury at 0° and at 22°. The question of exper-
imental method is important, since the compressibility of mercury is
small, and there are various effects which make determinations at high
pressures much more difficult than over a smaller pressure range. The
section comprises a discussion of the method and the various errors to
be avoided, an experimental determination of the compressibility of
the steel, which was needed in the computations, the actual data for
the compressibility of mercury, with a somewhat detailed discussion of
the way of adjusting them so as to give the best results, and finally, a
calculation from the data of the change of the various physical proper-
ties of mercury under pressure.

One of the chief difficulties in the experimental investigation of the
properties of bodies under pressure is the determination of the correc-
tion for the distortion of the containing vessel. This is particularly
true in the case of compressibility, where the change of shape and vol-
ume of the containing vessel is an effect of the same kind as that being
measured, and may often constitute a large part of the total change.

352 PROCEEDINGS OF THE AMERICAN ACADEMY.

To correct for the distortion of the containing vessel only indirect
methods are open, as direct observation of the vessel under high pressure
is out of the question. All of those indirect methods which are primary,
that is, which do not assume the correctness of the work of some other
observer, endeavor to determine in one way or another the compressi-
bility of the material of the containing vessel. This may be done by
measuring Young's modulus and the bending or the torsion coefficient,
and from these calculating the cubic compressibility by the identical
relations of the theory of elasticity ; or it may be done with the introduc-
tion of less questionable assumptions by measuring the linear compres-
sibility and then multiplying by three for the cubic compressibility.
This latter method in somewhat different forms has been adopted by
Richards ^ and the author. ^ Once the compressibility is known, the
change of volume of the vessel is found immediately by multiplying
the compressibility by the pressure. This assumes that the contain-
ing vessel changes volume without changing shape. This assumption,
which is made universally, seems necessary and unavoidable. There can
be little question, however, that the assumption is not entirely j ustified.
There are outstanding discrepancies between the determination of the
same compressibility by different observers, or by the same observer
with different apparatus, or indeed by the same observer with the same
apparatus on different occasions, that are beyond the limits of error of
the measurements. For instance, four very careful determinations of
the compressibility of mercury by de Metz "^ differed among themselves
by 5 per cent. The containing vessels were all of the same kind of
glass, and the elastic constants had been determined by direct exper-
iment. The only explanation of these discrepancies seems to be that
the distortion of the containing vessel is irregular, so that there is
change of shape as well as change of volume. The irregularities in
the results introduced by irregularities in the piezometer will, of course,
be proportional to the total correction introduced by the envelope, and
will be greatest in the case of the most incompressible liquids. Thus
for mercury in a glass envelope, the correction for the envelope is 60
per cent of the whole effect, while for water it is only o per cent.

There can be no doubt that these irregularities are due to lack of
homogeneity in the containing vessel, either imperfect annealing or
actual variation in the constitution of the material from point to point.
It is inconceivable that a perfectly homogeneous body of any shape,

^ Richards, loo. cit., 1907.

* Bridgman, These Proceedings, 44, 255-270 (1909).

' De Metz, Wied. Ann., 47, 706-742 (1892).

BRIDGMAN. — MERCURY UNDER PRESSURE. 353

when exposed to purely hydrostatic pressure, should suffer anything
except mere change of volume without change of shape. If, however,
the substance be heterogeneous, so that the elastic constants vary from
point to point, then the application of hydrostatic pressure will be fol-
lowed by change of shape, yielding of one part at the expense of an-
other. If the pressure is high enough, it is conceivable that the elastic
limit may be exceeded in some places and not in others, resultingin
greatly exaggerated change of shape. Even if the elastic limit is not
exceeded, there are other effects which will produce irregular action,
such as elastic after-effects and hysteresis, and these effects become
rapidly more prominent at high pressures. It follows, therefore, that
the irregularities of compressibility determinations over a wide pres-
sure range are going to be more than proportionally greater than the
irregularities over a narrow range.

All previous determinations of compressibility have been made under
fairly favorable conditions. The work to the highest pressures has
been done by Amagat, to 3000 atmos, in which he determined the
compressibility of the compressible liquids in a glass envelope. His
determinations of the compressibility of the most incompressible liquid,
mercury, were only to 50 atmos. The highest accurate work on mer-
cury seems to have been done by Richards to 500 atmos, a compar-
atively low pressure. Richards also used glass piezometers. The
highest previous work of any sort on mercury seems to have been done
by Carnazzi,^ to 3000 atmos, also with a glass piezometer. His accu-
racy was not such as to justify more than two figures in the final
result.

In determining the compressibility of mercury to pressures as high
as 12,000 kgm., as it was desired to do in this paper, we have conjunc-
tion of the causes most unfavorable to accuracy ; low compressibility
of the liquid, and greatly exaggerated irregularity in the distortion of
the containing vessel. The employment of a glass containing vessel
would seem to be out of the question. In a previous paper,' the lin-
ear compressibility of glass has been determined directly to 6800 kgm.
Over this lower range, irregularities were found amounting to 4 per
cent. In using a glass piezometer, this irregularity would be magni-
fied by the fact that the compressibility of glass is high compared with
that of the mercury. The ideal substance is one which can be ob-
tained in a state of great homogeneity, and which at the same time has
as low a compressibility as possible. Steel has these properties in a

" Camazzi, Nuov. Cim. (5), 5, 180-189 (1903).
^ Bridgman, loc. cit.

VOL. XLVII. — 23

354 PROCEEDINGS OF THE AMERICAN ACADEMY.

higher degree than any other substance, the compressibility being as
low as any except the platinum metals, and the homogeneity in an-
nealed pieces of soft steel being nearly perfect. The use of a piezom-
eter of steel in determining the compressibility of mercury up to 6800
kgm. has been described in the paper cited above. The advantages of
the steel piezometer have been discussed there, and independent ex-
perimental evidence has been presented showing that the compressi-
bility of a piece of mild steel is the same in every direction, and that
therefore the piezometer does not change its shape. The results ob-
tained with this method were regular, and in so far justify the use of
this material ; but further work has led to the conviction that there
was present in the method a source of error for which it is hopeless to
attempt to calculate the correction. This error is concerned with the
leak past the freely moving piston ; this leak is less on increasing than
on decreasing pressure, so that the previous results are all too small.
It seems impossible to determine in what way the error so introduced
will vary with the pressure. The total magnitude of the error is prob-
ably between 2 and 3 per cent.

The method adopted here attempts to keep the advantage of the
steel piezometer, while doing away with the uncertainty of the freely
moving piston. It was not possible to secure so regular results with
the new method as with the old, but on the other hand, any constant
source of error seems to be excluded. The method is a modification
of one used by Aimd ^^ in 1842, and since used in many modified forms
by other experimenters. In the original form, the liquid to be investi-
gated was placed in a glass bulb provided with a fine capillary com-
municating with a vessel containing mercury. The whole affair was
then lowered into the sea. Here the increase of pressure forced mer-
cury into the bulb, where it fell to the bottom and remained. On
withdrawing from the sea, the maximum volume compression was
measured simply by weighing the mercury forced in. Aimd's results
were very irregular and incorrect. The most obvious trouble with this
method is the tendency of the mercury to collect in drops at the mouth
of the capillary. On release of pressure, this drop flows back through
the capillary, and the resultant compressibility appears too low. The
difficulty may be minimized by making the capillary very small. This
is an easy matter when the capillary is made of glass, but when steel
is used as here, some special construction must be devised. The form
of piezometer adopted is shown in Figure 1. The upper piece B,
screws into the shell A. A tight joint between the two is made simply

10

Aira6, Ann. de Chim. et Phys., 8, 257-280 (1843),

BRIDGMAN. — MERCURY UNDER PRESSURE.

355

by tightly forcing the narrow edge C on the upper part B into the flat
seat at D. It is not desirable to attempt to use any packing material.
At the lower part of B there is a very fine channel, E, opening into A.
This channel is made by carefully drilling in B a 1/16 inch hole and
then plugging the hole with a pin along which a fine scratch has been
made. This fine scratch takes the
place of the glass capillary when the
piezometer is made of glass. It is
thus possible to regulate the size of the
channel at pleasure. It is a matter
of the greatest ease to make such a
channel that a pressure of only a few
pounds to the square inch will force
mercury through it in drops just
barely perceptible to the eye, and
much too small to be measured by
any ordinary balance. In all the work
with these piezometers no effect was
ever found suggesting in any way the
possibility of error introduced by cling-
ing of mercury to the mouth of the
channel.

The piezometer may be used in either
of two positions, upright or inverted.
When used upright, the body A is
filled with the liquid to be investigated,
water for example, and the cup at B
with mercury. The entire piezometer
is then placed in a pressure chamber
surrounded on all sides by a liquid, to
which pressure is applied. This takes
the place of lowering into the sea in

Aim^'s experiment. Mercury flows in through the narrow channel to
equalize the pressure within and without, and drops to the bottom.
On release of pressure, the water bubbles out through the mercury in B.
The piezometer is then unscrewed, the mercury in A weighed, and the
total change of volume at the maximum pressure calculated. Into this
calculation enter the compressibility of the steel of the piezometer and
the compressibility of the mercury. The latter can then be found in
terms of the compressibility of water by nearly filling the piezometer
with mercury on which floats a little water to fill the piezometer
completely. On application of pressure mercury drops through the
layer of water, and on release water comes out.

Figure 1. The steel piezom-
eter. This is filled with the Hquid
under investigation and exposed
to hydrostatic pressure all over.
The pressure forces a measurable
quantity of mercury into the
chamber A through the fine chan-
nel at E, and from this quantity
of mercury the change of volume
of the liquid originally filling A
may be found.

356 PROCEEDINGS OF THE AMERICAN ACADEMY.

In the inverted position, a sufficient quantity of mercury is placed in
the piezometer to cover the bottom, and the fluid with which the pie-
zometer is surrounded in the pressure chamber is chosen the same as
that within the piezometer. On the application of pressure, this fluid
is forced in, rising through the mercury, and on release the mercury
comes out. The quantity of mercury left is weighed, from which the
desired change of volume of the fluid is calculated. Here again it is
necessary to know the compressibility of the steel of the piezometer
and the mercury. The determination of the compressibility of the
mercury in the inverted position is as simple as that for finding the
compressibility of water in the erect position. The entire piezometer
is filled with mercury, and placed inverted in the water by means of
which pressure is transmitted. On application of pressure, water
bubbles up through the mercury, and on release of pressure, mercury
comes out. The compressibility of the water is involved here only as
a correction for the volume of the water forced in. In practice, how-
ever, it was found desirable to include a little water initially with the
mercury, so as to fill completely all the corners. The object of using
the piezometer in the inverted position, aside from the check on ac-
curacy afforded by two different arrangements of the apparatus, was to
find if possible any effect of the drop clinging to the mouth of the
channel. In view" of the fact that the surface tension of mercury is
greater than that of water, it seemed plausible that the minimum size
of a bubble of water that would detach itself from the mouth of the
channel and rise through the mercury would be less than the drop of
mercury that would fall through water. No such difference could be
found, however, in any of the work.

It has been noticed that the method demands the knowledge of two
compressibilities besides that of the fluid to be investigated. In the
case of mercury these two compressibilities are those of steel and
water. The correction for the steel was determined independently by
measuring the change of length of a rod under pressure and will be
discussed more in detail later in this paper. The effect of the water is
small at the low pressures, being simply the change of volume of the
slight amount of water forced in, but at higher pressures, where the
water may lose as much as 20 per cent in volume, the correction for
the change of volume of the water will be 20 per cent for the inverted
position and 30 or 40 per cent for the upright position. Given, then,
the correction for the steel, it is still necessary to run two sets of de-
terminations to get the compressibility of either water or mercury, and
naturally these two determinations give the compressibility of both
water and mercury. The data for the water are to be given in a fol-

BRIDGMAN. — MERCUEY UNDER PRESSURE. 357

lowing paper. In calculating the compressibility from these two sets
of data, one for the water and the other for mercury, the method of
successive approximations was applied. The compressibility of water
was first calculated, assuming the compressibility of the mercury to be
constant at its initial value at atmospheric pressure. A curve was
then plotted giving the volume of water against pressure. From this
curve for water, an improved curve for mercury was calculated, from
which again a better curve for water was found. In practice it was
not necessary to carry the steps further than this.

The relations connecting the compressibility of the water and the
mercury with the observed weights of mercury, etc., are given below.

Notation.

V = initial volume of Piezometer,
Fh,o= " " "water,

KHg = mercury.

Then r=rH,o+rHg.

At'H^o = shrinkage per initial unit vol. of water at pressure under
consideration.

Ai'Hg = " " " " ■' " mercury "

consideration.

Ai'Fe = " " " " " " steel "

consideration;

and in addition :

in the upright position

A Fng — vol. at atmos. pressure of mercury forced in
by the pressure in question,
in the inverted position

AT'Hg = voL of mercury forced out, etc.

A Fng is the same thing as the volume of the water forced in. The
corrected volume of the piezometer at any pressure is evidently
V-V.ArFe- It is a simple matter to verify the following equations:

Upright position

HjO J .- >

Ar _ ^ ^ Hg + >^-^^'Fe - ^\o ^?'H,0

' Hg + "^ ' Hg

358 PROCEEDINGS OF THE AMERICAN ACADEMY.

Inverted position

Ac

H,0

_AFH,+ FA.;Fe-FH,Ar>H,

Vnfi + A V,

Hg

A, _ A T-Hg + y^VTe - A^H^o ( I ^h,0 + ^ Vj,^)

* Hg

The following gives a discussion of the minor experimental details
that it was necessary to observe.

Considerable care is necessary in filling the piezometer to ensure
complete exclusion of air. The procedure in filling was as follows.
The piezometer A with the cover B held loosely over it in a suitable
frame was placed in a test tube containing distilled water. The test
tube was then connected to the air pump and the water boiled under
reduced pressure at room temperature, removing the occluded air.
The piezometer was then removed from the test tube, the weighed
quantity of mercury introduced, and then replaced in the test tube
which was again exhausted as before. The mercury had been cleaned
with acid and was freshly distilled. Finally, before raising the piezom-
eter above the surface of the water, the cap B was screwed into place
with a simple key. Removing from the test tube, the cap B was tight-
ened home by applying a spanner.

This tightening of the cap must be done with especial care, and to
irregularities in this most of the irregularities in the data could be
traced. Since the piezometer is made of a very mild steel, it is a com-
paratively easy matter to screw the cap in too far, stripping the thread
or shearing off the shoulder. This was avoided by graduating around
the top of A, and always screwing B in to the same mark. But even
at best, to secure a tight joint, it is necessary to force the cap in pretty
tightly, exceeding the elastic limit locally, and thereby introducing
probable irregularities as explained before. When the method was
first used, a great deal of trouble was found from such irregularities.
This was shown most convincingly by the fact that the volume of the
piezometer did not remain constant, but changed very slightly after
each application of pressure, usually becoming less. This change of
volume is not entirely due to the effect of the joint, because it could
be mostly removed by annealing. Nevertheless, since the effect of
annealing is to remove internal strains, and since internal strains are
doubtless introduced at the joint, there is probably some irregular
action introduced at the joint. This source of error remains the
chief objection to the method, although it can be greatly reduced by
proper manipulation. This consists in careful previous annealing, and

BRIDGMAN. — MERCURY UNDER PRESSURE. 359

seasoning by subjecting to pressure several times before the series of
measurements is begun. One at least of the previous applications
should be to a pressure as high if "not higher than that to be reached
during the measurements. After treatment like this the piezometers
show no further change of volume, and tbe results with any one are
fairly regular. It is a question, however, how good a criterion uniform-
ity of results and permanency of volume are for the uniform comi^ression
of the piezometer without change of shape. It must be confessed there
seems no valid reason why the piezometer after proper seasoning
should not settle down into a steady state in which it gives consis-
tent results with change of shape, and probably it does. The difference
of the results with different piezometers is probably to be explained by
this effect. The best that can apparently be done is to take the mean
of the determinations with several piezometers, all of which individually
give consistent results. All of these considerations apply chiefly to
determining the compressibility of the incompressible mercury ; they
have much less weight, and indeed are almost negligible when applied
to water.

There is one particular way in which it is very easy to produce
irregular results by strains in the piezometer, and one which caused
much trouble before the correct explanation was found. If the pressure
is pushed too high, the water freezes with sudden decrease of volume.
This was not expected when entering on this work, since the freezing
curve of water as found by Tammann^^ gives no evidence of the
existence of ice above zero. The fact is that there are other forms of
ice besides those found by Tammann, one of which is stable at room
temperatures. This will be treated in a following paper. The sudden
decrease of volume during freezing is accompanied by a rush of liquid
through the narrow channel, and, while this rush is taking place, by a
momentary excess of pressure outside over that inside. This excess
pressure may produce volume set, or if not sufficiently great for that,
at least set up internal strains which produce irregularities on subse-
(juent determinations. The irregularities so introduced may be com-
paratively very high; as much as 10 to 15 per cent in the case of
mercury on the next determination. The next value is nearly always
too low. The irregularities become smaller with subsequent determin-
ations, but the only satisfactory way is to anneal the piezometer again.
Many of the early data had to be discarded because of this freezing
effect.

As a consequence of the unforeseen freezing of water at temperatures

" Tammann, loc. cit., p. .315-.344.

360 PROCEEDINGS OF THE AMERICAN ACADEMY.

above zero under high pressure, it is impossible by this method to push
the compressibility determinations of mercury to the freezing curve of
mercury, as was desired. The difference between the freezing pressure
of water and mercury is not very great, comparatively speaking, being
about 1500 kgm./cm.^ at 15°. By pushing the pressure into the un-
stable region for water, it is possible to come closer than this to the
freezing curve for mercury. At 0° the approach was made to within 700
kgm., and at 22° to within 1000 kgm. Attempts to come closer than
this failed. On several occasions the two piezometers, one filled with
water and the other with mercury and water, were subjected to pressure
simultaneously beyond the freezing pressure of water. The water
alone successfully withstood this subcooling, but the water with the
mercury always froze. Even when freezing took place, a rough value
for the compressibility could be found by using in the calculations the
change of volume of the water on freezing. A compressibility for the
mercury was thus found lying on a smooth curve with the values at
lower pressures, but of course any such procedure as this is question-
able. In view of the strong probability that the compressibility of
mercury shows no unusual features in the unreached region, it seemed
unnecessary to take the measures that would be needed to explore this
region, such as the employment of some auxiliary fluid other than
water whose freezing point is higher than that of mercury.

It may be mentioned as confirming these views as to the part played
by internal strain in making the results irregular, that the irregularity
was always much greater after the freezing had taken place after high
super-pressures ; that is, after the freezing presumably had been most
rapid, and the excess pressure on the outside with its resulting defor-
mation greatest.

It will be noticed that the method is essentially an integrating ar-
rangement for measuring the total increase of pressure during the
process ; that is, at every increase of pressure mercury is forced into the
piezometer whether the previous maximum is thereby exceeded or not.
In using the method it is essential, therefore, that pressure should be
increased continuously to the maximum with no retrogressions. The
form of pressure apparatus used made this particularly easy to accom-
plish. Pressure was produced by a hydraulic ram, the larger piston of
which was 6 inches in diameter and the smaller 11/8 inches. The
6-inch piston was actuated by the pressure pump of the Soci^t^
Genevoise, the pressure being run as high as 600 kgm./cm.^

The motion of the piston was very slow because of the large volumes
involved. About 50 strokes of the pump were necessary for an in-
crease of pressure on the high pressure side of 1000 kgm./cm.^. Fur-

BRIDGMAN. — MERCURY UNDER PRESSURE. 361

thermore, the friction of the packing inaterial, while not very great,
retarded greatly the quickness with which the piston moved in response
to an increase of pressure. The piston might continue to move for
some minutes in response to an increase of pressure on the low-pressure
side. The result was that the step-like advance of pressure with each
stroke on the low-pressure side was entirely wiped out and converted
into a continuous advance on the high-pressure side. The only way in
which a retrogression of pressure was likely to occur was by dissipation
of the heat of compression. If pressure is rapidly pushed to a maximum,
there is produced an increase of temperature. The final equilibrium
pressure is lower than the maximum, which corresponds to an unknowTi
temperature. The difficulty was avoided by compressing so slowly
that as the pressure approached the maximum the compression was
sensibly isothermal. With the apparatus so designed as to reduce the
volume of the transmitting fluid to a minimum, it was easy to attain
this condition. By comparing results with slower and more rapid com-
pressions a safe rate was found. The maximum pressure of 12,000,
for example, could be reached with entire safety in seven or eight
minutes. On releasing pressure there was the reverse effect due to
cooling, but it is readily seen that there is no error introduced here
unless there is actual retrogression of pressure, which is just as easy to
avoid as with increasing pressure.

The temperature was kept constant during the compressibility de-
terminations by surrounding the pressure cylinder with a suitable bath,
at 0° with ice and water, and at 22° with an electrically regulated
thermostat. The piezometers were always submerged for some minutes
in this bath before the final adjustments were made. Thus if the com-
pressibility of water were being determined with the piezometer in the
upright position, the piezometer was submerged in a test tube of water
placed in the bath without the mercury in the upper cup. After tem-
perature equilibrium had been reached, the upper cup was carefully
dried with filter paper and the mercury introduced, the lower part still
being in the bath. If the piezometer was to be used in the inverted
position the procedure was more simple, merely waiting for tempera-
ture equilibrium while submerged in the upright position under water
or mercury as the case might be. The variations of temperature in the
bath at 22° were never more than a few hundredths of a degree. The
actual temperature was read with a standardized thermometer.

The volume of the piezometers was found by weighing when full of
water at a known temperature and when empty. The filling was per-
formed in the manner above and was more satisfactory than filling
with mercury and weighing, since by the use of water it was possible

362 PROCEEDINGS OF THE AMERICAN ACADEMY.

to entirely fill the cracks. The total volume of the piezometers was
1 or 2 cm.' for water and 3 Or 4 cm.^ for mercury. These small dimen-
sions were necessary to keep the size of the apparatus down within
reason, as it was necessary to have the walls of the retaining vessel
very heavy in order to withstand the pressures. The cylinder in which
the piezometers were placed had a hole 9/16 inches in diameter and was
4 inches on the outside. The small volume of the piezometers places no
restriction on the accuracy of the results, however. The weight of the
mercury involved in the compression might rise to 3 or 4 gm. for the
higher pressures. Weighings were made to 0.0001 gm., so that any
error in the weighings is entirely negligible.

Pressure measurements were made with an absolute gauge. This
gauge and the various precautions to be observed in its use are
described in a previous paper.

Compressibility of the Steel Piezometers.

The experimental determination of the correction for the compressi-
bility of the steel piezometer demands special consideration. The fact
must be emphasized that there is no method of determining compressi-
bility in which the compressibility of all the substances concerned can be
determined directly, that is, by the application of hydrostatic pressure.
There is always a residuum, whatever the method. Thus in the present
work, the compressibility of both the water and the mercury involve the
compressibility of the steel containing vessels. If an attempt were
made to determine by independent experiment the cubic compressi-
bility of the steel, the compressibility of the vessel in which the steel
was contained would turn up as a new unknown. The difference of the
compressibility of two substances is all that it is possible to get by
direct experiment. To get the absolute compressibility of either, the
compressibility of the other, the unknown residuum, must be determined
by some indirect method. To ensure the greatest accuracy, this resid-
uum should be so chosen as to be as small as possible in comparison
with the compressibility in question. Steel, as has been mentioned, is
an admirable substance from this point of view.

There are a variety of methods open for the indirect determination
of compressibility, all of which depend in some way on the theory of
elasticity. A method frequently adopted is to measure two inde-
pendent elastic constants of a material, such as Young's modulus, or
the torsion coefficient, or the bending modulus, and from these to cal-
culate the compressibility by the identical relations of the theory of
elasticity. In applying the identical relations, the assumption must

BRIDGMAN. — MERCURY UNDER PRESSURE. 363

be made that the material obeys Hooke's law within the stress range
employed, and that it is perfectly homogeneous and isotropic. With
these assumptions the identical relations are rigorously exact The
first of these assumptions seems open to but little question. It is the
second which is likely to give the most trouble, particularly when the
substance experimented on is in the form of hollow tubes, as when
the elastic constants have been determined for glass. This method
was employed by Amagat 12 and by de Metz,!^ among others.

Another method is to measure the linear compressibilty of the sub-
stance in question when subjected to hydrostatic pressure all over and
to calculate the cubic compressibility simply by multiplying the linear
compressibility by three. This seems preferable to the method of the
last paragraph, because the assumptions are reduced to a minimum.
The stress, a hydrostatic pressure, is in this method the same during
the indirect determination of the cubic compressibility as it is during
the actual use of the material in the piezometer. There seems much
less chance for complications to be introduced by nonhomogeneity of
the material than there is when the compressibility is calculated from
two elastic constants, such as Young's modulus and the torsion coeffi-
cient. The only assumption made here is that the material is equally
compressible in every direction, an assumption which is open to verifi-
cation by direct experiment. This verification has been made by pre-
vious experiments in the paper cited. This method has also been
used by several previous experimenters, for example Buchanan,^*
Amagat, 15 and Richards. 1^

In the paper already cited, the linear compressibility of steel was
determined at room temperatures up to 6500 kgm./ cm.^. These data
were inadequate for the present purpose, however, because they did not
run to high enough pressures, and the effect of temperature on com-
pressibility was not determined. But the method there used is entirely
satisfactory, and new results have since been obtained by it for the
purposes of this paper. Briefly, the method consists in enclosing the
metal to be experimented on, which is in the form of a rod, in a long
steel cylinder, within which it is exposed to the action of hydrostatic
pressure all over. The change produced by the pressure in the length
of the rod with respect to that of the cylinder is measured by a ring

" Amagat, C. K., 107, 618-G20 (1P88). Ann. de Chim. et Phys. (G), 22,
95-141 (1891).

" De Mctz, loc. cit.

" Buchanan, Proc. Roy. Soc. Lon., 73, 296 (1901).

" Amagat, C. R., 108, 727-730, 1889.

*^ Richards, loc. cit.

3G4 PROCEEDINGS OF THE AMERICAN ACADEMY.

slipping on the rod. The change of length of the cylinder itself is
measured directly from the outside.

In the previous work the rod was enclosed in a cylinder of soft tool
steel. The maximum pressure, 6500 kgm., was beyond the elastic
limit of this steel, so that the material did not remain isotropic. That
the elastic limit was exceeded is shown by the considerable hysteresis
in the observed elongation of the cylinder. The fact that there is
hysteresis suggests that possibly there may be also some slight degree
of warping. It was stated in the former paper that the only assump-
tion made in the whole work was in regard to this matter of warping,
that is, whether the change of length of the cylinder is the same in-
ternally as externally. The effect is probably slight, and in the absence
of any plausible way of calculating it was neglected altogether.

Apart from the question of the method used in the present work,
and not affecting its validity in the least, there was an error made in
the previous paper in the calculations from the data. Correction for
this error increases the former value for the compressibility of this steel
from 5.30 X 10"' to 5.59 X 10"'' at 20°. This also will change the
value for the compressibility of mercury, as will be explained later.

The tool steel cylinder was not available for the present work, be-
cause it would not reach the pressure reached here, 10,000 kgm./cm.'^
Another cjdinder of nickel steel of the same dimensions as the former
one of tool steel was made, therefore, and hardened in oil. With this
heat treatment, the elastic limit should be somewhere near 15,000 kgm.
The pressure was purposely kept at a low value, never exceeding 10,000
kgm., so as to run no risk of producing set in the inner layers of the
cylinder. That no such heterogeneity was introduced is made probable
by the fact that the cylinder showed no hysteresis, the relation between
extension and pressure being linear both for increasing and decreasing
pressure. The former measurements of this extension were made di-
rectly with a microscope, reading to 0.001 mm. For this work here, a
much more sensitive scheme was used, an adaptation of the Maarten's
mirror device so fast coming into general use among engineers. The
magnification employed here gave a motion of the scale of 5 cm. for an
actual elongation of 0.025 mm. The sensitiveness is, therefore, at least
twice that of an interference system, there is also the advantage of
great simplicity and steadiness, and best of all, the reading is given
directly on a scale, there being no necessity for keeping track of fringes.
The Maarten's mirror device disclosed no hysteresis in the elongation
of the nickel steel cylinder. The freedom from heterogeneity as shown
by the absence of hysteresis makes plausible also the absence of warp-
ing, although no direct measurements of this warping were possible.

BRIDGMAN. — MERCURY UNDER PRESSURE. 365

An attempt was made to show directly the presence of warping by-
measurements of the change of length of the exterior of the cylinder.
Measurements of the extension were made over the middle third and
the middle two thirds of the cylinder. Any very large warping might
be expected to destroy the proportionality of extension to length, since
presumably the warping is confined to the neighborhood of the ends.
No such effect could be found, however, within the limits of error which
were about 1 per cent.

The argument for the probable absence of warping may be stated as
follows. The change of internal length of the cylinder with which we
are concerned was measured between two points at each of which the
internal diameter of the cylinder undergoes an abrupt change. If the
elastic limit of the steel were exceeded, the resulting set and hetero-
geneity would naturally appear first at these places of sudden change
in the dimensions. The effect of heterogeneity at these places would
be to produce warping, that is, sections originally plane would no longer
remain plane. On the other hand, if the material were never strained
beyond the elastic limit, the warping would be negligible. Now the
cylinder has been shown by direct experiment to show no hysteresis,
and therefore probably not to have been strained beyond the elastic
limit. The cylinder, therefore, probably also shows no warping. In
any event, one would seem justified in accepting the readings of a
cylinder showing no hysteresis in preference to one where the hystere-
sis might amount to 16 per cent. The effect of warping, whatever it
is, can be only slight, since it is itself only a correction on a 5 per cent
correction term.

The new determinations made for this work with the nickel steel
cylinder were made on the same specimens as those formerly used,
which were from the same piece of steel as the piezometers. Deter-
minations were made at two temperatures, 10° and 50°, and up to 10,000
kgm./cm.^ There were only a few changes from the experimental pro-
cedure of the previous work. Pressure was measured by measuring the
change in the electrical resistance of a coil of manganin wire, instead
of a capillary of mercury. This is the pressure gauge that was used in
the later work of this paper, and it has been described in detail in a
previous paper. The fluid transmitting pressure was usually kerosene
instead of the former mixture of water and glycerine. At 10° and at
pressure above 8000, the kerosene becomes so viscous that the ring on
the test rod no longer slides freely. The great irregularity of the
points first obtained was traced to this effect. It may be avoided by
using gasolene instead of kerosene at the higher pressures. At 50°
the kerosene may be used without trouble over the entire pressure;

366

PROCEEDINGS OF THE AMERICAN ACADEMY.

range. The results obtained were not quite so regular as the former
results, doubtless because it was impossible to place the cylinder in a
position so favorable to the entire removal of all particles of grit after
every application of pressure. In this work the cylinder was placed

.7

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5000 10000

PRESSURE, KGM/CM^

Figure 2. Shows the change of length at two temperatures of a bar of
bessemcr steel 29.95 cm. long under uniform hydrostatic pressure. The zero
reading for each of these temperatures is arbitrary.

vertically in a thermostat, whereas in the former work it was placed
horizontally.

The results are shown in Figure 2. The values found for the com-
pressibility were O.OgSSS at 10° and 0.0g601 at 50°. The result of
the previous determination in the tool steel cylinder at 20°

was

BRIDGMAN. — MERCURY UNDER PRESSURE. 367

0.06559. A repetition of the former experiment with the tool steel cylin-
der gave O.OeSGS at 20°. It is to be noticed that this value is higher
than that previously found, and in the direction toward that shown by
the nickel steel cylinder. During the repetition of the experiment the
tool steel cylinder also showed less hysteresis than in the early deter-
minations, probably due to the gradual disappearance of the heterogen-
eity introduced by the previous high pressure during the two and one
half years for which the cylinder had been resting. During this last
set of determinations the pressure was never raised above 4000 kgm.,
which is below the elastic limit of the steel.

Whether the true explanation of the discrepancies is to be found in
the warping of the cross-section of the cylinder or not, the fact seems
to be that when the elastic limit of the material is exceeded there is
resulting hysteresis in the elongation, and that this hysteresis is accom-
panied by low values for the compressibility, the greater the hysteresis,
the lower the values. It seems to be justifiable therefore, to accept as
most probably correct the values given by this new determination with
the nickel steel cylinder. The values given above and the temperature
coefficient deduced from them were used in the following computations.

It is to be noticed that the elongation of the nickel steel cylinder
under internal pressure, which has appeared in the above as a correc-
tion factor, is sufficient to give the cubical compressibility of the
nickel steel. This is because, as was pointed out by Mallock ^"^ in
1904, the elongation of a hollow closed cylinder under internal pres-
sure involves only one elastic constant, the cubic compressibility.
This gives for the cubic compressibility 6.2 X 10"'' at 20°. The
results are not accurate enough to give the temperature coefficient by
this method. The high value of this result compared with that by
the direct observation of linear compressibility (62 against 58), is prob-
ably due to the difference in the materials, the latter value being for
an almost pure iron, while the former is for a nickel-chrome alloy with
little or no carbon. (Krupp's trade number for this steel is E. F. 60.0.)
It was shown in the previous paper that carbon alone makes very little
difference in the result.

This same method, the elongation of a hollow cylinder under inter-
nal pressure, has been recently used by Griineisen ^^ in determining
the cubic compressibility of various metals at different temperatures.
His results for two different specimens of iron at 18° varied from
58. X 10"^ to 63. X 10~^ The temperature effect on this last speci-

" Mallock, Proc. Roy. Soc. Lon., 74, 50 (1904).
" Gruneisen, Ami. Phys., 33, 1239-1274 (1910).

368 PROCEEDINGS OF THE AMERICAN ACADEMY.

o

men was found to be 3.1 X lO"^ for 100°, against 1.8 X 10"* for 40
as found above. Griineisen does not give the temperature coefficient
for the iron with the lower compressibility.

In view of the agreement of the results found here with those of
Griineisen, there can seem to be little doubt but that the results found
by Richards ** are affected by some constant error as has been claimed
by Griineisen. 20 The fact that the results here were found by as near
an approach to a direct method as possible, that is, by the measurement
of the linear compressibility, which also was the method used by
Richards, and the fact that these results agree with those of Griineisen,
which were obtained by more indirect methods from the theory of elas-
ticity, would seem to nullify Richards' contention that the results of
other observers have been in error because the theory of elasticity gives
results 30 per cent out of the way. Richards found for iron 38.5 X
10~* against 58.3 X 10~* above. Since his value for the compressibility
of mercury depends directly on his value for the compressibility of
iron, the effect of the correction will be to change very appreciably
the value for the mercury, as will be mentioned later. The source of
error in Richards' work is not entirely clear. He used an electrical
method, in which contact was made with a drop of mercury resting on
the top of the rod of iron to be measured. Change of shape of this
drop of mercury under pressure seems the most likely source of error.

The Data for the Compressibility of Mercury and
Calculation of Results.

Determinations were carried out at two temperatures, 0° and 22°.
The range is sufficient to give the variation of compressibility with
temperature. To get the second temperature derivative of compres-
sibility, observations at several other temperatures would have been
necessary, as well as a higher degree of accuracy than was possible to
attain in this work. The final values given are the mean of a large
number of determinations. At 0°, five different piezometers were
used, and over 90 determinations made over the pressure range from
0 to 7000 kgm. At 22°, two piezometers were used, and 38 points
determined between 0 and 11,000. The points at 0° were ob-
tained first and show considerable irregularities. As familiarity
was gained with the method, and the several sources of error men-
tioned above became recognized, it was found possible to obtain more

^' Richards, loc. cit.

20 Griineisen, Ann. Phys.. 25, 849 (1908).

BRIDGMAN. — MERCURY UNDER PRESSURE.

369

regular results. The values at 22° w6re found after this experience
had been gained, and with the two piezometers giving the best results
atO°.

The points obtained with all five piezometers at 0° are shown in
Figure 3, and the points with the best two of these piezometers in
Figure 4. The points found
with the two piezometers at
22° are shown in Figure 5.
The greater regularity of
these points is manifest.
In both of these figures not
all the points actually ob-
tained have been repre-
sented, for four or five
points, obtained directly af-
ter the freezing of the water
at too high a pressure, have
been discarded.

The data were adjusted
and the final values com-
puted in the following way.
The work was done indepen-
dently at each temperature.
A straight line was first
drawn passing through the
assemblage of points. It
was not necessary that this
line pass through the origin.
The deviation of the ob-
served points from the
points calculated by the lin-
ear formula was then deter-
mined. The deviations from
this line for each piezom-
eter separately were then

plotted on a very much enlarged scale against pressure, and a smooth
curve drawn through these deviation points. This deviation curve,
together with the fundamental linear equation, gave the best smooth
curve connecting change of volume with pressure as determined by
each piezometer separately. From these best smooth curves (five at
0°), points were determined at even pressure intervals, 500 or 1000
kgm. apart. At each of these evenly distributed pressures, the weighted

VOL. XLVII. — 24

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Figure 3. Collection of all the results with
five piezometers for the compressibility of
mercury at 0°.

370

PROCEEDINGS OF THE AMERICAN ACADEMY.

mean of these five points was taken as the best point at this pressure.
Weights were assigned to the smooth curves obtained with each pie-
zometer inversely as the arithmetic difference between the observed
deviation points and the smooth deviation curve. The weights at 0°

005

2 3
PRESSURE ,

KGM/CM'XIO

FiGtrRE~4. The results with the two best piezometers for the compressi-
bility of mercury at 0°. The right-hand vertical scale refers to No. 4, the
left-hand scale to No. 8, annealed.

varied from 1 to 7. Finally, a parabola was passed through these best
points, the deviations of these weighted best points from the parabola
were plotted against pressure, and the smooth curve through these
deviations, together with the parabolic formula, was taken as giving
the best possible relation between change of volume and pressure.
This was the process used in the final determinations. It has been

BRIDGMAN. — MERCUKY UNDER PRESSURE.

371

already explained that the calculation was by means of a method of
successive approximations, and that it was necessary to calculate the
compressibility of the water as well as that of the mercury. The de-

2 4 6 8 .10

PRESSURE, KGM/CM^XIO:

Figure 5. The change of volume of liquid mercury at 22° as obtained
with two piezometers. The right-hand scale is for No. 10, the left-hand one
for No. 8.

tails of this approximation process have been discussed already in the
general discussion of the method. Reference is made to a follo^ving
paper for the values for the compressibility for water. The procedure
in the first steps of the approximation process did not need to be so
elaborate as in the above final calculation.

372

PROCEEDINGS OF THE AMERICAN ACADEMY.

The data for 0° and the steps in the final process of adjustment are
shown in the tables. Table I. shows the points in the order in which

TABLE I.
Data for Compressibility of Hg at 0°.

Pres-

AriijO

Pres-

ArH,o

Pres-

Ai'HjO

sure,
kgm.

(uaed in
compu-

Ai;Hg.

sure,
kgm.

(used in
compu-

A^Hg.

sure,
kgm.

(used in
compu-

A^Hg.

cm.2

tation).

cin.2

tation).

cm.2

tation).

F

lEZ. No.

4.

PlEZ. No

.8.

PlEZ

. No. 8 (cont.).

5270

0.1415

0.01913

6810

0.1622

0.02245

1170

0.0477

0.00425

4520

1290

1621

6800

1620

2259

595

0259

0224

3750

1147

1370

6070

1530

2227

5090

1387

1771

3000
2220

0991
0796

1142
0847

5330
4540

1427
1294

1816
1533

6600

1598

2259

1450

0578

0538

3770

1151

1295

Ptf.z. No.

11.

6050

1527

1709

3020

0994

1068

6770

1617

2283

2230

0798

0831

6570

0.1594

0.02298

1000

0414

0337

1440

0574

0519

6200

1547

2197

500

0224

0170

1050

0432

0385

5450

1442

1941

2210

0794

0802

1830

0690

0667

4720

1325

1704

1410

0564

0512

2610

0897

0977

3940

1184

1434

2180

0786

0797

3400

1074

1211

3180

1028

1179

3090

1009

1128

4140

1222

1443

2400

0844

0896

3740

1145

1215

4910

1358

1685

1620

0631

0617

4500

1286

1543

5680

1476

1926

870

0366

0335

4500

1286

1566

6420

1575

2182

6570

1594

2310

5290

1418

1568

6070

1530

2068

5830

1497

2064

5270

1415

1760

4560

1297

1614

6570

1594

2340

6030

1525

2078

3790

1154

1357

5840

1499

2064

6760

1616

2310

2990

0987

1074

5090

1387

1829

6820

1622

2316

4300

1252

1578

P

lEZ. No.

10.

6630

1601

2234

3550
2820

1106

0948

1320
1054

1190

0.0485

0.00453

PlEZ.

No. 8, a

nnealed

2090

0766

0819

2010

0740

0745

1380

0553

0562

2780

0939

1035

6940

0.1636

0.02383

710

0305

0288

5950

1513

2135

6540

1591

2255

1390

0557

0502

6670

1605

2362

5810

1495

2027

2180

0786

0835

694

0298

0297

5050

1380

1790

1550

0610

0582

3570

1110

1310

4300

1251

1521

1110

0455

0441

4490

1284

1620

3540

1104

1279

2190

0788

0836

5220

1407

1881

2750
1980

0931
0730

0998
0722

6540

1590

2289

they were determined. The actual computation from the data it is
not necessary to show. The formula has already been given by which
these computations were made. In Table L, the values for the change

BREDGMAN. — MERCURY UNDER PRESSURE.

373

of volume of the water, which entered into the computation, are also
given, as this effect is rather large. Roughly, the correction intro-
duced by the water was about one third of the total effect due to the
change of volume of the mercury. These values for water were taken
from the values to be given in greater detail in the following paper.

e 7
PRESSURE. KGM/CM'X Id?

Figure 6. The deviations from linearity of the points obtained with one
piezometer. This shows the irregularities in the results introduced by internal
strains.

Figure 6 gives the deviations of the observed points of two of the
sets of readings of Table I. from a straight line. This line, of the form
W = a + bp, does not happen to pass through the origin, but gives
A F = 0.001 at ;? = 0. All the deviation curves, therefore, start from
the point A.V = —0.00100. In Table II. are given the values calcu-
lated with the help of the deviation curves for the five piezometers at
pressure intervals of 500 kgm., together with the weighted mean of
these values. Finally in Table III. are shown the values calculated by
the parabolic formula, the weighted experimental values, the devia-
tions, and the finally accepted values, obtained with the smooth
deviation curve shown in Figure 7.

The change of volume at any pressure and 0° may be found, either
by constructing a curve through the points of Table III., or more ac-
curately by computing at any pressure the change of volume by the
formula

Ay = ap + bp\

374

PROCEEDINGS OF THE AMERICAN ACADEMY.

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BRIDGMAN.

MERCURY UNDER PRESSURE.

375

TABLE III.
Data for Compressibility op Hg at 22°.

Pressure,
kgm./ cm.2.

■^I'HoO (used in
computation).

At^Hg.

Pressure,
kgm./cm.^

A^HjO (used in
computation).

Al'Hg.

PiEZ, No. 8

PiEZ. No. 10 (conL).

4G90

0.1258

0.01720

5840

0.1439

0.02132

58G0

1441

2079

4720

1264

1806

6980

1599

2453

3570

1052

1378

1170

0437

0451

2410

0787

0923

2350

0776

0898

1210

0450

0472

3530

1044

1313

1930

0657

0947

80S0

1740

2784

2950

0918

1087

9080

1863

3031

4140

1160

1530

10430

2012

3389

5350

1364

1855

r*11640

2128

4101 >|

6410

1521

2243

11030

2070

3720

7520

1670

2599

< 10130

1980

3257 I

8600

1806

2916

5690

1416

2129

9740

1938

3218

I 593

0245

0355 J

10180

1985

3377

9150

1872

3106

PlEZ. No. 1

0.

8080

1766

2765

10150

0.1982

0.03472

8200

1756

2984

9130

1869

3145

5290

1355

1926

8060

1740

2848

8290

1767

2887

6960

1596

2478

9210

1878

3113

* Freezes.

376

PROCEEDINGS OF THE AMERICAN ACADEMY.

where

log a =4.5819- 10,
log(-b) = 9.7569-20,

and applying to this computed value the correction given by the devia-

tion curve of Figure 7.

ul 3

f5 +.00001

?fe 0

OU1-.0000I

Q.C9

"I 2

5 3

===^-5i

3 4 5 G 7
PRESSURE. KGM/CM^XIO"^

Figure 7. The de\aation curve for the
change of vohime at 0°. This is to be used
with the formula on page 373.

The data for 22° are
shown in a corresponding
set of tables and figures.
The only difference is that
here the parabola was used
as the basis for both the
first and the final deviation
curves. Table IV. corre-
sponds to Table I., Figure
8 to Figure 7, Table V. to
Table II., and Table VI. to
Table III. The final for-
mula for computation at
any pressure is

where

Av =^ ap + bp\
loga = 4.5911 - 10,
log(-^) = 9.7782-20,

and the final deviation curve from this formula is given in Figure 8.

There are only a few previous determinations of the compressibility
of mercury with which these results can be compared, and all of these
are at comparatively low pressures, where the percentage accuracy of
the above work is naturally less than at the higher pressures. The
only way of making the comparison is to find what the compressibility
given by the above two expressions would be at atmospheric pressure.
The values found in this way from the above data are O.O538O at 0° and
O.O5395 at 22°.

The early work, done by Regnault,2i Grassi,** Jamin,23 Amaury et
Descamps,2* and Tait,*^ may be summarily ruled out as too inaccurate
for the comparison. The earlier of these determinations were made

" Regnault, Mem. Inst, de France, Six. Mom., 21, 329-428 (1847).

" Grassi, Ann. de Chim. et Phys., 31, 437-478 (1851).

" Jamin, C. R., 66, 1104-1106 (1868).

" Amaury et Descamps, C. R., 68, 1.564-1565 (1869).

*» Tail, Challenger Report (1889), Phys. and Chem., vol. II, p. 1-76.

BRIDGMAN.

MERCURY UNDER PRESSURE.

377

before the theory of elasticity was well understood, and the work of
Jamin, in particular, is a classical instance of how dangerous it is to
follow native intuition where the stress and strain system is at all

TABLE IV.

Adjustment of Data — Final Values of Compressibility of Hg at 22°.

Pressure.

kgm./cm.2.

A^Hg at 22".

Calculated,

Deviation.

Final

Value.

No. 8.

No. 10.

Weighted
Mean.

1000

0.00389

0.00389

0.00389

0.00384

+0.00005

0.00389

2000

0766

0766

0766

0756

+ 10

0766

3000

1129

1131

1130

1116

+ 14

1130

4000

1482

1485

1483

1465

+ 18

1483

5000

1818

1823

1820

1800

+20

1820

6000

2141

2149

2144

2124

+20

2144

7000

2451

2461

2454

2436

+ 18

2454

8000

2746

2761

2751

2736

+ 15

2751

9000

3026

3044

3030

3024

+06

3030

10000

3290

3313

3297

3300

-03

3297

11000

3540

3568

3549

3564

-15

3549

12000

3776

3809

3787

3816

-29

3787

2

1

Wt.

....

Cal

3ulated vak

log a

log{-b]

les are by the formula
= ap -\- bp^
= 4.5911 - 10
= 9.7782 - 20

complicated. Jamin's results were 50 per cent too small. Of the
more accurate work, Amagat^s gives O.O5379 for the pressure range
0 to 50 kgm., at a temperature apparently unspecified in the original

** Amagat, loc. cit.

378

PROCEEDINGS OF THE AMERICAN ACADEMY.

paper. DeMetz,27 ji^ quoting Amagat, however, gives 0.05.379 as Ama-
gat's value at 0°. The source from which this knowledge was obtained
is not clear. Amagat's results, obtained with seven different piezom-
eters, vary among themselves by 2 per cent. De Metz gives O.O5374
at 0° and a pressure range not over 50 kgm., as the mean of results

.00020

.00015

.00010

-^00005

0
'00005
.00010
00015
DOOlO
O00Z5
.00030

t:

s

J: ■ f

Pf "-]

■

1

JI

1 ||||

s

■!j:!:

"h

I't

+ F ■

:

:

.a

:; : . 1

:. J:

1
t

i

\

1

!

1

-,uJ-MurJ::

I :

s

-5:

11

1

i- J

i:i ;;

'■'-■■\^

\ ' '!-

\\

3 4-56

fci

I 2 3 4- 5 6 7 6 9 10 11 12

PRESSURE, KGM/CM'XIO:'

Figure 8. The deviation curve for the change of volume at 22°. Tliis 13
to be used with the formula on page 376.

with four piezometers differing among themselves by 5 per cent. De
Metz also gives the temperature coefficient of compressibility. This is
higher than the value found above, but is such as to bring de Metz's
value at 22° up to 0.06394, almost identical with the present deter-
mination at that temperature. Lately Richards ^8 has determined the
compressibility to 500 kgm. He gives O.O537I for the pressure range
0-500, at a temperature not specified, probably room temperature.
Previous work by Richards, however, had given a value for the tem-
perature coefficient of the mercury the same as that of the glass piezom-
eter. This temperature coefficient is very much smaller than found
above, producing a change from O.O537IO at 0° to 0.053724 at 20°.

27 Do Aletz, loc. cit.

"* Richards, loc. cit.

BRIDGMAN. — MERCURY UNDER PRESSURE. 379

It is to be noticed, however, that Richards' value involves directly his
own value for the compressibility of iron, which is almost certainly
much too low. If the more probable value O.OeSS is used instead of
Richards' value O.OeSS, the value of Richards for mercury becomes
O.O539I at room temperature. The change of compressibility with
pressure found by Richards is higher than that found above, dropping
from 3.80 between 0 and 100 kgm. to 3.60 between 500 and 600 kgm.
As mentioned in a previous paper, this is probably due to error in the
pressure gauge. Carnazzi ^9 has published data over a much wider
pressure and temperature range than the other previous observers, up
to 3000 kgm., and from 23° to 192°, but with less pretense to accur-
acy, as only two figures are given in the results. Carnazzi gives O.O537
as the initial compressibility at 23°. Since Carnazzi's results are the
only ones which give the change of compressibility with pressure over
an at all wide pressure range, it may be permitted to anticipate a little
in order to compare his results with the present ones. Carnazzi finds
a drop in the compressibility of 0.064 from 250 kgm, to 2750 kgm. at
23°, against 0.0625 of the present work. His change in the mean
dilatation between 23° and 53° is from 181 at 0 pressure to 157 at 3000,
against a change in the mean dilatation between 0° and 22° from 181
to 163 for the same pressures as found in the present work.

Finally, the results may be compared with the results of the previous
paper. *o It has been already stated that the method of the paper was
open to question, but it should be remembered, as was stated at the
time, that the primary object of that work was to find whether the
compressibility of mercury showed any marked change over a pressure
range from 0 to 6000, and that the data were obtained because of their
bearing on another question. The accuracy was sufficient for the pur-
pose in hand, and the employment of the method seems to have been
justified in view of the very much greater speed and ease of manipula-
tion. The initial compressibility at 20°, making correction as already
explained for the erroneous value used for the compressibility of steel,
was O.O5375.

Taken altogether, the agreement with the more accurate of the pre-
vious determinations is as satisfactory as could be expected : 380 at
0° against 379 of Amagat and 374 of de Metz, and 395 at 22° against
394 of de Metz and 391 of Richards.

^' Carnazzi, loc. cit.
^^ Bridgman, loc. cit.

380

PROCEEDINGS OF THE AMERICAN ACADEMY.

Discussion of the Data.

TABLE V.

VoLrME OF Hg at 0° AND 22°

These data may be used in mapping out the p-v-t surface, and for
giving certain information about the thermodynamic behavior of liquid
mercury under pressure. The proportional changes of volume given
above were calculated in the usual way, by taking the volume under

atmospheric pressure and at the
temperature in question as the unit
volume. To map the p-v-t surface,
correction must be made for the
change of volume with temperature
at atmospheric pressure. Thus, if
the volume when p = 1 and ^ = 0°
is taken as unity, the values given
by the process just mentioned for Ay
at 22° must be corrected by multiply-
ing by the ratio of the volume at 22°
and j!? = 1 to the volume at 0° and
/> = 1. The actual volume under
different pressures, and at 0° and at
22° is given in Table V. In this the
value for the total change of volume
between 0° and 22° was taken as
0.00398, as given by the most recent
work of Callendar and Moss ^i on the
expansion of mercury. It appears from
their work that the mean coefficient of
expansion at 0° is 0.0001805, while
the mean coefficient between 0° and
100° is 0.0001817. This gives for

Pressure.
kgm./cm.2.

Volume.

at (P.

at 22°.

0

1.00000

1.00398

1000

0.99626

1.00007

2000

99261

0.99627

3000

98905

99264

4000

98561

98909

5000

98231

98571

6000

97914

98246

7000

97607

97934

8000

97637

9000

97356

10000

97088

11000

96835

12000

96596

m.

the value O.O724, which is

evidently beyond the accuracy of this
work. That is, for the present pur-
pose, over the temperature and pres-
sure range involved, the isothermals may be assumed to be equally
spaced. This is sufficiently accurate at atmospheric pressure, and all
our experience with other more compressible liquids would lead us to
expect it to be all the more nearly true at higher pressures.

^1 CaUendar aud Moss. Proc. Roy. Soc. Lon., A, 84, 59^-597 (1911).

BRIDGMAN. — MERCURY UNDER PRESSURE.

381

Figure 9 shows the compressibility at these two temperatures and
different pressures. The compressibility plotted in Figure 9, is the

X

>-

-J

eg
<o

u
cr.

o
o

AO

39
38

31

36
35

3A

Ki;iiii'^

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i:
;; "iii 1

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i :::

33
31

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iJI

llirmliiut' \

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3\

pi:: ■

'

30

Hi^;-

V .: [ 1 1

' TT T TyitnTI

19
28
11
26

--

^

25

C.^ [bl;to;j:;;u;u;i;u3^;nr;;;M;::;^;..;;;;;};s;;^ii:;;ii,j;;t;::;u;;4n:i;«f;pKi;;;ft;::j;iuii::

I 23450789 10 II

PRE55URE ,KGM/CM'XI0:'

Litiiii^;«

12

Figure 9. The compressibility of mercury at two different temperatures.
This compressibiUty is the instantaneous compressibiUty ( y I •

thermodynamic quantity ( ^ ) , which is slightly different from the ordi-
nary meaning of compressibility as used above. It may be obtained at
0° directly from the parabolic formula and the deviation curve. At 22°
the results obtained from the parabolic formula and the deviation curve

382

PROCEEDINGS OF THE AMERICAN ACADEMY.

are to be corrected by about 0.4 per cent for the increased initial volume
at 22°. The results given in the figure are from smooth curves drawn
through the points so determined. The compressibility is less at higher
pressures, as it is universally for all liquids, and is greater at higher
temperatures, as it is for everything except water. The decrease of

I

?

-<

LiJ

.000180

.000175
.000170

.000105
.000100

.000153
.000150
.000145
.000140

n.m-

jiJiSffe t

i

IMSlii

tt|^ t ttj^ Hi '.

trs- -t^pt:"- :_

g:gj;g|55ii ;;

BH

: :

M: !::

Illlllll

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1

:::::::::

J : ; :: : |: ; ;

HI

^M

! 1 Hi HH'

: ; i : ^

nnn'ii''nii

■

■

0

PRESSURE.KGM/CMXIQ

6

3

FiGUKE 10. The mean dilatation per degree between 0° and 22° for mercury
as a function of the pressure.

compressibility with pressure is very nearly linear, but nevertheless
shows a tendency to become more rapid at higher pressures, which is a
little surprising. The decrease of compressibility with pressure is more
rapid at the higher temperature. Whether the compressibilities at
different temperatures would ever become sensibly equal cannot be
determined because of the entrance of the solid phase.

The dilatation of the mercury, or rather the derivative ( — ) , may

\drjp

be found from the distance apart of the isothermals at 0"" and 22°.
The results are shown in Figure 10. The dilatation becomes less at
higher pressures, the rate of decrease also becoming less as one would
expect.

The data so found, ( — ) and f — ) , are sufficient to give the dif-

ference of the specific heats at ditierent pressures, for we have the
relation,

BRIDGMAN.

MERCURY UNDER PRESSURE.

383

C/p — i/v — —

\dp)r

(5 .055

O .054-
^ .053

^ D5Z

O 051
Lh .050
^ .049
^ 0A&
O .047
{J .046

O

"^OAS

0

nn '^Sif

:: : i-

l[i|l;[-

llPt

:.4i:-Iih!:^Li:nt:r:4Hii4^ iitiiHi imift

Mil

^^'1

:. ::: :::::

;| 1 ■;

jjl i^g § [;;

i |1 U„:

.•■.[ll\i::i\B^l^\}^l:}

::*: T~

Hii

t-t^yis;

1 r ' 1

^^S|8|:

■11 Pi

im

E-i - -- ""

jHlg;;

ii||

^■-H (ff-

.:: i':

- ^ k

" + f Hi f ff

1 g-|l|jH:

it: 1

f-\

~

"" I— 1

5^ H

\-'^''-

miTnntri

mk^

Um

?n flH4^

Ip

iii:

■'■-^

l%i

™

44^^^^

::■:: ^i:

£■ li* ■

■flfl

li: . u:;

'IS?

i J; -

Hi

:: ,::

t

if

■1 ■ ■ t S

:t; t ::j

:n:':

:2^

|r

ilHlmtttt

:■ '■:

; :, ;

'11^

1 tr--

iii

1,, - f -*

:H:.i:l Jl

:::;;

ltllliitriiiiiiTiiiln;ii;iri

liiiniii

1 2 5 4. 5 6 7

pressure,kgm/cm^io."

Figure 11. The difference of the specific heats as a function of the pres-
sure in gm. cal. for a quantity of mercury occupying 1 cm.* at 0° and atmos-
pheric pressure.

The results in gm. cal. along the isothermal at 0° are given in Figure
11. The difference becomes less at high pressures, the rate of decrease
itself decreasing rapidly. The behavior is thus different from that of
water, which shows an increase.

The data are not sufficient to give the actual value of either specific
heat along the isothermals, but we can find the initial rate of variation
from the thermodynamic formula

\ dp Jr ' WJp

The work of Callendar and Moss ^* gives at atmospheric pressure and 0°

" Callendar and Moss, loc. cit.

384

PROCEEDINGS OF THE AMERICAN ACADEMY.

273 X O.O724

= - O.O5655,

Cp being expressed in ergs per cm.* and p in dynes per cm,
pressed in gm, cal. and kgm./cm.* this becomes

Ex-

m,-

0.06154.

This variation is so small that
over the pressure range here.

TABLE VI.

Cp AND Cv FOR Hg at 0°.

Pressure,
kgm.
cm.2

Specific Heat, gm. cal.

for initially Unit Vol.

(13.596 gm.)

Cp.

Cv.

0
1000
2000
3000
4000
5000
COOO
7000

0.4549
4547
4546
4544
4543
4541
4540
4538

0.4003
4035
4056
4063
4073
4073
4077
4079

we may assume it to remain constant
This would give a total change of Cp
of only 1/4 per cent for 7000 kgm.
Probably the change is actually
less than this. Table VI. shows the
values of Cp calculated with this
assumption, and also the values of
Cp found from the already calculated
values of Cp— C^. It is seen that while
Cp decreases with pressure, C^ in-
creases, the increase being more rapid
than the decrease. In computing the
date of the table, the value of Barnes
and Cooke ^^ for Cp at atmospheric
pressure and 0° was used, 0.03346 gm.
cal. per gm., or 0.4549 gm. cal. per
cm.^

There are several other quantities
of interest that may be deduced from
the given data. One of these is the
difference between the isothermal and
the adiabatic compressibilities. We
have the thermodynamic formula

\dpjr \^pj<t>

5 J;

The results are shown in Figure 12. The adiabatic compressibility,
therefore, on the isothermal t = 0°, decreases less rapidly than the
isothermal compressibility.

Intimately connected with the adiabatic compressibility is the tem-
perature effect of compression. For this we have

" Barnes and Cooke, Phys. Rev., 16, 65-71 (1903).

BRIDGMAN. — MERCURY UNDER PRESSURE.

385

.0^42

moj8

M

I jOJ6
.0,30

III

:|

1

4
t

: I

I

: :

It

1

1

Pii

M

1

i^

''^ ~

ii:zi|iti:j;;

1:

■

: ::

s

1

^iii

m^

M

ijiifc'

:h|

■^x..

!:l

1:*

i

4^

1

R^"

-^

:ii

1

m

1

K

■

■^

^ -T-T

ffl

1; ;

1

I!

1

!lf

1

i

"77

ill:

M

1

||3!

:.d

Mitt;! -.la

M

'Mtf^

^pl--

-^

:::

1

;

::

1

i^

1

IUJ-+|P

-3

1

:

;i

1

_ __:

^#1

^

f^

#: J5

R^

: :

■

: +

je

53

Bi

'r'Mpfr

S;i;:

^M

*;

1

ii

1

M

1

:|

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M

i^^y

1

i"^--i

0

PRE55URE.KGM/CM'X 10."'

Figure 12. The difference between the isothermal and the adiabatic com-
pressibilities as a function of the pressure.

O -0026
^ O0Z5
£ .0024
^. .0023
«^^ .0022

,£13.0020

0

PRE5SURE,KGM/CM'XIQ'

Figure 13. The heating effect of compression; that is, the rise of tem-
perature in degrees centigrade for an adiabatic rise of pressure of 1 kgm.

m.

c„

The numerical values of this quantity are shown in Figure 13. The in-
itial rise of temperature is, therefore, about 2°. 5 for 1000 kgm. The rise
of temperature becomes less at higher pressures, the rate of decrease also

VOL. XLVII.

25

386

PROCEEDINGS OF THE AMERICAN ACADEMY.

decreasing. The rise of temperature for 500 kgm. was found by actual
experiment by Richards 3* to be 1°.2, agreeing essentially with above.
The fact that this rise of temperature is less at high pressures might at
first sight seem surprising, since the work done by the external pres-
sure during a given pressure increase is increasing nearly proportionally

^.0150
2.0140
vo-0130
?^.0I20
Sd.OIIO
§.0100
^ .0090

-<

o

OO&O
.0070

^ .0000

I-

,jol5

"BlDOSO

PRE55URE,K6M./CM'XIQ'

Figure 14. The rate of change of internal energy with pressure along an
isothermal in gm. cal. for a quantity of mercurj^ occupying 1 cm.' at 0° and
atmospheric pressure. Notice that the sign of the derivative is negative.

to the pressure and the specific heats are nearly constant. It must be,
therefore, that most of the work done by external pressure goes toward
increasing the internal energy of the liquid, very little being left over
to increase the temperature. That this is true is seen at once from the
thermodynamic formula

\ dp J4>

which shows that the internal energy is increasing along an adiabatic,
and at a rate very nearly proportional to the pressure. The internal
energy decreases along an isothermal, however, as may be inferred fi-om
the value of the derivative given by

3* Richards, loc. cit. (1903), p. 40.

■P

dp)^'

BRIDGMAN. — MERCURY UNDER PRESSURE. 387

and shown in Figure 14. The curvature of Figure 14 is so slight,
however, that it seems probable that at a high enough pressure the
derivative will vanish and then become positive, so that ultimately
the internal energy will increase along an isothermal.

The Change of State Liquid-Solid.

The quantities involved thermodynamically in the passage of a sub-
stance from one phase to another at a given pressure and temperature
are the change of volume and the latent heat. From these quantities
the change of freezing temperature with pressure may be calculated by

dr tAV

Clapeyron's equation, -y =-rTr- -^'^^ ^^^ experimental difficulties

of determining the latent heat are almost prohibitive. This is because

in order to withstand high pressures the mass of the steel containing

vessel must be much greater than the mass of the substance under

experiment. Another method of finding these quantities based on

Clapeyron's equation was therefore used, as in practically all the work

done previously in this field. If the course of the freezing curve is

dr
known, -j- may be found at any point, which, together with the change

of volume at this point and the temperature of transformation, gives
the latent heat.

The data were obtained by three methods. The first gives simply
the course of the freezing curve. This was found by measuring the
electrical resistance at constant temperature as a function of the pres-
sure, freezing being indicated by a sudden drop in the resistance to
about one third its value for the liquid. The second method, by far
the most important, gives both the melting pressure and the change of
volume. It is the same as that used by Tammann,^^ and consists in
measuring the volume as a function of the pressure at constant tem-
perature. At the freezing pressure, the volume suddenly changes, so
that by plotting volume against pressure, the point of discontinuity
gives both the equilibrium pressure and the change of volume. The
third method is concerned with a single isolated quantity on the freez-
ing curve, the change of volume on freezing at atmospheric pressure.
The existing data were not accurate enough, so this quantity had to

^* Tammann, loc. cit., p. 204.

388 PROCEEDINGS OF THE AMERICAN ACADEMY.

be redetermined. The measurements were made by weighing mercury
under CS2, and plotting weight against temperature. Melting is ac-
companied by a sudden decrease in the displacement and so by a
sudden increase in the apparent weight.

The Freezing Curve by Change of Resistance.

The points on this curve were obtained on two separate occasions ;
the fall of 1909, and January, 1911, and with two different pieces of
apparatus. The data of 1909 are not as accurate as those of 1911, be-
cause the gauge was destroyed by an explosion before an entirely satis-
factory calibration was made.

The details of the apparatus have been described elsewhere. The
absolute gauge, against which the pressure measurements were made
directly, has been described in a separate paper. The details of the
glass capillary containing the mercury resistance, and the electrical
connections with the details of the insulating plug have been described
in the paper on the use of mercury as a standard of pressure. The
pressure range employed there was only 6800 kgm./cm.^ ; it has since
been found that the same arrangement of apparatus is good to at least
12,000 kgm./cm.^, the range of this paper. The measurements of elec-
trical resistance were made by a null method on a Carey Foster bridge,
exactly as in the preceding paper.

One slight change in the details of the measurements as made in
1911 should perhaps be noted, the employment of kerosene as the
liquid surrounding the glass capillary instead of a mixture of glycerine
and water. This avoids all possibility of short circuiting the terminals
of the plug dipping into the mercury cups, and also avoids the neces-
sity for carefully protecting these terminals. A light oil like kerosene
is necessary since a heavy oil, such as ordinary lubricating oil, freezes
at about 4000 kgm. at room temperature. It was found by inde-
pendent experiment that at least up to 12,000 kgm. the kerosene
does not become so stiff as to refuse to transmit the pressure
hydrostatically.

The experimental procedure was the one which would naturally sug-
gest itself, but there are a number of details of manipulation which
were necessary to observe. The resistance was measured at appropriate
intervals of pressure, the temperature being kept constant. After every
increase of pressure it was necessary to wait 10 or 20 minutes for the
dissipation of the heat of compression to the surrounding bath, which
was kept constant to within O^.Ol with a thermostat. With increasing
pressure it was never found possible to reach exactly the freezing pres-

BRIDGMAN. — MERCURY UNDER PRESSURE. 389

sure, but always the mark was overshot a little. It would have been
impossible to land exactly on the mark, in the first place because of
the mechanical difficulty of raising the pressure exactly the right amount,
in the second place because of the initial effect of heat of compression
which would keep the mercury liquid even if the pressure corresponding
to the bath temperature were reached, and in the third place, because
of the possibility of subcooling the liquid into the region of stability of
the solid. With increasing pressure it was always necessary, therefore,
to run past the point by from 200 to 400 kgm. Freezing was indicated
by a sudden drop in the resistance. This drop was not instantaneous,
but might continue for several minutes. Everything points to the
spontaneous formation of a crystalline kernal at some point in the
capillary, and then the advance of the surface of separation of solid
and liquid through the capillary at a rate depending on the amount
subcooling, etc.^® Freezing, when it had once started, usually ran to com-
pletion. This was because the volume of the mercury was so small that
the change of volume on passing to the solid state was not sufficient
to lower the pressure to the equilibrium value. To find the equilib-
rium pressure, the pressure on the solid phase was lowered until the
reaction to the liquid started, and then by rapid work at the pump the
pressure was so adjusted that the resistance was in a state of unstable
equilibrium, changes of pressure too small to measure on the gauge
sufficing to produce a very large increase or decrease of resistance.
With a little practice, one could keep the mercury in a partly melted
condition for any desired length of time. This was necessary in order
to avoid the effect of heat of compression, which might sometimes be
so large as to mask the effect sought. The heat of compression of
kerosene is so high that it is possible for a decrease of pressure in the
kerosene to bring about a freezing of the mercury, the adiabatic drop
of temperature with pressure for the kerosene being more rapid than
the drop of pressure with temperature on the freezing curve of mercury.
To be absolutely certain that there was no such effect the mercury was
always kept in the partially melted condition for twenty minutes be-
fore recording the equilibrium pressure. To avoid any possibility of
error from impurities absorbed by the mercury, pains were taken to find

** To measure the rate of advance of the surface would have been interest-
ing, but to be of value would have demanded some other disposition of ap-
paratus from that used. Evidently the rate of advance of the surface depends
more than anything else on the rate at which the heat of transformation ia
conducted away, which in turn will depend on the size of the glass capil-
lary, and the thermal conductivity of the surrounding liquid. Any results
obtained with the apparatus without modification would have had significance
only for this piece of apparatus.

390 PROCEEDINGS OF THE AMERICAN ACADEMY.

the equilibrium pressure with as little of the solid phase present as
possible. This evidently avoids the large depression of the fi-eezing
point which would result from the concentration of impurities in the
small remaining mass of liquid after the solid had nearly all separated
out. The precaution was probably supertluous because the mercury
was carefully purified to begin with, and no effect of such a nature was
ever detected.

One other source of error was guarded against which was especially
prominent in the earlier work of 1 909. The fluid transmitting pres-
sure from the lower cylinder, in which was the absolute gauge, to the
upper cylinder, in which was the mercury, was a thick mixture of either
molasses and glycerine or glucose and glycerine. It was necessary to
use such a mixture in connection with the absolute gauge in order to
avoid leak at the high pressures. But there is the disadvantage that
the viscosity of either of these fluids increases so rapidly with .pressure
that high pressures are not transmitted immediately through the con-
necting pipe from the lower to the upper cylinder. This connecting pipe
was 15 inches long and 1/16 inch internal diameter. That the pressure
■was transmitted slowly was shown by the fact that after pressure had
been increased in the lower cylinder by advancing the piston, the abso-
lute gauge in the lower cylinder indicated a fall of pressure for some
minutes, while the change of mercury resistance in the upper cylinder
indicated a corresponding rise, evidently due to the slow flow of liquid
from the lower to the upper cylinder. The effect was troublesome only
at the higher pressures, the pressure coefficient of the effect being very
high, and was very much greater for the mixture of glycerine and mo-
lasses used in 1909 than for the glycerine and glucose of 1911. In
the extreme case, glycerine and molasses at 12,000 kgm., it was neces-
sary to wait two hours for the equalization of pressure. For most of
the pressures used the effect disappeared more rapidly than the heat of
compression. To avoid error from this effect, the decrease of resist-
ance indicating freezing must come after an increase of pressure in the
lower cylinder, and the converse increase of resistance after a decrease
of pressure. The measurements were made Avith this in mind.

The temperature measurements above zero were made wuth a Ton-
nelot thermometer calibrated at the Bureau of Weights and Measures
in Paris. Below zero the readings of 1911 were made w^ith a toluol
thermometer calibrated at the Reichsanstalt, and in 1909 with a mer-
cury thermometer made by Green of New York, the zero correction for
which was the only correction applied. In any case, the errors in the
temperature readings were less than the possible error in the pressure.
The temperature was kept constant with an ordinary thermostatic de-

BRIDGMAN. — MERCURY UNDER PRESSURE.

391

vice ; a stream of ice water, or for the lower temperatures a stream of
CaCU brine, running constantly into the bath, which was automatically

TABLE VII.

Freezing Pressure at Different Temperatures by the Method of
Ch.ange of Electrical Resistance. Data of 1909.

Temp. oC.

Eqmlibrium Pressure, kgm. /'cm.2.

Difference,
kgm./ cm.2.

Observed.

Calculated.

+ 14.35
+21.0
+ 16.8

+ 10.06
+ 16.25
+ 4.04
0.00
0.00
- 8.52
-15.09
+ 9.68
+21.42

10720
11860
10850

9620
11010
8540
7730
7730
6060
4730
9690
12070

10600
11910
11060

9730
10960
8530
7730
7730
6040
4730
9660
11990

+ 120
- 50
-210

-110

+ 50

+ 10

0

0

+ 20

0

+ 30

+ 80

Calculated values by the formula
p = a(< + 38.85)
7730
^^^^^ « = 38.85
= 198.9

heated with a Simplex heating coil when the temperature fell too low.
The temperature did not vary more than 0°.01 during a run, whereas
a change of 0°.05 is necessary to produce a change in the equilibrium
pressure of 10 kgm. which was about the limit of accuracy of the gauge.
The temperature range of the experiment was from —15° to +20°.
Since the freezing curve as determined between +20° and —15° extra-

392

PROCEEDINGS OF THE AMERICAN ACADEMY.

polates almost linearly to the ordinary freezing point at —38°. 8 and
atmospheric pressure, it was not thought necessary to make the special
eflfort demanded to run a thermostat at temperatures below —15°.

One other remote possibility of error was guarded against. The
capillaries containing the mercury were fine, the bore being about

TABLE VIII.

Freezing Pressure of Mercury at Different Temperatures by the
Method of Change of Electrical Resistance. Data of 1911.

Temp. °C.

Equilibrium Pressure.
kgm./cm.2.

Difference
kgm. /cm.2.

Observed.

Calculated.

4.95

9.92

14.86

19.98

0.00

-14.40

-9.70

0.00

8570
9640
10600
11640
7680
4790
5630
7660

8660
9640
10620
11630
7680
4830
5760
7680

-90
0

-20

+ 10
0

-40
-130

-20

Calculated values by the formula
J, = a{t^- 38°.85)

'-.^ 7680

^^^'•^ " = 38.85

= 197.7

0.1 mm. It was thought barely possible that the curvature of the
surface might be sufficient to produce a rise of internal pressure in the
mercury sufficient to change slightly the external pressure required to
hold liquid and solid in equilibrium. This effect was shown to be
negligible by using two capillaries of different sizes, one three times
the diameter of the other. The equilibrium pressure found at 0°
with the larger capillary was 7680 kgm., and with the smaller 7660.
The divergence is in the direction to be expected, but it is of the same
order as the experimental discrepancies. The data of 1911 were ob-

BRIDGMAN. — MERCURY UNDER PRESSURE.

393

tained with the larger of the ahove mentioned capillaries; those of
1909 with one of intermediate size.

The actual data follow. Those for 1909 are in Table VII. and in
Figure 15. The data are given in the order in which they were col-
lected. The two determinations at the higher pressures after the run

3 4 5 6 7 8 9 10

PRESSURE, K6M/CM^XI0"?

Figure 15. The melting curve of mercury by the change of resistance
method.

with regularly decreasing pressures were made, the one at 9°. 68 to
correct the obviously bad point determined first of all, and the one at
21°. 4 to make sure that there had been no systematic error introduced
after the regular decrease of pressure of the first points. In addition,
the three points determined during the initial testing of the apparatus,
before the thermostat was installed, are given at the very end. The
temperature error here easily accounts for the discrepancies of these
last three points. As was stated before, the gauge with which these
determinations were made was destroyed before it could be satisfac-
torily calibrated. The data used in the reduction of the gauge read-
ings were simply the measured dimensions of the gauge, which could
not be determined with the requisite accuracy. The column showing
the calculated pressure must be taken, therefore, as merely evidence
showing the regularity of the results and slight departure from lin-
earity, and not as giving accurately the absolute pressures.

Table VIII. and Figure 15 give the results of 1911. The method by
which the results were calculated was the same combination of numeri-

394 PROCEEDINGS OF THE AMERICAN ACADEMY.

cal computation with graphical construction already used in finding
the compressibility. A straight line was passed through the point at
9640 and 9°. 92, and the departure of the observed pressure values
from those calculated by the linear relation plotted on a large scale.
A smooth curve was then drawn through the midst of these points, and
the final values calculated by applying to the smooth values the
small correction determined from the smooth curve.

The points of 1911, except for the two bad ones mentioned above,
lie on a smooth curve within the possible errors in reading the gauge.
The departure from linearity, although slight, is pronounced in the
direction of concavity toward the pressure axis, that is, less rapid rise
of freezing temperature at the higher pressures.

There seems no reason why the points of 1909 are not just as valu-
able in indicating the manner of departure from linearity as those of
1911, since all the pressure readings are affected alike by the incom-
plete calibration of the gauge. The error in the gauge readings of
1909 is simply due to inaccurate knowledge of the cross-section. The
following correction was applied, therefore, to the gauge constant of
1909. The best straight line through the points of 1911 was deter-
mined (graphically from the smooth correction curve) and also that
through the points of 1909. The former gives a change of pressure of
197.1 kgm./cm.*^ per degree rise of temperature ; the latter 199.2. The
observed pressures of 1909 were all reduced in the ratio of 197.1 to
199.2. A smooth curve was then passed through these corrected
values by the method described above. Finally, to determine the
most probable departure of the freezing curve from linearity, the mean
of the two correction curves, those for the data of 1909 and 1911, was
taken. These curves differ nowhere by more than the possible errors
in reading the pressure gauge. From this curve it is possible to find
immediately the tangent to the melting curve at the origin.

Finally, all these results may be collected into the following form.
At any given temperature the melting pressure is to be found by add-
ing to the pressure given by the formula p = 196.5 (t + 38.85) the
small correction term given graphically in Figure 16. The initial rise of
pressure per degree rise of thefreezing point is therefore 196.5 kgm./cm.^ ;
at 12,000 kgm. this has become only 1/2 per cent greater, so slight is
the departure irom linearity. The value of the initial slope, 196.5,
has no more certainty than the single series of observations of 1911,
but the departure from linearity shown in Figure 16 has the greater
weight which should be given to the mean of two independent series
of observations with different apparatus.

A number of data collected incidentally in the course of the work

BRIDGMAN. — MERCURY UNDER PRESSURE.

395

may be mentioned here, because they throw some light on certain
properties of mercury under pressure, even if these are not the thermo-
dynamic properties which are the particular subject of this paper.

The electrical resistance of the liquid mercury was usually measured
over the entire range up to the freezing pressure. The matter of the

o

Ul 80

60

20

CO

CL

./

/"

y

<^

^^-^

^

t

I A

\ (

I 1

3 . 10 , 12

PRESSURE, KGW/CM*XIO"^

Figure 16. Departure of the melting curve of mercury from linearity.
The initial slope is 196.5 kgm. for a rise of temperature of 1° C.

electrical resistance of mercury under pressure has already been treated
in a paper in which the pressure range was only 6800 kgm./cm.^ The
results obtained during the present work were pretty irregular, dis-
crepancies of 1 or 2 per cent not being rare; but within the limits of
error, the empirical formula given in the previous paper may be used
by extrapolation up to the freezing pressure, at least within the present
temperature range from — 1.5° to + 20°. The irregularities observed
in the present work were without doubt due to the strains set up in
the glass by the passage of the mercury from one state to the other. To
reach the accuracy of which the measurements are susceptible it would
be necessary to repeat the above resistance measurements, taking care
never to push the pressure beyond the freezing value.

The electrical resista,nce of the solid mercury was also usually meas-
ured. These results cannot be expected to much more than indicate
the order of the effect, for in addition to the comparatively small irregu-
larities mentioned above, as due to elastic after-effects and hysteresis,
comparatively large temporary alterations in the glass capillary are
probably produced by the freezing of the mercury. The results are

396

PROCEEDINGS OF THE AMERICAN ACADEMY.

given in Table IX. R is the resistance of the mercury reduced by
taking as unity the resistance of the liquid at atmospheric pressure
and the corresponding temperature. R for the liquid was obtained by
extrapolating beyond the freezing point to the pressure at which the
resistance of the solid was measured. The resistance of the soHd shows

TABLE IX.

Change of Electrical Resistance when Mercury Ch.a.nges from the
Liquid to the Solid at V.\rious Pressures.

Temp. °C.

Pressure, kgm./cm.2.

Resistance in Terms of Resistance at Atmos. Pres-
sure and Temp, of the Measurement.

Pressure on
the Solid.

Freezing
Pressure.

SoUd.

Liquid.

Change.

Ratio.

16.2

14.3

10.0

4.0

0.0

0.0

-15.1

10960
10660
9960
9220
7660
7610
5450

10870
10490
9640
8450
7650
7650
4680

0.211
247
234
251
264
241
258

0.761
764

777
791
817
816
863

0.550
517
543
540
553
575
605

3.61
3.09
3.48
3.15
3.09
3.39
3.35

a distinct tendency to become less at the higher pressures and tem-
peratures. The effect of temperature only would be to raise the resist-
ance. The pressure coefficient of resistance must be negative, there-
fore, as for all other pure metals, and must have a value at least such
that 200 kgm. increase of pressure produces a greater fall of resistance
than 1° rise of temperature produces rise of resistance. This means
that the pressure coefficient of the solid is greater than 0.0004/200 =
0.000002. The table also makes evident the tendency of the change
of resistance liquid-solid to become less at higher pressures and tem-
peratures. This indicates that the effect of pressure on the resistance
of the li(iuid is greater than the effect on the solid, as one would expect,
although the reverse is true for the temperature effect. This enables
an upper limit to be placed on the pressure coefficient of the solid, since
the coefficient of the liquid is known. This upi)er limit is about ten
times the lower limit set above. It hardly seems worth while to at-

BRIDGMAN. — MERCURY UNDER PRESSURE. 397

tempt to force the above very imperfect data to give more accurate
results.

It may be mentioned, however, that the above results are fully as
consistent as the results which have been obtained by previous ob-
servers for the electrical resistance of solid mercury at atmospheric
pressure. Thus Weber ^'^ found the following values for the ratio of
the conductivity of the solid mercury to that of the liquid out of which
it is freezing : 3.2, 4.2, 3.9, 4.0, 3.5, 4.0. Taking the reciprocals so as
to compare with the above form, these become 0.31, 0.24, 0.26, 0.29,
0.25 ; different measurements of the same quantity. Cailletet and
Bouty 38 give the single number 0.24, while Grunmach in his first
paper 39 gives 0.67 and redetermines it in a later paper ^^ as 0.40.
The high values of Grunmach are doubtless to be explained by the for-
mation of cracks in the mercury when freezing. This error can hardly
come in the present work. In explanation of the other outstanding
discrepancies, the fact does not seem to have been sufficiently consid-
ered that mercury freezes into crystals which may have different con-
ductivities in different directions. It is known that the conductivity
of bismuth, for example, may change by 60 per cent in different direc-
tions, and that of iron glance by 100 per cent. It is to be expected,
therefore, that the particular form of vessel in which the mercury is
frozen, by influencing the position in which the crystals tend to sepa-
rate out, would have an eff"ect on the apparent change of resistance
on freezing. *i

Finally, mention may be made of an unsuccessful attempt to get the
heat of transformation from these same resistance measurements. The
idea was to measure the depression of the freezing point occasioned by
dissolving some metallic impurity in the mercury, the commencing of
freezing being indicated by a kink in the curve giving resistance as a
function of the pressure. The depression of the freezing point gives
the heat of transformation by a well known formula. The difficulty
with the method is that there is no metal which gives a depression of

" Weber, Wied. Ann., 25, 245-252 (1885), and 36, 587-591 (1888).

38 Cailletet et Bouty, C. R., 100, 1188 (1885).

39 Grunmach, Wied. Ann., 35, 704-772 (1888).
" Grunmach, Wied. Ann., 37, 508-515 (1889).

*^ Since the writing of this paper Onnes (Kon. Akad. Wet. Proc., 4, 113-
115 (1911)) has given data from which the ratio of the resistance of solid to
liquid mercury may be found to be 0.237. This value was computed by the
author from the values given in Science Abstracts for the resistance of a given
quantity of mercury (172.7 ohms at 0°C., and 39.7 ohms in the solid state at
the melting temperature) .

398

PROCEEDINGS OF THE AMERICAN ACADEMY.

the freezing point sufficiently large to give the desired accuracy. Few
metals depress the freezing point at all, and those which do show a
eutectic point 1° or 2° below the normal. In a preliminary testing out
of this idea, the resistance of a 5 per cent Cd amalgam was measured
at 21°. 5. Beginning at between 1000 and 2000 kgm. the pressure
coefficient was found abnormally large over the pressure range up to

LJ

|007oHG. IOO%CD.

PROPORTION H6 AND CD.

Figure 17. Showing the raising of the melting curve of mixtures of mer-
cury and cadmium with increasing pressure.

and including 12,000 kgm., which is the freezing pressure of pure mer-
cury at 21°. 5. The time required in reaching eciuilibrium was also
abnormally long. Both these facts indicate the separating out of some
component from the amalgam. Between 1 2,000 and 1 3,000, this process
of separation seemed to have been completed, and from 13,000 to
13,500 the behaviour was entirely normal. The explanation is simple.
The effect of pressure is to raise the entire melting diagram Hg— Cd,
the Hg end more than the Cd end. (See Figure 17.) This raising is
presumably accompanied by a shifting of the proportions of the two
metals present in the eutectic mixture. The initial temperature and
proportion of the two metals present in the amalgam may be represented
by the point A (in this case ^ = 21°.r) and x = 5 per cent), but when the
pressure has risen sufficiently to bring the melting curve- up to A, with
further rise of pressure A slides along the rising curve, always at con-

BRroCMAN. — MERCURY UNDER PRESSURE. 399

stant temperature, shown by the point B on the highest melting curve
of the diagram, until the eutectic point is reached, where complete
solidification sets in. This takes place at a pressure slightly higher
than the normal freezing pressure for the pure mercury, as shown ex-
perimentally above, but the precise amount will depend on the unknown
way in which the proportions of the eutectic mixture have changed.
To obtain the data desired by this method, A must initially lie to the
left of the eutectic point corresponding to the particular freezing
pressure instead of to the right, as in the diagram. The results evi-
dently cannot be accurate, and it was therefore not thought worth
while to push the investigation further at this time, particularly since
the destruction of the gauge mentioned before came as the direct result
of the high pressure reached above. An investigation of the change of
eutectic proportions under pressure would make an interesting research
for its own sake.

The Equilibrium Data by the Change of Volume Method.

The method was essentially that of Tammann, and gives both the
change of volume and the pressure at a given temperature. It consists
in measuring the displacement of the piston by which pressure is pro-
duced as a function of the pressure. Freezing is indicated by an inter-
ruption of the regular rise of pressure with advance of the piston. It
is at once obvious that an absolute essential for the success of the
method, and at the same time the hardest condition to maintain under
high pressures, is the entire freedom from leak of the moving piston
and the other parts of the apparatus. Tammann found this trouble at
pressures above 2000 kgm./cm.^, and avoided it in part by using a very
heavy oil for transmitting pressure. In this present work a new pack-
ing device was adopted which secured entire freedom from leak even
with so thin a fluid as kerosene or mercury. Data will be given in
support of this.

The data needed at any point in addition to the equilibrium pres-
sure and temperature are the amount of the advance of the piston
during constant pressure, the quantity of liquid involved in the
change, and the cross-section of the advancing piston. The first two
may evidently be measured directly, but the last changes with pressure
by an amount not susceptible to direct measurement. Here, as in all
pressure measurements, the distortion of the containing vessel enters
as a disturbing factor. But it should be pointed out that here the
effect of the distortion is a minimum. It has been quite impossible up
to the present to make direct determinations of compressibility, for ex-

400 PROCEEDINGS OF THE AMERICAN ACADEMY.

ample, by this method, because the changes of volume of the liquid are
accompanied by unknown changes of volume of the same order in the
containing vessel. But here, where the changes take place at constant
pressure, the vessel remains constant during the change, and the only
distortion which need be taken into account at all is the change of area
of the cylinder, a change which is easy to calculate, and which further-
more never in the present work rose above 2 per cent of the total effect.
To make this matter clearer, take the example of water. A pressure
sufficient to change the volume of water by 20 per cent might intro-
duce a change of about 2 per cent in the volume of the very heavy
cylinders of this present work. This change of 2 per cent takes no
account of the change of volume introduced by the compression of the
packing of the various connecting pipes, etc., which are necessary if the
pressure is to be measured at all accurately. This change due to
the tightening of the packing is evidently incalculable, but may pre-
sumably be as large as the other effect. The change of volume as
indicated by the advance of the piston is affected, therefore, by a
quantity which may very reasonably be supposed to be 4 per cent on
20 per cent, that is, 1/5 of the total effect measured. Compare this
wnth the change of volume during freezing at constant pressure. Here
the change of volume of the rest of the vessel and the packing plays
no part whatever, the only correction is 2 per cent for the change in
cross-section of the cylinder. That is, a correction of 2 per cent which
may be approximately determined, against a wholly unknown correction
of 20 per cent. It should be remarked, however, that if once the com-
pressibility of the water has been determined in some other way, it may
be used in an apparatus of this form to determine the unknown distor-
tion, and so the compressibility of other liquids may be determined.

Description of Apparatus.

The apparatus consisted essentially of two cylinders, connected by a
piece of very heavy nickel steel tubing 12 inches long. The upper cylin-
der was placed in a hydraulic press, and the pressure was produced in
this by a piston forced down by the ram of the press. The amount of
motion of the piston was measured with a micrometer screw reading
to 0.0001 inch. There were no valves in any part of the apparatus, as it
is difficult to make these capable of withstanding high pressures. The
apparatus was initially filled entirely full of liquid after the air had
been exhausted wnth an air pump, and the piston was then introduced
into the upper cylinder. The dimensions of the various parts were
chosen so that the maximum pressure desired could be obtained with a

BRIDGMAN. — MERCURY TINDER PRESSURE. 401

single stroke. This upper cylinder was freely exposed to the air of the
room, with no special device to keep the temperature at any definite
value.

The lower cylinder contained the mercury, the subject of the experi-
ment, and was surrounded by a bath kept at constant temperature by
a thermostat. The mercury was contained in a cylindrical steel shell
fitting loosely the hole in the cylinder. The same kerosene which
entirely filled all other parts of the apparatus and transmitted pressure
from the upper to the lower cylinder also entirely surrounded the
walls of the shell containing the mercury. This arrangement was
necessary, because if the mercury had been allowed to come in contact
with the walls of the cylinder, the steel would have become amalga-
mated, and the cylinder speedily ruptured. Whereas, the steel shell
in which the mercury was contained being surrounded on the outside
by kerosene, and so being subjected to a purely hydrostatic pressure
equal all over, experienced no amalgamation whatever. ^^

Screwed into the bottom of this lower cylinder, directly immersed in
the kerosene and so subjected to the same pressure as the mercury,
was an insulating plug carrying a coil of manganin wire with which the
pressure was measured.

The procedure was as follows : After filling the apparatus with
kerosene, the thermostat was raised around it and adjusted to the
temperature desired. When a steady state was reached, the resistance
of the manganin coil was read on the Carey Foster bridge, thus giving
the pressure zero. The piston was then introduced into the upper
cylinder, and pressure increased to a value a few hundred atmospheres
short of the freezing pressure at the temperature of the thermostat.
After pressure equilibrium had been attained by dissipation of the
heat of compression, the pressure was read from the resistance of the
manganin coil and the position of the piston was read with the microm-
eter. Two readings of the resistance of the manganin were made
corresponding to the two positions of the eight-point switch of the
Carey Foster bridge. These readings were made before and after read-
ing the position of the piston. Since the circuits were non-inductive,
the bridge could be used with the galvanometer circuit permanently
closed. These two readings are, therefore, really two independent
readings of the pressure, and agreement between them is indicative of
the attainment of pressure equilibrium. It was not necessary to take
any such precautions in measuring the position of the piston, for the

*^ See These Proceedings, No. 14, 1911, for a discussion of the amalgama-
tion of steel under high pressures.
VOL. XLVII. — 26

402 PROCEEDINGS OF THE AMERICAN ACADEMY.

friction of the packing prevented all motion after the initial increase
of pressure.

The above procedure, reading of pressure and piston position, was
repeated at appropriate pressure intervals up to several hundred or
perhaps a thousand kgm. beyond the freezing pressure. On plotting
piston displacement against pressure, the freezing is shown by a dis-
continuity in the curve. Similar readings were also made on release
of pressure, and so another value for the change of volume found. On
releasing pressure the discontinuity is more sudden than with increas-
ing pressure, because it is impossible to superheat the crystalline solid
on decreasing pressure, but the liquid may be subcooled on increasing
pressure. Because of this, and for another reason to be explained
later connected with the distortion of the steel, the value found with
decreasing pressure was without exception accepted as the correct value.

In the use of this apparatus and in the calculation of the data, there
are numerous corrections or disturbing factors which will now be
considered in detail.

Leak. — As already stated, the most obvious and apparently the
greatest difficulty with the method, particularly at high pressures, is
the question of leak. It might perhaps be possible to correct for this
as was done sometimes by Tammann by weighing the quantity of liquid
escaping past the piston in a given time, but this correction would always
be unsatisfactory in cases where, as here, the total motion of the piston
during freezing is small (0.2 inch) and many extend over an hour or
more. It has been stated that there was absolutely no leak. This was
proved by the fact that the piston and upper end of the packing, when
removed from the cylinder after the end of an experiment, were always
perfectly dry, even though the total time over which pressure has been
applied might reach into several days, as it did on several occasions.
That there was no leak in any other part of the apparatus was proved
by the self-consistency of the results as well as by special experiment.
On one occasion pressure was left at 7500 over night, temperature
being kept constant with a bath of ice and water, and in the morning
had not dropped by as much as the smallest amount perceptible with
the manganin resistance, namely 2 kgm./cm.^

The effect of leak, if there were one, would be to make the values of
Ay during increase larger, and during decrease smaller. The values
did actually in the great majority of cases disagree in this way. That
this was not due to leak will be evident from a discussion of

Elastic After-Effects. — In the ordinary sense of the word, elastic
after-effects, as is indicated by the name, are purely elastic phenom-
ena, complete recovery after any application of stress always occurring,

BRIDGMAN. — MERCURY UNDER PRESSURE. 403

provided time enough is allowed. There are also other effects of some-
what the same general character, such as hysteresis, not usually in-
cluded in the name. But there will be included in this discussion any
effect in virtue of which the strain is not a single valued function of
the stress only. The general nature and interpretation of these ef-
fects is still obscure, but there are a few facts which are well known. For
instance, in all ordinary testing of materials it is first necessary to ac-
commodate the metal to the particular stress conditions of the moment.
The strain under a given stress is not the same the first time the stress
is applied as the second, and not until the application of the stress a
number of times does the strain come to depend always in the same
way on the stress. Even after complete accommodation has been at-
tained, the material may continue to show elastic after-effects, that is,
continued yield after the application, or continued recovery after the
release or stress. Or it may also show hysteresis. These effects be-
come increasingly important as the magnitude of the stress is increased,
or as the character of the stress changes from one uniform throughout
the mass to one changing from point to point. The effects become
most important of all when the material itself has become non- homo-
geneous by the exceeding of the elastic limit in some places while the
remaining parts are without permanent deformation.

Various effects of just this kind are to be expected in these exper-
iments, and may perhaps be fairly large in comparison with the usual
magnitude of the effects, because of the wide range of stress here em-
ployed. It should be pointed out that one advantage of this method,
namely, that the elastic deformation of the vessels does not enter the
results, is in part offset by the various effects of the kind mentioned
here, because in virtue of them the volume of the containing vessel
may change while freezing or melting is going on at constant pressure.
Furthermore, these effects, which are themselves intrinsically small,
may appear with magnified effect in the result. Thus the actual
change of volume of the mercury during freezing is about 1 per cent of
the total internal volume of the containing vessel, so that a change of
volume of 1/100 per cent of the containing vessel produced by elastic
after-effects during freezing will appear in the result magnified to 1 per
cent. As a matter of fact, there were found discrepancies between the
values under increasing and decreasing pressure amounting in the worst
case to 3 per cent.

It was possible, however, by an examination of the discrepancies
themselves and by a brief consideration of the method of experiment to
select from these the most probably accurate results. During the
course of an experiment, the stress history of the steel in its bearing on

404 PROCEEDINGS OF THE AMERICAN ACADEMY.

this efifect was as follows. Pressure was pushed to a value somewhat
short of the freezing pressure, the readings were made, and then pres-
sure increased again, etc., until the subcooled region had been entered
far enough for freezing to begin. This first stage might occupy an
hour. The second stage was that of approximately constant pressure
during freezing, which might require from an hour to an hour and a
half During the third stage, pressure was increased a few hundred
atmospheres beyond the freezing pressure, held at the maximum for a
while, and then decreased to the melting point again. This occupied
another hour. The fourth stage, melting at constant pressure, ran
more rapidly than freezing, but might consume an hour. Finally a few
readings below the freezing pressure, rarely more than half an hour.
It is to be noticed that during melting the pressure has been held in
the immediate neighborhood of the maximum for some hours, and that
this melting pressure is only slightly removed from the maximum,
whereas during freezing, the stress has j ust been increased over nearly
the entire range and the time for accommodation has been much
shorter. All our experience with elastic after-effects would lead us to
predict that during melting these effects would be very much less im-
portant than during freezing. We would furthermore predict that the
change of volume found during freezing would be greater than that
during melting, for the piston must advance to compensate for the
increasing volume of the steel vessels as well as for the decreased vol-
ume of the mercury.

These conclusions were verified by the data. The values found
during melting were always self-consistent, lying on a smooth curve,
and could be repeated. But those found during freezing might vary
wildly within the 3 per cent limit mentioned above. Furthermore, the
inconsistent results were always larger than the consistent ones, pro-
vided that the procedure was as described above. There seemed to
be no connection between the duration of the pressure and the amount
of the discrepancy.

We already have evidence enough to make it extremely probable
that the discrepancy was not due to leak, although it is of the right
sign. But the fact that the discrepancy is reversed in sign so as to in-
dicate a leak in instead of a leak out, if the stress is applied differently
from above, renders certain the conclusion that the effect is not due to
a leak. The succession of points on the melting curve, the procedure
in getting one of which was described above, was in general obtained
by starting at low temperatures and pressures and working up to the
higher values. Each maximum pressure, then, was higher than the
preceding maximum. But if the preceding maximum was higher than

BRIDGMAN. — MERCURY UNDER PRESSURE. 405

the following one, the discrepancy was reversed in sign, the values
during freezing being too low, while those during melting still lay on
the same smooth curve as before. This certainly cannot be due to
leak. Neither is it in accord with the general nature of other elastic
after-effects at low pressures. But other experience of this same general
nature at these high pressures indicates that this is probably the gen-
eral nature of the effect at high pressures. It is as if the subsequent
application of pressure, and possibly the change of temperature also,
changes somewhat the position of the molecules, like shaking a magnet,
so that they become free again to resume their natural elastic recov-
ery from the previous greater maximum. One experiment with a hol-
low steel cylinder subjected to external hydrostatic pressure strikingly
suggested the same general explanation. This cylinder had been pre-
viously subjected to a pressure many times beyond the elastic limit, so
that the metal had flowed toward the center, decreasing the internal
volume. On removing the pressure there was some slight elastic re-
covery of the internal volume, but not nearly as much as was to be
expected. But the next increase of external pressure produced in the
initial stages a very marked increase of internal volume, instead of
a decrease, the natural effect of the pressure. It must be that in some
way the pressure loosened up the molecules so that they were free to
resume their natural recovery.

Other slight differences suggest also that these discrepancies are of
the general nature of elastic after-effects. Because of breakage, several
different pieces of apparatus were used. The discrepancy was always
greatest with the thickest-walled vessels. It has been observed sev-
eral times in other connections that elastic after-effects are greater with
the greater mass of metal, because this allows greater heterogeneity of
strain and greater volume in which to store the effect, with consequent
longer time of recovery. At a given pressure the effect in a new piece
of apparatus was smaller before it had been subjected to the greatest
maximum than it was at this same pressure after being so subjected to
the maximum. In general, the effect was likely to increase with time,
showing fatigue of the metal. In one case, in the similar measure-
ments on water, to be described elsewhere, rupture of the vessel was
foreshadowed by an increase of the effect beyond 3 per cent.

There may be some slight effect of permanent set mixed up with
the above effects. An undoubted set was always very distinctly ob-
vious after the first application of the greatest maximum. This appli-
cation was usually made in a preliminary test in order to season the
apparatus before the measurements were undertaken. This applies
particularly to those three or four occasions after the lower cylinder

406 PROCEEDINGS OF THE AMERICAN ACADEaiT.

had been broken. The seasoning of the upper cylinder was done more
carefully, and is described elsewhere. The set must have been nearly
all removed by this seasoning, but any subsequent set would still affect
only those results for increasing pressure.

In view of all these considerations, the course actually adopted
seems justified ; namely, to retain only those values found during melt-
ing, that is, during decreasing pressure. In consequence, in some two
or three of these last determinations, and in many of those on water,
the experimental determination with increasing pressure was entirely
omitted.

Elastic Deformation. — It has already been stated that the only way
in which elastic deformation, that is, a deformation depending only on
the pressure, enters, is in the correction for the change of cross-section
of the upper cylinder. Although the value finally adopted for this
correction is small, only 1.8 per cent at 10,000 kgm /cm.*^, still it must
be admitted that the greatest uncertainty in the work is precisely in
determining this correction. The difficulty comes because of the very
high pressure employed, which renders doubtful the calculation by the
ordinary theory of elasticity. If the maximum pressure used in the
experiment, 12,000 kgm., were the greatest pressure involved, the case
would not be so doubtful, because the elastic limit of the steel is not
greatly exceeded here. Indeed, if it were possible to harden the steel
uniformly throughout its mass, reaching to a depth of 1 1/2 inches, the
elastic limit would not be reached until about 15,000 kgm., and there
would not be much question in applying the ordinary equations of
elasticity. But it is impossible to raise the ela.stic limit throughout
the metal by quenching, and the interior of the cylinder always shows
some set at 12,000. Since the accuracy of the whole method depends
on accurate knowledge of the cross-section it was necessary to remove
every vestige of set in this part of the apparatus. This was done by
subjecting the cylinder initially for five or six hours to a pressure of
24,000 kgm. This was sufficient to stretch the inside of the cylinder
from its initial value of 1/2 inch to nearly 9/16 inch. The cylinder
was then reamed out to 9/16 inch for its entire length, and this was the
form in which it was finally used. The effectiveness of the treatment
is shown by the fact that the cylinder has shown no further change of
so much as 0.0001 inch on the internal diameter.

The present condition of the cylinder is therefore far from one of a
state of ease ; there are certainly internal strains. But it should be
noticed that this fact in itself is not sufficient to destroy the applica-
bility of the equations of elasticity. Provided only that the metal
shows no further set after the first application, and that strain remains

BRIDGMAN. — MERCURY UNDER PRESSURE. 407

proportional to stress, any stress will produce the same additional
strain as the same stress applied from a state of ease. The long inter-
val of time for which the maximum pressure was exerted, and the
large excess of this pressure over any subsequent pressure, make it ex-
ceedingly probable that such a state has actually been reached. The
residual stress in the cylinder is then of exactly the same nature as the
stress in a gun with shrunk-on hoops, and the deformation may be
calculated by the ordinary theory. It may be mentioned, in support
of this position, that measurements have been made of the external
elastic deformation of another such cylinder of the same steel up to
10,000 kgm., showing agreement with the accepted theory to at least
5 per cent, with no trace of hysteresis.

The calculation of the actual deformation of the cylinder according
to the elastic theory would be impossible because of the indeterminate
nature of the boundary conditions. An approximate solution only
can be obtained, in which the end effects are neglected altogether.
This solution is nevertheless probably accurate enough, because the
end effect in other similar cases in which the rigorous solution is
known has been shown to be negligible. It is well to remember in
considering the validity of these approximations that the maximum
value of the correction at the highest pressure is only 1.6 per cent.

The internal diameter of the cylinder does not expand uniformly
under pressure. The expansion may be supposed to have its greatest
value at points removed from the position of the piston by at most a
few diameters. The expansion throughout the greater length of the
cylinder is constant, therefore, and equal to the value it would have in
a cylinder infinitely long and of the same radial dimensions. But for a
short distance beyond the head of the piston the expansion varies fi-om
its maximum value to a value which may be shown to become half this
maximum at the piston itself Now if we suppose that the cylinder is
so long that as the piston moves at constant pressure (during freezing
or melting) the locality of transition in dimensions travels bodily with
the piston, then a moment's consideration shows that the volume swept
out by the piston is equal to the length of stroke multiplied by the area
of the cylinder at its locality of maximum distortion. The assumption
does not seem forced in view of the fact that the length of the cylinder
is between ten and fifteen diameters.

The formula for the displacement under these conditions may bo
found in any book on elasticity. We have

_ hP ( a^ 21/ 4/x + 3k\
a2-62V2/* 3k ■ 12/x y

Whence the change of area, A^ =

408 PROCEEDINGS OF THE AMERICAN ACADEMY.

where h is the internal and a the external radius, /x the shearing modu-
lus, and K the compressibility modulus.

a was measured directly from the outside of the cylinder and was
3.536 cm.; b was found from a measurement of the plug at the end of
the piston after this plug had been forced to conform to the hole by
the application of high pressure. It has been already stated that no
change in b could be detected during the course of the experiments of
so much as 0.00004 cm. b was found to be 0.7183 cm. /a and k were
found by the ordinary equations of elasticity from Young's modulus,
taken as 2 X 10® kgm./cm.^, and Poisson's ratio, taken as 0.28. These
quantities vary only slightly in different grades of steel. The values
of /u. and K calculated in this way were found to be 7.81 X 10^ and
15.2 X 10^ respectively. Substituting in the formula gives directly

A^. = 0.00491 cm. for 10,000 kgm./cm.^.

2 X 0.00401
.7183
= 1.35 per cent for 10,000 kgm./cm.^.

Temperature Corrections. — There are a variety of temperature cor-
rections to be considered ; those which are to be met in any physical
measurement, and those which were peculiar to this particular work.
The ordinary corrections concern only the reading of the temperatures
and may be dismissed with a few words. Temperature about the lower
cylinder was maintained constant to 0°.01 with a thermostat. Above
zero this temperature was read with a Tonnelot thermometer calibrated
at the Bureau of Weights and Measures in Paris. The correction for
the zero was determined, but it was not necessary to apply any of the
other corrections. Readings on this are probably accurate to 0°.01.
Below zero, readings were made on a toluol thermometer, graduated to
0°.l, and calibrated at the Reichsanstalt. In addition to the correc-
tions of the Eeichsanstalt, the zero correction was applied. This is
accurate to 0°.l, which corresponds to the accuracy of the pressure
measurements.

Of the corrections peculiar to this work, the temperature effect on
the pressure readings was the simplest. The manganin resistance coil
with which pressure was measured was placed in the lower cylinder
with the mercury, and so was exposed to the same changes of tempera-
ture. It has already been shown in the paper on the gauge, that
within the temperature limits of this work the pressure coefficient of
resistance is constant. The only temperature effect is on the total
resistance of the coil, which, therefore, merely displaces the zero. This

BRIDGMAN. — MERCURY UNDER PRESSURE. 409

zero was usually redetermined directly at every temperature, but in a
few cases where it was inconvenient to release the pressure to zero
between two sets of readings at different temperatures a calculated
correction was applied. This correction was determined from an in-
dependent measurement of the temperature coefficient of the zero of
one of the four mangauin' coils with which pressure was measured.
These four coils were made from contiguous pieces of the same piece of
wire. The greatest change of the zero from this effect amounts to
400 kgm. between — 20° and 0°. Above zero the correction becomes
very much smaller, as this particular kind of manganin shows a maxi-
mum resistance at 28°. It will be noticed that it was necessary to
keep the bath temperature constant to only 0°.5, in order to remain
within the errors of the pressure readings.

By far the most serious correction is due to the fact that the lower
cylinder with the mercury under experiment is at one temperature,
while the upper cylinder where the measurements of the change of
volume are made is at another temperature, the temperature of the
room. It is readily seen that the change of volume during melting,
for example, as measured by the displacement of the piston of the
upper cylinder, will be in error by the expansion at constant pressure
of the liquid kerosene on passing from the temperature of the lower
to that of the upper cylinder. This error has the same sign during
both melting and freezing. The change of volume so measured will be
too large if the lower cylinder is colder than the upper, and too small
in the reverse case. The correction evidently becomes rapidly larger
with the increase in the difference of temperature, but because thermal
dilatation becomes less with increasing pressure, this correction fortu-
nately becomes smaller at high pressures, where it is harder to de-
termine. The maximum value for the correction in this work was
2 per cent over the range -f 20° to — 20°.

This correction seems to have been entirely overlooked by Tammann.
It might very possibly amount at the maximum to over 10 per cent for
temperature ranges over 100° such as he employed. The effect of the
correction will not be to change at all his co-ordinates of the melting
curve, but might possibly modify somewhat the way in which Ar
apparently tends toward zero at high temperatures and pressures.
This latter point has some theoretical significance in Tammann's theory
of solid-liquid.

The correction had to be determined by direct experiment, as there
were no data by which it could be calculated. The discussion, which
is somewhat long and involved, will be given in the following separate
section.

410 PROCEEDINGS OF THE AMERICAN ACADEMY.

The Tliermal Dilatation of Kerosene at Constant Pressure.

Since the accuracy desired was not very high, the maximum value
of the correction being 2 per cent, a procedure was adopted which was
rapid, but not accurate enough to employ in determining this quantity
as a physical constant interesting in itself. The method consisted
essentially in filling the entire apparatus with kerosene, lower as well
as upper cylinder, immersing the lower cylinder in the constant tem-
perature bath, and plotting piston displacement against pressure.
Then the lower cylinder was allowed to come to room temperature, and
again the piston displacement and the corresponding pressures noted.
The difference of displacement at the two temperatures gives the
change of volume of the kerosene which was in the lower cylinder on
expanding from the one temperature to the other. It is to be noticed
that this gives the thermal dilatation of a quantity of kerosene of un-
known mass but of known volume. To find the dilatation as ordinarily
defined, we should require the compressibility, so that we might know
the original volume of the kerosene which at the given pressure com-
pletely filled the lower cylinder. But the data as given by the experi-
ment are exactly the data needed in making the correction. For
suppose the change of volume of the mercury on melting at a certain
temperature and pressure is approximately 1 cm.^. We require to
know how much this 1 cm." of displaced kerosene has changed in
volume on passing from one temperature to another at constant pres-
sure, and we are not interested at all in the original volume of this

1 cm.^ of kerosene.

The procedure as roughly outlined above is evidently liable to a
multitude of errors. It is exactly similar to the corresponding method
of obtaining compressibilities against which objections were made in
the introduction. But it is to be said in extenuation that the cor-
rection is small, and that the maximum correction comes at the low
pressure where the objections of the introduction have little weight.
The correction at — 20° of 2 per cent corresponds to only 3500 kgm.
At this pressure and with a cylinder seasoned by exposing to 24,000 kgm.
there need be no hesitation even in applying the method to accurate
determinations of the compressibility. The correction at 0° and
7500 kgm. has already dropped to 0.6 per cent.

The corrections to apply in determining this maximum correction of

2 per cent are the corrections on the volume of the lower cylinder
brought about by the changes in temperature and pressure. The
volume was found by weighing the lower cylinder when full of mercury.
To be subtracted from this volume was the volume of a copper block

BRIDGA^IAN. — MERCURY UNDER PRESSURE. 411

inserted to reduce to manageableness the total quantity of the kerosene,
and the yolume of the manganin pressure gauge. The volume occupied
by the kerosene increases with pressure both because of the stretching
of the cylinder and the shrinking of the copper and the manganin
gauge. The stretching of the cylinder was calculated by the theory
of elasticity as outlined above. A slight modification of the formula is
necessary because the cylinder carries the end thrust of the pressure.
The total correction for the stretching of the cylinder is 1.4 per cent at
10,000 kgm. The effect of the copper and the small quantity of mica
washers in the insulating plug were assumed to be represented by the
compressibility O.O5I, the compressibility of the copper alone being
O.OeO. This correction amounts to 0.5 per cent at 10,000. Together,
the two effects produce a total change on the effective volume of kero-
sene of 1.00 cm. ^ per 10,000 kgm., on an initial volume of 28.6 cm. ^ The
correction for the thermal dilatation of the lower cylinder was found
from the known dilatation of steel at ordinary pressures, assuming it to
be independent of pressure.

In making the actual measurements, endeavor was made to avoid as
far as possible the small effect of mechanical hysteresis. The set of
readings at —15°, for example, was obtained as follows. The piston dis-
placement was measured with increase of pressure from 3500 to 5800
kgm. with the lower cylinder at -j-20° ; the low^er cylinder was then
cooled to —15°, and the displacement measured from 5800 back to
3500 ; and finally the lower cylinder was warmed again to +20° and
the displacement measured from 3500 to 5800. The difference between
the second curve and the mean of the first and the third, which differed
only very slightly, gives at any one pressure the expansion of the cor-
responding amount of kerosene on passing from —15° to -1-20°, since
the temperature of the upper cylinder was also -|-20°. This difference
was found for a number of pressures for the range 3500 to 5800, and
a smooth curve drawn through these differences. From this curve was
taken the difference corresponding to the freezing pressure of mercury
at —15°. This process was performed for four temperatures, —20°,
15°, —7°, and 0°, and four points were thus determined on the correc-
tion curve. It was not necessary to obtain other points above 0° on
the curve, because the correction was already small at 0° and the
other end of the curve is fixed by definition as passing through the
value zero at 20°. Through these five points, —20° to 20°, another
smooth curve was drawn, giving at any temperature the piston displace-
ment when the amount of kerosene in the lower cylinder passes from
that temperature to -t-20° at the pressure corresponding to the freez-
ing pressure of mercury at that temperature. Finally this curve gave

412

PROCEEDINGS OF THE AMERICAN ACADEMY.

the required percentage correction curve by translating piston displace-
ments into volumes and dividing by the volume of the kerosene in the
lower cylinder at the corresponding pressure as already determined.
The correction curve actually used is shown in Figure 18. It is ob-

-20

-10' 0 10^

TEMPERATURE.

ZQ"

Figure 18. The corrections duo to the thermal dilatation of the trans-
mitting liquid and the elastic deformation of the cyUnder to be applied to the
directly measured change of liquid mercury when it passes to the solid state.

tained by combining with this temperature correction the correction
already determined for the elastic deformation of the upper cylinder.

The correction curve so detennined is not linear, the values being
2.0 per cent at —20°, 0.6') per cent at 0°, and 0 at +20°. The depar-
ture from linearity is evidently due to the decreasing dilatation of the
kerosene under high pressures.

Temperature Correction for the Upper Cylinder. — In the form of appa-
ratus used in this experiment there is one other small correction because
the upper cylinder is exposed to the slightly varying room temperature.
If the room temperature changes during freezing, the observed change

BRIDGMAN. — MERCURY UNDER PRESSURE.

413

of volume is evidently incorrect by the thermal expansion at the partic-
ular pressure of the total quantity of kerosene in the upper cylinder.
The temperature changes were usually very slight. They were made
still smaller at the cylinder itself by enveloping this in a large mass of
cotton batting. The temperature of the cylinder was read with a
thermometer directly in contact with it. The correction demands an
approximate knowledge of the quantity of kerosene in the upper cylin-
der, which was obtained by measurement of the position of the piston.
The thermal dilatation of the kerosene at any given temperature was
found from the correction curve already described, making the justi-
fiable assumption that at constant pressure the dilatation is sensibly
constant over the temperature range. The maximum correction was at
—20°, where the dilatation is a maximum, and where the temperature
variation, 0°.7, happened also to be a maximum. The correction here
was 0.5 per cent. Above 10° the correction was entirely negligible.

Possible Change of State of the Transmitting Liquid. — The effect
of any freezing of the kerosene with contraction during the freezing
of the mercury would be to make the change of volume appear too
large. This possibility was entirely eliminated, however, incidentally
by the measurements determining the thermal dilatation of the
kerosene. At any given temperature these measurements extended
considerably beyond the freezing pressure of the mercury, and no evi-
dence of a change of state with change of volume was found.

Measurements of the Piston Displacement. — These measurements were
made with a Brown and Sharpe micrometer reading to 0.0001 inches.
The measurements were made between a point on the head of the
advancing ram which drives the piston and a fixed point on the frame
of the press against which the cylinder is pressed. There are two pos-
sibilities of error here. One, the most serious, is warping of the entire
frame of the press. Such an effect was detected and may give rise to
discrepancies of 0.002 inch over the entire stroke of 4 inches. It was
obviated by making four measurements of every displacement between
four pairs of points at the four corners of the frame of the press. The
second error may come from elastic deformation of the parts of the
press between the head of the ram and the fixed point on. the frame, so
that the measured change of length does not give the actual piston
displacement. The effect, which is in any event small, was obviated
by taking advantage of the fact that there is considerable friction in
the packings. In virtue of this it is possible to vary the pressure on
the low pressure end of the ram over a considerable range without pro-
ducing motion of the piston, and so without altering the high pressure.
Now it is the pressure on the low pressure end which produces distor-

414 PROCEEDINGS OF THE AMERICAN ACADEMY.

tion in the frame of the press, the cylinder at the high pressure end
taking up in itself the effects of the high pressure. The effect of dis-
tortion in the frame was avoided, therefore, by adjusting the low pres-
sure before every measurement of displacement to the same constant
value for all values of the high pressure in the immediate neighborhood
of the freezing point.

The Pressure Measurements. — The method of measuring these high
pressures, with a discussion of the various sources of error has been
given in another paper. Briefly, the pressures were obtained from the
measured change of resistance of a coil of manganin wire immersed
directly in the kerosene of the pressure chamber which contained the
mercury under investigation. The coils, four of which were used dur-
ing this investigation, were each calibrated separately against an ab-
solute gauge. These were capable of rejjroducing the gauge with as
much accuracy as the gauge itself could be read, which was about 8
kgm./cm.^.

The Data.

The actual determinations by this method extended over about two
months, from Oct. 13 to Dec. 3, 1910. In all, eleven points were de-
termined, from —20° to +18°, both with increasing and decreasing
pressure. The measurements were sandwiched in between similar
ones on water which are to be described in another paper. The ap-
paratus was taken apart and set up a great number of times, both in
the course of the ordinary manipulations attending the experiment
and in making those changes necessary because of the piecemeal ex-
plosion of various parts of the apparatus. There were at least five
such explosions during the experiment ; two lower cylinders being
burst, two ujjper cylinders, and one connecting pipe. The accuracy
of the work is spoken for by the fact that determinations with all these
different groupings of apparatus, including change of the pressure
measuring coils, gave points lying on the same curve. This does not
appear so strikingly from the actual data given, but it must be re-
membered that by far the greater number of measurements during this
time were made on water, where the same independence of the par-
ticular piece of apparatus is also shown. The first five measurements
on mercury were made with different combinations of apparatus ; the
last six were made with the same set up. The equilibrium pressures
found in all eleven sets of readings are equally worthy of acceptance,
but the volume measurements of the first five must be discarded be-
cause the effect of changes of room temperature was not sufficiently
recognized at the time, and no correction was applied for it. The

BRIDGMAN. — MERCURY UNDER PRESSURE.

415

data of the same period for water, however, where the total change of
volume is larger and the correction of less account, give consistent
values for the change of volume also.

First for the equilibrium pressure. This was ordinarily found at
only two points, one with increasing and the other with decreasing

,0.8

CO

LJ

X
o

^rO.B

z

LJ
hi

^0.4
0.

O

2 0.2

o
I-

£L

0.0

27

3i

35

39

PRESSURE. ARBITRARY UNITS.

Figure 19. Shows the discontinuity in the piston displacement during
freezing. (One division on the pressure axis corresponds to 900 kgm.)

pressure, but in order to make sure that this equilibrium pressure was
a perfectly definite quantity, independent of the quantity of mercury
melted, equilibrium was found, during the first two or three runs, with
various proportions of the solid melted. This is shown in Figure 1 9
(Oct. 13), where the piston displacement is plotted against pressure.
The vertical part of the curve shows the period of transition. The
equilibrium pressure thus appears to be the same whether the freezing
is nearly complete or only just begun. It is possible to get much

41G

PROCEEDINGS OF THE AMERICAN ACADEMY.

closer to the upper comer of the curve, as Avill be shown in the magni-
fied diagram later, but the lower corner cannot be approached very
much more closely, because of the subcooling of the liquid mercury.

The data are collected in Table X. and shown in Figure 20. These
data can be subjected to a calculation exactly like that used for the
equilibrium points found by the change of resistance method. A

TABLE X.

Freezing Pressure of Mercury at Different Temperatures by the
Method of Change of Volume.

Temp. C.

Pressure, kgm./ cm. 2.

Observed
during Increase.

Observed
during Decrease.

Observed
Average.

Calculated

[Linear Relation

-|- Deviation

Curve].

0.00

7570

7550

7560

7620

6.37

8905

8895

8900

8890

12.87

10230

10210

10220

10180

18.45

11360

11340

11350

11340

12.88

10130

10150

10140

10180

-19.9

36G0

3660

3060

3700

- 9.8

5610

5570

5590

5680

0.00

7590

7590

7590

7620

9.16

9455

9445

9450

9440

16.4

10910

10910

10910

10900

5.23

8650

8670

8660

8680

straight line was passed through the midst of the points, the deviations
from this line plotted on a large scale, and the best smooth curve drawn
through the deviations. The calculated values were obtained from
this smooth deviation curve and the original straight line. The points
are not so regular here as for the determination by the change of
resistance method, and the best smooth curve is open to greater ques-
tion. The deviations from linearity are nearly twice that found by the
resistance method, namely 140 against 60 kgm. at 12,000. This has

BRIDGMAN. — MERCURY UNDER PRESSURE.

417

as a result that the tangent at the origin as determined here gives a
rise of pressure of 195.5 kgm./cm.^ per degree, against 19G.5 found
before, a difference of 1/2 per cent. The two series are not really so
much different as this would indicate, because the smaller initial slope
of this present series is unduly inflaenced by the very evident greater

G 7 8 3
PRESSURE, KGM/CM* X \ol

Figure 20. The equilibrium curve of liquid and solid mercury obtained
by the change of volume method.

irregularity of the low-temperature points, and is compensated for by
the greater departure from linearity. If we are willing to admit that
the departure from linearity of the resistance measurements is probably
more nearly correct, and apply this departure to the seven determina-
tions by the present method above zero, we shall find as the average
slope 196.3 kgm./cm.^ at the origin, agreeing within 1/10 per cent of
the former value. In the rest of the work of this paper the best value
for the slope at the origin will be taken as 196.4 kgm./cm.'^ per degree,
and the departure from linearity given by the resistance measurements
will be taken as most probably correct.

The changes of volume corresponding to these equilibrium pressures
were all determined with the same set up of apparatus as already ex-
plained. These results are given in Table XL, and plotted against
temperature on an enlarged scale in Figure 21. The observed values
were obtained graphically from figures like Figure 19, drawn on a very
much enlarged scale. For this purpose, it was not necessary to plot
the actual pressures, but the position of the slider on the bridge wire
on which the resistance measurements were made was used instead.
This enables smaller changes of pressure to be measured with accuracy
than could be done in the other way. The absolute gauge against

VOL. XLVII. — 27

418

PROCEEDINGS OF THE AMERICAN ACADEMY.

which the calibration of the resistance was made has a limit of sensi-
tiveness of about 8 kgm./cm.^, while the resistance measurements are
sensitive to about 2 kgm. The scale of the graphical construction
was so enlarged that 1 cm. on the bridge wire goes into 5 cm. on the
diagram, and 0.01 inch piston displacement into 1 cm. on the diagram.

TABLE XI.

Change of Volume of Mercury on Freezing as a Function of the

Freezing Temperature.

Temp. °C.

Av, cm.' per gm.

Observed.

Corrected (1).

Corrected (2)
final.

-19.9

- 9.8
0.0
5.23
9.16
16.40

0.002533
2498
2448
2410
2376
2315

0.002503
2487
2458
2426
2399
2348

0.002515
2492
2454
2426
2399
2348

Ordinarily four points were found on the curve both above and below
the transition point, covering a range of from 500 to 700 kgm. in both
directions. Over this range, and within the errors of reading, the
curve connecting piston displacement with the position of the slider
on the bridge wire was almost without exception linear, and was
drawn in with a ruler. There was no tendency whatever for either
corner of the melting curve to be rounded off, indicating that the
change of state takes place at a single definite temperature and pres-
sure, and affording the best possible evidence of the sufficient purity
of the mercury. To this fact of absolutely sharp freezing is to be
attributed the self-consistency of the results. With water, where there
is some slight rounding off of the corners, the results are not so self-
consistent, although the total change of volume is larger.

The process of correction applied to the observed values is shown in
the table in two steps so as to give an idea of the magnitude of the
corrections. In column (1) the corrections for the thermal dilatation
of the kerosene on passing from the lower to the upper cylinder and

BEIDGMAN. — MERCURY UNDER PRESSURE.

419

the correction for the elastic deformation of the upper cylinder are
both applied. In the second and finally corrected column, the addi-

2.75

^70

2.G5 «?:

2.G0

c»

.00230

2.55 U

2.50

20° 10 0

TEMPERATURE

Figure 21. Shows the change of volume and of internal energy on passing
from the Uquid to the solid. The change of volume curve was directly observed,
and the experimental points are indicated. The change of energy curve was
calculated from the other data.

tional correction for the variation of room temperature is applied.
The sign of this correction changes with the direction of variation.
As appears from the figure, these points are self-consistent, lying on a

°~ zoao
£ laao

I38i)

CM

i I3G.0

-40 -30"

£0

-20" -10 0 10
TEMPERATURE

Figure 22. Shows the slope of the freezing curve as a function of the
equihbrium temperature.

smooth curve to at least the order of accuracy given above, 1 part in
2500, except the point at 9° which is only 1/10 per cent out. The
total displacement of the piston during freezing was about 0.2 inch,
the quantity of mercury used being in the neighborhood of 350 gm.
To obtain the above accuracy, therefore, it was necessary to take ad-
vantage of the utmost capacity of the micrometer, making all the
readings to 0.0001 inch. That the single measurements do enjoy this
degree of accuracy is made evident by a later very much enlarged
figure drawn for the purpose of showing the impossibility of subcooling.

420

PROCEEDINGS OF THE AMERICAN ACADEMY.

It is not claimed, however, that the absolute values at the high pres-
sures have quite so much accuracy as this self-consistency would in-
dicate, since probably the correction for the distortion of the upper
cylinder leaves room for greater uncertainty than this.

S3.20

S

g3.IO

CJ>

3.00

^2.90

H
Z 2.80

32.70

-40 -30 -20 -10° 0" 10° 20°
TEMPERATURE

Figure 23. The latent heat of solid mercury as a function of the equilib-
rium temperature.

It is gratifying to notice that the point determined at atmospheric
pressure by an entirely different method agrees perfectly with the
points found above, making the accuracy of both determinations very
probable.

P'rom these data the latent heat of transformation may be found at
every point of the melting curve by Clapeyron's equation,

All= tAv

dp

All was calculated from this equation at intervals of 10° from — 40°

dp
to -f 20°. -J- was found by adding to the constant value 196.4 kgm.

UT

per degree the correction found from the graphically constructed slope
of the curve showing the departure of the curve from linearity. The
results of this graphical construction are shown in Figure 22. The ab-
solute zero in the calculation was taken as — 278°.l C. The results in
mean gm. cal. per gm. of mercury are shown in Figure 23 and Table XII.

BRIDGMAN. — MERCURY UNDER PRESSURE.

421

The rise ofAE to a probable maximum is the most interesting feature.

The course of this curve is to be explained by the increasingly rapid

drop of A r at high pressures, this drop finally becoming more rapid

dp
than the increase in -j-- and in the absolute temperature.

ar

TABLE XII.

Change of Latent Heat on the Freezing Curve of Hg.

Temperature.

Ay
cm.3 per gm.

dp
dt

gm./cm.2.

Latent Heat

mean gm. cal.

per gm.

°C.

Abs.

-40

233.1

0.002535

196400

2.720

-30

243.1

2526

196500

2.828

-20

253.1

2515

196G00

2.939

-10

263.1

2492

196900

3.025

0

273.1

2454

197600

3.103

+10

283.1

2393

198350

3.149

+20

293.1

2311

199300

3.163

It will be noticed here, as for the change of volume, that the curve
does not give the usually quoted value for the heat of transformation
at— 38°.85, but here also it seems that there is considerable chance
for error in the previous value. The value always given is 2.82, which
was obtained by Person *3 in 1847. As far as can be discovered, this
is the only determination of this quantity which has ever been pub-
lished. Person's method consisted essentially in dropping the frozen
mercury at a temperature of about —42° into the water or turpentine
of a calorimeter, and noting the fall of temperature. The usual cor-
rections for radiation and the heat capacity of the vessel were applied.
The actual heat given to the calorimeter was the sum of the heat
given out by the solid in cooling to the transformation point, the heat
of transformation, and the heat of the liquid in warming to the tem-
perature of the calorimeter. The value Cp = 0.0,333 was assumed to
hold for the liquid over the temperature range. This is probably
nearly correct, but the assumption that Cp for the solid is the same as

« Person, Ann. de Chim. et Phys., 24, 257-264 (1848).

422 PROCEEDINGS OF THE AMERICAN AC/VDEMY.

for the liquid is probably open to greater question. The error intro-
duced by this cannot be very large, however, because of the small
temperature range over which the solid cooled. By far the greatest
possibility of error seems to be in the simple measurement of tempera-
ture. The thermometry of low temperatures must have been in a
chaotic state at the time, judging by the values given by Person for
known fixed temperatures. He gives the value on the air thermometer
of the melting point of mercury as —41°. This point is now known to
be — 08°. 85. He furthermore states that his alcohol thermometer read
higher than a mercury thermometer at — 20°. No statement what-
ever is made as to the corrections applied to the readings of this alco-
hol thermometer. If, however, he did apply the correction of the
mercury thermometer to the alcohol thermometer, then there is still
the possibility of great variation between — 20° and — 40°. The con-
sistent behavior of three calibrated alcohol thermometers which have
been used in this present work indicates a possibility of error of as
much as 3 per cent between — 20° and — 40°.

Person made three determinations of the latent heat, giving 2.77,
2.86, and 2.83, mean 2.82, as against 2.735 found above. The use of
this latter value seems to be justified, therefore, in preference to that
of Person.

Person's value for the latent heat has entered directly into the
determination by Regnault ** in 1849 of the specific heat of solid
mercury. Again the value of Regnault is apparently the only value
which we have of this quantity. The method of Regnault was exactly
the same as that of Person, except that the mercury was initially at
— 77°.7, so that the heat given out by the solid in cooling to the melt-
ing point was a very appreciable part of the total heat given out. In-
cidentally Kegnault's temperature measurement was very probably at
fault as well as Person's, for he gives — 40° as the melting point of
mercury. Regnault made two determinations of the mean specific
heat from — 77°.7 to the melting point, giving 0.0314 and 0.325.
Evidently the effect of a smaller latent heat of melting would be to
give a larger specific heat to the solid. Substituting the value found
above produces a change of 6.5 per cent in the values given by lleg-
nault, giving 0.0334 and 0.0346 respectively, mean 0.0340.

The data used in determining the change of volume may also be
used to give evidence on one point for which they were not intended.
The slope of the curve plotting piston displacement against pressure is
evidently going to be dilferent above and below the melting point be-

** Regnault, Ami. de Chim. et Phys., 26, 268-278 (18i9).

BRIDGMAN. — MERCURY UNDER PRESSURE. 423

cause of the diflFerence in compressibility between the solid and the
liquid mercury. The compressibility of mercury is small in any event,
and here the greater part of the piston displacement is used in com-
pressing the kerosene, so that only rough values can be expected from
the small difference. There is the further complication of the drift in
the temperature of the room. The slope does show a distinct ten-
dency to be less when the solid state is present, but the change is ir-
regular. It can be said, however, that the compressibility of the solid
at the freezing point is less than that of the liquid, the difference being
in the neighborhood of 10 per cent.

The Change of Volume of Mercury o^ Freezing at
Atmospheric Pressure.

It has already been stated that the necessity for redetermining the
change of volume at atmospheric pressure arose from the probable in-
accuracy of the previously accepted value (0.00260 cm.^ per gm.). The
inaccuracy of this number was first suspected when a set of values
found for Ay at different pressures, consistent among themselves to
1/25 per cent, did not extrapolate to within 2 per cent of 0.00260.
Investigation showed that the value 0.00260 is not a direct experi-
mental determination, but is obtained from the difference between the
density of the solid, as found by one observer, and the density of the
liquid as given by another. Since the change of volume is only about
3 per cent of the total volume, the density of both solid and liquid
must be known with an accuracy of sixty times the accuracy desired in
the change of volume. The following short discussion of these previous
experimental determinations will make clear that there are here possi-
bilities of error of fully the indicated magnitude.

The value of the density of the solid seems to be open to by far the
most serious question. The commonly accepted value, in fact the only
value with any claim to accuracy at all, was given by Professor Mallet *5
of the University of Virginia. Tlie method consisted in freezing a
weighed quantity of mercury in a glass bulb, and then determining
the quantity of alcohol necessary to fill the bulb to a fixed mark. The
largest possibility of error seems to be in determining the volume of
the bulb at the freezing temperature of mercury. This was found from
the quantity of mercury filling it at O'' and 100°, using Regnault's
value for the dilatation of mercury, and extrapolating back to the
freezing point. No account at all was taken of the possibility of per-

" Mallet, Proc. Roy. Soc. Lon., 26, 71 (1877).

424 PROCEEDINGS OF THE AMERICAN ACADEMY.

manent changes of volume of the glass hulb after subjecting to 100°.
That there is such an effect, very noticeable, is shown by the change of
zero of glass thermometers after subjecting to a high temperature. No
mention is made of the kind of glass ; if it were an American lead glass,
the effect would be comparatively large. The final value for the den-
sity of the solid as given by Mallet was 14.1932. This is the mean of
three values, 14.1S48, 14.1920, and 14.1929.

The density of liquid mercury at the freezing temperature is given
in Landolt and BiJrnstein's tables as coming from Vicentini and Omo-
dei,*® but the value given by them is as a matter of fact quoted from a
paper of Ayrton and Perry. *^ Their method consisted in reading
simultaneously the same temperatures between 0° and —38°. 85 with a
mercury in glass thermometer and an air thermometer. The readings
of one plotted against the other are stated to be " very nearly linear,"
from which the conclusion is drawn that the dilatation of mercury be-
tween 0° and —38°. 85 has the same constant value as that found by
Regnault to hold between 0° and +100". The density at — 38°.85 is
then calculated from the known density at 0°. No statement whatever
is made as to the degree of accuracy attained, or even as to the direc-
tion in which the plot of the air against the mercury thermometer de-
parts from linearity. However, the fact that one of the conclusions
drawn from the results is that mercury shows no maximum of density
in the neighborhood of the freezing point analogous to water, suggests
that the previous knowledge of this quantity was very imperfect in-
deed, and that the results of Ayrton and Perry themselves are not so
accurate as necessary for the present purpose.

A direct determination of this change of volume with the same ap-
paratus as was used at higher pressures and temperatures would have
been possible, but inconvenient for several reasons. Chief of these was
the difficulty of running a thermostat of the requisite size with suffi-
cient constancy at this low temperature. Furthermore, if a result con-
cordant with the others could be found by an entirely different method,
the results by the two methods would mutually support each other,
making any consistent error in either improbable.

The method used consisted in weighing a known quantity of mercury
under CS2 at different temperatures in the neighborhood of the melting
point. The weight varies with the temperature. When the tempera-
ture passes through the melting temperature, the mercury melts with
increase of volume, and the increased displacement causes a sudden

*6 Vicentini and Omodei, Atti di Torino, 23, 38-43 (1887-1S8S); and 22,
28-47, 712-726.

« Ayrton and Perry, Phil. Mag., 22, 325-327 (1886).

BRIDGMAN. — MERCURY UNDER PRESSURE. 425

change in the weight equal in amount to the weight of the displaced
CS2, that is, equal to the weight of CS2 of volume equal to the change
of volume of the mercury. The only quantities directly concerned are
the discontinuity of the weights and the density of the CS2 at the point
of discontinuity. It is not necessary to know even the temperature
accurately. Any consistent device for indicating changes of tempera-
ture, so that the weight may he plotted as some continuous function of
the temperature on either side of the melting point, is all that is
required.

The temperature was indicated by the resistance of a coil of fine
double silk covered iron wire, wound on a glass core 4 inches long and
placed in kerosene inside a thin- walled brass tube, which was immersed
directly in the CS2 in which the weighings were made. The coil was
not calibrated for absolute temperature, but the resistance could be
measured with an accuracy corresponding to changes of temperature of
0°.002. In addition, the temperature was read on a toluol thermome-
ter, graduated to 0°.l, which was also immersed in the bath. The
readings of the thermometer were taken only to give a check on the
readings of the resistance thermometer, since the thermometer readings
were inaccurate because of varying parallax and the necessity of remov-
ing the thermometer partly from the bath in making the readings.

The cold CS2 in which the mercury was weighed was contained in a
cylindrical Dewar flask, 2 inches in diameter and 12 inches long. The
inside of this was lined with a sheet of celluloid to protect the glass
from being scratched, and inside this a tube of heavy copper tubing,
5/32 inch thick, to promote rapid equalization of the temperature.
The most effective equalization of temperature, however, was provided
by a small turbine stirrer, reaching the entire length of the flask. This
was run constantly between readings, but was naturally stopped while
a weighing was being made. The mercury was contained in a thin
steel shell, 9/16 inch diameter, and 4 inches long, suspended by a fine
iron wire (0.007 inch diameter), from the beam of a sensitive balance
above. The quantity of mercury used was about 140 gm. It was pos-
sible to weigh this to 1/4 milligram, giving an accuracy on the discon-
tinuity of weight on freezing, which was about 0.6 gm., of one part in
2000. In the respect of sensitiveness, the CS2 is probably as convenient
a liquid as could be found, because of the high density and very low
viscosity and surface tension. Provision was made for warming the
bath after each weighing by passing a current through a small heating
coil immersed in the bath.

The experimental procedure was the natural one. The Dewar flask
was first filled with CS2 which had been cooled in another dish with

426 PROCEEDINGS OF THE AMERICAN ACADEMY.

CO2 snow and ether. In this was suspended the steel shell with the
mercury, which had been previously frozen. The temperature was then
raised to about —42°, and readings made at intervals of 0°.5. The
spontaneous rise of temperature of the bath during a weighing was so
small as to introduce no error. During warming, the weight increases
linearly, due to the larger thermal expansion of the CS2 than the mer-
cury. Melting is indicated by a rapid drop in the weight of about
0.6 gm. This drop is not instantaneous, but may extend over 1°.5,
showing temperature lag between the mercury and the bath while the
heat of transformation is being absorbed. Completion of melting is
indicated by resumption of the linear relation between weight and tem-
perature. To find the discontinuity in the weight, it is merely neces-
sary to extrapolate this straight line back to the point at which melting
began.

There are only a few special precautions to observe. The most
likely source of error is the formation of minute cracks in the mercury
when freezing. To obviate this, the mercury was poured into the steel
shell already filled with CS2, so as to ensure filling of all the corners,
and then frozen by placing merely the very bottom of the shell in the
freezing mixture. Freezing took place very slowly and uniformly from
the bottom, the surface of the finally fi-ozen mercury being as perfectly
convex as that of the liquid. Pains had to be taken to scrape away
from time to time the minute quantities of ice condensing on the
suspending wire. This wire was so fine that no correction whatever
had to be applied for the slightly varying depths of immersion during
the course of an experiment. Finally, it was necessary to determine
the density of the CS2 at the freezing temperature separately for each
experiment. This arose from the fact that during the preliminary
work a slight quantity of ether had been accidentally spilled into the
CS2, enough to decrease the density by 1 per cent. This gradually
evaporated, producing a slow rise in the density of the CS2 to a final
steady value. The density was given directly by the loss of weight of
the mercury and steel in the CS2 at the freezing temperature. There
seems no question whatever but that the density of the liquid mercury
at the freezing point is known with the accuracy demanded here, 1
part in 2000, although there may be reasonable question as to whether
its accuracy is 60 times greater, as it must be when used to give the
change of volume by a subtraction. The steel shell was only a small
part of the total weight, and its thermal dilatation is so well known and
so small that there is no danger at all in calculating the density of the
steel at —38°. 85 from the experimentally measured density at room
temperature. The accuracy of this procedure is vouched for by the

BRIDGMAN. — MERCURY UNDER PRESSURE.

427

fact that the density of the CSa when determined by weighing in it a
solid steel cylinder agreed within 1 part in 13,000 with the value found
by weighing in it the steel shell with the mercury.

Five preliminary determinations of the change of volume were made
giving results varying from 0.00253 to 0.00257. The chief cause of

180.990

(80.560

TEMPERATURE, ARBITRARY SCALE,

Figure 24. Shows the readings from wliich was found the change of
volume when mercury melts at atmospheric pressure. The scale above and
to the left refers to the solid mercury, and that below and to the right to the
liquid. The point A indicates the beginning of melting, and the point B
shows the completion of melting.

inaccuracy in these prehminary results was the irregular behavoir of the
resistance thermometer. This was due to the defective insulation of
the enamelled wire used in these first experiments. Replacing the
enamelled wire by silk-covered wire gave perfectly satisfactory results.
Advantage was also taken of this preliminary work to modify slightly
various details of apparatus and procedure.

Three independent determinations of the change of volume were
made with the final form of apparatus. The experimental points of
one of these determinations are shown in Figure 24. The mercury
was changed for each of these determinations, the total quantity being
varied by 10 per cent. The three values found, using the iron resist-
ance as the temperature indicator, were 0.002533, 0.002536, and
0.002532 cm.^ per gm. The same weighings plotted against the ther-
mometer readings (it is to be remembered that this was done merely
as a check) gave 0.002533, 0.002537, and 0.00252 respectively. The
thermometer points of the last determination were very irregular.

428 PROCEEDINGS OF THE AMERICAN ACADEMY.

The resistance points are to be taken as the correct ones, and the
mean of the three determinations, 0.002534, is accepted as the best
value. The departure from tlie previous value, 0.00260, is thus
nearly 3 per cent.

This result may be used to give a more accurate value than that of
Mallet for the density of the solid mercury at the freezing point. As-
suming for the density of the liquid at the freezing point the value of
Ayrton and Perry, 13.690, the density of the solid is found to be
14.182 as against 14.193 of Mallet.

This also enables a correction to be applied to the value of the
coefficient of dilatation of solid mercury as found by Dewar.^^ He
determined the density at —188°. 7 (in liquid air) and from Mallet's
value for the density at the freezing point calculated the coefficient of
thermal dilatation to be 0.0000887 over the range from — 38°. 8 to
—188°. 7. Substituting the above value for that of Mallet gives
0.0000907. Dewar's value for the density of mercury at the tempera-
ture of liquid air seems open to question, however. All of Dewar's
measurements of density at low temperatures depend on his value for
the density of liquid oxygen, which he gives as 1.137. The measure-
ments which he made on ice would seem to show a probable error
here. The value for the thermal dilatation of ice over the range 0° to
— 190° was found to be only half the known value from 0° to —20°.
So large a decrease seems hardly probable. A change in the funda-
mental constant so as to give a higher value to this dilatation would
also give a higher value to the thermal dilatation of mercury. Further-
more, a change in this direction would bring Dewar's value for the
dilatation of mercury into agreement with that of Grunmach,*^ namely,
0.000123 from — 38° to — 80°. This is apparently the only other value
we have. But Grunmach used a dilatometer method in which he made
no correction whatever for the effect of the glass envelope. The value
obtained by him for the change of volume on freezing with the same
apparatus is certainly wrong, namely, 5 per cent as against 3 per cent
found above, and this one fact is enough to cast discredit on the rest
of the work. There seems to be no value, therefore, which can be
accepted at present with confidence for the thermal dilatation of the
solid.

In view of the apparent uncertainty as to the value of the thermal
dilatation of the solid, it may perhaps be allowed to force the above
weighings to give what information they can on this point. It is not

" Dewar, Proc. Roy. Soc. Lon., 70, 237-246 (1902).
« Grunmach, Phys. ZS., 3, 133-136 (1902).

BRIDGMAN. — MERCURY UNDER PRESSURE. 429

expected that the value so obtained can do more than roughly indicate
the probable value, since this use of the data was not contemplated in
the original experiment. The information comes by observing at the
melting point the change in the slope of the curve plotting weights
against temperature. The slope is evidently connected with the
various thermal dilatations.
The exact expression is found to be

The subscript 1 refers to the liquid and 2 to the solid. i>cs. is the

J)
density of the CS2. The value -^ was taken to be 0.0014. This

amounts to assuming the value of the dilatation of CS2 to be 0.001,
which is the value given at 0° by Pierre's formula. There is room for

considerable question here, but the term into which — ^ enters is only

10 per cent of the other term involving the dilatation of the liquid
mercury.

Only the last two of the sets of weighings are available for this cal-
culation, the CS2 having then assumed an unvarying value for the
density. The dilatation of the solid calculated from these two sets
was 0.000165 and 0.000125, mean 0.00014. The value is extremely
rough, but probably as good as either the value of Dewar or Grunmach.

These data also give a rough incidental determination of the density
of CS2 at -38°.85. This was found to be 1.3460. It has been
already mentioned that this is probably slightly in error due to the
presence of a slight impurity of ether, but the above value was the
final value, and remained constant over two days, showing that what
little ether there was had nearly all evaporated. The density as cal-
culated by the third degree formula of Isid. Pierre is 1.3647.50 The
formula of Pierre is intended to hold only for the range 0° to 100°.
The discrepancy suggests at any rate the danger of using the formula
by extrapolation to considerable negative temperatures.

SUBCOOLING AND SUPERHEATING.

All these observations on the freezing and melting of mercury under
pressure also show that one property which apparently holds without

" Pierre, Ann. de Chim. et Phys. (3), 15, 325 (1845).

430

PROCEEDINGS OF THE AMERICAN ACADEMY.

exception at atmospheric pressure also holds under high pressure. This
is the fact that it is impossible to superheat a crystalline phase with
respect to the liquid phase, although the liquid may be subcooled.

SLIDER DISPLACEMENT. MM.

Figure 25. Shows on an enlarged scale the possibility of subcooling the
liquid but the impossibility of superheating the solid. The two curves have
been displaced, the one with respect to the other; the melting and freezing
actually takes place at the same pressure. One division on the pressure axis
corresponds to 40 kgm.

sometimes very considerably, with respect to the solid. Figure 25,
drawn on a very large scale, shows this fact. At the lower corner the
subcooling of the liquid with respect to the solid is shown, while at the
upper corner, where the pressure is decreased on the solid phase, is
shown the sharp change of state when the equilibrium pressure is over-
stepped. The slight irregularities in the points are due to errors of

BRIDGMAN. — MERCURY UNDER PRESSURE. 431

reading, the several points on the vertical part of the curve at decreas-
ing pressure differing among themselves by only 0.05 mm. of bridge
wire, better than the limit of reading, corresponding to pressure differ-
ences of 1 kgm./cm.^. The points plotted are the mean of two readings,
each to 0.1 mm. The same possibility of subcooling was found during
measurements by the change of resistance method.

Attempts to measure the amount of subcooling would have had no
absolute value, for its amount depends on many extraneous factors,
such as the size and shape of the glass capillary, the presence of small
particles of grit in the fluid transmitting pressure, and most important
of all, the element of time. The greatest amount of subcooling found
from the resistance measurements was 230 kgm. at 10°. 2, equivalent to
about l°.l. The mercury remained liquid under these conditions for
about 30 minutes, and did not freeze until the pressure was still fur-
ther increased.

This impossibility of superheating a crystal has been shown to be so
universally true that it is coming to be regarded in the light of a natu-
ral law. It holds whether the liquid melts with increase or decrease
of volume. No satisfactory explanation has yet been given of the fact,
however. Nearly all the explanations suggested, applicable at atmos-
pheric pressure, have attempted to make it in some way a surface
phenomenon, the melting beginning at the free surface and running
in toward the interior. In view of the fact shown above that super-
heating is also impossible under very high pressures, it would seem
somewhat doubtful whether this is the correct method of attack on the
problem. Under high pressures the surface of separation between the
solid and the surrounding liquid (mercury and kerosene, for example)
cannot be thought of properly as a free surface. The molecules of
mercury would seem no more free to assume their natural positions at
this surface than they would in the interior of the mercury itself. This
is particularly probable when it is remembered that the mercury melts
with increase of volume.

Conclusion.

In this conclusion an attempt will be made to show what bearing the
data may have on the theories of the liquid state and on our knowl-
edge of the change of state liquid-solid. As giving the best general
survey of all the data, a diagram is presented showing the isothermal
lines for the liquid and the sudden change on passing to the solid
state. (Plate.) The data from which this figure was constructed
are shown in Table XIII. Within the accuracy of this work the isother-
mals may be taken as equi-spaced, as already explained. The first

432

PROCEEDINGS OF THE AMERICAN ACADEMY.

thing to strike one on looking at the diagram is that the effects are
nearly constant over the entire range ; the compressibility does not
change markedly, nor does the dilatation, and the lines bounding the

TABLE XIII.

Points on the Isothermals of Liquid Hg.
(Computed from Experimental Curves at 0° and 22°.)

Volume

, cm.'.

Pressure,
kgm./cm.'.

—30°.

—20°.

— 10°.

0°.

+10°.

+20°.

0

0.99457

0.99638

0.99819

1.00000

1.00181

1.00362

1000

99207

992S0

99553

0.99626

0.99799

0.99972

2000

98760

98927

99094

99261

99428

0.99593

3000

98581

98743

98905

99067

99232

4000

98245

98403

98561

98719

98877

5000

98077

98231

98385

98540

COOO

97763

97914

9S005

98216

7000

97607

97756

97904

8000

97461

97608

9000

97182

S7327

10000

96915

97059

11000

96806

12000

96567

Change
of vol. on

0.03435

0.03418

0.03388

0.03337

0.03243

0.03142

freezing

Freezing
pressure

1740

3710

5670

7640

9620

11600

domain liquid-solid are nearly parallel. It is evident, therefore, that
any reversal of the ordinary effects or the appearance of critical points
must be far beyond the reach of the diagram. The diagram is com-
petent to show only the initial trend of the various effects.

For the liquid state the results are the same in general as those with

BRIDGMAN. — MERCURY UNDER PRESSURE. 433

which we are familiar for the more compressible liquids under lower
pressures. The compressibility and the dilatation both decrease with
rising pressure. This has as a consequence that the effect of rising
temperature is as usual to increase the compressibility. The behavior
of the specific heats is rather unusual, approximate constancy for Gp
and increase of C^ with pressure. For water, Cp — C^ increases instead
of decreasing. As a little surprising, but not unusual, it may be men-
tioned that the internal energy decreases along an isothermal with in-
creasing pressure, but increases, as is normal, along an adiabatic. This
means that along an isothermal the attractive force between the mole-
cules is still the dominant factor in the situation, even up to 12,000
kgm. At higher pressures a reversal of the effect is indicated, where
the repulsion between the molecules would become the important part.

The data are more suggestive in the light they throw on the change
from the liquid to the solid state. In this connection it may be useful
to outline briefly the present state of the theory, and the points at issue.

For the change of state liquid-vapor, the physical facts have been
worked out pretty fully until we now have a fairly definite understand-
ing of the nature of the process. This increase of knowledge has come
about almost entirely from the experimental side, the one thermody-
namic relation not being of much assistance. In particular, the existence
of the critical phenomena, and the possibility of the continuous pas-
sage from the liquid to the vapor were facts which were unexpected
before the actual experimental proof. There is no thermodynamics
which would predict the existence of such a point. Our present knowl-
edge of the nature of the equilibrium between liquid and solid is in
much the same state as the knowledge of the transformation liquid-
vapor before the discovery of the critical point. The fundamental
question as to whether a critical point exists or not is therefore of
greatest immediate interest.

At present, both the most important theory of the equilibrium between
solid and liquid and the most far reaching experimental work are due
to Tammann.61 The essential part of his theory, as opposed to Ost-
wald,52 Poynting,53 and others, is that for the transition solid-liquid
there is no critical point like that for the transition liquid-vapor. The
reason for this fundamental distinction is to be found in the essential
similarity between a liquid and a vapor on the one hand, and the essen-

'*■ Tammann, loc. cit.

"^ Ostwald, Lehrbufh dor Allgcmeinen Chemie, IF^, Verwandtschaftslchre,

3S9 (Engolmann, Leipzig, 1902).

" PojTiting, Phil. Mag. (.5), 12, 32 (1881).

VOL. XLVII. — 28

434 PROCEEDINGS OF THE AMERICAN ACADEMY.

tial dissimilarity between a liquid and a crystal on the other hand.
The molecules in both the liquid and the vapor are thought of as
arranged at random, " molekular-ungeordnet," the only difference be-
tween liquid and vapor lying in the average distance apart of the mole-
cules. Once let the average distance apart of the molecules appropriate
to the vapor and licjuid become equal, as they do at the critical point,
and all further distinction between the two phases vanishes. In par-
ticular, the heat of transformation vanishes as a consequence of the
equality of the volumes. But for the two phases liquid-crystal, there
is besides the distinction of density the further distinction that in the
crystal the molecules are arranged in some sort of a framework in
space. Equality of density of the two phases liquid and solid does not
mean identity, because the crystal still preserves the regular arrange-
ment of the molecules w'hich cannot hold in the liquid. In conse-
quence, the energy difference between the two phases need not become
zero when the volume difference vanishes ; that is, the heat of trans-
formation does not vanish at the same time with the change of volume,
and we do not have a critical point. Tammann goes further than
simply to deny the existence of a critical point. He concludes from
an examination of all the known data, chiefly his own experiments, that
for substances of the ordinary type of freezing with decrease of volume,
not only do the change of latent heat and the change of volume fail to
pass through the value zero at the same time, but that the change of
volume always becomes zero before the heat of transformation. It is
then an immediate deduction from Clapeyron's equation that the melt-
ing curve has a maximum. That is, there exists for every substance a
temperature so high that no pressure, however intense, will bring the
point of transition as high as this temperature. Above this tempera-
ture the substance is always liquid. This is really the essential part of
Tammann's theory of the shape of the equilibrium curve. It has been
immediately seized upon by geologists, and made the basis of many
speculations as to the state of the interior of the earth, the matter
there being supposed fluid because the temperature is higher than
the maximum.

The experimental evidence in support of this theory is meagre, the
pressure reached by Tammann being sufficient only to show a cur-
vature in the direction demanded by the presence of a maximum,
and an initial decrease toward zero of the change of volume more
rapid than the decrease of the latent heat. The only case in which
Tammann claims to have found a maximum, for Na2SO4l0H2O, must
be ruled out because of the complication introduced in the equilibrium
conditions by the water of crystallization.

BRIDGMAN. — MERCURY UNDER PRESSURE. 435

The evidence of the present data of significance for this question
as to the existence of either a critical point or a maximum are the
slope of the freezing curve, the variation of volume, and the variation
of the latent heat.

The freezing curve is concave toward the pressure axis, which is
curvature in the direction demanded by the presence of a maximum.
This direction of curvature is the same as that shown by all the melt-
ing curves of Tammann, who uses it as an argument tending to show
the existence of a maximum. But the curves liquid- vapor also invar-
iably show the same curvature, and here there is a critical point. It
is also easy for a curve to run to infinite temperature and pressure,
still being concave toward the pressure axis. The direction of curva-
ture would seem to give absolutely no presumptive evidence, therefore,
one way or the other.

The change of volume and the latent heat together may be consid-
ered. The change of volume alone invariably decreases with rising
temperature. This merely means that the phase with the smaller vol-
ume is less compressible. Tammann 's argument consists in showing
that the change of volume decreases along the equilibrium curve,
while the latent heat usually increases, or if it shows a decrease, the
decrease is slight in comparison with the decrease in the change of
volume. The change of volume becomes zero first, therefore, and we
have a maximum freezing temperature.

The curves for A V and the latent heat of this present work on mer-
cury have been already shown. A V decreases with rising temperature,
as it does universally. The latent heat curve is the significant curve,
because it increases apparently to a maximum and seems about to
descend. Tammann's argument would be perfectly valid for the first
6000 or 7000 kgm., but at higher pressures this reversal of the latent
heat curve invalidates the whole thing. There is no reason to antici-
pate that the decrease in A^ beyond 11,000 might not be rapid enough
to make it vanish with A V.

It is interesting in this connection to plot the difference of internal
energy between the solid and the liquid against temperature. The
difference is given by

AE=ATI — pAv.

^E shows the part of the heat of transformation which has been made
potential inside the mass. The Test of this heat goes into performing
mechanical work. The results are shown, with the steps of the calcu-
lation in Table XIV. and in Figure 21, in direct comparison with the
changes of volume. The energy decreases from the start along the

436

PROCEEDINGS OF THE AMERICAN ACADEMY.

equilibrium curve iu such a way that its ratio to Ar is nearly constant.
There seems no particular reason why this is not as significant a quan-
tity on the melting curve as the latent heat. It is true that it does not
enter the equations so simply, but the behavior at the points of special
interest on the melting curve is just as simple as that of A//. At the
critical point, for example, if there is one, where Ay becomes zero, but

TABLE XIV.

The Ch/Vxge op Internal Energy of Mercury on Passing from the
Liquid to the Solid at Different Temperatures.

Temp.
°C.

Pressure,
kgm. /cm.2.

Av
cm.2 per gm.

Work
gm. cal.

Latent
Heat.

i^H-pAv)

gm.
cal. per gm.

-28.66

2000

0.002525

0.118

2.848

2.732

-18.48

4002

2512

.235

2.951

2.717

- 8.31

6005

2486

.350

3.041

2.693

+ 1.87

8018

2443

.459

3.114

2.657

+12.06

10034

2377

.557

3.154

2.599

+22.24

12064

2296

.649

3.165

2.516

-J- remains finite, it is known that A/T" = 0. In this case A.E = 0
dp

also. If the melting curve shows a maximum, which is characterized

(17)

by Av = 0, and -j- = 0, then AH remains finite, as does also AE,

UiT

which in this case equals AIL The trend of AE on the melting curve
would seem therefore to be j ust as valuable an indication as the trend
of AH as to the possible existence of a critical point or a maximum.

The present data offer no evidence, therefore, as to the existence of
a critical point, except to show that if there is one it must be at
pressures higher than can be reached directly. The positive result
is obtained, however, that at high pressures there is a reversal in the
behavior of the latent heat such as to invalidate Tammann's argument
for a maximum.

As opposed to Tammann's argument for the impossibility of the exis-
tence of a critical point solid-liquid, it may be shown that it is
possible to conceive of a molecular mechanism by which the contin-

BRIDGMAN. — MERCURY UNDER PRESSURE. 437

uons passage from the " molekular ungeordnet " assemblage of the
liquid to the regular arrangement of the crystal on a space framework
may be accomplished. We may think of the molecules as cubes, for
example, with intense centers of force at the corners. As the mole-
cules wander past each other in the liquid state, there will be a
tendency for them to linger with the edges or the faces in contact. If
the time during which they so linger in symmetrical positions with
respect to each other becomes appreciable with respect to the total
time, we will have some approach to the properties of a crystal, the
approach becoming closer as the time of contact becomes relatively
greater. And entirely aside from the question of molecular structure,
there seems no difficulty in conceiving that if the temperature and
pressure are varied properly on a cubical crystal, for example, that
the three elastic constants might so change with respect to each
other that two of them should eventually become equal, giving the two
distinctive constants of an isotropic body, and so continuous passage
from a crystalline to an amorphous body.

Summary of Results.

Data have been collected in this paper sufficient to give the p-v-t
surface of the liquid, and the location and magnitude of the dis-
continuity in this surface when the liquid freezes to the solid over a
pressure range of 12,000 kgrn-Zcm.*^, and a temperature range from
— 38°.85 to +20°. Tables of various quantities of thermodynamic in-
terest are given for the liquid; such as the compressibility, the dilata-
tion, the change in the specific heats, the adiabatic compressibility,
the heat of compression, and the change in internal energy both along
an isothermal and along an adiabatic. For the change liquid-solid
the co-ordinates of the melting curve are given, the change of volume,
and the latent heat. The results do not show any behavior in the
liquid at high pressures opposite in character from that which would
be predicted from their trend at lower pressures. But for the change
solid-liquid, it seems that at high pressures there is a change in the
trend of the latent heat which invalidates Tammann's argument for
the existence of a maximum. If either a maximum or a critical point
exist for the transition solid-liquid it is at pressures higher than are at
present open to direct realization. Such a point could not well exist
at less than 50,000 kgrn-ycm.*^.

Apart from the main work of the paper a number of other quantities
relating to mercury have been determined, some of them very roughly,
either by a direct calculation from the new data given here, or else by

438 PROCEEDINGS OF THE AMERICAN ACADEMY,

a recomputation from the data of others, using in this recomputation
some of the improved values found here. These new quantities are: a
more accurate vahie for the density of the solid at —38°. 85, a rough value
for the thermal dilatation and the compressibility of the solid, an im-
proved value for the specific heat of the solid, the electrical resistance
of the liquid up to the freezing pressure, and the resistance of the solid
under pressure, including the pressure and the temperature coefficients.

Finally, the computations made necessary the determination of
another quantity of interest in itself, namely, the compressibility of
steel. This was determined up to 10,000 kgm. and at two temper-
atures, from which the temperature coefficient of compressibility is
found.

Acknowledgement is here made of several liberal appropriations
from the Riimford Fund of the American Academy of Arts and
Sciences with which the expenses of this investigation were partially
defrayed.

Jefferson Physical Laboratory,

Harvard University, Cambridge, Mass.

October, 1911.

Bridgman.— Mercury under Pressure.

CO .

PRESSURE, KGM/CM' X 10 .

Plate. Shows the isothermals at 10° intervals of liquid and BoUd mercury. The upper part of the diagram is for the liquid the lower for the solid. The
initial slope of the isothermals for the solid was not obtained by dkect experiment, but was found approxmiately by a computation.

Proc. Amer. Acad. Arts and Sciences. Vol. XLVII.

Proceedings of the American Academy of Arts and Sciences.
Vol. XLVII. No. 13. — January, 1912.

CONTRIBUTIONS FROM THE JEFFERSON PHYSICAL
LABORATORY, HARVARD UNIVERSITY.

WATER, IN THE LIQUID AND FIVE SOLID FORMS,

UNDER PRESSURE.

By P. W. Bridgman.

With Three Plates.

Investigations on Liqht and Heat made and published with Aid fbom the

RuMFOBD Fund.

CONTRIBUTIONS FROM THE JEFFERSON PHYSICAL
LABORATORY, HARVARD UNIVERSITY.

WATER, IN THE LIQUID AND FIVE SOLID FORMS,

UNDER PRESSURE.

By p. W. Bridgman.

Presented by G. W. Pierce, October, 11, 1911. Received October 6, 1911.

Introduction.

The purpose of this paper is the same as that of the immediately
preceding paper on mercury, — to indicate the nature of the funda-
mental facts which must be taken account of in any theory of liquids
valid for high pressures, and to find something about the nature of the
equilibrium between crystal and liquid. Both of these subjects are as
yet practically untouched. AU present theories of liquids are incom-
petent to explain known facts, and as for the theory of the equilibrium
liquid-solid, even the fundamental facts are unknown. It seems, more-
over, that these two subjects will find their best development side by
side ; one involves the other. Thus, any normal liquid may be made
to crystallize by the application of high pressure. The internal forces
producing crystallization must be present to some extent continuously
in the liquid, modifying its behavior more and more as the crystalliza-
tion point is approached. Yet no present theory of liquids takes ac-
count of these vector forces in the liquid which ultimately produce
crystallization, but supposes instead that the force between molecules is
uniform in every direction.

To be of significance the experimental study must be made over a
comparatively wide pressure range, the order of the pressures being
many fold greater than the pressures involved in the corresponding
study of the liquid- vapor change. The results of this paper reach to
20,500 kgm./cm.^, whereas the highest previous pressure under which
water has been studied was only 3500 kgm.

As compared with mercury, the results for water are much more
varied and richer in suggestion. It is well known that under ordinary
conditions water is abnormal in many respects. The effect of high

442 PROCEEDINGS OF THE AMERICAN ACADE^^5r.

pressure is to wipe out this abnormality. The manner in which the
abnormality disappears with increasing pressure is interesting. Be-
yond the disappearance of abnormality, the pressure has been pushed
far enough to suggest in one or more particulars what the behavior of
any liquid must be under very high pressures. The results with mer-
cury did not suggest this so strongly, because the effect of pressure is
much less on the properties of mercury than on those of water, so that
to produce the effects peculiar to high pressure will require a much
higher pressure for mercury than for water. Corresponding to the
abnormal behavior of the liquid at low pressures, and probably con-
nected with it, the solid also shows abnormal behavior at low pressures,
appearing in no less than five allotropic forms. In addition to these
five forms of ice with known regions of stability, there may possibly be
two others with no domain of stability whatever. All of these forms,
except ordinary ice, are more dense than water. With higher pres-
sures, accompanying the return of the liquid to normality, the tendency
of the solid to take new forms apparently disappears, the modification
of ice stable at high pressures giving indications of being the last form,
corresponding to the completely normal liquid. Here again the last
form of ice has been studied over so wide a range as to suggest what
may be the effects peculiar to high pressure for the equilibrium between
any normal liquid and its solid.

The experimental study of the allotropic forms of ice involves the
mapping of their regions of stability, by locating the transition curves,
whether to the liquid or to some other solid form, and the measure-
ment on these transition lines of the change of volume and the latent
heat of transformation. Five of the six possible stable triple points
have been found, and ten of the eleven possible stable transition lines
of equilibrium have been followed. The sixth triple point and the
eleventh equilibrium line lie at temperatures so low and at pressures
so high that the slowness of the reaction makes them practically impos-
sible to determine.

The methods used gave evidence on other points of interest, such as
the variation in the reaction velocity with changes of temperature and
pressure, the possibility of subcooling or superheating, and the com-
pressibility and dilatation of the solid under pressure.

The data on these different curves are so numerous and bewil-
dering in variety that there is considerable difficulty in choosing the
order of presentation. This difficulty is increased by the fact that the
paper itself was not planned from the beginning, but has been a growth.
The first intention was to measure the isothermal compressibility of
water at 0° and room temperature. The existence of a new modifica-

BRIDGMAN. — WATER UNDER PRESSURE. 443

tion of ice above 0° was not then suspected. When this was discovered
in the course of the compressibility measurements, the plan of the paper
was extended so as to take in the investigation of this new form of ice
over the same temperature range as the compressibility determinations.
The compressibility measurements were then completed and the inves-
tigation of this new form of ice taken up. This led into all the un-
suspected complications of the equilibrium conditions between the five
different forms of ice, which necessitated the expenditure of much more
time than had been anticipated. It then became necessary, for the sake
of completeness, to measure the compressibility of water in its region of
existence as a liquid below 0°. During this work with the various mod-
ifications of ice, experimental familiarity with the possibilities of high
pressure apparatus had been increasing, so that it became possible to ex-
tend the work on the ice first found to nearly twice the pressure range
reached in the compressibility measurements. This is the state of
the work as presented here. To be complete, the compressibility of
water should now be redetermined over an increased temperature range
corresponding to the increased pressure range, but this process of ad-
vancement might be continued indefinitely and a stop has to be made
somewhere. For instance, it would probably be possible with the means
now at hand to measure directly the compressibility and the dilatation
of these various forms of ice, and also the adiabatic compressibility of
the liquid. As it is, the pressures have been pushed far enough on
both the liquid and the solid to indicate what the general nature of the
effects for the highest pressures may be. The pressure required to in-
dicate this is higher for the solid than for the liquid, so that the lack
of complete parallelism between the results for the liquid and the solid
is partly justified.

The order of presentation finally chosen arranges the subject matter
in two parts. The first deals with the compressibility of the liquid at
different temperatures. The second, by far the longer, gives the data
for the different modifications of the solid, including the quantities
involved in the transition solid-solid as well as in the transition solid-
liquid. The order of presentation in the second part will be the natural
order, proceeding systematically fi-om the lower to the higher pressures.

This systematic order was not, as has been stated, the actual order
of the experiment. The existence of another form of ice stable at high
pressures and at temperatures above zero was first discovered by the
anomalous results of the compressibility determinations. The exist-
ence of this form was then made certain by the measurement of the
electrolytic conductivity of very dilute solutions, there being a change
in the conductivity when the transition occurs. Not until then was

444 PROCEEDINGS OF THE AMERICAN ACADEMY.

the present method adopted by which the equilibrium pressure and
change of volume were measured simultaneously, but even with this
new method the curve was followed down, from high temperatures and
pressures to lower temperatures and pressures. The domain of tem-
peratures and pressures in which Tammann worked (up to 3500 kgm.)
was approached with the distinct prejudice, therefore, that Tammann's
work was incorrect, because there seemed no possible connection be-
tween the curves given by Tammann and the curves at the higher
pressures. This prejudice makes more valuable, therefore, the essen-
tial verification of Tammann's work found at the low pressures. The
expected discrepancy was avoided by the remarkable versatility of ice
in appearing in diiferent forms.

The experimental methods are in large part the same as those used
in the preceding paper on mercury. Reference is made to that paper
for detailed discussion. Where new methods have been necessary,
discussion is given here in the appropriate place.

In presenting the data, the aim has been to give enough so that any
one could, if he wished, check the computations for himself Every one
of the original observations, except those marred by obvious accidents,
has been given. The table of contents should, however, enable one to
omit the generally uninteresting discussion of details of methods and
critical examination of data, and proceed to the discussion of the gen-
eral results. In connection with the equilibrium of the different solid
forms, it is suggested that some may find it clearer to read first the short
history of the experiment, the description of the general nature of the
experimental methods, and the description of the manner of appearance
of the new forms of ice given first under the heading " The curve
VI-L," and then under " The curve V-L."

Contents.

Introduction 441

Characteristic Surface of the Liquid 446

The Methods, Particularly that Used below 0° 447

The Data 451

Compressibility at 0° 451

Compressibility at 22° 453

Dilatation below 0° 458

Equilibrium between the Various Solids and the Liquid 462

Discussion of Tammann's Work 463

The Method of the Present Investigation 463

The Numerous Checks on the Accuracy of the Data 465

The I-L Curve 467

The Data, p, t, Av, AH, AE 468

The Initial Compressibility of Ice I 472

BRIDGMAN. — WATER UNDER PRESSURE. 445

The I-III Curve ' 473

The Apparatus for Low Temperatures 474

The Special Method for Measuring Change of Volume .... 476

The Conditions under which III Appears 478

The Data, p, t, Av, AH, AE 481

The III-L Curve 485

The Data, p,t,Av,AH,AE 486

The I-II curve 487

The Order of Experiment — Proof that II is Distinct from III 487

Conditions imder which II Appears 489

The Data, p, t, Av, AH, AE 490

The II-III Curve 493

The Special Method for Points on this Curve, both p, t, and Av 493

The Data, p, t, Av, AH, AE 496

The III-V Curve 497

Conditions under which the Curve may be Realized 497

The data, p, t, Av, AH, AE 499

The II-V Curve 500

General Characteristics of the Curve 500

The Data, p, t, Av, AH, AE 501

The V-L Curve 502

Conditions under which V Appears 502

The Actual Order of Experiment 503

The Data, p, t, Av, AH, AE 508

The V-VI Curve 509

General Characteristics 509

The Data, p, t, Av, AH, AE 512

The VI-L Curve 513

History of the Experiment 513

The Compressibility Measurements 513

Electrolytic Conductivity 514

The Apparatus for the Higher Pressures 516

The Data p, t, Av, AH, AE 518

Correction for Av Points at High Pressures 520

Digression on the Elastic Behavior of the Cylinder under High

Pressures 521

The Difference of Compressibility between Solid and Liquid . 523

The Triple Points 524

Values of p, t, Av, AH, AE, at these Points 524

Are the Various Forms really Solid? 526

Other Possible Forms of Ice 527

Different Modifications of Ice I 527

Another Possible Form at High Pressures 528

Subcooling and Superheating 530

Superheating with Respect to the Liquid Impossible 530

Realization of Unstable Forms, Persistent Nuclei in Solid and Liquid 531

Metastable Limit 532

Reaction Velocity 533

Enormous Variation with the Temperature 534

Compressibility of the Various Forms of Ice 535

446 PROCEEDINGS OF THE AMERICAN ACADEMY.

Volume on the Equilibrium Curves 535

Approximate Compressibility 536

Discussion of the Results 538

For the Liquid 538

The Nature of the Abnormalities of Water already Known . . 540
Compressibility and Dilatation of Water over the Range of this

Paper 541

Table of Volume for Equal Intervals of Pressure and Tem-
perature 539

Change from an Abnormal to a Normal Liquid 541

The IManner of Transition, Particularly below 0° . . . . 543
Comparison of Present Data with Values Extrapolated from

Previous Formulas, Probable Behavior at High Pressures . . 548

Difference of Specific Heats 550

Change of Internal Energy on an Isothermal 551

Adiabatic Compressibility and Temperature Effect of Com-
pression 552

For the Change of State Liquid-Solid 553

The Present Theories of Liquid-Solid; the Points at Issue . . 553
The General Shape of the Various Equilibrium Curves in their

Bearing on this Question 554

The New E\'idence given by the VI-L Curves and the Probable

Course of the Curve at Higher Pressures 555

Bearing on van Laar's Recent Theory 556

For the Change Solid-Solid 557

The Compressibility of "Water.

A complete thermodynamic knowledge of any substance over any
range of temperature and pressure is afforded by a knowledge of the
characteristic equation of the substance over that range (that is, the
relation connecting volume with temperature and pressure), and a
knowledge of the specific heat along some curve of the pressure-
temperature plane not an isothermal. For water, the specific heat is
known in its dependence on temperature at atmospheric pressure, that
is, along a line not an isothermal, so that theoretically all that is
needed for a complete thermodynamic knowledge of water is the
knowledge of the characteristic equation. This knowledge is evidently
given by the change of volume with pressure along various isothermals,
together with the change of volume along some line not an isothermal.
Practically this means that the characteristic equation may be found
by finding the isothermal compressibility at several different tempera-
tures and combining with the known dilatation at atmospheric pressure.

It does not follow, however, that all the thermodynamic data are
given with equal accuracy by the knowledge of these quantities. Thus

BRIDGMAN, — "WATER UNDER PRESSURE. 447

the specific heat, which involves a second derivative of the p-v-t rela-
tion, can evidently be found much less accurately than the compressi-
bility, for example. Therefore, while some hold is obtained by the
data of this paper on all the thermodynamic quantities, some of these
will be found more accurate than others.

Two methods were used in determining the compressibility. The
first is the same as that used in determining the compressibility of
mercury, and has already been fully described and critically discussed
in the previous paper. Briefly, it consists in enclosing the water to be
measured in a steel bottle, communicating at the upper end through a
very fine channel with a mercury reservoir. The bottle and the reser-
voir are completely immersed in a fluid to which pressure is applied.
The water contracts under pressure, mercury from the reservoir runs
in to take its place, falls to the bottom of the bottle, and is weighed
after pressure is removed. Compressibility was measured by this
method at two temperatures, 0° and 22°, and the same method evi-
dently might be used at any temperature above zero. Under pressure,
however, water may exist as the liquid at temperatures considerably
below zero, so that for a complete knowledge of the p-v-t surface of
water, the volume must be measured throughout this extended region.
The method just described is evidently not applicable here without a
troublesome variation of both temperature and pressure together dur-
ing a single measurement, and a second method was adopted.

The second method, which was used to obtain the changes of volume
below zero, assumes as correct the compressibility at zero as found by
the first method. The data given by this second method are the
thermal dilatation from zero at constant pressure for a number of dif-
ferent pressures. Combined with the known volume at zero, this is
evidently sufficient to give the volume at any temperature and pressure.

The apparatus used was the same as that already described in deter-
mining the data on the freezing curve of mercury, and consists of a
lower cylinder placed in a thermostat, and an upper cylinder in which
the pressure is produced by a moving piston. The water under ex-
periment is placed in a cylindrical steel shell in the lower cylinder.
The lower cylinder also contains the manganin resistance coil with
which pressure is measured. The measurements of pressure by this
method have been described in a previous paper. The remainder of
the lower cylinder and the entire upper cylinder is filled with gasolene,
by which pressure is transmitted to the water.

The experimental procedure was as follows. The temperature of
the lower cylinder was maintained at some value below zero by the
thermostat, and the pressure varied over the region of existence of

448 PROCEEDINGS OF THE AMERICAN ACADEMY.

water for this temperature. The piston displacement was plotted as a
function of the pressure for this temperature. The temperature of the
thermostat was then raised by a suitable amount, and the piston displace-
ment found as a function of the pressure for this new temperature.
This was done for four different temperatures, including zero. From
these four curves, with the help of an interpolation for temperature, the
piston displacement may be found for any temperature and pressure in
the region of the liquid water below zero. This displacement was
found at 5° intervals for several different pressures, increasing in steps
of 800 kgm. At each pressure, therefore, the thermal dilatation may
be found by taking the difference between the displacement at the
desired temperature and zero.

If the experiment were performed in the simple manner described,
evidently several very serious errors would be introduced. No account
whatever has been taken of the thermal dilatation of the steel cylinder,
which is not very large, or of the gasolene transmitting the pressure,
which is comparatively more important. These two disturbing effects
were corrected for by two auxiliary experiments. In the first, the lower
cylinder was almost entirely filled with a cylinder of bessemer steel,
and the displacement found for any temperature and pressure of the
region in question, exactly as for water. In the second auxiliary ex-
periment, the lower cylinder was entirely filled with gasolene, and the
displacement found as before. In applying the correction, the entire
interior of the apparatus may be thought of as consisting of two parts ;
one portion is that which would be occupied by the bessemer cylinder,
and the second portion is all the rest, including the remainder of the
lower cylinder and the upper cylinder. It is to be noticed that this
" first part of the volume " is purely fictive : it need not be actually
occupied by the bessemer. In the auxiliary experiment in which the
lower cylinder is filled with gasolene, this " first part of the volume "
is filled with gasolene ; in the actual experiment with water, the " first
part of the volume " is filled partly with the steel of the shell, partly
with water, and partly with enough gasolene to make up the difference.
The advantage in thus thinking of the volume as split up into two
parts is that the second part remains the same in the three experi-
ments. The displacement of the piston at constant pressure due to
change of temperature of the thermostat will evidently include, for " the
second part," the thermal dilatation of the cylinder, and what is impor-
tant, will be independent of the position of the piston in the upper
cylinder, since only the lower cylinder is involved in the change of
temperature. By taking the difference of the apparent dilatations at
constant pressure for the three experiments we shall obtain, therefore,

BRIDGMAN. — WATER UNDER PRESSURE. 449

two dififerences, from which the efiFect of the " second part of the vol-
ume " has been eliminated. These two differences involve the change
of volume with temperature at constant pressure of the material oc-
cupying the same volume that the bessemer steel would have under
the same conditions of temperature and pressure. The quantities en-
tering into the two differences are, therefore, the thermal dilatation of
bessemer steel, of gasolene, and of water at various pressures. Now the
thermal dilatation of bessemer steel is very small comparatively, and
is furthermore known to be little affected by changes of pressure. For
the accuracy required in this work, therefore, the change Of volume of
the steel cylinder, both with temperature and pressure, may be assumed
to be known. This leaves only two unknown quantities in the two
differences mentioned above, so that either may be found. The ther-
mal dilatation of the gasolene is found immediately from the difference
of the displacements of the two auxiliary experiments. It should be
noticed that the dilatation is used here in a sense slightly different
from the usual one in thermodynamics. The quantity given here is the
change in volume in cm.^ for 1° lowering of the temperature of the
quantity of gasolene which at that pressure occupies 1 cm.^. To find
the change of volume of the quantity of gasolene which originally at
0° and atmospheric pressure occupied 1 cm.^ we should need to know in
addition the compressibility of the gasolene. It is an advantage of the
method that it is not necessary to know this compressibility. It ir
now obvious why a knowledge of the compressibility of water at 0° is
necessary. The quantity of water is fixed. As the pressure is raised,
the part of the " first part of the volume " occupied by the water de-
creases in a way known, because the compressibility is known, and the
part occupied by the gasolene correspondingly increases. At any pres-
sure, therefore, the number of cm.^ of gasolene concerned in the total
dilatation of the " first part of the volume " is known, the dilatation
per cm.^, and so the total dilatation of the gasolene is also known, and
therefore the remainder of the total dilatation due to the water is
given immediately.

There are several minor corrections to be considered. The change
of volume as given in cm.^ by the displacement of the piston involves
directly the diameter of the piston. This changes with pressure.
This correction has been already discussed in the mercury paper and
found to be 1.35 per cent for 10,000 kgm. The magnitude is almost
negligible for the present work, but the correction Wias nevertheless
applied in making the computations. Furthermore, the volume swept
out by the piston at constant pressure during a change of temperature
of the lower cylinder does not represent accurately the change of volume

VOL. XLVII. — 29

450 PROCEEDINGS OF THE AMERICAN ACADEMY.

of the material of the lower cylinder. This is due to the fact that the
upper cylinder was kept at the constant temperature of 8° instead of 0°.
For example, let us suppose that the contents of the lower cylinder ex-
pand 1 per cent when the temperature is raised from — 20° to 0°. This 1
per cent passes from the lower cylinder at 0° to the upper cylinder at
8°, and in so doing experiences an additional increase of volume due to
the extra 8". The error introduced by assuming the piston displace-
ment to give the dilatation will be, therefore, in this example, about
0.5 per cent on the dilatation. This error was not corrected for in the
present work, since the accuracy of the largest dilatation found, judg-
ing only from the number of significant figures, was not over 2 per cent.

One experimental source of error did require correction. This is due
to the wearing away of the packing material of the piston by the enor-
mous friction during the advance of the piston. The effect is evidently
the same in its results as a leak, although there was absolutely no leak
of the liquid and only this wearing away of the packing during actual
motion of the piston. The effect was corrected for by making two
runs at every temperature with increasing and decreasing pressure, and
taking the mean. The discrepancy between the displacements during
increasing and decreasing pressure gave the amount of wearing of the
packing. This was of the order of 0.01 inch on a total stroke 3 inches.
The maximum correction was 0.013 inch. This correction was applied
to the next run at higher temperature. The correction so determined
incidentally covers the effect of hysteresis, elastic after-working, or of
viscous yield in the steel, all of which must be very small at these
comparatively low pressures.

The method used in making the calculations from the data was a
combination of arithmetic computation with graphical representation.
The graphical representation alone would not have been accurate
enough. This is because the changes of volume due to temperature
are very small in comparison with those due to changes of pressure in the
region in question, so that it was necessary to retain all the significant
figures given by the measurements. Piston displacement was measured
to 0.0001 inch on a total of 3 inches, but since the pressure measure-
ments were sensitive to only 1 part in 3000, the displacement readings
were retained only to 0.001 inch. The method was to pass the best
parabola through the experimental points at the various constant tem-
peratures ; calculate the displacement given by the parabola at the pres-
sure of the experiment ; plot on an enlarged scale the difference between
the observed displacement and the calculated displacement; pass a
smooth curve through these difference points ; and finally by combin-
ing the results given by the smooth deviation curve with the computed

BRIDGJL^N. — WATER UNDER PRESSURE. 451

values on the parabola, to find the displacements at equal pressure
intervals. This has the advantage of giving a curve perfectly smooth
to the last of the significant figures. Curves thus obtained for the dif-
ferent temperatures were then combined by plotting the displacement
corresponding to the same constant pressure against the temperatures
of the different curves, and smooth curves were drawn through these
points. This last step could be made entirely graphically, since the
change of displacement with temperature at constant pressure is
comparatively slight. From these two sets of smooth curves, the dis-
placement for uniform pressure intervals of 800 kgm. and uniform
temperature intervals of 5° was found over the entire region. These
points were found in this way for each of the three experiments, that
with water and the two auxiliary ones, and the difference of displace-
ment at corresponding pressures and temperatures combined in the
way already described.

The actual data above and below 0° follow. All the details of the
calculation of the compressibility at 0° and 22° by the first method
were the same as that used for determining the compressibility of
mercury. In fact, the two determinations, compressibility of water
and compressibility of mercury, were made at the same time and each
involves the other. It is to be noticed that the various disturbing
factors due to irregularities in the behavior of the steel bottle are much
less important in the case of water than they were in the case of
mercury. This is because of the higher compressibility of water as
compared with that of the mercury. Nevertheless, the effect of these
irregularities was distinctly felt here also, particularly if the pressure
had been allowed to reach so high a value as to freeze the water. The
best results were obtained with piezometers in which the water had
never been allowed to freeze.

At 0"^, four different piezometers were used, one before and after
annealing, so that there are really five independent sets of determi-
nations. Three independent points with a sixth piezometer, No. 1,
were also found, but were not used in the computations, because this
was the very first trial ever made of the method, and the piezometer
had been badly strained by a pressure considerably beyond the freezing
pressure, the existence of which was not then suspected. The actual
data are given in Table I. To afford a comparison of the regularity of
these results as against the values obtained for mercury, the actual
points for the second best piezometer. No. 6, are shown plotted in
Figure 1. If comparison be made with the mercury points it will be
seen that these of Figure 1 are distinctly better. The changes of
volume at even pressure intervals, obtained from smooth curves from

452

PROCEEDINGS OF THE AMERICAN ACADEMY.

the data of each of the five piezometers, is shown in Table II., together
with the weighted means. Finally, the deviation of the weighted
mean from a parabolic formula is plotted against pressure, and a

TABLE I.
Data for Compressibility of Water at 0°.

Pressure,
kgm. _

cm.2

Pressure,
kgm^ .
cm.2

At)

Pressure,
kgm.

cm.2

Ap

Pressure,
kgm. _
cm. 2

Aj)

Piez.

No. 6.

Piez.

No. 7.

Piez.

No. 3.

Piez. No. 5',

2190

0.0795

2190

.0831

5270

0.1467

6810

0.1589

2970

0979

2970

0993

4520

1348

6090

1505

3740

1137

3740

1139

3750

1184

6810

1603

4500

1282

4500

1289

3000

1012

6800

1618

5270

1412

5270

1417

2220

0832

6070

1523

6020

1496

6020

1528

1450

0590

5340

1412

6760

1618

6760

1626

6050

1552

4540

1270

7110

1657

7110

1666

6770

1651

3770

1116

1420

0595

2960

0981

1000

0423

3020

1003

2180
2960

0796
0995

3740
6570

1152
1636

500

0221

2230
1440

0806
0564

3740

1152

6750

1605

Piez.

No. 5.

1050

0421

6570
6750

1624
1629

6010
5260

1524
1416

1410
2180

0.0568
0776

1830
2610

0667
0919

6010

1547

4490

1290

3090

0989

3400

10.52

5260
4490
3740
2950

1429
1301
1151
0985

3740
2950
2200
1410

1139
0978
0786
0547

3740
4500
5290
5270

1265
1265
1391
1365

4140
4910
5680

1208
1366
1457

2200

1410

1000

500

0797
0.561
0420
0226

1000
500

0412
0227

6030
6760
7500

1457
1578

Piez. ]

6750
6050
5260

^0. 1.

0.1710
1501
1408

smooth deviation curve drawn. In only two instances does the smooth
deviation curve fail to pass through the points of the weighted mean.
The value given by this smooth deviation curve is to be taken as the
final value, and is also given in Table II. The change of volume is to

BRIDGMAN. — WATER UNDER PRESSURE.

453

be found at every pressure by combining with the change of volume
calculated by the formula

Av = op + hp^,

where log a = 5.5942 — 10,

and log (- h) = 1.3512 - 10,

the small correction term given by the deviation curve of Figure 2.

PRESSURE, KGM/CM^XIO^

FiouRE 1. The change of volume of water at 0° C. as obtained with pie-
zometer No. 6.

The data for 22° were obtained in exactly the same way. Only
three piezometers were used here instead of five as at 0°. The results
are slightly less irregular, owing to greater familiarity with the method

454

PROCEEDINGS OF THE AMERICAN ACADEMY.

and greater care exercised to keep the maximum pressure below the
freezing pressure. The data are given in Table III. ; the smoothed
values for each piezometer, the weighted means, and the final values

TABLE II.

Compressibility of Water at 0°. Comparison of Best Results with
Different Piezometers, Weighted Mean, and Final Values.

Ai!

Pressure,
kgm./cm.2.

i'o

No. 6.

No. 7.

No. 3.

No. 5.

No. 5'.

Weighted
Mean.

Final
Value.

500

0.0228

0.0222

0.0230

0.0230

0.0218

0.0224

0.0224

1000

0416

0408

0429

0409

0414

0414

0414

1500

0597

0586

0315

0605

0589

0593

0593

2000

0742

0721

0762

0736

0732

0732

0735

2500

0S79

0859

0904

0S60

0866

0869

0869

3000

0997

0992

1030

0967

0977

0994

0991

3500

1095

1099

1142

1068

1072

1097

1097

4000

1192

1193

1246

1168

1174

1195

1195

4500

1286

1288

1339

1253

1261

1287

1287

5000

1374

1375

1419

1333

1359

1374

1374

5500

1453

1454

1490

1407

1438

1452

1452

6000

1524

1523

1551

1474

1509

1520

1520

6500

1591

1589

1600

1541

1569

1586

1586

7000

1659

1652

1640

1600

1622

1644

1644

.6

1.7

.4

.3

.4

Weight

....

in Table IV. The change of volume at any pressure is to be found by
combining with the value given by the formula

where

Av = ap + h})^,
Yoga = 5.5139 - 10,

and

BRIDGMAN. — WATER UNDER PRESSURE.

log(— *) = 1.1239 — 10,

455

the correction given by the deviation curve of Figure 3. It is to be
noticed that both of these formulas, for 0° and 22°, take as the unit
of volume the volume which the given quantity of water occupies under
unit pressure at 0° or 22° respectively. To find the change of volume
of 1 gm. of water, a correction must be applied for thermal dilatation
between 0° and 22°.

W

005
.OOA

2 .OOZ

P J00\

p 0

OC -.001
O -002
H -.003

PBESSURE.KGM/CM'XIO."

Figure 2. The deviation curve for water at 0°. This is to be used in
combination with the formula on page 453 in determining the change of
volume at 0° C.

These data may be compared with those of Amagat ^ (Table V.).
In making this comparison, it must be borne in mind that this is a dis-
proportionally severe test of these data. Values taken from the low
end of a large range cannot be expected to show as small a percentage
of error as will values obtained with apparatus designed only for this
smaller range. In the present work very few actual experimental points
were found below 1000 kgm. ; the lower end of the curve is virtually an

1 Amagat, Ann. de Chim. et Phys. (6), 29, 68-136, 505-574 (1893).

456

PROCEEDINGS OF THE AMERICAN ACADEMY.

extrapolation to a known zero. The values of the present work are, with
only one exception, lower than those of Amagat. The absolute value
of the discrepancy becomes less at the higher pressures, as it should,

TABLE III.
Data for Compressibility of H2O at 22°.

Pressure,
kgm. /cm.2.

Pressure,
kgm. /cm.2.

Vo

Piez. No. 6.

Piez.

No. 7.

1460

0.0522

1460

0.0537

2660

0853

2660

0836

3790

1101

3790

1060

4950

1288

4950

1311

6120

1470

6120

1470

7180

1615

7180

1614

8290

1732

8290

1730

Piez.

No. 9.

3220

0981

3220

0.0978

2170

0732

2170

0730

4350

1206

4350

1202

9530

1889

9530

1999

10930

2041

10930

2046

12250

2619

12250

2612

5700

1458

5700

1469

6740

1571

6740

1612

7830

1708

7830

1754

495

0203

495

0204

995

0391

995

0403

6170

1493

6170

1488

8960

1839

8960

1832

10340

2394

10340

1983

11570

2634

11570

2147

since the comparison with the present values is made under more
favorable conditions at the higher pressures. The fact that the ab-
solute value of the discrepancy tends to become less, not greater,
shows that the fundamental unit of pressure must be essentially the

BRIDGMAN. — WATER UNDER PRESSURE.

457

same for the two determinations. Furthermore, the dilatation between
0° and 22°, as found by taking the difference of the compressions at
0° and 22°, is evidently going to show much less absolute difference
for the two sets of determinations than the compressibilities, suggest-

TABLE IV.

Compressibility op H2O at 22°. Comparison of Best Results with
Different Piezometers, Weighted Mean, and Final Values.

Pressure,
kgm. /cm.2.

Ail
"0 '

No. 6.

No. 7.

No. 9.

Weighted
Mean.

Final Value.

1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
11000

0.0383
0683
0933
1141
1316
1462
1595
1723
1850
1963
2036

0.0379
0667
0914
1123
1304
1460
1594
1702

0.0391
0684
0933
1145
1324
1485
1631
1761
1885
2000
2078

0.0383
0679
0928
1137
1314
1465
1600
1728
1855
1967
2042

0.0383
0679
0928
1137
1314
1465
1600
1728
1855
1967
2042

4

2

1

Weight.

ing that the two sets are each consistent with themselves, since they
show the same temperature effect.

Since this paper was written. Parsons and Cook 2 have published
data for the compressibility of a few liquids up to 4500 atmos. Their
results for water at 4° are shown in Table Ya. compared with the re-
sults of this paper. The agreement is closer than 1 per cent at

2 Parsons and Cook, Proc. Roy. Soc. A, 85, 332-349 (1911).

458

PROCEEDINGS OF THE AMERICAN ACADEMY.

the higher pressures. The results of Parsons and Cook differ from
those of Amagat in the same direction as those found here and by
about twice as much. The values given in the table as the result of
the present work were calculated from the data of Table XXXI. on
page 539.

.010 r

.009

.008^

.007

,006

005

.004^

.003 ;

DOZ ■

.001 ;,

liJ-OOl i

^ -.ooz ;

^-003
> -.004 i

o

»-

a

Cd

o
u

"1

■/

3 4 5 6 7

pressure.kgm/cm'xio:'

;inn':;;i;!rBrit

<3

10

Figure 3. The deviation curve for water at 22°. This is to be used in
combination with the formula on page 454 in determining the change of
volume at 22°.

The results obtained by the second method below 0° next concern
us. To give the original data would occupy so much space as to be
out of the question. The methods and the details of the calculation
have already been described. It is sufficient to give here some infor-
mation about the actual data, and the probable accuracy. Four runs
were made with water, at -15°.8, — 10°.2, — 5°.0, and 0°.0, and dis-
placement and pressure measured at respectively 8, 10, 14, and 17
points. Each of these pressure measurements was the mean of two
readings, and the displacement measurements the mean of four. The
auxiliary experiment with the lower cylinder full of bessemer was also
made at four temperatures : — 17°.7, -12°.2, — 6°.0, and 0°.0, and the
number of points at these temperatures was 14, 15, 13, and 16 respec-
tively. The auxiliary experiment with the lower cylinder full of gaso-

BRIDGMAN. — WATER UNDER PRESSURE.

459

TABLE V.
CoMP.uiisoN OF Results foe Compressibiutt op Water with

THOSE OF AmAGAT.

Aw.

AtO°.

At 22°.

Atmos.

kgm.
cm.2

Amagat.

This
Work.

5.

Amagat. ^hi^s^^

5.

500

1000
1500
2000
2500
3000

516
1033
1549
2086
2583
3099

0.0237
0440
0811
0763
0898
1017

0.0231
0425
0599
0753
0891
1013

- 6
-15
-12
-10

- 7

- 4

0.0216
0402
0565
0710
0839
0957

0.0220
0394
0552
0697
0829
0950

+ 4

- 8
-13
-13
-10

- 7

TABLE Va.

Pressure.

AFat4°.

Atmospheres.

kgm./cm.2.

Parsons
and Cook.

This Work.

0
500
1000
1500
2000
2500
3000
3500
4000
4500

0

516
1033
1549
2066
2583
3099
3615
4132
4648

0.000
0.022
0.042
0.059
0.073
0.086
0.098
0.109
0.120
0.130

0.0000
0.0226
0.0418
0.0591
0.0742
0.0879
0.1002
0.1103
0.1203
0.1306

460

PROCEEDINGS OF THE AMERICAN ACADEMY.

TABLE VI.

Dilatation op Water below 0° — Displacement op Piston at Regular

Intervals of Pressure and Temperature.

Pressure.

Piston Displacement, inches.

Slider Dis-

kgm.
cm. 2

placement,
cm.

-20°.

-15°.

-10°.

-5°.

0°.

Lower cylinder full of water.

3

800

0.642

0.636

0.627

0.623

6

1600

1.137

1.133

1.125

1.112

9

2400

i.542

1.533

1.521

1..508

1.483

12

3200

1.861

1.848

1.834

1.818

1.797

15

4000

2.126

2.118

2.108

2.093

2.073

18

4800

2.342

2.339

2.332

2.307

21

5600

2.544

2.521

24

6400

2.718

Lower cylinder full of bessemer.

3

800

0.427

0.423

0.419

0.415

0.411

6

1600

0.721

0.717

0.712

0.706

0.697

9

2400

0.936

0.9,32

0.927

0.920

0.912

12

3200

1.112

1.110

1.105

1.098

1.089

15

4000

1.268

1.265

1.262

1.2,57

1.251

18

4800

1.402

1.398

1.393

1.387

21

5600

....

....

1.524

1.520

1.516

24

6400

....

....

....

1.629

Lower cylinder full of gasolene

3

800

0.904

0.884

0.8.55

0.818

0.762

6

1600

1.494

1.470

1.442

1.411

1.378

9

2400

1.916

1.893

1.867

1.8,38

1.805

12

3200

2.276

2.2.56

2.228

2.203

2.176

15

4000

2.,554

2.5,38

2.. 520

2.499

2.473

18

4800

2.815

2.797

2.778

2.7,56

2.733

21

5600

3.036

3.023

3.008

2.991

2.971

24

6400

3.177

lene was made at only three temperatures: — 15°.2, — 7°.l, and 0°.0,
with 16, 16, 16 points respectively. All of these points, with very few
exceptions, lay on smooth curves consistently to 0.001 inch.

The results of the graphical computations of displacement and pres-
sure at equispaced points are shown in Table VL The displacement at

BREDGMAN.

WATER UNDER PRESSURE.

461

zero pressure is arbitrary in these tables. The data of these tables, to-
gether with the quantities of steel, water, and gasolene, are sufficient to
enable anyone to check up the computations. The weight of the steel
cylinder filling the lower cylinder was 286.345 gm. The weight of the
steel shell containing the water was 51.818gm. Theweightof the water

TABLE VII.

Dilatation of Water below 0° at Various Pressures.

Pressure,
kgm./cm.2.

Change

of Volume in cm.' per gm. on ch
Temperature to 0^

anging from Tabulated

-20°.

-15°.

—10°.

-5°.

0°.

-0.00173

-0.00057

0

800

-0.00015

00031

00062

0

1600

0.0000

0000

0000

0000

0

2400

0045

0038

0028

0017

0

3200

0052

0043

0029

0017

0

4000

0045

0040

0031

0017

0

4800

0034

0033

0022

0

5600

0023

0

was 26.775 gm. The density of steel was 7.840 at 17°, and it was
assumed that the cubical dilatation of steel was 0.00036 and the cubi-
cal compressibility 0.056 in kgm./cm.^ The volume in cm.' of the bore
of the upper cylinder, 1 inch long, was 4.117 cm.^ With increasing
pressure this increases 1.35 per cent for 10,000 kgm.

The results of the computations firom the data of these tables are
given in Table VII. and Figure 4, showing the proportional change of
the original volume at 0° and atmospheric pressure by which the water
shrinks at various pressures on passing from 0° to the temperature
listed.

From these results, both above and below 0°, the actual volume of the
water for regular pressure and temperature intervals has been found
and is given in Table XXXI. on page 539.

462

PROCEEDINGS OF THE AMERICAN ACADEMY.

C3
>

The Solid Phases of Water — Their Relation to Each Other

AND TO the Liquid.

In order to present these data systematically and clearly, reference
is made at once to the final equilibrium diagram for water and the

solids given at the end of
j)Qso| I 1.1,1 I I this paper. (Plate 1.) It

may produce less confusion
in referring to this diagram
to state briefly the identi-
cal relations which must
be satisfied in every such
diagram. There are three
of these relations. At
every triple point the
relative positions of the
three equilibrium curves
must be such that if any
one is produced into the
region of instability, it
shall fall within the angle
made by the other two. If
one phase is carried into
another by passing across
an equilibrium line at con-
stant pressure from a low
to a high temperature, then
the reaction runs with ab-
sorption of heat. And, if
one phase is carried into
another by passing across
an equilibrium line at constant temperature from a low to a high
pressure, the reaction runs with decrease of volume.

The different branches of the curves will be taken up in order, be-
ginning with I-L,3 I-lII, etc. The data to be given are the freezing
pressure at any given temperature and the change of volume. From
the relation between temperature and pressure on the freezing curve
at different points, the slope may be found, and this, combined with the
change of volume, gives the latent heat by Clapeyron's equation. The
data are presented in this order: observed change of volume, calcu-

5 .6
PRESSURE. HGWl/CM^X lof

FiGUEE 4. This shows as a function of the
pressure the change of volume of water on
passing at constant pressure from 0° to the
temperature indicated on the curves.

^ Throughout, the abbreviation L will be used in referring to the liquid.

BRIDGMAN. — WATER UNDER PRESSURE. 463

lated slope, latent heat, and then other quantities of thermodynamic
interest, such as the work done in passing from one form to the other,
and the change of internal energy.

In the early part of this work up to 3500 kgm. constant reference will
be made to Tammann,* since his are practically the only previous
experiments on ice under pressure. It will be well, therefore, to briefly
outline his work and show where it needs verification or completion.
Tammann's work consisted essentially in following out the equilibrium
curves without systematic measurements of the changes of volume. He
discovered the existence of two new forms of ice (II and III), and
studied their relations to water and ordinary ice (ice I). He obtained
points on the equilibrium curves I-L, III-L, I-III, and I-II. The
change of volume I-III and I-II was measured at a few points without
any very great accuracy. The greatest possibility of question as to
the results is in regard to the equilibrium curves I-III and I-II. Tam-
mann found that these curves cross at —37° and 2200 kgm. Now it is
necessary thermodynamically that a third equilibrium curve should
start from the point of intersection of two equilibrium curves with a
common phase. In this case the predicted equilibrium curve would be
II-III. Tammann found no such curve and even maintained that no
such curve was necessary, claiming that the thermodynamic argument
was valid only when the two phases were present simultaneously, and
that he had never been able experimentally to produce II and III
together. The argument seems inadequate, however, and in this work
the missing curve had been actually found. The other points of differ-
ence between this work and Tammann's are more or less minor in char-
acter ; there seems to be an error in Tammann's pressure measurements
of 100 kgm. at 2000, and he found a curious point of inflection in the
I-L curve, which does not seem actually to exist.

For convenience, the method used will be briefly outlined. It was
essentially the same as that of Tammann, and consists in plotting the
displacement of the piston by which pressure is produced against pres-
sure. Change from one form to the other is accompanied by change of
volume at constant pressure. This change of phase is shown, there-
fore, by a discontinuity in the curve piston-displacement vs. pressure.
The pressure at the point of discontinuity gives the equilibrium pres-
sure and the volume swept out by the piston, which is determined by
the amount of the discontinuity, gives the change of volume on passing
from one phase to the other. The water on which these experiments

* Tammami, Kristallisieren imd Schmelzen, pp. 315-344 (Barth, Leipzig,
1903).

464 PROCEEDINGS OF THE AMERICAN ACADEMY.

were made was placed in a steel shell, open at the top, and completely
surrounded by kerosene or gasolene by which pressure was transmitted.
Pressure was measured by observing the change of resistance of a cali-
brated manganin wire immersed directly in the same chamber with the
water. That the fluid transmitting pressure suffers no change of phase
which is accompanied by change of volume within the limits of meas-
urements was shown by direct experiment. Furthermore, that there
is no reaction under pressure between the water and the oil, which are
directly in contact, was shown by the sharpness of the freezing. See
Figure 31, page 515. The effect of an impurity is to make the discon-
tinuity less abrupt. In order to give additional evidence on this point,
in the course of the experiments the water was placed in shells of steel
or copper, directly in contact with kerosene or gasolene, in glass bulbs
directly in contact with kerosene, and in a glass bulb with a mercury
seal, the water coming in contact only with mercury and glass. The
results in all cases were identical.

Three different forms of apparatus were used according to the tem-
perature range. The first, for the middle range from —25° to -}-20°,
was the same as that used in the work on mercury. It consisted
essentially of two parts: an upper cylinder in which pressure was pro-
duced by an advancing plunger, communicating through a heavy tube
with a lower cylinder containing the water under experiment and the
pressure measuring coil. The lower cylinder was placed in a thermo-
stat. The various sources of error and the corrections have been dis-
cussed in the paper on mercury. One correction had to be determined
anew, since the values used in the mercury paper were not for a cor-
responding range of temperature and pressure. This is the correction
for the thermal dilatation of the kerosene or gasolene which passes
from the lower cylinder at the temperature of the experiment to the
upper cylinder at the temperature of the room. The manner of de-
termining this correction was the same as before. One correction
applied to the results for mercury was avoided here, namely the cor-
rection for the variation in the room temperature. This was made
unnecessary by a water jacket at constant temperature placed around
the upper cylinder.

The second piece of apparatus, for temperatures from —20° to —80'^,
was essentially the same as the first, consisting of two parts. But the
pressures for this temperature range are comparatively low, not reach-
ing over 4000 kgm., so that it was possible to make the lower cylinder
so small (1 inch o. d. by 8 inches long), that it could be placed in a
thermos bottle. The connecting tube was also made much smaller so
as to avoid conduction of heat into the thermos bottle. The method

BRIDGMAN. — WATER UNDER PRESSURE. 465

used in determining the change of vohime had to be modified with this
apparatus, since the reaction was so slow at the low temperatures. It
will be described in detail later.

The third piece of apparatus for higher pressures and temperatures,
0° to 76° and 6000 to 20,500 kgm., consisted of only a single cylinder
containing the water, the measuring coil, and the advancing piston.
For these high pressures it was necessary to use only one piece of
apparatus because of the impossibility of getting tubing to stand these
high pressures over any extended time. The water was placed in a
steel shell surrounded by kerosene as before. The cylinder, together
with the lower part of the hydraulic press by which the piston was
advanced, was placed in a thermostat. In this third form, therefore,
the correction for the change of volume of the transmitting fluid on
passing from one temperature to another is avoided. But at the
higher pressures another correction is introduced because of the slow
yield of the steel. This will be described in its place.

The data given for the ten equilibrium curves were all obtained in-
dependently of each other, at different times, with different fillings of
the apparatus, and in a number of cases with different pieces of ap-
paratus, either new pieces to replace those destroyed by explosions or
pieces of a different type. The consistency of the data obtained under
these various conditions is shown by the very close approximation
with which the identical relations are satisfied by the independent
data of the three curves at each of the three triple points.

At each triple point there are three independent checks. In the
first place, the absolute values of the equilibrium pressures and tem-
peratures are checked by the necessity for the three curves running
together to a point. In the second place, the values of the change of
volume are checked by the obvious condition that at the triple point
I-II-III, for example, the change of volume I-II plus the change
II-III must be equal to the change I-III. The third check is given
by the condition for the latent heats analogous to that for the changes
of volume. This third check involves, besides the values already
given, the values of the slope of the three curves meeting at the triple
point. This third check is the most difficult to meet and the most
sensitive, as it is well known that the derivative of an experimental
curve is subject to much greater error than the curve itself.

Such a triple check is afforded for the data of every one of the ten
equilibrium curves at at least one point : Five of the curves are rendered
still more secure by being tied down at both ends by a triple point, and
the other end of a sixth curve, I-L, is checked by the already known
data for 0°.

VOL. XLVII. — 30

466

PROCEEDINGS OF THE AMERICAN ACADEMY.

In the curves given for A V and the latent heat, the identical re-
lations at the triple point were kept in view. In some cases the curve
given does not seem to be the best possible through the individual
points. The departure from the best curve was occasioned by the
necessity of satisfying the identical relations at the triple point, and

o'

"^

S.-^

s •

n

i

■"s.

■*«.

■\

^

X

\

\

500

1000

1500

2000

PRESSURE, K6M/CM'

Figure 5. The freezing curve of ice I. The dotted line shows the slope at
0° computed by Clapeyron's equation.

the amount of departure gives a pretty good criterion of the self-
consistency of the data for the different curves.

The Curve I-L.

The points on this curve were obtained with the same apparatus as
that used for mercury. No special discussion is necessary. The data
were obtained on three separate occasions : February 2, February 23-24,
and March 15, 191 1. The equilibrium points are shown in Figure 5 and
A F in Figure 6 ; the actual data are given in Table VIII. The first
set is not accurate. It was taken only for fun one evening after the
supply of CaCU for running the thermostat had given out, so that the
temperatures are not sufficiently accurate. These points are not
shown in the diagram.

The second and third sets of readings give the equilibrium points
determined with sufficient accuracy. The second set suffices to give
the general shape of the entire curve, while the third set was taken
with more pains at the lower pressures in order to test more definitely

BRIDGMAN. — WATER UNDER PRESSURE.

467

the existence of a point of inflection at —4° as found by Tammann.
This third set was made with the apparatus directly connected to a
Cailletet pump of the
SocidtdGenevoise,with w
a capacity of 1000
kg./cm.'^. As a check,
the equilibrium pres-
sures as given by the
Bourdon gauge of this
pump are tabulated as
well as the pressures
given by the manganin
resistance. The slide
wire of the Gary Foster
bridge was especially
changed for this ex-
periment, so as to give
greater sensitiveness
in the measurements of
resistance. The read-
ings of the manganin
gauge are to be ac-
cepted as more trust-
worthy than those of
the Bourdon. Within
the limits of accuracy
of the readings, there
seems to be no point
of inflection on the
equilibrium curve as
found by Tammann,
but the curvature is
perfectly regular, in-
creasing more and
more rapidly at the
lower temperatures
and higher pressures.
The point of inflection

found by Tammann may very possibly be due to errors in the pressure
measurements. His values for the pressures in the neighborhood of
2000 are nearly 100 kgm. higher than those found here. The eff'ect
of introducing such an error into the gauge readings at some point on

-20^

-15" -10" -5

TEMPERATURE

Figure 6. The change of volume when ice I
melts to the liquid.

468

PROCEEDINGS OF THE AMERICAN ACADEMY.

the way up would be to give exactly such a point of inflection as he
found.

One check on the accuracy may be obtained from the known slope

TABLE VIII.
Data for the Equilibrium Curve Ice I- Water.

Date.
1911.

Temp.
C.°.

Pressure,

tgm./cm.2.

A

V, cm.3 per gm.

From Re-
sistance
Measure-
ment.

Bourdon
Gauge.

Uncor-
rected.

Corrected
for Dila-
tation of
Gasolene.

Corrected
for Dis-
tortion of
Cylinder.
(Final value.)

Feb. 2

-20.6

-18.7

-14.80

-12.40

2100
1890
1580
1370

23

-20.15

2000

0.1337

0.1312

0.1316

-16.15

1690

1257

1236

1238

24

-12.00

1320

1178

1160

1162

- 7.9

910

1103

1090

1091

- 4.0

520

0991

0980

0980

March 15

- 6.9

- 4.75

- 3.3

- 2.3

788
565
416
281

798
568
418

288

- 1.1

122

121

at 0°, calculated by Clapeyron's equation from the known latent
heat and the change of volume. This slope is given by the equation

dr
dp

a77"

Using the following values : AF = 0.0900, t = 273.1, A^= 79.82
gm. cal., 1 gm. cal. = 42.66 kgm. cm., we find

BRIDGMAN. — WATER UNDER PRESSURE. 469

^ = - 0.00722.

dp

It is to be noticed that this value is lower than the calculated value
usually given. This is because of the low value used for A F, which is
taken from the most recent work of Leduc.^ The effect of this change
is to bring the calculated value into better agreement with experimen-

dr
tal values. Thus Dewar « found recently for -^, 0.0072. The slope

at the origin as just calculated is shown by a dotted line in the diagram.
The agreement is within the limits of error.

Even over this very low pressure range there are practically no other
results to compare these with. Tammann is the only other observer
who has gone to high enough pressures to find the direction of curva-
ture of the curve, which agrees with that found here. Dewar has
published results up to 250 kgm., and stated without publishing the
data that the curve remains linear up to 700 kgm. The departure from
linearity found above is about 6 per cent at 700. Several other ac-
counts have been published of the effect of pressure on the freezing of
ice, but the work has either been done only to a few atmospheres, or
else the work to high pressures has been only qualitative, like that of
Mousson.''

The second set of readings above gives the only determination of the
change of volume made in the present work. The procedure in deter-
mining four of these five points was the same as that used for nearly all
the other determinations with water as well as with mercury. This
consists in plotting piston displacement against pressure during de-
creasing pressure. This has the advantage at higher pressures of
almost entirely eliminating the effect of elastic after-effects in the con-
taining vessel, but this procedure is less essential at lower pressures.
For all ordinary substances this procedure means that the change of
volume is measured during melting and has the advantage that it
gives perfectly sharp values, it being impossible to overrun the melt-
ing curve. But here, due to the fact that ordinary ice is less dense
than the liquid, the method gives the change of volume during freez-
ing instead of melting, so that it is possible to considerably overshoot
the mark before solidification sets in. The change of volume is so
large during freezing, however, that this is no practical disadvantage,
as it is with substances showing a smaller change of volume. The

6 Leduc, C. R., 142, 149-151 (1906).

« Dewar, Proc. Roy. Soc. Lon., 30, 533-538 (1880).

T Mousson, Pogg. Ann., 105, 161-174 (1858).

470 PROCEEDINGS OF THE AMERICAN ACADEMY.

fifth point of the above series was obtained in the inverse way, during
melting, proceeding from low to high pressures. The pressure corre-
sponding to —4° is so low that the elastic after-effect must be small,
but still it is noteworthy that this point shows- the greatest deviation
from the straight line. This inverse procedure at —4° was necessary
in this case because of the low pressures, the friction of the packing
being so great that pressure could not be reduced suihciently below
the equilibrium pressure to induce solidification from the subcooled
liquid when the regular procedure of running from high to low pressures
was adopted.

The correction applied to the change of volume for the thermal dila-
tation of the gasolene (the fluid transmitting pressure in this set of
experiments), was not determined directly at all points of the curve,
but only at the two end points. At 0° the correction is 0.9 per cent,
and at —22° is 2 per cent. The correction was assumed linear for
intermediate points. It makes no difference within the limits of error
whether temperature or pressure is taken as the independent variable
of this linear relation, and there seems little probability that the error
so introduced can exceed this 0.1 per cent. The tables give the values
corrected both for the thermal dilatation of the gasolene and for the
elastic deformation of the cylinder. This latter correction is 0.2 per
cent at the maximum.

The values of A F are shown in Figure 6. The open circles are the
observed points. The solid circle at —22° was not an observed point,
but is the value required at the triple point by the conditions of con-
sistency with the other data. In the AT diagrams for the other
equilibrium curves the values at the triple points are indicated in the
same way.

As an additional check on the values found here there is the known
change of volume at 0° as found by other observers. The recent work
of Leduc seems the most accurate. He gives for the value of the
density of ice at 0°, 0.9176, from which the change of volume is found
to be 0.0900 cm.^ per gm. The value of AV at o° as found by Leduc
is taken as the origin in the diagram. It is seen that the other points
are perfectly consistent with this value, thus confirming the accuracy
of the method. The relation connecting change of volume with tem-
perature is nearly linear, the curve being slightly concave toward the
temperature axis. Four of the points, including Leduc's, lie sensibly
on the curve ; one is 1 per cent too high, and the other 1.5 per cent
too low.

This value of Leduc is higher than that of most other observers, but
the discrepancy seems to be due to occluded air, which Leduc took

BRIDGMAN.

WATER UNDER PRESSURE,

471

particular pains to exclude. In these experiments in which the water
was frozen under pressure, any dissolved air, naturally, can have
only very little effect. Leduc's value, therefore, seems best for this
comparison.

It will be well here to explain the sign convention used uniformly
throughout th6 paper. A change of volume is taken as positive if the

TABLE IX.
Latent Heat, etc., on Equilibrium Curve Ice I-Water.

Temp.
C.°.

•Pressure,
kgm./cm.2.

Av.
cm.'/gm.

dp
dt '

VAV.

gm. cal.
gm.

AH.

(Latent
Heat)
gm. cal.

gm.

AE.

(Change of

internal

Energy)

gm. cal.

gm.

Directly

from
Curves.

Adjusted.

-20

1970

-.1313

74.6

74.0

6.06

57.7

63.6

-15

1590

-.1218

86.0

84.8

4.52

62.5

67.0

-10

1130

-.1122

99.0

98.4

2.96

68.0

71.0

- 5

610

-.1016

116.0

115.5

1.45

73.7

75.1

0

0

-.0900

138.5

138.5

0.00

79.8

79.8

volume increases when the reaction runs in the indicated direction.
Thus A V L-I is positive (water expands when it freezes to ordinary
ice) but A V I-L is negative. Similarly the latent heat. A//, is posi-
tive when heat is absorbed during the reaction, and ^E, the change of
internal energy, is positive when the internal energy increases. AZT
for the reaction L-I is negative, but positive for I-L. In general, as
already explained, A V is positive when the reaction runs from high to
low pressure and A// is positive when the reaction runs from low to
high temperatures.

From the curves giving the equilibrium points and the changes of
volume, the various data needed for computing the latent heat and
the change of internal energy may be obtained. These are given in
Table IX. for even temperature intervals. The values of A T were
taken from the line drawn through the observed points. Two values

of ~ are tabulated. The first set of values was obtained by graphi-
cal construction from the equilibrium curve at different points, these
values of ~ plotted and a smooth curve drawn through them. The

472

PROCEEDINGS OF THE AMERICAN ACADEMY.

first tabulated values

dp

are obtained from this smooth curve.

With these values of — , AZT was calculated. It was then necessary

to adjust the values of A/iT slightly so as to satisfy the identical relations
at the triple point. These new values of AZTare tabulated. The change

in the value of AZT demands a corresponding change in the values of -j-

which are given in the sec-
ond column. These latter
values are to be taken as'the
most probable values. The
difference between the two
columns shows the amount
of adjustment necessary,
and gives an idea of the accu-
racy of the data. Of course,
as already explained, the
slope is very much more sen-
sitive to slight errors than
the observed values of jt?and
t themselves. This same
process of adjustment has
been used on all the equilib-
rium curves. In some cases,

/

y

y/

/

^

/

/

/

80

75 .
70 £

S5<
o

60 o

55

-25"

-20" -15° -10°
TEMPERATURE

-5°

Figure 7. The latent heat and the change

of internal energy on the I-L curve. -, dp . ,,

where ~- is very small, no

change has been necessary. The data of Table IX. are shown graphi-
cally in Figure 7.

The data give some hold on the actual compressibility of the solid
at different points on the equilibrium curve. At 0° this may be cal-
culated without approximation from the observed data. The thermal
dilatation and compressibility of water at 0°, and the thermal dilata-
tion of ice at 0°, are already known. These present data give the
change of A F with temperature and pressure on the equilibrium curve.
These four quantities evidently suffice to determine the compressibility
of the solid at 0°, for we have for small changes of ^:> and t,

where the subscript (1) denotes the liquid and (2) the solid.

BRIDGMAN. — WATER UNDER PRESSURE. 473

A v(p,t) = V, (p,t) - r, 0,0 = A F (0,0) + dj^ [_(j^)- (|,)

--[(tx-c^);j-

This holds for any values of dp and dt. On the equilibrium curve,

and we have

dr = -r- dp,
dp

dAV dAV dr f^^'A , (djA^^

dp ~ dr dp~ \dpjr' \dp J ' dp[_ \dT Jp \ Q^- A J
Everything in this equation is known except ( "^-^ ) •
We have f ?^M = O.O452 kgm./cm.'^ (Amagat),

— , = + O.O3I52 (Vincent),8
dr Jj,

dr

-—- = — 0.00722 [already computed ; see p. 468].

—J— = — 0.00200 [from these experiments].
Substituting these values in the above expression, we find

\dpj.

O.O436.

The compressibility of ice, with the larger volume, is therefore about
1/3 less than the compressibility of the liquid. There seem to be no
published experimental data with which to compare this value.

The Curve I-III.

The existence of this new variety of ice, III, was discovered by Tam-
mann, who obtained it by increasing the pressure on ordinary ice to
about 2500 kgm. at temperatures between —22° and — G0°. The nota-

8 Vincent, Phil. Trans. A, 198, 463-481 (1902).

474 PROCEEDINGS OF THE AMERICAN ACADEMY.

tion used here is the same as that used hy Tammann. In the present
work this variety of ice was found in another way, coming fi'om high to
low pressures at about —22°, and from the domain of stability of a vari-
ety of ice stable only at higher pressures. It was obtained first with
the same apparatus as that used on the I-L curve. Two points on
equilibrium curve I-III and two unsatisfactory measurements of the
change of volume were made with this apparatus, but all the subse-
quent determinations were made with the apparatus especially de-
signed for low temperatures. A short description of this new apparatus
will not be out of place.

This had three different pressure chambers instead of only two as
formerly. The upper cylinder in which pressure was produced by the
advance of the piston was the same as that used before. This was
jacketed with running water from a large tank, so as to be maintained
at a constant temperature. Communicating directly with this, and ex-
posed freely to the air of the room, was a block of nickel steel with
provisions for three connections. In one of these holes for connections
was placed the manganin resistance plug with which pressure was
measured. No temperature correction had to be applied to the readings
of this, therefore. The third connection in the block was to the cylin-
der containing the water to be experimented on. This cylinder was
of hardened nickel steel, 8 inches long, 1 inch o. d., and 1/2 inch
i. d. The water to be experimented on was placed directly in the cylin-
der, nearly filling it. The remainder of the cylinder was filled with
gasolene communicating through the connecting block with the pres-
sure-producing cylinder. Some hesitation was felt at first about al-
lowing the water to completely fill the interior of the cylinder, instead
of being placed in a cyhnder exposed to pressure on all sides. Fear
was felt that the water in freezing might so expand itself against the
sides of the cylinder as to be able to support an appreciable stress, so
that a hydrostatic pressure applied by means of the gasolene to the up-
per part of the frozen ice cylinder would not be transmitted uniformly
to all parts of the mass of ice. In the first few experiments an at-
tempt was made to avoid the possibility of the effect by providing
means for the gasolene to penetrate to the neighborhood of all parts
of the ice. This was done with a tube of very thin sheet copper, closed
at the bottom, but open at the top to the gasolene, placed axially in
the cylinder, and extending throughout the mass of water. The pre-
caution proved needless, however, since there were no discrepancies to
be ascribed to this cause when the device was omitted.

It was necessary to use gasolene as the transmitting fluid because of
the low temperatures. Kerosene becomes too stiff to transmit pres-

BRIDGMAN. — WATER UNDER PRESSURE. 475

sure, and the gasolene itself gave evidence of considerable viscosity at
the lower temperatures. Attempt was made to use a still lighter oil
to avoid altogether this viscosity. Pentane was tried, but after a
number of failures had to be abandoned. There is evidently some ac-
tion under pressure between the pentane and either the water or the
ice. The action seems to be one of solution. In every case water
found its way sooner or later through the long connecting tube to the
manganin resistance coil, where it short-circuited the coil, making
measurements impossible.

The nickel steel cylinder containing the water was supported from
above by means of the connecting pipe in a cylindrical Dewar flask,
2 inches diameter and 10 inches long. The low temperature was ob-
tained with solid COa and ether, or usually CO2 and gasolene, this being
much cheaper and giving nearly as low a temperature as the ether.
No thermostatic regulation was used with the apparatus. The thermal
insulation provided by the bath proved sufficient so that the slight
amount of regulation necessary could be performed from time to time
by hand, by dropping in small masses of solid CO2. The bath liquid
was stirred by blowing bubbles of air into it through a tube reach-
ing to the bottom of the flask. It was possible with very little effort
to keep the temperature constant to 1/2°, which was sufficient for
most requirements, since in the region of these experiments the equi-
librium pressure is affected only slightly by changes in temperature.
Greater constancy of temperature was attained by the exercise of a
little more care when this was necessary.

Temperature was measured with a nickel resistance thermometer.
This was a coil of bare nickel wire wound in spiral grooves on a hard
rubber cylinder, which was immersed in kerosene in a thin, tightly
fitting tube of glass. The top of this tube was carefully stoppered
to prevent the condensation of moisture around the leads. The
glass tube, 3/8 inch o. d., was immersed directly in the temperature
bath. The response to changes of temperature was always very
prompt. The resistance of this wire was measured on the same bridge
wire of the same Carey Foster bridge as that on which the measure-
ments of the resistance of the manganin coil for pressure were made.
Either the nickel or the manganin resistance, with the appropriate
extension coils, could be connected with the bridge wire by two double-
throw mercury switches in paraffin blocks. The temperature was ordi-
narily read both before and after the readings of pressure and piston
displacement. The coil was calibrated by comparison at 0°, —50°, and
—80° with a nickel resistance thermometer of Leeds and Northrup,
which had been calibrated at the Bureau of Standards. The sensitive-

476

PROCEEDINGS OF THE AMERICAN ACADEMY.

ness was sufficient to detect changes of 0°.03. The coil was tested
for permanent changes, elastic after-effects, etc., by frequent calibra-
tions in melting ice at 0°. That it was perfectly satisfactory is shown
by the fact that the zero has not changed by 0°.03 since the coil was
set up.

A special method for determining the change of volume at the low
temperatures was made necessary by the extreme slowness of the reac-
tion. At the higher tempera-
tures, between —20° and —30°,
the reaction runs rapidly enough
so that the ordinary procedure is
available, but at lower tempera-
tures this is not possible. On one
occasion, such an attempt was
made at —70°. After four hours
waiting at a pressure several
hundred kgm. removed fi-om the
equilibrium pressure, the reaction
had not yet shown any signs of
drawing to completion, and the
attempt was given up. The new
method is made possible by the
fact that the equilibrium pressure
is very nearly constant. Figure 8
illustrates the method. The first
part of the process consists in-
getting the change of volume by
the ordinary method at some
temperature where the reaction
runs with convenient rapidity.
This consists in measuring the
piston displacement at constant
temperature at several points on
each side of the equilibrium line indicated at (1), (2), (3), (4), (5), (6).
After reaching (6) the piston displacement is kept constant, but the
temperature is reduced, the water now being in the form of ice III.
The pressure is measured at several points with decreasing temperature
until the point A is reached. The apparatus is so small that complete
temperature equilibrium is attained in at most 5 minutes after chang-
ing the bath temperature. At the point A the pressure is reduced at
constant temperature by changing the displacement, until the point B is
reached, still to the right of the equilibrium line. From B, temperature

n

>

C

n

PRESSURE

Figure S. Shows the cycles described
in finding the change of volume I-III.

BRIDGALiN. — WATER UNDER PRESSURE. 477

is raised at constant displacement to the point C. Here the pressure
is lowered to D, the reaction now running with sufficient speed because
of the higher temperature. From D, two excursions to low and then
back to high temperatures are made exactly as from (6), the water
now being in the form of ice I. The result of all these manoeuvres is
that we have sufficient data to find the displacement corresponding
to any temperature and pressure, and so the displacement on opposite
sides of the equilibrium line corresponding to the two phases I and III,
The difference of this displacement at any temperature is evidently the
same as if the reaction had run at that temperature, but the slowness of
the reaction is avoided. The change of volume is calculated directly
from the difference of displacements as usual. It was in general
necessary to measure the displacement at at least three points on each
side of the equilibrium line, since the relation between displacement
and pressure is not sufficiently linear to allow a linear extrapolation
from two points to the equilibrium line. For greater security, four or
five points were usually taken.

The data are such that they contain internal evidence of their self-
consistency. After a complete cycle like the above, the starting point
ought to be reached again, if there has been no change in the appara-
tus in the meantime. This condition was always approximately ful-
filled, the piston returning within a few thousandths of an inch to the
original position. Failure to return exactly to the starting point is
probably due partly to elastic after-effects in the steel cylinders, and
partly to wearing away of the rubber packing on the end of the piston.
There was never any leak. The slight discrepancy was corrected for
by assuming that it had grown uniformly with the time. It will be
noticed that the cycle as described above is such that the effect of any
such error is at a minimum, since the two paths nearest the equilibrium
curve on either side were described in succession.

The method is applicable here because of the fact that the equilib-
rium lines run so nearly parallel to the lines of constant displacement
that it is possible to approach very near to the equilibrium line over
the entire range. The method evidently would not apply without
modification to points on the I-L curve, for example.

The slowness of the reaction which made necessary a modified method
of determining the change of volume is also evidently going to have its
effect on the equilibrium determinations. At the low temperatures,
the reaction runs so slowly that it requires a very long time for pressure
to return to the equilibrium values, if it has once been changed. The
behavior was such as to give the impression that the equilibrium pres-
sure might never be reached, there being a domain of indifference

478 PROCEEDINGS OF THE AMERICAN ACADEMY.

within which the viscosity is sufficient to keep the reaction from run-
ning, even if the equilibrium conditions are not satisfied. This has been
stated to be the fact by Tammann. The equilibrium points at the low
temperatures were found by approaching as close as practicable to
equilibrium from each side, and taking the mean. The tables of the
actual data show how broad the band of indifference is and how rapidly
it increases in breadth at the low temperatures.

For these determinations with this new piece of apparatus, ice III
was usually obtained from ice I. The procedure was to freeze water to
ice I at a low pressure, and then increase the pressure on ice I at a
temperature in the neighborhood of —30°. It was always necessary to
pass considerably beyond the transition curve before the reaction
started. On several occasions at — 28° the pressure was carried so far
over the I-III curve as to arrive at the prolongation of the I-L curve,
at which melting took place immediately, it never being possible to
carry a solid into the domain of the liquid. I melts to the liquid even
if the liquid is relatively unstable with respect to another solid phase.
At the temperature —28° it was never possible to keep the unstable
liquid long enough to make an accurate determination of the equilib-
rium pressure. The rough values fell within the limits of uncertainty
on the smooth prolongation of the I-L curve. When the phase III
did appear at temperatures above —30°, the reaction from I to III ran
with explosive rapidity. Sometimes it was possible to hear a sharp
click in the apparatus announcing the sudden change of volume.

Aside from the fact that it is possible to pass over the boundary line
between two solid phases without the reaction running, the actual
amount of possible trespassing has little significance. It is changed by
alterations in the size and shape of the containing vessels, is affected
by slight impurities, and most of all depends on the element of time.
It may be mentioned, however, that under pressure the viscosity of the
substances seems to be so great that mechanical shock has little if any
part in starting the reaction, as it does under ordinary circumstances.
It was never found possible to start a reaction from an unstable phase
by smart blows on the outside of the apparatus with a hammer. This
was tried both when the unstable phase was a solid and a liquid.

After the phase III had once been obtained, the other points on the
equilibrium curve were obtained with decreasing temperature. At
every new temperature, the piston was pushed in a little, the pressure
then falling back to the equilibrium value, and then the piston was
withdrawn slightly, pressure rising to the equilibrium value. The
mean of these was taken as the equilibrium pressure. Sometimes at
the higher temperatures, where the reaction velocity is high, equilib-

BRIDGMAN. — WATER UNDER PRESSURE.

479

TABLE X.

Data for the Equilibrium Curve Ice I-Ice III.

Date,
1911.

Temp.
C.°.

Pressure,
kgm.
cm .2

Ay.

cm.'/gm.

Corrected

Value.

Date,
1911.

Temp.
C.°.

Pressure,
kgm.
cm.2

Av.

cm.3,'gm.

Corrected

Value.

Feb. 16

-22.80

2120

-0.1910

April 6

-52.5

2100-

-25.25

2120

-0.1861

-50.0

2110+

Mar. 24

-32.0

2150-

-62.0

2000-

-31.7

2150+

-61.2

2100+

-24.7

2110*

-32.8

2150-

Mar. 29

-33.8

2170-

-32.6

2150+

-28.7

2150+

-26.5

2120*

-26.7

2140V

AprU 18

-27.6

2110+

•

-23.5

2130V

-22.4

-.1831

April 5

-33.4

2170+

-29.1

.1903

-33.0

2160-

-35.7

.1966

-28.1

2150*

-41.7

.1948

-23.1

2140^

-49.6

.2018

-21.5

2140*

-56.6

.2042

April 6

-26.4

2120+

-63.8

.2059

-25.9

2100-

-70.8

.2071

-31.0

2110+

April 20

-23.3

2134*

-30.7

2110-

-24.5

2136*

-38.6

2120-

-27.8

2153*

-38.4

2130+

-31.5

2163*

-43.5

2130-

-37.2

2182*

-42.5

2150+

-46.0

2179*

480 PROCEEDINGS OF THE AMERICAN ACADEMY.

PRESSURE

2000 4000

Figure 9. The various equilibrium curves between I, II, III, V, and the
liquid.

BRIDGMAN. — WATER UNDER PRESSURE. 481

rium was approached from only one side. By proceeding in this way
from high to low temperatures, it was possible to prolong the curve
considerably into the region of stability of 11. A point was thus found
at — 62°.0, showing a subcooling of 28°. If the pressure had been in-
creased on ice I at *his temperature, ice II and not ice III would have
separated out.

The actual data are given in Table X. Those of February 16 were
obtained with the same apparatus as that used for the mercury ; all the
others with the smaller apparatus for lower temperatures. The plus
or minus signs after the pressures show whether the value was ap-
proached from above or below. Three different manganin coils were used
in making the measurements. The data of April 6 were obtained with
a new coil which had not yet been sufficiently seasoned. For this reason
the data of April 6 are slightly in error as to the absolute value of the
pressure, but are competent to show the shape of the equilibrium
curve. The data of April 20, taken with especial care to show the
actual shape of the equilibrium curve, give more significant figures
than one is entitled to for the absolute pressure, but the variation of
pressure is accurately indicated by the figures given.

The equilibrium points are shown in Figure 9, in which are shown
also the other equilibrium curves in the vicinity. The shape of the
curve is given by the points of April 6 and 20, which agree, but the
best value for the absolute pressure is to be given by the mean of
the points at the upper end of the curve. On the same pressure and
temperature scale as the complete diagram for ice and water this
equilibrium curve appears nearly vertical, but on the scale shown here
it is seen to have unmistakable curvature, being concave toward the
temperature axis, and at one part parallel to that axis. At this point
of parallelism, the latent heat of transformation is zero ; above it is
positive, below negative. This point is approximately at —40° and
2150 kgm.

The equilibrium curve I-III as found by Tammann shows the same
general shape, concavity toward the temperature axis. But Tammann's
vertical tangent is between —40° and —50°. The total change of
pressure from the triple point at —22° to the maximum is practically
the same, 50 kgm., but Tammann does not find so pronounced a cur-
vature below the maximum as is found here. On the whole, however,
the agreement in the shape of the curve as found in these two indepen-
dent determinations is as good as could be expected, particularly when
it is remembered that the discrepancies are at the low temperatures
where the reaction runs very slowly. But the actual value of the
pressure as found by Tammann at —22° is higher than that found

VOL. XLVII. — 31

482

PROCEEDINGS OF THE AMERICAN ACADEMY.

here, 2200 against 2115. Tammann's pressure measurements were
made with a Bourdon gauge, which is not accurate at high pressures.
There are two pieces of evidence to show that Tammann's pressures
may be wrong ; the supposed inflection point on the I-L curve, which
has been already mentioned, and the behavior of Uie I-III curve above
the I-II-III triple point, which will be dealt with later.

C3

-.tJOO

UJ

2

5

|j_.190

o

C9

Z
<

-70°

-00° -50° -tO° -30°

TEMPERATURE

•30°

Figure 10. The change of volume III-I.

The values for the change of volume obtained on April 18 with the
method described are given also in Table X., and shown in Figure 10.
The most striking feature is the enormous value of the change, being
about 20 per cent. The values extend into the unstable region over
a temperature interval twice the interval of stability, which is from
—22° to —35°. The values given have been corrected in the usual
way for the elastic distortion of the cylinder and the thermal dilatation
of the gasolene. Owing to the wide temperature range, this latter
correction is unusually large, rising to 6 per cent at the lowest tempera-
tures. The curve drawn through the points is forced a little so as to
give consistent results at the triple points, at —22° passing about 1/4
per cent too low and at —35° 1/4 per cent too high.

The actual procedure in getting these change of volume points was
not exactly the ideal one described above. Below —35°, III is un-
stable, and the reaction to 11 might run at any time. The path 6 A
(Figure 8) was described successfully and two points found on the
lower end of BC before the reaction to II ran. On raising the tempera-

BRIDGMAN. — WATER UNDER PRESSURE.

483

ture above the II-III curve, the reaction ran back to III, so that at
C the phase present was III, as it should be. The line 6 A was per-
fectly straight ; it was assumed, therefore, that the line CB would also
have been perfectly straight if it had been possible to trace it out for
its entire length.

TABLE XI.
Latent Heat, etc., on Equilibrium Curve Ice I-Ice III.

Temp.
C.°.

Pressure,
kgm./cm.2.

cm.^/gm.

dp
dt

pAF.

gm. cal. /gm.

gm. cal./gm.

gm. cal./gm.

-60

2117

.2049

5.4

10.13

-5.5

4.6

-50

2160

.2023

2.0

10.24

-2.1

8.1

-40

2178

.1992

-0.6

10.17

+0.7

10.9

-30

2156

.1919

-3.2

9.69

3.5

13.2

-20

2103

.1773

-5.3

8.74

5.6

14.3

The upper ends of the lines of equal volume for the phase I, that is,
the lines ED and FG above the triple point at — 35°, bear less and less
to the right, and at their extreme upper ends are actually bearing to the
left. This would mean a negative thermal dilatation for ice I at these
temperatures. The effect deserves to be investigated for its own sake.
The effect is so slight as to make very little difference for the purposes
of this paper, however, and it was not investigated further. That
there may be such an effect is borne out by the rather sharp change in
the curvature of the A V curve at the triple point —35°, while the
accuracy of the A V curve is made very probable by the closeness with
which it checks at the two triple points. Pettersson ^ claims to have
found that ordinary ice at atmospheric pressure shows a negative dila-
tation between — 35° and — 25°.

Table XI. gives the values taken from the equilibrium and the
change of volume curves for the various quantities involved in the
determination of the latent heat and the change of energy. The
values of ^E and A// are shown graphically in Figure 11. The in-
ternal energy of III is greater than that of I, and practically all this
change of energy comes from the mechanical work absorbed when I

' Pettersson, Vega Expedition, vol. 2 (1883).

484

PROCEEDINGS OF THE AMERICAN ACADEMY.

6M. CAL. PER GM.

passes to III. The latent heat is small ; above — 40° I absorbs heat on
passing to III, below — 40° it gives out heat.

BRIDGMAN. — WATER UNDER PRESSURE.

485

The Curve III-L.

The points on this curve were more difficult to obtain accurately
than those on any of the other nine equilibrium curves. This is

TABLE XII.
Data for the Equilibrium Curve Ice III-Water.

Date, 1911.

Temperature,
C.°.

Pressure,
kgm. /cm. 2.

AV cm.'/gm.
Corrected Value.

Feb. 1

-18.55

2820

-20.00

2510

-17.95

3110

Feb. 16

-18.40

3000

.0301

March 2

-20.80

2420

.0373

because of the extreme slowness of the
reaction, accounted for in part by the
comparatively small change of volume
and the large heat of reaction. This
does not prevent, however, a fairly
accurate knowledge of the properties
of the curve, since the curve is short,
reaching over only 1500 kgm., and it
is tied down by a triple point at
either end.

The apparatus used for this curve
was that of the mercury determina-
tions, temperature being kept constant
with a thermostat. This was neces-
sary because of the great effect of
temperature on the equilibrium pres-
sure on this curve.

Five points on the equilibrium curve
were obtained, and two on the change
of volume curve. These are shown
in Table XII. and Figures 9 and 12.
The equilibrium points are satisfac-

Y

---\

.045

.040'

.035

5

tiJ

.030^

>

025 u
o

,020

<

X

o

-2^° -20° -18" -16
TEMPERATURE

Figure 12. The change of vol-
ume when III passes to the liquid.

486

PROCEEDINGS OF THE AMERICAN ACADEMY.

tory enough. The greatest difficulty was found with the A V points.
These are evidently irregular, but with the two other known points on
the curve at the triple points, the curve itself cannot be far from that

TABLE XIII.

Latent Heat, etc., on the Equilibrium Curve Ice III-Water.

Temp.
C.°.

Pressure,

kgm.
cm.2

Ay.

cm.'
gm.

dp/dt.

pAV.

gm. cal. _
gm.

AH.

gm. cal.
gm.

A^.

gm. cal
gm.

Directly

from
Curves.

Adjusted.

-22.0
-20.0
-18.5
-17.0

2115

2510
2910
3530

0.0466
.0371
.0.301
.0231

• 180
240
326

450

186
246
320
443

2.31
2.18
2.05
1.90

50.9
54.1

57.4
61.4

48.6

51.9
55.4

59.5

drawn. The relation between temperature and change of volume was
assumed linear within the limits of error.

Three points on this equilibrium curve were found by Tammann.

The shape of his curve agrees
with that found here within the
limits of error, but the absolute
values of the pressure found by
Tammann are higher than those
given, as already explained.
Tammann gives no values for A V
on this curve.

The values deduced from these
curves for All and AE are given
in Table XIII. and in Figure 13.
Very slight changes in the co-
ordinates of points on the equi-
librium curve make enormous
changes in the value of the slope
and AZT. Thus, raising the upper
triple point from — 17°.2 to — 17°.0 changed the calculated value of
AH from 94 to 64. This latter value is taken as the more nearly
correct, because it checks with the other values at the triple point.

-^

65

60 o
cc

UJ

<

50 s
o

45

.22°

-21°

-20° -13° -18
TEMPERATURE.

-17°

Figure 13. The latent heat and the
change of internal energy when III
passes to the Uquid.

BRIDGMAN. — WATER UNDER PRESSURE. 487

even though the V-L curve has to be slightly raised to pass through
the point.

The Curve I-II.

We return now to the curve meeting the I-III curve at the lower
temperatures, the I-II curve. The points on this curve were found
with the low temperature piece of apparatus.

The data, shown in Table XIV., were obtained on five separate occa-
sions with three different manganin resistance coils. The first three
sets, on March 24, 29, and April 5, were obtained before the points on
the I-III curve were obtained at the low temperatures.

The whole investigation at the low temperatures was approached
with the prejudice that Tammann must have been wrong. In particu-
lar, the existence of two separate modifications of ice, II and III, with
only slightly different properties, was thought to be explicable by some
instrumental error. This prejudice was strengthened by Tammann's
failure to find the triple point I-II-III, or any points on the melting
curve of II, although he must have passed over this curve if there were
such a one. His failure to find the II-L curve was difficult to explain
because the reaction from solid to liquid always runs, and in this case
the accompanjdng change of volume is fairly high. The work of the
first three days still further strengthened the impression of error in
Tammann's work. It showed conclusively that there was a modifica-
tion of ice different from III in equilibrium with I at low temperatures,
but seemed to show that this was not the variety supposed by Tam-
mann. The points of the three days all lay on the same curve, which
was headed exactly for the intersection of the I-L and the V-L curves
both prolonged into the region of stability of III. It seemed probable,
therefore, that Tammann's II was nothing but our V in the unstable
region.

The determinations of these two days were made with two different
coils, one a well seasoned one that had been maltreated in many ex-
plosions, and the other a brand new one. After several days' work
suspicion was drawn to these coils and they were checked by measuring
with them the equilibrium pressure on other already well established
curves. Both on the I-III curve and the III-V curve they gave
results consistent with each other but about 100 kgm. higher than the
previous values. There seems no reason to doubt, therefore, that these
coils were both in error and, by a stroke of luck, by the same amount.
This disposed definitely of the idea that the new ice was V subcooled.
The values tabulated are corrected by this quantity 100 kgm. There
seems no reason why these readings should be entirely discarded ; they

488

PROCEEDINGS OF THE AMERICAN ACADEMY.

TABLE XIV.
Data for the Equilibrium Curve Ice I-Ice II.

Date, 1911.

Temp.
C.°.

Pressure,
kgm./cm.'.

Date,
1911.

Temp.

c.°.

Pressure,
kgm. /cm. 2.

AV.

cm.^/gm.
Corrected.

March 25

-64.7

1960

April 5

-63.7

1910+

-66.8

1950

-53.6

2000+

-65.2

1960

-52.2

1970-

-59.2

1900-

April 6

-69.5

2020+

-58.7

1980+

-76.5

1670-

-52.1

1980-

-58.7

1900-

-51.5

2020+

-58.0

2000+

-45.7

2040-

-50.0

2010-

-45.5

2060+

-49.0

2060+

-38.0

2110=^

-40.1

2100-

March 29

-78.8

1690-
1840+

-39.5
-53.4

2120+
2000-

-54.1

1990-

-54.5

2040+

-53.0

2030+

April 18

-36.9

2110=^

-46.7

2050

-35.7

0.2187

-46.4

2070

-41.7

.2172

-40.8

2130-

-49.6

.2169

-40.0

2130+

-56.6

.2159

April 5

-78.8

1780+
1640-

-63.8
-70.8

.2154
.2145

-65.6

1850-

-78.0

.2145

seem perfectly satisfactory in giving the shape of the equilibrium curve,
on which the pressure varies only slightly, even if the absolute value
of the pressure is somewhat high.

BRIDGMAN. — WATER UNDER PRESSURE. 489

The last set of determinations on April 6 and 18 were \vitli still
another coil, a comparatively new one, but one which had been suffi-
ciently seasoned. This coil gave readings consistent with the previous
values on the l-III and II-V curves, and gave the same shape for the
curve as that found with the two previous coils. There seems to be
no question but that these are the correct values.

This variety of ice was obtained by increasing the pressure on I at
low temperatures. The temperatures used here ranged from —65° to
—80°. At —80° it is possible to run as much as 1000 kgm. beyond
the transition curve before the reaction begins to run. Even so far
removed from equilibrium as this, the reaction runs slowly and never
seems to run to completion. The table shows the discrepancies in the
stationary pressures when approached from above and below. The
other points on the curve were obtained with regularly increasing tem-
perature after the lowest. The temperature was raised as high as
—23° to get the last point. The succession of points found in this
way lie on a curve running nearly linearly with increasing temperature
and pressure up to about — 35°, where it turns and proceeds upwards
nearly vertically. This verifies the form found for the curve by
Tammann. This curve as found by Tammann crossed his I-III curve.
Tammann advances as an argument against there being a true triple
point at the point of intersection the experimental fact that it was
possible to start with II at low temperatures, to proceed along the
equilibrium curve with increasing temperature across the I-III curve
into the supposed region of stability of III, and then to retrace one's
steps, following down the original curve into the region of II where the
two curves I-III and II-III are unmistakably different. This possi-
bility, surprising as it seems, was verified also by direct experiment.
The points of April 6 at —40° and —53° on the I-II curve were
separated by points at — 32°.5 and —26°. 5, which are in the supposed
region of stability of III.

The whole mystery is cleared up by the discovery of the II-III equi-
librium curve. It may be permitted to anticipate the results as they
were found on this curve in so far as they are needed to explain the
curious facts found on the I-II curve. In the first place, the existence
of the II-III curve puts beyond question the fact that there are two
varieties of ice, II and III. The point of intersection of the II-III
curve with the I-II and the II-III curves is at —35°, the triple point.
This point is also the point at which the change in direction of the
supposed I-II curve was found. Above this point the modification II
passes into the modification III. The absolute regularity with which
this turning point was found, both here and by Tammann, is to be ex-

490 PROCEEDINGS OF THE AMERICAN ACADEMY.

plained by the experimental fact that it is impossible to superheat II
"with respect to III. In the course of these experiments it has never
been possible to carry II the slightest distance into the region of III,
the reaction running as inevitably as the reaction from a solid to a
liquid when the solid is heated to the melting point. Furthermore
this reaction, when it does run, runs with great velocity, since the tem-
peratures are sufficiently high. The change is furthermore accompa-
nied by a comparatively small change of volume. This evidently
accounts for the curve having been overlooked by Tammann. The
supposed crossing of the two curves I-II and I-III found by Tammann
is to be explained by slight errors in the pressure measurements. The
greatest difference between the curves is 30 kgm. This is the second
bit of evidence alluded to on p. 482, that Tammann's absolute pressure
measurements may be in error. The turning point of the curve found
by Tammann is at the same temperature as that found here, —35°.
The impossibility of superheating II also explains Tammann's inability
to find points on the II-L curve. Apparently it is impossible to reach
this. II appears to be surrounded on all sides by other solid phases.

The behavior of III with respect to II is not the reverse of II
with respect to III. It is possible to subcool III greatly with re-
spect to II. The amount of subcooling possible depends on a va-
riety of factors. One of the most important of these is the interval
of time which has elapsed since the water had previously existed in
the form 11. It is a fact verified repeatedly on all the other curves as
well as on this particular one, that it is very much easier to obtain a
phase after it has once been present in the apparatus. Thus it is pos-
sible to subcool III at least as far as —70° with respect to II, provided
that II has never been formed. But if II has been formed previously,
the reaction from III to II is very likely to run on passing from
the III to the II region. This explains why it is possible to move up
along the II-I curve, pass to the I-III curve, and then on decreasing
temperature pass again to the I-III curve.

The points obtained experimentally have been classified with these
facts in view. The points of March 25, 29, and April 5 obtained at
temperatures above —35° after coming from lower temperatures on
the I-II curve have been listed on the I-III curve in the tables.

The points are plotted in Figure 9. These points are the mean of
the points found with increasing and decreasing pressures at tempera-
tures very close to each other. "Within the limits of error the points
lie on a straight line. The two lowest points are irregular because of
the extreme slowness of the reaction. It is interesting to notice that
the line as drawn is heading straight for the absolute zero, the equilib-

BREDGMAN. — WATER UNDER PRESSURE.

491

rium pressure becoming zero at this temperature. Because of the
slowness of the reaction it would be well nigh impossible to verify this
conjecture experimentally. Except for the constant pressure error al-
ready mentioned, the curve as found by Tammann is of approximately
the same shape as that found here. These figures give a drop in the

-80

-70

-00° -50'

TEMPERATURE

40°

30"

Figure 14. The change of volume when II passes to I.

equilibrium pressure of 360 kgm. between —40° and —80°, whereas
Tammann gives 340 kgm. Tammann does not draw the line as straight,
however, but prefers to make it slightly concave toward the tempera-
ture axis. This would bring the equilibrium temperature at atmos-
pheric pressure up somewhat higher than the absolute zero.

The changes of volume, found by the method already described, are
given in Table XIV., and shown graphically in Figure 14. Because of
the fairly large difference in slope between the equilibrium curve and
the lines of equal volume, the actual cycles described in measuring A V
did not have the exact location shown in Figure 8. The lower parts
of both DE and GF, which were fairly close together, projected over
the equilibrium line into the region of stability of II. The upper end
of the line CB was managed so as to just clear reaching into the region
of I. This evidently introduces no essential error, since the compres-
sibility and dilatation of one phase do not change on passing into the
region of another. The difference merely means a somewhat wider
extrapolation to determine the displacement on the equilibrium curve
corresponding to the phase II, but this disadvantage is offset by the
fact that what was an extrapolation for the phase I has now become an
interpolation.

The change of volume is seen to be linear with temperature (or pres-
sure) within a maximum error of 1/2 per cent. Only one point, that
at —35.7°, shows a discrepancy as much as this, the average departure
from linearity being in the neighborhood of 1/8 per cent.

Tammann gives three values for the change of volume which he lists
as I-II, and two values listed as I-III. One of the supposed I-II values

492

PROCEEDINGS OF THE AMERICAN ACADEMY.

is above —35°, however, so that this must now be tabulated as I-III.
He finds for I-II at -76°, 0.171 em.Vgm., and at -55°, 0.180. These

■75 -65 -60° -55°

-50°

AE

_ I

-aS

-8 2
-10

5 -40° -35 -30° -25

TEMPERATURE

Figure 15. The latent heat and the change of internal energy when I
passes to II.

values are considerably lower than the values found here. Tammann
appears to have overlooked entirely the correction for the thermal dila-

TABLE XV.
Latent Heat, etc., on Equilibrium Curve Ice I-Ice II.

Temp.
C.°.

Pressure,
kgm./cm.2.

Av.
cm.3 /gm.

dp
di'

pAF.

gm. cal./gm.

AH.

gm. cal./gm.

AE.

gm. cal./gm.

-75
-65

-55
-45
-35

1794
1886
1980
2072
2164

0.2146

.2154
.2162
.2170
.2177

8.35
8.35
8.35
8.35
8.35

9.02

9.52

10.03

10.54

11.06

-8.31

-8.77

-9.22

-9.68

-10.15

0.71
0.75
O.Sl
0.86
0.91

tation of the fluid transmitting pressure ; the effect of applying this
correction would be to bring his values still lower. Tammann's results
do agree with the present ones in showing an increase in the change of
volume at higher temperatures, but Tammann finds a rate of increase

BRIDGMAN. — WATER UNDER PRESSURE. 493

four times that found here. Tammann states concerning his own data
that his temperature coefficient is in all probability too high. His value
at —33.5° for the supposed change I-II, but really for I-III, is 0.193
cm./gm. This agrees exactly with the value found here at the same tem-
perature for the known change I-III, giving another bit of evidence from
Tammann' s own data that above— 35° II changes spontaneously to III.
Tammann's value for the change I-III at —45° is 0.192, giving a tem-
perature coefficient of the opposite sign from that found here. The
actual values for the I-III change agree much better with the values
found here than for the I-II change. The present values for I-III are
0.1904 at —32.5° and 0.2005 at —45°.

The data taken from these two curves needed in the calculation of
AZTand A^are shown in Table XV. and Figure 15. I gives out heat
on passing to II and absorbs work. The work is greater than the heat,
so that the internal energy increases on passing from I to II.

The Curve II-III.

This has been already stated to have been the curve overlooked by
Tammann, but demanded thermodynamically. The discovery of it
places beyond question the essential difference between the two varie-
ties of ice II and III. The change of volume on this curve is very
slight, so that it is easy to overlook it altogether, as did Tammann. A
special method had to be used here in determining these equilibrium
points. It is the reverse of the usual method. The usual method
consists in changing the piston displacement and so the pressure at
constant temperature. Change of phase is indicated by change of
displacement with constant pressure. In the modification of the
method used here, the displacement is kept constant and the tempera-
ture changed. The resulting change of pressure is plotted as a func-
tion of the temperature. Change of phase, accompanied by a slight
change of volume, is indicated by a discontinuity in the direction of
the temperature-pressure line.

At any given temperature during this change of phase there is only
one corresponding pressure, the equilibrium pressure, unlike the for-
mer method, where the piston displacement may have any value within
a considerable range corresponding to the same pressure and tempera-
ture. The change of volume is so slight that the interval of discon-
tinuity in the direction of the temperature-pressure line extended over
only 1° and 100 kgm. The method was made practicable by two
things, the smallness of the containing cylinder, resulting in a very
rapid attainment of temperature equilibrium, and the fact already

494 PROCEEDINGS OF THE AMERICAN ACADEMY.

noted, that it is impossible to superheat II with respect to III. Evi-
dently if it had been necessary to superheat II even a single degi'ee in
order to start the reaction, the change of volume would not have been
sufficient to carry the pressure automatically back to the equilibrium
value, and the reaction would have run to completion.

The procedure in getting the points was to start with II at some
pressure and temperature below the equilibrium line, and to raise the
temperature by small intervals. Arrival at the equilibrium line was
shown by an abnormally large rise of pressure. This pressure and
the corresponding temperature gave one point on the equilibrium line.
The reaction was not allowed to run to completion, because of the
difficulty of recovering II after it has once been changed to III, but the
pressure was immediately raised from the equilibrium pressure, bring-
ing the material back into the region of stability of II, and causing the
reverse reaction III-II to run to completion. Another equilibrium
point was then found starting with this higher pressure.

The job was a rather fussy one because of the narrowness of the
critical temperature interval The temperature had to be maintained
by dropping solid CO2 into the DcAvar flask, and some little practice
was necessary before satisfactory results were obtained. Determina-
tions of the curve were made on three occasions. The first two sets
confirm the last set, but sufficient adeptness had not yet been attained
with the method, and the points were discarded.

The final points, four in number, are shown in Table XVI. and Fig-
ure 9. The curve rises with increasing pressure from lower to higher
temperature and is convex upward ; it is terminated at either end by
triple points, at the lower end by the point I-II-III, and at the upper
end by the point II-III-V. This curve is new ; there are no previous
results with which to compare it.

The change of volume determinations were made also with a slightly
modified method. The usual method of measuring piston displace-
ment at constant temperature would have been available if the meas-
urements had been made with decreasing pressure from the region of
II to that of III, but the method was undesirable practically for two
reasons. There was the difficulty of maintaining the temperature in
the Dewar flask constant for a sufficiently long interval of time by
hand, and there was the necessity of running down to the veiy lowest
temperatures in order to recover II for the next determination after
the reaction to III had been allowed to run to completion. This
would have required much time and would have been very wasteful of
solid CO2.

The method used was a modification of that used in finding the I-II

BRroCMAN.

WATER UNDER PRESSURE.

495

and the I-III points, namely, measurement of pressure as a function
of temperature at constant displacement. The chauges II-III and
II-V were measured at the same
time, so that some anticipation is
necessary in describing the method.
The diagram (Figure 16) illustrates
sufficiently the paths described. The
start was made at the point A with
the phase II. The approximately
vertical lines show the paths at con-
stant displacement on which the
pressure, temperature, and displace-
ment are all known. The dotted lines
show the connecting paths on which
it was not necessary to know these
values. The result of describing all
these paths is to give a knowledge
of the displacement corresponding to
any pressure and temperature in
either the region of stability of II or

III or V. The discontinuity of displacement on the three equilibrium
curves can be found immediately, and so the change of volume. It is

PRESSURE

Figure 16. Shows the cycles
described in finding the changes
of volume II-III and II-V.

-35 -33 -31" -29" -U -25"
TEMPERATURE.

Figure 17. The change of volume when II passes to III.

to be noticed that the paths are described in such an order that one
can easily apply the very small correction for wearing away of the
packing or for viscous yield in the steel. The final point B is for the

496

PROCEEDINGS OF THE AMERICAN ACADEMY.

phase 11. The diagram illustrates the impossibility of carrying II
into the region of stability of either III or V, but the possibility of
subcooling both III and V into the region of 11.

TABLE XVI.
Data for the Equilibrium Curve Ice II-Ice III.

]

Date, 1911.

Temperature,
C.°.

Pressure,
kgm./cm.2.

AV.

cm.3/gm.
Corrected.

April 19

-33.4

2290

-31.0

2580

-28.0

2910

-26.0

3220

April 20

2400

0.0188

2710

.0171

3050

.0157

3390

.0152

The experimental values of A V so found are given in Table XVL
and Figure 17. The actual volume of II is seen to be less than that

of III. The percentage
discrepancy of two of the
points may rise as high as
2 per cent, but this means
only a comparatively slight
absolute error, less than 1
part in 2000 on the original
volume. The A V curve is
convex toward the tempera-
ture axis which is unusual.
The values for A^ and
A^ deduced in the usual

Figure 18. The latent heat and the change W are given in Table
of internal energy when II passes to III. XYLL and l^igure 18. Ill

gives out heat on passing
into II and absorbs work. But the mechanical work is comparatively
small, so that the internal energy of II is less than that of III.

-35

-33° -31° -23 -zr
TEMPERATURE

-25

BRIDGMAN. — WATER UNDER PRESSURE.

497

This completes the description of the equilibrium curves of the
varieties of ice already known. This last curve had not been found
before, and the rest of the curves to be described involve either one or
two of the new varieties of ice found at higher pressures.

TABLE XVII.
Latent Heat, etc., on the Equilibrium Curve Ice II-Ice III.

Temp.
C.o.

Pressure,
kgm./cm.2.

AV.

cm.'/gm.

dp/dt.

pAV.

gm. cal.
gm.

AH.

gm. cal.
gm.

AE.

gm. cal.
gm.

From
Curve.

Adjusted.

-34.0

2230

0.0206

100

107

-1.08

12.4

11.3

-3L0

2530

.0179

125

130

-1.06

13.2

12.1

-28.0

2910

.0164

152

154

-1.12

14.5

13.4

-25.0

3370

.0148

184

189

-1.17

16.3

15.1

The CunvE III-V."

The points on this curve were usually obtained from above, coming
from the region of stability of V into that of III. The reaction does
not usually run of itself at temperatures above — 25^; between —25°
and —18° it is usually possible to reduce the pressure on V as far as
the V-L curve, where V melts completely to water without the appear-
ance of III. Below —25°, however. III is pretty certain to separate
from V on passing slightly beyond the equilibrium curve. The points
were usually obtained first at low temperatures and then at higher.
Proceeding in this way it is easy to get the changes of volume also,
although this did necessitate the reaction running to completion,
because the reactions on this curve proved particularly sensitive to the
previous appearance of the phase desired. If III and V had both been
present recently, the reaction would run almost immediately, in either
direction, at any temperature, on passing over the transition curve.

It has been already noticed that it is possible to carry both III and
V do^ATi into the region of stability of II. Corresponding to this pos-
sibility we have the realization of the prolongation of the unstable curve
III-V into the region of II. A point on this curve has been found at

" For the notation V instead of IV for this new variety of ice, see p. 528.
VOL. XLVII. — 32

498

PROCEEDINGS OF THE AMERICAN ACADEMY.

—35°. The change in reaction velocity between III and V at different
temperatures shows a greater and more striking change than that on
any of the other curves. At the upper end, in the neighborhood of
—20°, the velocity is explosive. It is possible to withdraw the piston

TABLE XVIII.
Data for the Equilibrium Curve Ice III-Ice V.

Date, 1911.

Temperature,
C.°.

Pressure,
kgm./cm.2.

AV.

cm.3/gm.

Corrected Value.

Feb. 1

-25.05

3460

-24.20

3460

-23.00

3500

-21.50

3500

-20.30

3500

-18.35

3500

Feb. 16

-25.25

3510

0.0541

-22.80

3510

547

-20.40

3520

546

-18.40

3550

547

April 20

-22.1

3549

-19.4

3559

-24.4

3542

-29.0

3527

-35.3

3514

-23.0

.0570

by an amount corresponding to nearly the entire volume change of the
reaction, and not be able to detect any change at all in the pressure,
so rapidly does the change occur. While only 15° lower, at —35° the
reaction runs so slowly that the attaining of complete equilibrium is a
matter of several hours. This is the reason that the attempt was not
made to prolong the equilibrium curve further. It is evident that we

BRIDGMAN. — "WATER UNDER PRESSURE.

499

have here something entirely different from the mechanism of ordinary
chemical reactions which produces change of reaction velocity with tem-
perature. For chemical reactions

-30

-15

the temperature coefficient of
velocity is almost universally in
the neighborhood of 100 per
cent for 10°, a value enormously
lower than that found here.

The actual determination of
the equilibrium points was made
on three occasions, February .1
and 16, and April 20. The first
two were with the apparatus for
the middle temperature range,

that used with the mercury. These were made with the thermostat to
keep the temperature constant. This apparatus was. also used to give
the changes of volume. The data of April 20 were taken with the low
temperature apparatus. The particular object of this latter set was

TABLE XIX.
Latent Heat, etc., on Equilibbitjm Cttrve, Ice III-Ice V.

-£5 -20

TEMPERATURE.

Figure. 19. The change of volume
when V passes to III.

Temperature,
C.°.

Pressure,
kgin./cm.2.

AV.

cm.3/gm.

dp
dt'

gm. cal./gm.

AH.

gm. cal./gm.

AE.
gm. cal./gm.

-35.0

3470

0.05446

2.75

4.43

-0.83

3.60

-30.0

3495

5454

2.75

4.46

-0.85

3.61

-25.0

3508

5461

2.75

4.49

-0.87

3.62

-20.0

3522

5469

2.75

4.51

-0.89

3.62

to obtain as accurately as possible the slope of the transformation
curve, the previous data having shown that it was nearly vertical-

The equilibrium points are shown in Table XVIII. and Figure 9.
The slope of the equilibrium curve is the slope given by the data of
April 20, but the absolute value of the pressure as given by the mean
of the other points is more likely to be correct. The equilibrium line
is straight within the limits of error. The slope is in the same direc-
tion as for the curve I-II, but is less. There is no possibility of this
line heading for the absolute zero.

The changes of volume, four in number and taken with the mercury

500

PROCEEDINGS OF THE AMERICAN ACADEMY.

UJ

Q.

apparatus, are given in Table XVIII. and Figure 19. The change is
constant so far as could be judged from the points themselves, but the
best values at the triple points would demand a slight decrease of this

volume with decreasing temper-
ature. In addition to the four
points listed above, there is a
fifth determination on April 20
by the method described on p.
495. This is higher by 4 per
cent (0. 2 per cent of the original
volume) than the previous point.
In view of the fact that the first
four points very approximately
satisfy the requirements at the
triple points, there seems little
doubt that they are the correct
ones.

The values of ^H and ^E
calculated from these data are

<

C9

-0.83

-0.89

-35"

-30 -25

TEMPERATURE

-20"

Figure 20. The latent heat and
the change of internal energy when
III passes to V.

given in Table XIX. and Figure 20. Ill gives out heat on passing
into V and absorbs work. The heat is very small, much less than
the work, resulting in an increase of internal energy on passing from
III to V.

The Curve II-V.

This curve has some of the properties of the II-III curve. It is
characterized by small change of volume and by the fact that II passes
into V immediately when the temperature is raised beyond the curve.
The method of determining the points was the same as that of the
II-III points. This was the last of all the equilibrium curves to be
obtained. It was found after sufficient skill had been attained with
the method, so that it was necessary to obtain the points only once.
For this reason, the observation that it was impossible- to heat II into the
region of V was not tested by so many trials as the corresponding change
II-III, and has therefore not quite so much probability of being abso-
lutely true. The reaction velocity on this curve drops very much faster
than it does on the II-III curve with decreasing temperature. This
might, at lower temperatures, result in the apparent possibility of
bringing II into the region of V, even if the reaction were actually
running. This slowness of reaction makes very difficult the determi-
nation of the equilibrium points at the low temperatures, the deter-
mination being difficult enough anyway, because of the small change

BRIDGMAN. — WATER UNDER PRESSURE.

501

of volume. It would probably not be possible to extend this curve to
very much lower temperatures than are given here. In partial expla-
nation of the difference in the behavior of the reaction velocity with

TABLE XX.
Data for the Equilibrium Curve Ice II-Ice V.

Date, 1911.

Temperature,
C.°.

Pressure,
kgm./ cm. 2.

AT/.

cm.3/gm.

Corrected.

April 19
AprU 20

-34.00
-30.50

-27.7
-25.8

4200
3970
3800
3650
3700
4000
4280

0.0408
406
398

temperature on the two curves II-III and II- V, it is to be noticed that
on the latter curve decreasing temperature is accompanied by increas-
ing pressure, which of itself would tend to slow the reaction because of
increasing viscosity, whereas on the former curve the retarding effect ; >f
decreasing temperature is offset by the accelerating effect of deciv-cS-
ing pressure.

The equilibrium points, four in number, are given in Table XX. and
Figure 9. These points lie on a
straight line, the temperature ris-
ing with falling pressure.

The change of volume points,
obtained by the method already
described for the II-III curve, are
shown in Table XX. and Figure
21. The change is sensibly con-
stant on this curve. This means
that the relation between com-
pressibility and dilatation is such

that the changes of temperature and pressure on the equilibrium curve
produce the same change of volume in both II and V.

•041

".039
N -35°

o

o •

o

-30° -25°

TEMPERATURE

-20"

Figure 21. The change of volume
when V passes to II.

502

PROCEEDINGS OF THE AMERICAN ACADEMY.

The values of ^H and AjE!, computed from these data, are given in
Table XXI. and Figure 22. II absorbs heat on passing to V and ab-
sorbs work. The internal energy of V is greater, therefore, than that

of II.

TABLE XXI.

Latent Heat, etc., on the Equilibrixjm Cuhve, Ice II-Ice V.

Temp.

C.°.

Pressure,

kgm._

cm.2

A7.

cm.'
gm.

dp/dU

pAF.

gm. cal.

gm.

AH.

gm. cal.
gm.

AE.

gm. cal.
gm.

From
Curve.

Adjusted.

-34.0
-31.0
-2S.0
-25.0

4200
4010
3800
3570

0.0401
401
401
401

75.6
69.8
62.4
55.0

68.4
68.4
68.4
68.4

3.95
3.77
3.57
3.36

12.4
13.9
15.1

15.9

16.4
17.8
18.7
19.2

The Curve V-L.

V was the second variety of ice found in this present work, the first
being that stable at higher pressures, namely VI. It seems worth while

to give here a short account
of the actual order of the
experiments, as it illus-
trates well the capricious
character of these reactions.
Ice V was first found at
—S°. An experiment was
being run on the change of
volume of ice VI when pass-
ing to water. Pressure
was being decreased ; it
had passed over the equi-
librium pressure and a
sufficient interval of time
had elapsed to allow the
Figure 22. The latent heat and the change pressure to automatically
of internal energy when II passes to V. restore itself to the equi-

librium value. The change
to V occurred without warning. By good fortune, a reading at the
bridge was being made at the particular instant, so that the entire

20

S 18

jS^

--

"

u

QC
ul

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TEMPERATURE

-25"

BKIDGMAN. — WATER UNDER PRESSURE. 503

process was observed There was a sudden increase of pressure, fol-
lowed by a slow fall past the equilibrium value VI-L to a final sta-
tionary value several hundred atmospheres lower down. This second
stationary pressure had all the properties of a new equilibrium pressure,
since the pressure was automatically restored to this value after
withdrawal of the piston. After sufficient withdrawal of the piston,
the pressure dropped in the normal way. The explanation, in view
of the facts as they now appear with the complete diagram before one,
is that ice VI at —8° was unstable. It had partly melted when it
flashed suddenly into V with increase of volume and increase of
pressure. The form V now found itself in the presence of water beyond
the equilibrium curve. The water froze to V with decrease of pressure
back to the equilibrium curve V-L. At the time, however, this expla-
nation was adopted with considerable hesitation. No experience had
been had of the very high reaction velocity possible between solids.
After this set of readings, pressure was left at 2000 kgm. over night,
the temperature graduaUy rising.

The next morning another run was made at —6°. The liquid froze
to VI at —6° perfectly properly, with no trace of V. Pressure was in-
creased considerably beyond the equilibrium value at —6° and then
decreased. On the way down a new transformation point was found
at pressures higher than either the VI-L curve or the supposed V-L
curve. The new reaction ran with unusual velocity, equilibrium being
attained in the time usually required for temperature equilibrium. On
decreasing pressure further, the VI curve was passed over without in-
cident, but a new equilibrium pressure was found lower down on the
prolongation of the probable V-L curve of the day before. The expla-
nation suggested itself that the upper transformation point was on the
V-VI curve, the lower on the V-L curve. Some slight irregularities
in the data made it desirable to dismount the apparatus after this run.
During these experiments, the water had been enclosed in a glass bulb,
as this was one of the series of experiments to detect if possible any
effect of the transmitting liquid on the water. The glass bulb was
found crushed to fragments, evidently because of the reaction between
two solid phases with sudden increase of volume.

In the apparatus as set up next time, the glass bulb was discarded,
therefore, and the water placed directly in a shell of copper. With this
apparatus no trace whatever could be found of the new phase V.
Measurements were made on the equilibrium and change oif volume
VI-L to temperatures as low as —20°. Lower temperatures could
not be easily attained because of the trouble with the CaCla cooling ar-
rangements. The subject was then dropped for a couple of months ;

504

PROCEEDINGS OF THE AMERICAN ACADEMY.

in the meantime the data required for the mercury paper were
finished.

On taking the matter up again, the only difference that presented
itself between the two runs, one giving V and the other not, was that
in the former run water had been in the presence of glass. The appa-
ratus as set up again was
made to differ from the for-
mer set up, therefore, only
in the fact that splinters
of Jena chemical glass were
placed in the water, which
was again included in a
copper shell The very first
attempt at —10° was suc-
cessful. Pressure was in-
creased beyond the VI-L
line, the reaction VI-L had
started, and the equilibrium
pressure had been reached,
when the phase V put in an
appearance, displacing VI.
Briefly, the mere addition or
subtraction of the fragments
of glass appeared to be the
determining factor. When it was desired to work on VI in the sub-
cooled region, the glass was omitted ; when V was desired, the glass
was added. Even then the appearance of V was under surprising
conditions. V was never formed directly out of the water, but always
in the presence of the phase VI. Furthermore, V showed a preference
for appearing only when VI, water, and glass were present together,
usually during determinations of the equilibrium pressure Vl-water,
either during increasing or* decreasing pressure. The facility with
which V might replace VI was the source of some annoyance. Once
a day's work was lost because V had successfully come in without
being noticed V might, however, form directly fi:om the solid VI, as
described above. All this holds only for the initial appearance of V,
it being very much easier, as already explained, to produce it after it
had appeared once. It was possible in this way to get V to separate
directly from the liquid, if it had appeared recently before.

Figure 23, plotting piston displacement against pressure, shows well
the way in which V might appear. With increasing pressure, the
water froze regularly to VI, as shown at A. The point F shows the

PRESSURE.

Figure 23. Shows the* way in which V
may appear. The dotted line C-D indicates
the sudden transition from VI to V.

BRIDGMAN.

•WATER UNDER PRESSURE.

505

possibility of subcooling the water before the reaction starts. The pres-
sure was then increased on the phase VI to the point B without iiiui-

TABLE XXII.

Data for the Equilibrium Cur\'^ Ice V-Water.

Date,
1910.

Temp.

Pressure,
kgm. /cm. 2.

AV.

cm.Vgm.
Corrected.

Nov. 11

-7.8

4860

0.0541

14

-6.0

5200

0512

19

-8.9

4140(?)

1911

Jan. 30

-10.1

4490

0702

-18.75

3420

-16.65

3680

-11.00

4440

Jan. 31

-14.5

3910

- 4.0

0578

Feb. 2

-20.6

3050

3

- 2.0

5940

0552

4

-13.1

4030

0747

8

-15.45

3770

0765

- 9.50

4600

0693

9

- 7.17

5010

0623

- 4.3

5480

0586

- 0.88

6120

11

- 7.65

4890

0636

- 4.60

5420

0587

- 1.40

6020

0519

13

-10.8

4480

0693

-10.5

4460

0663

-14.2

3900

0724

14

-17.65

3460

0790

-20.80

3040

0839

-14.32

3780

0753

22

- 1.60

6040

0543

dent. On decreasing pressure beyond C, VI suddenly changed to V
with increase of pressure to D. This change took place so far beyond

506

PROCEEDINGS OF THE AMERICAN ACADEMY.

the equilibrium line that the change of volume VI-V was not sufficient
to raise the pressure to the equilibrium value VI-V. From D, pressure
was regularly reduced to E, the melting point of V. Beyond E, the
curve of increasing pressure was retraced.

These remarks about the manner of appearance of V hold only for
temperatures above —25°. At lower temperatures, V may be made to

U)

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a.

2
iij

V-

-10

-20

0

o

3000

4000

5000

6000

PRESSURE, KGM/CM?

Figure 24. The freezing curve V-L.

separate from the solid phases III or II without the presence of glass.
In any event, V was the hardest of any of the solid forms to obtain,
the only certain way being via II, which demanded lowering the appa-
ratus to below —60°.

The actual determination of the points on the V-L curve was made
with the apparatus for the middle temperature range, temperature
being kept constant as usual with a thermostat. The equilibrium
points are shown in Table XXII. and plotted in Figure 24. As is seen,
these points were obtained on a large number of occasions, with differ-
ent pressure measuring coils, and with nearly all possible combinations
of all the pieces of apparatus ever used with this general tyjDe of appa-
ratus, part after part being replaced as it was destroyed by explosion.
The lower part of the equilibrium line is a trifle high, still passing
through a number of points, but not through the mean of all the points.
This was demanded in order to obtain consistent values for the latent
heat at the triple point L-III-V, the slope of the upper end of the
III-L curve being extraordinarily sensitive to small changes, as already
explained. The curve as given does not differ by over 0.2° from the
best curve through the points for V-L alone. The curve as given ex-

BRIDGMAN. — WATER UNDER PRESSURE.

507

tends to —21°, 4° into the region of stability of III. It is known, how-
ever, that it is possible to extend the curve as far as —25°. On one
occasion a point was found here, but it is not sufficiently accurate to
plot, owing to defective temperature control. The behavior at the
upper end of the V-L curve is the exact opposite of that at the lower

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-10"

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TEMPERATURE

Figure 25. The change of volume when V passes to the liquid.

end. It was not found possible to prolong the equilibrium curve of
V and L the slightest distance into the region of stability of VI, V
always passing spontaneously into VI. This was tried several times ;
the reaction runs if the penetration into the VI region is even as slight
as 1°.

More or less trouble was found in determining the change of volume.
When kerosene was used as the transmitting fluid, there seems to be
some action below 0°, either between the water or the ice and the kero-

508

PROCEEDINGS OF THE AMERICAN ACADEMY.

sene. This results in a slight rounding off of the corners of the dis-
placement-pressure curve, so that the actual discontinuity is difficult
to determine. This would point to a solution of the water in the
kerosene. The rounding off of the corners is not enough to affect
appreciably the equilibrium pressure. The effect was on the whole

TABLE XXIII.
Latent Heat, etc., on the Equilibrium Curve, Ice V-Water.

Temp.
C.°.

Pressure,
kgm.

cm.2

AV.
cm.'
gm.

dp

dt

pAV.

gm. cal.
gm.

AH.

gm. cal.
gm.

AE.

gm. cal.
gm.

From
Curve.

Adjusted.

-20.0
-15.0
-10.0

- 5.0

- 0.0

3140
3800
4510
5440
6360

0.0828
754
679
603
527

123
140
160
184
210

123
139
157
ISO
208

-6.10

-6.72
-7.18
-7.69

-7.85

60.5
63.4
65.9
68.1
70.0

54.4
56.7
58.7
60.4
62.2

less marked when gasolene was used as the transmitting fluid. The
change of volume points are given in the same table with the equi-
librium points and also in Figure 25. All the data before February 10
were obtained with kerosene as the transmitting fluid ; gasolene was
used for the results obtained afterwards. The gasolene points are on
the whole better, although the difference here is not sufficient to have
necessitated the use of gasolene instead of kerosene. The changes of
volume VI-L are much more affected by the transmitting fluid, below
zero, than are the changes V-L. The first two values of November 11
and 14 are not plotted, since the design of the apparatus in the first
few attempts was not good. Small portions of the water were likely
to separate from the rest after a single freezing, so that unless the
pressure was carried considerably beyond the freezing pressure, part
of the water was likely to remain liquid, giving too low an apparent
change of volume. The lowness of these first two points is to be
explained in this way.

Within the limits of error, the relation between temperature and
change of volum.e is linear. The lower end of the curve is about 1 per
cent higher than what would be demanded by the points themselves.
This was made necessary by the conditions at the critical point.

BRIDGMAN. — WATER UNDER PRESSURE.

509

The values of AZT and ^E found from these data are given in Table
XXIII. and Figure 26. Water gives out heat on passing into V, and
absorbs work. The work is very much less than the heat, so that the
internal energy of V is less than that of the liquid.

The Curve V-VI.

This is the last of the curves of equilibrium between two solid
phases. The manner in which the curve was first found has been
already described. The character-
istics of this curve are the same as
those ofthe other solid-solid curves ;
very high reaction velocity at the
upper end, with enormously re-

jo

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-25° -IQ° -15° -10° -5' 0"
TEMPERATURE.

Figure 26. The latent heat and

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z

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l\ 22 23 24 25 2G

PRESSURE, ARBITRARY UNITS.

Figure 27. False equilibrivim at
low temperatures on the V-VI curve,

the change of internal energy when V due to the slowTiess of the reaction

passes to the liquid.

and the viscosity of the soUds.

tarded reaction velocity at the lower temperatures. The slowing of
the reaction was so great as to make impracticable the determination
of points lower than —25°. Anomalous results obtained once or twice
are to be explained by the slowness of the reaction velocity. The
nature of the anomaly is shown in Figure 27, plotting piston dis-
placement against pressure. It is as if there were two discontinuities,
at A and B, and so two transition points. The explanation is prob-
ably as follows. The reaction from VI to V starts at the upper end of
the steel shell. This reaction runs with increase of volume, so that the
layer of the new ice V may form a protecting layer over the remainder
of the old ice VI below. This protecting layer is capable of stand-
ing some appreciable stress at this high pressure and low tempera-
ture, so that changes of hydrostatic pressure do not reach the nest of

510

PROCEEDINGS OF THE AMERICAN ACADEMY.

ice VI below, until the pressure has been reduced by an amount cor-
responding to the strength of the ice V. An exactly similar effect was

TABLE XXIV.
Data for the Equilibrium Curve, Ice V-Ice VI.

Date, 1911.

Temp.
C.°.

Pressure,
kgm./cm.2.

AV.

cm.'/gm.
Corrected.

Jan. 30

-10.10

0.0396

31

-14.5

6360

378

- 4.1

400

Feb. 1

-16.60

6320

346

3

-18.1

6380

-24.65

6320

-22.70

6360

-19.90

6370

-12.05

6370

-12.08

6380

383

- 2.00

6380

4

-13.1

6360

396

20

-19.7

6360

386

-16.8

6370

384

-13.9

6370

384

21

-11.25

6370

386

22

- 8.15

6390

380

- 5.00

6380

387

- 1.60

6380

386

found once on the III-V curve at —25°. That the ice in passing from
one solid to another is capable of exerting considerable stress is shown
by the occasional rupture of the steel shells containing the water.

BRIDGMAN. — WATER UNDER PRESSURE.

511

-5

h

<:

LiJ-15
Q.

:e

-20

•25

These were 9/16 inch o. d. and about 3/64 inch thickness of wall.

In fact, it seems rather surprising that

the effect did not prove troublesome on

more than these two occasions.

The regular apparatus for the middle

temperature range was used in finding

these points. Some skill in manipulation

was necessary to arrive on the curve at all.

The procedure was to start with the water bJ

impregnated with glass splinters and raise § "10

the pressure at a temperature somewhere

between —10° and —20°. On sufficiently

overpassing the unstable VI-L curve, VI

would separate out. After some little

while V would appear. With the first

signs of its appearance, indicated by a rise

of pressure, the pressure was increased as

rapidly as possible, in a few seconds, to

the V-VI curve, where the automatic

change of volume was sufficient to ensure

retaining of the equilibrium pressure after

freezing of the remaining mass of liquid.

This method of procedure was made neces-
sary by the fact that at the temperatures

at which it is easy to obtain V, it is possi-
ble to pass from either side of the V-VI curve into the region of

instability on the other side, without the reaction running. At higher

temperatures, nearer the triple
point, it is not possible to carry

V so far into the region of VI,
corresponding to the fact already
noted that at the triple point
itself it is impossible to carry

V any distance at all into the
region of VI.

The equilibrium pressures and
temperatures are shown in Table
XXIV. and Figure 28. The
equilibrium line is nearly at con-
stant pressure, but there is an
unmistakable though slight in-
crease of pressure at the higher temperatures. Within the limits of
error, the equilibrium curve is a straight line.

6300 6400 .

PRESSURE, KGM.CM?

Figure 28. The equilib-
rium curve V-VI.

-15 -10

TEMPERATURE

Figure 29. The change of volume
when VI passes to V.

512

PKOCEEDINGS OF THE AMERICAN ACADEMY.

The change of volume points, obtained by the usual method of
observing the piston displacement at constant temperature, are given
in Table XXIV. and Figure 29, plotted on a very much enlarged scale.

TABLE XXV.

Latent Heat, etc., for the EQuiLrBRiuM Curve, Ice V-Ice VI.

Tempera-
ture,
C.°.

Pressure,
kgm._
cm.2

AV.

cm.3
gm.

dp
dt

VAV.

gm. cal.

gm.

AH.

gm. cal._
gm.

gm. cal.
gm.

-20.0

-15.0

-10.0

- 5.0

0.0

6365
6370
6374
6377
63S1

0.03809
3828
3847
3866

3886

.80
.80
.80
.80

.80

5.682
5.716
5.748
5.779
5.812

-0.181
-0.185
-0.190
-0.195
-0.199

5.50
5.53
5.55
5.58
5.61

Here again the points found before February 10 with kerosene as the
transmitting fluid show much less regularity than the points obtained
afterward with gasolene. The kerosene points have been omitted from

^ 5.G0

bJ 5.40

a.

o -0.180
o

4/Y

-0.200

-20' -15" HO' 5' 0'

TEMPERATURE.

Figure 30. The latent heat and the change of internal energy when V
passes to VI.

the diagram. The effect may be due in part to the increased viscosity
of the kerosene under pressure. Within the limits of error, the rela-
tion between V and temperature is linear, the change becoming less
at lower temperatures as one would expect.

BRIDGMAN. — WATER UNDER PRESSURE. 513

The missing triple point, mentioned at the beginning, is evidently
given by the intersection of this line, V-VI, with the line II-V. This
point is apparently situated at about —65° and 6300 kgm. Evidently
the reaction velocity will be so slow at these temperatures and pres-
sures that it would be hopeless to try to reach it. The missing equi-
librium curve starting from this point is evidently II- VI. There is
even less chance of realizing this than of getting down to the triple
point, always assuming of course that some new variety of ice does not
appear.

The values of the latent heat and the change of energy calculated
in the usual way from the data are given in Table XXV. and Figure
30. The latent heat, owing to the approximate perpendicularity of the
equilibrium curve, is almost vanishiugly small. V gives out heat on
passing to VI, but absorbs work. The heat is almost negligible com-
pared with the work, so that the internal energy of VI is greater than
that of V by nearly the amount of this work.

The Cur\^ VI-L.

This modification of ice was the first one discovered in the present
work, and has engaged more attention than any of the other forms.
It has been studied over a pressure range of more than 16,000 kgm.,
nearly three times the pressure range of all the other modifications
put together. So far as can be judged, this is the final form of the
solid. This ice shows characteristics in its behavior different from any
of the others, characteristics which are particularly significant for the
theory of the solid-liquid states. In fact, this is the only modification
stable over a pressure range wide enough to indicate what may be ex-
pected at still higher pressures, as yet unreached.

The manner in which this variety of ice was first found in the course
of the measurements of compressibility has been already described in
the introduction. The appearence of this ice resulted simply in an
irregular disturbance at the upper end of the compressibility curve.
It was evidently impossible to make any accurate measurements by
this method of the freezing pressure or of the change of volume. All
that could be stated about the freezing pressure was that it was less
than a certain value, the maximum pressure reached during a run
when there was a disturbance, and all that was known about the change
of volume was that it was higher than a certain value, tlie discontinuity
in the compressibility curve. The lower and upper limits so set on
these quantities were found to be consistent with the more accurate
values found later.

VOL. XLVII. — 33

514 PROCEEDINGS OF THE AMERICAN ACADEMY.

At the time that these disturbances were found no great confidence
was felt in the explanation that the effect was really due to the freezing
of the water. All of the compressibility measurements were made in
the presence of mercury. Now it had been already found that mercury
freezes under pressure, and at pressures very close to those actually
found. At 0°, for instance, the freezing pressures of water and mercury,
according to the final accurate determinations, are about 6400 and
7600 kgm. respectively, and these two transitions seemed much closer
together in the preliminary work because it was necessary to super-
press the water considerably before freezing begins, while the super-
pressure required for mercury is very small. It is true that there were
very great quantitative difficulties in the way of supposing the effect
due to the fi-eezing of the mercury, but still the neighborhood of the
mercury freezing point produced a sensation of disquietude.

In order to definitely rule out the possibility of complications from
the neighborhood of the fi-eezing point of mercury, a form of experiment
was devised in which there was no mercury present. This was the
experiment also briefly alluded to in the introduction on the electroly-
tic conductivity of water. The water was placed in a shell of steel or
glass, and the conductivity measured between two concentric brass
cylinders attached to the insulating plug and suspended in the water.
The pressure chamber was filled with kerosene by which pressure was
transmitted directly to the water. There was no mercury anywhere
about it. The water was not absolutely pure, ordinary tap water being
used, which was sufficiently conducting for the purpose. In one case
distilled water with 1/10 per cent HCl was used. The resistance was
measured with a Kohlrausch bridge and a telephone in the usual way.
At high pressures there was unmistakable evidence of some sort of
change. The electrolytic resistance at first decreased with rising
pressure, passed through a flat minimum, rose slowly, and then very
rapidly to several times the former value, the rapidity being such as to
be almost equivalent to a discontinuity. This pressure of sudden rise
was taken as the freezing pressure, since it would be natural to suspect
the solid incapable of conducting. The pressure of transition was
measured in this way at several temperatures. In all, three sets of
readings were made with different forms of apparatus, and the last one
six months after the first. In the last determination, the existence of
the effect independent of the mercury having been already established,
the water was enclosed in glass with a mercury seal, the more effect-
ively to prevent absorption of impurities from the kerosene. The three
sets of determinations gave perfectly consistent results. A brief state-
ment as to the existence of a new variety of ice as proved by these

BRIDGMAN. — WATER UNDER PRESSURE.

515

Z
lu

bJ

o

<

_i

a.

CO

PRESSURE

Figure 31. Shows the sharp
change of volume during freezing.

experiments was published in the Physical Review, vol. 31, 1910,
p. 606. The values as found by these measurements lie on a straight
line, and agree with the possible limits found with the compressibility
measurements, except that at the highest temperature, 22°, freez-
ing had once been found to take place during the compressibility
measurements at a pressure lower
than that found here. This was
disconcerting.

The transition curve as found in
this way did not give all the in-
formation needed for a complete
statement of all the quantities
involved in the change. A com-
plete statement thermodynamically
could be made if it were possible
to measure also the change of
volume during the change. This
seemed at first sight of doubtful
possibility. Tammann had made
such measurements up to 2000
kgm., but had not been able to go

much higher because of leak. As it was, even at 2000, a correction
had to be applied for the leak, which was furthermore made as small
as possible by the use of a heavy oil, such as castor oil. In the
present work it was necessary to go to many times this pressure,
the equilibrium pressure even at 0° being 6400 kgm. The difficulty
was furthermore increased by the necessity for using some very light
and mobile oil to transmit pressure, the castor oil freezing absolutely
solid under such pressures as were to be used here. It was felt, there-
fore, to be a real step when it was found that the packing used in the
previous high pressure work was entirely satisfactory -when used for
this purpose. It is possible with it to retain liquids as mobile as ether,
CS2, pentane, or mercury, absolutely without leak, up to the highest
pressures attainable. Measurements of the change of volume have been
made up to 15,500 kgm., and this limit was set by yield of the steel
cylinders and not by failure of the packing. The readings of the piston
obtained were consistent to a few ten thousandths of an inch. The
only troublesome effect found with the packing was a slight wearing
away by abrasion, owing to the enormous friction. This effect was
troublesome only over a wide pressure range ; for the limited motion
of the piston during freezing or melting the effect was negligible.

It was also a part of the preliminary work to show that the freezing

516 PROCEEDINGS OF THE AMERICAN ACADEMY.

is sufficiently sharp to give trustworthy measurements of the change of
volume. The presence of impurity in the water will be shown by a
rounding off of the corners of the melting curve and by a change in the
value of the equilibrium pressure with the relative proportions of liquid
and solid present. Figure 31, chosen at random from the earlier meas-
urements, shows the sharpness of freezing and the consequent freedom
from impurity. In the majority of subsequent measurements, the ques-
tion of absence of impurity having been settled, it was customary to
find only one value for the equilibrium pressure, corresponding to a
mixture varying from one third to two thirds liquid.

The equiHbrium points obtained by the change of volume method
were found to be consistently lower than the supposed transition points
found by the method of change of resistance. There can be no ques-
tion whatever but that the change of volume points are the correct ones.
The cause of the discrepancy probably is the formation of the eutectic
mixture of ice and salt.

Measurements made with the electrolytic conductivity method after
the completion of the rest of the experiments, with the new apparatus
giving also the piston displacements, showed that the flat minimum in
the conductivity curve previously referred to occurs at nearly the pres-
sure of the beginning of freezing. Evidently at first pure ice separates
out, leaving the remaining liquid richer in whatever salt produces the
conductivity. The total quantity of this salt remains nearly constant,
but its concentration and so its association are increasing, so that on
the whole we have a decrease in the conducting power. When the
pressure has been carried so far that the concentration reaches the
eutectic value, the solid salt separates out with the pure ice and we
have the sudden jump in the resistance. That this was the case was
also suggested by a fact observed once or twice when using water in
glass with a mercury seal. This was that the sudden discontinuity
might be either a short circuit or an open circuit. Evidently the short
circuit is due to the penetration of the mercury through the mass of
ice along the core left by the freezing of the pure ice to the walls of the
tube.

The points on the VI-L curve were obtained with two different pieces
of apparatus. The points between —-20° and 20° were found with the
apparatus already described as used for the middle temperature range.
For the higher pressures, up to 20,500 kgm., another form was used.
The particular point of weakness in the middle temperature apparatus
is the connecting tube. The new form for the highest pressures was
made in one piece, therefore. This has been already described as the
third piece of apparatus. It is to be noticed that with this there is no

BRIDGMAN. — WATER UNDER PRESSURE.

517

correction necessary for the thermal dilatation of the transmitting fluid.
These measurements to the highest pressures "were made after the com-
pletion of all the others. It was confidently expected to find a new
variety of ice, but none was found.

The pressure measurements with the high pressure apparatus were

ftn'

Kf)

^

-^

^40

<^

Q.

2

UJ

1- 0

X

/

<^

/

^

-20

/

/^

10

12

14

.-3

13

20

PRESSURE, KGM/CM^ X 10'

Figure 32. The freezing-cun^e VI-L.

made in the usual way by measuring the resistance of a coil of manga-
nin wire. This had been calibrated by comparison with an absolute
gauge up to 13,000 kgm., which was about the limit of the gauge. The
pressures above this were obtained by a linear extrapolation, therefore.
There does not seem much danger in Soing this in view of the fact that
the relation is linear within 1/10 per cent up to 13,000.

For the middle temperature range the high pressure apparatus offers
the advantage of fewer connections over that actually used. There are
practical difficulties in the way of its use below o°, however. It is
necessary to submerge the entire lower end of the hydraulic press with
the cylinder into the constant temperature bath. There is considerable
flow of heat out of the bath along the heavy connecting bars of the
press. It would for this reason have been difficult and expensive to
have maintained temperatures below zero with the CaCU solution.
Points have, however, been obtained with the high pressure apparatus
over the entire range above zero.

The equilibrium points are given in Table XXVI. and Figure 32. A
greater variety of groupings of apparatus have been used for the points

518

PROCEEDINGS OF THE AMERICAN ACADEMY.

TABLE XXVI.
Data for the Equilibrium Curve Ice VI-Water.

Date,

Temp.

Pressure,

AV.

Date,

Temp.

Pressure,

AV.
cm.'/gm.
Corrected.

1910.

C.°.

kgm./cm.2.

cm.'/gm.
Corrected.

1911.

C.°.

igm. cm. 2.

Oct. 7

0.0

6380+

0.0914

8

0.0

6360+

916

6360-

0915

6360-

906

8

0.0

6360+

908

9

1.05

6500

6340-

908

2.55

6660

12

6.4

7170+

876

March 3

-3.4

5970

908

7150-

880

-6.2

5630

943

15

14.0

8380+

4

- 3.2

5990

923

18

15.0

8360+

- 9.2

955

19

14.80

8330+

798

— 12.2

5040

1014

8310

798

6

-10'4

5280

981

24

2194

9470+

712

-11.3

5160

971

9450-

710

-12.5

5030

963

25

18.4

8840+

776

-14.5

4870

978

Nov. 3

18.42

8800-

758

April 28

30.0

10660

4

10.63

7710+

878

38.2

12120

7710-

842

45.2

13360

2.90

6770-

903

May 8

30.2

10680

0.0593

5

4.78

6960-

888 >

9

38.0

12040

556

1.65

6580

911

45.8

13410

11

0.0

6360

916

53.4

15050

- 7.8

5470

13

38.4

12120

618

14

- 4.0

5910

48.0

14140

541

- 4.2

5910

938

55.5

15670

566

17

-11.7

4890

853

61.6

17200

18

-16.5

4440

900

67.5

18500

-19.6

4100

936

25

35.0

11450

647

19

0.0

6370

914

30.0

10590

671

- 8.9

5390

994

25.0

9790

713

- 6.0

5630*

931+

26

25.0

9680

705

959-

20.5

9050

758

21

-12.2

5080+

1035

15.0

8260

795

5050-

1004

0.0

63.50

928

22

-10.9

5160+

959

29

0.0

6360

902

T OO

51£0-

916

15.1

8180

797

Jan. 28

- 5.7

5690+

997

20.1

8890

754

1911.

5690-

914

30

25.1

9650

707

30

-10.1

5200

1044

30.1

10450

676

- 6.0

5750+

31

35.0

11470

629

5740-

40.0

12330

590

31

-14.5

4680

45.0

13380

512

Feb. 1

-16.60

4590

June 1

45.0

13380

563

2

-12.75

4850

13

51.8

14700

516

7

0.0

6340+

932

64.30

17840

6350-

895

72.15
76.35

19670
20670

BRIDGMAN. — WATER UNDER PRESSURE.

519

on this curve than for any other. It was on this curve, for instance,
that the test was made of the possibility of interaction between water
and the substances in contact with it. The water was used in steel or
copper or glass vessels, in contact with kerosene or gasolene or mercury.
No difference in the equilibrium pressures could be found with any of

«

^.100

^.030
o

2-080

>.O70

O

y.oGo

z

<
I

,050

•

— . *r%^

• ^

-20' -10' 0° 10' 20" 30° 40' 50"
TEMPERATURE

Figure 33. The change of volume when VI passes to the liquid.

these different forms of apparatus, but below zero it did seem desirable
to use gasolene instead of kerosene. Figure 31 shows piston displace-
ment aaainst pressure for one of the points on this line. The corners
of the curve were seldom more rounded than here. The pressure
measurements on this curve were made with six different manganin
coils.

Figure 32 shows that the equilibrium curve runs perfectly smoothly,
without incident of any kind, from the lowest temperature of the sub-
cooled region, —17°, to the highest temperature and pressure, 76° and
20,500 kgm. The curve is convex upward, like all the other curves of
equilibrium between the liquid and the other solid forms of water. At-
tention is called to the five bad points lying off the equilibrium curve
at the lower end.

The change of volume is shown in the same table with the equilib-
rium points, and graphically in Figure 33. All the values that were

520 PROCEEDINGS OF THE AMERICAN ACADEMY.

ever obtained have been given in the table, but not all these are
plotted. In the earlier work, A V was found both during freezing and
melting, that is, with increasing and decreasing pressure. In the
paper on mercury a detailed discussion is given, showing why the
values found during decreasing pressure are very likely to be in error.
None of these values are plotted. When it has not been specifically
stated in the table, the value has been obtained during* decreasing
pressure. Furthermore, all the points obtained with the kerosene as
the transmitting fluid below 0° have been discarded from the figure,
with the exception of the three low points to be mentioned later.
Nearly all the other points found with the kerosene below zero lie
above the curve given.

At the highest pressures there is an entirely new source of error
which justifies the discarding of certain points. Before the explana-
tion was found, considerable trouble was given by the points apparently
lying on two distinct parallel curves. A succession of points on the
low curve, not very regular, was first found, reaching up to 55°. The
pressure was then pushed to 18,500 for an equilibrium point, and then
after that, more change of volume points were found at lower pressures.
These all lay on the high curve. Some of these points were determined
three times with different fillings of the apparatus, giving almost
identical results, and the measurements were extended back to 0° to
compare with the results with the other piece of apparatus, giving
approximate agreement here also. The high curve was then followed
out again to higher temperatures, giving good points until at 45° the
value jumped again to the low curve. The possibility of a new kind
of ice was ruled out by the regularity of equilibrium points. Explan-
ation was found in the viscous yield of the steel. This has the curious
property of going on at a uniform rate during the time occupied by an
experiment, not being asymptotic as one might expect. This yield
had been carefully looked for at the lower pressures and not found.
During the long course of the experiments so much practice had been
obtained that during these last measurements the readings of pressure
and piston displacement were made with almost clock-like regularity
every six minutes. The yield was so slow as to be imperceptible dur-
ing that interval of time, and the readings were made with such regu-
larity that the effect was not discovered, as it otherwise would have
been, by irregular points on the curve. Once the effect was discovered,
it was found entirely competent to account for all observed discrepan-
cies, since the melting occupies a fairly long time, between one and two
hours. Another point at 45° was then found, applying a correction for
the yield by noting its rate during the half hour before and after change of

BEIDGMAN. — WATER UNDER PRESSURE.

521

state. This corrected point lay consistently with the others on the high
curve. Evidently the succession of high points found at the same pres-
sures, as well as the previous low points, is to be explained by the season-
ing effect of the maximum pressure of 18,500, which was applied between
the two sets. The last low point is due to the passing to the viscous

TABLE XXVII.
Latext Heat, etc., on Equilibrium Curve Ice VI-Water.

Temp.
C.°.

Pressure,
kgm./cm.2.

AV.

cm.3/gm.

dp

/dt.

pAV.

gm. cal.
gm.

AH.

gm. cal.
gm.

AE.

gm. cal.

gill.

From
Curve.

Adjusted.

-15.0

4790

0.0980

100.5

99.6

10.99

59.0

48.0

-10.0

5280

960

103.2

108.5

11.87

63.0

51.1

- 5.0

5810

938

112.4

113.8

12.77

67.1

54.3

0.0

63G0

916

118.8

120.0

13.66

70.4

56.7

+ 5.0

7000

884

125.1

125.8

14.51

72.5

58.0

10.0

7640

844

132.0

132.7

15.13

74.4

59.3

15.0

8310

798

140.0

140.0

15.56

75.5

59.9

20.0

9000

751

148.3

148.5

15.84

76.6

60.8

30.0

10590

663

167.3

167.3

16.45

78.8

62.3

40.0

12390

590

189.0

188.7

17.14

81.7

64.6

50.0

14430

523

213.7

215.4

17.69

85.3

67.6

60.0

16690

477

243.0

242.9

18.68

90.5

71.8

state again, after the seasoning effect had disappeared in time or had
been overcome by too high a pressure. After the point at 45° another
point was found at 52°, applying the correction for yield, and found to
he on the high curve consistently with the others. It did not seem
worth while to attempt points at still higher pressures, because the
correction becomes more difficult to apply at the high pressures, both
because the yield is becoming more rapid, and because the yield does
not remain uniform in time at the highest pressures.

The behavior of this cylinder is interesting from the point of view

522

PROCEEDINGS OF THE AMERICAN ACADEMY.

an

8S

/

80

y'

y

7Fi

^

570

o

ft-fis

X

/

/

y

/

• fin

/

^

^

y

/

/

/^

C3Rn

/

/

45

/

of elasticity. It shows the impossibility of obtaining perfect elasticity
very much beyond the original elastic limit. This cylinder had been
previously seasoned for use in this work by subjecting it for some hours
to 28,000 kgm. The hole was then bored out from the original 7/16
inch to 1/2 inch. The 28,000 kgm. had produced a stretching at

the inside from 7/16 inch to
perhaps 15/32 inch. Even
this high pressure did not
completely do away with
viscous yield at pressures
as low as 10,500. Another
interesting feature is the
approximate constancy of the
rate of yield over a pressure
range of 5000 kgm., from
10,500 to 15,500, as shown by
the fact that the low points
are nearly all the same dis-
tance below the correspond-
ing high points. This, too,
bears out an observation
made before, that elastic
after-effects, hysteresis, yield,
etc., are greater in larger
masses of metal. This cylin-
der was 4 1/2 inches o. d.
and 1/2 inch i. d. No such viscous yield was found in the cylinder
with which the change of volume of mercury was measured up to 11,000.
This cylinder was 3 inches o. d. and 9/16 inch i. d., and had been
previously subjected to 24,000 kgm.

In view of this yield, therefore, the values at the higher pressures
which were evidently affected by this yield ha^ve not been included \\x
the figure. The curve connecting AF^ with the temperature has a
point of inflection, which is not shown by any of the other curves.
This is of significance, as will be seen.

The values of A^ and t^E found in the ordinary way are shown in
Table XXVII. and Figure 34. The point of inflection in both these
curves is the particularly interesting feature. Water on passing to VI
gives out heat and absorbs work. The work is less than the heat, so
that the internal energy of VI is less than that of the liquid.

The data obtained with the high-pressure apparatus may be used to
determine one other quantity which the other apparatus could not give,

0° 10° 20° 30° 40°
TEMPERATURE

-20 -10

50° 60°

Figure 34. The latent heat and the
change of internal energy when VI passes
to the Uquid.

I

BRIDGMAN.

WATER UNDER PRESSURE.

523

that is, the difference of compressibility between solid and liquid.
This may evidently be found from the difference of slope above and
below the melting point of the curves connecting piston displacement
with pressure. If everything had been ideally perfect the other appa-
ratus should have given it too, but the quantity to be determined is

I .OiioU
h .0100

^ 4

DO

«o .0^30
to 5
U

q:

a. .0^80

1

y .0,G0

z *

u

Pi .0.50

O ,0^40

10 20° 30° 40° 50° eO°
TEMPERATURE.

Figure 35. Showing the directly determined values for the difference of
compressibility between VI and the liquid at various equihbrium temperatures.

very small, and the irregularities introduced by the transmitting liquid
passing from one vessel to another at a different temperature, which
might not be perfectly constant, were so great as not to admit of any
results of value. With the high-pressure cylinder, everything is in one
piece, and there are fewer complications. The values obtained even
with this are very irregular, but they are given as having some value
in pointing out the direction of the effect at high pressures. The
points are shown with sufficient accuracy in Figure 35. This shows a
very rapid decrease in the difference of compressibility at high temper-
atures and pressures.

This completes the presentation of the actual data. The points
were determined separately, those on one equilibrium curve being inde-
pendent of those on another. But the curves drawn through the
points, particularly those for the latent heat and the change of volume,
have not been in all cases the best curves through the points of the

524

PROCEEDINGS OF THE AMERICAN ACADEMY.

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single equilibrium curves in
question, but have been influ-
enced by the behavior of the
two neighboring curves meeting
at the triple point. Some dis-
cussion of the way in which these
data were adjusted at the triple
points seems called for.

The Triple Points.

The equilibrium curves them-
selves were in all cases, except
one, accurate enough so that the
three curves met at the triple
point naturally, without the
slightest forcing. The one excep-
tion is the lower end of the V-L
curve, already mentioned, where
it seemed desirable to raise the
lower end by 0°.2. Even this
curve as thus raised is not actu-
ally inconsistent with the data.
The values of the co-ordinates of
the triple points are shown in
Table XXVIII.

In selecting the best values
for the change of volume, the
greatest weight was attached to
the curve which was evidently
most self-consistent. The values
on the other two curves were then
so adjusted as to give consistent
results with the least violence
possible. The full details of the
process are shown in the table,
which gives the final values, and
in parentheses the values found
from the individual curves before
this process of adj ustment. The
signs are so chosen that the
change of volume is an increase

BRIDGMAN. — WATER UNDER PRESSURE. 525

when the reaction runs in the direction in which the symbols read. At
every point, the sum of the two smaller changes is equal to the larger.

An adjustment was necessary in seven out of thirteen possibilities.
The average adjustment was about 5 parts in 10,000 ; the maximum, 7
parts in 10,000 of the original volume. The points on the III-L curve
were so difficult to obtain, as already explained, that the entire course
of this curve was in large measure determined by the behavior at the
two triple points at either end.

With regard to the values for the latent heat and the change of
internal energy, there was room for more difference of opinion as to the
best way of making the adjustment. The latent heat, given by the

formula ^H = T^v -J-, is seen to depend on the change of volume,

already fixed, and on the slope of the equilibrium curve. The slope
was detennined graphically from the equilibrium curves. There is
chance for considerable error here, and the possibility of introducing
comparatively large changes into AZf by a very slight raising or low-
ering of the equilibrium curve, too slight in all cases except that of
III-L mentioned to introduce a perceptible change in the co-ordinates
of the triple point. On the equilibrium curves solid-solid, which run
approximately vertically, the latent heat is usually so small as to have
very little effect in the adjustment. It was possible to determine this
latent heat with a fair degree of accuracy, however, and so this was left
without adjustment, the other values being adjusted so as to be consis-
tent with it.

Evidently when the values of the latent heat are properly adjusted,
the values of the internal energy will also be consistent, because these
differ from the latent heat only by a quantity involving the change of
volume, which is already consistent at the triple point.

The tables already given, under the equilibrium curves separately,
enable an estimate to be formed of the amount of adjustment necessary,

dp dv

Two values are listed both for -7- and A^. The first value of ~ was

dt dt

obtained directly by graphical construction from the equilibrium curves,

and from this the first value of A// was calculated directly, point by

point. The final value given for t^H is the value taken from smooth

curves so drawn as to check at the triple points. From this final value

of Afl^'the final value of ~- was calculated, and listed in the column

dt

of final values. Table XXIX. gives the values of Af/ at the triple

points. The III-L curve is the only one that it was necessary to juggle

with in any way, and this has already been explained. The symbols

526

PROCEEDINGS OF THE AMERICAN ACADEMY.

are so chosen that heat is absorbed when the reaction runs in the direc-
tion in which the symbols read. Thus, the heat 1-L is given as 79.8.
This means that heat is absorbed when I passes to water.

The changes of internal energy at the triple points are also given in
Table XXIX. The positive sign means that the reaction runs in the
direction indicated with increase of internal energy.

TABLE XXIX.
Latent Heat and Internal Energy at the Triple Points.

Point.

III-L-I

II-III-I

V-III-L

V-II-III

VI-V-L

A// gm. cal./gni- (in the first lines).
AE gm. cal. /gm. (in the second lines) .

III-L

II-III

V-III

V-II

VI-V

50.9
48.6

12.3
1L2

0.9

- 3.6

-16.0
-19.3

0.2

- 5.6

L-I

III-I

III-L

II-III

V-L

-56.1

-62.8

- 2.2
-12.2

61.4
59.5

16.9
15.7

70.1

62.4

III-I

II-I

V-L

V-III

VI-L

- 5.2

-14.2

10.1
■ 1.0

62.3
55.9

0.9

- 3.6

70.3
56.8

There are several considerations of interest in connection with the
diagram that are not directly concerned with the data as given. These
are the questions as to our knowledge that these forms are actually
solid, as to the possibility of other forms of ice, the possibility of exist-
ence of any form out of its region of stability, and the question of re-
action velocity.

Are the Various Forms Really Solid?

This is the first question that naturally presents itself as to this
work. The experimental evidence so far has merely been that there is
a discontinuous change of volume ; the new modifications have not
been seen ; it is impossible to take the pressure off and examine them,
because they are unstable ; why then are we justified in assuming that
they are solids and not liquids 1 No direct evidence on this point has
been collected in this work ; the improbability of their being anything
except solids seems so great as to make needless the special arrange-
ment of apparatus necessary to give a direct proof. This was doubly

BRIDGMAN. — WATER UNDER PRESSURE. 527

needless, since Tammann has already given direct proof that II and III
are solid.

The most striking evidence of Tammann is for III. Tammann cooled
a steel cylinder containing ice III to the temperature of liquid air, then
released the pressure and took ice III out and examined it. The tem-
perature was so low that the reaction from III to I did not run imme-
diately. Ill was solid and gradually changed to ice I with large
increase of volume. In another experiment Tammann placed an elec-
tric contact maker in the water. Freezing to a solid was shown by the
refusal of the contact maker to work, both for III and II.

That V and VI ai-e also solid is made probable by two bits of evi-
dence. In the first place, the reactions, between V and III and V and
VI are exactly similar to those between I and III and I and II. There
is no mistaking the difference between a reaction solid-solid and liquid-
solid. In the second place, when the reaction. VI-V runs with
increase of volume, the containing vessel, whether a glass bulb or a
fairly heavy metal cylinder, may easily be destroyed. In this reaction
V has the larger volume. It, then, must be^solid, and probably VI also.

The possible crystalline forms of the different modifications seem to
be impossible of direct observation. It would be possible to insert
windows in the apparatus and look at all the forms, but this would
probably give no information whatever. On several occasions the
apparatus was opened and the cylinder of ice I, which had frozen under
pressure, was removed. This was always a perfectly structureless,
translucent mass, capable of giving no information whatever as to any
of its crystalline properties.

Other Possible Forms of Ice.

In a recent paper Tammann i^ has stated the probable existence of
a fourth variety of ice, very much like ordinary ice in its properties.
The evidence for this, was very meagre. Slight discrepancies found on
the equilibrium curve I-L could be explained by it ; also a momentary
rise of pressure on one occasion after the fall of pressure proper to
melting had begun. Seven successive attempts of Tammann to get
the same effect again failed. It is evident that the discrepancies on
the I-L curve might be due to pressure errors ; a new manometer used
by Tammann gave pressures 50 kgm. lower than the former one, and
we have already seen that the crossing of the I-III and the I-II curves
found by Tammann must be set down to pressure errors. Finally,
Tammann states that ice IV may separate out from water when cooled

" Tammann, ZS. Phys. Chcm., 72, 609-631 (1910).

528 PROCEEDINGS OF THE AMERICAN ACADEMY.

to —7°. The fact that there is a different modification is shown by-
placing the ice so formed in a dilatometer, and warming slowly. At
—2° there is a sudden increase of volume of about 1/10 per cent, fol-
lowed by regular increase of volume and melting at 0°. The ice IV
appears, therefore, to have a slightly less volume than ice I. In this
experiment, sufficient attention does not seem to have been paid to the
possibility of there being internal strains in the ice. It seems plausible
that the water, freezing suddenly as it must at —7°, might so freeze as
to produce a slight volume compression. On increasing temperature,
this strain is relieved by the softening of the ice in the neighborhood
of the melting point. This weakening of the ice near the melting
point has been established by experiment. At high pressures it is un-
doubtedly true that internal strains may produce anomalous effects, as
was found on at. least two occasions.

Entirely apart from.Tammann, however, there is independent experi-
mental evidence of the possibility of two forms of ice, differing in den-
sity by 1/10 per cent, the amount found by Tammann.. Two modern
experimenters, Nichols ^^ and. Vincent, ^^ as well as several previous
observers, have each found that the density of ice may have either one
of two distinct values. The* difference seems to be connected with the
manner of formation of the ice, whether natural or artificial. The nat-
ural ice, when kept for some time, tends to assume the value for the
artificial ice. Barnes, i* however, failed to verify the work of Nichols,
and the most recent work of Leduc suggests that the discrepancies may
possibly be due to dissolved air.

The question is as yet unsettled, with the probability, however, that
the ice does not exist. In order to leave open the possibility of the
establishment of its existence, however, the numeral IV has been re-
served for this according to Tammann, and the first of the two new
varieties found in this paper has been called V.

Besides this, there have appeared from time to time spasmodic
notices concerning ice existing in crystalline forms other than the hex-
agonal. This is usually natural ice, which has been subjected to in-
tense cold in the far north. None of these statements seem to have
been subsequently verified, however.

In the course of the present work evidence was obtained as to the
possibility of the existence of another form at high pressures. It seems

" Nichols, Phys. Rev., 8 (Jan., 1899).
^3 Vincent, loc. cit.

" Barnes, Trans. Roy. Soc. Canada, 3, Sect. Ill, 3-27 (1909), and Phys.
Rev. (July, 1901).

BRIDGMAN. — WATER UNDER PRESSURE. 529

probable that the five discrepant points found on the lower end of the
VI-L curve may be due to the presence of some other form of ice than
VI. These points were obtained on two separate occasions more than
two months apart. Every one of the equilibrium points which have
ever been obtained has been plotted in the diagrams, except a few
where the temperature control was defective, and which have been
mentioned. There are nowhere any points lying so far off the curve
as these five. It seems hardly probable that the five worst points
should have all been bunched in the same place, all lying consistently
on a new curve. The probability of there being a new kind of ice is
strengthened by the change of volume measurements made at these
same points. These points are shown on Figure 33 for the change of
volume VI-L. They lie far below the smooth curve, further than even
the wildest of the discarded points, and they also lie consistently on
another curve. The probability seems very strong for another modi-
fication of ice. This modification, if it does exist, is unstable in the
locality found, V being a more stable form. Whether this new form
has any region of stability at all is open to question ; there is no neces-
sity for it.

Whether there are still other forms stable at the highest pressures is
of course a matter of pure conjecture. No inconsistencies were ever
found suggesting in any way the existence of another form in the
region studied. The domain of stability of ice VI as found is already
five times more extensive than that of any of the other modifications.
Furthermore, the course of the freezing curve and of the change of
volume curve is such that both of these curves could be extended
without difficulty to infinite pressures and temperatures. VI seems at
any rate suited to be a final modification.

In this connection, some comment seems called for as to the possi-
bility of predicting new forms. Of course it is well known that there
is no such possibility from the equations of thermodynamics alone ; the
domain of existence of any form may be extended indefinitely in either
direction without running into thermodynamic inconsistencies. But
every substance, besides satisfying the identical relations of thermody-
namics, also satisfies its own particular characteristic equation. This
characteristic equation is determined by the special internal mechanism
of the substance in question. It seems a jwiori possible that the
approach of a new form should be heralded by some change in the
mechanism, which should have its effect on the characteristic equation.
But no such effect as this has been noticed. One substance may be
extended across the boundary line into the unstable region beyond,
with no appreciable change in either the compressibility or the dilata-

VOL. XLVII. — 34

530 PROCEEDINGS OF THE AMERICAN ACADEMY.

tion, the two quantities determining the characteristic equation. And
on an equilibrium line, the neighborhood of a triple point does not
cast its shadow before, either by a change in the direction of the equi-
librium line, or of the change of volume line, or of the curves of latent
heat or internal energy. So far as the data presented in this paper
are concerned, there seems to be no way of making the prediction.
Nevertheless the conviction remains that if one had a complete de-
scription of the internal mechanism, it would be possible to find some
criterion as to the possible stability of other configurations. What
additional data are needed to give a sufficient knowledge of the
jnechanism? The question is an interesting one for investigation.

The Possibility of Subcooling or Superheating.

The facts regarding this subject have nearly all been mentioned in-
cidentally in the course of the detailed description of the experiments.
Although no observations of the possibility of subcooling or superheat-
ing were made separately for their own sake, yet the observations
collected incidentally on this subject are nearly as numerous as all the
other observations together- The effect was of course observed during
every measurement of a change of volume, and frequently on other
occasions. It was likely to be a very troublesome effect, preventing
the appearance of the modification desired, so that at least sufficient
familiarity had to be obtained with the slight regularities shown by
the apparently confused mass of facts so that the modification of ice
desired could be forced to appear.

First with regard to the solid phases. It has been found possible to
go across nearly every one of the boundary lines into the region of
instability on the other side. I has been found in the region of III
and II ; II in that of I (at low temperatures) ; III in that of I, II, and
V ; V in that of III, II, and VI ; and VI in that of V. The only ex-
cursion of this kind which has not been found possible is that of II into
the region of III or V. This latter reaction always ran immediately
on passing the slightest amount into the neighboring country. For
the other reactions no fixed limits could be set to the extent by which
it was possible to overstep the boundary. The amount depends on the
size and shape of the vessel, on the materials in contact with the ice,
on the element of time, and on caprice. In general, however, the
limits became narrower at high temperatures, as cme would expect.

With regard to the passing from the solid to the liquid, the experi-
ence here is but a verification of the experience of everybody else ;
that it is impossible to superheat a crystalline phase with respect to

BRIDGMAN. — WATER UNDER PRESSURE. 531

the liquid. No good reason for this has ever been given, but no excep-
tion has ever been found, and it is coming to be regarded as a law of
nature. One would think that if there were ever a chance to find an
exception it would be here, where the materials are made viscous by the
high pressure, and where the reaction must run with increase of volume
against the pressure, doing considerable external work.

On the other hand, it is the easiest possible matter to subcool the
liquid with respect to any one of the four solid phases bordering on
the domain of the liquid. In fact, it is often a matter of some diffi-
culty to start the reaction liquid-solid, superpressures of 1500 or 2000
kgm. being sometimes necessary. The amount of superpressure or
subcooling necessary to start the teaction is again a matter of caprice.
On the VI-L curve, however, where the greatest range was open to
observation, there seemed to be in general a tendency for the subcool-
ing to increase at high pressures.

In consequence of the possibility of carr3dng one phase into the
region of another, it is possible to prolong certain of the equilibrium
lines beyond the triple point into the region of instability beyond,
thus realizing equilibrium points between two unstable phases. The
equilibrium lines which have thus been extended are : I-L into the
region of II, III-L into the region of I (by Tammann, not in the pres-
ent work), III-L into the region of V, I-III into the region of II, III-V
into the region of II, and VI-L into the region of V. It may also be
possible to extend II-III into the region of I, although this was not
tried. The only curves which it was found experimentally impossible
to extend were II-III into V, II-V into III, and V-L into VI. There
seems to be no obvious generalization about the possibility of extend-
ing these curves; everything seems to depend on the particular
character of the substances in question. There was one plausible
generalization from only two instances, which was missed by a very
narrow margin, namely that it is impossible to extend a melting curve
at the upper end into the region of another solid. The attempt always
failed on the V-L curve, and until the very last day failed on the III-L
curve. On this very last day, when the change of volume points II-
III-V were being found, it was desired to pass from III to V. The
greatest difficulty was experienced in doing this. Pressure was in-
creased on III at about — 20° to 4500, and the temperature then raised
until III began to melt, thus spoiling the generalization. It was finally
necessary to lower the temperature to — 40° before V appeared. It is
therefore conceivable that there are circumstances when V-L might be
extended into VI, or II raised into the region of III or V.

It may be mentioned that at every triple point there is at least one

532 PROCEEDINGS OF THE AMERICAN ACADEMY.

equilibrium line which it has not been found possible to cross. At
four of the five triple points there are two such lines, and at the fifth,
I-II-III, the possibility of carrying II into the region of I was not
tried. At three of the five points water is one of the substances, so
that the statement is obviously true ; at the other two points the solid
II has the same relation to the solids above it that the solids above
have to the liquid above them.

It was not found possible to extend any two of the curves so far
into a region of instability as to give a triple point between three un-
stable phases, nor was the third unstable curve starting from this un-
stable triple point ever found. This third curve would have no region
of stability whatever. The nearest approach to this was in the exten-
sions of the III-L and VI-L curves. No especial attempt was made to
realize such an unstable triple point, however, as it would have been a
matter of considerable difiiculty, but there seems no reason why such
a point should not be found.

No such constancy was ever found in these subcooling experiments
as to suggest the necessity of the existence of the metastable limit, as
is claimed by many writers. With a particular piece of apparatus it
may be possible to obtain fairly consistent results, but when the appa-
ratus is being continually changed as it was here there seems to be no
obvious regularity. There is no reason why there should be, if the for-
mation of the nucleus of the new phase, which starts the reaction, is a
matter of chance as seems likely. Owing, however, to the fact that
there is at every triple point one equilibrium curve which it is not pos-
sible to cross, there are going to be lines reaching from every one of the
triple points limiting the existence of one or more of the phases, which
give the same impression as the metastable lines recently drawn by
Tammann in the neighborhood of the triple point I-III-L for water,
and also in the neighborhood of a triple point of phenol. ^^

In one respect the possible amount of subcooling showed great regu-
larity and is of sufficient significance to deserve special mention. This
is the fact, already noted, that a form is much more likely to appear
again if it has appeared recently before. This fact was of great con-
venience in obtaining the change of volume points, because here one
phase has to be allowed to be completely replaced by another, and the
first phase is then wanted again in obtaining the second AF point.
Very little difficulty was experienced in getting the desired form to ap-
pear under these circumstances. This was particularly true on the
V-VI and the V-L curves, the modification V being the hardest to

" Tammann, ZS. Phys. Chem., 75, 75-80 (1910).

BRIDGMAN. — WATER UNDER PRESSURE. 533

obtain initially. On the V-L curve a succession of A V points was ob-
tained without difficulty, V always putting in an appearance when de-
sired, separating directly from the liquid with very little subcooling,
although V was never obtained directly from the liquid the first time,
bat only by way of VI after considerable subcooling. This ability of

V to separate directly from the water could be retained for several
hours at points removed 1000 or 2000 kgm. from the equilibrium
curve. The ability was once retained over night, pressure not being
far removed from the equilibrium curve. The disposition to react de-
pends both on the element of time and on the amount by which pres-
sure has been changed from the equilibrium value. This predisposition
to react is lost if a third modification has intervened. Thus, on the
occasion mentioned, when III was melted at 4500 kgm. in the endeavor
to obtain V, only a half hour previously the reaction II-V had been
running in either direction with the greatest facility. The subsequent
conversion of II into III resulted in the complete loss of disposition of

V to appear.

In explanation, there must be some structure in both the liquid and
the solid not ordinarily accounted for, some nucleation or aggregation of
the molecules left as a heritage from the previous modification, which
is particularly adapted to fall back again into the old position. The
possibility of such nuclei in the solid must show that the molecules in
a crystal are not arranged in the absolutely symmetrical way usually
thought of. The fact that these nuclei may persist for some time in
the solid does not seem so surprising as the fact that they exist at all.
For the liquid, the reverse is the case. The existence of nuclei might
be expected ; they are known to exist even in a gas, but that these
nuclei may persist for some hours in an assemblage of molecules sup-
posed to be in constant interchange with each other might not be ex-
pected at first. The disappearance of these nuclei is a matter of
extraordinary slowness, considering the usual times involved in the
motion of the molecules as a liquid. Doubtless the formation of these
nuclei is intimately connected with the freezing of a liquid for the first
time. The freezing can start only from one of these nuclei. The for-
mation of one of these nuclei in an unimpregnated liquid is a matter
of chance, and until the molecules do happen to fall together into the
right position the freezing cannot start.

Reaction Velocity.

Here again no accurate measurements were made. The velocity
depends on too many things to allow quantitative results of value

534 PROCEEDINGS OF THE AMERICAN ACADEMY.

without the expenditure of a great deal of time. These disturbing
factors are such as the size and shape and material of the containing
vessel, the rapidity of heat conduction, and the distance from the equi-
librium line. But just as for the question of subcooling, so here, every
measurement ever made, whether of the equilibrium pressure alone or
of the change of volume, involved this matter of reaction velocity.
One had to be sure before making a reading that the reaction had
stopped running, and in the endeavor to waste no more time than was
necessary the progress of the reaction was constantly watched, so as
to make the reading as soon as possible after sensible equilibrium had
been reached.

There are two distinct types of behavior of the reaction velocity,
according as the reaction is between a solid and a liquid or between
two solids. In general the reaction between solid and liquid was slower
than between solid and solid. The time for the completion of the re-
action liquid-solid was about two hours on the I-L, V-L, and lower end
of the VI-L curve. No particular variation in this time was noticed
from one end to the other of the I and V curves, but at the upper end
of the VI-L curve, the velocity had been very appreciably accelerated,
the time for completion of the reaction at the upper end being about
one hour. On the III-L curve, as already mentioned, the reaction was
very much slower. It was not practicable here to wait for the reaction
to run to completion, but the equilibrium points were taken as the
mean of values approached from above and below. This shows that
the velocity depends on the form into which the water is transformed
as well as on the heat of reaction, for the heat IlI-L is of the same
magnitude as that of the neighboring modifications I and V. On all
the curves the velocity seemed the same for melting as for freezing.

The most striking behavior of the reaction velocity is shown by the
reaction solid-solid. The velocity ranges from explosive rapidity at
the end near the triple point to such sluggishness 20° further down as
to make further prolongation of the equilibrium curve out of the ques-
tion. Of course the very low heat of reaction would lead one to expect,
other things being equal, a high rate of transformation, but that the
heat of reaction has practically nothing to do with it is shown by the
enormous temperature coefficient of reaction velocity, while the heat
of reaction is practically independent of temperature. The slowness
of the reaction does not depend so much on the actual temperature as
on the nearness of the triple point. Thus I-II is explosive at its triple
point, —35°, while at —35° III-V is almost impossible ; III-V is ex-
plosive at its own triple point, —17°, but at this temperature V-VI
may take a couple of hours to run to completion.

BRIDGMAN. — WATER UNDER PRESSURE. 535

The explanation does not suggest itself. The mere fact of such
rapid reactions between solids is itself sufficiently surprising. It does
not seem as if the mechanism could be the same as that of an ordinary
chemical reaction. It is as if the molecules changed from one crystal-
line arrangement to another by snapping round on their axes, like the
supposed molecular magnets of a piece of iron in a magnetic field.
The high temperature effect is difficult to account for. Certainly no
known viscosity effect has so high a temperature coefficient.

Some connection seems likely between this high velocity at the
triple point and the impossibility of superheating a solid. There is no
doubt but that at this point the molecules of the solid have a perfectly
astounding possibility of motion. The passage to the liquid may still
depend on the chance formation of nuclei in the solid, but the freedom
of motion of the molecules in the solid may be so great as to secure
the practically instantaneous formation of the proper grouping. This
recalls the question proposed a few pages back as to the possibility of
predicting the presence of a new phase from the behavior of a single
other phase. Here we have a hint as to the possibility of predicting a
third phase by an enormous reaction velocity between two others.

The Compressibility of the Different Forms of Ice.

These compressibilities have not, with one exception, been directly
measured, but it is possible, nevertheless, to obtain some idea as to this
magnitude for those varieties of ice which are anywhere in equilibrium
with the liquid. This includes all the varieties except II. The com-
pressibility of VI has been directly measured above 0°, and the initial
compressibility of ice I has been computed. It has been already stated
that the data do not possess the requisite accuracy to permit a direct
determination of the compressibility of the other forms of ice. The
approximate determination comes by finding the actual volume of the
different kinds of ice along the equilibrium lines. The volume of
water is known along these lines, and also the change of volume when
the liquid passes into the solid, so that the actual volume of the solid
may be obtained. This volume will change with temperature and
pressure along the equilibrium line. The approximation to the com-
pressibility is made by assuming that the change of volume due to
changes in temperature along an equilibrium line is negligible com-
pared with the change due to pressure. The error so introduced may
be found at 0° for ice I at atmospheric pressure, where it is 3 per cent.
Furthermore, at any point except in the immediate neighborhood of
the origin, the thermal expansion of the ice is very probably less than

536 PROCEEDINGS OF THE AJIERICAN ACADEMY.

that of the liquid with which it is in contact. This enables us to put
an upper limit of 10 per cent as the probable error introduced by
assuming all the change of volume along an equilibrium curve to be
brought about by changes of pressure.

The complete values of the volume are shown in Table XXX., which
gives the approximate compressibility along these curves. For com-
parison, the approximate compressibility of the water at the corre-
sponding pressure and temperature is also given. In consequence of
the change of volume due to temperature, the quantity listed as com-
pressibility is too big on the ice I curve, and too small on the other
curves which rise to higher temperatures with higher pressures. The
compressibility of the ice is uniformly less than that of the water, as
one would expect, varying from 1/3 to 2/3. On all the curves except
the III-L curve, the compressibility shows a very marked decrease
with rise of pressure, the decrease being more rapid proportionally for
the liquid. The same decrease would probably also have been shown
on the III-L curve, if it had been possible to make the measurements
of the change of volume with greater accuracy. On the I-L curve,
the change for a range of pressure of only 2000 kgm. is abnormally
high. This might be accounted for by a negative temperature coeffi-
cient of expansion of ice at the lower end of the curve. The change of
volume measurements I-III have already suggested this as a possi-
bility. The change of compressibility with pressure is greatest at the
low pressures, being particularly great in the region of instability of
VI. In general, when one variety of ice replaces another, one would
expect the new form stable at the higher pressures to show the lower
compressibility, corresponding to the smaller volume ; but this is cer-
tainly not true in the case V-VI, and probably not true when III re-
places I. The compressibility of each modification seems to be a
property inherent in that modification, depending probably on the
symmetrical arrangement of molecules in the crystal, and not depend-
ing so directly on the volume.

As verifying these values very roughly, the directly determined
difference of compressibility between L and VI has been shown in
Figure 35. The values are evidently not of any great regularity. The
only two points found below 15°, at 0°, are much too high. These would
give a value for the compressibility at 0° of .O53O as against .O56 from
the data above, .O56 being too small. But in the region where the points
are thicker, between 15° and 50°, the agreement is better, discrepan-
cies being of the order of O.O5I. These points run to higher pressures
than the actual determinations of the compressibility of water, and do
show strikingly the rapid decrease in the difference between the com-

BRIDGALiN.

WATER UNDER PRESSURE.

537

TABLE XXX.

Volume and Approximate Compressibility op Ice on Equilibrium

Curves.

Pressure,
kgm./cm.2.

Temp.
C.°.

Vol. of

Water

cm.3 /gm.

A 7.

cm.'/gm.

Vol. of Ice

cm.3/gm.

Approx.
Compressi-
bility of Ice.

Compressi-
bility of
Water at
Same Point.

Ice I-Water.

0

0

1.0000

0.0900

1.0300

O.O435

O.O452

500

- 4.1

0.9777

0998

1.0775

1000

- 8.7

9588

1096

1.0384

O4I6

37

1500

-14.0

9414

1201

1.0315

2000

-20.3

9253

1318

1.0571

O58

29

Ice III-Water.

2000

-22.5

0.9250

0.0476

0.8774

-\

O.O43O

2500

-20.1

9099

373

8726

[o.OiOl

26

3000

-18.3

9874

286

8688

24

3500

-17.0

8867

231

8636

''

21

Ice V-Water.

3500

-17.0

0.8870

0.0785

0.8085

4000

-13.6

8781

733

8018

0.0572

O.O4I9O

4500

-10.1

8694

681

8013

5000

- 7.0

8610

634

7976

53

164

5500

- 4.2

8543

• 590

7953

6000

- 1.6

8478

549

7929

47

140

6500

+ 0.6

8418

516

7902

Ice VI-Water.

4500

-18.0

0.8689

0.0985

0.7705

5000

-12.8

8601

968

7636

o.oao2

O.O4I64

5500

- 7.7

8536

940

7596

6000

- 3.2

8472

928

7544

0572

140

6500

+ 1.1

8418

905

7513

7000

5.0

8370

882

7488

55

126

8000

12.0

8271

810

7455

48

120

9000

19.5

8156

755

7401

43

110

10000

26.0

8055

697

7358

37

104

538 PROCEEDINGS OF THE AMERICAN ACADEMY.

pressibility of water and VI with rising pressure. This point has some
bearing on the discussion of the general nature of the change of state
solid-liquid at high pressures.

Discussion of the Eesults.

So far in this paper merely the numerical results have been pre-
sented, without much discussion of their significance. For the liquid,
the change of volume at different temperatures and pressures has been
found, without discussing the shape of the p-v-t surface which these
combine to give. For the solid states, the data have been presented
for each variety of ice separately, without any consideration of the
general features which may be common to all. The object of this dis-
cussion is to give a comprehensive survey of all the results, especially
for the transition liquid-solid, and to point out the theoretical signifi-
cance of these data at very high pressures.

For the liquid, the results will have their chief interest in showing how
water passes from an abnormal liquid at low pressures to a normal one
at high pressures. The data do not have so much suggestiveness for a
theory of the liquid state as would those for some normal liquid, and
in any case it would be dangerous to generalize from the behavior of a
single substance, but the results at the higher pressures do suggest
at least the nature of the effects to be expected in general at high
pressures.

The results for the liquid at even temperature and pressure intervals
have been collected in Table XXXI. In this table the smoothed re-
sults obtained separately above 0° and below 0° have been given with-
out any attempt to smooth the values of either set so as to make con-
nections with those of the other. But the fact that the two independent
sets of determinations do run smoothly into each other makes probable
the accuracy of the work. Above 7000 kgm. the value of the thermal
dilatation used in computing the table was obtained by an extrapolation.
This is probably good up to 10,000 kgm. in giving the actual volume
at any temperature and pressure within the narrow range of existence
of liquid water, but the use of the tables in any theoretical consider-
ations demanding knowledge of the derivatives would be dangerous at
the highest pressures. Above 3000 kgm., and indeed above 2000 kgm.,
the dilatation has been assumed to be independent of the temperature
over the range of 22°, as has been sufficiently shown by the work of
Amagat. For values below 2000 the variation of the dilatation as
found by Amagat has been used in computing the table. Of course
below 0° the variation of dilatation with temperature was given by the
data of this paper.

BRIDGMAN. — WATER UNDER PRESSURE.

539

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'-<oO'-i-*ot^r^t-~<x)Oi

O 00 O -^ C^5 ^ CJ OC t^ «3 LO
OC50505030300COOOOOCO

O ^ C5 O CO O
• ti 0-1 o o x t^
■ Oi 05 C5 00 00 00

• CO CO i>-

•CO OC-O

• Ci O 00

ooooooooooooooooooooo
oooooooooooooooocooo

lO O 'O O 'O O '-0 O 'O O 'O O 'O O LO O '- w '■. o
i-H rH ca (M CO CO -^ "* LO i-Q CD O 1-- t-^ cc X _. _. CP

540 PROCEEDINGS OF THE AMERICAN ACADEMY.

Before discussing the shape of the p-v-t surface as given by the deter-
minations of compressibility, it may be well to review briefly the known
behavior of water, especiallj'' with regard to the differences it shows
"when compared with ordinary liquids.

All ordinary liquids show a decreasing compressibility with rising
pressure, the compressibility decreasing faster than the volume, and
they also show an increasing compressibility with rising temperature.
The mathematical equivalent of this last statement is that the thermal
dilatation decreases wdth rising pressure. This normal behavior is
exactly as we would expect if we regard the liquid as composed of
nuclei of more or less invariable volume, separated by spaces which
may be altered in size by pressure and temperature. It is not
necessary for a qualitative understanding of the phenomena even to
inquire whether these nuclei are subatomic or atomic ; that is, whether
the major part of the compression is given by the change of volume of
the spaces between the atoms or by changes in volume of the atoms
themselves.

For water the effects are anomalous. The compressibility decreases
with rising pressure, as it does for everything else, but with rising
temperature the compressibility at first becomes less, passes through a
minimum, and then becomes greater again. This minimum is situated
at about 50°. The position of the minimum is nearly independent of
pressure but the minimum itself becomes less and less pronounced
with rising pressure, and at 3000 kgm. has entirely disappeared.
Corresponding to this anomalous behavior, the dilatation shows anom-
alous behavior with rising pressure, becoming greater with greater pres-
sure at tempere.tures below 50°. It has been recognized by Amagat as
possible, however, that at temperatures below 50° the dilatation would
decrease with rising pressure at pressures sufficiently high. In the im-
mediate neighborhood of 0° and atmospheric pressure, there are special
anomalies connected with the maximum density point. In particular,
the temperature of maximum density, which at atmospheric pressure is
at about 4°, is depressed by rising pressure. This depression of the
maximum density point is nearly linear with the pressure, and is so
rapid that at 300 kgm. it has fallen below the freezing temperature at
that pressure. So much has been shown by Amagat, ^^ who worked up
to 3000 kgm. The results may be briefly summed up in the state-
ment that water, abnormal at low temperatures and pressures, tends
to become normal at high temperatures and pressures.

Now consider the information given by the present data, examining

" Amagat, loc. cit.

BRIDGMAN. WATER UNDER PRESSURE.

541

first the compressibility data above zero. Of coarse the rough facts
already known appear immediately from an inspection of the figures.
The compressibility decreases strikingly with rising pressure and is

less at 22° than at 0°. Figure 36 shows the compressibility (=(--])
at 0° and 22°. At 10,000 kgm. it has decreased to 1/4 of its initial

8 7

PRESSURE, KGM/CM^ X 10"?

Figure 36. The compressibility ijr-) of liquid water as a function of
the pressure at 0" and 22°. ^"^^''

value. The figure shows also the crossing of the compressibility
curves ; at low pressures the compressibility at low temperatures is
higher than it is at high temperatures, but with rising pressure the
abnormality disappears, and beyond 4000 kgm.. the compressibility is
higher at the higher temperatures. The variation of thermal expansion
between 0° and 22° is shown in Figure 37. This rises to a maximum
at nearly 4000 kgm. and then falls again. The rise to the maximum
is much more rapid than the fall away from it. This maximum verifies
the surmise of Amagat that the dilatation at any temperature would
ultimately decrease with rising pressure for pressures sufficiently high.
The position of this maximum evidently corresponds to the crossing of
the two compressibility curves at 0° and 22°, for we have

0.

dt\dpj ~ d])\dt ) ~
The usual explanation of the abnormalities shown by water at atmos-

542

PROCEEDINGS OF THE AMERICAN ACADEMY.

pheric pressure is on the basis of polymerization. The effect of de-
creasing temperature is to increase the polymerization. For the
present purpose we may think of the molecule stable at higher tem-
peratures as a single molecule and that at lower temperatures as a double
molecule, although the latter is more probably triple and the former

PRESSURE. KGM/CM^ X 10".^

Figure 37. Shows the total change of volume of water between 0° and
22° as a function of the pressure.

double. The double molecule must furthermore be thought of as
occupying more than twice the volume of each of the single molecules
of which it is composed. The effect of a decrease of temperature on
volume is twofold : a decrease such as takes place in any normal liquid,
and an increase due to the clustering of single molecules into double
ones. This increase becomes increasingly rapid at low temperatures
because of the increasingly rapid polymerization. At 4° it has become
sufficiently rapid to neutralize the natural decrease, and at lower tem-
peratures volume increases with falling temperature. The way in
which polymerization is affected by pressure can best be discussed after
reviewing the data below 0°.

The data below 0° show still more strikingly than those above 0°

BRIDGMAN. — WATER UNDER PRESSURE.

543

>

TEMPERATURE

Figure 38. The relation
between voliune and temper-
ature for a normal liquid.

the abnormality at low pressures followed
by normal behavior at high pressures. No
previous measurements seem to have been
made within this region, although the
principal effects are within the reach of
previously attainable pressures. At at-
mospheric pressure the study of water
at low temperatures is prevented by the
accident of freezing. It will pay us, how-
ever, to imagine what would be the relation
between temperature and volume on the
present theory of polymerization if it were
possible to subcool the water indefinitely.
At high temperatures we evidently expect
the water to behave normally, for its mol-
ecules are all single molecules of the same
kind, and similarly at very low tempera-
tures, where the molecules are all double
molecules, we should expect the behavior
to become normal again. The curve
connecting volume with temperature for a

normal liquid is of the form shown in
Figure 38, the dilatation becoming
more rapid at high temperatures.
These considerations lead us to pre-
dict, therefore, a curve of the shape
shown in Figure 39 for water. Ex-
perimentally it has been found pos-
sible to follow this only as far as
—10°, not far enough to reach the
first point of inflection. The effect
of increasing pressure must be to
change in some continuous way the
curve of Figure 39 into that of
Figure 38.

The data indicate very strikingly
the way in which the abnormality is
effaced. Figure 40 shows this. In
this figure the relation between vol-
ume and temperature for various
constant pressures is plotted directly from the data of Table XXXL
Each separate curve is drawn to scale, but the curves for different

TEMPERATURE

Figure 39. Hypothetical rela-
tion between volume and temper-
ature for liquid water if it could
be subcooled indefinitely without
freezing.

544

PROCEEDINGS OF THE AMERICAN ACADEMY.

pressures have been pushed together, so as to come within the limits of
the drawing. The actual separation of the curves is about ten times
that shown. The pressure and the value of the volume at 0° are
indicated on each curve. The manner of transition from abnormal to
normal is shown distinctly, and requires no comment. At 1500 kgm.

,0000
,9776

w

-20° "15

-10" -5" 0" 5
TEMPERATURE,

Figure 40. Curves showing the relation between volume and tempera-
ture of water for various constant pressures. The numbers in the body of
the diagram show the constant pressure of each curve; the numbers to the
right show the volume at 0° of the liquid at the indicated pressure. If drawn
to scale the curves should be separated about ten times as much as shown.

we actually have realized a curve with both a minimum and maximum,
like the conjectural curve at atmospheric pressure. The curves show
one thing in connection with the previous experiments, namely, that the
depression of the maximum density point with pressure cannot continue
linear with pressure much beyond 300 kgm., the limit of the previous
experiments, but the temperature of the maximum becomes nearly

BRIDGMAN. — WATER UNDER PRESSURE. 545

independent of the pressure until the maximum entirely disappears at
higher pressures.

Figure 40 shows the results only to 3000 kgm. Up to this point the
dilatation at 0° has been increasing with rising pressure. But the fact
that the curves of Figure 4 pass through a maximum at about 3200
kgm. indicates a return to normal behavior. From here on the di-
latation decreases with rising pressure. The position of this maxi-
mum evidently corresponds to the position of the maximum of the
dilatation at 3700 kgm. found between 0° and 22°. One would expect
some change in the position of the maximum toward lower pressures
at lower temperatures, but even if there were none, the agreement is
perhaps as good as could be expected when one considers how very
small the experimental quantities are which are involved below 0°.

As far as 4000 kgm., the curves of Figure 4 have been in perfect
accord with the manner of transition shown in Figure 40. Above
4000, however, if the curves are extrapolated in the direction in which
they are heading, there will be new abnormalities. This extension is
not actually possible physically, for the same reason that the h3rpo-
thetical curve connecting volume and temperature at atmospheric
pressure was not possible, namely because the water freezes. But the
extension may be made, nevertheless, for the purposes of speculation.
It is seen that this new abnormality at high pressures and low temper-
atures consists in a crossing of the lines again, so that at 5000 kgm.,
for instance, water would expand on passing from -15° to -20°, just as
for water at 0" and atmospheric pressure. The explanation suggests
itself that this new abnormality is due to the new variety of ice which
is about to separate out, either V or VI. At any rate, the idea seems
perfectly plausible that each of the forms III, V, and VI is a solid form
of water in a different state of polymerization, and that this polymeri-
zation should be shown by anomalous effects in the liquid. There cer-
tainly seems to be a strong presumption raised for this possibility by
the present data. A more accurate experimental investigation would
be well worth making, but would require new methods and apparatus.

We now have enough material in the behavior of the curves both
above and below 0° to see what the role of pressure in wiping out the
abnormalities must be. The one significant fact is that the pressure
wipes out the abnormalities where they stand, without any percepti-
ble shifting of their temperatures. Thus above 0°, the temperature of
minimum compressibility is very nearly constant at 50°, independent
of the pressure. Increasing pressure merely makes this minimum at
50° less and less pronounced until it has entirely disappeared. And
below 0° the abnormalities remain confined to the 15° or 20° below 0°,

VOL. XLVII. — 35

546 PROCEEDINGS OF THE AMERICAN ACADEMY.

the effect of pressure being merely to smooth out the variation of
curvature. Now this is distinctly what one would not expect at first.
The usual explanation of the normalizing effect of pressure is to sup-
pose that the amount of polymerization, the cause of the irregularities,
is decreased by rising pressure. This is the assumption made by
Rontgen ^^ and Sutherland. ^^ The effect of this evidently would be
to displace the region of abnormality from high to low temperatures,
which is what we have seen does not happen. The explanation is
rather to be found in supposing that the pressure merely reduces the
effects of polymerization uniformly at every temperature without
necessarily reducing the amount. This means that the difference of
volume between the double molecules and the two single molecules
becomes rapidly less at higher pressures ; in other words, that the
double molecules possess an abnormally high compressibility. This
seems an entirely plausible hypothesis in view of the abnormally large
volume of the double molecules. At high pressures, then, the poly-
merization, even if it occurs, is unable to produce volume effects, and
might as far as we are concerned be entirely neglected. There may be
effects on the specific heats, which cannot be detected from the pres-
ent data. The explanation of the various pressure effects on this
basis is simple. The anomalous decrease of compressibility with rising
temperature is due to the fact that at the higher temperatures the
double molecules with abnormally high compressibility are becoming
fewer. When pressure has become so high that there is no longer dis-
tinction between the associated and the dissociated molecules, the
behavior of the liquid becomes normal. This explanation leaves en-
tirely open the question as to whether pressure actually increases or
decreases the amount of polymerization. One would naturally expect
an increase. The explanation also leaves open the possibility of the
polymerization being to several different groups, more complicated than
doublets or triplets. This possibility is suggested by the appearance
of the several allotropic forms of ice.

It is to be noticed that in assuming that the molecules are compres-
sible we have not by any means assumed that the actual change of
size of the molecules under pressure is the chief factor in the change
of volume of the substance as a whole under pressure. In fact it is
almost certainly true that the greater part of the total change of
volume is due to the closing up of the spaces between the molecules.
The substance as a whole may have a greater or less compressibility

" Rontgen, Wied. Ann., 45, 91-97 (1892).
"^Sutherland, Phil. Mag., 50, 460-489 (1900).

BRIDGAIAN. — WATER UNDER PRESSURE.

547

according as its structure is more or less compressible. Thus liquid
water is more compressible than ice I, although it has the smaller
volume and is composed of molecules which are themselves less
compressible.

TABLE XXXII,

The Volume of Water Calculated by Tumurz's Formula Compared

WITH Experiments.

Volume.

cm.'/gm.

Pressure,
kgm.

cm. 2

0°

22°

Tumlirz.

Experiment.

Difference.

Tumlirz.

Experiment.

Difference.

0

0.9964

1.0000

-.0036

1.0030

1.0020

+ .0010

1000

9560

0.9586

+.0026

0.9629

0.9636

-.0007

2000

9237

9265

+.0028

9318

9340

-.0022

3000

8983

9009

+ .0026

9067

9090

-.0023

4000

8778

8805

+.0027

8861

8881

-.0020

5000

8607

8626

+ .0019

8690

8703

-.0013

6000

8464

8480

+.0016

8544

8552

-.0008

7000

8341

8356

+.0015

8419

8417

+.0002

8000

8311

8288

+ .0023

9000

8216

8161

+ .0055

10000

8132

8049

+.0083

With regard to the bearing of these data on the theory of liquids,
the theory itself does not seem to be at present far enough advanced
so that these data can settle definitely any crucial questions. In fact,
there do not seem to be any clear cut questions waiting for settlement.
Nearly all the work done so far on liquids has been in modifying van
der Waals' equation by making assumptions which seem more or less
plausible about the way in which the forces between the molecules,
the distances between the molecules, or the energy of the molecules
vary with the temperature and pressure, and the chief aim of all this
activity seems to have been the production of an equation with as few

548 PROCEEDINGS OF THE AJVIERICAN ACADEMY.

constants as possible which should accurately represent the behavior
of as many liquids as possible under changes of temperature and
pressure.

The bearing of these data for water on the theory of liquids as de-
veloped in this way may be best shown by testing how well the equa-
tions already proposed are applicable by extrapolation over this wider
pressure range. For this purpose we may choose the equation given
by Tumlirz ^^ as perhaps the best. Tumlirz has applied his formula to
the data of all the liquids studied by Amagat over a pressure range of
3000 kgm. and a temperature range of 40^" or 50°, with really remark-
able agreement. Tumlirz's formula has the form

{p -f P)(y -a) = RT,

where a and R are constants for any given substance, and P is a
function of the temperature only, to be determined by experiment.
The significance of the assumption evidently is that the covolume
(proportional to the total volume of the molecules) is independent of
pressure and temperature, and that the internal pressure P is not
affected by changes of volume at constant temperature. The re-
sults calculated by Tumlirz's formula, and the actual experimental
results are shown in Table XXXII. The constants used at 0° in the
calculation are those given by Tumhrz. At 22°, P was found by in-
terpolation from Tumlirz's values above and below to be 7152. At 0°,
the agreement is fairly satisfactory, and the discrepancies are of the
same order throughout the entire pressure range. The discrepancies
are greatest at the low pressures, corresponding to the abnormal be-
havior of water here. At 22°, for the lower pressures, the discrepancy
is about the same as at 0°, but the most interesting thing about these
values at 22° is the very evident failure of the formula at high pres-
sures. The values given by the formula for the compressibility
become small too rapidly at the high pressures.

This question as to the behavior of the compressibility at high
pressures is the first one that would occur to one as of significance
for the theory of liquids at high pressures. That is, does the
volume shrink toward a limiting value in the way indicated at low
pressures, or is there some other effect introduced by the high pressure?
The physical picture of the mechanism of the liquid suggesting this
question is that of an assemblage of molecules with intervening spaces.
Is the change of volume of the molecules themselves under pressure
sufficient to produce an appreciable effect after the intervening spaces

» TumUrz, Sitzber. Wien, Bd. CXVIII, Abt. Ila (Feb., 1909), pp. 1-39.

BRIDGMAN. — WATER UNDER PRESSURE.

549

have been shut up? The present conception of the atom as a planetary-
system of electrons would suggest that there are possibilities of enor-
mous change of volume within the atom itself, and that the compression
of the atom is going to continue uniform over a relatively enormous
pressure and volume range, just as under ordinary circumstances a

TABLE XXXIII.
Vakiotts Thermodynamic Properties of Water at 22°.

Pressure,

kgm._

cm.2

Cp — Cv.

gm. cal.

gm.

\apJt

gm. cal.

gm.

\0p/^ \Op/T

(Pi

0

1000
2000
3000
4000
5000
6000
7000
8000

0.0079
164

279
430
498
517
492
417
.279

-0.00159
-0.00117
-0.00104
-0.00104
-0.00071
-0.00049
-0.00019
+0.00019
+0.00068

0.0637
54
75
95
95
85
71
54
33

0.0016
19
23
26
26
24
22
19
15

gas obeys Boyle's law for a relatively very gTeat range of volume and
pressure. The fact is that at high pressures the compressibility does
remain larger than the formula of Tumlirz demands, whether this is
due to a compressible atom or not. The same thing is shown also by
the curve of Figure 36 giving compressibility against pressure. The
tendency of this curve is to become asymptotic to some value greater
than zero, the compressibility changing very slowly at high pressures.
At 5000 kgm. the compressibility has dropped to 1/3 of its value at
atmospheric pressure, while at 10,000 it is 2/3 of its value at 5000.

The compressibility curves for 0° and 22° also indicate one other
thing that would be expected, that at sufficiently high pressures the
compressibility will become independent of the temperature, or in
other words, that the dilatation will approach a value, probably zero,
independent of the pressure.

550

PROCEEDINGS OF THE AMERICAN ACADEMY.

The data obtained for the liquid are sufficient to enable us to calcu-
late certain other quantities of thermodynamic interest. Two of these,
the difference of the specific heats and the change of internal energy
along an isothermal, may be calculated directly from the given data.
Two others, the adiabatic compressibility and the rise of temperature

rp

e
PRESSURE, KGIvj/CM^XIO"?

Figure 41. The mean difference of the specific heats of the liquid for
the temperature range 0°-22°.

produced by compression, may be computed roughly, merely indicating
the direction in which these quantities change under pressure.
The difference of the specific heats is given by the formula

c„

Cp —

Xdr)^

{'A

The quantities entering this equation have been determined directly.
The computed values for 22° are shown in Table XXXIIL, and graphi-
cally in Figure 41. The general behavior is a rise to a maximum at
5000 and then a decrease. For a normal liquid Cp — Cp probably de-
creases continuously with rising pressure. This has been shown to be
the case for mercury in the previous paper. The significance of the
maximum is, then, merely a repetition of the old story that at high
pressure water loses its abnormality and becomes normal. The meas-
urements have not been made to high enough pressures to show the
reversal of curvature on the descending branch of the curve, which
would show complete attainment of normality. The values of Cp — Cp

BRIDGMAN. — WATER UNDER PRESSURE.

551

found here directly differ from those given by the formula of Tumlirz.
This formula, used by extrapolation, would demand a continuous in-
crease in the value of Gp — C^ to infinite pressures, suggesting again
that there is an effect entering at high pressures not taken account of
or foreshadowed by the behavior at lower pressures.

+.0005

o

UJ

a

<
(J

u

: -.0005

-.0020

PRESSURE, KGM/CM^XIO"!

FiGUEE 42. The change of internal energy of the liquid per kgm. rise of
pressure along the isothermal at 22°.

The change of internal energy may also be found directly,
we have the thermodynamic relation

For this

The computed values are shown in Table XXXIII, and Figure 42.
Initially the internal energy decreases along an isothermal, but the
rate of decrease becomes rapidly less with rising pressure, eventually
changing sign, so that at the higher pressures the internal energy in-
creases on an isothermal with increasing pressure. This means that
initially the work done in compressing the water is more than lost by
dissipation of the high heat of compression, but at higher pressures,
the mechanical work per unit rise of pressure has increased so rapidly
because of the high pressure that part of the mechanical work ex-
pended in compressing the water is retained as increased potential
energy after temperature equilibrium has been restored. Except for a
region of abnormal curvature, between 2000 and 5000, which is evi-
dently due to the change from an abnormal to a normal liquid, the

552 PROCEEDINGS OF THE, AMERICAN ACADEMY.

behavior of ( — | found here is probably typical for any liquid. For

mercury, [ — ) is initially negative, but it becomes greater alge-
braically with rising pressure, so that in the mercury paper it was
suggested that probably at high enough pressures the energy would
increase instead of decrease along an isothermal. Here we have an
actual case where the pressure has been pushed far enough to secure
this increase. This might have important applications to astrophysics
or geophysics, since it shows the possibility of storing up very large
amounts of energy in the interior of a star or the earth in virtue of the
pressure alone, quite apart from the high temperatures.

Two other quantities of thermodynamic interest, the adiabatic com-
pressibility and the temperature effect of compression, may be roughly
approximated to. For these we have the formulae

dv
and ['A=^''

(

dp J 4, Cj

p

Both of these involve the specific heat, which cannot be found from the
data obtained, for the specific heat involves the temperature derivative
of the dilatation by the well-known relation

\dpjr '"Wj^

Measurements of the compressibihty at a number of temperatures

would be necessary to obtain this. At high pressures, however, I — 2 )

\dT Jp

becomes less very rapidly. Amagat's data for water show that al-
ready at 3000 kgm. and for a temperature range at least from 0° to 30°

( — I has vanished within the limits of accuracy. We may assume,
ydr-Jp

then, that at high pressure Cp shows a very slow change. For the
rough approximation given here, Cp was taken as constant at 0.9.
Tumlirz found Cp at 2000 to be 0.86, but, as already remarked,
his value is probably too low. The merely suggestive values for

( — I — ( — I and ( ^ ) calculated in this way are shown in Table
\dpj^ \dpj^ \dpj^

BRIDGMAN. — WATER UNDER PRESSURE. 553

XXXIII. The difference between adiabatic and isothermal compressi-
bility increases to a maximum and then decreases. The rise of temper-
ature produced by the application of 1 kgm. pressure also increases
and then decreases again. The normal behavior of both these quanti-
ties, as shown by mercury, is a continuous decrease, so that here again,
we have an effect of the transition from abnormal to normal.

The quantities involved in the change of state from one form to
another are shown collectively in the folder at the end, where the
equilibrium curves, the change of volume curves, and the latent heat
curves are plotted on the same scale for all the modifications. The
fundamental question as to the change of state liquid-solid may be
stated much more definitely than any fundamental question for the
theory of liquids. This fundamental question is as to the ultimate
behavior of the liquid-solid curve. Does it end abruptly, indicating a
critical point for the transition solid-liquid as many have maintained,
or does it rise to a maximum and then descend, as Tammann has
claimed in combating the idea of a critical point, or does it merely
continue rising indefinitely to infinite pressures and temperatures?
Evidently none of these things have happened within the domain of
the present diagram for water, nor have they happened in the low
range up to 3000 or 4000 used before for any other liquid. The only
hold we get on this question is by an extrapolation. In this we are
very greatly helped by the behavior of the latent heat and the change
of volume, for evidently an extrapolation of the equilibrium curve
alone is absolutely incompetent to decide whether it is going to stop
abruptly or not. But if this curve has an end or a maximum, then the
latent heat and the change of volume must behave in a definite manner
with respect to each other. At a critical point, the latent heat and
the change of volume must vanish together, while at a maximum, the
change of volume becomes zero, the latent heat remaining finite.

Tammann's argument for the probable existence of a maximum
comes from observing the general trend of the latent heat and the
change of volume on the equilibrium curve. Tammann could not make
any very accurate measurements of the change of volume, but they
were accurate enough to show that for the substances tried up to 2000
or 3000 kgm. the change of volume becomes less at high pressure, but
the latent heat remains nearly constant. The change of volume is
approximately linear with temperature on the equilibrium line. Whence
by an extrapolation, Tammann concluded that the change of volume
would pass through zero before the latent heat, and that therefore the
equilibrium curve has a maximum. He has calculated the probable
position of this maximum for a number of substances, assuming the

554 PROCEEDINGS OF THE AMERICAN ACADEMY.

melting curve to be a parabola, but this extrapolation is open to very
great question. He himself remarks that at high pressures the equi-
librium curves tend to show less curvature than one would expect from
their behavior at low pressures.

The idea of a maximum seems opposed to our common-sense feeling
of what to expect. If there is a maximum, it is possible by taking the

substance through an isothermal cycle
from the domain of the liquid into
that of the solid and back into that of
the liquid again to find a necessary
connection between the compressibility
of liquid and solid over a wide pressure
range. This is unexpected in view of
our present experience that there is no
necessary connection between the prop-
erties of liquid and of solid. It is to

iij

0.

PRESSURE be noticed that the nearest approach

Figure 43. Tammami's com- *« ^ maximum found here, on the
plete equilibrium curve between H-L curve, was neatly avoided by the
liquid and crystal. The crystal appearance of another form of ice.
is stable only within the closed Proceeding from the probable exist-
region. ^^^g ^^ ^ maximum, Tammann has

developed his well-known theory of the
nature of the complete equilibrium curve between liquid and solid.
The ideal curve (Figure 43) according to this theory is a closed curve,
the crystalline solid having existence only in the interior of the curve.
The complete curve may not be realizable for all substances, since part
of the curve may fall at negative pressures or at temperatures below
the absolute zero. As a matter of fact, only the two upper quadrants
have been realized for known substances, and even then, no substance
has been found in both the two upper quadrants. The upper left-hand
quadrant is that for normal substances, while the upper right-hand
quadrant shows the behavior of water and ice I.

We turn now to the evidence on these points afforded by the present
work on water. First for the equilibrium curves alone. These all
show curvature in the direction demanded by Tammann's complete
diagram, on the I-L curve the fall of temperature becoming more rapid
at higher pressures, and on the other curves the rise of temperature
becoming less rapid with rising pressure. Except on the I-L curve,
this behavior is just exactly what one would expect on nearly any con-
ceivable theory, the effect of temperature becoming less at higher
pressures. This is the behavior also on the liquid-vapor curve, which

BRIDGMAN. — WATER UNDER PRESSURE. 555

ends in a critical point. From the point of view of Tammann's theory,
it is unfortunate that the form I gives place to III at higher pressures,
for in the ideal diagram the behavior of I is the normal behavior at
high pressure and that of III at low pressures, while here we have a
form which should be adapted for the high pressures giving place at
high pressure to one apparently appropriate to low pressures.

The change of volume curves next concern us. These also all show
the general behavior demanded by Tammann's theory, the change of
volume solid-liquid becoming algebraically less at high pressures. On
the I-L curve this means that the change becomes numerically greater.
The approximate reason of this has already appeared from the discus-
sion of the compressibility of the solid to be merely that the solid is
more incompressible than the liquid, whether it has the greater or
smaller volume. The curvature of these change of volume curves is
also everywhere, except for the curve VI-L, such as to suggest that
the change of volume becomes zero at some finite temperature not very
far removed firom the temperatures actually reached.

The latent heat curves also bear out Tammann's point of view, for
they all rise at the higher temperatures on the equilibrium curves.
The direction of curvature of these latent heat curves appears to be
governed by no such general rule as the change of volume curves, since
the curve may be either concave or convex toward the temperature
axis.

So far, for the forms of ice I, III, and V, which are stable at low
pressures, everything seems as indicated by Tammann's theory. It
should be remarked that the pressure range of existence of these forms
is twice that reached before. It is on the VI-L curve, however, which
reaches to much higher pressures, that we find the significant sugges-
tion as to what to expect at still higher pressures. This suggestion
comes from the change of volume curve, which shows a pronounced
point of inflection in the neighborhood of 30".^^ Below 2.0°, the curva-
ture is like that for the other modifications at low pressures, indicating
the vanishing of the change of volume at perhaps 50° or 60°, but
beyond 30° the change of volume decreases less and less rapidly
with rising temperature, with the possibility of becoming asymptotic.

2° With regard to the effect of probable experimental error at the high
pressure it is to be said that the effect of this would be to make the inflec-
tion shown in the diagram appear less pronounced than it really is. The
change of volume at high pressures is too low if anything, because in making
the correction for the change in the bore of the cylinder under pressure it was
assumed that the increase of bore is linear with pressure, whereas, if anything,
it increases more rapidly at high pressures.

556 PROCEEDINGS OF THE AMERICAN ACADEMY.

That is, at the high pressures there is no indication that the change of
volume will ever become zero- This inflection in the volume curve is
also mirrored by a corresponding inflection in the latent heat curve,
which rises more and more rapidly at the upper end. Also this change
of direction of the volume curve occupies the same general locality as
the region on the compressibility curves for the liquid where the com-
pressibility ceases to decrease as fast as one would expect from the be-
havior at low pressures. This behavior of the volume curve, together
with that of the latent heat curve, shows in the first place that the
latent heat and the change of volume do not vanish together, so that
there can be no critical point, and in the second place, that the change
of volume apparently will not vanish at any finite temperature, so that
we will not have a maximum as supposed by Tammann, but the curve
will rise instead to infinite pressures and temperatures.

Recently J. J. van Laar^i has been developing a theory of the solid
state which is more far reaching than that of Tammann, in that it at-
tempts to show the actual mechanism which makes a liquid pass to the
solid. This theory explains the solid state by the association of the
simple molecules to molecular complexes. For the sake of simplicity,
the theory has been developed for the case where the complexes are
double molecules, although this restriction is not necessary. Given,
then, a liquid in which both single and double molecules may exist,
van Laar has found, by writing down the thermodynamic potential of
the two kinds of molecules, how the dissociation of the double mole-
cules into single molecules varies with pressure, volume, and tempera-
ture. Accompanying the dissociation is a change of volume, for the
volume of the double molecule is not in general twice that of the two
single molecules from which it comes. This change of volume, due to
dissociation, is found to so modify van der Waals' equation, which is
still supposed to hold for either kind of molecule separately, that an
isotherm now has two maxima and two minima, instead of the single
maximum and minimum of van der Waals' original equation. This
evidently means the existence of a new phase, the solid, the equilib-
rium conditions of which are determined in the same way as the equilib-
rium conditions liquid-gas of the ordinary equation, by applying the
condition that the work done in a reversible isothermal cycle is zero.

By detailed numerical computation, van Laar has shown how on this
theory the equilibrium pressure solid-liquid changes with increasing
temperature. The results are similar to those of Tammann in that a

" van Laar, Proc. Amster., 11, 765-780 (1909); 12, 120-132, 133-141
(1909); 13, 454-475, 636-649 (1910).

BRIDGMAN. — WATER UNDER PRESSURE. 557

maximum melting temperature and a maximum melting pressure are
both predicted. That is, in Figure 43, van Laar has the same maxi-
mum and the same right-hand vertical tangent as Tammann, but the
results differ from Tammann 's in that the minimum and the left-hand
vertical tangent cannot exist, or at any rate if they do, they must
always lie at temperatures below the absolute zero and at negative
pressures.

These results of van Laar were obtained with the specific assump-
tion that the actual volume of the molecules, and so the change of
volume when a double molecule passes into two single molecules, is
independent of temperature and pressure. This is almost certainly not
the case. The value of the compressibility of water at high pressures,
the way in which the abnormalities are smoothed out in the neighbor-
hood of 0°, and the point of inflection in the A F curve for VI above 0°,
all suggest most strongly that the assumption is not true, and further-
more that it is not approximately enough true to enable even the gen-
eral character of the melting curve to be predicted at high pressures.

The conclusion of the whole matter seems to be that at high pres-
sures, over 10,000 kgm. for water, we have a new effect appearing,
probably connected with the compressibility of the atoms. This means
that at high pressures the compressibility of the liquid and solid are
going to become more and more nearly equal, which will have as a con-
sequence that the equilibrium curve will continue rising indefinitely.

Besides the data just discussed for the liquid-solid curves, we have
the corresponding data for the solid-solid curves. There is no theory
at present of the equilibrium solid-solid, and the data here only bear
out a remark of Roozeboom 22 that different allotropic solids would be
expected to show every conceivable relation to each other. Two triple
points between three solid phases had been found, l-II-III, and II-
III- V. The first of these is of a type already known, but the second is
of a type of which, according to Roozeboom, no examples have yet been
discovered. This is Roozeboom's sixth type.23 The equilibrium lines
are for the most part straight, but this merely indicates that the com-
pressibility and thermal dilatation of the solids are nearly constant
over the range of temperature and pressure in question, as one might
expect. The only curved equilibrium lines are I-III and II-III. In
both of these III is involved. But it was to be expected a priori that
III is a form of ice with more variable properties than the others, be-

*2 Roozeboom, Die Heterogenen Gleichwichte, vol. 1, p. 206. (Vieweg,
Braunchweig, 1901).

^' Roozeboom, loc. cit. p. 202.

558

PROCEEDINGS OF THE AMEEICAN ACADEMY.

cause of the close approach of its equilibrium curve with water to a
maximum. In general, the internal energy increases on passing from
a solid stable at low pressures to the solid stable at higher pressures,
but III-II is an exception. The most interesting features found for
the equilibrium solid-solid are the probable passing of the I-II curve
through the absolute zero, the enormous increase in reaction velocity
on approaching a triple point, and the existence in one crystalline form
of nuclei about which crystallization to another form may begin.

Acknowledgment is here made of several liberal appropriations from
the Rumford Fund of the American Academy of Arts and Sciences,
with which the expenses of this investigation were partially defrayed.

Jefferson Physical Laboratory,
Harvard University, Cambridge, Mass.,
October, 1912.

PLATE 1.

The equilibrium diagram between the Uquid and the five solid modifications
of water.

PLATE 2.

The change of volume when one modification passes to another under
equiUbrium conditions.

PLATE 3.

The latent heat when one modification passes to another under equilibrium
conditions.

BRIDGMAN. — WATtR UNDER PRESSURE,

PmTE I.

Bridgman. — Water under Pressure.

Plate 2.

Briogman. - Water umoer Pressure.

PUiTE 3.

TEMPERATURE.

Proc. Amer. Acad. Arts and Sciences. Vot. XLVII.

-80' -60° -40° -20° 0° ZO" 40° 60' fiO*

TEMPERATURE

Proc. Amer. Acad. Arts and Sciences. Vol. XLVII.

1

o
q:

90

80

70

60

.50

-J
<

"40

.30

I 20

^10

bJ

^0

-10

^

.^

K^

g-r

-80* -B0° -40° -20° 0° 20° 40° 80° 80*
TEMPERATURE

Ppoc. Amer. Ac*n. Art"; ano Sciences. Vol. XLVII.

Proceedings of the American Academy of Arts and Sciences.
Vol. XLVII. No. 14. — January, 1912.

CONTRIBUTIONS FROM THE JEFFERSON PHYSICAL
LABORATORY, HARVARD UNIVERSITY.

ON AN ELECTROMAGNETIC THEORY OF
GRAVITATION.

By D. L. Webster.

V

CONTRIBUTIONS FROM THE JEFFERSON PHYSICAL
LABORATORY, HARVARD UNIVERSITY.

ON AN ELECTROMAGNETIC THEORY OF GRAVITATION.

By D. L. Webster.

Presented by B. O. Peirce, November 8, 1911. Received November 8, 1911.

The desirability of an electromagnetic theory of gravitation has been
pointed out many times, by Maxwell,^ Lorentz,^ and others, who
would assume that gravitation is due to a slight excess in the attrac-
tion of an electric charge for one of the opposite sign over its repulsion
for an equal one of the same sign; and also by Einstein and his fol-
lowers, who would have changes of gravitational attraction propagated
with the velocity of light. But Maxwell and Lorentz had no proof of
the truth of their theory, or reason for belief in it, other than that it
might connect gravitation and electricity; and even Einstein had no
proof, but only the fact that if the velocity were different from that of
light, we should have a means of detecting absolute motion. The ob-
ject of this paper is to give some reasons for belief in the electromag-
netic theory, and to point out some of its most surprising results.

Objections have been raised against such a theory, principally on the
ground that it would involve gravitational aberration like the aberra-
tion of light, but I hope to show that the electromagnetic theory
involves no such consequences. Wiechert^ and others have also
objected on the ground that gravitation is essentially different from
electrostatic force, especially in its ability to penetrate even the densest
matter without appreciable change. But it may be proved, with no
other assumption than that a dielectric affects electrostatic force only
through the displacement of negatively charged particles within it, that
the uniform gravitational permeability of all dielectrics is no argu-
ment against the electromagnetic theory. And it has been proved by
Gans * that the equality of the gravitational permeabilities of vacuum
and conductors is also consistent with such a theory.

* Maxwell, Electricity and Magnetism, Vol. 1, p. 40.

2 Versl. K. Ac. van Wet., 8, 603 (1900); 8, 616 (1900).
' Wiechert, IJber die Relativitatsprincip und Ather, Phys. Zeitsch., 12,
18-19.

* Phys. Zeitsch., 6, 803.
VOL. XLVII. — 36

562 PROCEEDINGS OF THE AMERICAN ACADEMY.

Notation. — The notation used in this paper will be that of Gibbs,
in which all vectors may be distinguished by being printed in Claren-
don type, while scalars will be in italic type. Thus, a would be a
vector, and a a scalar. The magnitude of any vector a will be denoted
by|a|.

The scalar product,

• (a^b^ + a^b^ + a^bj),

of two vectors a and b will be denoted by a-b; and their vector
product,

i (a^b, - a,b,) + j (a,b^ - a^b,) + k (a,b^ - a,b^),

by axb, where i, j, and k are the unit vectors in the directions of a?, y,
and z, respectively.

The symbol V will be used for the operator.

(

.3 .a , a
1 V- +Jh- + k —

ox dy oz

so that va is the gradient of scalar a, a vector; V -a is the diverg-
ence of vector a, a scalar ; and v xa is the curl of vector a, another
vector.

The "mass" of a body must be understood to mean its mass as
measured on a system of axes on which it is at rest; and similarly the
density, which will be denoted by the letter p, will mean the limit of
the ratio of the mass in a volume element to the volume of the element,
with the above interpretation of the word mass. The mass of a body
will, therefore, be a measure of the amount of matter, or " gravita-
tional charge" in the body, which will be different for moving bodies
from the "inertia" usually understood by the word mass.

Other Theories of Gravitation. — With this notation we may now
examine the results of various methods by which we might imagine the
changes of gravitational force to be propagated.

First, let us imagine, according to what I shall call " Theory I," that
the changes of gravitational force due to any changes in the position
of matter take place at the same instant at every point in space. In
this case, if g is the gravitational force per unit mass at any point.

g

^■v///;* = -^///r''^'*

where r is the distance from the volume element dr to the point at
which the integral is to be evaluated, x^ the unit vector in the direc-

WEBSTER. — AN ELECTROMAGNETIC THEORY OF GRAVITATION. 563

tion from the element, and h the gravitation constant, 6.480 X 1()~'

cm

-„ • This assumption involves the existence of " absolute time "

gm. sec.

and instantaneous action at a distance, but is a possible hypothesis if

these are possible.

The hypothesis which I shall call " Theory II " is the consequence

of most of the mechanical explanations of gravitation, such as the

well known Le Sage theory, and theories of attraction through the

pressure of invisible radiation or through the pulsations of slightly

compressible electrons in a less compressible fluid. According to this

theory the attraction at any time t on any particle is determined by

the matter that occupied each volume element at a time \i— j,\

where C is some very large velocity, and r is, as above, the distance
from the element. In this case, if we let [p] equal the value of p in
the element at this time, we have

^-d'sr^^''^

For " Theory III " let us suppose any particle moving uniformly to
carry a perfectly symmetrical system of lines of force with it, so that
at any instant the forces due to it at all equidistant points will have
equal intensities and be directed exactly towards it. But if its motion
is changed by an infinitesimal amount, let us suppose that the disturb-
ance of the force is propagated with a velocity C relative to that of
the particle at the time the change of its velocity takes place.

In this case,

00

where / is the distance at which the matter would have been at time

t, that occupied the element dr with density [p]' at the time ( ^ — 7-, )'

if it had kept since that time the velocity it then had. We may also
say

„__^. f rr bJriVr

^~ J J J r\l+B^-2BrTj

where B is the ratio of the velocity of the matter in the element dr at
the time [ t — y^) to the velocity C.

564 PROCEEDINGS OF THE AMERICAN ACADEMY

For " Theory IV " let us assume that there is another vector h re-
lated to the vector g in the same way that magnetic force is related to
electric, and that these vectors satisfy the set of equations :

V • g = — 4 irpk

V -11 = 0

ah

V xg = -

d{Ct)

f = g -+- Bxh,

where f is the force per unit mass due to the gravitational force g and
" gravimagnetic " force h. It will be noticed that these equations are
very much like the electromagnetic equations :

V • E = 4 TTC

V -H^O

aE

VxE = —

d{ct)

F = E + pxH

where E and H are electric and magnetic forces, c the charge per unit
volume, P the ratio of the velocity of the charge at any point to the
velocity, c, of propagation of electromagnetic disturbances, and F the
force per unit charge due to electric and magnetic forces.

If we assume with Einstein that there is no ether, and no universal
or absolute time, we readily see that these theories are all inconsistent
with this belief, with the single exception of the special case of Theory
IV which we may call "Theory V," in which C = c. If, on the other
hand, we assume the "conditional relativity principle," of Wiechert ^
and assume the existence of ether and absolute time, we see a wider
range for Theory IV than that obtained by merely giving different
values to C, in that Theory IV does not define any particular state of
motion that may be assumed to be the state of absolute rest, and un-

Wiechert, Relativitatsprinzip und Ather, Phys. Zeitsch., 12, 18-19.

WEBSTER. — AN ELECTROMAGNETIC THEORY OF GRAVITATION. 565

less we make such a definition we have no single- valued definition of
any of our time derivatives, even though we have a definition of abso-
lute time. The physical significance of this statement is that, accord-
ing to Theory IV, all gravitational disturbances must be propagated
with a velocity C through an ether that is not necessarily at rest relative
to the electromagnetic ether. Therefore to define Theory V completely
in terms of Theory IV, we must say that the two ethers must be at
rest relative to each other, and that the two velocities C and c must
be equal.

Objectio7i against Theories I-III. — If we now examine further the
consequences of these theories, we shall see that Theory I, if not im-
possible, is highly improbable ; and that Theory V is the only other
that does not involve a continual increase of energy of any system of
gravitating bodies.

Assuming the unconditional relativity principle, all but Theory V
are, of course, impossible. But assuming the conditional relativity
principle, we see that Theory I involves either instantaneous action
through a medium that is also capable of propagation of disturbances
with a finite velocity, or else it involves true "action at a distance."
Also it has been shown by Wilkens ® that the changes of the perihelion
of Mercury and other astronomical phenomena, which are consistent
with the electromagnetic theory, are inconsistent with Theory I.

These difficulties make it necessary to look for some other theory,
such as II. But if we assume the truth of this theory, we must say
that the components of a binary star revolving in circles about their
centre of gravity will each be accelerated at time ^ by a force directed

towards a point where the other was at time ( ^ — 7^ ) ; and this force

will have a component in the direction of motion which is an infini-
tesimal, if C is allowed to become infinite, of the order of | B | for the
other body. But no matter how large C may be, this component of
the force will never be absolutely zero. Hence the ever increasing
kinetic energy would tear any such system apart, even though the
components were unequal and the orbits not circular ; and even a
rotating planet would increase its energy of rotation until it burst,
and would continue increasing its energy forever, even after disrup-
tion ; so that, if Theory II held, the earth and the whole solar system
would have gone to pieces long ago and left not even the law of the
conservation of energy for a vain consolation.

Theory III might be expected to remove this difficulty, but it does

« Phys. Zeitsch., 7, No. 23, 846.

566 PROCEEDINGS OF THE AMERICAN ACADEMY.

not, though it does reduce the component of force in the direction of
motion to an infinitesimal of the third order. For if we consider a
system where Ai and A2 are the positions of the two masses m^ and 7^2,
revolving in circular orbits at the time t, B^ and B2 their positions at

the time it y~ ) and ( t ^r^ )' ^^^ ^1 ^^^ ^2 the positions

they would have occupied if they had kept since the above-mentioned
times the velocities they then had, we see that Ci and Bi must always
lie on the same side of the line A^Ai produced. If the velocity C
becomes infinite, the distances from C^ and C2 to the line Aj^A^ are
obviously infinitesimals of the third order, but they can never be ex-
actly zero ; and hence there will always be a forward component of
force that must ultimately produce the same disastrous results that
we have seen in Theory II. Hence we see that Theories II and III are
almost certainly false.

Theory IV. — Let us now suppose that Theory IV is correct, and
examine its consequences. By Green's Theorem it may easily be
proved that the gravitational energy liberated in scattering any distri-
bution of gravitating matter to infinity is

-8S///^'*

if the matter is all at rest. But if the matter is in motion, we must
add to this, to get the gravitational energy liberated in bringing it all
to rest at infinity,

Wk J J J^

sr ■ ■ ■^^^^-

And if the ratio of the velocity of matter at every point to that of
light is the vector point function p, the total kinetic energy in the uni-
verse is

///

pc^ (E-' - 1) dr

where R = Vl — ^^- We may now assume as in the corresponding
electromagnetic case, that the integrands in the above expressions
actually represent the energy that would be removed in the scattering
process from the volume elements for which they are evaluated, and

WEBSTER. — AN ELECTROMAGNETIC THEORY OF GRAVITATION. 567

hence that the energy in a region T of any distribution of matter acted
upon only by gravitational forces is

///

{pc^ {Br^ - 1) _ -L (g. + h'^)} dr.

While this assumption is not necessarily true for any finite region, it is
certainly true in the limit for a sphere whose radius is allowed to be-
come infinite.

Gravitational Radiation. — We may prove the following theorem :
If a distribution of matter is affected by forces of which none but
those of gravitational origin do any work, the energy, Eg, within any
closed surface, S, which neither matter nor electromagnetic energy
enters or leaves, and which has a normal at every point, will increase
or decrease at such a rate that

dE. . 1 rr . ^s

d(Ct)

= +i^/>'"

where dS is the element of surface considered as a vector in the direc-
tion of the exterior normal.

The truth of this theorem depends on that of the above assumption
about the energy in the region T, but it is certainly true for the in-
finite sphere.

The proof (like that of Poynting's theorem), is as follows : If 7^ is
the space within S,

^' ^ fff^'''^^" ~ ^^ "■ 8^- ^^' + ^'^^ ^'

dK

1 / 3g , , ah \ ) -

-- (g • V xh — h • V xg) - ^.g • B ^ dr.
4:7r )

5G8 PROCEEDINGS OF THE AMERICAN ACADEMY.

But pg • B is the increase of kinetic energy per unit volume per unit Ct
for a volume element moving with the matter in it ; hence

d(Ct)

T

Q. E. D.

To find the amount of negative gravitational energy radiated from
an accelerated particle when it is at rest, we may make use of the re-
sult of the corresponding electrical case. In this case, if the charge on
the electron is e, and the accleration is a, and the unit vector in the
direction from the electron to the point considered is ii, the electric
force due to radiation at a distance r is

E = - 4- ^p.

where a^ is the component of a perpendicular to fi, and the magnetic
force due to acceleration is

H = + -^ axri = TixE."'

The magnitudes of these forces are seen to be equal, and the directions
at right angles. For the corresponding gravitational case, we need
only to change the signs of these expressions and substitute mk for e,
and C for c, and we have

mk

"pi

, mk

h = -' ^ axri = Tixg.

We now see that

. _ m^k% 2 _ m^k^ , .2

' For proof see Lorentz, " Theory of Electrons," Chapter 1.

WEBSTER. — AN ELECTROMAGNETIC THEORY OF GRAVITATION. 569

But if we now have two particles with constant accelerations, op-
positely directed, we see that the vectors g and h for one of the par-
ticles will have nearly opposite directions to the corresponding vectors
for the other particle at points very far from the two masses. For
such points we may then say the total gravitational force is

_ _^ mir22ipi + W2?'ia-p2

The fraction B'p^/^pi will have a meaning only in a case where it is
multiplied by a product of a scalar by a^i, or in a case where a^i and
2ip2 have the same direction, as in the limit ^i = oc , when it will ap-
proach a scalar limit. Unless this limit is — mi/mz, g will be an infini-
tesimal of the order of l/n. But if lim apa/a^i = — mjmxt then we
readily see that g and h are both infinitesimals of the order of \/rx or
of a higher order, and gxh is of the order of Xjrx or higher. But
this is possible for all directions only if m-iji.^ = — m^^^, and therefore
in this case, and only in this case,

rLzffs^^-^^ = o

where S is & sphere of radius r, surrounding the particles. Hence we
see that there is no radiation of negative energy from a pair of uni-
formly accelerated particles momentarily at rest, if, and only if,

mi&i = — m-^2.

Radiation from a Rotating Body. — Since Theory IV, with C ^ c,
is inconsistent with the unconditional relativity principle, we must, in
assuming the truth of it, assume the existence of an ether and an
absolute system of simultaneity. But if now we assume that gravity
is transmitted through an ether that is independent of the electro-
magnetic ether, and moving through it, we must assume the time
to be the same absolute time in both cases, and the lengths to be
measured in absolute units of length.

If, with these assumptions, we consider the motion of a body rotating,

570 PROCEEDINGS OF THE AMERICAN ACADEMY.

undisturbed by external influences, about an axis of symmetry that is
at rest in the gravity ether, we may determine whether it can satisfy
the condition

'^ =0.

d{Ct)

It might now be supposed that we could not do this by determining
whether

because the radiation from an accelerated electron already in motion is
not the same as if it had the same acceleration when at rest. But it is
obvious that, if we consider any direction making given angles with the
directions of the velocity and acceleration, the ratio of the rate of
radiation in that direction in the case with velocity to the corresponding
rate in the case with no velocity is a function of only the magnitude of
the velocity and the angle between the velocity and acceleration, and
not a function of the charge or acceleration of the electron. Hence we
see that, if we consider a case where the two variables that determine
this ratio are the same for every point of the infinite sphere, we may
then, and only then, say that there is no radiation of negative energy
from a pair of uniformly accelerated gravitating particles if, and only if,

midii = — m^^^.

Returning to our rotating body, which may be any solid, liquid, gas,
or collection of very minute particles like Saturn's rings, provided only
that all points in any ring of infinitesimal cross-section around the axis
shall have the same density and the same constant angular velocity
around it, we see that the condition that no energy shall be radiated to
infinity from the body is that there shall be no radiation to infinity from
any of these rings.

First let us assume that the axis is stationary in the gravity ether
and perpendicular to the direction of motion of the electric ether
through it, and let us see when this condition will be fulfilled. For
simplicity let us consider first only the case of a collection of particles
such as Saturn's rings or a rotating nebula with no internal forces but
those of gravity. In such a case it is obvious from symmetry that if
the inertia of a particle were proportional to its mass and independent
of its velocity, the system could rotate indefinitely, preserving always
its symmetry about the stationary axis, and, since the accelerations at
opposite points would be equal, opposite, and constant, not radiating

AVEBSTER. — AN ELECTROMAGNETIC THEORY OF GRAVITATION. 571

any energy. But since the inertias of two equal particles would be
unequal when they were going in opposite directions not perpendicular
to the direction of motion of the electric ether, we see that if the
system were brought into the condition assumed above, the accel-
erations at opposite points would be unequal and there would be
radiation. Hence to avoid radiation we must have the two ethers
relatively at rest.

If we introduce internal forces other than those due to gravity, we
make the problem much more complicated, but it is evident that the
results would be of the same general nature, and that if the two ethers
were relatively at rest there would be absolutely no radiation.

With this assumption of relative rest, we may now solve the problem
of the radiation from such a collection of minute particles rotating
about its axis, and at the same time moving through the ethers with a
velocity comparable to that of light. From the similarity of the
gravitational equations to the electromagnetic, we see that if we intro-
duce a gravitational relativity principle, exactly like the electro-
magnetic relativity principle with C substituted for c in all formulas,
the condition that two equal volume elements opposite to each other in
the body shall not radiate negative energy to infinity is that the
accelerations of the matter in them measured in the gravitational units
of moving distance and local time shall be equal and opposite.

We may now suppose the particles to be brought into positions and
velocities that appear at a certain instant of the gravitational local
time of a system moving with the axis to be absolutely symmetrical
about the axis. But since the equation " force equals rate of increase
of momemtum," holds only when the electromagnetic units of local
time and moving distance are used, we see that the accelerations of
opposite particles are equal in the gravitational system only if all the
corresponding units are equal, or if

C=c.

And we see also that if other internal forces are introduced, the problem
is again more complicated, but that we have a similar result, that there
is absolutely no radiation of negative energy from any body rotating
about an axis of symmetry only with Theory V.

Radiation from two or more Gravitating Bodies. — If, however, we
consider the more general case of two or more bodies moving under the
action of no forces but those of gravity, we shall find a small amount
of radiation even with Theory V. But this unavoidable radiation is
very small, being in general for any pair of bodies less than the product

572 PROCEEDINGS OF THE AMERICAN ACADEMY.

obtained by multiplying the radiation from one of them alone by the
square of the ratio of their relative velocity to the velocity of light.
And we shall prove that while, for small bodies, this radiation is due
only to the changes in the accelerations in the time required for
propagation of radiations from one to the other, Theory IV involves
radiations that may be larger than this in any desired ratio, and that
are due to actual differences of mass acceleration.

To prove this, let us determine, from the equations of Theory IV, the
accelerations of two masses, nii and m2, moving through the gravity
ether with equal opposite velocities parallel to that of the electric
ether, and whose ratios to C are Bi and B2., let the direction of w be that
of Bi and let us suppose the two particles to be moving so that niz is in
the direction of the axis of?/, at a distance a from mi, at the instant
considered. If now we let ri be the distance of any point from mi , in
a direction making an angle Oi with that of ^, we have the gravitational
force due to mi, neglecting that due to radiation and change of Bx in
time Ti/Cy directed towards mi at every point, and of intensity

l&i I=^(l-B,^)(l-B/^sin^^O"^,
t'l

while the gravimagnetic force due to mi is

hi = Bixg^i.

These formulas may be proved by substitution in the equations of
Theory IV, assuming Bi constant.

Therefore, neglecting radiated forces from mi and change of Bi, the
force acting on tn^ is

m^fi = ^2 (gi + Baxhi).
Therefore

Similarly

m,2i, = - j ^-^ B, (1 - B,^)-' (1 - B2 . BO.

mi^i = + j ^^^ Bi (1 - B.^r (1 - Bi ■ B2).

Since

B., = - B,

we have

miB,i = — nizB-i

if, and only if,

Bi = B„

or

Pi = - P2,

in which case the forces due to radiation are also equal and opposite.

"WEBSTER. — AN ELECTROMAGNETIC THEORY OF GRAVITATION. 573

Therefore to avoid continually increasing energy we must again have
the two ethers at rest relative to each other.

Now let us consider a similar case where the centre of the line join-
ing them is not at rest in the ether. Here we may again introduce the
gravitational relativity principle and with the aid of the gravitational
local time and auxiliary distance units thus defined, we may solve the
problem exactly as we did the one above. But we now see that if the
velocity of mi in the new system is in the direction of the velocity of
the new system by the old, and if

B/ = - B/

where primes denote measurement on the moving system, then, since
the electromagnetic units of apparent distance and local time are
different from the corresponding gravitational quantities,

Pa' ^ p/, and /?/ it Bi
unless C — c.

It seems strange at first sight that Theory V is not overthrown by
the same considerations that proved Theory III impossible even for the
case of a rotating body. But the arguments used in that case do not
apply here ; because every particle in the body is affected at every
instant by forces radiated from the other particles, and it is obvious
from qualitative considerations that they will exert a backward force on
the particle of the order of | P' ^ | times the total force on it, and it
is further evident from the fact that the radiation theorem proves that
there is no gain of energy that this force must exactly balance the for-
ward component of the non-radiational force.

Reasons for Preference of Electromagnetic Theory. — We now see
that Theory V is the only theory we have examined, except the
practically impossible Theory I, that does not involve an extremely
improbable, continual increase of energy in any rotating planet, sun,
or nebula. With such a continual increase of energy it is doubtful
if the solar system could have been formed. Furthermore, Theory
V is the one that involves the least radiation of negative energy,
which we see is a destructive process, from such a system as the solar
system is at present. Of course, we cannot prove that the solar system
would yet have gone to pieces with more radiation than this, but we
can say that if there had been enough additional radiation of this sort
it would have.

We have, however, a much more convincing argument, for if we think
of such laws as the law of the minimum possible loss of heat in electric

574 PROCEEDINGS OF THE AMERICAN ACADEMY.

currents, the principle of " Least Work " so useful in civil engineering,
the principle of " Least Action " or " Hamilton's Principle " in dynamics
of matter and of electricity, and many other laws of this sort, it seems
highly probable that, if there must be destructive radiation of gravita-
tional energy, the laws by which such radiation takes place should be
those involving the least amount of it.

Another argument of the same general nature is furnished by the
extreme simplicity of the fundamental equations of natural phenomena,
such as the equations of electrodynamics, either in Maxwell's form or
in terms of scalar and vector potentials, the equation for the flow of
heat in a solid, and many others, that all combine to make us believe
that, if there is one set of equations for gravity that are simpler than
all other possible equations not involving improbable results, these are
the ones that express the phenomena correctly. This argument of
eimplicity is all the more striking if we write the electromagnetic equa-
tions in the remarkably simple form that they assume when expressed
in the four-dimensional vector analysis of Lewis.* This analysis
gives us a set of gravitational equations of equal simplicity, if, but
only if, we adopt the electromagnetic theory. And for Theory V we
have not only a similar set of equations, but, when we consider their
meaning, a simpler explanation of their fundamental causes than can
readily be found with any other theory. With these considerations
combined with the experimental evidence furnished by the planet Mer-
cury, it seems as though we could hardly help believing in this theory.

To see what Theory V means we have only to consider the theory
that matter is made up wholly of electrons and the corresponding posi-
tive charges. If now we suppose every positive charge at rest to repel
every other positive charge with a weaker force than that with which it
attracts an equal negative charge in the same relative position, the ratio
of the difference between these forces to the attractive force being a
very small number G, we see that every particle of matter at rest will
attract every other particle with exactly the observed force if G is
properly chosen. And if now we suppose that the magnetic force from
a moving positive charge has a smaller effect on another moving posi-
tive charge than on an equal negative one with the same relative posi-
tion and velocity, and that the ratio of the difference between them to
the force between those of opposite signs is the same number G, the
existence of the vector h is explained. But we must assume forces
between two negative charges to be equal and opposite to those between
positive and negative, for, as Gans * has shown, this set of assumptions

* These Proceedings, 46, No. 7, October, 1910.
. » Gans, Phys. Zeitsch., 6, No. 23, 803.

WEBSTER. — AN ELECTROMAGNETIC THEORY OF GRAVITATION. 575

is the set which makes the gravitational permeability of any conductor
equal to that of a vacuum. And we see, furthermore, that if electro-
static forces are to obey the principle of relativity, and the first of these
assumptions is made, the second and the obedience of the force of
gravity to the relativity principle are necessary consequences of the
first.

By comparison of the electrostatic repulsion of two electrons, whose
ratio of charge to inertia is 5.595 X 10"*'^, with the gravitational attrac-
tion between two spheres, we would find that

G^=1.67 X 10-*-,

if the fundamental positive charge were similar to the negative elec-
tron. ^^ This readily accounts for the fact that its existence has never
been experimentally observed.

We may or may not, as we please, assume that this slight difference
between the forces is produced by the same cause which produces the
rest of the forces, but from the fact that it is transmitted through the
same ether, with the same velocity, it seems most reasonable to assume
that it is due to the same cause.

Consequences of this Theory, Negative Energy. — One of the most
surprising facts about the electromagnetic theory of gravitation, and
one with most surprising consequences, is the fact that we have to
introduce the conception of negative energy, both potential and kinetic,
distributed through the space around any gravitating matter. And
by the term, "negative energy," we cannot mean a mere diminution
of the positive energy in the space, as the following considerations
will show.

First let us consider the energy radiated from an accelerated mass,
whose inertia is balanced by the inertia of some mass at a great dis-
tance, so that the radiations of gravitational energy cannot interfere
for a considerable time. We now see that during that time the transfer
of energy across any element of surface dS per unit ct is

--i^gxh-dS,

^•^ Since the inertia of an electric charge e on a sphere of radius a is propor-
tional to eVa, G is different from the above value if the fundamental positive
charge has not the same e/o as the electron, where a in this case is a sort of
average radius of points in the electron or positive charge. But the fact that
k is the same for all kinds of matter indicates that, if there is only one kind
of positive electricity, with only one value of G, it must be collected in funda-
mental charges for all of which e/a is the same. Hence we have reason to
believe that all atoms of positive electricity are probably alike.

576 PROCEEDINGS OF THE AMERICAN ACADEMY.

but that if we draw two surface elements, dSi and dSg, parallel to each
other and perpendicular to the same line of the vector gxh at a dis-
tance dx apart, we see that, if dSa is in the direction of gxh from dSj,
the energy radiated from a mass that is accelerated for an infinitesimal

time crosses dSg at a time — units of time later than that at which it

c

crosses dSi, so that the transfer is actually in the direction of gxh.
But such radiated energy has lost all connection with its source, and
there is no positive energy radiated, hence it is negative energy that is
transferred in the direction of gxh across these surfaces.

It is also interesting to notice that in the case of a mass moving with
uniform velocity the vector gxh has the same direction as the motion
at all points in the plane through this mass perpendicular to this direc-
tion. This also indicates that the mass carries negative energy with it
as it moves. But if the mass is not charged with electricity, the elec-
tric and magnetic forces due to the electrons and corresponding positive
charges within it are zero at points outside the mass. Therefore, the
electromagnetic energy is wholly within it, and the external gravita-
tional energy cannot be considered as a mere diminution of the electro-
magnetic energy on any theory that assumes the existence of positive
energy only. To calculate the energy in terms of the electric and

magnetic forces we must distinguish between the forces due to positive

+ +
charges which we may call E and H, and those due to negative charges,

which we may call E and H. In this case the total energy of the dis-
tribution is

00

= hffl^^^ ~ ^^ ^^' ^ ^'^ "^ ^^' + H^) -I- 2(E • E + H . H)} dr,

CO

where we have exactly the same distribution of total energy in each
element ; and we have made a change only in assuming that the whole
positive charge and whole negative charge have each a much larger
amount of positive energy than the total energy of the system, but
that negative mutual energy of the two distributions more than neu-
tralizes their positive energy in all volume elements outside the mass,
and fails to do so only within the mass.

Stresses in the Gravitational Field. — We have by no means yet ex-
hausted the store of interesting facts connected with this negative

"WEBSTER. — AN ELECTROMAGNETIC THEORY OF GRAVITATION. 577

energy. For the similarity of the gravitational equations to the
electromagnetic tells us that we may expect gravitational energy to
have inertia, like that of electromagnetic energy, and also that we may
expect to find stresses in the gravitational field like those of the elec-
tromagnetic field. By the word "stress" I mean, of course, "force per
unit area," but it must be thoroughly understood that "force" is
defined merely as " that which produces acceleration in anything pos-
sessing inertia," so that the force must be thought of as accelerating
the electromagnetic or gravitational energy of the medium rather than
the medium itself, which is incapable of motion.

From the exact similarity of the gravitational field around a distri-
bution of moving masses to the electromagnetic field around a similar
distribution of charges constrained to move in similar paths, and from
the fact that the mechanical forces of the fields in one case are exactly
opposite to those in the other, we see that the stresses in the gravita-
tional field are exactly opposite to those of the electromagnetic field.
This gives us the following set of stresses : a pressure along the lines

of g with a tension across them, each of intensity - — - , equal to the

negative energy per unit volume of the vector g ; and a pressure along

the lines of li with a tension across them, each of intensity ^—7, equal

to the negative energy per unit volume of the vector h. These results
look, at first sight, impossible, especially when we notice that these
stresses have such enormous values as six hundred tons per square cen-
timeter at the surface of the earth, and forty thousand tons per square
centimeter on the sun ; because it appears as if the forces in a static
distribution would be in a state of unstable equilibrium, in which the
least disturbance would cause the lines of force to crumple into a hope-
less tangle, but it will appear presently that this is not the case at all.
Negative Inertia. — To see why not, we may again consider our
corresponding electrical case, and consider the similarity of the vectors
ExH and gxh, which have exactly similar lines with proportional
intensities at different points, and, what is most important, the same
direction in every case. And, as Lorentz ^^ proves, in space containing
no matter, the force due to the stresses on the surface of any element
dr in an electromagnetic field is

/ , a(E:<H) X

\4 7rc2 dt J

^^ Lorentz, Theory of Electrons, chapter I, p. 23 et seq.

VOL. XLVII. — 37

578 PROCEEDINGS OF THE AJVIERICAN ACADEMY.

Therefore we see that in empty space in the gravitational field we have
force due to the stresses on the surface of the element (It equal to

\ 4 7rc2^ ^t )

But the vector gxh represents the rate of flow of negative energy per
unit volume, and hence it appears that, if the stresses in the electro-
magnetic field accelerate positive energy with its ordinary inertia, the
stresses in the gravitational field, which act against the acceleration,
must accelerate negative energy with its negative inertia. It is now
evident that since the system of stresses we have in the gravitational
field would give unstable equilibrium in a set of lines of force with pos-
itive inertia, they give stable equilibrium in a similar set with negative
inertia. And furthermore, it is evident that if we reverse the signs of
both stress and inertia, as we do in changing from electromagnetic to
gravitational conditions, the motions in free space of the negative grav-
itational energy will be exactly like those of the corresponding positive
electromagnetic energy.

To see what effect this negative inertia of the gravitational field has
upon the motion of any mass, we may consider its kinetic energy for
different velocities. For a small sphere, either positively or negatively
charged, and subject to the deformations required by the relativity
principle, the electromagnetic energy for any velocity may be shown
to be Amc^Ii~^, where Am is the electromagnetic inertia and Avtc^
the electrostatic energy when it is at rest. If we now assume that mat-
ter is made up of minute electric charges, we see that if these charges
are near enough to each other to have their fields of energy overlap
to any appreciable extent, then if m is the sum of the inertias of the
particles in a body when separated, and hence the gravitational mass
of the whole body, the inertia of the whole body may be a different
quantity in. If the overlapping is that of fields of charges of opposite
sign, it will make m' less than m, but if it is that of fields from those
of the same sign, it will make m' greater than m. But if unbalanced
effects of this sort could occur, it is evident that we could expect equal
masses of different substances to have different inertias, and since these
different inertias have never been observed, we may neglect such effects
and say that the electromagnetic inertia of any body is the sum of the
inertias of its component charges. This has been tacitly assumed

in developing the theory, and we now see that it is a reasonable
assumption. *2

^2 This assumption is inconsistent with the idea that positive electricity
may be freely penetrable to negative electrons, as has sometimes been sup-

WEBSTER. — AN ELECTROMAGNETIC THEORY OF GRAVITATION. 579

Since the body as a whole is subject to the same deformations with
change of velocity, we may prove that if its gravitational energy when
at rest is —mgC^, its gravitational energy when in motion will be
— nigC^Rr''; so that the effect of the negative inertia of the gravitational
energy will be to reduce the total inertia in the ratio 1 : {\—mg/m).

This result is so important that it is well to look at it also from the
point of view of inertia as the property of resisting acceleration. In
the case of a positively charged body which is accelerated, we see that
every element of charge in it will radiate forces which have at all points
outside the element components in the direction opposite to that of
the acceleration. Therefore, during a constant acceleration each ele-
ment will be acted upon by forces radiated from other elements which
will hold it back by an amount proportional to the acceleration. But
in the gravitational case the corresponding forces will act in the direc-
tion of the acceleration, and will therefore help, instead of hinder, the
action of the accelerating force. And it will not be noticed that since
these forces are inversely proportional to the distance between the ele-
ments, the inertias thus obtained will be inversely proportional to any
dimension in two similar but unequal bodies with equal charges or
masses. We also see that if we extend these considerations to cases of
variable accelerations, the electromagnetic effects introduce the ten-
dency to increase the rate of change of acceleration which has the ef-
fect of a force in the direction of this rate of the order of

e^ da.
c^di

and independent of the size of the body. Much use has been made
of this in the theory of emission and absorption of light. We see, too,
that the gravitational energy will introduce a similar force, whose ratio
to that of the electromagnetic energy is not nig/m.

It appears now, on account of these changes in the inertia of bodies
by the gravitational energy, that we must modify the statements made
above about the lack of radiation of negative energy from bodies mov-
ing under the action of gravitation. But the modification is not so
great as might be supposed, because the case of the symmetrical body
rotating on its axis of symmetry still involves no radiation, and the
radiation in other cases is still less than what could be expected with
other theories. Hence we see that in spite of this modification of the
theory, the arguments for its preference over all others are still valid.

posed ; but it is only one of many objections to this idea, so that the incon-
sistency need not cause much doubt as to the truth of the assumption.

580 PROCEEDINGS OF THE AMERICAN ACADEMY.

To form an idea of the extent to which the inertia of a large mass
is diminished by the gravitational energy, we may calculate the ratio
vig/m for a sphere of uniform density p and radius a. In such a case,
at all external points whose distance is r the vector g has the intensity
km/r^, while at internal points its intensity is kmr/a^. The energy
is now

1 C^

— nigC^ = — -— I i-n-r^g^dr,
Stt/c Jo

which is readily shown to be

Sm^'k

Hence we see that

5 a

mg
m

3 mk Att kpa^
~ 5 c^a~ 5 c'^

For a sphere of homogeneous density and of size and mass equal to
that of the sun, we have

m = 2.0X 10'^ a = 7.0 X 10'°, k = 6.5 X 10"^ c^ = 9.0 X 10'",

17)

SO that -^ = 1.2 X 10-' •

m

The inertia of the sun is therefore diminished by about one part
in a million by the gravitational energy it possesses.

Consequences of Negative Inertia. — Small as it is, this minute
diminution of inertia shows clearly the way to the ultimate condi-
tion of the universe. For we may imagine the sun and all the rest
of the stars radiating their heat away as they drift through space,
and having the supply renewed only by occasional collisions, each one
of which combines the masses of the colliding bodies into a mass as
great as both together, but with an inertia, after the heat of collision
is lost,!^ not as great as the sum of those of the original masses.
Thus a time will come when one of the masses formed by this process
will have actually less inertia than one of the parts of which it is made
up, and will readily be accelerated to enormous velocities by the least
attractions. And at last there will be formed a tremendous mass, of
the order of 10® times the mass of the sun, whose inertia will be nega-

" Because heat is a form of motion of bodies with electromagnetic mass,
we may consider it as electromagnetic energy, with inertia like that of any
other such energy.

WEBSTER. — AN ELECTROMAGNETIC THEORY OF GRAVITATION. 581

tive ; 1* SO that instead of being drawn towards its neighbors in space
by their attractions it will appear to avoid them as if it were repelled,
while they, being drawn towards it by its enormous attraction, will
pursue it as it flees from them.

The more sluggish of them will soon be left far behind, but the
livelier ones, with the least inertia, will draw nearer and nearer, until
at last one will overtake it, hit it from behind and slow it down. By
this process its negative inertia will be further increased, until it has
collected to itself all matter with positive inertia within reach.

This process will be repeated in many different parts of the universe
until at last all matter will be collected in enormous masses with
negative inertia. They will then act as if they all had positive inertia
but repelled each other, and, therefore, there will be no more collisions.
But their heat will be lost by radiation, with no chance to renew the
supply, and at last, if the present laws of nature still hold, the uni-
verse will be cold and dead forever.

Are all Forces Electromagnetic? — And now that we see that the
reason gravitational forces obey the principle of relativity is the fact
that they are really electromagnetic forces, and now we know from
the Michelson-Morley experiment that all internal stresses in even the
most rigid bodies obey the same principle, we may say that we have
at last some evidence to show that all such stresses are of electro-
magnetic origin. And we may now say that the principle of relativity
applies to all the laws of nature because it applies to all the laws
of electromagnetic phenomena, and because all the laws of nature are
laws of electromagnetic phenomena.

Jefferson Physical Laboratory,
Cambridge, Mass.

" It might be supposed, at first sight, that just when the inertia became
zero in the process of losing electromagnetic energy, the mass might have
an infinite acceleration. But it will be noticed that the tendencies to resist
change of acceleration, not being in the ratio — mg/m, will not be equal and
opposite, so that no such effects will occur,

Proceedings of the American Academy of Arts and Sciences.
Vol. XLVII. No. 15. — January, 1912.

CONTRIBUTIONS FROM THE CHEMICAL LABORATORY
OF HARVARD COLLEGE.

A REVISION OF THE ATOMIC WEIGHT OF
PHOSPHORUS.

By Gregory Paul Baxter, Charles James Moore and
Arthur Clarence Boylston.

CONTRIBUTIONS FROM THE CHEMICAL LABORATORY
OF HARVARD COLLEGE.

A REVISION OF THE ATOMIC WEIGHT OF PHOSPHORUS.

SECOND PAPER. — THE ANALYSIS OF PHOSPHORUS

TRIBROMIDE.

Bt Gregory Paul Baxter, Charles James Moore and Arthur

Clarence Boylston.

Presented Dec. 13, 1911. Received Dec. 7. 1911.

In a recent investigation by Baxter and Jones ^ upon the atomic
weight of phosphorus by the analysis of trisilver phosphate, the con-
stant in question was found to have the value 31.04, if silver has the
atomic weight 107.88, or 31.03 if silver is given the value 107.87.
While this result is in good accord with those of most earlier experi-
menters in the same field, Ter Gazarian,^ on the other hand, from the
density of phosphine, has recently obtained a considerably lower
value, 30.91. So large a difference as this obviously needs explana-
tion, and the most promising method of solving the problem seemed
to be to analyze some other compound of phosphorus.

In the research upon silver phosphate some uncertainty was in-
troduced by the fact that the salt contains only 7.7 per cent of phos-
phorus, so that the percentage error in determining the molecular
weight of silver phosphate is many times multiplied in the calculation
of the atomic weight of phosphorus. In this respect phosphorus tri-
bromide is somewhat better suited for the purpose, since it contains
11.5 per cent of phosphorus. Hence in spite of very considerable
difficulties in the preparation of the tribromide in a pure state, and
in its analysis, we were led to choose this substance for further in-
vestigation of the subject.

In outline the method followed was to synthesize phosphorus tri-
bromide by the action of pure dry bromine on pure dry phosphorus

1 These Proceedings, 45, 137 (1910); Jour. Amer. Chem. Soc, 32, 298;
Zoit. anorg. Chem., 66, 97.

2 Jour, de Chim. Phys., 7, 337 (1909); 9, 101 (1911).

586 PROCEEDINGS OF THE AMERICAN ACADEMY.

in a vacuum. The product, which contained a slight excess of bro-
mine, was fractionally distilled in a vacuum, and, as soon as the
excess of bromine had been eliminated, various fractions were col-
lected and analyzed for bromine in the usual way, after decomposition
with water and oxidation of the phosphorous acid produced.

Purification of Materials.

Water. — All the water used in this research was prepared from
the laboratory supply of distilled water by further distillation, first
from an alkaline permanganate solution, and then a second time,
after the addition of a trace of sulphuric acid, through a block tin
condenser. No rubber or cork was used in the connection between
the condenser tube and the Jena glass still.

Ammonia. — The best commercial ammonia was distilled into the
purest water.

Nitric Acid. — C. P. concentrated acid was distilled through a
platinum condenser, with rejection of the first two thirds of the dis-
tillate. It was always carefully tested in a nephelometer for traces
of halogens.

Bromine.^ — This substance was freed from all but a trace of
chlorine by distillation from solution in a concentrated solution of
potassium bromide. The product was next converted into potassium
bromide by addition to a solution of recrystallized potassium oxalate.
In order to remove iodine the solution of potassium bromide was
boiled for some time, with the occasional addition of small amounts of
the partially purified bromine which had been saved for this purpose.
Toward the end of the boiling several small portions of potassium
permanganate and sulphuric acid were added to remove last traces
of iodine. Next the solution was evaporated to dryness and the dry
salt was fused in a large platinum crucible to destroy organic matter.
From the fused potassium bromide bromine was prepared as needed
by solution in water and the addition of sufficient potassium per-
manganate and sulphuric acid to oxidize three fourths of the bromide.
In this process the bromine was distilled a second time from a bro-
mide, and since this bromide was already nearly pure, last traces of
chlorine must have been eliminated from the product. The bromine
was separated as far as possible from water, and was dried by re-
sublimed phosphorus pentoxide, from which it was distilled imme-

2 For a discussion of methods for purifying bromine see Richards and
Wells, These Proceedings, 41, 440 (1906); Baxter, Ibid., 42, 204 (1906); Jour.
Amer. Chem. Soc, 28, 1325; Zeit. anorg. Chem., 50, 392.

BAXTER. — ATOMIC WEIGHT OF PHOSPHORUS. 587

diately before use. A quantity of bromine which had been thus
treated was evaporated on a steam bath in a glass dish, which was
then tested for residual phosphoric acid with negative results.

Phosphorus. — The method used for purifying the phosphorus was
distillation with steam. In the case of the phosphorus from which
the tribromide for the first series of analyses was prepared, the dis-
tillation was assisted by a current of carbon dioxide, and was not
repeated. The phosphorus used for the second and third series of
analyses was twice distilled with steam, the greater portion at atmos-
pheric pressure, a small portion at reduced pressure, in an apparatus
constructed wholly of glass. The purified material was preserved
under water until used. Portions of these specimens were carefully
tested for arsenic by the Berzelius-Marsh method and were found
to contain less than one part in one million of the latter element.
We are indebted to Mr. W. A. Boughton for carrying out these
tests.

Silver. — Pure silver was prepared by methods which have already
been found to be very effective. Since these methods have been de-
scribed in detail several times in papers from this laboratory,* only a
brief outline of the procedure is given here. Heterogeneous silver re-
sidues were reduced with zinc and sulphuric acid, and thoroughly
washed with water. The metal was dissolved in nitric acid, and silver
chloride was precipitated by a large excess of hydrochloric acid.
After the precipitate had been washed it was dissolved in ammonia and
reprecipitated with hydrochloric acid. The resulting chloride was
reduced with alkaline sugar solution and the metal was fused on
charcoal. After cleansing with sand and etching with nitric acid, the
buttons were dissolved in nitric acid, and the metal was precipitated
with pure ammonium formate. The thoroughly washed product was
fused with a blowpipe on a crucible of the purest lime. Electrolytic
deposition with silver nitrate as the electrolyte and with a dissolving
anode of the pure silver buttons followed, and the electrolytic crystals
were fused in a current of pure hydrogen on a boat of the purest lime
provided with compartments so that the resulting buttons weighed from
two to ten grams. After the buttons had been etched with nitric acid
until their surfaces were uniformly crystalline, they were thoroughly
washed with ammonia and pure water, and finally heated to 400° in a
vacuum. The pure silver was preserved in a desiccator over fused
potassium hydroxide.

* See especially Richards and Wells, Pub. Car. Inst., No. 28, 16 (1905);
Jour. Amer. Chem. Soc, 27, 472; Zeit. anorg. Chem., 47, 70.

588 PROCEEDINGS OF THE AMERICAN ACADEMY.

Hydrogen Peroxide. — Merck's " Perhydrol," containing 30 per
cent hydrogen peroxide, was found to be free from sulphuric acid and
halogens and to leave no residue upon evaporation. Hence it was
employed without further treatment.

Nitrogen. — Atmospheric nitrogen free from oxygen was obtained
by Wanklyn's well-known method of passing air through very con-
centrated ammonia solution, and then over hot copper gauze in a hard
glass tube. The excess of ammonia was removed by scrubbing with a
dilute solution of sulphuric acid in three large gas-washing bottles.
Since hydrogen is formed by the catalytic decomposition of a portion
of the excess of ammonia, this impurity was oxidized in a hard glass
tube filled with red hot copper oxide, and the gas was then dried in
six towers filled with beads drenched with concentrated sulphuric acid
and a long tube filled with resublimed phosphorus pentoxide. Finally
the gas was passed through a third hard glass tube filled with hot
copper to combine with any last trace of oxygen. The apparatus in
which these operations were carried out was constructed entirely of
glass with ground glass connections throughout.

Preparation of Phosphorus Tribromide.

Much time was consumed in finding a satisfactory method of pre-
paring pure phosphorus tribromide. It was obvious at the outset that
the substance must be rigorously protected from access of moisture, in
order to avoid the formation of hydrobromic and phosphorous acids.
This object was most simply gained by synthesizing the tribromide
in a vacuum from bromine and phosphorus which were initially dry.
But since phosphorus dissolves in its tribromide, and can not be readily
separated from the latter substance by distillation, an excess of bro-
mine was added at the beginning. Fortunately it was necessary to
add only a slight excess of bromine, since a surprisingly small amount
of phosphorus pentabromide can be detected in the tribromide by its
darker color, especially at high temperatures. This dark color is un-
doubtedly due in large part to dissociation of the pentabromide into
tribromide and bromine. The comparatively easy elimination of the
pentabromide from the tribromide also depends upon this dissocia-
tion, for the free bromine can be removed by distillation in the first
fractions.

At first the attempt was made to remove the excess of bromine by
distillation from red phosphorus. But either the red phosphorus still
contained traces of the yellow modification, or else the red modification
dissolves in the tribromide and vaporizes vvith it when distilled (pos-

BAXTEK. — ATOMIC WEIGHT OF PHOSPHOKUS. 589

sibly as a lower bromide ^). At any rate the tribromide prepared in
this way contained far too little bromine, as was shown by the results
of its analysis.

Much better results were obtained by simple distillation in a vacuum.
Although the boiling point of the tribromide is thus much lowered,
the dissociation of the pentabromide is sufficiently complete to secure
rapid elimination of the excess of bromine. As stated before, the dis-
appearance of the bromine can be followed by the color of the distillate
and residue. If material is collected for analysis as soon as the bro-
mine has apparently been eliminated it should yield at any rate a
minimum value for the atomic weight of phosphorus, unless decomposi-
tion of the tribromide into a lower bromide occurs during the distillation.
In the latter case, however, the composition of different fractions of
distillate would probably not be constant.^

The synthesis of the tribromide was effected in an apparatus con-
structed entirely of glass shown in the figure on page 590. About
fourteen grams of pure phosphorus were freed as completely as possible
from water by cooling and pressing between folds of hardened filter
paper. The phosphorus was weighed to a centigram and placed in the
distilling flask D, which had previously been filled with nitrogen through
the stopcock A. The flask was then fitted to the separating funnel B
by means of a well ground and polished joint C, but it was not con-
nected to the remainder of the apparatus at E, and the capillary tube F
opened into the air.

In order to dry the phosphorus completely, the flask was surrounded
with boiling water and for four hours a slow current of pure dry nitro-
gen was forced in at A and flowed out at the end of the constricted
tube F. The melted phosphorus was agitated from time to time by
shaking the flask in order to liberate any steam which might have been
entangled mechanically and to bring new material to the surface of
the phosphorus. During this operation a portion of the phosphorus
distilled into the cool tube F, and a small amount was vaporized into
the air. Probably, too, a small amount of acids of phosphorus was
produced since slight oxidation of the phosphorus necessarily took
place while it was being introduced into the flask. As soon as the
phosphorus had been dried in this way, the end of the constricted tube
F was sealed, the stopcock A was closed, and the flask, after being
cooled, was exhausted as completely as possible through the stopcock
S by means of the Topler pump "W. All the ground glass joints were
made gas tight by means of a minimum quantity of syrupy phosphoric

" Besson and Foamier, Compt. Rend., 150, 120 (1910).

590

PROCEEDINGS OF THE AMERICAN ACADEMY.

=^=<^^^S^^^;ss<

•K5?

BAXTER. — ATOMIC WEIGHT OF PHOSPHORUS. 591

acid, and outside this, to prevent the absorption of moisture, soft paraf-
fine was smeared.

Next the calculated amount of pure dry bromine was measured from
a burette into the separatory funnel B and the funnel was stoppered.
After cooling the flask containing the phosphorus with ice water to re-
duce the violence of the reaction, bromine was slowly admitted. The
rapid evaporation of a portion of the bromine produced the solidification
of the remainder. This solid bromine, upon falling into the flask, reacted
violently with the phosphorus until a considerable amount of tribromide
had been formed. As soon, however, as sufiicient tribromide had been
produced to dissolve the unchanged phosphorus the action became much
less violent so that the bromine could be introduced more rapidly.

When nearly the theoretical amount of bromine had been used, the
flask D was immersed in hot water in order to decompose a small
amount of solid pentabromide which formed in the upper part of the
flask. The bromine thus liberated diffused to the bottom of the flask
where it combined with the residual phosphorus dissolved in the tri-
bromide. More bromine was then admitted in very small portions
until the warm tribromide acquired the reddish color which indicated
an excess of bromine. The end of the reaction can be determined so
sharply by the color that the excess of the bromine probably never
amounted to more than a few hundredths of a gram, whereas nearly
one hundred and twenty-five grams of bromine in all were used in
each preparation.

When it was certain that an excess of bromine had been added, the
flask D with the tribromide was surrounded with ice water and nitro-
gen was allowed to enter through A, until the pressure inside the flask
was greater than atmospheric. The end of the tube F was then broken
off, and the remainder of the apparatus, which had previously been
filled with dry nitrogen, was attached by the gound joint E. The flasks
D, G, J, K, M, and N were next exhausted through 0, while the stop-
cocks A, R, S, and T were closed. In order to prevent access of bro-
mine to the mercury of the Topler pump, a U-tube V filled with fused
potassium hydroxide was located between the pump and the remainder
of the apparatus, and this U-tube was cooled with concentrated cal-
cium chloride solution and ice.

During the fractional distillation of the tribromide to remove the
excess of bromine it was highly desirable to protect the bulbs 1 to 8, in
which the tribromide was eventually to be collected, from contact with
the first fractions. This was effected by passing the first fractions
through the side tube L into the bulbs M and N, while the bulbs 1 to 8
were cut off" from the rest of the apparatus by the valve P. This valve

592 PROCEEDINGS OF THE AMERICAN ACADEMY.

was so perfectly made that it was nearly gas tight with no lubricant.
Nevertheless, in addition, nitrogen was maintained at atmospheric pres-
sure on the far side of the valve, so that the slight leakage produced a
slow reverse current of nitrogen through the valve into the pump by
way of the bulbs M and N.

Under as low a vacuum as could be obtained with the pump the tri-
bromide was first distilled from D to G by surrounding D with boiling
water and G with ice water. A small residual fraction was left in D,
in order to make certain the elimination of phosphorus acids and pos-
sible oxybromide. During this distillation any phosphorus which had
originally distilled into the tube F and still remained uncombined was
converted into tribromide by the excess of bromine. A second similar
distillation from G to J and K followed, with rejection of the last few
grams in G. The material invariably contained an excess of bromine
at this point. The capillary tube H was now sealed with a blowpipe
and the flasks J) and G were thus disconnected from the apparatus.
Next the bulbs M and N were cooled with ice and the tribromide in J
was boiled while the bulb K was gently warmed. The vapor from J in
bubbling through the warm liquid in K carried with it all the excess of
bromine in both bulbs. Furthermore it is probable that if the tribro-
mide contained a trace of hydrobromic acid, the latter substance was
eliminated at the same time as the bromine. The distillate collected
in M and N as tri- and pentabromide. As soon as ten grams of mate-
rial had been distilled from J and K the residue, amounting to consid-
erably more than one hundred grams, was nearly colorless ; nevertheless
five times as much more was distilled into M and N before this part of
the apparatus was sealed off at the capillary L. Thus when the stop-
cock 0 was closed, the impure distillate was entirely cut off from the
remainder of the apparatus.

The bulbs 1 to 8 were then exhausted by opening the stopcocks of
the U -tube U and at the point T, while E, was closed. The U-tube con-
tained resublimed phosphorus pentoxide to prevent the possibility of
back diffusion of moisture into the bulbs. The valve P, into which a
piece of soft iron had originally been sealed, could now be pulled from
its seat by means of a magnet so that the bulbs J and K were connected
with the pump through the bulbs 1 to 8.

In distilling the remainder of the tribromide into the small bulbs the
one nearest the pump was filled first by surrounding it with ice water,
while the other seven were immersed in beakers filled with boiling
water. As soon as bulb 8 was three-fourths filled with material, bulb 7
was cooled with ice water, and so on until all were filled. All the
residual material in J and K was distilled into bulb 1.

BAXTER. — ATOMIC WEIGHT OF PHOSPHORUS. 593

The train of bulbs 1 to 8 was next sealed off with a blowpipe at the
capillaries, and the individual bulbs were separated from the connect-
ing tubes by sealing the capillary tubes. Great care was taken in
sealing the capillaries to avoid decomposing the tribromide, by first
heating them gently to evaporate any tribromide with which they
might be wet. There never was any sign of decomposition of the tri-
bromide during this process.

The final samples of the tribromide were almost colorless when cold,
but the very slight yellowish tint of the cold substance was materially
increased by a rise in temperature. Since no difference in color could
be detected between the first and last samples collected, it seems prob-
able that phosphorus tribromide really possesses a slight yellowish tint.

Two series of samples of tribromide were distilled and sealed in bulbs
fi-om two different preparations of material. Ten fractions were col-
lected in the first series and eight in the second.

In a third preparation the removal of the bromine was accelerated
by distillation from metallic silver. The bulbs J and K were partly
filled with fine electrolytic crystals of the purest silver which had been
freed from moisture by ignition in a vacuum. After the tribromide
had been distilled into J and K, and the excess of bromine had been
distilled into M and N, the capillary tube L was sealed as described
before. Then the bulbs J and K with the residual tribromide were
warmed for some time with constant shaking before the tribromide was
finally distilled into the collecting bulbs.

The Determination oe the Weight of the Tribromide and

ITS Analysis.

In the analysis of the tribromide it was first decomposed with water,
and then the bromine was precipitated as silver bromide. The reduc-
ing effect of phosphorous acid upon silver salts is well known, so that
the necessity was obvious of oxidizing the phosphorous acid. This
operation was a somewhat delicate one, however, since the hydrobromic
acid also is easily oxidized, with consequent loss of bromine. Hydrogen
dioxide was eventually found to be the safest oxidizing agent, although
its action on the phosphorous acid is not particularly rapid. In pre-
liminary experiments the bulb of tribromide was broken under water
and the oxidation was then effected by hydrogen peroxide in dilute
nitric acid solution. In the final experiments the method of breaking
the bulb under an ammoniacal solution of hydrogen dioxide was em-
ployed, since in this way the greater part of the oxidation was almost
instantaneously effected. Then after some time the solution was anidi-

VOL. XLVII. — 38

594 PROCEEDINGS OF THE AMERICAN ACADEMY.

fied with nitric acid and allowed to stand for a further period. Even
then it is probable that oxidation was not quite complete, for if the
bromine is precipitated with any considerable excess of silver nitrate,
even in the presence of much nitric acid, the silver bromide is percep-
tibly discolored. On the other hand, if the amount of silver salt used
is very nearly equivalent to the bromide present, the precipitate
retains its lemon-yellow color even when left for days under the
solution.

Since the determination of the weight of the tribromide and its
analysis are so intimately connected, they are described together.

The weight of the tribromide was found in each analysis by weigh-
ing the bulb with its contents, and then, after breaking the bulb, col-
lecting and weighing the glass. The bulb was first carefully cleaned
on the outside and dried, and left in a desiccator over sulphuric acid
for at least twenty-four hours. Its weight in air was then found by
substituting standardized weights for the bulb on the balance. The
buoyant effect of the air was estimated by finding the volume of the
bulb in the usual way from the loss in weight under water of known
temperature. The conditions of the atmosphere were taken into ac-
fcount in calculating the buoyant effect of the air on the bulb and
weights. Since the bulb was exhausted when sealed no correction is
necessary for the space in the bulb not filled with liquid.

After the bulb had been weighed and its volume determined, it was
placed in a 300 cc. thick-walled Erlenmeyer flask together with some-
what over one hundred cubic centimeters of redistilled ammonia and
ten cubic centimeters of pure 30 per cent hydrogen dioxide. A glass
stopper which had been very carefully ground into the neck of the
flask, was inserted, and the flask was shaken violently enough to break
the bulb. The heavy tribromide reacted quietly at the bottom of the
aqueous solution, until at the end of about five minutes decomposition
was complete. The flask was then allowed to stand twenty-four hours,
■with occasional shaking. This long standing was necessary to allow a
small quantity of ammonium bromide fumes to be collected in the
aqueous solution.

The flask, cooled to produce inward pressure, was next carefully
opened and the solution was filtered into a three-liter ground-stoppered
precipitating flask, while the particles of glass were collected upon a
small filter paper. This filter was very thoroughly rinsed with pure
water until the filtrate and washings amounted to about 1200 cc.

In order to find the weight of the glass the filter was burned at as
low a temperature as possible in a weighed platinum crucible. When
the weight of the glass, corrected to vacuum, was subtracted from the

BAXTER, — ATOMIC WEIGHT OF PHOSPHORUS. 595

corrected weight of the bulb and the tribromide, the weight of the tri-
bromide in vacuum was obtained.

In order to make sure that this method of finding the weight of the
glass was a satisfactory one, it was tested by several blank experiments
with bulbs containing no tribromide. These bulbs were first weighed
in the air unsealed, and then were treated in exactly the same way as
bulbs containing tribromide. In two cases the fi-agments of the bulbs
were collected upon a weighed Gooch-Munroe-Neubauer crucible. In
the first three, however, the glass was collected upon a small filter
paper as in the analyses.

Weight of Bulb. Weight of Glass recovered. Difference,

grams. grams. gram.

1.20098 1.20097 -0.00001

0.99814 0.99813 -0.00001

1.01851 1.01846 -0.00005

1.12986 1.12994 +0.00008

1.0843S 1.08441 +0.00003

Since in every experiment the weight of the glass collected agrees with
that of the bulb within 0.00008 gram and is never more than 0.00005
gram less than that of the bulb, it is evident that no important
amount of glass is lost either by passing through the filter paper or
by solution in the ammoniacal liquid.

The filtrate containing ammonium bromide was next acidified by the
addition of about 40 cc. of concentrated nitric acid diluted to about
300 cc. Since bromine was sometimes temporarily set free during the
addition of the acid, the acid solution was poured into the bromide
through a thistle tube the stem of which extended to the bottom of
the flask. Thus, although bromine might be set free at the dividing
surface between the bromide and the nitric acid, no bromine ever
reached the upper surface of the liquid, owing to unoxidized phosphor-
ous compounds in the bromide solution. The thistle tube was thor-
oughly rinsed into the flask, the stopper of the flask was moistened
and put in place, and the flask was gently agitated to mix the solutions.
It was then allowed to stand for forty-eight hours. In no case was
there any evidence that bromine was permanently set free by the nitric
acid, for after the mixing of the solutions they were always colorless,
and when the flasks were opened after two days' standing no odor of
bromine could be detected, although 0.00001 gm. is readily perceptible
in 3 liters of air.^

* Baxter, Thorvaldson and Cobb, Jour. Amer. Chem. Soc, 33, 329 (1911).

596 PROCEEDINGS OF THE AMERICAN ACADEMY.

During the standing in acid solution the oxidation of the residual
phosphorous acid progressed, but even at the end of the period it was
not quite complete. Precipitation of the silver bromide immediately
after acidification invariably resulted in darkened salt, but after forty-
eight hours an apparently pure product was obtained, if no appreciable
excess of silver was used.

The bromine in each sample was determined in two ways, first by
finding the amount of silver necessary to combine with it, second, by
weighing the silver bromide formed. Both determinations could be
carried out with the same sample of tribromide.

A quantity of silver equivalent to the tribromide within a very few
tenths of a milligram was weighed out and dissolved in nitric acid in a
flask fitted with a column of bulbs to prevent loss of material by spat-
tering. After the silver solution had been freed from oxides of nitro-
gen by dilution and heating, about 40 cc of concentrated nitric acid
was added and the whole was diluted to a volume of about one liter.
The silver solution was then quantitatively added to the bromide
solution, with constant agitation, and the stoppered precipitating flask
was allowed to stand for several days with occasional shaking. When
the precipitate had coagulated and settled so completely that the
supernatant liquid was apparently clear, portions of the solution were
tested in a nephelometer ^ for excess of bromide or silver. As a matter
of fact, bromide was always found in slight excess. The deficiency of
silver, which was never more than a very few tenths of a milligram,
was made up as nearly as could be estimated by means of a hundredth
normal solution of silver nitrate. After thorough shaking and stand-
ing until the solution was perfectly clear, tests for excess of bromide or
silver were again made. If necessary this process was repeated, until
eventually the amounts of bromide and silver were equivalent. Owing
to the slight solubility of silver bromide at this point the solution re-
mained essentially clear, even in the nephelometer, when either bromide
or silver solution was added.

The solution was now allowed to stand for a week with occasional
shaking and then was tested again in the nephelometer. Usually a de-
ficiency of one or two tenths of a milligram of silver was found, owing
apparently to extraction of occluded soluble bromide from the silver
bromide. This deficiency of silver was supplied and the solution was
left for another week before being tested again, and this process was
repeated until in the course of a week no further change in the solu-
tion took place. In a few analyses the solutions were tested over a

' Richards and Wells, Amer. Chem. Jour., 31, 235 (1904); 35, 510 (1906).

BAXTER. — ATOMIC WEIGHT OF PHOSPHORUS. 597

period of four months, but in no case was an appreciable change in the
end-point found after it had remained constant for a week. In most
cases the final end-point was reached within two weeks.

This difficulty from occlusion by the silver bromide was unexpected
since it has not been met to the same extent in other similar cases in
this laboratory. 8 In fact, it was not discovered in this research until
Analyses 1, 2, 5, 9, and 10 of Series I had been completed. After its
discovery several unsuccessful attempts were made to eliminate the
occlusion. In Analyses 6 and 19 the solutions of ammonium bromide
and silver nitrate were each diluted to nearly four liters before precipi-
tation. In these two analyses, on account of the large size of the pre-
cipitating vessel no attempt was made to collect the silver bromide,
since the results of the comparison with silver were no different from
those obtained in more dilute solution. Although occlusion of bromide
seemed to be diminished in extent by this modification, the time
necessary for the establishment of equilibrium was not materially
lessened. Even in Analysis 6, where the bromide solution was added
to the silver solution, the occluded substance seemed still to be a
soluble bromide. Cooling the solutions to the temperature of ice water
before precipitation seemed to accentuate the occlusion.

As soon as a permanent end-point had been reached, the precipitate
was thoroughly washed by decantation with pure w'ater and collected
upon a weighed Gooch-Munroe-Neubauer crucible. The crucible and
contents were heated gradually to nearly 200° and were kept at that
temperature for eighteen hours or more. Then they were cooled and
weighed by substitution for a similar counterpoise. In order to find
the moisture retained by the dried precipitate it was transferred as
rapidly and completely as possible to a small porcelain crucible which
was immediately weighed with its cover. Then the silver bromide
was fused by heating the small crucible contained inside a much larger
one. During the solidification of the bromide the system was carefully
rotated so that the fused bromide was stirred and caused to solidify in
a thin layer. The loss in weight on fusion was then determined. This
loss seldom amounted to more than 0.001 per cent of the weight of the
salt. The fused bromide was always clear and light yellow, whereas
an astonishingly small percentage of impurity is capable of producing
perceptible darkening of the salt.

Since silver bromide possesses an appreciable solubility in water, ^ the

' See, however, Richards and Rtaehler, Jour. Amer. Chem. Soc, 29, 632
(1907); Ber. d. d. chem. Gesell., 39, 3G18.

» Bottger, Zeit. physik. Chem., 46, 602 (1903), 0.00008 gm. per Uter at 20°;
Kohlrausch, Ibid., 50, 536 (1905), 0.00011 gm. per liter at 21°.

598

PEOCEEDINGS OF THE AMERICAN ACADEMY.

Ag = 107.880

SERIES I.
PBrs : 3Ag

Br = 79.916

Number
of
Anal-
ysis.

Frac-
tion
of
PBrs.

Weight of

PBrs

in

Vacuum.

Weight of

Ag

in

Vacuum.

Deficiency

of

Ag.

Corrected
Weight of

Ag in
Vacuum.

Ratio
PBra : 3 Ag.

Atomic
Weight

of
Phos-
phorus.

1

1

grams.

5.05293

grams.

7.11494

gram.

0.00010

grams.

7.11504

0.836668

31.031

2

2

4.71056

5.63017

0.00005

5.63022

0.836657

31.028

3

3

4.72373

5.64553

0.00030

5.64583

0.836676

31.034

4

4

6.47622

7.74048

0.00000

7.74048

0.836669

31.031

5

5

4.61956

5.52120

0.00020

5.52140

0.836665

31.030

6

8

7.62060

9.10809

0.00040

9.10849

0.836648

31.025

7

9

3.83321

4.58153

0.00010

4.58163

0.836648

31.025

8

10

4.72578

5.64800

0.00035

5.64835

0.836666

31.030

Avera

?e . . . .

....

. . . .

0.836660

31.031

Ag = 107.880

SERIES II.
PBrs : 3Ag

Br = 79.916

Number
of
Anal-
ysis.

Frac-
tion
of
PBrg.

Weight of

PBrg

in

Vacuum.

Weight of

Ag

in
Vacuum.

Deficiency

of

Ag.

Corrected
Weight of

Ag in
Vacuum.

Ratio
PBr3:3Ag.

Atomic
Weight

of
Phos-
phorus.

16

1

grams.

3.21808

grams.

3.84619

gram.

0.00030

grams.
3.84649

0.836628

31.018

17

2

5.77604

6.90359

0.00020

6.90379

0.836648

31.025

18

5

5.51730

6.59400

0.00056

6.59456

0.836644

31.024

19

6

7.15048

8.54603

0.00050

8.54653

0.836653

31.026

20

7

7.94753

9.49900

0.00030

9.49930

0.836644

31.023

21

8

4.30924

5.15044

0.00030

5.15074

0.836625

31.018

Averag

;e . . .

....

0.836640

31.022

BAXTER. — ATOMIC WEIGHT OF PHOSPHORUS.

599

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PROCEEDINGS OF THE AMERICAN ACADEMY.

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BAXTER. — ATOMIC WEIGHT OF PHOSPHORUS.

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602

PROCEEDINGS OF THE AMERICAN ACADEMY.

Ag = 107.880

SERIES III.
PBr3 : 3Ag

Br = 79.916

No.
of
Anal-
ysis.

Frac-
tion
of
PBr,.

Weight of

PBrj

in

Vacuum.

Weight of

Ag

in

Vacuvun.

Deficiency
of
Ag.

Corrected
Weight
of Ag in
Vacuum.

Ratio
PBraiSAg.

Atomic
Weight
of
Phos-
phorus.

27

1

grams.

4.39626

grams.

5.25417

gram.

0.00030

grams.

5.25447

0.836671

31.032

28

3

7.07758

8.45917

0.00040

8.45957

0.836636

31.021

29

4

4.19854

5.01821

0.00030

5.01851

0.836611

31.013

30

6

7.26540

8.68375

0.00030

8.68405

0.836637

31.021

31

8

7.75072

9.26366

0.00040

9.26406

0.836644

31.023

Average

0.836640

31.022

Average of Series

I, II, and III . .

0.836647

31.025

filtrate and wash waters were evaporated to small bulk, and after a
slight precipitate of silicic acid had been removed by filtration, was
diluted to 100 cc. Portions of the solution were then analyzed for
silver by comparison in the nephelometer with standard silver nitrate
solutions, after the addition of an excess of bromide. In each analysis
the amount obtained in this way exceeds slightly the amount to be
expected from the solubility of silver bromide, owing doubtless to col-
loidal silver bromide which escaped the crucibles. A correction for the
silver found in this way, estimated as bromide, was added to the weight
of the main mass of silver bromide.

The precipitating flask was rinsed with ammonia, and, if the solution
was found to contain silver, the quantity was determined in a similar
fashion in a nephelometer and a correction applied.

The preceding tables contain the results of all the analyses which
met with no accidents. A considerable portion of the preliminary
work on the methods of preparation and analysis was done by A. C.
Boylston. The perfection of the apparatus and methods, and all the
final preparations and analyses were made by C. J. Moore.

Weighings were made on a No. 10 Troemner balance sensitive to a

BAXTER. — ATOMIC WEIGHT OF PHOSPHORUS. 603

very few hundredths of a milligram, while the gold-plated weights were
carefully standardized to hundredths of a milligram by the method
described by Richards, i*'

Vacuum corrections were applied as follows:

Specific Gravity.

Vacuum Correction.

Weights

8.3

+0.000145

AgBr

6.47

+0.000041

Ag

10.49

-0.000030

Glass

2.5

+0.000335

The following table, which gives the ratio of silver used to silver
bromide obtained in the same analysis, strengthens the view that
the precautions taken to prevent reduction of the silver salts by the
phosphorous compounds and occlusion by the silver bromide were
effective.

Analyses.

Ag : AgBr.

1 and 9

0.574461

2 and 10

0.574478

3 and 11

0.574446

4 and 12

0.574463

5 and 13

0.574462

7 and 14

0.574454

8 and 15

0.574451

16 and 22

0.574486

17 and 23

0.574473

18 and 24

0.574466

20 and 25

0.574473

21 and 26

0.574478

27 and 32

0.574470

28 and 33

0.574448

29 and 34

0.574472

30 and 35

0.574446

31 and 36

0.574431

Average .

. 0.574462

Although the average

result is

very slightly higher than the value

which has already been

shown by

Baxter "

to be the most probable

" Jour. Amer. Chem. Soc, 22, 144 (1900).

" These Proceedings, 42, 201 (1906); Jour. Amer. Chem. Soc, 28, 1322;

Zeit. anorg. Chem., 50, 389.

604 PROCEEDINGS OF THE AMERICAN ACADEMY.

one, 0.574453, the difference, which is less than 0.002 per cent, is too
small to be significant.

In examining critically the results recorded in the foregoing tables
it should first of all be noted that a given percentage error in the
experimental work is multiplied nine times in the calculation of the
atomic weight of phosphorus. That is, an experimental error of one
one-hundredth of a per cent affects the atomic weight of phosphorus by
0.027 unit. The highest value for the atomic weight of phosphorus in
these tables is 31.040, the lowest 31.013, a difference corresponding
exactly to one one-hundredth of a per cent in the experimental work.
On the whole, however, the agreement of the results is better than
this, since, of the thirty-six results, twenty-seven fall between the limits
31.035 and 31.021, a difference only half as large. In other words, the
different specimens of material seem to be identical as far as the
method is capable of testing this point.

In each series, if the first iraction, that of the highest number, 8 or
10, contained an excess of bromine, it would have yielded too low a
result, while if decomposition occurred during the distillation, with the
possible production of lower bromides of phosphorus, the residual frac-
tion, 1, would have yielded too high a result. The only differences in
each series, however, seem to be purely accidental. Furthermore, the
three series yield average results in practical unanimity.

In the following table the final average of this research is compared
with that of Baxter and Jones with silver phosphate:

Ag = 107.88

Ag = 107.87

Ag = 107.86

PBra
AgsPO^

31.027
31.04

31.024
31.03

31.021
31.02

Summary of Results.

1. A method is described for the preparation of pure phosphorus
tribromide.

2. It is shown that the precipitation of the halogen of phosphorus
halides after decomposition with water, can safely be done only after
the oxidation of the greater portion of the phosphorous acid produced.

3. A method is described for the determination of the bromine in
phosphorus tribromide by comparison with silver and as silver bromide.

4. The molecular weight of phosphorus tribromide referred to silver
107.88 is found to be 270.775, whence phosphorus has the atomic
weight 31.027. If silver is taken at 107.87, the atomic weight of

BAXTER. — ATOMIC WEIGHT OF PHOSPHORUS. 605

phosphorus becomes 31.024. These values agree very closely with
those found by the analysis of silver phosphate by Baxter and Jones.

An attempt to prepare and analyze phosphorus trichloride in a simi-
lar manner is now under way in this laboratory.

We are particularly indebted to the Carnegie Institution of Washing-
ton for generous pecuniary assistance in carrying out this investigation.

Cambridge, Mass.
December 1, 1911.

I

Proceedings of the American Academy of Arts and Sciences.
Vol. XLVII. No. 16. — March, 1912.

POL YCERELLA ZOO BO TR YON.

Bt W. M. Smallwood.

POLYCERELLA ZOOBOTRYON.i
By W. M. Smallwood.

Presented by E. L. Mark, October 12, 1911. Received December 30, 1911,

Contents.

Page

I. External Characters 609

11. The Systems of Organs 611

1. The Integument 612

2. Anatomy of Digestive System 613

3. Histology of " " 616

4. The Liver 616

5. The Kidney 617

6. The Heart and Blood Gland 618

7. Anatomy and Histology of the Reproductive System . 618

8. The Genital Ducts 622

9. The Nervous System 624

10. Histological Structure of the Pedal GangUon .... 626

11. Special Sense Organs 628

I. External Characters.

In a previous paper (Smallwood, : 10), the general external features
of this new species (Figure 1) were described; a part of that descrip-
tion follows, as I desire to present at
this time a complete account of the
morphological characters of the spe-
cies— the histology as well as the
anatomy.

" Polycerella zoobotryon is a small
nudibranch, from 5 to 6 mm. in length Figure 1. Polycerella zoobo-
and 1 1/2 mm. wide. The body is tryon, dorsal view. Magnified 8
thickest just anterior to the branchial diameters,
plumes. The shape is much as in

Polycera — elongated, narrow, and about as high as broad. Body com-
pressed, smooth, sloping rather abruptly from the branchial plumes

* Contributions from the Bermuda Biological Station for Research No. 24,
and from the Zoological Laboratory of Syracuse University.

VOL. XLVII. — 39

610 PROCEEDINGS OF THE AMERICAN ACADEMY.

posteriorly until it merges into the long, pointed tail, which is much
narrower and thinner than the body, and nearly one third the total
length of the animal. The head is blunt and squarish. The ten-
tacles are cylindrical, non-retractile, and one fourth the length of the
rhinophores.

" The rhinophores are non -retractile, cylindrical, each having from
three to six cup-like, equidistant folds on the posterior surface of its
distal two-thirds.

" On the sides and dorsum of the body there are a number of short,
clavate papillae, the tips of which are translucent. The number is not
constant, but ranges from 16 to 19. Their distribution is as follows :
— Of eight which are constant in position, two occupy the median
plane, one of them behind the rhinophores about one sixth of the dis-
tance between base of branchial plumes and rhinophores, the other in
front of the plumes about one fourth of the same distance. The re-
maining six are arranged in pairs near the median plane, one pair a
little in front of the rhinophores and distant from each other about the
thickness of a papilla ; a second pair slightly in front of the posterior
median papilla and a little further apartthau the an terior pair; the
third pair nearly as much behind the plumes as the posterior median
papilla is in front of them ; these are still further from each other.

" In addition to these eight papillae, there are on the dorsum near its
lateral margins from eight to eleven papillae. There are four on each
side, or four on one side and five on the other, or, finally, five on one
side and six on the other.

" The ground color is whitish, mottled with light brown arranged in
irregular splotches. A less abundant darker brown is disposed in
streaks across the lighter brown. The foot is white and without any
color markings. Its margin, as well as the tips of the papillae, is
translucent.

" The foot is smooth and slightly notched anteriorly. The mouth is
T-shaped [or a vertical slit]. The anal opening is subcentral in posi-
tion, and the excretory orifice is just posterior to it, both being sur-
rounded by the gills.

" The gills consist of four or five more or less irregularly branching
plumes.

"When at rest, the body is shortened, the tentacles drop back
alongside the body, and the rhinophores lie on the dorsum. The
papillae, which are constantly in motion when the animal is crawling,
are bent dorsally when it is at rest, and are often knobbed. Under a
low power lens one can see the long cilia in motion. The animal
assumes a variety of positions while in this resting state, and it fi-e-

SMALLWOOD. — POLTCERELLA ZOOBOTRYON. 611

quently rests on its back. The foot may be fully expanded or much
contracted. When the animal was placed in a weak solution of
methylene-blue in sea-water, the cup-like folds on the rhinophores
appeared as swellings, and after a few hours the lateral papillae and
rhinophores were sloughed off.

" The eggs are laid in a cylindrical mass of jelly. The number varies
from one hundred to three hundred in each mass. Each animal lays
several egg-masses.

"The animals are very hardy, living in confinement for over six
weeks."

11. The Systems of Organs.

The several systems of internal organs of Polycerella zoobotryon are
so compactly grouped that it makes their interpretation difficult. The
thin integument is rendered quite firm by the presence of numerous
rod-shaped spicules. Between the integument and the various inter-
nal organs there is what remains unoccupied of the secondary body
cavity, or coelom. In gross dissection one can recognize the anterior
portion of the digestive system, consisting of the short buccal region,
the dorsal suctorial bulb, and the ventral odontophore. The esophagus
is distinguished with difficulty from the several reproductive ducts.
The nerve collar of ganglia is so minute as to be made out only with
fairly high powers of the dissecting microscope. Immediately posterior
to the above organs lies the two-parted visceral mass, nearly concealed
on the dorsal side of the liver and kidney chamber. The remaining
portion of the secondary coelom is filled by the oval posterior visceral
mass, which is composed of the liver and the hermaphroditic glands,
bearing on their dorsal surface the stomach-intestine, kidney, and
heart. The exact relationships of these several organs can be made
out only by the aid of stained sections. Whole animals were fixed in
either Hermann's fluid, Mliller's fluid, or a picro-acetic mixture, the
first two giving the best results. After remaining in Hermann's fluid
for ten days, admirable adequately stained sections were secured,
which have enabled me to make out some of the more perplexing con-
ditions of the minute anatomy. Several specimens left in Hermann's
fluid for three weeks were useless because they had become so brittle.
Sections were made in the three principal planes of the body ; these,
together with dissections of several of the organs, have furnished the
material for this study.

The observations on the living animal and the collection of the
material were made in January, 1909, at the Bermuda Biological Sta-
tion. I desire to express to the Director, Professor E. L. Mark, and to

612

PROCEEDINGS OF THE AMERICAN ACADEMY.

the local authorities my appreciation of the courtesies extended to me
during this time.

1. The Integument.

The integument consists of an outer epidermal layer, the cells of
which vary much in appearance, and a dermal layer of loosely united

-a
a-

FiGURE 2. Spicules of the foot, aa.bb., lateral margins of foot,
lucida, one inch ocular, and one-sixth inch objective. X 612.

Camera

connective-tissue cells. The epidermis is strongly ciliated on the sur-
face of the foot, and the cilia can be traced up the sides of the body,
although here they are much shorter ; the dorsum is entirely destitute
of cilia. The basal corpuscles at the base of the cilia are conspicuous.
The pigment of the integument is deposited in roundish vaculated
masses mostly at the inner ends of the epidermal cells. In the dorsum
the epidermal cells are broad, short, and highly vacuolated, but in
passing ventrally they gradually change to the elongated, cylindrical,
richly cytoplasmic cells of the foot. The cells in the epidermis of the
foot are fully twice as long as those on the back and are much crowded.
The glands of the foot are simple, flask-shaped, multicellular glands
having a small lumen. None of the epidermal cells of the foot appear
to be glandular, as are many of those on the sides and dorsum, and on
the rhinophores. The cells covering the gills constitute a thin colum-
nar epithelium of a simple character. Histologically the foot is dis-
tinguished by a thicker epidermis, numerous glands, and a larger
amount of connective tissue and irregularly shaped muscle cells.
The dermis contains numerous spicules, which vary in size from 15

SMALLWOOD. — POLYCERELLA ZOOBOTRYON.

613

to 60 micra in length and 1.4 to 3 micra in diameter. Each spicule is
rounded at the ends and has a number of spiny enlargements. The
largest spicules (Figure 2) are found in the foot. Their arrangement
does not follow any plan, except that in the rhinophores and the
several integumentary processes they are mostly parallel to one
another.

2. Anatomy of Digestive System.

The mouth opens by a vertical slit directly into a short passage
about 10 micra long, the buccal cavity (Figure 4, cav. hue). The pos-

FiGTJKE 3. Diagram showing the general topographical relations of diges-
tive, reproductive, and renal systems as seen from above, atr.gen., genital
atrium; bb.suc, suctorial bulb; cam.ren., kidney chamber; ga.-int., stomach-
intestine; gen.a., anterior genital mass; gen.p., posterior genital mass; oes.,
esophagus; par.so., body wall; ren., kidney; urt., ureter.

terior part of this passage expands to form the pharynx, into the
posterior end of which open three hollow organs ; ventrally the ante-
rior end of the radula sac {sac. rad.) ; more dorsally, the esophagus
{oes.); and still more dorsally, the cavity of the suctorial bulb {bb. sue).
The walls of the buccal cavity are largely composed of muscles and
have a thickness of 12-15 micra. The dorsal portion of the buccal
cavity is directly continuous with the enlarged suctorial bulb, the wall
of whose fundus often attains a thickness of .30 micra. The posterior
wall is not more than one half as long as the anterior. The distance

G14

PROCEEDINGS OF THE AMERICAN ACADEMY.

from the mouth opening to the most dorsal portion of the suctorial
bulb is about 70 micra, the cavity of the bulb being 25 micra long
(Figure 4). The suctorial bulb is often in contact with the nerve
collar.

The radula is borne on a roundish muscular mass 13 micra in
diameter. The radula sac is practically cylindrical and 12 micra in

66. sue

sacrad-

•or.

'-par. 80.

Figure 4. Diagram to show relation of organs to the pharynx, bb.suc,
suctorial bulb; cav.buc, buccal cavity; oes., esophagus; or., mouth; par.so.,
body wall; phx., pharynx; sac.rad., radula sac.

diameter (Figures 3, 4, sac. rad.) ; it projects 10 to 15 micra from the
dorsal surface of the muscular mass. The total number of rows of
teeth is 33-35, of which 18-20 are in the radula sac ; in the posterior
end of the sac are the beginnings of from 2-4 more rows. Each row
contains eight teeth, the median tooth being absent, which gives
the following formula 3-1-0-1-3. The first lateral tooth (Figure
5 ^') is large and of a deep amber color ; it is seven micra long and
its greatest width is 11/2 micra. The lateral margin bears a wing-
like projection 1/2 micron wide. The median edge of the distal half
of the tooth is somewhat crenulated, producing the effect of a number
of minute rounded teeth. This crenulated margin comes into close
contact with the same region on the opposite tooth. Laterally there
are three small teeth, the marginals ; the first, though the largest of
the three, is not more than 3 micra long and one micron wide ; these

SMALLWOOD. — POLYCERELLA ZOOBOTRYON.

615

three marginals are not so deeply colored as the first lateral and have
smooth outlines (Figure 5, l^, /"\ /"').

Verrill ('80, p. 386) gives the characteristics of the radula of the
genus Polycerella as follows : " Odontophore with six rows of teeth ;
median row absent ; inner laterals large, curved, with three denticles ;
two outer rows much smaller, simple
hook-shaped." Balch ('99, p. 150)
gives for P. davenportii, "Radula
almost as in P. emertonii Verrill
('80-81, p. 387 ; '82, p. 548), rhachid-
ian tooth wanting ; pleurae strongly
hooked with accessory points, large ;
uncini two, sickle-shaped. Formula
2-1-0-1-2." The genus characters
of the teeth should be modified, both
in reference to the number of rows
of teeth and to the shape of the outer
laterals, so as to read as follows : —
Odontophore with six to eight rows
of teeth, median row absent, inner
laterals large, slightly curved ; outer
rows much smaller, may or may not
be curved.

The esophagus (Figures 3, 4, oes.),
as it arises from the dorso-posterior

angle of the pharynx, has a diameter of 15 micra, which it retains
until it expands into the stomach. It passes dorsally and poste-
riorly 100 micra, until it reaches the anterior surface of the posterior
genital mass, where it turns abruptly to the right, entering the liver
and passing through it for a short distance. As it emerges fi-om the
liver, it expands into the stomach-intestine (Figure 3, ga.-int.), the
anterior extremity of which is beneath the renal chamber. The stom-
ach-intestine is dorsal to the posterior hermaphroditic mass, and it
reaches its greatest width near its anterior end, becoming gradually
smaller until the anal opening is reached. There is no differentiation
into stomach and intestine. The stomach-intestine receives two sepa-
rate bile ducts, each connected with an independent bile sac. The
duct of the smaller sac opens into the floor of the anterior end of the
stomach-intestine, while that from the much larger bile sac opens into
the posterior third of the organ.

A single pair of salivary glands, each about 28 micra long and 12
micra in diameter, opens into the posterior part of the pharynx just an-

FiGUKE 5. l^, First lateral tooth;
I n, I "I, II ^, second, third, and fourth
lateral teeth drawn under one-sixth
in. objective and one in ocular, with
the aid of a camera lucida.

616 PROCEEDINGS OF THE AMERICAN ACADEMY.

terior to the origin of the esophagus. Each gland is flask-shaped, the
neck of the flask being only one half the diameter of its fundus. These
glands are partly covered by the nerve collar. In the wall of the buc-
cal tube there are a considerable number of smaU glands that open
into the buccal cavity.

3. Histology of Digestive System.

The walls of the buccal cavity, the pharynx, and the suctorial bulb
are lined with a firm, thin layer of chitin, which is as deeply colored as
the first row of lateral teeth. In the suctorial bulb and the posterior
region of the pharynx the chitin is thinner and less deeply colored.

The esophagus is lined for its entire length with a ciliated epithe-
lium, which makes up about one half of the thickness of the wall, the
remaining portion being made up of connective-tissue and muscle cells.

The wall of the stomach-intestine is composed of a thick inner epi-
thelial layer, with a well marked basement membrane, and a very thin
outer layer of muscle and connective tissue, which in many places is
only one or two cells thick. The cells in the epithelial layer are large,
but from the basement membrane to the free surface the distance is
noticeably short. The free end of each cell is highly vacuolated ; the
nucleus is basal and surrounded by fine cytoplasmic granules. These
cells show little variation in their appearance throughout the length of
the stomach-intestine.

The cells of the salivary glands are quite uniform in size, possibly a
little longer in the larger part of the gland. Each cell is nearly cylin-
drical ; its nucleus is basal, and its cytoplasm finely and homogeneously
granular.

4. The Liver.

The liver occupies more than one half of the posterior visceral mass ;
its anterior two-thirds is surrounded by the hermaphroditic gland (see
infra), which extends inward some distance, though the liver lobules,
lying between the germinal follicles, extend in many places to the sur-
face. The posterior third of the visceral mass is composed entirely of
the liver, which is made up of numerous racemose lobes, giving it a
rather loose appearance. The lobules of the liver open by minute
connecting ducts into one or the other of the two bile sacs, the greater
number opening into the posterior one, which is much the larger.

The cells are stained brown in Hermann's fluid, owing to the action
of the osmic acid on the granules surrounding the numerous, rather
large vacuoles contained in each cell. The free ends of the liver cells
are irregular in outline and the cavity of the lobe, which in the granu-

SMALLWOOD. — POLYCERELLA ZOOBOTRYON.

617

lar part of the liver they surrouud, is filled with the same granular
cytoplasmic mass containing vacuoles, the cell apparently breaking
down after it becomes filled with the
hepatic secretion. The gland cells
are long and irregularly flask-shaped,
the neck being attached to the base-
ment membrane (Figure 6,/). The
liver cells apparently regenerate the
portion which breaks down, as there
are no small basal cells and the large
nucleus near the base of the cell is
surrounded by numerous compactly
arranged cytoplasmic granules. In
the minute ducts leading into the
bile sac the cells are more regular
and much shorter (Figure 6, e), while
those lining the bile duct itself are
ciliated.

5. The Kidney.

The nephridial organ (Figure 3,
ren.) covers the upper surface of that
portion of the posterior visceral mass
which lies to the right of, the esoph-
agus and j ast anterior to the stomach.
It does not extend down over the
right side and usually does not exceed
40 micra in width. It consists of an
irregular number of tubules immedi-
ately ventral to the pericardium. The
cells are polygonal, their free ends
being mostly transparent and appar-
ently without concretions. A short
duct connects the kidney with the
real chamber (cam. ren.), which is

FiGUHE 6. a, Ciliated cells from
the mouth of the prostate duct; b,
ordinary lining epithelial cells from
prostate duct; c, cells from edge of
glandular patch of prostate gland;
d, cells of glandular patch of pros-
tate gland; sec, secretion; c, cells
from duct leading from hver lo-
bules; f, hver cells. All drawn with
camera lucida, one inch ocular,
and one-twelfth inch oil immersion
objective. X 612.
a large bilobed sac. The dorsal lobe
is 80 micra long, being much longer than the ventral lobe (50 micra).
This large sac, 90 micra wide and 70 micra deep in its greatest extent,
lies over the esophagus and projects beyond the anterior margin of the
posterior genital mass (Figure 3, com. ren.). On the floor of the renal
chamber there is a fold which nearly fills the passage into the kidney
and is covered with long cilia. There seems to be a minute pore

618

PROCEEDINGS OF THE AMERICAN ACADEMY.

through the wall of the renal chamber, in the region of the ciliated fold,
which opens into the pericardium. The ureter of the kidney (Figure
3, tirt.) is a small duct of uniform diameter, which follows the right
contour of the stomach-intestine, and opens ventral to, and slightly at
the left of, the anus.

6. The Heart and Blood Gland.

The blood gland is an irregular compact mass of minute round cells
lying dorsal to the suctorial bulb and anterior to the nerve collar. The
enlarged middle portion of the oviduct is often partly imbedded in
this gland.

The heart consists of an anterior ventricle and a posterior auricle,
the latter being partly divided. The pericardial cavity is nearly filled

by the distended heart, the walls of

par. tis. c'onl.

Figure 7. Edge of the ventricle
of the heart showing the brandling
muscular cells, par.tis.c'ont., connec-
tive-tissue wall. Camera liicida, one
inch ocular and one-twelfth inch
oil-immersion objective. X 612.

which (Figure 7) are composed of
connective-tissue cells and branch-
ing cells, which are interpreted as
the contractile tissue of the heart
because they are so similar to the
evidently contractile cells of the
foot. The blood passes to the va-
rious parts of the body through
irregular sinuses, there being no
clearly defined blood vessels ap-
parent in my preparations. The
fact that the cavities of the gills
open directly into the secondary
coelom is submitted as further evi-
dence that there are no well defined
blood vessels.

7. Anatomi/ and Histology of the
Heproductive System.

The general features of the re-
productive system are similar to
those of most Nudibranchs. An hermaphroditic gland surrounds most
of the liver, the two organs forming a conspicuous mass and nearly fill-
ing the posterior half of the secondary coelom. The hermaphroditic
gland is usually designated as the posterior genital mass (Figure 3,
gen. p.), the anterior genital mass (gen. a.) consisting of the albumen
gland and the nidamental gland, which are united into one general body,
and a prostate gland. The prostate gland lies posterior to the albumen

SMALLWOOD. — POLYCERELLA ZOOBOTRYON. G19

and nidamental glands and is more conspicuous on the left side. The
posterior genital mass projects forward over the dorsal aspect of the
anterior genital mass, concealing about one half of it as seen from above.
Into the genital atrium open the oviduct and receptaculum seminis
close to each other and also the penis sac. The detailed relation of
each duct to the posterior and anterior genital masses and to the
genital trium is presented in the following paragraphs.

Posterior Genital Mass.

In the posterior genital mass the arrangement of the male and fe-
male portions does not follow any definite plan ; the ultimate tissue
from which the germ cells are derived is a columnar epithelium com-
posed of short and broad cells. This epithelium is much folded, form-
ing follicles which project inward toward the center of the genital
mass. A cross section of the genital mass shows many knob-like re-
gions of eggs and sperms projecting almost to the center of the mass.
Between such projections the liver cells of the anterior region often
extend to the surface. Elsewhere in the anterior two thirds of this
genital mass the germinal follicles envelope the liver in a layer of
varying thickness. Each follicle is exclusively occupied by growing
eggs or sperm cells.

The sperm cells in the material collected in January seem to be
mostly in a state of maturity, but the eggs exhibit all stages of devel-
opment. The maturing eggs show in a clear manner the relation of
the nucleus to the formation of deutoplasm. All stages from the
young ova to the mature egg are seen in the same section. In the
young ovum the cytoplasm is evenly and finely granular ; as it increases
in size, small spherical droplets appear in close contact with the nuclear
membrane ; as growth continues several rows of droplets are distin-
guishable surrounding the nucleus. In the more mature egg finger-
like masses of these droplets extend from the nucleus toward the
periphery of the cell; these continue to become more numerous until
the early finely granular condition is obliterated. In Hermann's fixa-
tion these deutoplasmic droplets are of all shades from a deep brown
to black, indicating that at least a considerable portion of their sub-
stance is of a fatty composition. Miiller's fixation followed by the usual
iron haematoxylin gives the best differentiation for the study of the
growth of the deutoplasm.

The numerous follicles open into an irregular series of minute ducts,
which are finally collected into the common hermaphroditic duct. Be-
fore taking up the course of this duct, it is necessary to describe the

620 PROCEEDINGS OF THE AMERICAN ACADEMY.

Anterior Genital Mass.

The anterior genital mass consists, as already mentioned, of the mu-
cous gland, the nidamental gland, and the prostate gland. The first two
unite to form a simple, conspicuous mass, each gland consisting of a
number of foldings of a greatly thickened epithelium. After fixation in
Miiller's fluid, it is not easy to distinguish between these two glands, as
their tubules have no constant position or shape ; but after fijcation in
Hermann's fluid the resulting difi"erentiation of the contents of the
cells enables one to recognize at a glance the difference between the
mucous and the nidamental regions. The actual space occupied by
the mucous tubules is about one third as great as that occupied by the
nidamental tubules, and the former are found mostly on the back and
left sides, although a few extend into the center of the anterior genital
mass and are there surrounded by the nidamental tubules. The out-
line of these combined glands is not regular, because some of the nida-
mental tubules project into the liver.

The nidamental cells are light colored after fixation in Hermann's
fluid, the cell walls and nuclei being the only parts stained. In the
animal thus fixed, the cells were congested, almost obliterating the
lumen of the tubule, while in the one prepared in Miiller's fluid and
stained in iron haematoxylin the cytoplasm was faintly tinted and the
cells shrunken so as to leave a large lumen. The mucous-gland cells
which were fixed in Hermann's fluid were stained a deep brown, this
color being due to the presence of numerous spherical bodies which
fill the cell. This is the differential reaction which enables one to
distinguish between these two glands. An animal that had recently
discharged its mucous secretion was fixed in Miiller's fluid and stained
in haematoxylin followed by Bordeaux red. It showed the presence
of a few small bodies in the distal ends of the flask-shaped cells. The
large bodies took the haematoxylin stain in the center and the Bor
deaux red around their periphery, while the small ones, just forming
in the cytoplasm, took an exclusively Bordeaux red stain. It would
seem, then, as if this secretion of the mucous cells was not a chemi-
cally homogeneous substance.

The prostate gland of Polycerella zoohotryon (Figure 8, gl. prost.),
unlike that of Polycera (Pohl, : 05, p. 434), is not folded, but consists
of a large flask-like sac, the fundus of the flask being on the left side
of the body, and its neck continuous with the prostate duct. The
histology of this gland presents the following points of interest. The
cells composing the main lining of the gland are elongated and mutu-
ally flattened ; the nucleus is prominent, the cytoplasm finely and uni-

SMALLWOOD. — POLYCERELLA ZOOBOTRYON. 621

formly granular. For a short distance (from 15 to 20 micra) from the
opening of the prostate duct, the cells (Figure 6, a) are narrow and
elongated and carry long cilia, often 3 micra in length. The nucleus
is much smaller than in any of the other cells, and the cytoplasm is
coarsely granular.

The fundus of this flask-shaped prostate is largely occupied by the
glandular area, a patch of thickened epithelium about 50 micra across.
The cells in this glandular area are greatly enlarged, even at the edge
of the patch, as shown in Figure 6, c. The conditions represented in
Figure 6, d, show the number of layers of cells and their arrangement.
At the bottom of the figure are some small basal cells which, together
with a few larger ones, make up two rows similar in appearance to the
cells regularly lining the gland (Figure 6, b), except that cells are fre-
quently found in the second row which show the beginnings of the
secretion so common in the distal cells of the glandular patch. The
cells which cover the free surface of the glandular patch are greatly
enlarged, especially in that part of each cell which is distal to the nu-
cleus. The cytoplasm contains a number of spherical masses which, in
preparations fixed in Hermann's mixture, are made up in part of 1 to 3
blackened corpuscles, the remaining portion of the mass taking no
stain. The whole effect is like that of a vacuole containing differen-
tiated bodies. After fixation in Miiller's fluid, followed by haematoxy-
lin, these masses are not apparent. That these minute bodies are
secretions of the cell is abundantly shown by the fact that identical
bodies nearly fill the prostate gland, and that special drops similar in
form are often attached to the ends of these cells (Figure 6, d).

There are also found in the contents of the prostate gland numer-
ous spermatozoa, and some bodies which it is difficult to explain from
the present preparations. They are of about the size of the nuclei in
the distal cells of Figure 6, d, but the detailed structure has degenerated
to such an extent that one cannot recognize any relationship between
them and other cells or parts of cells found in the organism. Pohl (: 05,
p. 434) finds abortive, undeveloped eggs in the ampulla of the sperm
duct, which may be the key to the explanation in this case. The bodies
appear much like pseudo cells in Hydra (Wager :09, Figure 14, Plate
3), which would mean that some undeveloped eggs had been set
free and were being broken down in the prostate gland. A second ex-
planation is equally probable: that the distal ends of the gland cells
break off and the nucleus gradually undergoes degeneration. In only
one instance, however, was there any evidence of such a breaking off
of the tip end of the cell (see condition of one of the cells in Fig-
ure 6, d) ; but I am convinced that this is not the usual method of

622

PROCEEDINGS OF THE AMERICAN ACADEMY.

discharging the secretion, or it would happen frequently and there
would be more than this one instance in the several animals studied.
But the large number of these bodies in the immediate vicinity of the
glandular patch is very suggestive, and leads one to think that these
bodies are escaped nuclei. The ends of some of the other cells in the
glandular patch were frayed, as if the distal part had been lost.

8. The Genital Ducts.

1. The hermaphroditic duct emerges from the central and dorsal
region of the posterior genital mass. As it leaves the genital mass it

^- rtp.sem.

Figure 8. Drawing made partly from a dissection and partly from a recon-
struction from sections, to show the prostate gland, its duct, the oviduct,
and their relation to the hermaphroditic duct and receptaculum seminis.
dt.her., hermaphroditic duct; dt. prost. + cop., prostate and copulation duct;
gl.prosL, prostate gland; o'dt., oviduct; rcp.sem., receptaculum seminis.

turns, passing to the left side, and continues in this direction until it
comes into contact with the body wall, where it turns forward. It then
bends ventrally, and finally reaches the middle of the front surface of
the anterior genital mass. Here it makes a sharp turn to the right,
passing below the esophagus, and becomes partly enveloped by the
nidamental gland. As the hermaphroditic duct emerges from the an-
terior right side of the anterior genital mass, it turns ventrally 25
micra and enlarges its diameter from 3 to 15 micra to form an ampulla.
From the ampulla the duct courses dorsally over the right anterior
surface of the nidamental gland and opens into the duct of the pros-

SMALLWOOD. — POLYCERELLA ZOOBOTRYON. 623

tate gland. A short distance before the formation of the ampulla, the
hermaphroditic duct receives the duct from the mucous gland.

2. The prostate (Figure 8) duct is relatively short, only 100 micra
long, and its walls are 20 micra thick. As it emerges from the pros-
tate gland it turns ventrally and anteriorly to open without further
change of course into the genital atrium.

3. The receptaculum seminis (Figure 8, rep. sem.) is an elongated
sac 85 micra long, 50 micra wide, and 25 micra thick, located on the
right side dorsal to the prostate gland and ventral to the kidney cham-
ber. The duct from the receptaculum seminis is 25 micra long and 8
micra thick ; it opens into the prostate duct as shown in Figure 8. In
copulation, then, the penis enters the prostate duct, which makes it
appropriate to designate this duct as the vagina.

4. The oviduct opens with the prostate duct into the genital atrium.
From its origin it passes dorsally and to the left until the left side of
the body is reached. There it turns anteriorly and then crosses to
the right side, this time over the suctorial bulb, finally terminating in
the genital atrium. The oviduct (Figure 8, o'dt.) is divided into three
regions : (1) a terminal, thick-walled, muscular portion 45 micra wide,
extending from the prostate duct to the middle region ; (2) this is short
but much wider, being 60 micra in diameter, and thin walled ; it lies
over the suctorial bulb ; finally (3), the initial part is for 50 micra of
its length not more than 30 micra wide. The large cavity in the mid-
dle region of the oviduct contains a considerable amount of detritus ;
the only structures that could be identified were parts of the polyzoan,
upon which this species feeds. This region would seem to be, there-
fore, similar to a spermatheca, although placed in the oviduct. The
duct from the albumen gland opens into the oviduct in the last third
of its course, about 20 micra from the genital atrium.

5. Penis and vas deferens. A fleshy triangular valve separates the
opening of the penis sac from the prostate duct and oviduct. The peni?
sac, 30 micra wide, may run crosswise in front of the anterior genital
mass or back close to the body wall and lateral to the anterior genital
mass (Figure 3). The penis has a general width of 10 micra, its end
becomes expanded into a head 12 micra wide. The duct running
throughout the center of the penis is 4 micra wide and heavily ciliated.
Bergh ('92, p. 149) states that the penis of Polycerella is armed with
hooks. Verrill ('80, p. 387), in describing P. emertonii, makes no men-
tion of the reproductive organs. Balch ('99, p. 151) says, "No arma-
ture of the penis could be made out in sections, but this was perhaps
owing to poor preservation." The enlarged end of the penis in P. zoo-
botryon is unquestionably ciliated and in specimens fixed in four dif-

624

PROCEEDINGS OF THE AMERICAN ACADEMY.

ferent fluids no evidence of hooks on the penis appeared. Inasmuch
as Bergh cites as his only authority Verrill, it is apparent that his
statement " penis armata " is a mere supposition based on the fact that
it is armed in Polycera. Therefore, this characterization of the genus
Polycerella will have to be changed to " penis unarmed."

The vas deferens is a narrow duct of uniform diameter throughout
its entire length opening into the prostate duct ; it passes by several
turns to the base of the penis, the latter part of its course depending
upon the position of the penis in the body. The vas deferens is heavily
ciliated throughout its whole length.

■pd.p.

FiGUHE 9. Drawing (diagrammatic) of nervous system seen from the right
side, gn.buc, buccal ganglion; gn.cb., cerebral ganglion; gn.olf., olfactory-
ganglion; gn.opt., optic ganglion; gn.pd., pedal ganglion; gn.vsc, visceral gan-
glion; n., nerve to integument; n.olf., olfactory nerve; n.pd.a., anterior pedal
nerve; n.pd.p.; posterior pedal nerve; oc, eye; ot'cys., otocyst.

9. The Nervous Si/stem.

The nervous system is simpler in some respects than it is in the
larger Eolidae and in some of the Doridae, although showkig the same
concentration of the ganglia into a nerve collar around the esophagus
immediately behind the pharynx. There are three pairs of large gan-
glia,— cerebral, pedal, and visceral, — the usual small pair of buccal
ganglia, and several minor ganglia to be described afterwards.

The cerebral ganglia (Figures 9, 10, gn. cb.) are nearly spherical, the
antero-posterior diameter being slightly shorter than the others. They
are the largest of the ganglia, each being about 30 by 20 by 20 micra,
and cover the dorsal surface and a small part of each side of the esoph-
agus. The cerebral commissure (Figure 10, co'ins. cb.) is three micra
long and six micra wide. The cerebro-pedal connective (Figure 9)

SMALLWOOD. — POLYCERELLA ZOOBOTRTON.

625

gn.opl.

is short and narrow (5 micra long and 3 micra in diameter), while the
cerebro-buccal connective, arising just anterior to the cerebro-pedal
connective, is long and slender. Broadly joined to the ventral anterior
face of each cerebral

gruvsc-

■ co'nt.vsc. pd.

ganglion is an olfactory
ganglion (Figures 9, 10,
gn. olf.) ; a faint constric-
tion is the only external
indication of it. The
olfactory ganglion is ap-
proximately spherical and
gradually tapers off into
the large (7 micra) nerve
(ji. olf.) that eventually
penetrates the base of the
rhinophore. With the
lateral surface of each
cerebral ganglion is con-
nected a spheroidal optic
ganglion {gn. ojjt.). As
this is sessile on the cere-
bral ganglion, there is no
conspicuous cerebro-optic
connective. Joined to
the optic ganglion is the
simple eye.

The pedal ganglia lie
ventral, and slightly pos-
terior to the cerebral and
are somewhat smaller (22
by 20 by 29 micra). The

'gn.olf.

d

gn.pd^^'^'^co'nt.vsc.-pdr

Figure 10. Four camera-lucida drawings
(a, b, c, d) of the three pairs of gangUa in va-
rious positions to show their relative sizes and
their connectives and commissures, co'ms.cb.,
cerebral commissure; co'^ns.pd., pedal commis-
sure; co'nt.vsc.-pd., viscero-pedal connective;
gn.cb., cerebral ganglion; gn.olf., olfactory
ganglion; gn.opt., optic ganglion; gn.pd., pedal
ganghon; gn.vsc, visceral ganglion; 7i.olf., ol-
factory nerve; oc, eye.

pedal commissure (Figure 9, co'ms. pd.) is 20 micra long and 4 micra in
diameter ; it lies behind and ventral to the cerebro-pedal connectives.

The visceral ganglia (Figures 9, 10) are small (10 by 10 by 10 micra)
in comparison with the cerebral and pedal, and lie in close contact with
each other. They are situated at the side of, and posterior to, the
esophagus back of the pedal commissures. In a frontal section is
found an interesting form of connection between the visceral and
pedal ganglia (Figure 10, a/nt. vsc.-pd.). These connectives are 15
micra long and 4 micra in diameter ; they form a distinct chiasma
with no apparent mingling of the fibres and clearly show the chiasto-
neuric affinities of this gasteropod.

VOL. XLVII. — 40

626 PROCEEDINGS OF THE AMERICAN ACADEMY.

The buccal ganglia (Figure 9) are irregular in outline, each ganglion
consisting of two parts, the smaller of which lies on the lateral wall of
the buccal mass, while the larger is on its ventral surface. The buccal
commissure is short, lying on the ventral side of the buccal wall.

Nerves. — In addition to the several commissures and connectives
already described, the ganglia have the following nerves. Each of the
cerebral ganglia gives off from its posterior surface a small, short nerve
which goes to the oviduct. From its dorsal posterior surface arises a
large nerve which bends ventrally, passing immediately back of the
optic ganglion. This nerve is enlarged on the right side of the body
by ganglionic cells. From this ganglionic enlargement some branches
pass to the distal portion of the oviduct and penis, others to the lateral
body wall and mantle edge. On the left side no corresponding gan-
glion was detected, the nerve simply giving off many branches to the
lateral and posterior body wall. The olfactory portion of the cerebral
ganglion is the source of the largest nerve in the body. This nerve
extends along the side of the pharynx, sending off to the rhinophore a
branch, which spreads out into a wide, much-flattened nerve that is
distributed to the integument of the rhinophore. The nerve continues
anteriorly beyond the base of the rhinophore giving off several branches
to the region around the mouth, while one branch enters the base of
the tentacle. Just dorsal and anterior to the olfactory lobe a small
nerve (Figure 9, n.) arises which goes directly to the integument dorsal
to the mouth.

Each pedal ganglion sends to the foot two large nerves, the anterior
and posterior pedal nerves. On the right side a third nerve arises
from the posterior surface of the right pedal ganglion and goes to the
base of the penis.

Each of the visceral ganglia gives off a single nerve which is dis-
tributed to the lateral and posterior wall of the pharynx and a small
nerve to the anterior genital mass.

10. Histological Structure of the Pedal Ganglion.

The several ganglia are essentially like one another histologically,
the conditions represented in the pedal ganglion being typical. Each
ganglion is closely invested in a connective-tissue capsule. Figure 1 1
is a longitudinal (parasagittal) section through the right pedal ganglion,
showing the cerebro-pedal connective on the left and the origin of the
anterior pedal nerve ventrally. There are a few large and many small
nerve cells having the base of the cell directed toward the connective-
tissue capsule. The number of nerve cells is much less in the ventral

SMALLWOOD.

POLYCERELLA ZOOBOTRYON.

627

region. Each cell is of the usual unipolar type, and while many send
their axons directly into or through the cerebral mass, others send
theirs for some distance between other cells before leaving the ganglion.
The center of the ganglion is occupied by a feltwork of nerve fibres.
Axons in small groups course through this feltwork and pass out into

Figure 11. Parasagittal section of the right pedal ganglion, co'nt.cb.-pd.,
cerebro-pedal connective; ivlr.tis.co'nt., connective-tissue sheath; n'gli.,
neuroglia; n.pd.a., anterior pedal nerve.

the pedal nerve. Axons in the pedal connective can readily be traced
through the ganglion into the pedal nerve. The neuroglia cells (Fig-
ure 11, n'gli.) are few in number and found only around the periphery
of the ganglia.

The larger of the nerve cells give a more pronounced reaction to the
various reagents than the smaller ones do, although no constant struc-
tural differences are observable. The nucleus is proportionately very
large and rich in chromatin, while the cytoplasm is finely granular and
contains a few vacuoles. In fixation with Hermann's fluid there are a
number of blackish bodies in the cytoplasm, and bodies apparently sim-
ilar are found in the ganglion outside of the nerve cells. Bodies having
a similar appearance are also present in the epithelial cells of the repro-
ductive ducts. These bodies are probably fat or related substances
blackened by the osmic acid contained in the fixing fluid.

628

PROCEEDINGS OF THE AMERICAN ACADEMY.

ivtr.tis.co'nt.

-crn.

P^9-\k-?

11. Special Sense Organs,

Otocyst. — The ear sac (Figure 9, ot'cys.) is of an oval outline, its
longest diameter being 7.5 micra, and it lies embedded in the dorsal
surface of the pedal ganglion. The otokonia are numerous, minute
oval bodies not more than 0.6 micron long.

Olfactory organ. — The rhinophore possesses a large nerve that sends
off numerous branches during its passage from the base to the tip of

the rhinophore. It is difficult to be
certain just how the axons of this
nerve terminate in the epidermis.
The individual branches can be made
out at least half way to the surface
of the epidermal epithelium, and I am
inclined to believe that they simply
terminate in free, unmodified fibrils
between the epithelial cells. The ol-
factory nerve sends a branch into the
tentacle and several into the region
of the lips. Here, also, the individual
fibrils appear to end in a similar
manner to those in the rhinophore.
It is probable that the general snout
region, as well as the rhinophores,
interprets olfactory stimuli, as both
are innervated by a single nerve aris-
ing fi-om the olfactory ganglion.

Eye (Figure 12). — The eyes, as
already stated in connection with the
description of the cerebral ganglia,
are in close contact with the optic
ganglion. Each eye is completely
enveloped in a connective-tissue capsule, which contains a greater
amount of connective tissue, nuclei, and fibres than is found in similar
tissue surrounding the ganglion. At the base of the eye the capsule is
easily traced and is seen to be continuous with that surrounding the
ganglion.

Each eye presents, within the cellular capsule, a single layer of
cells, which is divisible into an anterior portion, the cornea, and a pos-
terior, the retina. These together completely enclose the lens and a
cup-shaped mass of pigment. The lens (Figure 12, Ins.) is an oval or
pear-shaped body completely filling the pigment cup and projecting

Figure 12. Eye. crn., cornea;
ivlr. tis. co'nt., connective-tissue
sheath; Ins., lens; pig., pigment;
rtn., retina. Camera lucida, one
inch ocular and one-twelfth oil-
immersion objective. X 612.

SMALLWOOD. — POLYCERELLA ZOOBOTRYON. 629

somewhat beyond its anterior rim, where it is in contact with the
cornea. The pigment (jyig.) is very dense, consisting of numerous
small granules which appear to be located in the retinal cells. At
least I was not able to make out the existence of more than this one
layer of cells, though it is possible that maceration preparations would
have disclosed the presence of other (pigment) cells. The pigment
layer is thickest at the bottom of the cup, becoming gradually thinner
toward the cup's lips. The cornea and retina apparently consist of
only a single layer of cells arranged radially ; the cells of the cornea
{cm.) are much flattened, and stain faintly. The layer contains but
few nuclei in front of the lens. The cells become cubical in the region
of the retina {rtn.\ the center of which is occupied by a single large
cell with a conspicuous nucleus. Inasmuch as the eyes were not
especially fixed and stained for histological study, it was impossible to
analyse further the retina or to determine the course of the fibrillae
after they enter the retina. Strands of fibrillae were traced from the
cerebral into the optic ganglion and thence to the proximal border of
the retina.

Bibliography.

Balch, F. N.

'99. List of Marine Mollusca of Coldspring Harbor, Long Island,
with Descriptions of one new Genus and two new Species
of Nudibranchs. Proc. Boston Soc. Nat. Hist., vol. 29, no.
7, pp. 133-162, 1 pi.

Bergh, R.

'92. System der Nudibranchiaten Gasteropoden. In Karl Semper's
Reisen im Archipel der Philippinen, Theil, 2, Bd. 2, Heft
18, pp. 993-1165. Also separately, Weisbaden: Kreidel,
173 pp.

Pohl, H.

:05. Uber den feineren Bau des Genitalsystems von Polycera quadri-
lineata. Zool. Jahrb., Abt. f. Anat., Bd. 21, pp. 427-452,
Taf. 25, 26.

Smallwood, W. M.

:10. Notes on the Hydroids and Nudibranchs of Bermuda. Proc.
Zool. Soc. London, 1910, pp. 137-145, text-figures 7-10.
Contributions Bermuda Biol. Sta., No. 18.

630 PROCEEDINGS OF THE AMERICAN ACADEMY.

Verrill, A. E.

'80-81. Notice of recent Additions to the Marine Invertebrata of
the North-eastern Coast of America, with Descriptions of
new Genera and Species and Critical Remarks on others.
Part II. Proc. U. S. Nat. Mus., vol. 3, pp. 356-405, Dec,
1880 — Jan., 1881.

Verrill, A. E.

'82. Catalogue of Marine Mollusca added to the Fauna of the New
England Region during the past Ten Years. Trans. Conn.
Acad. Arts and Sci., vol. 5, pt. 2, pp. 447-599, pis. 42-44,
57, 58.

Wager, R. E.

:09. The Oogenesis and Early Development of Hydra. Biol. Bull.,
vol. 18, no. 1, pp. 1-38. 4 pis.

Proceedings of the American Academy of Arts and Sciences.
Vol. XLVII. No. 17. — Makch, 1912.

CONTRIBUTIONS FROM THE JEFFERSON PHYSICAL
LABORATORY, HARVARD UNIVERSITY.

THE ANOMALOUS MAGNETIZATION OF IRON

AND STEEL.

By B. 0. Peirce.

CONTRIBUTIONS FROM THE JEFFERSON PHYSICAL
LABORATORY, HARVARD UNIVERSITY.

THE ANOMALOUS MAGNETIZATION OF IRON AND

STEEL.

Bt B. Osgood Peirce.

Presented May 10, 1911. Received January 2, 1912.

In 1863, von Waltenhofen, who had been making experiments upon
the retentiveness of bars of iron and steel for magnetism, discovered
the phenomena which usually bear his name. If an increasing current
(/), ending in the maximum value /', be sent through a long solenoid,
the final value of the magnetic moment of a solid bar of originally de-
magnetized soft iron or steel within the solenoid frequently depends,
not only upon the final strength of the current, but also upon the man-
ner of growth of the current in attaining this intensity. The moment
will be greater if the current be suddenly applied in full strength than
if it be made to grow slowly, either continuously or by short steps. If,
after the current has remained steady for a short time, at the strength
/', it be made to decrease to zero, the residual moment of the bar will
usually be less if the current be suddenly opened than if the decrease
be made slowly, by gradually introducing more and more resistance,
and the demagnetizing factor of a given cylinder is considerably less
when computed from observations made by the method of sudden re-
versals, than if it is determined by slow, step-by-step changes in the
exciting current.

Von Waltenhofen also encountered some cases of apparently anoma-
lous magnetization which he describes in the following words taken from
his paper in Volume 120 of Poggendorff's Annalen :

"Es ist mir oft aufgefallen, dass die magnetischen Riickstiinde in
weichen Eisenkernen bei wiederholter, ganz gleicher, temporJirer Mag-
netisirung desselben Stabes, sehr ungleich ausfallen. Noch befrem-
dender aber war mir eine Erscheinung, die ich an einem sehr dicken
Eisencylinder zuerst wahrgenommen habe, und welche darin bestand,
dass der nach Aufhebung des magnetisirenden Stromes zuriickgeblie-

634 PROCEEDINGS OF THE AMERICAN ACADEMY.

bene Magnetismus im Vergleiche mit dem verschwundenen temporaren
Magnetismus manchmal sogar die entgegengesetzte Polaritat hatte. . . .
In der Magnetisirungsspirale wurde ein vollkommen unmagnetischer
Cylinder von moglichst weichem Eisen, 103 mm. Liinge und 28mm.
Burchmesser, mit zunehmender Stromintensitat soweit magnetisirt, dass
sein temporares Moment nahezu = 60 war. Nach plotzlicher Strom-
unterbrechung ausserte er das entgegengesetzte remanente Momente
—0.20, und zeigte auch nacb wiederholten plotzlichen OefFnungen der
wieder geschlossenen Kette entschieden negative (anomale) Riick-
stande. Dagegen zeigte sich nach allmahlich eingeleiteter Aufhebung
des magnetisirenden Stromes jedesmal ein bedeutendes, mit dem tem-
poraren Momente gleichnamiges Residuum. Wenn der Strom hierauf
in derselben Richtung abermals bergestellt, sodann aber plotzlich un-
terbrochen wurde, zeigte sich das mit der temporaren Magnetisirung
gleichnamige Residuum, welches nach allmahlicher Stromaufhebung
immer wenigstens den Betrag 0.30 hatte, nahezu auf 0 reducirt ; konnte
jedoch durch Wiederholung dieses Verfahrens nicht merklich unter 0
herabgebracht werden. Wenn aber hierauf die magnetisirende Strom-
richtung gewechselt wurde, so trat nach plotzlicher Unterbrechung
wieder eine ganz entschiedene anomale Magnetisirung auf. So oft der
Eisencylinder mebrere Tage in ostwestlicher horizontaler Lage unbe-
riihrt gelassen war, zeigte er sich wieder vollkommen unmagnetisch,
und ergab bei Wiederholung des zuerst beschriebenen Versuches wieder
das anomale Residuum —0.20. Wenn dagegen die remanenten Mag-
netismen nicht durch liingeres Liegenlassen, sonderu durch entmagneti-
sirende Strome verschwinden gemacht worden, gelang es nicht, so
auffallende anomale Magnetisirungen hervorzubringen."

Seventeen years after the publication of von Waltenhofen's results,^
Righi,2 who was apparently unacquainted with his work, printed in the
Comptes Rendus an account of some similar experiments of his own.
He says : " On sait que le rapport entre le magndtisme remanent et le
magndtisme temporaire d'une barre d'acier envelopde par une bobine
magndtisante devient de plus en plus petit si la barre est de plus en
plus courte et grosse." " Si Ton prend des barres d'un meme acier et
de meme diam^.tre mais de longueurs ddcroissantes, on doit arriver
h une certaine longueur qui ne donne pas det magndtizatiou, pendant
qu'avec des longueurs moindres on doit obtenir une polarity rdmanente
opposde k celle de la bobine." "Si le courant est tr^s fort, le ph6-
nomfene de la polaritd anomale ne se produit qu'apr^s avoir magndtisd
la barre quelquefois dans les deux sens."

1 A. v. Waltenhofen, Pogg. Ann., 120, 1863.

2 A. Righi, Comptes Rendus, 90, 1880.

PEIRCE. — ANOMALOUS MAGNETIZATION OF IRON AND STEEL. 635

During the last thirty years, many persons ^ have studied the von
Walteohofen phenomena as they affect the hysteresis cycles of straight
rods and of closed cores of iron, and some of these have discussed the
bearing of their own measurements upon the theory of anomalous mag-
netization. G. Wiedemann * always maintained that his own researches
and those of Eighi showed that eddy currents in the iron, accompany-
ing surges in the exciting circuit, accounted best for the observed facts.
It seemed to von Waltenhofen, however, that the strange reversals of
polarity which he had noticed could not be due to induced currents
caused by sudden changes in the exciting circuit, and he explained
them as consequences of the inertia of the molecular magnets turning
in a viscous medium. Fromme,^ Auerbach, Ewing, Peuckert, Zielin-
ski, and others who have written upon the subject, seem to agree on
the whole with von Waltenhofen's views.

The present paper attempts to throw some light upon the theory of
the von Waltenhofen effect by a discussion of a number of experiments
made for the purpose of determining the conditions under which anom-
alous magnetization appears. It leaves to a future article a consider-
ation of some of the theoretical aspects of the subject.

The Demagnetizing of Stout Pieces of Iron or Steel.

It is to be said at the outset that almost every piece of iron to be
obtained nowadays in the market is more or less strongly magnetized

3 C. Fromme, Wied. Ann., 5, 1878; 13, 1881; 18, 1883; 33, 1888; 44, 1891.
F. Auerbach, Wied. Ann., 14, 1881; 16, 1882; Winkelmann's Handbuch der
Physik, Bd. V (214). W. Peuckert, Wied. Ann., 32, 1887. P. Bachmetjeff,
Rep. der Physik, 27, 1891. Ziehnski, Mitt. a. d. Telegraph-Ing.-Bureau d.
Reichspostamtes, 2, 1896. Ruecker, Inaugural Dissertation, Halle-Witten-
berg, 1905. Peirce, These Proceedings, 43, 1907; 46, 1911. L. A. Babbitt,
These Proceedings, 47, 1911.

* "Schon bei Gelegenheit der von Righi wiederholten Versuche von
V. Waltenhofen iiber die anomale Magnetisirung, hatte Ref. [Wiedemann]
erwahnt, dass sich dieselben volHg aus dem Auftreten alternirender Induc-
tionsstrome in der Masse des Eisens beim schnellen Oeffnen des magnetisi-
renden Stromes u. s. f. ableiten lassen, von denen ein spater auftretender
weniger dichter, die Magnetisirung durch einen vorhergehenden dichteren
Strom vernichten resp. umkehren kann. Die anomale Magnetisirung ist
also rein secunddr." — Beiblatter der Annalen der Physik, 5, 1881.

' "Gegeniiber den Bemerkungen des Herrn Ref. [Wiedemann] halte ich
meine Ansicht aufrecht, dass ich durch meine Versuche mit Eisendraht-
biindeln, welche ebenfalls den Unterschied der permancnten Momente in
der regelmassigsten Weise zeigten, schon nachgewiesen zu haben glaube,
dass Inductionsstrome keinesfalls zur Erklarung ausreichen konnen." —
Wiedemann's Annalen, 13, 1881.

636 PROCEEDINGS OF THE AMERICAN ACADEMY.

when it comes into the hands of the observer, and that it is often very
difficult, if not impossible, to demagnetize a massive block thoroughly.
If a slender rod be placed inside a long solenoid in circuit with the
secondary coil of a suitable open-core transformer, and if this coil be
slowly drawn off the core with the help of some mechanical device, it
is possible to send through the solenoid a long series of currents, alter-
nating in direction and gradually decreasing in intensity, and thus to
demagnetize the rod well enough for most purposes. The Jefferson
Laboratory has three large sets of apparatus of this sort.

The process just described, however, does not succeed very well with
stouter rods, for several seconds may be required to establish a steady
current in the solenoid under a steady electromotive force if the core
be large, and the use of alternating currents of commercial frequencies
is barred out. The solenoid current may be reversed in such a case,
at sufficiently long intervals, by means of a mercury commutator geared
to an electric motor. Such a commutator, made several years ago by
Mr. George W. Thompson, the mechanician of the Jefferson Laboratory,
enabled Mr. L. A. Babbitt ® to demagnetize very completely the finely
divided core of a large toroidal transformer, though a number of hours
were spent each time in the process. With irregular masses of metal
this process also is often ineffective, and it is not always successful
with short cylinders. A piece of soft Bessemer steel 5 centimeters
long, recently cut from a long rod 3 centimeters in diameter, in the
Jefferson Laboratory, was found to be slightly magnetized, and Mr.
Thompson and Mr. John Coulson attempted to demagnetize it in a
solenoid about 38 centimeters long, consisting of about 1460 turns of
large wire. They began the series of alternately directed and slowly
decreasing currents with one of more than 40 amperes, corresponding
to a field within the solenoid before the iron was introduced of about
1700 gausses, but the iron was still magnetized in the old direction,
with nearly the same intensity, at the end of their work.

In demagnetizing a stout piece of iron by currents alternating in
direction, it is well to put the metal slowly through a succession of
complete hysteresis cycles with gradually decreasing ranges, but if this
be inconvenient, the iron may be surrounded by a thick copper shell,''
the eddy currents in which will prevent the magnetic changes in the
iron caused by a sudden reversal of the main switch from being so vio-
lent as they otherwise might be. As will appear more clearly in the
sequel, the distribution of the magnetization in a stout iron cylinder

8 These Proceedings, 47, 1911.

' Shuddemagen, These Proceedings, 43, 1907.

PEIRCE. — ANOMALOUS MAGNETIZATION OF IRON AND STEEL. 637

in a solenoid which carries a current of given strength is different ac-
cording as the current attained its final value slowly or suddenly, and
it very much facilitates the demagnetization of such a piece, if the
currents be applied slowly and decreased gradually.

4000

Figure 1.

It is often assumed that a piece of iron may always be completely
demagnetized by heating it uniformly nearly to a white heat, maintain-
ing it at this high temperature for some time, and then allowing it to
cool slowly in a place where it will not be exposed to any magnetic
forces ; but in practice the procedure often fails, especially with mate-
rial which has once been irregularly magnetized or which is not quite
homogeneous. The spherical shield of a new DuBois-Rubens Panzer
Galvanometer in the Jefferson Laboratory proved to be slightly magnet-
ized and consequently useless for the purpose for which it was made.
This was heated to nearly a white heat, kept hot for about half an
hour, and then very slowly cooled in a protected space, without causing
it to lose appreciably its original magnetization ; a repetition of the
process was also unsuccessful.

638 PROCEEDINGS OF THE AMERICAN ACADEMY.

Most of the specimens mentioned in the experiments discussed below
were packed, one or two at a time, in fine iron filings, enclosed in a
piece of large iron pipe provided with screw caps at the ends, and then
heated thoroughly for some time, under a power blast, in a gas furnace.
The pipe was surrounded by fire bricks and after the fire had been re-
moved it was allowed to cool for many hours with its axis perpendicu-
lar to the earth's meridian before the annealing process was regarded
as complete. In this manner most of the pieces were fairly well de-
magnetized. Of course, the permanent magnetic moment of an iron
cylinder of length only twice as great as its diameter, is never very
strong, but it was usually possible to detect some evidences of magnet-
ization in every piece tested, A stout cylinder acquires a fairly large
temporary moment, even when it is held with its long axis perpendicu-
lar to the earth's field, and it is very necessary to adjust the relative
positions of such a specimen and a magnetometer by which it is to be
tried, so that this magnetization shall not affect the measurements.
The short iron cylinders which von Waltenhofen used must have been
very soft indeed if they really lost their magnetization completely when
left to themselves, with their axes perpendicular to the meridian, for a
number of days.

Cases of Magnetization "Which are not Really Anomalous.

In many cases of so called " anomalous magnetization," it is evident
that a strong magnetizing field applied in one direction has been suc-
ceeded by a weaker field in the opposite direction, and when this latter
has been removed, the magnet has the polarity of the first field. This
is of course not wonderful except as we may regard all hysteresis
phenomena as mysterious. Figure 1 shows a hysteresis diagram for
an iron rod about 80 diameters long, with a number of loops corre-
sponding to " side trips " within the main figure. It is clear that if
the rod has been magnetized by a positive current so that the mag-
netic condition while the current is flowing is represented by the point
N, and if the current be then stopped so that the condition of the rod
is denoted by A and an oppositely directed current which gives rise to
a field not greater than the abscissa of the point V be applied and then
removed, the resulting magnetization of the rod will be represented by
some point of the line OA. If the negative field is greater than OC,
the polarity of the rod while the current is on will be negative, but if
it be not too strong the polarity will be positive when the field is off.
This phenomenon is relatively pronounced in the case of a short, stout
rod where OA is short and the slope of the lower side of an inner loop

PEIECE. — ANOMALOUS MAGNETIZATION OF IRON AND STEEL. 639

is almost parallel to the line KVAN which may be nearly straight. An
example will make this statement clearer.

Table I. gives the material for a kind of hysteresis diagram for a cer-
tain round rod of hardened tool steel, 2.8 cm. in diameter, and 12 cm.

^

-0

/

^

z
o

/

3

o

z

//

■n

E

l\

/

1

A

1

//

B

CURF

iENT

N

//

v/

/

//

/

/

y^

^

p-

1

Figure 2. Magnetic cycle for a piece of Seebohm and Dickstahl's special
magnet steel 12 centimeters long and 3.5 square centimeters in cross section.
If the exciting current be dropped from its highest strength to 0, and then re-
versed and given such a strength as to carry the magnetism to the negative
value represented by the point V, the residual magnetism will be shghtly
positive when the current is taken off.

long, when magnetized in a certain long solenoid. The column headed
" H " gives the strengths in gausses which the fields within the solenoid
would have if the rod were not there ; the strengths of the exciting
fields in the rod would be very hard to determine even if they did not
vary firom point to point in the metal. The numbers under " N " are
proportional to the flux strengths through the central cross section of
the rod.

If a positive current corresponding to H = 976 were sent through
the solenoid and were then stopped, a negative current corresponding

640 PEOCEEDINGS OF THE AMERICAN ACADEMY.

to H =^ — 35 would make the magnetization of the rod negative while
running, but a negative current corresponding to H = — 150 could be
used without making the magnetization negative when the current was
taken off. A case like this may puzzle the observer if he does not
happen to know that the rod he is using — which does not seem to be

TABLE I.

H.

N.

H.

N.

960

551

0

+ 24

900

530

- 60

- 18

840

509

—120

- 61

780

489

-180

-103

720

467

-240

-137

660

443

-300

-191

600

420

-360

—231

540

392

-420

—272

480

361

-480

-316

420

321

-540

-354

360

279

-600

-391

300

237

-660

-422

240

195

-720

-451

180

144

-840

-504

120

110

-900

-528

60

66

-960

-551

very strongly magnetized — has in fact been exposed to some very in-
tense field in the process of manufacture, but this phenomenon is very
different from the one which von Walteuhofen describes.

The Anomalous Magnetization of Short Cylinders.

The most characteristic examples of really reversed magnetization
are to be found, perhaps, among short, stout rods of soft iron and steel,
&S, von Waltenhofen and Righi explained many years ago. If such a
rod, originally annealed and demagnetized, be placed within a long
solenoid and be subjected to a magnetizing field of suitable strength,
and if the exciting current be then gradually reduced to zero by the
introduction of more and more resistance into the circuit — by very
small steps, if not continuously — the remanent magnetism will have
the same sign as, but only a small fraction of the strength of, the mag-
netization induced in the rod when the current was running. If, how-
ever, the current be suddenly interrupted by the opening of the circuit.

PEIKCE. — ANOMALOUS MAGNETIZATION OP IRON AND STEEL. 641

it frequently happens that the sign of the residual moment is opposite
to that while exposed to the field. Figure 3 shows a typical case of a
certain kind, that of a solid piece of carefully annealed " Cold Rolled
Shafting " 8 centimeters long and 3 centimeters in diameter. The " de-
magnetizing effect of the ends " in a rod of these dimensions is, of

Figure 3. The ordinates of these curves show the magnetic condition of
a soft cylinder of mild steel 8 centimeters long and 3 centimeters in diameter,
when the exciting current had been taken off — gradually, in the case of the
full curve — suddenly in the case of the curve OPQ in which the negative
ordinates indicate anomalous magnetization.

course, very great, and the residual moment in this instance was for
many currents less than one per cent of the moment originally induced
in the metal. The long, uniformly- wound solenoid used for this ex-
periment had a number (n) of turns per centimeter of its length such
as to make Avn/lO almost exactly 25. In the figure, which represents
a large number of observations, the horizontal unit corresponds to a
field of 100 gausses if the iron were taken out of the solenoid. The
actual field to which any portion of the rod was exposed for any value
of the exciting current was of course difficult to determine. When
the exciting current was suddenly broken a small spark appeared, and
if the strength of the current was not greater than about 30 amperes,
the remanent moment was of reversed sign.

VOL. XLVII. — 41

642 PROCEEDINGS OF THE AMERICAN ACADEMY.

The rod was at the outset in a nearly neutral condition. A small
current (t) was at first applied to the solenoid, and then, with the help
of a set of high-resistance rheostats made by the Simplex Electric
Company, the rod was put many times through a hysteresis cycle with
this current, positively or negatively directed, to mark the limits.
After this the same current was slowly applied again and gradually
removed, and the remanent induction through the central cross section
of the rod was measured by means of a small test coil of very fine insu-
lated copper wire, so mounted that it could be quickly slipped off the
rod and removed from the solenoid while the rod itself remained in
situ. This flux was found for both directions of the magnetizing cur-
rent. Then the current was applied gradually as before and the cir-
cuit was broken by a sudden blow upon a simple switch, and the rema-
nant flux was determined for both directions of the exciting field. The
ballistic galvanometer used was a low-resistance d'Arsonval instrument
made for the purpose by Mr. Coulson, who worked with me in making
all the observations recorded here. The scale distance was about five
meters, and the telescope was focussed upon a real image of the scale
formed about two meters in front of the object glass, by a lens used as
the cover glass of the galvanometer mirror.

The process just described was repeated for each of a series of cur-
rents of increasing intensities, and in this manner material for the
curves shown in Figure 3 was obtained.

It is, of course, possible to use a magnetometric method in testing
the residual magnetism of short rods, but although we have made a
large number of determinations in this way, we have found it incon-
venient for several reasons. It will appear later that the lines of mag-
netization in the case of an anomalously magnetized rod are so folded
together that the external effect of the remanent magnetism is usually
small, and if a conveniently large magnetometer deflection is to be ob-
tained, the rod must be very near to the needle. It is not safe to
remove the iron fi:om the solenoid in order to test it outside, for a
slight blow might seriously alter the moment, and if the magnetism is
to be measured while the specimen is in its place within the solenoid,
the magnetometer must be set up near one end of the solenoid, where
it will be violently disturbed by the exciting currents and the fields
incident to the process of forcing the iron so many times through the
hysteresis cycles by which it is prepared for the tests. If a stout speci-
men of soft iron is placed with its axis horizontal and perpendicular
to the meridian, a moment large compared with the residual moment
to be measured is induced in it by the earth's field, and it is practi-
cally difficult to prevent this transverse magnetization from masking
the eff"ect to be measured.

PEIRCE. — ANOMALOUS MAGNETIZATION OF IRON AND STEEL. 643

111 all the observations mentioned in this paper the solenoid was
placed with its axis perpendicular to the meridian, and in all but a
very few instances to be mentioned specially, the rod was tested while
inside the solenoid.

In almost every instance, also, the exciting current was applied

-^F

/

^

^

/

y

^c

z

/

-^

y

^

o

z
■n

--'

y

/

/

^

^

B

/

/

^

^ .

X^

/"

^

/

0

\

y

/

CURF

ENT

\

A

/

Figure 4. OGF and OAB show the flux of magnetic induction through
a rod of very soft steel 2.86 cm. in diameter and 12 cm. long, after the mag-
netizing field had been gradually and quickly removed, respectively. OEC
shows on a reduced scale the flux in the rod while it was exposed to the mag-
netizing field.

slowly to the magnetizing coil. That is, the circuit was closed with
a very much greater resistance in it than was finally needed, and this
was gradually reduced to the proper amount. If the circuit was sud-
denly closed with this final resistance in it, the residual moment of the
rod was much smaller in absolute value, whether the current had been
gradually or suddenly reduced to zero, than if the rise of the current
had been slower.
Figure 4 shows the results of tests similar to those described above,

644

PROCEEDINGS OF THE AMERICAN ACADBMT.

but made upon a phenomenally soft bar of mild steel 12 centimeters
long and about 2.86 centimeters in diameter. The line OEC, which is
nearly straight, represents the induction flux through the central cross

L

/

z

D

C

o

/

/

o

z

r-
C
?<

/c

/

/

/

/

/

^

-

0

0

\

\

CURRE

NT

y

/

/

\

P

/

Figure 5. A cylindrical shell, about 12 centimeters long and 2.8 centimeters
in outside diameter, was exposed in a long solenoid to exciting currents of
various intensities. OCL represents the flux tlirough the central cross section
of the cylinder when the current was running, and OPQ, drawn on a some-
what exaggerated scale, the remanent flux when the circuit was suddenly
broken. The horizontal unit corresponds to a field of 25 gausses in the sole-
noid when the iron was not there.

section of the bar while the metal was under the action of the mag-
netizing field. Each ordinate has only one nine-hundredth of the
length it would have if the scale of this curve were the same as for the
other lines in the figure. The ordinates of OGF give the remanent
flux when the slowly applied exciting current was as slowly reduced to

PEIRCE. — ANOMALOUS MAGNETIZATION OF IRON AND STEEL. 6-15

zero. The line OAB shows the residual flux after the current had
been suddenly interrupted. The solenoid used in this work has 1460
turns in a length of 47 centimeters. The horizontal unit in the dia-
grams corresponds to about 80 gausses for the field (47rw //lO) in the
solenoid due to the current in its coil. A discharge of 1 microcoulomb

—

0/

'"^

-^

/

'

X

\.

z
o

c

1

/\

^^'

- •"

^

-^^

^

--^

\

w

o

1 /

^

V
N

\

V

-n

i

1

//

\

u

1
1

/

/

'

1 1
1 1

/

1

/

o

c

URRE

NT.

Figure 6. The ordinates of these curves represent the residual magnet-
ism in a certain short, stout piece of soft steel magnetized in a solenoid,
when the exciting current had been suddenly interrupted. A positive ordi-
nate indicates reversed or anomalous magnetization. The observations
recorded in each curve were taken after the specimen had been newly an-
nealed, and the differences between the curves show that it is difficult to
demagnetize a cylinder of such dimensions completely.

sent through the low-resistance galvanometer would cause a throw of
186 miUimeters of the scale, and a throw of 1 millimeter corresponded
to a flux of about 0.74 maxwells through the steel. The vertical unit
in the diagram for the lines OGF, OAB, is 15 maxwells. It is evidence
of the extraordinary magnetic softness of this specimen that whereas
the flux through the rod corresponding to the point C was 70,000 max-
wells, this sank to 11 3 maxwells when the current was slowly removed.
Figure 5 represents the results of experiments upon a soft steel shell
about 12 centimeters long, 2.83 centimeters in outside diameter, and

646

PROCEEDINGS OF THE AMERICAN ACADEMY.

1.9 centimeters in diameter inside. OCL represents the flux through
the central cross section of the shell when the current was running, and
the lower curve shows the residual flux upon a relatively larger scale.
This residual flux is reversed for solenoid fields less than about 200
gausses.

CURRENT.

>

0

\

^

"n'*-

~^~^

■\^

^

o

v

/

X-

H

\ \

/

^

o

z

\1

M

\

■n

\

N

L

r

\

/

r

/

^

^

/

P

*

Figure 7. This diagram shows magnetic bias in a short rod of cold-drawn
mild steel. This resisted the ordinary processes for demagnetizing the iron.

The three pieces of steel to which the curves of Figures 3, 4, and 5
belong were all freshly annealed just before they were- magnetized, and
the same precaution was taken in the case of almost every other speci-
men mentioned in this paper. The most careful reannealing does not
generally bring a stout piece of iron which has been exposed to a
strong field exactly back to its original magnetic state, though the
differences are often so small as only to be discoverable when the speci-
men is tested for anomalous magnetization. Figure 6 shows such a
test made upon a soft piece of Bessemer steel freshly annealed before
the observations recorded in each curve. The residual moments were
themselves very small and the differences were in absolute value very
small indeed but are evidently real.

Figures 7 and 8 show the results of experiments made upon two
pieces 12 and 8 centimeters long, respectively, cut from a rod of cold-
rolled shafting about 3 centimeters in diameter. Each piece was ex-
posed to a long series of magnetic fields alternating in direction and
gradually decreasing in intensity, with the hope that this process
would remove any magnetization that the rod might have acquired in
the making, but both pieces show a decided bias which was too strong
to yield to such treatment. In Figure 7, OPQ is the residual mag-
netism after currents which have caused positive moments have been

PEIRCE. — ANOMALOUS MAGNETIZATION OF IRON AND STEEL. 647

suddenly destroyed. OMNL shows the remanent magnetism after
currents which have caused negative moments. The first curve indi-
cates that the residual magnetism was reversed in sign, but this was
never the case after negative currents. In Figure 8 similar curves are
shown for the shorter specimen and it appears that some of the nega-

^

^

G

_^

/

^

o

°\

y

1

c

JRREN

T

z

D

C

5

V

■^

o

z

•n

r

\

\

?<

X

\

5-^

^^

__^

■ "

0

''

Figure 8. Magnetic bias in a rod of cold-rolled shafting which the de-
magnetizing process used could not remove.

tive currents left anomalous residuals. Annealing removed the bias
from the first piece almost completely.

Apart from details the observations recorded in this section are in
general agreement with much that has been written upon this subject
as given ^ in Wiedemann's EleMricitdt. Wiedemann denotes by T the
total magnetic moment of a bar when exposed to the action of a mag-
netizing field and by P the residual moment after the field has disap-
peared. He uses the suffixes a and / to denote that the moment of
which he is speaking has been reached by a gradual change in the
exciting field or by a very sudden one. He says that Tf is always
larger than Ta and Pa than Pf, algebraically considered, but these
differences are only large in short rods. Pf is slightly increased if the
rod to be magnetized is surrounded by a thick tube of nonmagnetic
metal. {Pa — Pf) /Pa is smaller for bundles of insulated soft iron wire
than for solid rods of the same dimensions. Inversion comes with
longer rods when the exciting field is weak than when it is strong.
Some of these statements will need to be discussed in the light of ex-
periments upon divided cores. The statement copied by Wiedemann

* Bd. iv, §§ 338-340.

648 PROCEEDINGS OF THE AMERICAN ACADEMY.

that if the iron core has been already magnetized in the normal direc-
tion by a current which has been slowly brought to zero, anomalous
magnetization does not occur when a second current is applied in the
same direction and then suddenly stopped, runs counter to all our
experiences. Specimens which have not been really demagnetized
show, of course, all sorts of abnormal behavior, but we have found it
easy, with suitable cores, to get reversals after a slowly applied current
has been slowly removed, by breaking suddenly a current in the same
direction whether this last was applied slowly or suddenly. If a
quickly applied current has been slowly cut off, we can get reversals
by quickly breaking a current in the old direction, applied either
quickly or slowly. If we apply either slowly or quickly a current in a
fixed direction, then open it suddenly, and repeat this process a score
of times, the reversal usually occurs at every break of the circuit with-
out any reversal in direction of the exciting current. The remanent
magnetism after a slow break, is greater if the current was quickly
applied, but, as we have seen and as Wiedemann's statements would
lead us to expect, anomalous magnetism occurs more regularly if the
current has been slowly applied.

As Righi pointed out in 1880, if one cuts a number of pieces of dif-
ferent lengths from a stout steel rod and, beginning with the longest
and taking them in order, tests the sign of the remanent magnetiza-
tion of each after the exciting field has been suddenly destroyed, one
often arrives at a length where anomalous reversals begin and continue
for shorter pieces. Figures 9, 10, 11, are founded upon a set of such
tests made upon rods cut from the very soft bar which furnished the
specimen to which Figure 4 belongs. The diameter of the bar was
about 2.83 centimeters, and the lengths, in centimeters, of the pieces
used were 40.1, 31.8, 20.9, 18.0, 13.6, 12.0, 10.0, and 8.0. Figure 9
shows the residual fluxes through the centres of the pieces for all the
specimens except the first and the fifth. These are all reversed in sign,
but the amounts are extremely small because of the remarkable softness
of the material. The horizontal unit corresponds to a solenoid field of
20 gausses, the vertical unit is about 7 maxwells. The first piece, 40
centimeters long, showed a slight reversed moment for excitations in
the solenoid up to about 38 gausses, but the ordinates of the positive
loop were not so high as the other curves of the series might lead one
to expect them to be. Figure 10 shows the residual fluxes after the
exciting currents had been slowly reduced to zero. The horizontal unit
is here 80 gausses and the vertical unit 30 maxwells. Figure 11 shows
the induction fluxes through the cross sections of the rods while they
were in the magnetizing fields. The horizontal unit is in this case 80

PEIRCE. — ANOMALOUS MAGNETIZATION OF IRON AND STEEL. 6-49

P4

CO

I I

0

2

a

a>
o

CO

3
O

a>

■§

O

b

CD
>

m
O

Si

INDUCTION FLUX

650

PROCEEDINGS OF THE AMERICAN ACADEMY.

gausses and the vertical unit very nearly 14,000 maxwells. Of 42,000
maxwells which the 8 centimeter long piece had under an exciting cur-
rent of 16.4 amperes, only about 55 maxwells remained when the current
had been gradually destroyed, and this for a cross section of about 7
square centimeters.

/

-^

/

/

/

o

H

/

o

z

•n

r

-0

I-

/

^

■^

J

/^

/

/

^^

/

^^

^<

■^

^^

/

/

y^

•--^

^

_-^

//

^

■^^

b"*

#

^

.^"^

0

(

;uRRE^

JT.

Figure 10. Residual magnetism of normal sign in rods of very soft mild
steel of different lengths.

It is usually difficult to get a piece of Bessemer steel 3 centimeters
in diameter and even 30 centimeters long so £oft, magnetically consid-
ered, that it will show abnormal residual magnetism, and the metal just
mentioned is exceptional, as has already been said.

Pieces cut from a certain round rod of soft steel, of lengths in centi-
meters 30, 15, 8, 6.8, and of diameter 1.6 centimeters, all refused to
reverse when tested, but reversal finally appeared in a piece about 6.4
centimeters long.

It is often impossible to make a stout piece of hardened tool steel
reverse unless its length be made so smaU that the observations become

PEIRCE. — ANOMALOUS MAGNETIZATION OF IRON AND STEEL. 651

doubtful. The next table (Table II.) records the results of observa-
tions made upon a certain piece of glass-hard tool steel, 12 centimeters
long and 3 centimeters in diameter. The solenoid used in this experi-
ment, one of a large number at our disposal, was 176.2 centimeters long
and had 5526 turns of insulated wire divided up into three coils of 1837,

^^

^

^

-S

y

/

^

2

/

/

/

/V

y

y

O

c

/p

/

/

/

/

^'

z

?

c

X

/

/

y

/

/

y

y

f'

^,^p

//

/

/^

^

^

X^

^

-^u

^

"o

cu

RRENT.

Figure 11. Magnetism induced by different exciting fields in a set of
rods of various lengths.

1847, and 1847 turns respectively. The first column gives the inten-
sity of the exciting current and the second column, on an arbitrary scale,
the remanent magnetism, which always had the sign of the magnetizing
field which had just been suddenly interrupted.

TABLE

II.

I

N.

0.2

2

2.0

98

0.4

6

2.5

148

0.6

17

3.0

196

0.8

23

4.0

302

1.0

31

5.0

415

1.5

61

652 PROCEEDINGS OF THE AMERICAN ACADEMY.

There is here no trace of anomalous magnetization.

If a strong current running through a solenoid containing a core of
magnetizable metal, be suddenly broken, there will be, under favorable
circumstances, an oscillatory discharge across the spark gap, and accord-
ing to Wiedemann's theory, which was based upon the numerous experi-
ments of early observers * upon the magnetization of steel needles by
discharges from Leyden jars, the phenomena of anomalous magnetiza-
tion are to be explained by the action of oscillating currents rapidly
decreasing in intensity, induced in the outer portions of the core under
test. Through the kindness of Mr. William Otis Sawtelle, who has a
large revolving mirror driven by a powerful motor, and devices which
he has himself designed and constructed' for photographing electric
sparks under various conditions, we were able to make sure that in the
cases of the apparatus which we used in our experiments upon anoma-
lous magnetization the discharge, when we suddenly opened the circuit,
was uniformly oscillatory in character. Mr. Sawtelle and Mr. Coulson
photographed a large number of these sparks ; and, from their results,
there cannot be any doubt, I think, that there were usually several hun-
dred reversals in direction while the visible discharge lasted. With one
of our solenoids, the period proved to be about l/58000th of a second,
and Professor G. W. Pierce, who most kindly tested one of our coils by
itself, showed that such frequencies were to be expected. In each of
the spark photographs, the record crossed the plate many times and
the growth of the spark length with the time when the circuit was sud-
denly opened could be studied from them. It appeared that the man-
ner of throwing the circuit open had very little effect upon the character
of the discharge. When the current in the solenoid circuit is brought
to zero by the continuous introduction of more resistance into the cir-
cuit, we do not expect that alternative currents will be induced in the
core. It is difficult, however, to get any satisfactory theory upon
which to base a mathematical investigation of the results of currents
induced in a core of soft iron by oscillations decreasing in amplitude in
a neighboring circuit. Even if the courses of such currents in a non-
magnetizable core could be satisfactorily treated, and this seems difficult
without a more accurate knowledge than we have about the behavior of
the exciting current oscillations, we should not have any clear light

' Savary, Ann. de Chim. et de Physique, 34, 1826. Von Liphart, Pogg.
Ann., 116, 1862. Paalzow, Pogg. Ann., 117, 1862. Reiss, Pogg. Ann., 122,
1864. J. Henry, Scientific Writings, pp. 203 and 293. Rayleigh, Phil. Mag.,
38, 39, 1870. Rutherford, Phih Trans., 189, 1897. Wilson, Electrician, 51,
1903. Fleming, Proc. Roy. Soc, 74, 1903.

PEIRCE. — ANOMALOUS MAGNETIZATION OF IRON AND STEEL. 653

upon what happens in a core magnetized in lines which are often closed
within the metal, after the magnetizing current has been removed and
the changes which come from the rapidly changing demagnetizing forces
from the ends of the core itself are going on. We may content ourselves
at present, therefore, by showing that, so far as we know, oscillations
are always present in the circuit of the exciting current when anomalous
magnetization is afterwards to be detected in the core. We must not
close our eyes, however, to the fact that the demagnetizing forces due
to the magnetic distribution itself complicate the problem.

Residual Magnetization in Bundles of Fine Iron Wire.

The remanent magnetism in a bundle of fine iron wire so shellacked
as to prevent electric flow from one wire to the next, should be inter-
esting because the effects of eddy currents in the core itself are nearly
avoided. Fromme's work in this direction seems not to have been con-
clusive, and it will be instructive to consider two or three experiments.

Two similar solenoids were placed horizontal with their common axis
perpendicular to the meridian, and with their nearer ends about 15
centimeters apart. These solenoids were so connected in series that a
current sent through the circuit did not affect the needle of a magneto-
meter between them. A bundle of fine, varnished iron wire forming a
cylinder 12 centimeters long and 3 centimeters in diameter was then
introduced into one of the solenoids and tested to make sure that it
had been properly demagnetized. A small current was next sent
through the circuit and the wire put several times through the cycle
corresponding to this current. Then the circuit was suddenly broken
so as to bring the current from its full value to zero and the needle
deflection caused by the residual magnetism was observed. This pro-
cess was then repeated for a series of currents of increasing strengths.
The results of the work are given in Table III. H represents the
strength which the current would cause in the solenoid if the disturb-
ing effects of the iron itself were not present. D shows the deflections
of the needle on its scale caused by the residual moments. It is evident
that there was nothing here similar to the abnormal magnetization of a
soft iron solid cylinder of the same dimensions under similar conditions.

TABLE

III.

H.

D.

H.

D.

10

19

150

182

19

45

211

208

37

81

301

233

63

112

420

253

89

138

530

263

110

156

654 PROCEEDINGS OF THE AMERICAN ACADEMY.

A bundle of the same size as the last (12 centimeters long and 3
centimeters in diameter) was then made of pieces 12 centimeters long
cut from Bessemer steel wire some of it 2.4 millimeters in diameter and
some of it twice as large. In this case the wires were not varnished
and eddy currents were not wholly prevented. The observations were
made by determining the induction flux through the central cross
section of the bundle, first, when the exciting current was running
and then after it had been suddenly destroyed. The first column in
Table IV. gives the strength of the field in the solenoid (47rw//10) ;
the other columns give, on an arbitrary scale, the flux values.

TABLE IV.

H.

N.

N'.

10

293

6.8

19

592

15.0

36

1144

30.1

60

1900

52.0

84

2740

71.6

108

3490

87.2

145

4700

113

201

6900

140

290

9200

166

400

13800

188

501

17300

210

These results represent very fairly all our experiences with bundles
of iron wire. Although most transformers show the von Waltenhofen
phenomena unless the cores are very minutely divided, I have never
been able to get even an approach to a reversal of sign of the magnet-
ism of the short packages of fine wire that I have used. One of these,
which was about 3 centimeters in diameter, was only 6.8 centimeters
long.

In a stout iron cylinder made up of a small number of large pieces,
anomalous magnetism is frequently to be found. Figure 12 shows the
results of an interesting test upon a short cylinder of soft Bessemer
steel, at first solid and then slit in a milling machine lengthwise with a
very thin saw. The forms of the curves which show the magnitudes of
the anomalous magnetization in these cases are similar, but the effect
of the slits is very marked.

As has been already explained, we usually opened a circuit, when
this had to be done suddenly, by a sharp blow upon a switch, but wo
experimented with other devices without finding that any of them was

PEIKCE. — ANOMALOUS MAGNETIZATION OF IRON AND STEEL.

655

better. At one time we broke the current by shattering a short piece
of glass-hard steel wire introduced for the purpose into the circuit,
but we did not discover that this process led to different conclusions
from those which we reached with the more convenient key.

Figure 12. This diagram shows anomalous residual magnetism in the
case of a piece (P) of soft Bessemer steel, 12 cm. long and 2.8 cm. in diameter.
The full curve was obtained with the cylinder intact as shown at T, the dotted
curve, after the specimen had been sUt lengthwise in the manner shown at Q.

Anomalous Magnetization in Cylinders Formed of Shells

AND Cores.

As will appear more clearly in the sequel, many of the lines of po-
larization in a short, anomalously magnetized solid cylinder form closed
curves wholly inside the metal, and a cut made in the iron in the form
of a cylindrical surface coaxial with the surface of the specimen would
seriously interfere with this arrangement because there would be a very
sensible reluctance at the crack. "We should expect, therefore, that
the magnetic characteristics of an, iron cylinder formed of a cylindrical
core and a coaxial shell would be in some respects dififereut from that
of a solid cylinder, and this is the fact.

656

PROCEEDINGS OF THE AMERICAN ACADEMY.

Figure 13 gives two curves, the first, OKED, belonging to a shell of
diameters 2.83 and 1.93, with a core of diameter 1.60 centimeters ; the
second, OGPQ, to a shell of diameters 3.20 and 2.20, with a core of
diameter 1.90. In each of these cases the residual magnetism is re-
versed in sign for comparatively small currents, then direct for currents

Figure 13. The ordinates of each of the curves of Figure 13 show the
remanent magnetism in a combination of a soft Bessemer shell and core when
the slowly applied exciting current has been suddenly broken. A negative
ordinate indicates that the residual magnetism has a sign opposite to that
of the field in the solenoid when the current was running.

somewhat stronger, and for large currents is again reversed with no
apparent desire to become again positive. Curve LMNZ of Figure 14
belongs to a shell of diameters 2.83 and 1.93 with a core of diameter
1.90. The gap between core and shell is here narrower than in the
cases just mentioned, and the curve which gives the magnitude of
the residual magnetization in terms of the exciting current, while of
the same general form as those of Figure 13, does not cross the axis of
abscissas, and the residual moment is reversed for all the excitations
shown in the curve.

PEIRCE. — ANOMALOUS MAGNETIZATION OF IRON AND STEEL. 657

Figure 15 shows some observations made upon a shell and core which
were not very successfully demagnetized. A slight bias exists : ABC
and PQZ show the residual fluxes through shell and core, the first for
currents which give a negative moment while they are running, the
second for positive currents.

CURRENT.

Figure 14. Two similar shells of soft steel, one intact, the other sUt length-
wise by a thin saw cut, were used successively over the same core. LMNZ
and OAB show the fluxes through the combinations in the two cases.

Figure 16 shows how greatly the manner of building up the current,
which is then to be quickly broken, affects the amount of the negative
or reversed magnetizations. Both of these curves show anomalous
magnetization for moderate currents, but the residual flux is very
much greater if the current is built up gradually than if it is built up
suddenly.

The gap between core and shell in the combinations X and Y of
Figure 13 and some others we have used, was purposely made wide
enough to permit of the introduction of a very thin ring coil to em-

VOL. XLVII. — 42

658

PROCEEDINGS OF THE AMERICAN ACADEMY.

brace the core alone and thus make it possible to study separately
the behavior of each part of the system. The results of experiments
of this kind proved instructive, as will appear from an account of a
typical case.

^^^

B~-*-

■"^

z
o

/

N

c
o

/

1

\

c

/
/

/

\

\

/

J

7

V

\

\

y

A

0

\

c

URREN

T

y

/

\

y

"^

q""^

FiGiTRE 15. A combination of shell and core, made of soft Bessemer steel,
was demagnetized as completely as possible and then tested in a long sole-
noid. The magnetizing current was built up gradually and then suddenly
broken. The ordinates of ABC show the residual flux through the metal
when the current gave a negative moment before it was interrupted, the
ordinates of PQZ show the remanent flux for oppositely directed currents.
There was a bias in the specimen which showed that the process of demag-
netizing it had not been wholly successful, and the anomalous magnetization
is of different magnitude on the opposite sides.

A cylindrical shell 12 centimeters long, the diameters of which were
3.00 and 2.27 centimeters, was used with a core 1.90 centimeters in
diameter to form a combination (Z) which, after being thoroughly de-
magnetized, was placed in a long solenoid and exposed to a series of
magnetizing fields, each a little stronger than the preceding. At every
step, the metal was put a number of times through the hysteresis
cycle corresponding to the exciting current employed, and then the
fluxes through the central cross sections of core and shell were meas-
ured while the current was running. In Table V. H represents the

PEIRCE. — ANOMALOUS MAGNETIZATION OF IRON AND STEEL. 059

field (47rw//10) due to the current in the solenoid, F is the flux in
maxwells through the combination of core and shell, N is the flux
through the core alone, and N' is the flux which the core would carry
if the whole flux through the system were uniformly distributed. The
area of the cross section of the core was about 47 per cent of that of
the combination.

TABLE V.

H.

F.

N.

N'.

N/F.

10

1270

130

595

0.102

20

2500

215

1170

0.086

30

3670

295

1720

0.080

40

4830

365

2270

0.076

50

5990

430

2820

0.072

60

7150

500

3360

0.070

70

8310

565

3920

0.068

80

9470

630

4450

0.067

90

10640

700

5000

0.066

100

11820

765

5500

0.065

125

14800

930

6950

0.063

While the slowly built up current is running steadily the flux in the
core, which should be nearly half that through the whole combination
if the flux is to be uniformly distributed, is very much less.

When in the case of this combination (Z), the slowly built up current,
so directed as to make the flux positive while it is running, is very
slowly decreased to zero, the remanent flux through the system is posi-
tive, but the flux in the core becomes negative, in the manner indicated
by the figures in Table VI. in which F, N, S, are the induction fluxes
through the whole combination, the core, and the shell, respectively.

TABLE VI.

H. F. N. S.

50 +86 -322 +408

100 +122 —410 +530

150 +132 —370 +500

200 +141 -318 +459

250 +149 —265 +415

300 +155 —213 +368

While the remanent flux through the system increases regularly with
the strength of the current, the oppositely directed fluxes in the shell
and the core decrease after reaching maximum values.

660

PROCEEDINGS OF THE AMERICAN ACADEMY.

In all work with short bars of iron or steel, the " demagnetizing
force due to the ends " becomes very important. The outer portions
of a very short magnet often reverse the direction of the polarization
in the inner portion so that most of the lines of polarization are closed
within the metal and the effect of the magnet upon a magnetometer

z

u

c

^

-i
o

^ s

z

•n

r
c

Ni

\

A

\

\

/

/

w

_-*

\

/ M^^^

X

\

0

Q

CURRE

NT. U

FiGUEE 16. A shell and core of soft Bessemer steel about 12 cm. long
were exposed to a magnetizing field of given strength in a long solenoid, and
the exciting current was then suddenly broken. The ordinates of the curves
OSU and OWQ represent the remanent induction flux through the central
cross section of the specimen, when the solenoid current was slowly built up
and suddenly appUed, respectively. A positive ordinate represents a reversal
of magnetism in these curves.

needle is often very slight indeed. If a cylindrical shell with a core
of loose steel wires be placed inside a solenoid of stout wire and a
powerful current be then suddenly sent through the coil, the wires will
be thrown violently out of the shell if the latter be short and stout, in
a direction which shows that the moment induced in them by the ex-
citing current was opposite in sign to that of the shell. This experi-
ment is sometimes very striking.

If, in the experiments upon the combination Z, the exciting current
was suddenly destroyed, the flux in the shell became instantly negative,

PEIRCE. — ANOMALOUS MAGNETIZATION OF lEON AND STEEL. 661

while the remanent flux in the core was positive just as it was when the
current was running through the solenoid circuit. See Table VII.

TAE

JLE VII.

H.

F.

N.

a

10

- 7

+ 57

- 64

20

-18

+134

-152

40

-25

+ 180

-205

50

—21

+184

-205

100

- 5

+178

-183

150

+ 4

+170

-166

200

— 4

+171

-175

250

-17

+214

-231

300

-30

+320

-350

At H= 1100 gausses F gave a negative throw far off-scale, and N a
similar positive throw. At this excitation, however, the solenoid cur-
rent had to be so strong as to heat the coil rapidly and we did not
attempt to make careful determinations of these fluxes. If F were
plotted against H we should get a curve of the form shown in
Figure 13.

All the combinations of shell and core that we have used give a set
of fluxes for the F column which vary with the excitation in much the
same way that the whole flux for Z does. There is always — so far as
my knowledge goes — an increase in N from a low value near the out-
set to a rapidly increasing one at high excitations, but sometimes the
increase is regular and sometimes not. As an instance of a very rapid
increase in N beginning near a given excitation, I may cite the case of

TABLE VIII.

I.

F.

N.

0.22

- 18

+ 14

0.42

- 4.7

+ 33

0.82

—12.2

+ 78

1.44

-16.3

+118

1.77

-18.0

+138

2.25

—17.2

+148

2.73

-15.7

+162

3.43

-10.1

+177

5.00

+ 2.7

+197

7.60

+ 10.3

+308

2.10

-20.1

+664

662

PROCEEDINGS OF THE AMERICAN ACADEMY.

a certain combination of nearly the same dimensions as Y of Figure 13,
which was tested in a solenoid for which 47rw/10 was very nearly
equal to 25. The first column in Table VIII. gives the intensities of
the exciting currents used, the second and third columns the fluxes
after the currents had been suddenly interrupted.

L in Figure 1 7 represents a combination of two coaxial shells and a
core, very accurately made and carefully annealed by Mr. Thompson.
The diameters, in centimeters, of the five cylindrical surfaces were 1.12,
1.58, 2.53, 3.00, 3.96. This system was treated like all the other test
pieces and the fluxes through all three members were determined after
the currents which had been slowly applied had been slowly brought to
zero and again after they had been suddenly destroyed. Tables IX.
and X. give the remanent fluxes for the slow breaks and for the quick
breaks respectively. I represents the solenoid current in amperes.

TABLE IX.

I.

Core. Inner Shell.

Outer Shell.

0.60

- 7.8 - 38

+ 58

1.41

- 25.6 -160

+225

4.70

- 56.5 -292

+428

8.50

- 84.0 -276

+474

17.00

-156.0 - 34

+294

44.50

- 41.4 +215
TABLE X.

+ 47

I.

Core. Inner Shell.

Outer Shell

0.60

+ 6.2 + 83

- 109

1.41

+ 12.1 + 174

— 223

4.70

— 2.5 + 299

- 318

8.50

- 0.7 + 364

- 366

17.00

+ 1.9 + 652

- 674

44.50

+155.0 +1445

-1922

The signs are nearly all difi'erent according as the current is slowly
or quickly destroyed.

The observations already described represent fairly all our 'work
upon combinations of solid shells and cores and it remains to mention
the special case represented by the nearly straight line of Figure 14.
Here the shell was of the same dimensions and of similar material as
that used in the work which led to the curve LMNZ in the same
figure, but this shell was slit through lengthwise by a single saw cut
which prevented currents from circulating around it. Many of our

PEIRCE. — ANOMALOUS MAGNETIZATION OF IRON AND STEEL.

663

specimens were made 12 centimeters long so that our observations
might be more easily comparable with some which von Waltenhofen
and Fromme made.

We have seen that if in a combination of a shell and a core the
exciting current be gradually reduced to zero, the residual magnetiza-

FiGURE 17. The forma of some of the test pieces.

tion of the shell is usually normal and that of the core reversed. If,
however, the current is suddenly broken, the magnetization of the
shell is often reversed and that of the core is normal. These facts may
be proved by removing the specimen from the solenoid and testing the
two pieces which then seem to be strongly magnetized, separately with
a compass or magnetometer. The separation of the members of the
system alters the polarization in each, however, and the process is not
to be recommended in accurate work.

It is very difficult to study the residual magnetism in a very short,
stout soft iron cylinder, whether this be normal or anomalous, by the
use of iron filings, for since so many lines of polarization are closed
within the metal, the external action of the magnetization is usually
small. In the case of a combination of a shell and a core, where the
gap prevents the arrangements of polarization from being what they
would be in a solid cylinder of the same dimensions, it is often practi-

664

PROCEEDINGS OF THE AMERICAN ACADEMY.

cable to show by the aid of very fine filings that lines emerge into the
air fi"om the outer filaments at one end of the specimen and go into the
metal again at the same end at points nearer the axis.

The Influence of an Iron Shell upon the Magnetic Behavior
OF A Short Cylinder within It.

Some mild steel cylinders of the dimensions of the cores used in the
combinations already described do not show the phenomenon of anom-
alous magnetization very strikingly when used by themselves, and it
seemed desirable to make a series of tests upon a short piece of very
soft steel about 3 centimeters in diameter, without and with shells. I
have used very mild steel of various kinds for most of the observations
mentioned in this paper, because it is much more homogeneous than
the best procurable wrought iron, which is apt to include patches of
oxide and slag which hinder the free passage of eddy currents in direc-
tions perpendicular to the grain of the material.

Tables XL, XII., and XIIL, give the flux through this core when the
slowly applied current /, which created the field H = 4,TrnI/10 within
the solenoid, was in action, after it had been gradually reduced to
zero, and after it had been suddenly destroyed. The numbers in the
columns headed N, N', N", belong respectively to the cases where the

TABLE

XL

CUKRENT

' On.

h.

N'.

N".

N'".

40

+ 3110

+ 747

+ 681

65

+ 5450

+1120

+1012

176

-fl4480

+2560

+2330

370

+31200

+5360

+4740

452

t • •

+6720

+5850

TABLE

XII.

Slow Break.

H.

N.

N'.

N".

20

+ 8

- 12

- 25

50

-f 20

- 42

- 97

100

+ 35

-142

-173

150

+ 51.

-191

-204

200

+ 66

-216

-223

300

-f 92

-233

-235

400

+105

-248

-242

PEIRCE. — ANOMALOUS MAGNETIZATION OF IRON AND STEEL. 665

core had no shell, where the shell of soft mild steel had the diameters
4.45 and 3.30 ; and where the shell made of fine, soft, varnished iron
wires had diameters of 4.90 and 3.35 centimeters respectively.

TABLE

XIII.

Quick Break.

H.

N.

N'.

N".

40

-18

+ 73

+ 74

65

-23

+ 106

+138

176

-18

+ 115

+209

378

+11

+ 30

+220

576

+42

+ 14

+216

In the solid shell the alternating eddy currents which "Wiedemann
had in mind may encircle the core, but this would not be possible in
the core made of shellacked wire. It is evident that both shells exert
a strong demagnetizing effect upon the core, even while the current is
running in the solenoid. All the results here tabulated agree in gen-
eral with those quoted in the last section. In the case of the solid
shell, the moment of core and shell taken together will usually be re-
versed after certain strengths of current, but this is never the case when
the shell is finely divided. Figure 18 shows a typical instance. The
solid core is surrounded by a wire shell, and when the exciting current
is suddenly destroyed the core has a reversed magnetization for values
of H up to about 350 gausses, as is shown in curve OQR. The whole
flux through the combination of core and shell as indicated by the
curve OWV is never negative, though for high excitations, when the
flux through the core is strongly positive, the flux through the shell
itself may be small. In one case under an exceedingly high excitation,
the line corresponding to OQR bent down again something like the
curves of Figure 13, but the observations were so difficult to manage
that I did not attempt to follow this out in other cases. A value of H
above 1700 or 1800 is hard to maintain without heating the metal and
the solenoid employed unduly, which masks the effect to be studied.

The Influence of a Thick Copper Shell upon the Magnetic
Behavior of a Short Cylinder within It.

Many years ago Fromme enclosed a stout piece of soft iron which
he was testing in a thin shell or shield of copper and was able to prove
that this shell did not prevent the iron from showing anomalous mag-
netization when the magnetizing field about it was suddenly destroyed.

666

PROCEEDINGS OF THE AMERICAN ACADEMY.

Our experiences agree with his if the shell is very thin, but seem to
show that a thick enough copper shell will always prevent a reversal of
the magnetization in a soft iron core inside. The records of experi-
ments on two or three specimens of soft steel with shells of different
thicknesses will make clear the nature of the phenomena.

w

.-- —

•■^^

/

^

/

\

z

/

s

o

\

J5

/

\

■•^

0

/

\

r

\

\

?<

\
\

.-"

. •

■

-B

/ ^

.

1

r

/

/

~- -

-V

/
/

0

/

CURRENT

/

/

1

/

1

m^

^

1

1

w

1

\

/

\

/

\

/

\

/

N

"~0

^/

Figure 18. A represents a solid core 12 centimeters long, and B, a shell
made of fine, soft, varnished iron wire. This combination was magnetized
in a long solenoid by a current gradually applied, and then this current was
suddenly interrupted. OWV represents the induction flux through the cen-
tral section of shell and core, OQR the flux through the core alone. The
vertical unit is 50 maxwells, the horizontal unit 100 gausses.

Table XIV. gives some results obtained in using a mild steel cylinder
1.9 centimeters in diameter and 12 centimeters long, with a copper
shell of the same length, and with diameters of 3.80 and 2.90 centime-
ters. The second and third columns give the fluxes in maxwells
through the central cross section of the iron when the exciting current
has been slowly, and quickly, brought to zero.

PEIRCE. — ANOMALOUS MAGNETIZATION OF IRON AND STEEL. 667

TABLE XIV.

Core inside

Shell.

H.

Slow Break

Quick Break,

22

+ U.9

+ 5.5

39

+29.6

+ 13.3

60

+57.2

+24.3

170

+73.3

+45.0

255

+79.0

+52.7

430

+91.7

+72.5

When the shell was removed the fluxes were those given in Table XV.

TABLE XV.
Core alone.

H.

Slow Break.

Quick Break,

22

+ 13.5

- 9.6

39

+25.3

-17.7

100

+54.0

-14.2

218

+64.0

+13.6

430

+73.8

+48.3

The eddy currents in the copper made the gradual reduction of the
current by the introduction of resistance into the circuit more continu-
ous and prevented the magnetizing field from vanishing suddenly when
the circuit was broken.

A freshly annealed piece of Bessemer steel 1.6 centimeters in diame-
ter and 12 centimeters long was tested alone, and inside each of two
copper shells of its own length, with wall thicknesses of 1.20 cen-
timeters and 0.47 centimeters respectively. Table XVI. shows the
fluxes through the central cross section of the iron for slow removals
of the excitation. The fluxes for the thick shell, the thinner shell, and
for the core without any shell, are given in the columns headed A, B,
C. Table XVII. gives the corresponding figures for the case where the
exciting current was suddenly destroyed.

TABLE XVI.

Slow Break.
H. A. B. C.

38 + 45.5 + 42.4 + 37.6

64 + 84.2 + 71.5 + 67.0

168 +162.4 +126.0 +108.0

360 +207.0 +163.0 +112.5

668

PROCEEDINGS OF THE AMERICAN ACADEMY.

TABLE XVII.
Quick Break.
r H. A. B. C.

22 + 17.3 + 7.0 -15.5

39 + 33.4 +13.8 —27.4

64 + 60.8 +20.6 —34.3

168 +127.0 +37.0 -18.9

360 +168.0 +81.5 +35.5

Only a few typical numbers are here given but these and many

others are used in plotting the curves given in Figure 19. The line

Figure 19. A soft core was used successively with a thick copper shell,
with a thinner shell, and without any shell. OS, OT, OU show the remanent
fluxes when the magnetizing fields were slowly removed; QV, QZ, QW the
fluxes if the field had been suddenly destroyed.

QW which has QR. as its horizontal axis shows the reversed magneti-
zation when the core has no shell. OS, OT, OU show the fluxes for
slow breaks, QV, QZ, QW for the quick breaks.

PEIRCE. — ANOMALOUS MAGNETIZATION OF IRON AND STEEL. 669

As has been already explained, some of our slow breaks were made
continuously with the help of a specially constructed rheostat, and
others, sufficiently well for the purposes, by introducing, by relatively
small steps, a series of resistances into the circuit. This last process
which was not, of course, perfectly continuous, was used in the experi-
ment recorded in Tables XVI. and XVII. and the effect of the copper
in preventing any sudden change in the induction flux in the iron is
evident from the figures given.

Although many complications may occur if a piece of iron or steel to
be tested has a magnetic bias, or has not been uniformly tempered, the
experiments described in this paper seem to lend support to the theory
that the residual moment of an originally neutral bar which has been
magnetized in a solenoid, is always norm al unless the current cnits
way to extinction oscillates to and fro. When the exciting current is
destroyed without oscillating in direction, even though the process be
finished in a small fraction of a second, the remanent magnetization
has the same sign as the magnetizing field. It appears that a bundle
of very fine soft iron wire cannot be made to show anomalous mag-
netism and that a thick copper shell placed over a solid bar of mag-
netizable metal prevents reversals of magnetism under circumstances
which would produce them if the shell were away.

It seems probable that in a short, stout rod of iron or steel exposed
to a magnetizing field, the intensity of magnetization in the inner por-
tions is less than in the outer filaments and that usually when the field
is removed the direction of the polarization at the axis is opposite to
that of the polarization at the outer surface. The direction of the lines
at the outer surface may be normal or anomalous according to the man-
ner in which the exciting current comes to its end, but in any case
many of the lines of magnetization form closed curves wholly within
the metal.

The placing of a thick iron shell either solid or constructed of fine
insulated wire, about a core exposed to a magnetizing field, reduces the
flux through the core, and, if the exciting current be reduced gradu-
ally to zero, the shell usually reverses the sign of the moment which
the core would otherwise have had. If the circuit of the exciting cur-
rent be suddenly broken, the residual magnetism of the core is often
changed in sign by the presence of the shell. A finely divided iron
shell never acquires anomalous magnetization when its exciting current
is suddenly destroyed, but such a shell acts magnetically upon either a

670 PROCEEDINGS OF THE AMERICAN ACADEMY.

solid or a divided core and often reverses the sign which the core would
have without it.

It is difficult to make even short, stout pieces of glass-hard tool steel
show anomalous magnetization, and it is impossible to reverse the
magnetism of very long pieces of soft iron where the end effects are
not sensible.

The experiments of Mr. L. A. Babbitt, as well as previous experi-
ments of our own, seem to show conclusively that none of the von
Waltenhofen effects are to be looked for in massive transformer cores
if these are made of fine varnished wire. I have never seen anomalous
magnetism in a uniformly annealed closed ring.

It is evident that if the solenoid current in a test for anomalous
residual magnetism be suddenly broken, the change in the electro-
magnetic field in the iron is much more rapid when the core is made
of lengths of fine, varnished wire than when it is solid and eddy cur-
rents in it shield the inner filaments. Indeed, if the core be made of
wires of a uniform size, the average rate of change of H with the time
is roughly proportional to the area of one wire. If, however, the
circuit be suddenly closed, the change in the field in the iron caused
by the exciting current cannot be made instantaneous even if eddy
currents be wholly shut out, and the effect of dividing the core is not
so striking. If the magnetized particles of a piece of iron are imbedded
in a quasi viscous medium, the rapidity of the changes in the forces
acting upon the molecules should affect the magnetic properties of
the iron.

My thanks are due to the Trustees of the Bache Fund of the
National Academy of Sciences, who have lent me some of the appara-
tus used in making the observations mentioned in this paper.

The Jefferson Physical Laboratoby,
Cambridge, Mass.

Proceedings of the American Academy of Arts and Sciences.
Vol. XLVII. No. 18. — March. 1912.

CONTRIBUTIONS FROM THE CHEMICAL LABORATORY
OF HARVARD COLLEGE.

PYROSULPHURYL CHLORIDE AND
CHLORSULPHONIC ACID.

By Charles Robert Sanger and Emile Raymond Rfegel.

PYROSULPHURYL CHLORIDE AND
CHLORSULPHONIC ACID.

By Charles Robert Sanger and Emile Raymond Riegel.

Presented October 13, 1909. Received January 11, 1912.

Contents.

Historical.

Action of Metallic Chlorides on Sulphur Trioxide 674

Action of Non-metalhc Clilorides on Sulphur Trioxide 675

Action of Hydrochloric Acid on Sulphur Trioxide 680

Relation of Pyrosulphuryl Chloride and Chlorsulphonic Acid to Each

Other; their Separation and Purification . 681

Historical Summary (Table I) 683

Results of this Investigation.

General Methods for the Preparation of Pyrosulphuryl Chloride and

Chlorsulphonic Acid (Table II) 686

Preparation of Pyrosulphuryl Chloride 690

Regeneration of Chlorsulphonic Acid 692

Properties of Pyrosulphuryl Chloride 692

Preparation of Chlorsulphonic Acid 693

Properties of Chlorsulphonic Acid 693

Experimental.

Preparations 1 to 9; Pyrosulphuryl Chloride 694

Purification of Pyrosulphuryl Chloride and Determination of Constants 697

Boiling Point 697

Specific Gravity 698

Melting Point 699

Vapor Density 701

Analysis 701

Preparations 10 to 17; Chlorsulphonic Acid 702

Purification of Chlorsulphonic Acid and Determination of Constants . 703

Dissociation 703

Behavior under Distillation 706

Fractional Crystallization 709

Melting Point 711

Specific Gravity 711

Boiling Point 711

Vapor Density 711

Analysis 712

Properties of Mixtures of Pyrosulphuryl Chloride and Chlorsulphonic

Acid (Table III) • 712

Action of Water on Pyrosulphuryl Chloride and Chlorsulphonic Acid 714

Summary 717

VOL. XLVII. — 43

674 PROCEEDINGS OF THE AMERICAN ACADEMY.

During certain investigations in this laboratory it became necessary
to find better methods for the separation and purification of pyrosul-
phuryl chloride and chlorsulphonic acid than heretofore described, and
to determine with greater accuracy their more important physical con-
stants. It was very soon evident, not only that much of the literature
on the subject was valueless, since most observers had worked with a
mixture of the two substances or with impure material, but also that a
separation of the mixture into pure components or a complete purifi-
cation of either body could not be readily accomplished on the lines
laid down by these observers. We have succeeded, however, by uti-
lizing some of the facts already known and others which became evi-
dent in the course of our investigation, in preparing both of these
bodies in quantity and of great purity. ^

Historical.

Action of MetalUc Chlorides on Sulphur Trioxide.

The complete history of pyrosulphuryl chloride and chlorsulphonic acid
begins in 1822-1823 with the study of the reaction between sulphur
trioxide and sodic chloride at high temperature by Sertiirner,^ Doberei-
ner,3 and Gmelin.* Sertiirner had erroneously considered the products
to be hydrochloric acid and sodic sulphate ; Dobereiner thought that a
gaseous compound of chlorine and sulphur dioxide was formed, while
Gmelin showed, although only qualitatively, that the gaseous product
was a mixture of chlorine and sulphur dioxide. Rose ^ in 1836 investi-
gated the reaction at low temperature, using other metallic chlorides as
well. Fused sodic chloride absorbed anhydrous sulphur trioxide, forming
a solid, transparent mass, which, when heated, gave chlorine and sulphur
dioxide, similarly to Gmelin 's observation. Undoubtedly, as R. Wil-
liamson 1* also points out. Rose had in his hands the sodium salt of
chlorsulphonic acid. Rosenstiehl ^ in 1861 distils a mixture of fused

* Acknowledgment is due to Mr. Laurence Haines Whitney for much assis-
tance in the beginning of this investigation, particularly in the separation of
pyrosulphuryl chloride and chlorsulphonic acid by crystallization and centrif-
ugal filtration at low temperature, and in the study of the use of phosphorus
pentoxide as a dehydrating agent, both in the preparation of the two bodies
and in the conversion of chlorsulphonic acid to pyrosulphuryl chloride.

2 Gilbert's Ann., 72, 109 (1822).

3 Ibid., 72, 331 (1822).

4 Ibid., 73, 209 (1823).

B Pogg. Ann., 38. 117 (1836).

6 Compt. rend., 53, 658 (1861); Jahresb., 1861, 120; Rep. chim. pur., 4, 60
(1861).

SANGER-RIEGEL. — PYROSULPH. CHLORIDE-CHLORSULPH. ACID. 675

sodic chloride and excess of sulphur trioxide until the retort contents
were completely melted. On rectifying the distillate over fused sodic
chloride, he obtained a liquid boiling at 145-150°; specific gravity,
1.762; vapor density, 3.76 (referred to air), which he considered from
the analysis to be pyrosulphuryl chloride. These properties, however,
together with the fact that it reacted violently with water, show a con-
siderable admixture of chlorsulphonic acid. This is apparently the
only source of the statement one finds in the literature that pyrosul-
phuryl chloride is formed by heating sodic chloride with sulphur
trioxide.''

Action of Non-metallic Chlorides on Sulphur Trioxide.

Rose 8 in 1838 passed the vapor of anhydrous sulphur trioxide through
sulphur monochloride at low temperature. On fractioning the product,
an oily liquid of specific gravity 1.818 at 15° was obtained, boiling at
145°, which was slowly decomposed with water. This was the first prep-
aration of pyrosulphuryl chloride, but it undoubtedly contained chlor-
sulphonic acid which is invariably formed whenever sulphur trioxide is
chlorinated in the presence of even a small amount of water (v. Table II),
and there may have been some sulphur monochloride present, since the
boiling point of the latter, 138°, is so near that of the main product.
By using phosphorus trichloride Rose obtained a similar liquid, boil-
ing between 137° and 165°, containing much phosphorus. In 1839
Rose,® with the idea of preparing sulphuryl chloride, discovered in the
same year by Regnault,^*' mixed fused sodic chloride with "pure"
pyrosulphuryl chloride, probably prepared by a modification i* of his
original method, in which he distilled sulphur monochloride with ordi-
nary fuming sulphuric acid. A solid mass was formed, resembling that
which he had previously obtained ^ by the action of sodic chloride on
sulphur trioxide. Distillation gave chlorine, sulphur dioxide, and a
liquid boiling at 145°, which he concludes to be pure, undecomposed
pyrosulphuryl chloride. PYom consideration of our work, the result is
clear. There was much chlorsulphonic acid in the supposed "pure"
pyrosulphuryl chloride, and this was converted to its sodium salt, from
which the unchanged pyrosulphuryl chloride was distilled. If Rose

'' E. g., Roscoe and Schorlemmer, Treatise on Chemistry, I, 438 (1905);
Dammer, Handbuch, I, G67 (1892).

* Ann. d. Phys. u. Cham., 44, 291 (1838); Berzelius Jahresb., 19, 201 (1840);
Gmelin, Handbuch, I, 778.
» Pogg. Ann., 46, 167 (18.39).
" Compt. rend., 7, 895 (1838).
" Pogg. Ann., 46, 177 (1839).

676 PROCEEDINGS OF THE AMERICAN ACADEMY.

had known that this was a process of rectification, we might have had
pure pyrosulphuryl chloride at an earlier date. The further researches
of Rose ^2 do not throw any light on the preparation of either body.

A. Williamson i* in 1854, by the action of phosphorus pentachloride
on "sulphuric acid" (strength not stated), obtained a liquid boiling
at 145°, decomposing violently with a small amount of water, quietly
with an excess. No method of purification is given, nor are there any
analyses of the product, but Williamson concludes that it was chlor-
sulphonic acid, and advances for the first time the theory of the suc-
cessive substitution of the hydroxyls in sulphuric acid by chlorine. He
makes a crude sodium salt, and considers the acid itself to be identical
with the preparation of E-ose,* for in his opinion that contained "the
elements of water." Williamson obtains a "similar" acid by the ac-
tion of hydrochloric acid on sulphur trioxide, which must be taken as
the first use of this reaction in the preparation of chlorsulphonic acid.
Though both of his products were impure, the first probably contained
some pyrosulphuryl chloride, the second none.

R. Williamson i* in 1857 states that chlorsulphonic acid can be
made by the action of chloride of sulphur and chlorine on sulphuric
acid and by the combination of chlorine and sulphur dioxide in contact
with heated platinum black. The product of the first reaction is said
to have the same properties as that obtained by A. Williamson, but
details of purification, properties, and methods of analysis are lacking.
From information supplied by A. Williamson, it is stated that contin-
ued distillation of the body leads to its decomposition into sulphuric
acid and sulphuryl chloride.

Schiff 1^ in 1857 shows that the supposed compound of phosphorus
pentachloride and sulphur trioxide obtained by Persoz and Bloch !•
was identical with the preparation of A. Williamson, and obtained by
the reaction a liquid boiling at 140-150°, which decomposed with water
into sulphuric and hydrochloric acids.

Baumstark ^^ in 1866, using phosphorus pentachloride with fuming
sulphuric acid, obtained a liquid boiling from 145° to 156°, mainly at
150-152°, decomposing gradually with much water, violently with a
small amount. The agreement of the vapor density (4.10) with the

" Pogg. Ann., 52, 57 (1841); 85, 510 (1852).

" Proc. Roy. Soc, 7, 11 (1854); Phil. Mag. (4), 7, 365 (1854); Jour. Chem.
Soc, 7, 180 (1855); Jour, prakt. Chem., 62, 377 (1854); Ann., 92, 242 (1854).
" Jour. Chem. Soc, 10, 97 (1858); Jour, prakt. Chem., 73, 73 (1858).
« Ann., 102, 114 (1857).
" Compt. rend., 28, 86 (1849).
" Ann., 140, 75 (1866).

SANGER-RIEGEL. — PYROSULPH. CHLORIDE-CHLORSULPH. ACID. 677

calculated (4.03) and the analysis indicated a pure chlorsulphonic acid,
but there was probably enough pyrosulphuryl chloride present to raise
the low density which pure chlorsulphonic acid usually shows owing to
its dissociation. Similarly, Williams ^^ in 1869, repeating the Wil-
liamson reaction in the latter 's laboratory, is led by density (4.56) and
analyses to consider his product pure chlorsulphonic acid. The boiling •
point is not given.

The first recorded use of carbon tetrachloride as a chlorinating agent
is by Schiitzenberger ^^ in 1869. On warming this with sulphur tri-
oxide until the phosgene was expelled, a product was obtained boiling
at 130°, reacting "at once" with water, and giving " figures leading
to the formula S2O5CI2." The sulphur trioxide was evidently hydrated
and the product contained much chlorsulphonic acid. In the next year
Armstrong 20 repeated the reaction and suggested its use as a source of
phosgene. His product boiled between 141° and 145°, was difficult to
purify, and did not decompose water easily. The analysis corresponded
more nearly to that of pyrosulphuryl chloride. Substituting chloro-
form for carbon tetrachloride, Armstrong obtains what he considers
from the analysis to be a mixture of the two bodies. He also investi-
gates the action of phosphorus trichloride on sulphur trioxide, but with
unsatisfactory results.

Prudhomme ^i in 1870 tried the action of hexachlorethane on sul-
phur trioxide in a closed tube at 150°. The product boiled at 140°
and was considered to be pyrosulphuryl chloride. No analytical data
are given.

The study of the question by Michaelis 22 in 1871 and succeeding
years is of interest. Using sulphur trioxide " free from hydrate " with
phosphorus pentachloride he obtains " pyrosulphuryl chloride " accord-
ing to the reaction :

2SO8 + PCU = SaOeCU + POCI3.

The product boiled at 143°, acted quietly with water, and had a
specific gravity of 1.819 at 18°. With sulphuric acid, the reaction was
considered to be

3H2SO4 + PCle = SSOgHCl + HPOs + 2HCI

" Jour. Chem. Soc, 22, 304 (1869); Zeitschr. f. Chcm., 12, 665 (1869).
" Compt. rend., 69, 352 (1869); Jahresb., 1869, 209; Ann., 154, 375.
20 .1. prakt. Chem., 109, 244 (1870); Ber., 2, 712 (1869) and 3, 7.30 (1870).
" Compt. rend., 70, 1137 (1870); Ann. Chem. Pharm., 156, 342 (1870).
" Jena Zeitschr., 6, 235 (1871); Zeitschr. f. Chem. (2), 7, 149 (1871).

678 PROCEEDINGS OF THE AMERICAN ACADEMY.

and the product "pure" chlorsulphonic acid. It boiled at 158.4° and
had a specific gravity of 1.776 at 18°. No sulphuryl chloride was
formed by the action of phosphorus pentachloride on either sulphur
trioxide or chlorsulphonic acid, as Williamson ^^ and Schifif ^^ had
stated, nor, according to Odling ^3^ by treating plumbic sulphate with
phosphorus oxychloride. While Michaelis did not obtain pure pro-
ducts, he at least brought out the association of the two bodies in the
chlorination product, and his results show the influence of hydration of
the sulphur trioxide. In another paper,^* in 1871, he obtains chlor-
sulphonic acid from sulphuryl chloride and water and from sulphuryl
chloride and sulphuric acid. The Carius ^^ reaction of phosphorus
pentachloride on plumbic sulphate gave neither body. In a third
paper 26 in 1873 he makes chlorsulphonic acid from concentrated sul-
phuric acid and phosphorus trichloride in a current of chlorine. Geu-
ther 27 had tried this without chlorine.

Miiller^s in 1873 prepares "chlorsulphonic acid" with phosphorus
pentachloride and " moderately fuming " sulphuric acid. He also dis-
tils a mixture of fuming sulphuric acid and phosphorus pentoxide in a
current of hydrochloric acid gas, and considers the product identical
with that made by the action of hydrochloric acid on sulphur trioxide.
There are no data by which the quality of these preparations may be
judged, and they were probably quite impure. Clausnizer 29 in 1878
prepares chlorsulphonic acid according to Michaelis by action of phos-
phorus trichloride on sulphuric acid in a current of chlorine, obtaining
a boiling point of 150-151° at 726 mm. Thorpe 30 hi 1880 uses the
Rose reaction with sulphur monochloride to prepare " pyrosulphuryl
chloride," which boils at 139.59°, corr., with specific gravity 1.85846 at
0° referred to water at 4°. By action of phosphorus oxychloride on
" the strongest oil of vitriol," he prepares " chlorsulphonic acid," boil-
ing at 155.3°, corr., with specific gravity of 1.78474. He finds that
chlorsulphonic acid is completely converted to sulphuryl chloride and
sulphuric acid by heating for some hours at 200°.

Ogier^i in 1882, during a thermochemical study of the oxychlorides
of sulphur, prepared pyrosulphuryl chloride by the first method of
Rose; the product boiling at 140.5° and reacting quietly with water.
A preparation of " chlorsulphonic acid " by the Armstrong reaction of
sulphur trioxide and chloroform showed violent action with water. No

23 Gmelin, Handbuch, 1, 169. 28 Ibid., 6, 227 (1873).

2* Jena Zeitschr., 6, 293 (1871). 29 ibid., H, 2007 (1878).

25 Ann., 106. 307 (1858). »<» J. Chem. Soc, 37, 3.58 (1880).

26 Ibid., 170, 1 (1873). 3i Compt. rend., 94, 82 (1882).

27 Ber., 5, 924 (1872).

SANGER-RIEGEL. — PYROSULPH. CHLORIDE-CHLORSULPH. ACID. 679

boiling point is given for this product, and Armstrong's opinion is over-
looked, that the reaction gives a mixture of the two bodies. In a sec-
ond paper ^2 Ogier determines the vapor density of what was probably
the same or a similar preparation of pyrosulphuryl chloride. As his
analyses convinced him of the purity of his product, the deviation of
the density (3.70) from the theoretical (7.49), together with his ina-
bility to synthesize pyrosulphuryl chloride from sulphur trioxide and
sulphuryl chloride, causes him to find here an exception to Avogadro's
Kule!

In contrast to the previous confusion, the work of Konovalofi"'^ in
1882 is clear. This author prepared pyrosulphuryl chloride by the
method of Schiitzenberger,!® using twice distilled sulphur trioxide, in
which, however, the actual amount of moisture was not determined.
During the reaction and subsequent distillation, moisture was excluded
and connections were of glass. The product boiled at 153° (752 mm.) ;
another preparation at 152.5° (740 mm.). The specific gravity was
1.872 at 0°. Water acted slowly. The analyses were good, and the
vapor density (in aniline, 7.31 ; in nitrobenzene, 7.27) showed that
Avogadro's Rule was not in immediate danger of overthrow. Konova-
loff notes that the boiling point of his product was much higher than
that of previous observers, notably that of Ogier, and considers that
previous preparations may have been contaminated with chlorsulphonic
acid, which dissociates easily. On mixing equal parts of his product
with chlorsulphonic acid prepared by the Williamson ^^ method, a boil-
ing point of 140-146° was obtained, with vapor density of 4.10 at 210°.
From four parts of water and one hundred parts of his product, he
obtained a liquid boiling at 139-140°, with vapor density of 4.07.
Ogier, 34 in reply, admitted the possibility of a small amount of chlor-
sulphonic acid in his product, but not enough to lower the vapor den-
sity to 3.70.

Heumann and Kochlin ^'^ in 1883 were unable to synthesize pyrosul-
phuryl chloride from sulphur trioxide and sulphuryl chloride. Using
the method of Rose,* they obtained a product which they did not think
could contain chlorsulphonic acid, since it was " unchanged " by distil-
lation with phosphorus pentoxide. Yet it boiled at 145-147°, with
vapor densities from 5.84 in aniline to 2.58 in sulphur, and gave in-
conclusive figures on analysis. They think that dissociation of pyro-
sulphuryl chloride takes place into sulphur trioxide, sulpliur dioxide,
and chlorine, and is nearly complete at the boiling point of sulphur.

32 Compt. rend., 94, 217 (1882). " ibij., ge, 66 (ISS:?).

" Ibid., 95, 1284 (1882). ss Ber., 16, 479 (1883).

680 PROCEEDINGS OF THE AMERICAN ACADEMY.

Possibly the work of Konovaloff had escaped their observation. Later
in another paper,36 from the vapor density at 184°, they decide that
chlorsulphonic acid (2 vols.) at that temperature is completely dis-
sociated into sulphur trioxide, sulphur dioxide, chlorine, and water

(8 vols.).

Konovaloff 3T in 1883, applying again his entirely correct theory of
the necessity for anhydrous reagents, obtained through the Rose reac-
tion with sulphur monochloride a pyrosulphuryl chloride boiling at 152-
153°, with vapor density of 7.2 at 210°.

Since 1883, little more concerning the chlorination methods has been
published. Erdmann^s in 1893, as did Armstrong earlier, proposes
the reaction of Schutzenberger,^' with slight modifications, as an
economical method for preparing phosgene. The residue he con-
siders a mixture of pyrosulphuryl chloride and chlorsulphonic acid.
Moureau ^9 in 1894, by the action of thionyl chloride on sulphuric acid
of specific gravity 1.84, obtains a product boiling at 130-157°, which
he concludes to be a mixture of the two bodies. Prandtl and Borin-
ski ** have used the method of Schiitzenberger in the investigation
cited below, and show that both bodies are present in the reaction
product.

Action of Hydrochloric Acid on Sulphur Trioxide.

As previously mentioned, A. "Williamson, ^^ ^^ 1854 was apparently
the first to use this reaction, of which chlorsulphonic acid and not pyro-
sulphuryl chloride is the product. The reaction was repeated in 1857
in A. Williamson's laboratory by R. Williamson,^* but no details are
given. Dewar and Cranston *° in 1869, also, by the " direct action of
sulphuric acid on hydrochloric acid," obtain a substance "with all the
properties ascribed by Williamson."

Much more definite is the work of Beckurts and Otto *i in 1878,
who advised the use of a fuming sulphuric acid, slightly crystalline at
ordinary temperature, " containing from 38 to 39 per cent of sulphur
trioxide." *2 Their product boiled between 149° and 152.7°, mainly
at 151.7-152.7°, and was apparently fairly pure. Beckurts and Otto
consider that, if chlorsulphonic acid and sulphuric acid give pyrosul-

36 Ber., 16, 602 (1883).

3' Compt. rend., 96, 1146 (1883).

38 Ber., 26, 1990 (1893).

39 Bull. Soc. Cliim. (3), 11, 767 (1894).
*« Chem. News, 20, 174 (1869).

« Ber., 11, 2058 (1878).

*^ This would mean about 94 per cent actual sulphur trioxide, or about
66 per cent available (v. Table II, p. 687).

SANGER-RIEGEL. — PYROSULPH. CHLORIDE-CHLORSULPH. ACID. 681

phuric acid and hydrochloric acid, according to Williams, ^^ the for-
mation of chlorsulphonic acid by their method must be due to the
concentration of the hydrochloric acid, i. e.,

H2S2O, + HCl ^ H2SO4 + SO3HCI.

Though Miiller^s in 1873 had added phosphorus pentoxide to the
fuming acid, presumably to increase the yield, it is not clear that
he understood the action of the hydrochloric acid to be on the free
sulphur trioxide only. Beckurts and Otto could not substantiate the
result of A. Williamson,** furthur studied by Behrend ** and later
proved by Ruff,*^ that chlorsulphonic acid, heated to 170-180°, gives
sulphuric acid and sulphuryl chloride, for they considered that sulphur
dioxide and chlorine were the primary products ; sulphuryl chloride a
secondary one.

Nothing new in regard to this method has apparently been published
in the past thirty years. We find further no specific statement of its
use in the preparation of material for investigation. Though it has un-
doubtedly been employed, yet most of the preparations of chlorsul-
phonic acid, so called, seem to have been made with non-metallic
chlorides.*®

The contribution of Ruff *5 in 1901 to the knowledge of chlorsulpho-
nic acid is important, and throws light on the somewhat discordant
observations of former investigators. He does not state the method of
preparation, but this is of no importance to his paper. He studies the
decomposition to sulphuryl chloride and sulphuric acid by means of
catalysers, and bases on this study a valuable technical method for
the preparation of sulphuryl chloride. In Ruff's opinion, no chlorine
or sulphur dioxide is formed at the boiling point, nor between 170° and
180°, but only at higher temperatures.

The Relation of Pyrosulphuryl Chloride and Chlorsulphonic Acid to
Each Other ; their Separation and Purification.

The simultaneous formation of pyrosulphuryl chloride and chlorsul-
phonic acid by the action of chlorides on a hydrated sulphur trioxide,
though noted by some observers, does not receive serious consideration
until taken up by Konovaloff, who showed that the dehydration of
chlorsulphonic acid by phosphorus pentoxide was only partial,*'' but

*' Quoted by R. Williamson (note 14, p. 676).

** Rer., 8, 1004 (1875).

" Ibid., 34, 3509 (1901).

" E. g., Besson (note 48, p. 682).

682 PROCEEDINGS OF THE AMERICAN ACADEMY.

was able to convert pyrosulphuryl chloride to chlorsulphonic acid by
addition of water. ^3 Heumann and Kochlin ^5 ^{^ not think that there
was any dehydration of chlorsulphonic acid by phosphorus pentoxide.

Billitz and Heumann *^ in 1883 heated chlorsulphonic acid (method
of preparation and properties not given) with nearly equal weight of
phosphorus pentoxide. The product, redistilled over phosphorus
pentoxide, boiled at 145-147° at 724 mm., and the analysis was close
to the theory for pyrosulphuryl chloride. The vapor density was
5.89, with evidence of decomposition. Clearly the dehydration was
only partial. Conversely, by adding 3 grams of water to 40 grams of
pyrosulphuryl chloride, the product boiled at 154-158° at 723 mm.,
reacted violently with water, and gave an analysis corresponding
more nearly to chlorsulphonic acid.

Besson *8 iu 1397 studied the purification of the two bodies, but the
method of preparation, vapor density, specific gravity, and analyses of
his crude products are not given. Crude pyrosulphuryl chloride con-
tained chlorsulphonic acid, chlorine, sulphur dioxide, and sulphur
trioxide, and could not be distilled at ordinary pressure without de-
composition into the last three. Mercury at low temperature removed
the free chlorine ; at 60° took the chlorine from the compound, setting
free sulphuf dioxide and trioxide. At 100° in a closed tube, sulphur
dioxide was the only gaseous product, mercuric sulphate and chloride
being formed! Most of these decomposition phenomena may of course
be ascribed to the chlorsulphonic acid present. By using phosphorus
pentachloride, Besson thought to remove the sulphur trioxide and to
dehydrate the chlorsulphonic acid in his crude pyrosulphuryl chloride,
but his product boiled at 142-143° (765 mm.). Apparently, distilla-
tion at 15 mm. gave what he considered pure products ; pyrosulphuryl
chloride boiling at 53°, chlorsulphonic acid at 65°. The former gave
white crystals at — 39° ; the latter did not solidify at — 75°. The boil-
ing point of chlorsulphonic acid at 765 mm. was 152°. Besson could
not cause sulphuryl chloride and sulphur trioxide to unite either in
sunlight or at 100°.

During the preparation of this pS,per, the completion of which has
been unavoidably delayed, Prandtl and Borinski *9 have proposed a
method for the preparation of pure pyrosulphuryl chloride which de-
pends on the destruction of the chlorsulphonic acid in the mixture
formed in the Schiitzenberger reaction. The method is considered by
them to obviate the necessity for use of anhydrous material and ex-

« Ber., 16, 483 (1883). *» Compt. rend., 124, 401 (1897).

« Zeitschr. anorg. Chem., 62, 24 (1909).

SANGER-RIEGEL. — PYROSULPH. CHLORIDE-CHLORSULPH. ACID. 683

elusion of moisture in carrying out the reaction, as recommended by
Konovaloff. It was clear to them, from the color reactions with tellu-
rium and selenium, as well as from analyses of the fractions, that the
two bodies were both present and could not be separated by fractiona-
tion. On the assumption that chlorsulphonic acid is more readily
attacked by water than pyrosulphuryl chloride, they treat the crude
distillate with ice in a freezing mixture. The lower layer of pyrosul-
phuryl chloride is separated from the upper of sulphuric acid, and dis-
tilled, with or without phosphorus pentoxide. Seventy per cent of the
crude pyrosulphuryl chloride was recovered, boiling at 150° (720 mm.).
The analysis gave almost theoretical figures, and the specific gravity
was 1.876 at 0° ; 1.844 at 18°. Vapor density determinations by the
Meyer method gave 7.15 and 7.27 (theory, 7.49). In making these,
the bulb of the apparatus was heated with phosphorus pentoxide before
adding the substance. Other trials, without this desiccation, gave
5.94 and 6.32.

Prandtl and Borinski find the action of tellurium and selenium use-
ful in distinguishing between the two bodies, Chlorsulphonic acid
gives with the first a cherry red color, with the second a dark green,
while pyrosulphuryl chloride gives no color with either. They consider
that pyrosulphuryl chloride is not converted to chlorsulphonic acid by
water, but directly to sulphuric and hydrochloric acids. Adding five
grams of water to sixty grams of pyrosulphuryl chloride (equal mole-
cules) they obtain sulphuric acid and a distillate boiling at 140-147°,
which they consider to be unaltered substance, since it dissolved in
water slowly and was not colored by tellurium.

Historical Summary.

The table on the follo^ving two pages shows briefly the results ob-
tained by former investigators:

The Results of this Investigation.

It is clear, from consideration of the foregoing and from our own
work, that the most reliable preparations of pyrosulphuryl chloride
were those of Konovaloft' and of Prandtl and Borinski, while Beck-
urts and Otto have described the only reasonably pure preparation of
chlorsulphonic acid. It is evident, also, that while either body, with
proper precautions, may be prepared without a large admixture of
the other, or of the decomposition products of either, yet it is some-
what doubtful whether an absolutely pure preparation of either has
been made, especially in large quantities. Further, the widely differ-

684

PROCEEDINGS OF THE AMERICAN ACADEMY.

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SANGER-RIEGEL. — PYROSULPH. CHLORmE-CHLORSULPH. ACID.

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686 PROCEEDINGS OF THE AMERICAN ACADEMY.

ing properties obtained by this long list of observers renders a revision
of the constants desirable.

In deciding upon the purity of the products too much reliance has
been placed by most investigators on the analysis. The difference be-
tween the two molecular weights, 233 and 215, is so small that even a
very careful analysis might not detect a sufficient admixture of one
body to influence the properties of the other (v. Table III, p. 713), nor
show contamination by a slight amount of the products into which
each body is easily decomposed.

In the separation and purification we have found most suggestive
the early statements of Rose concerning the action of fused sodic
chloride, the distillation under diminished pressure and the determi-
nation of the solidifying points as suggested by Besson. As a test of
purity we have paid little attention to the analysis, but have relied
upon the wide difference in melting points, the specific gravity, the
action with water, the characteristic appearance of the two bodies in
the solid state, and the color reactions with tellurium and selenium as
given by Prandtl and Borinski.

General Methods for the Preparation of Pyrosulphuryl Chloride
and Chlorsulphonic Acid.

The reaction of Schiitzenberger,!* in which sulphur trioxide is acted
upon by excess of carbon tetrachloride, is the one best adapted to the
preparation of pyrosulphuryl chloride, since the reaction runs more
nearly to completion, and excess of reagent is easily removed. While
the presence of chlorsulphonic acid has been suspected or shown by other
investigators in the crude product, yet it has not been definitely
pointed out that the hydration of the sulphur trioxide would deter-
mine the proportion of each body in the mixture, at least roughly, and
that by varying the strength of the sulphur trioxide a preponderance
of either body may be secured. This we have found to be true, and
we can therefore say, in general, that either pyrosulphuryl chloride
or chlorsulphonic acid may be made by the Schiitzenberger method.
The proportions of each body theoretically formed in the reaction by
using different concentrations of sulphur trioxide are given in the fol-
lowing table, though it will be shown that these proportions do not
hold good when the concentration of the sulphur trioxide is less than
89 per cent.

SANGER-RIEGEL. — PYROSULPH. CHLORIDE-CHLORSULPH. ACID.

687

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100 parts

give Chlorsul-
phonic Acid.

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a. Limit for formation of chlorsulphonic acid by the Schiitzenberger reaction:

2SO3 + 3H2O + CCL = 2H2SO4 + COCI2 + 2HC1
6. Limit for formation of chlorsulphonic acid by the Williamson reaction:

SO3 + H2O + HCl = H2SO4 + HCl
c. Limit for formation of pyrosulphurj^l chloride by the Schiitzenberger reaction:

2SO3 + H2O + CCI4 = 2SO3HCI + COCI2

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G88 PROCEEDINGS OF THE AMERICAN ACADEMY.

From the reaction

(1) 2S08 + CCI4 = COCI2 + S2O6CI2

we should have only pyrosulphuryl chloride when the sulphur trioxide
is absolutely anhydrous, as Konovalofif ^^ and others have shown. But
from the reaction

(2) 2SO3 + H2O + CCI4 = COCI2 + 2SO3HCI,
(Reaction c of Table II.)

the moisture conditions of which are fulfilled by ordinary fuming sul-
phuric acid, H2S2O7, we should theoretically get only chlorsulphonic
acid as the product. We may assume in this case that pyrosulphuryl
chloride would be at first formed according to (1) and then decom-
posed according to

(3) S2O5CI2 + H2O = 2SO3HCI.

If now we increase the hydration of the acid, we should expect the
chlorsulphonic acid to be decomposed according to

(4) 2SO3HCI + 2H2O = 2H2SO4 + 2HC1.

The limit of this decomposition is shown by combining equations (1),
(3), and (4):

(5) 2SO8 + 3H2O + CCl, = COCI2 + 2H2SO4 + 2HC1
(Keaction a of Table II.)

and we should expect no chlorsulphonic acid to be formed at a concen-
tration equivalent to 2S03"3H20.

With a weaker acid, however, the greater concentration of the water
causes a greater proportional decomposition of the chlorsulphonic acid
and a larger amount of sulphuric acid ; in other words, less sulphur
trioxide is effective in attacking the carbon tetrachloride. Hence, as
the proportion of water in the acid increases, there is less than the
theory of chlorsulphonic acid found, more sulphuric acid left, and the
limit of the formation of chlorsulphonic acid is reached sooner. The
maximum effect (Preparation 8, p. 696) appears to be at a concentra-
tion of between 22 and 23 per cent of water. From 100 parts of the
monohydrate, SO3H2O (18.37 per cent water) we should get about 22
parts of chlorsulphonic acid instead of 59.4 parts (Preparation 9)
as would appear from Table II. From 100 parts of the hydration
3S03'2H20 (13.04 per cent water), there would be about 52 parts of
chlorsulphonic acid instead of 105.5 parts (Preparation 7).

Now, as the concentration of the acid decreases to the hydration
2SO3 • H2O (10.11 per cent water) there is less and less tendency to de-

SANGER-RIEGEL. — PYROSULPH. CHLORIDE-CHLORSULPH. ACID. 689

composition of the chlorsulphonic acid, and the latter approaches
closely to its theoretical maximum at this point, as shown by Prepara-
tion 2, p. 695. This is indicated also in Preparations 1 and 2 by the
small amount of sulphuric acid left in the reaction.

In view of the fact that chlorsulphonic acid has a greater avidity
for water than pyrosulphuryl chloride (p. 714), reaction (3) may not
be entirely completed before its product is acted upon according
to reaction (4). Hence the limit of the formation of pyrosulphuryl
chloride may not be exactly at the hydration 2S08 • H2O (reaction c of
Table II), but at a somewhat greater concentration of water. This
is indicated by the yield of pyrosulphuryl chloride in Preparations 1
and 2, which is higher than would be expected. Conversely, the yield
of chlorsulphonic acid would be less at this concentration. The
amount of sulphuric acid would be greater, which is borne out also by
these preparations.

The hydration of the sulphur trioxide will similarly influence the
chlorination by sulphur monochloride according to the reactions : —

(1) 5SO3 + S2CI2 = 5SO2 + S2O5CI2

(2) 5SO3 + S2CI2 + H2O = 5SO2 + 2SO3HCI.

Here, while the reaction is complete, the boiling point of the sulphur
monochloride is so near to that of each of the two bodies as to make
purification by distillation practically impossible. With the chlorides
of phosphorus, the reactions not only do not run to completion, but
the purification of the product is complicated by the presence of phos-
phorus bodies. The use, therefore, of the chlorides of sulphur and
phosphorus is of no value, especially as carbon tetrachloride is now so
cheaply obtained.

We have found that the separation of the pjn-osulphuryl chloride
and chlorsulphonic acid formed in the Schiitzenberger reaction is com-
pletely accomplished by the addition of fused sodic chloride in excess
and subsequent distillation under diminished pressure. The pyrosul-
phuryl chloride is unaffected by the sodic chloride and is distilled off.
The chlorsulphonic acid is converted to its sodium salt, remains in the
distillation residue, and may even be regenerated from this by distilla-
tion with fuming sulphuric acid. The recovery is not advantageous,
however, owing to the difficulty of purifying the product. We have
also found that pyrosulphuryl chloride may be separated in a mixture
of the two bodies by crystallization. When the mixture is cooled and
centrifu gaily filtered below the melting point of p)a'Osulphuryl chloride
(ca.— 37°), a very pure product is obtained, — the chlorsulphonic acid,
with some pyrosulphuryl chloride, remaining entirely in the filtrate.

VOL. XLVII. — 44

690 PKOCEEDINGS OF THE AJIERICAN ACADEMY.

This method, however, is not practicable for any but small amounts,
and there is danger of contamination by the moisture of the air.

In the preparation of chlorsulphonic acid the best method is the
treatment of sulphur trioxide with hydrochloric acid, which must be
ascribed to A. Williamson, ^^ though first put in practical form by
Beckurts and Otto.*^ Most convenient is a liquid oleum containing
as much sulphur trioxide as possible according to the reaction :

H2SO4 + SO, + HCl = H3SO4 + SO3HCI.

No pyrosulphuryl chloride can be formed, and the product is made
practically pure by distillation with hydrochloric acid.

While chlorsulphonic acid may be formed under certain conditions
by the addition of water to pyrosulphuryl chloride, the reaction does
not serve as a method of preparation. Similarly, though dehydration
of chlorsulphonic acid by phosphorus pentoxide takes place, it is only
partial and hence of no advantage as a means of preparing pyrosul-
phuryl chloride.

The Preparation of Pyrosulphuryl Chloride.

The procedure adopted by us in treating sulphur trioxide with car-
bon tetrachloride according to the method of Scblitzenberger is as
follows : — A round-bottomed flask of suitable size is sealed to the
tube of an upright condenser, the upper end of the tube being carried
some distance above the jacket of the condenser. A few centimeters
below the top of the tube is sealed a side-tube of smaller bore, leading
to a flue. An absorption bottle for the phosgene may be used here if
desired. Through a rubber stopper in the top of the condenser tube
and leading below the side-tube passes a separating funnel.

The oleum is prepared from an ordinary fuming acid by the addition
of the requisite amount of solid sulphur trioxide, the proportion of the
last in the mixture being determined by titration. For analysis, the
oleum is weighed in a thin glass bulb, sealed after being filled. The
bulb is broken under considerable water in a tightly stoppered bottle,
the contents of which, when homogeneous, are made up to a definite
volume. The carbon tetrachloride is a crude commercial product,
dried over calcic chloride.

The dry apparatus is placed on a steam bath and carbon tetra-
chloride added through the condenser tube. The separating funnel
containing the oleum is placed in position. The flask is then heated
gradually and the oleum is run in slowly, the rate of addition being
governed by the evolution of phosgene. After the addition of the

SANGER-RIEGEL. — PYROSULPH. CHLORIDE-CHLORSULPH. ACID. 691

oleum, the heating is continued for some time after the evolution
stops. The proportion of carbon tetrachloride to oleum should be
about two to one.

As a partly solid oleum or " anhydrous " sulphur trioxide is less
easy to handle, we have preferred to use as strong a mixture as will
remain liquid at ordinary temperature,^® though the yield of pyrosul-
phuryl chloride is less. If one wishes to use- the stronger reagent,
however, the apparatus may be so modified that the top of the con-
denser tube is sealed and the* separating funnel containing the melted
trioxide is connected directly with the flask by means of a two-holed
rubber stopper, through the second hole of which passes the con-
denser tube instead of being sealed to the flask. Without this arrange-
ment the melted substance would solidify in passing through the
con denser. SI

The contents of the flask are transferred to a distilling flask and
fractioned ; the first portion, up to 120° or 130° containing a little
phosgene and excess of carbon tetrachloride, being rejected. The
second fraction, which may run to 160°, is best redistilled and that
portion boiling above 130° submitted to the following separation : —
The mixture is placed in a roomy distilling flask, cooled by ice, and
treated with small portions of fused, powdered sodic chloride, dried
before use by heating to ca. 150° and cooled in a closed bottle. The
amount necessary is calculated from the amount of water in the oleum
and hence the probable quantity of chlorsulphonic acid present. From
ten to twenty per cent in excess of that called, for by the following
equation is necessary.

SO3HCI + NaCl = SOsNaCl " + HCl.

When the evolution of hydrochloric acid has ceased, and this may be
promoted at the end by gentle warming, the pasty or partly dry mass
is distilled under about 20 or 30 mm. pressure. For this purpose we
extend the side-tube of the flask by sealing on a tube of about 50 cm.,
which is then surrounded by a short condenser jacket. Over the end
of the lengthened side-tube is slipped a distilling flask of suitable size,
fastened by a rubber stopper so that the end of the tube dips into the
belly of the flask. The side-tube of the receiver is connected with the
exhaust and manometer ; a system of absorption tubes filled with stick

60 From 92.5 to 95 per cent total SO3.
^^ See also Preparation 6, p. 696.

^* For the preparation and analysis of sodic chlorsulphonate, see Ruff
(note 45, p. 681).

692 PROCEEDINGS OF THE AMERICAN ACADEMY.

sodic hydroxide being interposed as a precaution against corrosion by
the acid vapors. The flask containing the reaction mixture is closed
by a rubber stopper carrying a thermometer, and is about three-
quarters immersed in an oil bath, the temperature of which is con-
trolled by a second thermometer. The suction is applied until the
hydrochloric acid is drawn off, and the oil bath is then gradually
heated. The pyrosulphuryl chloride in the mixture distils with little
or no decomposition, leaving the sodic chlorsulphonate as a dry mass.
The oil bath, as distillation slackens, is kept for some time at a some-
what higher temperature than the boiling point of the pyrosulphuryl
chloride, but a considerable amount of the latter adheres to the
residue.

The product thus obtained melts after solidification within a few de-
grees of the proper point, and a single rectification over a small quantity
of fused sodic chloride under diminished pressure is usually sufiicient to
give a perfectly pure product.

Regeneration of the Chlorsulphonic Acid. — We at first thought that
it would be practicable to recover from the sodium salt residue the
chlorsulphonic acid of the original reaction product, — even perhaps to
use the Schiitzenberger method for the preparation of both bodies by
employing an oleum of suitable strength. While by distillation of the
residue with excess of fuming sulphuric acid according to the equation

SOsNaCl + H2S2O7 = SO3HCI -f NaHSaO, "

the chlorsulphonic acid is indeed regenerated, it is in an impure state
and its purification is not worth while, since a pure product is so easily
obtained by the Williamson method.

The Properties of Pyrosulphuryl Chloride.

Pyrosulphuryl chloride is a colorless liquid, fuming slightly in moist
air and becoming turbid when added to a small amount of water. It
sinks in water as an oil, gradually decomposing into chlorsulphonic acid,
which in turn gives sulphuric and hydrochloric acids as final products.
Chlorine and probably sulphur dioxide may be formed in small amount.
It boils at 152.5° to 153° at 766 mm., and is not appreciably dissociated
at this temperature, if perfectly dry, but complete absence of moisture
is difficult to secure, as the substance is very hygroscopic. At a pres-

"' We do not assume the formation of such a salt, though it is supposed
to exist (e. g., Schultz-Sellac, Ber., 4, 109 (1871)). The reaction is, however,
more complete when the fuming sulphuric acid is in this proportion.

SANGER-RIEGEL. — PYROSULPH. CHLORIDE-CHLORSULPH. ACID. 693

sure of 19 mm., it boils at 56-57° without decomposition. It crystal-
lizes easily at low temperature and melts at —37.5° to —37°. The specific
gravity at 20°, referred to water at 4°, is 1.837 ; at 0° (water at 4°),
1.872. There is no appreciable dissociation at the boiling point of ani-
line. It is not colored by the addition of finely divided tellurium or
selenium.

For the properties of mixtures of pyrosulphuryl chloride and chlor-
sulphonic acid, see page 712 and Table III (page 713).

The Preparation of Chlorsulphonic Acid.

In carrying out the Williamson reaction

H2SO4 + SO3 + HCl = H2SO4 + SOsHCl,

the oleum should contain as much sulphur trioxide as possible. It is
placed in a roomy distilling flask, closed by a three-holed rubber stopper
and mounted on a tripod. Through one hole of the stopper passes a right-
angle tube slightly constricted at its lower end, extending to the bottom
of the flask. Through the second hole is attached a distilling tube in
one piece, surrounded by a condenser jacket, and the third hole carries
a thermometer.

The hydrochloric acid gas is conveniently generated by slowly adding
crude, concentrated sulphuric acid from a dropping funnel to crude con-
centrated hydrochloric acid contained in a generating flask. The gas is
carefully dried by passing at least two Emmerling towers containing
glass beads saturated with concentrated sulphuric acid, and a (J-tube
with phosphorus pentoxide. The gas is passed through the oleum
slowly, at room temperature, until there is no further evidence of ab-
sorption, the flask and condenser being inclined so that any condensed
vapor may run back. At the end, the contents of the flask are distilled
in a current of dry hydrochloric acid gas, the portions distilling below
145° and above 160° being rejected. A rectification of the middle
portion in hydrochloric acid results in a product of sufficient purity for
all purposes for which the substance may ordinarily be required, but an
absolutely pure product is obtained only by crystallization at low tem-
perature, as will be shown in the Experimental Part.

The Properties of Chlorsulphonic Acid.

Chlorsulphonic acid is a colorless liquid which fumes very strongly in
moist air. If added to water, it reacts with explosive violence, and is
immediately decomposed into hydrochloric and sulphuric acids. Chlo-
rine and sulphur dioxide are also formed in small amount. It cannot

694 PROCEEDINGS OF THE AMERICAN ACADEMY.

be boiled without partial dissociation, but, when equilibrium sets in, the
boiling point is about 151-152° at 765 mm. The slight dissociation is
partly into hydrochloric acid and sulphur trioxide (which react partially
to form water, sulphur dioxide, and chlorine); partly to sulphuryl chloride
and sulphuric acid. The latter dissociation may be brought about at
the boiling point by a catalyser. At a pressure of 19 mm. it boils at
74-75°, but the dissociation into hydrochloric acid and sulphur trioxide
is increased ; still more at from 2 to 4 mm., the boiling point being then
approximately 60-64°. At the boiling point of aniline, the dissociation,
though not complete, amounts to about two volumes. It crystallizes
readily at low temperature and melts at —81° to —80°. The crude acid
requires a lower temperature for solidification, changing into a vitreous
body, which becomes viscous at about —130° to 125° and sometimes partly
crystalline. The specific gravity at 20°, referred to water at 4°, is 1.753 ;
at 0° (water at 4°), 1.784. With finely divided tellurium, chlorsulphonic
acid gives a cherry-red color, which persists for several hours, fading
gradually to purple, then pink, and becoming finally colorless. With
finely divided selenium, it gives a moss green color, which gradually
becomes a fainter green, then yellow, and finally colorless.

For the properties of mixtures of chlorsulphonic acid and pyrosul-
phuryl chloride, see page 712 and Table III (page 713).

Experimental.
Preparations of Pyrosulphuryl Chloride.

1. 105 g. oleum (90 per cent SO3) were added to 110 g. CCU (10
per cent over theory) in an hour. 22 g. distillate were obtained up to
130°; 83 g. from 130° to 155° (chiefly 150-152°), and the residue was
less than 2 g. The main fraction melted at —128° and was chiefly
chlorsulphonic acid. This was treated with 50 g. fused sodic chloride
and distilled, a U-tube *** in liquid air being placed after the receiver.
9 g. distillate were obtained from 53° to 60° (26 mm.); the U-tube con-
tained a little hydrochloric acid. The melting point of the distillate,
—39°, showed a fairly pure pyrosulphuryl chloride. The dry residue
was treated with 125 g. oleum (91 per cent SO3) and distilled, a bottle
cooled by ice and salt being placed before the U-tube in liquid air. At
78-87° (23 mm.) 46 g. of distillate were obtained, melting at —128-125°,
s. g. 1.767 at 20°. In the cooled bottle was a little sulphur trioxide,
in the U-tube a little hydrochloric acid.

The yield of chlorsulphonic acid is low owing to insufficient carbon

" Figure 1, p. 697.

SANGER-RIEGEL. — PYEOSULPH. CHLORIDE-CHLORSULPH. ACID. 695

tetrachloride, for much of this reagent escapes with the phosgene. The
pyrosulphuryl chloride is high, but it is clear that both bodies are formed
in the reaction and that chlorsulphonic acid is the chief product.

2. 116 g. oleum (90 per cent) were added to 225 g. CCI4 (over twice
the theory) in 45 minutes, and the mixture fractioned after standing
over night. From 65° to 130°, 112 g. were obtained ; from 145° to 153°,
137 g., melting at —128°. There was little residue. The 137 g., treated
with 81 g. salt (120 per cent theory) gave 14 g. distillate at 56-57°
(23 mm.) melting at —37-36°. The residue was not examined. The
yield of crude mixture, 91 per cent, has been improved by excess of
carbon tetrachloride, and it is again shown that only a small amount of
pyrosulphuryl chloride is formed from a low oleum.

3. 108 g. melted SOs (98.9 per cent) were added to 220 g. CCI4 in
45 minutes and fractioned after 48 hours. 165 g. were obtained up to
130° ; 106 g. from 139° to 141°, and there was little residue. By re-
distilling the first fraction, a little more was added to the second, giving
110 g., boiling mainly at 140°, melting at —41-40°. This treated
with salt and distilled gave 84 g. at 60° to 62° (25 mm.), melting at
—38-35°. The residue was not examined. The yield of crude pyro-
sulphuryl chloride, 84 g., is about 70 per cent of the theory.

4. 175 g. oleum ^93.4 per cent) were added to 347 g. CCI4 in 90
minutes, the product standing over night. 176 g. were obtained up to
130° ; 189 g. between 130° and 152°, and the residue was slight. The
main fraction melted chiefly at —90°, but there was a residual solid not
melting until —45-40°. 103 g. of the main fraction, with 50 g. salt
(150 per cent theory) gave 39 g. distillate at 50-55° (21 mm.), melting
at— 43-38°. The distillation was continued up to 80° (bath, 150°),
which evidently caused decomposition, as there was much hydrochloric
acid in the U-tube, a little chlorine, and, from its melting point, con-
siderable sulphuryl chloride. The residue from the salt treatment was
distilled with 130 g. oleum (89.3 per cent), slightly in excess of the
theory. At 70-76° (21 mm.), most of the product, 64 g., came over,
but the heating was continued to 87° (bath, 153°). The U-tube con-
tained hydrochloric acid, chlorine, and sulphuryl chloride. On redistil-
lation, 56 g. were obtained at 75-78° (23 mm.), melting at —133-127°.
Considerable sulphuric acid was left in the flask, and in the U-tube
was some sulphuryl chloride. The yield of crude mixture, 189 g., is
about 75 per cent of the theory. The proportions of the two bodies,
39 g. and 56 g., are in the direction of those which should have been
recovered from 103 g. of crude mixture, —36 g. and 67 g. The decom-
position of the chlorsulphonic acid was in accord with the observations
of other workers and with those made later by ourselves.

696 PROCEEDINGS OF THE AMERICAN ACADEMY.

5. 445 g. oleum (93.2 per cent) were added to 496 g. CCI4 (138 per
cent) in two hours, and the product stood over night. 131 g. were
obtained up to 135° ; 497 g. from 135° to 150°, little being left in the
flask. A second fractionation increased the fraction from 135° tol51° to
534 g., melting at —120-1 15°, but redistillation gave 474 g. from 134° to
154°. This is 81 per cent of the theory. 134 g. of the product, with
65 g. salt (50 per cent excess) gave 31 g. boiling at 40-49° (19-23 mm.)
and melting at —37°. The sodium salt, with fuming acid, gave 65 g.
crude chlorsulphonic acid boiling at 80-85° (25 mm.). According to
Table III we should expect 45 g. and 89 g. respectively.

6. 300 g. melted SO3 (98.9 per cent) were covered with 572 g. CCI4
in a one-liter flask provided with a long condenser and placed on a
sand bath. There was but slight action in the cold ; on gentle heating
for two hours the reaction was complete. After distilling off the excess
of CCI4, very little came over up to 135° ; nearly all distilled from 135°
to 141°. Yield 345 g. or 85 per cent. On treatment with 50 g. salt,
there was little evolution of hydrochloric acid, and, on distillation at
atmospheric pressure, most of the product came over at 149°. Re-
distillation at 76° (74 mm.) with a second quantity of salt gave a very
pure product, melting at —37° (corr.). This is Sample C, page 699.

7. 150 g. sulphuric acid (85.9 per cent SO3) were added to 300 g.
CCI4 and heated for 10 hours. The product was homogeneous. On
distillation, 40 g. were obtained up to 120° and 74 g. from 120° to 158°,
which, from its appearance and action with selenium and tellurium,
was chiefly chlorsulphonic acid. The residue, 100 g., was sulphuric
acid.

8. 150 g. sulphuric acid (77.0 per cent SO3) were added to 300 g.
CCI4 and heated for 10 hours. There was no evidence of phosgene
during the heating and the product separated into two layers. 279 g.
CCI4 were recovered, with faint odor of phosgene. The fraction from
90° to 140° weighed 5 g. ; that from 140° to 160°, 3 g., and neither gave
any test for chlorsulphonic acid. The residue, sulphuric acid, weighed
141 g.

9. 100 g. sulphuric acid (82.0 per cent SO3) were heated with 200 g.
CCI4 for 5 hours. Phosgene was given off" and the product was homo-
geneous. After distilling off excess of CCI4, a fraction of 2.5 g. was
obtained from 150° to 153°; a second, of 22.5 g., from 153° to 160°.
Both were evidently chlorsulphonic acid, from appearance and tests.
The residue, sulphuric acid, weighed 80 g.

It is clear that the two bodies are formed practically in proportion
to the hydration of the oleum used, provided the concentration of the
sulphur trioxide is at least 89 per cent. Below this percentage no

SANGER-EIEGEL. — PYROSULPH. CHLORIDE-CHLORSULPH. ACID, C97

pyrosulphuryl chloride results, and the yield of chlorsulphonic acid is
rapidly diminished by the increasing proportion of water. The eco-
nomic preparation of pyrosulphuryl chloride demands an oleum contain-
ing at least 95 per cent of sulphur trioxide and a large excess of carbon
tetrachloride.

The purification of the products of some of these preparations is
given in the following.

Purification of Pyrosulphuryl Chloride and Determination of

Constants.

Boiling Point. — 106 g. of crude substance from Preparation 5
were twice distilled over salt, and 70 g. were obtained boiling at 55-57°
(18 mm.), with melting point of —38-35° (corr.).
This product was then distilled into a 3 -way ' ^

Bredt ^^ receiver, the arms of which carried (i) a
small distilling flask, (2) a Y-tube in which
samples could be sealed off for analysis, melting
point, and vapor density, and (3) a flask adapted
to the arm of the pyknometer in which the spe-
cific gravity was to be determined. The entire
distillate came over at 56-57° (19 mm.) Sam-
ple A.

15 g. of the above were distilled from an oil
bath in the flask in which they were collected.
The thread of the corrected thermometer was
entirely in the vapor. A U-tube ^® in liquid air
connected with the receiver. Distillation

was

began at 142°, the thermometer rose rapidly, and
all came over mainly at 152-153° (766.6 mm., Figure 1.

corr.). The U-tube contained some barely visible
white specks, melting at room temperature with odor of sulphur diox-
ide. 50 g. of the original distillate, some of which had been open to
the air, were also distilled. While the boiling point was again chiefly
from 152° to 153°, it was not perfectly constant, and there was more

^'^ Anschlitz, d. Destination unter vermindertem Druck, 1895.

"^ Tiiese U-tubes, the construction of which is clear from Figure 1, are
readily made from pieces of wide and narrow tubing to fit the Dewar liquid
air container. The position of the side-tube prevents its being clogged by
solids. By rapid work weighings can be made within half a gram; condensed
gases are evaporated at room temperature, hquids may be poured off, and a
residual solid weighed in its turn. Very satisfactory approximations may
be made in this way.

698

PROCEEDINGS OF THE AMERICAN ACADEMY,

evidence of decomposition in the form of unweighable white and yellow
specks from which a test for chlorine was obtained.

The 84 g. from Preparation 3 were then distilled with 20 g. salt at
low pressure, with special precautions against access of moisture, as
provided by the apparatus shown in Figure 2. Dry air was passed

through the system for 2l
hours and the glass was
gently warmed. The inlet
tube at A was then sealed
off, the system exhausted,
and the liquid distilled from
F to F'. After about 60 g.
had come over at 63-68°
(25 mm.), with some evi-
dence of decomposition pro-
ducts in the U-tube, the
heating was discontinued
and the tube sealed off at B.
The 60 g. were then distilled
at 766 mm., corr,, a well-
dried flask and another
U-tube in liquid air being
added at C, The first few
drops came over at 148-
150°, and all the remainder
from 152.5° to 153°. There
were only faint specks in
the U-tube. Sample B.
From these two results the boiling point of pyrosulphuryl chloride
may be placed at 152.5° to 153° at 766 mm. There is probably a ten-
dency to slight decomposition at the boiling point, since the absolute
exclusion of moisture from such a substance is well nigh impossible.

Specific Gravity. — The specific gravity of Sample A was taken by
means of a carefully calibrated Ostwald pyknometer from a portion
sealed until use.

Figure 2.

1. At 20°, 14.0408 g. substance occupied the same volume as 7.6333

g. water. S. g. 20^ 1.8352

4°

2. At 20°, 14.0401 g. substance occupied the same volume as 7.6333

g. water. S. g. 20^ 1.8351

4°

SANGEK-RIEGEL. — PTEOSULPH. CHLORIDE-CHLORSULPH. ACID. G99

From Sample B, the following figures were obtained :

3. At 20°, 14.0425 g. substance occupied the same volume as 7.6333

g. water. S. g. 20° 1.8354

4°

4. At 20°, 14.0508 g. substance occupied the same volume as 7.6333

g. water. S. g. 20^ 1.8365

4°

The specific gravity of Sample C (Preparation 6) after taking a melt-
ing point determination, was 1.8364 at 20°, referred to water at 4°.
It was again distilled with salt under diminished pressure. Of this
product,

5. At 20°, 14.0538 g. substance occupied the same volume as 7.6333

g. water. S. g. 20^ 1.8369

4°

6. At 20°, 14.0525 g. substance occupied the same volume as 7.6333

g. water. S. g. 20^ 1.8367

4°

7. At 0°, 14.3292 g. substance occupied the same volume as 7.6423

g. water. S. g. 0^ 1.8718

4°

8. At 0°, 14.3277 g. substance occupied the same volume as 7.6423

g. water. S. g. 0^ 1.8716

4°

(The data above are corrected in order to give the figures for specific
gravity: weights of water to 4°, all weights to vacuum.)

The specific gravity of pyrosulphuryl chloride at 20°, referred to
4°, is therefore 1.837 ; at 0°, referred to water at 4°, 1.872.

Melting Point. — The determination of this constant, which plays a
very important part in the purification of pyrosulphuryl chloride and
chlorsulphonic acid and their differentiation, was made in two ways.
The first method, particularly available for small quantities of substance,
is analogous to that so commonly employed in the determination of
the melting point of organic substances, in which the material is placed
in a thin-walled " capillary " tube, closed at one end. This we shall
refer to as the "capillary method." In the second, which we shall call
the "immersion method," the thermometer is placed in a test tube
containing a comparatively large (Quantity of (substance, so that the en-
tire thread may be covered by the substance when melted.

A Rothe ^^ thermometer filled with pentane was used, 35 cm. long,
graduated from 30° to —200° in whole degrees. As this was grad-

"' Zeitschr. f. Instrumentcnkunde, 24, 5 (1904).

700 PROCEEDINGS OF THE AMERICAN ACADEMY.

uated for complete immersion and in the capillary method most of the
stem would be outside the bath, the reading was several degrees too
high. For this method, therefore, the standardization of the instrument
was based upon a definite depth of bulb immersion, the substance being
always level with the bulb. As fixed points there were taken, at sev-
eral room temperatures, the boiling point of oxygen (—182.8°), the
sublimation point of a thin, homogeneous mixture of carbon dioxide
and absolute alcohol (—78.3°), and the melting point of pure mercury
(_39°)_58 ^fhe corrections thus determined were well suited for tem-
peratures between —100° and —50°, but in the region of —28°, the
uncorrected melting point of pyrosulphuryl chloride, the variation for
a degree in the stem temperature (determined by a mercury thermom-
eter alongside) was considerable. To avoid troublesome corrections at
this point, the melting point of pure mercury was taken in the same
manner and at the same time as that of the sample. As the melting
points of mercury and pyrosulphuryl chloride differ by only two de-
grees, the correction could fairly be assumed to be the same for each.
In the immersion method, the fixed points were the boiling point of
oxygen, the sublimation point of the carbon dioxide-alcohol mixture,
and the temperature of melting ice ; corrections being made from a
curve plotted from these.

The bath used was a naphtha, liquid and mobile at —150°, contained
in a small beaker, which in turn was immersed in a beaker of liquid
air. The inner beaker was covered by a stout filter paper, fastened
under the rim in order to prevent the naphtha from becoming opaiiue
through condensation of moisture and carbon dioxide. The filter paper
was provided with suitable holes for the thermometer, concentric
stirrer, etc.

The liquid to be tested is introduced into the capillary tube by
warming and cooling the latter ; sometimes the powdered frozen liquid
can be added in the ordinary way. In either of the two methods, ca-
pillary or immersion, the tubes are placed in the bath and the liquid in
them solidified under stirring of the bath. The liquid air beaker is
then lowered and the temperature of the bath allowed to rise as slowly
as possible, under careful stirring. This retardation, which may be
accomplished by the approximation of the liquid air, is necessary, as
otherwise the bath may rise several degrees in one minute and a fusion
may take place between too great extremes. The rising thread is al-
ways read, and care is taken to see that it is unbroken, a frequent
danger in these instruments.

«>8 Constants from Ostwald-Luther, Hand- und Hiilfsbuch, 1910.

SANGER-RIEGEL. — PYROSULPH. CHLORIDE-CHLORSULPH. ACID. 701

Two portions of Sample A, the second having remained sealed until
used, gave respectively— 38° to— 37° and — 37.5°to —37°, by thecapillary
method. Of Sample B a portion melted from —37° to —34.5° by the
immersion method. Further precautions in using this method were
taken in the examination of Sample C. The tube containing the sub-
stance was provided with a two-holed rubber stopper, through one hole
of which passed the thermometer. The other hole carried a T-tube,
through the vertical portion of which moved the stirrer. Into the side
arm was passed a gentle current of dry air, to prevent access of mois-
ture to the substance. The melting tube was immersed in a bath of
alcohol at a temperature two to four degrees higher than that of the
substance. Four determinations with Sample C gave an average of
-37.3°.

The melting point of pyrosulphuryl chloride may be placed, there-
fore, at -37.5° to -37°.

Vapor Density. — The determinations of vapor density were made
by the Victor Meyer method at the temperature of boiling aniline
(184°). The weighing bulbs and the apparatus were very carefully
dried and the eudiometer calibrated. Readings of the volume of air re-
placed were not made until the meniscus had long remained constant.
The following results were obtained :

Substance. £-^1^^^ T°.

1. Sample A 0.0480 g. 5.72 21

2. Sample A 0.2102 g. 27.53 23

3. Sample A 0.0625 g. 6.90 23.3

4. Sample C 0.1382 g. 16.95 26.5

5. Sample C 0.2501 g. 28.90 27.5

Calculated for S2O5CI2

These determinations show that pyrosulphuryl chloride does not dis-
sociate appreciably at a temperature of 184°, and it is less likely to do
so at its boiling point. The presence of traces of moisture, which are
not easy to guard against, would lower the vapor density slightly. In
this connection, the addition of phosphorus pentoxide to the bulb of
the Meyer apparatus by Prandtl and Borinski *3 is not admissible in
the presence of a possible impurity of chlorsulphonic acid, which
would thereby be dehydrated.

Analysis. — A volumetric analysis was made of Sample 3. 1.1657
g. substance were prepared for titration as in the analysis of oleum,
p. 690.

Bar.
Corr.

Vapor
Density.

739.8

7.2

742.6

6.6

1 736.8

7.8

744.6

7.1

742.6

7.5

. • . .

. 7.49

702 PROCEEDINGS OF THE AMERICAN ACADEMY.

1. 100 c.c. (1/5) of the solution required 35.88 c.c. KOH (0.9078 N/5)

2. " " " 35.88 CO. KOH (0.9078 N/5)

3. " " " 21.74 c.c. AgNOa (N/1; Volhard)

4. " " " 21.69 c.c. AgNOs (N/1; Volhard)

A gravimetric analysis of Sample C resulted as follows:

5. 0.9400 g. substance gave 2.0352 g. BaS04

6. 1.0806 " " 2.3009 g. BaS04

7. 1.1917 " " 1.5891 g. AgCl

8. 1.1813 " " 1.5751 g. AgCl

Found. gif^^^

Sulphur: (1) 29.93, (2) 29.93, (5) 29.75, (6) 29.80 29'.82

Chlorine: (3) 33.14, (4) 33.07, (7) 32.99, (8) 32.99 32.98

Preparations of Chlorsulphonic Acid.

10. Dry hydrochloric acid gas was passed into 150 g. oleum (91.1
per cent) for two hours, the flask being kept cool by ice water. After
expulsion of the hydrochloric acid, distillation between 149° and 170°
(chiefly 152-155°) yielded 101 g. (theory, 113 g.), and the residue,
which was practically all sulphuric acid, weighed 72 g. (theory, 73 g.).
On treating the 101 g. with 60 g. salt and distillation under diminished
pressure, only 1.5 g. were obtained, which, from melting point and action
with water, appeared to be unchanged chlorsulphonic acid.

11. 165 g. oleum (89.3 per cent) were used. The flask was not
cooled. The yield of distillate between 135° and 164° was 89 g. (theory,
100 g.), and the residue was 97 g. (theory, 96 g.).

12. 147 g. oleum (89.3 per cent) were treated as in Preparation 11.
The product was then distilled in a current of hydrochloric acid, and
88 g. (theory, 89 g.) were obtained from 148° to 151°, the residue
weighing 82 g. (theory, 86 g.).

13. 526 g. oleum (93.9 per cent) were saturated with hydrochloric
acid as in Preparation 11. Of the total increase in volume, two thirds
resulted from passing the gas rapidly for two hours, one third in an
additional five hours. On distilling in hydrochloric acid, 528 g. were
obtained, boiling chiefly from 150° to 154° (theory, 512 g.).

14. The oleum contained 86.2 per cent SO3. The method was as
in Preparation 11, but weights were not recorded.

15. 419 g. oleum (88 per cent) were used ; the method was as in
Preparation 11. 261 g. product were obtained, the distillation with
hydrochloric acid being very slow (theory, 212 g.).

16. 333 g. oleum (85.3 per cent) were heated on the steam bath and

SANGER-EIEGEL. — PYROSULPH. CHLORIDE-CHLORSULPH. ACID, 703

hydrochloric acid passed for seven hours. The product, distilled with
hydrochloric acid, gave 107 g. distillate under 162° (theory, 97 g.).

17. 550 g. oleum (89.3 per cent), treated asiu Preparation 16, gave
on distillation with hydrochloric acid, 375 g., boiling mainly from 149°
to 151° (theory, 333 g.).

The amount of chlorsulphonic acid formed in the Williamson reaction
depends upon the percentage of sulphur trioxide in the oleum not com-
bined as sulphuric acid. The sulphuric acid is unchanged. No pyro-
sulphuryl chloride is formed. Attempts to increase the yield from a
low oleum by addition of phosphorus pentoxide during the chlorina-
tion, according to Muller,^^ were unsatisfactory. While the total
weight of product was somewhat increased, yet it was probable that
some pyrosulphuryl chloride was formed by the dehydration of the
chlorsulphonic acid by phosphorus pentoxide.

The reaction mixture is best distilled in a current of hydrochloric
acid. As will later be shown, the chlorsulphonic acid thus obtained is
fairly pure and is made no purer by distillation, owing to the partial
dissociation at the boiling point. A pure product is obtained only by
crystallization, as will be shown.

Purification of Chlorsulphonic Acid and Determination of Constants.

The instability of chlorsulphonic acid under heating was to be in-
ferred from the work of other observers, but we hoped to be able to
purify it by distillation at reduced pressure, and proceeded for some
time under that assumption. It became evident, however, that all our
efforts to get a pure product by distillation, whether at normal or re-
duced pressure, were nullified by the invariable presence of decomposi-
tion products, and that the decomposition was relatively complex.
While the subject requires further investigation, we may state here,
however, the facts concerning the dissociation which appear most prob-
able from our work and that of others.

The Dissociation of Chlorsulphonic Acid. — Under ordinary condi-
tions of temperature and pressure, and in absence of moisture, chlor-
sulphonic acid is stable. If, however, it is subjected to diminished
pressure or to increased temperature, or to a combination of the two,
a partial breaking down occurs, which is proportional to the change of
conditions. We regard this breaking down, from our own observations
and those of others, as taking place primarily in two directions, which
we may represent as follows:

(1) 2SO2OHCI T^ 2SO3 + 2HCI

and (2) 2SO2OHCI = SOaClj + S02(OH)2.

704 PROCEEDINGS OF THE AMERICAN ACADEMY.

Following the analogy of the reduction of sulphuric acid hy nascent
hydriodic and hydrobromic acids, the products of reaction (1) are
more or less changed according to

(3) 2SO3 + 2HCI = SO2 + CI2 + S02(OH)2,

while the products of reaction (2) become, to a greater or less extent,

(4) SO2CI2 + S02(OH)2 = SO2 + CI2 + S02(OH)2 ;
hence the ultimate observed dissociation would be represented by

(5) 2SO2OHCI = SO2 + CI2 + SO3 + H2O,

the same result being reached in whichever direction the breakdown
primarily started.

Under diminished pressure, at temperatures from 60° to 80°, we have
found reaction (1) to take place, and in proportion to the decrease of
pressure. The greater dissociation at the lower pressure is due, ac-
cording to the principle of Le Chatelier, to the fact that the vapor
increases in volume, and, indeed, the effect of a pressure as low as 1 to
4 mm. is to pump out the more volatile hydrochloric acid, hence that
portion of the distillate which is condensed by liquid air (Figure 2)
contains relatively much more hydrochloric acid than sulphur trioxide.^^
As we have found also sulphuryl chloride, sulphur dioxide, and chlorine
among the products of distillation under diminished pressure, with a
residue of sulphuric acid, we consider that reaction (2) occurs to a
slight extent, and also reaction (3), though to a less degree than at
higher temperatures.

At atmospheric pressure and at the boiling point, reaction (1) takes
place, as Williams ^^ and Ruff *^ have stated. But, while the primary
action is less than at low pressure, the secondary action (3) is greater,
and we find more sulphur dioxide and chlorine, with a larger residue
of sulphuric acid, than under lower conditions of temperature and
pressure. The presence of sulphuric acid, however, is partly accounted
for by reaction (2), for we find sulphuryl chloride among the products
of distillation at ordinary pressure, and, indeed, in greater quantity
than when the pressure is low. That sulphuryl chloride is formed
under these conditions was not recognized by Ruff, but he showed
clearly that the presence of a catalyser brings about reaction (2) at the

^^ The presence of sulphur trioxide in chlorsulphonic acid distilled at this
pressure was indicated by the analysis and specific gravity of the product, and
was confirmed qualitatively and quantitatively on careful fractionation of the
product at ordinary pressure.

SANGER-RIEGEL. — PYROSULPH. CHLORIDE-CHLORSULPH. ACID. 705

boiling point, and, indeed, not only to the apparent exclusion of (1)
and (3), but to the completion of (2).

In addition to the phenomena of dissociation as expressed by the
above reactions, we have found that the sulphur trioxide formed by
the dissociation dehydrates the chlorsulphonic acid to a slight extent,
giving pyrosulphuryl chloride.®®

(6) 2SO2OHCI + SO3 ^ S2O5CI2 + S02(OH)2.

As to the character of the dissociation at temperatures above the
boiling point, we can ourselves offer no direct evidence. Behrend **
obtained a good yield of sulphuryl chloride by heating in a closed tube
at 170° to 180°, and considered that reaction (2) took place. Beckurts
and Otto *^ explain the reaction by the equations

(7) 2SO2OHCI = CI2 + H2S2O6,

(8) H2S2O6 = SO2 + S02(OH)2,
(9)_Cl2 + SO2 = SO2CI2.

Since they found chlorine and sulphur dioxide in the closed tube at
180°, reaction (9) would not be complete. But Ruff found the equilib-
rium at 170° in a closed tube to be

(2) 2SO2OHCI ^ SO2CI2 + S02(OH)2
2.5 mol. 1 mol. 1 mol.

and lowered the temperature of complete decomposition to the boiling
point by the catalyser. As in the presence of the catalyser Ruff found
that no more sulphuryl chloride was formed by passing chlorine and
sulphur dioxide into the boiling chlorsulphonic acid than without
them, they were not essential to the formation of sulphuryl chloride,
and reaction (9) evidently did not take place. It is also unnecessary
to assume reactions (7) and (8) to explain the formation of sulphur
dioxide and chlorine.

Ruff considered that at temperatures higher than 180° reactions
(1) and (3) took place; Heumann and Kochlin^s that chlorsulphonic
acid was completely dissociated at 442°, according to reaction (5), but
at 184° they found the dissociation incomplete.

That sulphuryl chloride, chlorine and sulphur dioxide are coexistent
products of the dissociation at temperatures short of that necessary for

*" For the hydration of pyrosulphuryl chloride by sulphuric acid, v. p. 717.
VOL. XLVII. — 45.

706 PROCEEDINGS OF THE AMERICAN ACADEMY.

complete dissociation is undoubted. Whether we shall ascribe the for-
mation of the last two of these bodies to reactions (1) and (3) or to
reactions (2) and (4) is immaterial. But it is not unreasonable to
suppose that reaction (1), which at diminished pressure and compara-
tively low temperature is predominant over reaction (2), becomes not
only secondary to reaction (-2) at atmospheric pressure and higher
temperature, but also that, at the highest temperatures noted, it
would merge into reaction (5).

Whatever may be the mechanism of this rather complex dissociation,
it is certain that distillation of chlorsulphonic acid at any pressure will
result in a product which may contain, in varying amounts, sulphuryl
chloride, chlorine, sulphur dioxide, sulphur trioxide, hydrochloric acid,
and sulphuric acid. The disagreeing results of previous observers on
the constants of chlorsulphonic acid are therefore easily explained,
for their products, though often of sufficiently good quality for practi-
cal purposes, were contaminated by more or less of these dissocia-
tion products, and hence showed varying boiling points, specific
gravities, etc.

By distillation with hydrochloric acid, reaction (1) obviously runs to
the left, and there should be little tendency to dissociation. Ordinary
distillation, at atmospheric or low pressure, will not purify. After
realization of this fact, we turned to crystallization, as will be shown.

Behavior of Chlorsulphonic Acid under Distillation. — In Prepara-
tions 10 and 11 above, in which the distillation was without hydro-
chloric acid, the product is contaminated by the products of dissociation,
and the apparent yield is less. In the others, there is a greater or less
amount of hydrochloric acid present and probably less of the dissocia-
tion products.

The crude preparations of chlorsulphonic acid showed a very charac-
teristic behavior on cooling. At —70° to —80°, the liquid becomes
thicker and gradually viscous as the temperature falls. At —130° to
—140° an amorphous, vitreous mass is formed, which under rising
temperature becomes gradually viscous again from —140° to —120°,
averaging, say, at —130°, and is limpid at about —85°. This behavior
differentiates the substance sharply from pyrosulphuryl chloride, which
gave definite crystals at —40° to —35°, and at —70° to —60° even when
containing 90 per cent of chlorsulphonic acid. But, while the differen-
tiation was clear, the melting evidently indicated impure chlorsul-
phonic acid.

Preparation 11 became viscous at —133-127°. At 24-27 mm. it
boiled chiefly at 80-82°, and the solidified product softened at —125-
117°. The specific gravity was 1.786 at 20°. To avoid the presence

SANGER-RIEGEL. — PYROSULPH. CHLORIDE-CHLORSULPH. ACID. 707

of sulphuric acid, which was suggested by the specific gravity and boil-
ing point of Preparation 11, the subsequent preparations were distilled
with hydrochloric acid, as described above.

Preparation 12 boiled from 147° to 151°, became viscous at —138-
130°, and had a specific gravity of 1.745 at 20°. Distilled at low pres-
sure, it boiled from 77° to 81° (24-31 mm.), softened at —130-125°,
with specific gravity of 1.765. Three more distillations at low pressure
did not essentially change these properties, and the preparation was
evidently as pure as this treatment was likely to make it. 29 grams
boiled at 145-150.5° for the first half; 150.5-152° (762 mm.) for the
second. The presence of white fumes of sulphur trioxide towards the
end emphasized the decomposition, and about half a gram of residue
was left, which was mainly sulphuric acid. A vapor density determi-
nation in aniline (184°) gave 2.6 and 2.4 (theory, 4.04). A volumetric
analysis gave : chlorine, 30.00 ; sulphur, 28.02 (required, 30.43 and
27.52).

We did not study the decomposition in the course of these distilla-
tions by means of the liquid air tube (Figure 1) as in the subsequent
trials. The product was probably more impure than would appear
from the properties, for the impurities compensated each other to a
certain extent. But the specific gravity and decomposition pointed to
the presence of sulphur trioxide at least.

The study of the portion of Preparation 1 (46 g.), which had been
recovered from its sodium salt, is now of interest. This was viscous at
—128-125°, with specific gravity of 1.767 at 20°, and boiled at 78-
87° (23 mm.). On distillation at atmospheric pressure, a few drops
came over at 148-149°, but the greater part at 151-152°. There
was some decomposition and a few drops of sulphuric acid were left.
On distilling again, one fifth came over from 147° to 149°, the rest
chiefly at 150-152°. A third distillation increased the amount from
146° to 150° to one half, the rest mainly from 150° to 153°. Little resi-
due was left in the last two cases. The product now became viscous
at —136-127°, but at —85° crystals appeared, which melted at —69°.
The specific gravity was 1.755 at 20°. Two more distillations carried
the beginning to 140°, a third to 100°, whence came a rapid rise to
144°, and two more distillations brought much under 100°. Sulphuric
acid in small quantity was left in the flask each time, and there was
evidence of chlorine. The melting point of the product was —126";
then crystals separated, melting at —70°. The specific gravity was
1.756. On distilling again, a few drops were collected below 100°.
These gave an oil with water, dissolving quietly. The melting point
was —51° (corr., — 60°). This was evidently sulphuryl chloride and

708 PROCEEDINGS OF THE AMERICAN ACADEMY.

not pyrosulphuryl chloride.^i as shown by the boilmg and melting
points and by the low specific gravity.

Preparation 10, which was viscous at —124°, was regenerated irom its
sodium salt and studied with more care as to exclusion of moisture.
It boiled at 73-75° (21 mm.), became viscous at —128-126°, and had a
specific gravity of 1.767 at 20°. 60 grams of this were then distilled at
atmospheric pressure until about one third came over. Of the remain-
der, about 10 grams were distilled at low pressure (t°, 63°, p., 24 mm.),
a U-tube with liquid air being used. In the U-tube was found a
small amount of solid, with properties resembling those of sulphuryl
chloride. The residue was then placed in the apparatus described on
page 698 (Figure 2). After passing dry air through the system for
an hour, the liquid was distilled into the second flask at 76-78°( 23 mm.),
when the second flask was sealed off and the distillation conducted at
ordinary pressure. It began at 139°, and was chiefly from 149° to 150°.
The formation of gas was evident and chlorine was found in the liquid
air tube. Sulphuric acid was left in the residue. The distillate be-
came viscous at —128° ; a few crystals were visible at —80°, disappear-
ing at —67°.

The study of the crude product of Preparation 13 was to throw more
light on the question. This had boiled, in hydrochloric acid, within
closer limits, 150-154°, than previous preparations. The latter, owing
to presence of much hydrochloric acid or of products of dissociation,
had taken the vitreous form on cooling, becoming viscous at a higher
temperature without separation of crystals. In this case, however, the
viscous liquid became solid with crystals at —110°, which disappeared
at —70°.

330 grams of this preparation were distilled at 19 mm., after drawing
off most of the excess of hydrochloric acid by exhaustion. 58 grams
were collected from 67° to 76°, 177 grams from 75° to 78° and 55 grams
were left, largely sulphuric acid, which had probably distilled in the
hydrochloric acid current. In the U-tube was much hydrochloric acid ;
a little chlorine. The first fraction became viscous at —127°, crystal-
lized at —93°, and melted at —54°. The corresponding figures for the
second were —134-129°, —87°, and —74°. In both fractions cooling
caused no separation of crystals. The second fraction, on redistillation
at low pressure, became viscous at —130°, crystallized at —83°, and
melted at —72°. There was again no separation on cooling. In the

®^ We prepared a small quantity of sulphuryl chloride by the method of
Ruff. This boiled at 69-71" and melted at —58-56°, corr. With water it formed
an oil, dissolving quietly. The specific gravity of sulphuryl chloride is given
as 1.661 at 21°; the boiling point 75°.

SANGER-RIEGEL. — PYEOSULPH. CHLORIDE-CHLORSULPH. ACID. 709

liquid air tube there was still much hydrochloric acid, some chlorine,
and a few particles melting at —13°. Two subsequent distillations at
low pressure resulted in a product reacting quietly and completely
with water, leaving no oil. There was not much decomposition, but
evidence of a little sulphuryl chloride. The crystallizing point was
—80°, the melting point —70°. This product, distilled in the dry sys-
tem (Figure 2) boiled at 65° to 69° (14-17 mm.), and, at 76S mm., the
first half came over at 137-151° ; the second at 151-152°, There was
very little residue and very little in the U-tube, chiefly hydrochloric
acid. On cooling, no vitreous body separated, but only the crystalline,
and at —75°. That there was probably sulphuryl chloride present
was shown by a redistillation, from which a portion was obtained boiling
from 103° to 141° and melting at —52°. Analysis of the product showed
too low chlorine and too high sulphur, as in Preparation 12, and the
two preparations were probably similar.

A study of the remainder of Preparation 13, by repeated distillations
at very low pressure, showed an increasing tendency to decomposition,
and, indeed, more in the direction of equation (1) (page 703). The
boiling point was 60° to 64° at 2 to 4 mm. The details need not be
considered here, but there was clear evidence of more hydrochloric acid
and sulphur trioxide, with less sulphuryl chloride. The amount of
chlorine, by analysis, in the main body became less ; the sulphur higher.

The deleterious effect of distillation at low pressure was strikingly
shown in the treatment of Preparation 14. This crystallized readily with-
out giving the vitreous solid, and melted at —80°, corr. After distilla-
tion at 68-70° (15-17 mm.), the product would not crystallize at all,
even on inoculation with crystals from another preparation. The spe-
cific gravity was 1.782 at 20°, showing the probable presence of sulphur
trioxide.

Fractional Crystallization of Chlorsulphonic Acid. — It seems there-
fore certain that chlorsulphonic acid cannot be purified by distillation,
that it is an unstable body, and that even the purest specimens here-
tofore obtained, including our own, must have been contaminated by
the dissociation products.

The boiling point must be always somewhat in doubt. In order to
obtain identifying constants which would be less affected by temperature
and pressure, e. g., the melting point and specific gravity, we had re-
course to fractional crystallization.

200 g. of Preparation 17 became viscous at —132°, crystallized at
—100°, and melted at —72°. The entire amount was brought to crystal-
lization and then partly melted. 83 g. of solid were then drawn out of
the melted mass by a spirally bent glass rod previously inserted. These

710

PROCEEDINGS OF THE AMERICAN ACADEMY.

r

i

J

83 g. were then remelted and allowed to partly crystallize, and from the
second, half-melted mass 42 g. were taken out. After three more sim-
ilar fractional crystallizations, 8 g. were finally obtained, which became
viscous at— 130°, crystallized at —98°, and melted at —72° (—80°, corr.).
This product reacted quickly and violently with water, and left no oil.

A gravimetric analysis gave : S,
27.66 ; CI, 30.32 (Calculated: 27.52
and 30.43). When cooled below
—85°, crystallization was not set up
by addition of crystals of either sul-
phuryl chloride or pyrosulphuryl
chloride. On stirring or upon addi-
tion of crystals of chlorsulphonic
acid, the separation was immediate.

Now, as we had satisfied ourselves
by experiment that small amounts of
both sulphuryl chloride and p}Tosul-
phuryl chloride would alter the
melting point appreciably ; as both
of these substances gave a residual
oil with water, even when present in
small quantity, and, finally, as the
method of preparation precluded
even traces of either substance, we
could not but conclude that this
preparation of chlorsulphonic acid
was very pure, and that the true
melting point must be in the region of —80°. It remained, therefore, to
repeat the fractional crystallization in such a manner that access of
moisture to the avid chlorsulphonic acid should be avoided as far as
possible.

For this purpose, the apparatus shown in Figure 3 was devised, which
consists of the glass separator, F, and test tube, E. The construction
is clear from the figure, except that P is a perforated platinum cone
fitting snugly into the lower part of F. F, in this case of 50 c. c. cap-
acity, can be placed in a liquid air container. The outlet tubes at A
and D are connected with drying tubes of phosphorus pentoxide.
Through B may be passed a stirrer. By closing B and applying suction
at A, the liquid is drawn from E into F. When the liquid has been
partly solidified in F by immersion in the cooler, the residual melted
portion is drawn back into a fresh test tube in place of E, while the
crystals are held back by the platinum cone. The crystals are then
melted in F and drawn into a third test tube at E.

Figure 3.

SANGER-RIEGEL. — PYROSULPH. CHLORIDE-CHLORSULPH. ACID. 711

The 261 g. of Preparation 15, which melted at —79°, corr., were in-
troduced into the separator in several portions, and cooled until nearly
solid. Crystallization was spontaneous or induced by slight stirring.
The crystals were then allowed to half melt, and the residual liquid was
drawn out. The remelted crystals, united, were put into the separator
a second time and the crystallization repeated. The second crop of
crystals was then used for determination of constants.

Melting Point. — Three determinations of melting point by the im-
mersion method (page 699) gave— 81°, —81°, and— 81.5°, an average of
—81.2°, which, corrected, becomes —80.2°. Taking this into consideration
with the result of the fractional crystallization of Preparation 17, we
may place the melting point of chlorsulphonic acid at —81° to —80°, corr.
The purity of the twice crystallized product of Preparation 15 is shown
by the slight change in melting point following the treatment.

Specific Gravity.

1. At 20°, 13.4138 g. substance occupied the same volume as 7.6333

20°
g. water. S. g. .^ 1.7533

2. At 20°, 13.4145 g. substance occupied the same volume as 7.6333

20°
g. water. S. g. ^ 1.7536

3. At 0°, 13.6420 g. substance occupied the same volume as 7.6423

g. water. S. g. ^ 1.7839

4. At 0°, 13.6410 g. substance occupied the same volume as 7.6423

0°
g. water. S. g. j^- 1.7838

(The data above are corrected in order to give the figures for specific gravity:
weights of water to 4°, all weights to vacuum.)

The specific gravity of chlorsulphonic acid at 20°, referred to water
at 4°, is therefore 1.753 ; at 0°, referred to water at 4°, 1.784.

Boiling Point. — The boiling point of this sample was compared with
that of other preparations. About 60 g. were distilled at 765 mm., corr.,
with thread of thermometer in the vapor. Ten per cent of the distillate
came over at 144-151°, with traces of hydrochloric acid and chlorine.
The remainder boiled between 151° and 152°, with no evidence of decom-
position in the liquid air tube, which was placed after the receiver.
There was a slight residue of sulphuric acid.

Vapor Deyisity. — The determinations of vapor density were made by
the method of Victor Meyer at the temperature of boiling aniline (184°).
The same precautions were taken as in the case of pyrosulphurjd
chloride.

712 PROCEEDINGS OF THE MIERICAN ACADEMY,

o„i,<,+„„„„ C.c. Air T^o Bar. Vapor

Substance. replaced. ^ • Corr. Density.

1. 0.0522 g. 17.93 19.5 751.1 mm. 2.4

2. 0.0516 g. 18.15 19.5 751.1 mm. 2.4

Calculated for SO3HCI 4.04

Analysis. — A gravimetric analysis resulted as follows:

1 0.9145 g. substance gave 1.1272 g. AgCl
1.2557 g. substance gave 1.5480 g. AgCl
0.5364 g. substance gave 1.0824 g. BaS04
0.7266 g. substance gave 1.4655 g. BaS04

1.
2.
3.

4.

Foimd

Calculated

for SO3HCI,

Chlorine: (1) 30.49, (2) 30.50

30.43

Sulphur: (3) 27.72, (4) 27.71

27.52

Properties of Mixtures of Pyrosulphuryl Chloride and Chhr-

sulphonic Acid.

The presence of the two bodies in the product of the Schiitzenberger
reaction and their close relation to each other rendered of interest a
comparison of certain properties of their mixtures. As differentiating
properties were selected the melting point, boiling point, action with
water and with finely powdered tellurium and selenium. The samples
of pyrosulphuryl chloride and chlorsulphonic acid used were free fr'om
any admixture of the other. The amounts of mixture made up averaged
30 grams. The chlorsulphonic acid gave with tellurium an instantane-
ous cherry red, persisting for several hours but finally fading. With
selenium it gave an immediate moss-green, gradually becoming fainter,
then yellow in about an hour, fading in three hours. No colors were
obtained with pyrosulphuryl chloride. The table on p. 713 (Table
III) gives the results concisely.

From inspection of this table it will he seen that a little over
five per cent of chlorsulphonic acid in a mixture of the two bodies
would give a color reaction and depress the melting point. Ten per
cent would not only give a color reaction, but would cause a consider-
able lowering of the boiling point and a more immediate action with
water. Thirty per cent would give a strong color reaction, a marked
action with water, and a marked lowering of the melting point. A
chlorsulphonic acid containing thirty-five per cent of pyrosulphuryl
chloride would hardly be distinguished from pure material by the color
reactions and the action with water, nor would the boiling point suggest
much impurity, but the presence of pyrosulphuryl chloride in such a
mixture might be inferred from the melting point. It is noteworthy,

SANGER-RIEGEL. — PYROSULPH. CHLORIDE-CHLOESULPH. ACID. 713

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714 PROCEEDINGS OF THE AMERICAN ACADEMY.

also, that the boiling point of a mixture containing 18 to 30 per cent
chlorsulphonic acid is within close limits and lower than that of either
component.

The Action of Water on Pyrosulphuryl Chloride and Chlorsulphonic
Acid and the Separation of the Two Bodies.

Both pyrosulphuryl chloride and chlorsulphonic acid are decomposed
by water, the latter far more quickly, according to the equation :

(1) SO2OHCI + H2O = S02(0H)2 + HCl.

The formation of chlorine in small quantity from this reaction is evi-
dent from the color of the product and its action with potassic iodide.
This is probably due to a slight dissociation from the heat of reaction,
and a consequent oxidation of the hydrochloric acid by the sulphur
trioxide (reactions (1) and (3), pages 703 and 704).

The action of water upon pyrosulphuryl chloride might take place in
two ways : either a direct conversion to sulphuric acid and hydro-
chloric acid according to

(2) S2O5CI2 + 3H2O = 2S02(OH)2 + 2HCI

or with intermediate formation of chlorsulphonic acid, according to

(3) S2O5CI2 4- H2O = 2S02(0H)C1,

the chlorsulphonic acid being then decomposed according to equation
(1). The observed formation of chlorine in this reaction also might be
ascribed to dissociation of either body under the heat of reaction.

Konovaloff,33 who added to 100 parts of pjo-osulphuryl chloride 4
parts of water (theory for equation (2), 25.1 parts; for (3), 8.4 parts),
obtained a mixture of the two bodies. Billitz and Heumann,*^ who
used 7.5 parts to 100, found that chlorsulphonic acid was the chief
product. Prandtl and Borinski,*® with the proportion of 100 of sub-
ctance to 8.3 of water, obtained a product which still reacted quietly
with water and gave no color with tellurium, tbus showing, according
to our results in Table III, at most a small amount of chlorsulphonic
acid. They concluded, therefore, that the reaction took place accord-
ing to equation (3), but was very gradual and, in that instance, in-
complete. This opinion would seem to be substantiated by their
method of separation of the two bodies, which depends upon the selec-
tive attack of water in the form of ice upon the ice-cooled mixture, the
chlorsulphonic acid being completely broken down and but little of the
pyrosulphuryl chloride.

SANGER-KIEGEL. — PYROSULPH. CHLORIDE-CHLORSULPH. ACID. 715

The question was studied by us in several ways : a. Pyrosulphuryl
chloride was dissolved in chloroform and one molecule of water added,
drop by drop. Hydrochloric acid was given otf and a liquid separated
which was shown to be sulphuric acid. The chloroform solution was
then distilled to expel the solvent. The residue hissed with water,
left some oily drops and solidified from —30° to —100°. It was then dis-
solved in chloroform, and a second molecule of water added as before.
Hydrochloric acid was again given off, and sulphuric acid separated.
The residue from the chloroform evaporation hissed more violently with
water than before, and solidified at —95-100°. A similar treatment
•with a third molecule of water gave hydrochloric acid in clouds, more
sulphuric acid separated, and the chloroform solution yielded a small
residue, which still gave the reactions of chlorsulphonic acid and solid-
ified below —80°. The reaction was followed quantitatively, though
roughly, and the amount of sulphuric acid was somewhat below that
demanded by equation (2).

Evidently in this experiment the reaction has taken place in two
stages, represented by equations (3) and (1), the net result being ac-
cording to equation (2), though the last action was not entirely
complete.

b. Pyrosulphuryl chloride was dissolved in carbon tetrachloride,
and water was added directly in the proportion of 8.4 to 100 (equa-
tion (3)). The mixture was allowed to stand over night. From a por-
tion the solvent was evaporated by a rapid current of dry air ; the
turbid residue reacted quietly with water. The remainder was evap-
orated at a gentle heat, and left a residue which also gave no violent
action with water. This would seem to show that reaction (3) had
not taken place exclusively, but probably reaction (2) incompletely,
though, of course, at least 18 per cent of chlorsulphonic acid may have
been present according to Table HI, 5.

c. Pyrosulphuryl chloride was exposed to the moist air of the room
in a beaker covered with a watch glass for seven days, and a portion
tested each day with water. There was no evidence of chlorsulphonic
acid, — merely a diminishing quantity of pyrosulphuryl chloride, until,
on the last day, the residue was sulphuric acid alone. The beaker
walls were covered with aqueous hydrochloric acid.

d. 8.3 parts of water were added to 100 parts of p)TOsulphuryl
chloride, cooled to 0°, and shaken under ice cooling for an hour. The
liquid became turbid at first, and a little gas containing chlorine was
evolved. In twenty minutes the mixture was decidedly yellow. At
the end, two layers were formed, the lower, from its action with water,
being apparently unaltered pyrosulphuryl chloride and the upper sul-

716 PROCEEDINGS OF THE AMERICAN ACADEMY.

phuric acid. The amount of unaltered substance was greater than if
only one molecule of water had been added according to equation (2).

e. 8.1 parts of water were added to 100 parts of pyrosulphuryl
chloride warmed to blood heat. Hydrochloric acid was given off, and
the mixture separated into two layers, sulphuric acid and apparently
unchanged pyrosulphuryl chloride, colored by chlorine. The amount
unaltered was again greater than would have been expected if some-
what less than one molecule of water (8.1 parts) had acted according
to equation (2).

From Experiments h, c, d, and e it might be concluded that pyrosul-
phuryl chloride was directly converted by water to hydrochloric and
sulphuric acids, except for the fact that a considerable admixture of
chlorsulphonic acid might show no violent action with water (Table
III), and that, in Experiments d and e, the amount of unaltered pyro-
sulphuryl chloride is greater than it should be if only one third had
been converted to hydrochloric and sulphuric acids. Experiment a,
however, shows that there is an intermediate stage of conversion, — to
chlorsulphonic acid. In general, a greater concentration of water will
bring about a more complete decomposition of the pyrosulphuryl
chloride, after the admixed chlorsulphonic acid has been disposed of,
and, in addition, the reaction is furthered by a high temperature or
long contact, or by both. If the reaction mixture is at once distilled,
the first product, chlorsulphonic acid, may be isolated. This is shown
by our investigation of the Prandtl and Borinski method of separation,
in which distillations of moist " pyrosulphuryl chloride " obtained by
this method gave invariably large amounts of chlorsulphonic acid.
One instance will suffice :

/. 133 grams of moist "p)TOSulphuryl chloride," which had no longer
given any evolution of hydrochloric acid on adding ice, thus, showing
the chlorsulphonic acid in the original mixture to have been decom-
posed, were distilled. Up to 148°, 75 g. were obtained ; from 148° to
153°, 40 g. Both fractions reacted violently with water and gave a
strong red color with tellurium.

We are now in a position to explain why the results of Konovalofif
and of Billitz and Heumann differed from those of Prandtl and Bo-
rinski. The first three authors apparently distilled their mixture of
pyrosulphuryl chloride and water within a short time, and therefore
obtained more chlorsulphonic acid, since at the higher temperature the
pyrosulphuryl chloride was hydrated more quickly and there was
not enough water left to entirely decompose the chlorsulphonic acid
formed. The last two, however, distinctly state that the cooled mix-
ture stood over night before separation and distillation, hence, at the

SANGER-RIEGEL. — PYROSULPH. CHLORIDE-CHLORSULPH. ACID. 717

hwer temperature, the chlorsulphonic acid was more quickly hydrated
and therefore not evident in the product of the subsequent distillation.

On this point depends much of the success of the Prandtl and
Borinski method, as our study of it shows. If ice be added to a cooled
mixture of the two bodies, the chlorsulphonic acid will be decomposed
and a part of the pyrosulphuryl chloride. The latter must not be
separated at once and distilled, but the mixture must stand for some
time. The sulphuric acid does not always form the upper layer, since
the specific gravities of the two are so nearly the same. Addition of
concentrated sulphuric acid or a little water will bring the pyrosul-
phuryl chloride to the bottom. After separation, the addition of
phosphorus pentoxide to the moist pyrosulphuryl chloride is not op-
tional, as Prandtl and Borinski contend, but necessary, if the minimum
amount of chlorsulphonic acid is to be formed on distillation. With
proper precautions, the method can be made to give a fairly pure prod-
uct, though the entire absence of chlorsulphonic acid is not assured.
The 3^ield is, however, not over 70 per cent, as Prandtl and Borinski
state, and may be less.

In this connection, the behavior of pyrosulphuryl chloride toward
concentrated sulphuric acid is of interest. There is no immediate
action, but a partial hydration takes place on standing. The two im-
miscible substances were sealed in a tube and allowed to stand in the
cold for a month. The product was homogeneous. On opening the
tube there was no excess of pressure ; on mixing a portion of the con-
tents with water, a violent reaction took place and hydrochloric acid
was given off. This indicates the formation of chlorsulphonic acid.
Since we have shown that chlorsulphonic acid is partially dehydrated
by sulphur trioxide (p. 673), we may express both results again by
writing the reaction (6) in this place also :

S2O5CI2 + H2SO4 1:; 2SO3HCI -f SOs,
or S2O5CI2 + 2H2SO4 U 2SO3HCI -f H2S2O7.

This condition of equilibrium explains why, in the preparation of
chlorsulphonic acid by the Williamson method, the formation of pyro-
sulphuryl chloride is impossible, since the large amount of sulphuric
acid would cause the reaction to run to the right.

^&^

Summary.

The work of previous investigators on the action of sulphur trioxide
upon certain chlorides is reviewed as briefly as possible and the results
summarized in tabular form (Table I).

718 PROCEEDINGS OF THE AMERICAN ACADEMY.

Pyrosulphuryl chloride is obtained in a perfectly pure state and its
chief constants determined. A rapid method is devised for finding
melting points at low temperatures.

Chlorsulphonic acid is shown to be unstable when subjected to dis-
tillation, but it is purified by crystallization and its chief constants are
determined.

It is confirmed that the Schiitzenberger reaction of sulphur trioxide
upon carbon tetrachloride, which is best adapted to the preparation of
pyrosulphuryl chloride, gives also chlorsulphonic acid when the sul-
phur trioxide is in the form of oleum, and it is shown that the propor-
tion of the two bodies in the product depends roughiy upon the
hydration of the oleum (Table II). It is also shown that, with a
hydration corresponding to that of pyrosulphuric acid, 2S03' HoO, or
greater, only chlorsulphonic acid is formed, and that, while the limit
of the formation of chlorsulphonic acid is theoretically at the hydra-
tion corresponding to the formula 2S03' 3H2O, yet the increasing
concentration of the water up to the latter point results in a more
rapid decomposition of the chlorsulphonic acid than the theory
demands.

A method of separation of the products of the Schiitzenberger reac-
tion is described, by which the pyrosulphuryl chloride may be com-
pletely freed from chlorsulphonic acid, and the latter may also be
recovered.

The conditions under which pure chlorsulphonic acid is best pre-
pared by the Williamson method are studied, and it is confirmed that
the action of the hydrochloric acid is only upon the sulphur trioxide
in the oleum in excess of that corresponding to the formula SOs" H2O.

The dissociation of chlorsulphonic acid is studied and discussed.

Properties of mixtures of pyrosulphuryl chloride and chlorsulphonic
acid are given (Table III).

The action of water upon pyrosulphuryl chloride is studied.

In conclusion, we desire to express our indebtedness to the C. M.
Warren Fund of Harvard University for assistance in defraying the
expense of the liquid air used in this investigation.

Hakvakd University, Cambridge, Mass.,
December, 1911.

Proceedings of the Americaii Academy of Arts and Sciences.
Vol. XLVII. No. 19. — March, 1912.

THE FALL OF A METEORITE.

By Elihu Thomson.

THE FALL OF A METEORITE.
By Elihu Thomson.

Presented January 10, 1912. Received January 30, 1912.

While on a trip west last spring I took the opportunity of visiting
the remarkable formation in Arizona known as Coon Butte, also called
" Meteor Crater." This formation has been made the subject of several
memoirs which have appeared from time to time during a number of
years past. To these papers references may be made for details of ex-
ploration and measurements. In view, however, of the marked diverg-
ences of opinion concerning origin, it seemed desirable to determine, at
least to one's own satisfaction, which of the explanations was in accord-
ance with the facts. The spot had been known for many years as the
locality for numerous meteorites, unique in containing diamonds ; the
so-called Canon Diablo specimens. Canon Diablo is a few miles west
of the crater.

More recently these iron masses have been found to contain notable
amounts of platinum and iridium, metals which have in the past few
years advanced in price at an extraordinary rate.

The careful study of the class of bodies which include meteorites
can doubtless assist us materially in understanding what goes on in
the universe around us. They are messengers with a story. My per-
sonal interest was aroused when I was a fortunate witness to the great
meteor shower in the early morning of November 14, 1867. This
shower which was recurrent in thirty-three years was found to be due
to meteoric masses, the path of which was identical with the orbit of
Tempels' Comet, which was undergoing disintegration. Owing to
some perturbation or displacement of the orbit the visitation failed
to reappear in 1900.

In reaching the Meteor Crater we ride west over the Atchison, To-
peka and Santa Fe railroad enjoying the wonderful scenery of the
Painted Desert, its coloring and atmosphere. We may comfortably
pass the night at Winslow in northern central Arizona. Taking the
train next morning toward Sunshine Station, a few miles further

VOL. XLVII. — 46

722 PROCEEDINGS OF THE AMERICAN ACADEMY.

west, if we are intent on noticing the peculiarities of the land
around us we will soon see off to the southwest and rising out of
the nearly level plain a peculiar hill or elevation ; a butte with an
apparently flat top and whose slopes have a grayish color distinguish-
ing it completely from the red soil which covers this territory. Though
it may be eight or ten miles away it is still a conspicuous object not
from its height but from its form. It has an artificial look as if some
great reservoir for water storage had been built. There is no other
elevation near it. From Sunshine Station it is reached by a drive
south of about six miles, over the plain sparsely covered with vegeta-
tion, and with here and there outcropping fantastic forms of red rock
of a few feet in height.

As we approach Coon Butte, or Meteor Crater, the impression does
not change except in the realization of the scale on which it exists.
Distances are so deceptive in the clear air of the desert that it had
seemed close at hand when we were still miles away. At last we reach
the foot of the slope and climb it to a height of about 150 feet. We
are now at the top looking down into a great bowl-shaped hole, the
upcast rim of which we had seen from afar. This rim is a nearly
circular ridge, very steep or even vertical on its inner part and slop-
ing gradually to the plain on all sides. But the thing which rivets
the attention is the deep cavity enclosed by this rim, comparatively
flat at the bottom with surrounding talus slopes from the walls,
in which walls are exposed various rock strata, broken, contorted, dis-
torted, and uplifted. The bottom of the crater is about 570 feet below
the rim, or more than 400 feet below the general level of the plain
outside.

The sight is most impressive. The diameter of the opening is
roughly three quarters of a mile ; at the widest part a little over 4,200
feet.

The circular hill or rim of this huge hole is composed of material
evidently uplifted, crushed and pulverized in part and cast out from the
crater. Much of it is finely pulverized white silica from a white sand-
stone which underlies an upper stratum of limestone. Fragments of
the limestone layer of all sizes are seen ; some of them very large.
The slope of the rim extends for about a quarter to half a mile but
there is scattered material three miles or more away. Blocks of lime-
stone and sandstone cap the ridge, ranging up to 30 feet in diameter,
while one block 10 feet through, is half a mile distant. The most
significant constituent of the upcast ridge, is, however, meteoric iron
in pieces of varying size, and so-called shale ball iron or oxidized
meteoric iron ; — oxidized because in its composition there was chlorine

THOMSON. — THE FALL OF A METEORITE. 723

enough to cause rapid rusting after it entered the earth's atmosphere
and became subject to moisture.

The plain around the crater has yielded numerous masses of the
iron, some of them several hundred pounds in weight, and one dis-
covered during the past summer weighs about 1700 pounds.

The amount of rock blown out of the crater cavity could not have
been less than two or three hundred millions of tons, not considering
the large amount which fell back and which now lies at the bottom of
the bowl-shaped hollow of the crater. Nowhere else on the earth's
surface has meteoric iron been found so spread about.

Yet there remains an unsolved problem. What became of the enor-
mous meteoric mass, or the cluster of them which was capable by its
impact of displacing so large an amount of rock 1 Allowing only one
ton to every 20 or 30 tons of ejected material, we still have about 10
millions of tons of meteoric iron to account for. This would constitute
a solid mass of between 400 and 500 feet in diameter.

The attempts to explain this crater as the result of volcanic action, or
as produced by a steam explosion from below, are certainly to be re-
garded as rather far fetched in view of the presence and mode of occur-
rence of the meteoric irons, and the many evidences presented which
seem to me to lead inevitably to the conclusion that here indeed we
have a huge impact crater and that only. Tbe floor of the crater is
overlain with sedimentary deposits of an aquatic nature, the washing
of the walls and talus indicating the existence at some time of a small
lake or pond. Below this is a vast bed of mingled materials, mostly,
however, the pulverized white sandstone or " rock flour," the result of
crushing of the rock layers such as now surround it.

For exploration a shaft has been sunk into this bed of a nearly pure
silica, but contrary to expectations it had to be discontinued. Water
was reached at about 200 feet below the crater floor and the extremely
fine silica rock flour thus became a most typical and troublesome quick-
sand and limited the depth of the shaft. Recourse was had to drill
holes, about 28 of which have been sunk to various depths not far from
the central area, and some of these have reached the underlying and
undisturbed red sandstone layer at about 850 feet below the crater
bottom.

The material brought up has shown evidence of disseminated mete-
oric iron and nickel, but no large masses were found. Specimens of
the silica metamorphosed by heat and steam under pressure, causing a
partial aqueous fusion, have been secured.

Careful magnetic tests conducted by Prof W. F. Magie, head of the
Physics Department at Princeton, have failed of result, probably because

724 PROCEEDINGS OF THE AMERICAN ACADEMY.

these iron masses have too low a magnetic susceptibility under the very
small values of magnetic force such as exist at low latitudes ; particu-
larly as the vertical component can alone be expected to yield indica-
tions of the presence of buried masses of iron.

If further exploration is carried on it is possible that a system of in-
duction balance testing as proposed by me would be more fruitful,
though experiment alone could determine that fact.

From many considerations which it would take too long to enumer-
ate it seems probable that if a large mass or cluster has buried itself at
this spot, it now exists under the southern and southwestern wall of
the crater and not near the center. It is a significant fact that the
rock layers exposed under the rim at the south show evidences of an
uplift of about 100 feet while still retaining their approximately hori-
zontal position. The depth of penetration is probably not more than
1200 feet, in which case the buried masses would lie upon or be slightly
embedded in the upper part of the underlying red sandstone layer,
which the bore holes put down near the center of the crater have shown
to be undisturbed there.

In a recent report referring to Coon Butte, Bulletin 435 of 1910 of
the United States Geological Survey, Mr. N. H. Darton says : " After
an examination of the crater and consideration of all that has been
written, I believe we have no evidence adequate to explain its origin.
The hypothesis that it was caused by the impact of a meteor as urged
by Tilghman, Barringer, Fairchild, and Merrill is in accordance with
some of the features but does not accord with the all-important fact
that no meteor is present, as has been demonstrated by many bor-
ings." He forgets that only 28 test holes were put down and all near
the center of the crater and that such bodies rarely if ever fall verti-
cally. If a single large mass of 500 feet in diameter fell, to be sure of
finding it would demand the sinking of not less than 500 to 600 holes
if the whole crater is to be explored. He says further : " It is agreed
that if there was a meteor it must have been at least 500 feet in diame-
ter. The occurrence of a few tons of meteoric iron in the vicinity and
mingled with some of the debris on the rim and in the crater is an
enigma." He goes on to favor a suggestion by Gilbert that it was a
volcanic steam explosion that produced this crater, forgetting again
that the real key to the situation is the presence of the meteoric iron
in the way it is found to exist.

A considerable expenditure of time and money has been made in
exploring this unique crater. This has been carried on largely by
Mr. D. M. Barringer, to whom belongs the credit of pointing out the
meteoric origin of the crater and collecting the proofs thereof. To him

THOMSON. — THE FALL OF A METEORITE. 725

I am indebted for the opportunity of conveniently visiting and examin-
ing the formation, and also for publications, charts, slides, and other
material.^

The uncovering of a mass of millions of tons of iron containing about
8 per cent nickel would have great commercial value. Add to this the
fact that analyses show the iron to contain an average of about 6/10
ounce of platino-iridium to the ton and the value is much enhanced.
Besides, there is an undetermined amount of diamond present.

All of the iron examined and even the oxidized shale ball iron shows
the characteristic Wiedmanstatten figures regarded as proof of meteoric
origin. Such a structure, it may be remarked, is probably the result
of slow cooling in the interior of a large body and under compression.
This structure is stated to disappear when the iron is heated to about
900° C.

What happened at the Meteor Crater may be briefly outlined as
follows : A large mass, or more probably a cluster resembling a small
comet, passed so near to the earth as to be deflected sufficiently to
cause it to strike. Its velocity, reduced by retardation in the air, may
have been not more than two or three miles per second when it struck
earth. As it penetrated the dry plain, some of the smaller and still
more retarded and slower moving pieces following in the rear of the
main cluster were diverged therefrom and so fell at various distances
around the crater. As soon as the main body reached the wet rock
layers superheated steam was generated at high pressure, pulverizing
and metamorphosing the silicious rock, and producing an enormous
lateral pressure which the disturbed and uplifted strata together with
the horizontal compression as shownjn the structure of adjacent rock
masses clearly indicate. As the mass advanced the pulverized mate-
rial in its path and around it would be swept backward almost as a
fluid and would expand outwardly at the same time, fracturing the
adjacent rock layers, up-casting and folding back the strata, and dis-
charging the enormous mass of pulverized and mixed rock material
which now forms the circular rim. This blast would entangle the

* Mr. D. M. Barringer, conceiving the impact theory to be the correct one,
collected largely at his own expense, and through a period of years, the evi-
dences thereof and has published his results in the following papers, to wit,
"Coon Mountain and Its Crater," Proceedings of the Academy of Natural
Sciences of Philadelphia, December, 1905; " Meteor Crater in Northern Cen-
tral xVrizona," read before the National Academy of Sciences at its meeting at
Princeton, November 16, 1909. To these papers of Mr. Barringer reference
may be made for an abundance of interesting detail with illustrations and
maps.

726 PROCEEDINGS OF THE AMERICAN ACADEMY.

smaller fragments of meteoric iron now found in the rim. Finally, as
the masses of material came to rest there would settle back into the
excavation a large part of the pulverized material leaving the sheer
rock walls as they now are, upturned at various angles even to almost
complete inversion in some places. The material which did not fall
back to the crater would rest on the upcast walls and slope away upon
the surface of the plain in a fairly symmetrical manner. In their flight
through the air the iron was burning into oxide ; the heat and debris
were left behind in the wake or trail. What reached the earth was
comparatively if not actually very cold, retaining in its interior, as it
were, something of the cold of space.

It may be of interest here to present if possible a brief statement of
what must happen during the flight of a meteoric mass through our
air. In general, the earth's atmosphere acts so effectually as a protec-
tive sheath that only a few of the very numerous bodies variously
known as shooting stars, aerolites, and meteors ever reach the earth's
surface. If the velocity of a body entering from the outside is very high
relatively to the earth, thirty or forty miles per second, for example,
the crushing strains brought upon it by the air resistance in its path
may be great enough to break it into fragments, while the high tem-
perature of the compressed air opposing its movement melts or vapor-
izes the material composing it. Stony masses, like pieces of rock,
would yield to fracture and dissemination more readily than masses of
solid iron. This fact may itself account for so large a proportion of
the bodies which reach the ground being composed of iron. Rock
masses are occasionally found, surviving, perhaps, because of low en-
tering velocity. The iron meteors are so strong as to resist enormous
crushing strains. The metal iron is, however, so freely combustible
that when exposed to a blast of hot, compressed oxygen it is burned
into fused oxide very rapidly. So with the iron meteors in their flight.
They are virtually blown upon by a highly heated blast of compressed
air containing so much oxygen as to cause them to burn like tinder.
The survival of a stony meteor, or aerolite, until it reaches the ground
must therefore depend upon its entering the air at comparatively low
velocities, or upon its being retarded in a long flight through the very
thin higher air whereby it loses much of its initial speed before enter-
ing the denser air below, while the survival of an iron meteorite de-
pends on its velocity being insufficient to develop crushing strains
great enough to fracture it into small masses, and upon the size of the
meteor itself, or of its fragments, if fractured. A small iron mass at
high velocity will burn away so rapidly in the dense oxygen in front
of it that the whole mass will be consumed and dissipated before any

THOMSON. — THE FALL OF A METEORITE. 727

of it reaches ground. The whole energy of the flight will go into the
trail or train. The fused iron oxide as soon as formed on its surface
is blown off and left behind in the trail which marks the course of the
body in the air. If, however, the iron mass or fragment is large, and
its velocity insufficient for crushing or further breaking, it may not be
entirely burned during its flight and some of it may reach the ground
or the sea while still retaining a considerable velocity. It may bury
itself in the earth to a depth more or less great. In the case of an iron
meteorite there are two sources of heat energy and attendant lumi-
nosity, the high compression of the air in front of it and the wastage
by combustion of iron in the hot compressed oxygen. The mass is in
fact virtually blown upon by a blast oi oxygen in a high state of com-
pression. As evidence of the rapidity and effectiveness of such com-
bustion reference may be made to the work of the acetylene oxygen
blowpipe now used to cut through masses of iron, as in clearing wrecks
and the like. The product of the combustion in these cases is mag-
netic or black oxide of iron in a fused and perhaps partly vaporous
state, and this is removed or blown off" the surface of the iron mass as
fast as it is formed. Melted pear-shaped drops have indeed been ob-
served as falling out of the track or train left by a meteor in its course
through the air. They are probably iron cinder or fused magnetic
oxide. It will be understood from this that the energy given out as
heat is not delivered to the body of the meteor as such, but is carried
off" in the air and oxide layer ripped off" and left behind in the train.
It has not been unusual to dig up a meteor seen to fall, and find it
stone cold or only slightly warmed. Entering the air from space its
temperature wiU naturally be very low, not much above absolute zero.
Its flight in the air lasts so short a time that its conductivity for heat,
even when it is of solid metal, is not adequate for the instant passage
of heat to its interior. It can possess only a thin skin of hot material,
a mere film in which the temperature gradient is very steep or abrupt,
and this film is constantly blown off" or removed as soon as its tempera-
ture of fusion is reached. This temperature is about 1500° C. The
case may be illustrated by turning a vigorous blast of heated air upon
a piece of ice supported in any way. The ice melts rapidly and the
water formed is blown off" as fast as it appears, while what remains is
none the less ice to the end of the process. It is even possible that
the blast be highly heated so as to boil the water formed without essen-
tially changing the result of causing the ice to melt away rapidly but
remain while so diminishing a piece of ice to the last. But the ice is
not combustible. Let us therefore substitute for it a ball of wood or a
mass of combustible and turn thereon a blast of hot oxygen or air. The

728 PROCEEDINGS OF THE AMERICAN ACADEMY.

combustible will burn on the outside and the heat be carried off in the
products of combustion blown from it ; while if we stop the experiment
at any time we will find the interior of the mass remaining still solid
and cold.

Hence in the case of a large iron meteor there is no such thing pos-
sible as an instantaneous vaporization of the whole mass. On enter-
ing the thin upper air it will condense the air immediately in front of
it, increasing its temperature and raising the density of the oxygen to
a point to begin the combustion of the outer layers of the moving mass.
If the velocity be extremely high, the opposing pressure in front as it
passes into lower air may be sufficient to crush the mass into fragments.
The smaller pieces formed will now burn and the rate of waste by com-
bustion be greatly increased. This process may go on until the whole
is consumed and dissipated in the train. But if the velocity is not high
enough for this, the mass either does not fracture or the breaking soon
ceases and the remaining flight is marked by combustion or fusion and
the continual cleansing of the surface of its fused products, as outlined
above. If any of the mass has size enough to endure the rapid waste
by oxidation, there may at the last remain a greater or less fraction of
the original ma,ss, which reaches the earth's surface in the solid and
relatively cold condition, embedding itself in the earth or in the sea.
The indications then are that a body which has so survived will neither
be moving at an excessive velocity as compared with that of a projectile
from a high-powered gun, nor be a hot body on striking, except as to a
mere film of its outer surface. As such bodies rarely descend vertically
they must pass through many miles of comparatively dense air when
their course is more or less horizontal or inclined to the vertical. This
and their irregular form renders possible a very great retardation ; far
exceeding in proportion that experienced by a well proportioned cannon
shot in its flight. If crushing or fracturing took place, angular frag-
ments would be split off, very irregular in form, making very poor pro-
jectiles, retarded rapidly. The crushing of the mass by opposing air
pressure can be compared to the result of the explosion of a charge of
nitroglycerine upon a mass of iron, the effect produced being that due
to a high gas pressure suddenly formed. But the pressure which would
be needed to fracture an approximately round and solid mass of cold
nickel iron is very great, so great in fact that it is probable that only
those meteors moving relatively to the earth at the very highest veloci-
ties would experience it. In fact it may be doubted that such fracturing
often occurs with a solid iron meteorite of round form, on account of
the somewhat gradual retardation, smaller in the upper air and increas-
ing as the body reaches denser air, thus gradually robbing the body of

THOMSON. — THE FALL OF A METEORITE. 729

its velocity. A large iron meteorite or a cluster of them has therefore
a considerable chance of survival in spite of the rapid waste by burning,
while the smaller ones may disappear by combustion while still in the
air, especially if the initial velocity be high. But, entering air at a
comparatively low velocity such as five to ten miles per second, an iron
meteor of more than a few ounces in weight will probably survive in
part. I have been particular to lay stress on these actions, as they en-
tirely negative an idea which has been advanced to account for the fail-
ure to find large masses of embedded iron at the Arizona Crater. It
has been claimed that the mass was vaporized on striking, a possibility
which is impossible, as I am compelled to regard the matter.

The age of Coon Butte, the great Meteor Crater, is of course uncertain.
How long a time has elapsed since the fall 1 In the absence of definite
data for computation we can only guess. However, from the apparent
absence of much erosion it must be comparatively recent. While the
country is dry, it does rain at times and there are high winds. The
climate may have been more moist in times past as is rendered probable
by the evidences of water in the crater formerly. The age of certain
cedar trees on the slope tend to place the date back perhaps of 500 to 1000
years. A mere surmise would be 2000 to 3000 years ago as the possi-
ble time of the meteoric fall.

It is stated that the Indian tribes inhabiting the region in a reserva-
tion just north of the railroad have an ancient tradition of the fall of a
large body of fire from the sky which killed a number of their tribe. It
is also stated that they now hold the spot in some superstitious awe fi:oni
the fact that they send to the crater slopes for the white silica, which is
sprinkled about during their ghost dances. I cannot, however, person-
ally vouch for these statements without further investigation.

Such craters as this meteor crater if formed many thousands of years
ago would probably be obliterated by erosive influences, and even in
the desert the shifting sands would finally cover them. The water,
the frost, vegetation, the atmosphere are against their indefinite pres-
ervation as features of the landscape. Let us imagine, however, a large
body such as our moon, in a vacuum, with no atmosphere, no water,
no winds, no frost, no vegetation, then, if any such impact took place
the record must be left for all time ; not quite unimpaired perhaps, for
a subsequent impact may superpose its effect tending to obliteration of
the first effect. Moreover, in the lapse of millions of years there may
be accumulations of cosmic dust or small particles gathered up from
space which will partly cloud over or cover the lower portions. But
even in this case the higher ridges will remain. It is indeed no new
idea that the lunar craters, instead of being the result of volcanic

730 PROCEEDINGS OF THE AMERICAN ACADEMY.

actions, may be in fact impact craters. This idea was put forward by
Proctor in 1873 and further enforced by Gilbert some fifteen years or
more ago. If they are volcanic then the comparatively diminutive
moon has been the theatre of tremendous volcanic disturbances, which
without water or other gases and vapors would be unlikely according
to the views of some authorities on volcanic action on the earth. If the
lunar craters are not volcanic, then the scarred face of our moon is a
record of terrific impacts of bodies of all sizes, probably occurring dur-
ing its early history millions if not billions of years ago. The earth
must also have shared in this bombardment, the traces of which are
entirely obliterated. Perhaps its surface was at that time molten.
There are marked differences between the now existing volcanic craters
on the earth and the lunar craters. On the moon they do not exist
along any lines of weakness as on the earth, and they have not built
up chains of cinder cones topped by craters of restricted dimensions.
They occur on the moon belter skelter, alongside of each other, any-
where, everywhere over its much scarred surface. They exhibit the
greatest range of sizes or diameters from the smallest dots visible by
our most powerful telescopes to the huge basins such as Clavius nearly
150 miles across. Large craters are dotted with others, smaller in size,
anywhere, it may be on the floor of the crater or in its walls or their
slopes. These parasitic craters appear to be absent in such craters as
Tycho and Copernicus, which, however, with some others, are distin-
guished by extensive systems of whitish streaks running for hundreds
of miles in a general direction radially over all irregularities of sur-
face. Unlike the earth's great volcanoes, the floor of the lunar craters
is in nearly all cases considerably below the general level of the sur-
rounding surface.

The Meteor Crater in Arizona has this same characteristic and in
fact if looked down upon from above would appear like a lunar crater
transplanted to earth. The proportional depression of the crater floor
to the height of the upcast rim is much the same. The outer slope of
the rim and its relative extent are likewise very similar. The agree-
ment is, to say the least, highly suggestive of a similarity of origin.
The lunar craters do not show great rivers of lava coursing down the
slopes and covering the lower levels. There is indeed a notable ab-
sence on the moon of such evidences. Those whitish streaks around
Tycho and Copernicus, bear far more the appearance of an instanta-
neous scattering of material in a vacuum (and therefore moving out-
wardly in a straight course) than they do of product of a prolonged
volcanic eruption which in the case of such large craters must have
lasted for years. Any such surrounding deposits would have been

THOMSON. — THE FALL OF A METEORITE. 731

spread more generally and uniformly around the crater instead of in
streaks. The appearances suggest a sudden splash. The central moun-
tain or hill, so common a feature of the larger lunar craters, shows no
volcanic vent. Its existence is then more compatible with the idea of
a reaction, or " kick back," an inrush similar to that which occurs on
dropping a stone into a pool of water, except that in the case of the
lunar crater it is composed of solid fragments or more or less pulver-
ized rock. This central hill is absent in the smaller craters, as in
those comparable in size with the Arizona Crater. The most ancient
craters on the moon have had time to become softened in outline and
in a measure obliterated by cosmic dust. This may be the reason why
so few show the system of radiating streaks so characteristic of Tycho
and Copernicus. A thin lunar atmosphere, afterward lost, may have
prevented their formation. The fact that the craters of Tycho and
Copernicus are so clean cut, so sharply defined, so deep, free from par-
asitic craters or subsequent impacts, and still surrounded by the exten-
sive, unobliterated system of streaks, would in this view, make them
the result of the very latest or more recent large impacts which the
moon has sustained.

The hypothesis of meteoric origin for the lunar craters has been com-
batted on the ground of the absence of tangential or grazing impacts.
There may be some reason for this absence. If most of the effect was
due to the fall of bodies moving in a general path similar to that of the
moon, we could understand the case as one in which the gravitation of
the moon itself tended to change the path from a horizontal direction
and so prevent grazing impact. There are, however, some grooves or
furrows on the moon's surface the most perfect example of which is the
Great Valley of the Lunar Alps which looks very much as if made by a
projectile at last arrested and in part deposited on the plain beyond.
Near this also is the formation called the Straight Range which is
remarkably suggestive of a glancing blow ; as if a large body had failed
to embed itself on the first impact and had tumbled along, ruffling the
surface and shedding debris until its velocity was at last checked.

If it be correct to regard the moon as having been separated from the
earth early in the history of our planetary system, there must have been
a large amount of scattering at the time of separation. The earth would
have retained the gases and water vapor almost wholly so that the moon
would have gone off without an atmosphere. The moon and the earth
also would gather up most of the material so scattered and the moon
might then have accumulated its scars, or at least the earlier ones. The
fall of any large mass would of course obliterate all smaller indentations
made before its occurrence not only at the place of impact but for some

732 PROCEEDINGS OF THE AMERICAN ACADEMY.

distance around it. This seems to have occurred with such craters as
Tycho and Copernicus. If we go farther back in time and think of the
possible building up of the sun and planets of our system by gradual
accretions such as are now taking place when a meteor enters our air,
but which at some time, as many millions of years ago, occurred on a
far grander scale, we can understand the craters on the moon as the last
records of such a process, and the Meteor Crater in Arizona as the larg-
est known record on the earth, all others belonging to the earliest ge-
ological periods having been obliterated.

In the solar system the survival of the fittest rules. The numerous
comets with highly elliptical orbits must succumb and be gathered up by
those bodies like the sun, and by the planets which perform their rounds
in a less erratic way with orbits nearly circular. If the conclusion be
correct that the comets actually belong to and form part of our system,
then the thought is permissible that at an early period they were innu-
merable and that they have been reduced and obliterated in feeding
those masses, like themselves originally, which, however, possessed more
conservative orbits, to use that term.

That the meteoric masses which come to earth are solid and have a
structure strongly suggests that they are fragments of a much larger
body.

The solidity suggests either a high temperature or a high pressure
due to gravitational forces, or both. Particles floating in free space
could never themselves form such dense and solid aggregations. When
as in the Arizona crater irons we find diamonds, we are fairly sure of
high pressure having existed. When we find also a coarse crystalline
structure and segregation we think of a long time of slow cooling.
When we see that the solid mass is not only coarse but that the parts
are divided by fine crevices or small cracks we infer the sudden relief
from high compression, when the material was cold and solid. In short,
we infer that we have before us a fragment of a large body which in the
long lapse of time had consolidated and cooled, and which later has
been torn to pieces, disrupted into fragments large and small. Was it
a collision of two large bodies in space, such as may have given rise to
a great, irregular nebula like that in Orion 1 Doubtless collisions can
occur but they must be very rare.

The order of nature, however, may easily involve the more or less
close passage of large orbs, either still hot or cooled off, past each other
at a distance of a few millions of miles. In such a case the stupendous
tidal and centrifugal actions attendant on the neutralization of gravity
on a line joining the centers of the two bodies must inevitably result
in crushing them, as if an irresistible force were exerted in all other di-

THOMSON. — THE FALL OF A METEORITE. 733

rections than along the line joining them. This crushing would result
in two streams or jets of material rushing out in diametrical directions
at velocities of a great range of magnitudes, and they might in some
cases, but not in all, be violent enough to produce very high tempera-
tures and consequent vaporization. Each body so disrupted would then
pursue its way no longer a spherical body but as a new-born spiral neb-
ula, the internal forces of which would again set to work to gather up
what matter remained outside of that widely dispersed in space. Thus
new solar systems would be born from the wreck of those preceding.
This involves a modification of the time-honored nebular hypothesis of
La Place and is in line with the ideas of Chamberlin and Moulton in
their planetesimal hypothesis.

We are led to suspect that this is indeed the process of nature, a pro-
cess which has gone on from an infinite or indefinite past and which
will continue as long as a ray of light gan traverse the ether of space.
To me the idea that the universe is like a clock running down is repug-
nant. Even though uranium, radium, thorium are disintegrating grad-
ually, and we have no evidence of their generation by any process, there
may be some source, as under the enormous pressures within a large
orb, where such elements and perhaps others of still higher atomic weight
and greater instability arise. Here again the law of survival holds, the
electrons in the atom having unstable orbits being cast out in reducing
the body to simpler and more stable forms, just as in the solar system
the erratic comets must be eventually swallowed up and lost.

Proceedings of the American Academy of Arts and Sciences.
Vol. XLVII. No. 20. — March, 1912.

AN ALGEBRA OF PLANE PROJECTIVE GEOMETRY.

By H. B. Phillips and C. L. E. Moore.

AN ALGEBRA OF PLANE PROJECTIVE GEOMETRY.
By H. B. Phillips and C. L. E. Moore.

Presented by H. W. Tyler, February 14, 1912. Received January 29, 1912.

Introduction.

1. The Ausdehnungslehre of Grassmann ^ has been applied to prob-
lems in geometry in two ways. In the form of vector analysis it has
been used in solving problems of a metrical type. In the form of point
analysis (with homogeneous coordinates as a basis) it has been used in
problems of a descriptive nature. In projective geometry both of these
methods have certain advantages and also certain disadvantages. The
values of distances and angles occurring in vector analysis are useful as
variables in terms of which to express projective relations. Yet the fact
that these quantities are invariant under Euclidean motion has no place
in projective geometry. The ternary form of the point algebra is of
great value, but it is a decided disadvantage that XA and A (where A
is a point) though distinct are not descriptively distinguishable. It is
our aim in this paper to show how this coefficient A can be interpreted
as an angle invariant under a group of motions determined by the alge-
bra itself and thus while using the homogeneous form retain the essen-
tial advantages of the metrical system.

"We first develop the two systems of analysis in a purely projective
way. Assuming that points and lines are represented by letters and that
addition follows the usual laws, we find that there must exist exceptional
elements somewhere in the plane. In fact, expressions AA, where A is a
point and A infinite, are not subject to the laws of addition. In the lan-
guage of coordinate geometry such points correspond to infinite values of
the coordinates and hence lie on a line. Likewise the lines Aa where a
is a line and A infinite are exceptional lines passing through a point.
Thus in such a system of algebra there exists a fixed point and a fixed
line. We define our additions relative to these. In the vector addition
the sum of two points A and B is a point C such that the harmonic of
the singular line with respect to C and the fixed point is the harmonic
of the same line with respect to A and B. This addition is characterized

^ Gesammelte Werke, Vol. I, 1896.

VOL. XLVII. — 47

738 PROCEEDINGS OF THE AMERICAN ACADEMY.

by the fact that AA is in general distinct from A. In the point addition
the sum of two points A and B is the harmonic of the singular line with
respect to those points. For this addition A.A is in general coincident
in position with A. The two additions are closely related. In fact, each
is representable in terms of addition processes of the other kind. When
the singular line is taken at infinity these additions agree essentially
with those of Grassmann.

2. In the case of point addition A and XA have the same position.
According to Mobius these quantities differ in weight. To give a geo-
metric interpretation to this weight we conceive a point as a sort of
double fan-shaped spread consisting of all the lines through the point
and between two limiting lines. The size of the point is then measured
by the angle (directed) between these limiting lines, and the weight of
the point is this angle. We are thus led to define a species of angle in
which the total angular magnitude about a point is infinite. The finite
angle determined by two lines is that one which does not contain the
singular point.

In the same way we represent a line by a segment; of itself and the
magnitude of the line by the length of that segment. We thus define
a sort of distance in which the locus of point at a fixed distance from a
given point is a straight line. This distance between two points is the
dual of the angle between two lines. It has a definite algebraic sign
and along each line not passing through the singular point assigns a
definite positive direction.

Distance and angle are invariant under a three-parameter group of
collineations (projectively equivalent to motions leaving area invariant)
for which the singular point and line are fixed elements. These colline-
ations leave invariant the correlations having the fixed point and line
as coincidence loci. There are two cases depending on whether the
fixed point is on the line or not. The first of these gives a distance
theory similar to that in a minimum plane. The second does not occur
as a special case of distance defined relative to a conic.

3. In terms of this linear distance and angle there is a very simple
theory of the triangle. Most rational relations of ordinary trigonometry
involving distances and sines of angles are replaced by similar relations
involving distances and angles. In case the singular point is on the
singular line there is a linear relation between the sides and also between
the angles of a triangle making both distance and angle similar to angle
in ordinary geometry. If the point is not on the line, however, any
three parts determine the triangle. Every part is then rationally ex-
pressible in terms of any three, and similar triangles do not exist.

In this system there is no right angle, and distance from point to line

PHILLIPS AND MOORE. — ALGEBRA OF PROJECTIVE GEOMETRY. 739

does not properly exist. There is, however, a number associated with a
point and line which has some of the properties of distance from point
to line. We define an area that has the usual sum properties and in
fact becomes identical (after proper choice of unit) with Euclidean area
when the singular line is thrown to infinity.

In the course of the work we use the notations AB and ABC for seg-
ment and area respectively. Interpreting these as products we find that
they have the properties of Grassmann's products. They are definable
in terms of our distance, angle and area, in the same way that outer
products are expressible in metrical concepts of Euclidean geometry.

The method used in this paper is not postulational. In fact, we are
more interested in the results than in the method of obtaining them.
In some cases our definitions have not been as simple as possible. In
accordance with our primary aim we have interpreted quantities neces-
sarily existing in the algebra instead of introducing notions that were
not required.

4. It is our purpose to use this scheme in the solution of problems
in projective geometry. Two ways of doing this are suggested. In the
first place the above scheme of distance and angle gives us a great va-
riety of coordinate systems. We may, for example, represent a point
by its distance from two fixed points (singular point not on singular
line) and a line by the angles it makes with two fixed lines. The equa-
tions of point and line are then of first degree and the incidence relation
bilinear. The distance between two points is a bilinear function of their
coordinates. Similarly for the angle between two lines. The differen-
tial of arc is of the form

xdy — ydx.

A kind of curvature is easily defined and thus we build up a differen-
tial projective geometry of plane curves.

In the second place we may start with the theory of the triangle. In
terms of our distance, angle and area, we can then express descriptive
relations such as perspectivity, inscribability in a conic, etc., and by pro-
cesses similar to those in Euclidean geometry determine fi-om these their
projective consequences. This is especially easy since the expressions
determining one part of a triangle in terms of three others are all ra-
tional. It is our intention to develop these applications in a later
paper.

§ 1. Addition.

5. The addition of two points A, B naturally divides itself into two
cases depending on the significance given to AA. In metric geometry
these two additions have been defined in terms of metric concepts. If

740

PROCEEDINGS OF THE AMERICAN ACADEMY.

AA 2 is a point different in position from A, the addition familiar to
all is the well known vector addition. If AA is a point coincident
in position with A, but differing from it in magnitude, the sum of two
points is commonly defined as the centroid of the two points. We
shall here define these two additions in terms of projective notions.

Vector Addition.

6, To define the sum of two points A, B when A times a point differs
in position from it, we assume a line f as reference line and a point 0
as origin. Then the sum A + B is the point C determined as follows:

Figure 1.

Let D be the harmonic of f with respect to A, B. Then take a point
C so that D is the harmonic of f with respect to C, 0. The point C
thus obtained is the point required, and we express the relation be-
tween the points by the equation

A + B = C.

(1)

The geometric construction for C is shown in Figure 1, and is seen to
be the ordinary vector construction where the line f has replaced the
line at infinity.

From the above definition the point

A + A = 2A

* In this paper capitals will be used for points, small letters for lines.
Points or lines occurring as algebraic quantities will be represented by claren-
don type, their magnitudes by italics. Geometric points or lines may, how-
ever, be represented by italics when no ambiguity results. Greek letters will
be used for numbers.

PHILLIPS AND MOORE. — ALGEBRA OF PROJECTIVE GEOMETRY.

741

is the point on the line OA such that A is the harmonic of f with re-
spect to 2A, 0. The point

2A + A = 3A

from the definition is constructed as follows: Let C be the harmonic
of f with respect to 2A, A and then construct the point 3A so that C
is the harmonic of f with respect to 3A, 0. It is at once seen from

3A

the construction of 2 A that C is the point — - . From the theory of

cross ratios it is also seen that the relation between 3A, A is expressed

by the cross ratio

(0,f|3A, A) = 3.

In like manner the points AA for integral values of A are constructed.
If X is the reciprocal of an integer /*, the point AA can be constructed
thus: Take a point B not on the line OA and construct the points

B, 2B, 3B, fiB.

Figure 2.

Connect /iB to A and let the line cut f in P. Draw a line from the point
B to P. Where PB cuts 0 A is the point required, for the same harmo-
nic relations hold among the A's as among the B's. The construction
of the points AA for rational values of A is now evident. For irra-
tional values of A the construction is obtained by limiting processes.
From the theory of cross ratios it is seen that the relation between A
and AA is expressed by the cross ratio

742

PROCEEDINGS OF THE AMERICAN ACADEMY.

(0,f|AA,A)=X,

and every point on the line OA can be represented in the form XA.

7. The point

AA + fjiB,

where A and B are not collinear with 0, is constructed in the same
way as the point A + B, and has the following relations to the points
A and B.

Figure 3.

(1) The point H where the line joining 0 to XA + /tB cuts the line
AB is such that

(Hf|AB)=-^

A

AA + mB = (A + /x)H. (f)

In order to prove the above relations we shall first prove the fol-
lowing lemma :

^ two lines intersecting in 0 and cutting / in Q and R are cut hy
two other lines {intersecting f in P, S) in A, C and B, D respectively,
and if through 0 any arbitrary line is drawn cutting AB in H, CD in
K, and fin T, then

(OQiAC)_(HP[AB)

(ORIBD) (KSICD)*

PHILLIPS AND MOORE. — ALGEBRA OF PROJECTIVE GEOMETRY. 743

Figure 4.

Let M be the intersection of AB and CD, and project all points on f
from 0 and M. The two ratios above can then be written as follows :

(OQIAC) _ (LQJPS) _

(OR I BD) ~ (LR I PS) ~ ^^^ ' ^^^

(HP|AB)_(TP[QR) _ .

(KS I CD) (TS I QR) ~ ^ ' ^^^ '
but (RQjPS) = (SP|QR),

which proves the lemma.

If we apply the above lemma to Figure 3, replacing C by XA, D by
fiB, and K by ^ (AA + /xB), it is at once seen that H divides AB in

the cross ratio — - with respect to f For, in this case.

(KS|CD)=-1,

(OQIAC) = i,

(OR|BD) = --
From which it follows that

(HP|AB) = -^.

A
This shows that H is independent of the position of 0.

744 PROCEEDINGS OF THE AMERICAN ACADEMY.

To prove the second relation connecting A, B, H we have from the
lemma

(OQ|AAA)_ (BF|AH)
(OTIHK) ~(/.BSi\AK)'

and, from the theory of cross ratios,

(OQ|AAA)=^,

(BP[AH) = ^,

(/iBS|AAK) = 2.

Therefore

(OT|HK) = -^ or (OT|KH) = ^ + '*

A+M V I / 2

This last relation is equivalent to the statement that

But

K = i (aA + fxB).
Therefore

XA + mB = (A + m) H. (2)

8. From the construction of A + B the sum is seen at once to obey
the following algebraic laws :

A + B = B + A,

AA + AiA = (A + )u) A.
If A + B = A + C then B = C.

The associative law

(A + B) + C=A+(B + C) = A + B4-C

evidently holds for points on a line passing through 0. To prove that
it holds for any three points A, B, C, project them on a line drawn
through 0 from two different points P, Q on f Let the projections be
A', B', C and A", B", C". The sum A + B + C will project into
A' + B' + C and A" + B" -f C". The sum A + B + C will then be

PHILLIPS AND MOORE. — ALGEBRA OF PROJECTIVE GEOMETRY. 745

at the intersection of the line joining P to A' + B' + C with the line
joining Q to A" + B" + C", which is independent of the way in which
A, B, C are combined.

9. For the dual of the above addition we assume a point 0' as
reference point, and a line f as reference line. Then from duality we
see that the lines Aa all pass through the same point on f. The sum
a + b is formed by drawing a line c harmonic of 0' with respect to
a, b. Then drawing the line d so that c is the harmonic of 0' with
respect to f ', D, the relation between c, d is

d = 2 c.

The relations between Aa, fxh, a, b are the same as in the case of
points. That is, the line h joining the point of intersection off and
Aa + /*b with the point of intersection of a, b is such that

(hO'iab)^-^ (1)

Aa + ^b = (A + fx) h. (2)

The reference elements 0', f need not be the same as 0, f. How-
ever, if the addition of points and its dual are to be used together, the
line joining AA, AB should be X times the line joining A, B. The line
joining AA to AB intersects the line AB on f, for XA and AB (for vari-
able A) are two projective ranges with 0 as self-corresponding point,
and consequently the ranges are perspective. The line f joins corre-
sponding points (corresponding to the infinite value of X) and therefore
lines joining pairs of corresponding points must pass through the same
point on f Then if the line joining A A, AB is to be A times AB the
line f must coincide with f The dual argument will show that 0'
should coincide with 0. The fundamental or reference system for this
vector addition then consists of a line f and a point ().

The line f is exceptional in the addition for there is no way shown of
finding the sum of two distinct points on this line.

Point Addition.

10. In this case AA 3 is coincident in position with A but differs from
A in magnitude. The number A indicates the magnitude of XA. In
the case of vector addition we saw that all points on a line through 0

^ Throughout the discussion of point addition points denoted by A, B, C, . . .
will always be understood to be unit points.

746 PROCEEDINGS OF THE AMERICAN ACADEMY.

can be represented as multiples of one of them. Then if an arbitrary
line AB, not passing through 0, is drawn in the plane, all points on a
line through 0 can be expressed as multiples of the point in which
this line cuts AB. Now project all points of the plane on the line AB.
Each point in the plane will be uniquely represented on AB if we use
the following convention for magnitude. Let K be any point and let
OK intersect AB in C. If K = AC we shall say that the projection on
AB of the point K is the point AC. That is, the point in which K pro-
jects is considered as having a magnitude X and is coincident in posi-
tion with C. We thus see that all points on OK will project into the
same point C, but the projection of each point will be looked upon as
having a diiferent magnitude. Now to find the sum XA + fxB we will
consider AA and fxB as represented vectorially and find the vector sum,
then project the three point AA, /xB, AA + /^B on AB. The projections
will have the magnitudes X, fx, \ + /x (see equation (2)) respectively.
If the point AA + fxB projects into (X + fx) C then for points on the
line AB we shall say that

AA -h /aB = (A -f fi) C.
From equation (2) the point C is such that

(Cf|AB) = -^.

The definition of this sum is then independent of the origin chosen for
the vector addition. The reference element for this addition consists
of the line f and we have : The sum of two points AA, /xB of magnitude
A, fx respectively is a point (A -f /i) C of magnitude X -\- [i, dividing

A, B in the cross ratio — ^ with respect to f.

A

The line f is a line of exceptional points. The sum of two distinct
points on this line is not defined and the sum of two coincident points
on f may be any given point of the plane, and therefore violates the
uniqueness of the sum ; besides, A times a point P on f is not necessarily
a point coincident in position with P.

The magnitude of the sum was seen to be the sum of the magnitudes.
The difference

A-B

will be a point P of magnitude zero such that

(PflAB) = l.

and consequently P must be on f This point P is an exceptional point
then because it is of zero magnitude and yet is not algebraically equiva-

PHILLIPS AND MOORE. — ALGEBRA OF PROJECTIVE GEOMETRY. 747

lent to zero. The line f plays the role of the line at infinity, and the
point P of zero magnitude is analogous to zero times infinity.

11. By duality we obtain a definition for the sum of two lines Aa,
/jib of magnitudes A, fi respectively. For this addition we assume a
fundamental point F and

Xa + fjib

is a line c of magnitude A + /t* such that

(CF|ab)=-^.

The point F is an exceptional point, i. e. all the lines passing through
F are exceptional in the same sense in which the points on f were ex-
ceptional. The difference a — b is the line of zero magnitude joining
the point F to the intersection of a and b. Here also the Hue of zero
magnitude passing through F is not algebraically equivalent to zero
but indeterminate. It is analogous to zero times infinity. The com-
plete fundamental system then consists of a line f and a point F.

12. Starting with the definition of point addition the vector addition
could be derived from it. Thus take a fixed point 0 and represent
any point A in the plane by the difference 0 — A. The addition of
these quantities will lead exactly to the vector addition with which we
started. The two additions are then related in such a way that either
can be derived from the other.

From the definition of point addition as derived from the vector ad-
dition it follows that the point addition obeys the same algebraic laws
as the vector addition.

Vectorially any point in the plane can be expressed in terms of two
independent points A, B, where the line AB does not pass through 0.
Then choosing A, n properly any point in the plane can be represented
by A A -I- /xB. For the point addition, however, AA + //B represents
only the points of the line AB, where neither A nor B is on f. In this
addition, however, any point X of the plane can be expressed as

where A, B, C are three non-collinear fixed unit points not on f. That
is, the numbers A, ft, v can be so determined that this relation holds for
any point whatever of the plane. To show this connect X to B. This
line will cut AC in Q, which can be expressed in terms of A and C.
Then X can be expressed in terms of Q, and B. Thus

(A + I/) a == AA -h . C
{\ + H + v)X = (k + v) a + mB = ^A -f ^B + vC.

748 PROCEEDINGS OF THE AMERICAN ACADEMY.

Since A, B, C are linearly independent, if

A + /i + v = 0

then X is on f.

From the above equations

(A + /i + v) X - yuB = (A + v) a.

Hence

A + n -r V

where P is the point in which BQ cuts f. Similar relations involving

A, V can be obtained. Since A, fx, v are proportional to uniquely de-
termined cross ratios the expression for X is unique.

§ 2. Distance and Angle.

13. We have considered two kinds of addition, either of which is
expressible in terms of the other. The vector addition gives for the
points of the plane a non -homogeneous, two-dimensional representa-
tion, the point addition, a homogeneous three-dimensional. The latter
is more satisfactory for descriptive problems and will be assumed as
the fundamental addition throughout the remainder of this paper. It
has been remarked that expressions of the form B — A, when A and
B are unit points, then combine according to the vector addition.
Through a study of their expressions we shall derive a sort of distance
that is intimately connected with the subject under discussion.

14. Vectors. We have seen that B — A represents a point of zero
magnitude on f We might infer that, if

B - A =- D - C,

the lines AB and CD pass through a common point on £ This is
proved by writing the equality in the form

A + D = B + C.

The line f thus has the same harmonic E with respect to A, D and

B, C. Let AD and BC cut f in P and Q. Then from the intersection
of AB and CD the points A, E, D, P and B, E, C, Q are perspective.
Since f joins two corresponding points, it must pass through the inter-
section of AB and CD. Writing the equality in the form

A-C=B-D

PHILLIPS AND MOORE. — ALGEBRA OF PROJECTIVE GEOMETRY.

749

we see also that AC cuts BD on f. Thus the relation of the four
points is shown by the diagram (Figure 5).

Figure 5.

Conversely, if the points A, B, C, D have the positions shown in the
figure, f has the same harmonic with respect to A, D and B, C, or

Consequently,

A + D = B + C.
B - A = D - C.

If the four points lie on a line cutting f in P, we project, irom some
other point on f, the points A, B to M, N on a second line through P.
Then from the intersection of MC and f we project N to D' on AB.
By construction

B-A = N-M = D'-C
Hence, if

B - A = D - C,

the points D and D' must coincide. The relation of the four points is
shown in Figure 6.

The quantity B — A has properties very similar to those of the
vector AB in the ordinary vector analysis. In fact, the expressions
B — A add exactly like vectors if the line f is at infinity. On account
of this similarity we shall use the term vector to indicate the quantity
B-A.

750

PROCEEDINGS OF THE AMERICAN ACADEMY,

If

B - A = A (D - C)

(3)

we might say that AB is X times as long as CD. In what follows we
shall assume this relation of lengths only when the points A, B, C, D
lie on a line. In that case A, B can be expressed as linear functions of
C, D, those points being assumed to be distinct and not on f Since
the sum of coefficients in any linear point identity must be zero, the
expressions will be

Then

Hence

Now from (2) we have

Figure 6.

A = Ai C + (1 - Ai) D,

B = A2 C + (1 — Aa) D.

B - A = (Ai - A2) (D - C).
A = Aj — Aj.

^^= (API CD)

where P is the intersection of CD with f. Hence from the properties
of double ratios

Ai = (AC|DP),
A2 = (BC|DP).

PHILLIPS AND MOORE. — ALGEBEA OF PROJECTIVE GEOMETRY. 751

And consequently

A = (AC I DP) -(BC I DP). (4)

It is to be observed that X is finite for all positions of A and B dis-
tinct from P, but becomes infinite when one of these points coincides
with P. One of the points A or B being fixed, there is an unique
position of the other which gives A a particular value.

Distance.

15. In this way we determine the relation between the magnitudes
of vectors on lines intersecting on f, but arrive at no relation between
vectors not so situated. To obtain a more general relation we define
distance as a scalar quantity, or number, determined by two points
not on f and such that distances AB * along any line are proportional
to the corresponding vectors B — A. In symbols

distance AB = AB = K(B - A)

when K is a constant for pairs of points A, B on a given line but may
(and usually does) change from line to line.

It is not obvious that there exists a distance satisfying the above
definition. We shall first show (if it exists) what such a distance
must be. We shall find that it is not unique and then shall make a
further assumption of a function theoretic nature. Finally we prove
that the distance found has the properties required.

From the definition we see that for points on a line, if

B - A = \ (D - C),

AB = XCD.

From the latter equation follows the former provided AB is not zero.
In particular

AB = - BA (5)

showing that distance is directed. Putting in this equation B = A,
it follows that

AA = 0. (6)

Furthermore, since

B-A + C-B = C-A,

* The notation AB will be used to denote the distance from A to B.

752 PROCEEDINGS OF THE AMERICAN ACADEMY.

for collinear points

AB + BC = AC. (7)

16. Distance on a line. The definition of distance can be satisfied
for points on a given line in two ways.

(1) There may exist two points C, D on the line such that CD is
finite and not zero. For every number X and point A of CD there
exists an unique point B on CD such that

A - B = A (C - D),

Hence there exists an unique point on the line at any given distance
from the point A.

(2) There may exist two distinct points C, D on the line such that
CD equals zero. In this case the above equation shows that the
distance between any two points on the line CD (but not on f) is zero.
For the point P in which CD cuts f, X is infinite. Hence

AP= 00 • 0

is indeterminate. We assume that this distance may have any value
whatever. Here again we find an unique point at a distance not zero
from A.

Along most lines our distance will be of the first type. Along
certain lines, however (analogous to minimal lines in metric geometry),
distance will be of the second type.

17. Distance in the plane. Along each line through a point A is
a single point at a given distance from A. There is a certain locus
of these points. We assume that this locus is an analytic curve.
Since it cuts each line through A in a single point it is then a straight
line. Thus the locus of points at a given distance from a given point
is a straight line.

We assume that there exist distances AB not zero. Let

where ^ is a constant not zero and A, B points not on f. If A is held
fixed B describes a line b cutting f in P. If B is held fixed A describes
a line a cutting f in a point Q. Distance along any line through A
except AP is of type (1). Along AP it is of type (2). Similarly
distance along every line through B except BQ is of type (1). Let
the intersection of AP and BQ be F. Through any point Ai except F
there passes a line AiA or AiB along which distance is of type (1).
Therefore, for any such point Ai there exists a line of points b, such

PHILLIPS AND MOORE. — ALGEBRA. OF PROJECTIVE GEOMETRY. 753

that AiBi = k. The only line through Ai for which distance is of
type (2) is the line joining Ai to the intersection of bi and f The
intersection of two such lines must be exceptional, and since F is the
only exception it follows that along any line through F the distance
between two points not on f is zero and conversely if the distance
between two non-coincident points is zero, their joining line passes
through F.

We have just shown that if in the relation

AB = ^

A is held fixed, B describes a line b cutting f in a point P on the Hne
AF. To determine more exactly this relation between A and b we
consider the pairs of points A, B along a line CD not passing through
F. On this line A and B satisfy an equation

B-A=D-C

where C, D is a particular pair. From the construction for equal
vectors it is seen that A, B are corresponding points of a collineation on
CD for which P is the only double point. In general to each point A
corresponds a line b and for fixed B, A lies on a line. Hence to points
A on a line CD correspond lines b through a point. Furthermore,
these lines b pass through points B which are projective on CD with A.
The correspondence between A and b is therefore a correlation. Since
A and B coincide only on f, that line is the locus of points lying on
their corresponding lines. To a point P on f corresponds a line through
P. The distance from P to any point of this line being finite the dis-
tance between ordinary points on the line must be zero. Hence the
line passes through F. This is true whether we hold A or B fixed on
f Hence F and f are corresponding elements in the correlation.

The preceding results may be summed up in the statement that if
AB and CD are equal, B and D lie on the correspondents of A and
C with respect to a correlation in which F and f are corresponding
elements and f the coincidence locus. The construction of these cor-
relations depends on whether F is or is not on f

18. Point F on line f. We first consider the case in which the
point F is on the line f We have seen that the locus of points at a
given distance from a point A is a line through the intersection of
FA with f In the present case all such lines pass through F. The
correlation that determines equal distance is degenerate with F as
singular point. The distance from this point to any point whatever
is indeterminate.

VOL. XLVII. — 48

754

PROCEEDINGS OF THE AMERICAN ACADEMY.

Take two lines AC and BD passing through F. Since all points of
BD are at the same distance from A and all points of AC at the same
distance from D, and AB = — BA,

AB = AD = CD.

Figure 7.

Therefore the distance from any point of a line through F to any point
of another line through F is constant. The distance between two
points depends only on the lines joining them to F.

Figure 8.

Take any line CD, not passing through F, as a scale. Let distances
along this line be proportional to the corresponding vectors. Then
any distance AB is equal to the distance CD into which it projects

PHILLIPS AND MOORE. — ALGEBRA OF PROJECTIVE GEOMETRY. 755

from F. The ratio of two vectors on a line is a difference of double
ratios involving the end points of the vectors and the point of inter-
section of their line with f. That ratio is then unchanged when we
project from F upon another line. Therefore distances as here con-
structed are proportional along any line to the corresponding vectors
and consequently satisfy our definition.

In this case equal vectors are always of equal length, i. e. the oppo-
site sides of a parallelogram are equal (parallel lines intersecting on f ).
This is shown in Figure 8. Let ABCD be a parallelogram. Draw FA
and FB to cut CD in M and N. Then since the vectors MN and CD
are equal,

AB = MN = CD.

We shall see later that if F is not on f, equal vectors on different lines
are not in general of equal length.

Figure 9.

19. Point F not on line f. If F is not on f, the locus of points at a
given distance from a point A is a line through the point P in which
FA cuts f. The locus of points at a constant distance from P is the
line FP. The equation

AB = ^

gives for fixed A a line b, the locus of points B, and b is the corre-
spondent of A in a certain correlation. If a certain point G and its

756 PROCEEDINGS OF THE AMERICAN ACADEMY.

corresponding line d are given, we construct b the correspondent of A
as follows. Draw AF and CF cutting f in P and Q and let CA cut f in
E,. To R corresponds the line FR. Then since three points A, C, R
on a line must have corresponding to them three lines through a point,
b, d, and FR pass through a point. Let d cut FR in K. Then PK is
the line b required. The construction is shown in Figure 9.

To construct on any line through A a distance AB equal to a distance
CD, we construct the line b and where it cuts the line through A is the
point B required. If on a fixed line CD we determine a scale making
distances along that line proportional to the corresponding vectors
D — C, our construction enables us to transfer the scale to any other
line except f and so to assign to every pair of points, not on f, a dis-
tance. We must still show that this construction is consistent (if two
distances so constructed are equal to a third, they are equal to each
other) and that the resulting distance has the properties assumed in
the definition.

We first show that if C and D (Figure 9) are held fixed, A and b are
correspondents in a correlation. The figure gives for each point A an
unique line b. If A moves along a line, since F and C are fixed, P and
R describe, on f, ranges projective with A. Also K describes on d a
range projective with R. Therefore P and K describe on f and d pro-
jective ranges. Also when A is on CF, P and R, and consequently K,
are at Q. Since the ranges on f and d have a self- corresponding point
Q, the line PK passes through a fixed point. Thus as A moves along
a line, b turns about a point. Furthermore, b describes a pencil projec-
tive with the range described by A. The correspondence between A
and b is therefore a correlation.

In particular if A is on f, A and R coincide. To R therefore cor-
responds the line RF. Also if A is at C, b coincides with d. The
fact that Ab, Cd, and R, FR are pairs of corresponding elements in a
correlation shows that the three lines intersect in K and thus deter-
mines the relation between A, B and C, D. If AiBi and A2B2 are both
equal to CD, we have just shown that Ai, bx and A2, b2 are correspond-
ing pairs in a correlation which gives for a point R on f the line RF.
Therefore Ai, Bi and A2, B2 are related by the same kind of diagram
as A, B and C, D. Consequently, if two distances are by this con-
struction equal to a third, they are equal to each other.

We now show that distances as constructed along any line AB are
proportional to the corresponding vectors B — A. We have already
remarked that vectors along a line preserve their ratios when projected
upon another line from a point on f. If we hold A and C fixed
(Figure 9) we may consider AB as resulting from CD by first projecting

PHILLIPS AND MOORE.

ALGEBRA OF PROJECTIVE GEOMETRY.

757

from Q upon RF and then from P upon AB. Vectors on AB have
therefore the same ratios as vectors on CD. Since distance has been
defined as proportional to the vector along CD, it is proportional to the
vector along any other line AB.

20. It has been mentioned that two vectors on different lines may
be equal though their lengths are not equal. This is shown in
Figure 10. Let AC and BD intersect on f at P and let AB, CD cut
PF in M, N. The vectors AB and CD are equal. Suppose now

Figure 10.

Then, by proportionality

and

Also since NA = NC,

AB = CD.

AM = CN,

BM = DN.

AM = AN.

Consequently P must be on the line AF. For the same reason B lies on
the line FP. The vectors AB and CD are then zero. Non-vanishing
equal vectors on different lines can not have the same length unless the
point F lies on the line f

21. Summary. In this section we have found a species of linear
distance defined by a point F and line f The distance between any
two points on a line through F (but not on f) is zero. The distance
between a point on a line through F and the point in which that line
cuts f is indeterminate. The distance between two distinct points of a
line not passing through F is finite and not zero but becomes infinite

758

PROCEEDINGS OF THE AMERICAN ACADEMY.

when one of the points is on f. The locus of points at a constant dis-
tance from a point A is a line b through the intersection of FA with f.
For fixed distance A and b are correspondents with respect to a definite
correlation in which F and f are corresponding elements and f, the
locus of points whose lines pass through them. On any line distances
AB are proportional to the vectors B — A. Equal vectors on different
lines have equal length if F is on f, but not otherwise.

Angle.

22. Point vectors. Just as A — B may be considered as a point of
zero magnitude on f, or as a vector associated with the segment AB not
crossing f, so a — b may be considered as a line of zero magnitude
passing through F or as a point vector associated with the angular seg-
ment (or vector) not containing F.

Figure 11.

Point vectors have properties dual to those of line vectors. Thus, if

a — b = 0 — d

ac and bd are points of a line through F. The relation of the lines a,
b, c, d is shown in the diagram (Figure 11).

If a-b = X(c-d)

where c, d are distinct and a, b, c^ pass through a point, we shall say
the angle ab is X times the angle cd. In this ca.se, if p is the line join-
ing F to the common point,

A=(ac|dp)~ (bcldp) (8)

PHILLIPS AND MOORE, — ALGEBRA OF PROJECTIVE GEOMETRY.

759

and X is finite for all positions of a and b distinct from p but becomes
infinite when one of these lines coincides with p.

23. Definition and properties of angle. We now define angle as a
scalar quantity determined by two lines not passing through F and
such that pairs of lines through a point give angles proportional to the
corresponding point vectors. We further assume that one of the lines
being fixed and the angle kept constant, the locus of the other line is
an analytic curve. That locus is then a straight line.

Figure 12.

Angle is thus the dual of distance. We find accordingly that there
exists a line f such that if two lines (not passing through F) intersect
on f, their angle is zero. If one of the lines passes through F, the angle
is indeterminate. Two lines not intersecting on f determine an angle
that is not zero. This angle is finite if neither of the lines passes through
F, but infinite if one of them passes through that point. If

ab = k,

the locus of b for fixed a is a point B on the line joining fa to F. The
correspondence between a and B is a correlation in which f and F are
corresponding elements and F is the locus of lines passing through their
corresponding points. There are two cases depending on whether F is

760

PROCEEDINGS OF THE AMERICAN ACADEMY.

on f, or not. The constructions for equal angles are shown in Figures
12 and 13. _ _

The equal angles are ab and cd. In Figure 12,

h-k = l

m.

24. In the discussion of distance we found besides the fixed line f
(locus of exceptional points in our algebra) a fixed point F', that need

FiGTTRE 13.

not be the fixed point of our algebra. Again in the discussion of angle
we have a fixed point F (locus of exceptional lines) and a fixed line f ,
which need not be the fixed line occurring in the algebra. If we trans-
form the plane by a coUineation leaving F', and f fixed, the ratios of dis-
tances will not be changed. If then there are to exist fixed relations
between distances and angles in a figure (between sides and angles of
a triangle, for example) the ratios of angles must be at the same time
unchanged. We therefore choose the same fixed elements for distance
and angle. These must then be the exceptional elements F and f in
our algebra.

Distance as here discussed has a definite algebraic sign and hence
along every line is assigned a definite positive direction. In Euclidean
geometry there is no definite direction along a line because by a rotation
preserving distance one direction can be turned into the other. That
it is not possible, by our construction for equal distances, to rotate one

PHILLIPS AND MOORE. — ALGEBRA OF PROJECTIVE GEOMETRY.

761

direction along the line into the other is shown in Figure 14. Rotation
of AB around A causes B to describe the line BP. We have defined
AB to be the segment not crossing f. Hence, as B passes P, the seg-
ment AB changes into the segment AB' not crossing f (i. e. connecting
A to B' by way of infinity). Thus all segments into which AB can be
rotated lie on the same side of AF and consequently one end of the line
AB cannot be rotated into the other.

Figure 14.

A point describing (from A to B) any one of the segments AB (Figure
14) determines the same direction of rotation about F. Distances are
then positive or negative according as their description gives rotation
in one direction or the other around F.

Similarly the angle ABP is the angle which does not include F. If
A is held fixed and B moves along BP, the angle is not changed. As
B passes P the angle changes into AB'P. If around B we rotate the
side AB into the side BP, the direction of translation (of the point of
intersection of AB with f ) along f is always the same. Hence an angle
is positive or negative according as this translation along f is in one
direction or the other.

In Euclidean geometry we have an unique direction of angle about
any point since the equation

angle = const.,

one side being fixed, factors into two linear conditions and so gives a
separation of classes, but no definite direction along a line since

distance = const.,

762 PROCEEDINGS OF THE AMERICAN ACADEMY.

one point being fixed, is an irreducible quadratic form. Our distance
and angle are more like Euclidean angle tban Euclidean distance.

Metric representation of points and lines.

25. We wish to obtain a representation of point and line which dis-
tinguishes A and AA in the case of point addition. Then AA is coinci-
dent in position with A but diflFers from it in something that we have
called magnitude. Grassman replaced a line by a segment joining two
of its points. Then a and Aa give segments differing in length. We
wish in this section to determine, if possible, a representation in which
a line is replaced by a segment beginning at an arbitrary point of the
line, and a point by a sector beginning at an arbitrary line through the
point and to determine an addition of these segments or sectors such
that their addition relations shall be the same as those of the corre-
sponding lines or points.

Consider the lines through a point A not on f We assume that to
a line through A, corresponds a segment AB, to a segment AB a point
B, and conversely. Since there is a [1,1] correspondence between the
lines and the points B, it follows that to an addition of lines corresponds
an addition of points, and that the two additions have the same formal
laws. Since a and Aa are represented by different segments, B and AB
are different points. The addition of points thus suggests the vector
addition of § 1. The segments corresponding to lines through a point
should then add like vectors from that point as origin. Distances along
a line being proportional to the corresponding vectors, a and Aa should
be represented at A by segments whose lengths have the ratio A.

We thus represent a line of magnitude A by a segment of length A
joining two points A, B of the line. Unit lines are represented by
segments of unit length. These segments are like localized vectors in
physics. Segments on the same line are proportional to their lengths.
Segments on different lines may be added by moving them to the point
of intersection of the two lines and there adding them like vectors.

To add two lines Ac, /xd, of magnitudes A and fi, we construct, at
their point of intersection A, segments of lengths A, ju, ending in the
points C, D. We then draw through A and the harmonic of f with
respect to C, D the line h required. Our earlier method of constructing
the sum Ac -\- fid. was to draw a line h through A such that

(hd|cF) = -^.

That the two constructions are consistent follows since F and P (Fig-

PHILLIPS AND MOORE. — ALGEBRA OF PROJECTIVE GEOMETRY. 763

ure 15) determine the same cross ratios with triads of lines through A.
In fact, let

It was shown in § 1 that

ABi = AB2 = 1.
A (ABO + H- (AB2)

Figure 15.

intersects B1B2 in a point H such that

(HBi I B2P) =

M

26. To add two segments we have moved them to the point of in-
tersection of their lines. If the two lines intersect on f, this is not pos-
sible. We shall now derive a construction for the sum of two segments
not at the same point. We have seen that equal vectors along a line
(also equal segments on a line) project from a point on f into equal
vectors on any other line. Since the sum of segments at a point is
determined by harmonic constructions involving only those segments
and f, it follows that addition relations connecting segments through a
point are projective from a point on f Any sum of segments may be
found by a succession of processes consisting of moving two of the seg-
ments to the point of intersection of their lines and then adding them
vectorially. Hence any linear relation connecting segments holds for
the projections of those segments upon any line from a point on f

764

PROCEEDINGS OP THE AMERICAN ACADEMY.

This gives us a means of constructing the sum of two segments AB

and CD. Let DA and BC cut f in P and Q. The sum AB + CD lies

on some line LM through the intersection of AB and CD. From P

(Figure 16) AB + CD is projected upon any line into a segment limited

by the lines PC, PB. Likewise from Q it projects into a segment

limited by QA, QD. Let PC intersect QA in L, and PB intersect QD

in M. Then

AB + CD = LM.

-f5»

M

Figure 16.

27. Just as we represent a line by a segment (sequence of points
between two given points) so we represent a point by a sector (sequence
of lines between two given lines). The sector used is the one no line
of which passes through F. A point of magnitude A is represented by
a sector of angle A.

We conceive that the points in a discussion are thus replaced by
fan-shaped spreads (the lines extending on both sides of the point).
This spread, or sector, may be rotated about its vertex without chang-
ing its value by merely keeping the angle constant. Two of these
sectors may be added vectorially after turning them around until the
initial lines are the same. Let the sectors then be ab and ac and let
the harmonic of F with respect to b and c be d. Then

ab -I- ac = 2ad.

The sum of any two sectors may be found at once by a construction
dual to that for adding segments (Figure 17).

PHILLIPS AND MOORE. — ALGEBRA OF PROJECTIVE GEOMETRY. 765

We thus have two means of finding the sum

AA + fxB.

The one is an anharmonic construction involving the points A,B and
the line f. The other is a harmonic or vector construction involving
the sectors A.A, nB and the point F. These constructions are both used
in ordinary geometry, but the one only for adding points, the other
only for adding lines. We have used both constructions in dual forms
for both purposes.

>r

Figure 17.

§ 3. The Triangle.

28. In this section we shall apply the notions of distance and angle,
as given in the previous section, to the study of plane figures, in par-
ticular to triangles. We have already seen that many properties are
quite different according as the point F is on the line f or not. We
shall therefore consider these two cases separately, taking first the
case in which F is not on f and then the other as a special case.

Case I. Point F not on line f.

29. Relation between distance and angle. A comparison of the
construction for equal distances with that for equal angles shows that
the two are given by the same diagram. The group of collineations
that leaves distance unaltered will then leave angle unaltered and con-
versely. We should therefore expect these quantities to be related.

When A is fixed and

AB = const.

766 PROCEEDINGS OF THE AMERICAN ACADEMY.

B lies on a line b. The same figure gives

ab = const.

where b is a fixed line and a is a line making a constant angle with b
(Figure 18).

Figure 18.

This amounts to saying that if two sides of a triangle are equal the
opposite angles are equal and have values independent of the third side
or angle. Thus with every distance AB is associated an angle ab. With
any equal distance is associated the same or equal angle, since as pre-
viously mentioned the construction for equal distances at the same time
makes the angles equal.

We shall determine the relation between these corresponding dis-
tances and angles. For this purpose take two distances AB and AC
along the same line and with them the corresponding angles ab and ac
(Figure 19). Let FA and AB cut f in P and Q. Draw FQ cutting
PB and PC in D and E.

In the isosceles triangles ABD and ACE

Z ABD 8 = Z BAD,

^ The angle ABB is the angle whose first side is AB and second side BD
and which does not contain F. Thus in the figure the angle ABD is the
angle ABP. The triangle ABD is isosceles in the sense that

PA = DB.

We shall later call triangles isosceles or equilateral when the sides described
in a definite order around the triangle are equal, i. e. when

BD = DA.

Hence

PHILLIPS AND MOORE. — ALGEBRA OF PROJECTIVE GEOMETRY.

Z ACE = Z BAE.
^ Z ABD Z BAD

767

ac

Z ACE Z CAE •

From the definition of angle this last expression is the double ratio of
the lines AD, AE, AB, AF, i. e. equal to

(DE i QF) = (BC I AQ) = (CB | AQ).

Figure 19.

From the definition of distance the last ratio is

iib AG

AC
AB

Hence

or

ac
ab-AB

AB'
ac • AC.

We have already remarked that ac is uniquely determined by AC. If
then we keep AC constant

ab-AB = k.

The product of side and angle in an isosceles triangle is an absolute
constant. We shall choose the units so that the constant is unity.

Then

ah =

AB

(9)

768 PROCEEDINGS OF THE AMERICAN ACADEMY.

Angle is therefore of dimension minus one in distance. In fact, since
angle and distance are dual if there is to be a dimensional relation be-
tween them the first should be of the same dimensions in the second
that the second is in the first. The dimensions could then be only
1 or —1 in distance.

Now ZBAD= ^

AB
and BD = Ali = AB.

Hence ZBAK = =.

AB^

We may consider the line BD as a circle of radius AB and center A.
(The same line may be considered as a circle in an infinite number of
ways but to each center corresponds a unique length of radius. Any
point on AF may be taken as center of the same circle BD.) Then
the angle at the center is given by

30. Triangle relations. Analogy with Euclidean geometry leads
us to expect relations between the sides and angles of a triangle. We
shall now determine these relations.

Let ABO be the given triangle. Draw the lines as indicated in fig-
ure 20. Denote the length of the sides BC, CA, AB by a, h, c re-
spectively and the angles CAB, ABC, BCA by A, B, C respectively.

Then a 4- i + c = BC -f CA -t- AB = BE -I- DA + AB == DE.
Also = = (EA I DB) = (QS [ PR) = (BH | AB) = =

Therefore A=^ = .M=, = ^^'. dD

At

I AB • DA

B

a-\-h -^ c

ac

ri

a-i- b + e

Similarly £ = „" ^ (12)

a6 • <^^>

PHILLIPS AND MOORE. — ALGEBRA OF PROJECTIVE GEOMETRY.

These relations solved for a, h, c give

A+B+C

a =

b =

c =

BC '

A+B+C
AC '

A + B + C
AB '

769

(14)
(15)
(16)

FiGUKE 20.

which have the same form as before as they should have by duality.
These equations can be solved for any three of the quantities A, B, C,
a, h, c in terms of the other three. Thus any three of these parts deter-
mine the triangle uniquely. In particular the three angles determine
the triangle and therefore similar triangles do not exist.

We can construct a triangle having any three given lengths for sides.
In fact, take any segment BC of length a. Construct lines at distances
c, b from B and C respectively. These lines intersect in a point A such
that the triangle ABC has the sides required. There is no relation be-
tween the three sides of a triangle. Since any three parts determine
the triangle there is no relation between any three parts. Since we have
already found three independent equations connecting the six quantities
it follows that any other must be a consequence of these.

VOL. XLVII.

49

770 PROCEEDINGS OF THE AMERICAN ACADEMY.

It is to be noted in particular that the three angles of a triangle are
not functionally related. The reason that the angles of a triangle in
Euclidean geometry are so related is because angle is there of zero di-
mension in distance. The three angles of a triangle being homogeneous
functions of zero dimensions in the sides are functions of two ratios

-, -, and hence must be functionally related.
c c

From (11) by division we get

A

a + h-\- c

a

A
a

abc

B C
~ b ~ c'

Hence — = — = — (17)

abc ^ ^

a set of relations similar to the sine proportions in trigonometry. In
this system angle often replaces sine of the angle in ordinary trig-
onometry

31. Area. To determine the sides and angles of a triangle a direction
around the triangle must be given. In speaking of the triangle ABC

Figure 21.

we shall assume this direction to be A, B, C. The lengths of the sides
are there AB, BC, CA and the angles ab, be, ca where a is opposite A,
b opposite B, etc. Quantities such as area connected with a triangle
may depend on this direction of description.

We define the line area of a triangle as a scalar quantity, determined
by three points taken in a definite order, such that triangles having a
vertex in common and their bases on the same line have areas propor-
tional to the lengths of their bases.

Take two triangles ABC and AB'C having the same vertex A and
bases BC, B'C on the same line (Figure 21).

PHILLIPS AND MOORE. — ALGEBRA OF PROJECTIVE GEOMETRY. 771

Consider the triangle AC'C. AC = — c', and angle AC'C = — C, where
C is the angle of the triangle AB'C. Then from relation (17) we have

i- = p or b'C' = ha

0 0

Then if we have the relation

Area ABC a

Area A'B'C ~ a"

multiplying both numerator and denominator by the above equality
we have

Area ABC ahC

Area A'B'C db'C

The two terms of the right member are equal to the sum of the sides
of the respective triangles. Hence

Area A^B^C^ = «' _ <^' + ^' + c'
Area ABC ~ a ^ a -\- h -\- c '

Triangles having the same vertex and bases on the same line have line
areas proportional to their perimeters.

Starting with the triangle ABC by a succession of operations consist-
ing of moving a side along its line and changing its length, we arrive
finally at any triangle A'B'C. Since under each of these operations the
area is changed in the same ratio as the sum of the sides, it follows that
the areas of any two triangles are proportional to their perimeters. We
choose the unit of area such that

Area ABC = a + b + c. (18)

That this expression for area has the properties required is evident
since it is determined by an ordered sequence of three points, and since
as already shown two triangles having the same vertex have perimeters
proportional to their bases.

Perhaps the most fundamental property of area is the sum property,
i. e. that the area of a region is the sum of the areas of its parts. This
is a property of the sum a + b + c. For if we divide a triangle into
two triangles by a line through one of the vertices the sum of the pe-
rimeters of the two is equal to that of the original triangle since the divid-
ing line is counted twice in opposite directions. If then we define the

772 PROCKKDINfJH OF TIIK AMKKK'AN A(MI)KMY.

aroa of any cloHod ]t()\y^oi\ &h the Hum of the areas of the triaiig](w into
which it can h(5 diviihid tlio area of any [joly^'on will he its i)erinieter.

32. Similarly w(! (hilino th(! atif/lc air/i of a trian^de a,s a .scalar (|iian-
tity (leturminod hy throe lines taken in a dclinite onUir and Huch that
triangle.H having,' the Hame vertex and hases on tlio Hame line haveareaH
proportional to the angles at the vertex. Hy a pnjjier ehoiee of units
the angle area takes the lurm

Area ahc = A -\- B -\- C. (19)

Defining the angle area in general aw liaving tlio sum pro])erty we see
that any cloHed jxjlygon has an angle area equal to the Hum of the angles
betw(!en c(jnHecutive sifleH.

33. 'I'he formulae for Ihc two areaH may he written in other forms that
hIiovv more chvuly the analogy with the ordinary trigonometric formulae
for area. 'J'h uh I'rom the equation

. __ a + h -\-c

^- Fc

wo have

Area ABC = a -\- 0 + c = bcA

analogouH to the formula

2 Area ABC = ho sin A

in trigonometry. Our foruiula thuH corroHponds to tho formula for
twice the ordinary area.^
Again from the equation

_A -^ n + o

"*" JJC
wo have

Area abc = A + /i -^ (.' = aliO

which is to be comi)ared with tho ordinary formula

2 Area abc = « sin B sin C

In both of thoHO i)airH of formulae for area angle replaces tho sine of an
angle of trig(jnometry.

• Ah (he prcMcnt, Hcheme of HiHianrc and anKle in entirely diHtJncI from tho
ordinary diHliiiKu; and un)^l<', llif one Ixinj^ lincur, I he oilier (luiulriil ie, il. (Idch
not Hoem udviHuble to complicate! our formuhm hy the introduotJon of tho
multi|)lier \ neocHHary to make t}ie analogy eoinplctc 'I'he only c-aHe eoinrnon
to I he. two HyHtcniH in that in wliicli Mm' (^rcular j)oiuLH uL infinity coincide,
which corrcHpond.s t,o our Hchemu wh(!n 1<' iH <jn f.

PHILLIPS AND MOORE. — ALGEBRA OF PROJECTIVE GEOMETRY. 773

Another analogy is obtained by comparing the ordinary area of a
sector of a circle with our corresponding area of an isosceles triangle.
The area of sector of angle A and radius b is

The area of our isosceles triangle having a vertical angle A and the
sides AB = AC = b is

-b'A

which can be obtained from the formula Area = bcA, remembering
that in the isosceles triangle AB = b, OA = c= — b. Thus in this case
angle replaces angle.

34. In connection with the similarity between the trigonometric
formulae in this geometry and in the ordinary geometry, it is interest-
ing also to note some of the similarities and differences of the geometric
relations of triangles in the two cases. The following theorems are
good illustrations.

I/the sides BC, CA, AB of a triangle are cut by a transversal in the
points A\ B', C respectively, then

C'A A'B B'C^ _

C'B A'C B'A

For writing the three vertices in order to denote the line area of the
triangle we have (Figure '22)

A^B^C C'FA FC^ WC C^A^B _
C'B'A ■ B'C'C ■ C'A'C ■ C'A'B " A'C'A ~ ^'

Since triangles having the same vertex and bases ou the same line have

774 PROCEEDINGS OF THE AMERICAN ACADEMY.

line areas proportional to the lengths of their bases, this relation can
be written

A'C B'A B'C A'C BC;__

C'B' CB' C'A' A'B C'A
which is equivalent to

C'A A'B BC _

C'B A'C B'A

The converse of this theorem is immediately seen to be true.

/4

Figure 23.

1/ through any point 0 in the plane of a triangle ABC lines are
drawn to the vertices cutting the sides opposite A, B, C in A', B', C re-
spectively, then

rC C^ FA __

A'B C'A B'C
For we have the identity (Figures 23 and 24),

oh pc of oa pc ob _
ocof'oa'pc'pbpa'" *

which becomes, on rearranging the terms,

OT-PC PF-PA 0^-OB^^
OA-OC^'oT'CBOC-PF •

PHILUPS AND MOORE. — ALGEBRA OF PROJECTIVE GEOMETRY. 775

or since triangles with the same vertical angle have areas proportional
to the product of the including sides.

Rearranging

OA'C OB'A OC'B

OAC OBA' OCB

OA^C OB^A OC^B
OBA' ■ OCB' ■ OAC

C

7 = 1.

= 1.

But triangles having the same vertex and bases on the same line have
line areas proportional to their bases. Hence

A'C B'A C'B

7=1,

BA' CB' AC

which on changing the sign of the denominators becomes

A'C B'A C'B

AB' B'C C'A

= - 1.

The converse of this theorem is also easily proved. These two theorems
are the same for ordinary geometry as they are here, and in fact the
demonstrations here given are applicable to either geometry.

In this geometry we have duals of the two preceding theorems, which
is not the case in ordinary geometry.

776 PROCEEDINGS OF THE AMERICAN ACADEMY.

If from a point in the plane of a triangle lines a', b', c' are drawn
to the vertices A, B, C respectively, then

c'a a'b b'c _
c'b a'c b'a

and conversely, if the above relation holds, the three lines a', b', c' pass
through the same point.

If any line b iyi the plane of the triangle abc cuts the three sides in
A', B\ C\ respectively, and the lines a', b', c' are drawn from these
points to the opposite vertices, then

a'c c'b b'a _

a'b c'a b'c

and conversely, if this relation holds, the three points A', B\ C' lie on
a line.

From these theorems result many propositions analogous to those of
ordinary geometry:

Lines intersecting the base of a triangle on f divide the other two sides
into jjropmrt tonal parts. (It should not be expected that the bases of
the triangles thus formed have the same ratio, for this would be equiva-
lent to symmetry which does not exist in this geometry.)

If one of the vertices of a triangle is joined to F and lines are drawn
from any point mi this line to the other vertices these li?ies divide the
angles into proportional jyarts.

Lines drawn from the vertices to the mid points of the opposite sides
of a triangle meet in a point which is a point of trisection for the me-
dians, the longer part being toward the vertex.

The bisectors of the angles of a triangle meet the opposite sides in three
p)oints on a straight line. It should be observed that the three bisec-
tors in this geometry cannot all cut the opposite sides between the
vertices. This is because the angle was defined to be that one which
does not contain F.

If through any point 0 in the plane of a triangle ABC, lines OA^
OB, OC are drawn, intersecting the opposite sides in A', B', Cf ; and
if A'B', AB meet in G, B'C, BC in H and A'C, AC in K, tJie points
G, H, K lie on a straight line.

35. Point-line Invariant. In this system we have nothing analo-
gous to perpendicularity, and there is no minimum distance from point
to line. If then we are to find a quantity analogous to the distance
from a point to a line in Euclidean geometry the analogy must have as

PHILLIPS AND MOORE. — ALGEBRA OF PROJECTIVE GEOMETRY. 777

its basis some other property. Now the distance from the vertex to
the base of a triangle is ordinarily determined by the formula

h = b sin C.
Hence in our system we try the value

It is evident from the definition that S depends only on the positions
of A and BC, for we have

B

c

and hence

8 = bC=cB =

a + b + e

a

(20)

The first value of 8 shows that it is independent of the position of B
along the line, the second, that it is independent of the position of C
along the line.

FlGtTRE 25

To determine more exactly the meaning of this quantity 8, we draw
lines FA and FB meeting f in P and Q. Let BC cut AQ in C, FP in
D, f in R.

778 PROCEEDINGS OF THE AMERICAN ACADEMY

From the triangle ABD we get

^ BD + DA + AB
o = •

BD

Since in the isosceles triangle ABC, AB = CB = c = — a , and since
DA = 0, being measured on a line passing through F, the above relation
can be written

g ^ BD + c ^ BD-a ^ CD ^ (CB|DR) = (AF|DP).
BD BD BD ^

Thus the invariant 8 is the cross ratio determined by the point A,
the point F and the points in which FA cuts the given line BC and
the line f.

From the fundamental relations of the triangle we have

a + h^c _ A + B+ C

a ~ A '

Therefore

^^AJ,B±C^ (21)

which is the same function of the angles that the former is of the dis-
tances. It is to be noted also that if A describes a line passing through
R, 8 will be unchanged.

The group of collineations which leaves F, f fixed leave S invariant
although distance and angle are not invariant.

36. Metrical Illustration. When we throw the line f to infinity the
system takes an interesting metrical form. The equation

AB = const.

gives for fixed A a line b parallel to FA (Figure 26).

For points B on this line the distance AB is then a constant times
the Euclidean area of the parallelogram ABF. Further, our distances
along the line AB are proportional to the Euclidean distances and there-
fore to the area of the parallelogram. Hence distance from a point A
is proportional to the area of the parallelogram ABF, or

AB = kn ABF
where ^ is a function of A.

PHILLIPS AND MOORE. — ALGEBRA OF PROJECTIVE GEOMETRY.

Similarly from B we have

BA = ki E7 BAF.
Now BA = - AB

779

and
hence

n ABF = -n BAF,
ki = k,

Figure 26.

and

AB = k O ABF

where k is constant for all values of A and B. We may choose the
units so that k equals unity. Then

We know that

consequently

AB = O ABF.
BC

(22)

ab =

AB^

-T OBD
ab =

(OAC)^ OAC*

(23)

780 PROCEEDINGS OF THE AMERICAN ACADEMY.

Thus distance is the moment of Euclidean distance with respect to F
and angle is the reciprocal of a moment.

It is to be observed that the sum of the three sides of a triangle is
twice the Euclidean area. In fact,

Figure 27.
AB + BC + CA = 2 (ABF + BCF + CAF) = 2 ABC.

This is another justification for calling the sum of the sides of a triangle
the area of the triangle.

Case II. The Point F on the Line/.

37. In this case distances are equal if they project from F into equal
vectors on a line. All triangles having vertices A, B, C respectively
on fixed lines passing through F have equal sides, but may have differ-
ent angles. Hence in this case it is not possible to express an angle
in terms of the sides as was done in Case I.

Furthermore (Figure 28).

AB + BC = AD + DC = AC.

Similar relations hold for angles. We thus have two equations con-
necting the parts of a triangle.

« + ^ + c = 0,

(24)

We should expect one other relation. This may be found as follows:
Let AB, BC, and CA cut f in P, Q, R. Then

| = g = -(DA|CIl)=-(FP|QR).

PHILLIPS AND MOORE.

ALGEBRA OF PROJECTIVE GEOMETRY.

781

Since angles are proportional to the point vectors determined at a
fixed point by their intersections with the line f, we may consider them
as represented by vectors on f measured relative to F as infinite point.
Thus

I = 1^ - - (RQIPF) = - (FPIQR).

Consequently

and

a

A

h~

'' B'

a

b

c

A~

B~

G

(25)

These equations, together with the two already found, form a set of
three independent relations connecting the six parts of a triangle. A

Figure 28.

triangle can be constructed having a given side and two given angles.
There cannot then be more than three relations connecting the six
parts, and therefore any other is a consequence of these.

38. Point-line Invariant. If we have a fixed point A and a fixed
line LM and take a triangle with vertex A and base BC on the line LM,
we have from the above relation

8 = bC=cB, (26)

which shows that the quantity S is an invariant here just as in Case 1.

782 PROCEEDINGS OF THE AMERICAN ACADEMY.

There is one difference, however, for in Case I this invariant was ex-
pressible as a ratio of distances, and consequently was independent of the
unit of length assumed. In this case 8 is not so expressible. It is not,
therefore, an absolute invariant, but depends upon the units.

39. Area. The line area again will be defined by the property that
triangles having the same vertex and bases on the same line have
areas proportional to their bases. By the same argument as used in
Case I it is seen that

Area ABC _ ahC
Area A'B'C ~ a'b'C"

and the same argument will show that the factor of proportionality is
the same for the whole plane and hence can be assumed to be unity,
and we write

Area ABC = ahC. (27)

It is to be kept in mind that here the area is not equal to the perim-
eter, for the perimeter is zero.

By duality the angle area of the triangle ABC is

Angle area ABC = aBG. (28)

§ 4. Products.

40. We have represented a line by a segment joining two of its
points A and B and have used the notation

AB

to represent this segment. We shall now consider this expression as
the product of two unit points and seek to determine its laws of com-
bination. When the points are not unit points we shall take the
product to be the segment "^ AB multiplied by the product of the mag-
nitudes of the points.

The operation of multiplication will be denoted by writing the quan-
tities together as is done in ordinary algebra. A dot between quanti-
ties will indicate how the quantities are to be associated, e. g. AB • CD
will be used to indicate that the two products AB and CD are to
be multiplied together.

' It should here be kept in mind that segment is not to be confused with
its length, which measures only the magnitude of the segment. The length
of a segment can be zero without the segment being zero, which is the case
of a segment of a line passing through F.

PHILLIPS AND MOORE. — ALGEBRA OF PROJECTIVE GEOMETRY. 783

From the fact that segments are directed we see that the product of
two points obeys the alternative law

AB = - BA. (29)

Also when the two points coincide the segment is zero, that is,

AA = 0 (30)

On the other hand, if

AB = 0,

either the magnitude of one of the points is zero or the segment is
zero. Then if neither point is a zero point and the product vanishes,
the two points will coincide. Here again it is well to note that the
product of two points on a line through F does not necessarily vanish
although the segment is of zero length or magnitude.

41. We have used the notation

ABC

to represent the triangle determined by the three points. We shall
consider this also as the product of the three unit points and take it to
mean the line area of the triangle determined by the three points. If
the points are not unit points, the product will mean the area multi-
plied by the product of the magnitudes of the points. From this defini-
tion we see that the product vanishes if the three points are on a line,
neither point being on f. Conversely, if the points are not zero points
and the product vanishes, they are on a line. Therefore

ABC = 0

is a necessary and sufficient condition that the three points be linearly
related, i. e. collinear.

From the fact that area is directed we see at once that

ABC = BCA = CAB = - ACB = - CBA = (31)

42. From duality we now define the product of two lines as the
sector determined by the two lines multiplied by the product of the
magnitudes of the lines. When the two lines coincide the sector
vanishes and we have as for points

ab = 0.

Conversely, if the lines are not zero lines, ab = 0 is the condition that
the two lines should coincide. In the case of two lines as in the case

784 PKOCEEDINGS OF THE AMERICAN ACADEMY.

of two points it should be kept in mind that the magnitude of the
sector may be zero without the product necessarily being zero, e. g. if the
lines intersect on f In this case the magnitude of the sector is zero,
but the product is not zero. If we now take the two lines a and b as
represented by segments starting at the point of intersection, thus

a = BC b = AC

where A, B, C are unit points, then

AB - AC == (ABC) A. (32)

Since the magnitudes of the lines a, b are represented by the lengths
of the segments, from the definition the product would be BC • AC • Aj
where A^ represents the sector determined by the two lines. But A^
can be written &s A -A where A means a unit sector and the product
takes the above form.

The product of three unit lines is defined to be the angle area of
the triangle determined by the three lines, and the product of any three
lines is this product multiplied by the product of the magnitudes of
the lines. When the three lines pass through a point the angle area
of the triangle is zero and conversely. Hence, TTie necessary and suffi-
cient condition that three lines a, b, c (not zero lines) should pass through
the same point is

abc = 0.

Since the angle area is also a directed quantity

abc = boa = cab = — bac = (33)

43. The product of a line a and a point A will be defined as the
invariant 8 of the point and line multiplied by the product of the
magnitudes of the point and line. The invariant vanishes when and
only when A lies on a. Therefore if neither a nor A are zero elements,
the necessary and sufficient condition that A lies on a is

Aa = 0.

If the line a is represented. by a segment of length a determined by two
unit points B and C, then irom the above definition

ii.2i = aAb = aABc (34)

= a (A Be)
= A {acB).

That is, the product of a point and a line (represented by one of its
segments) is equal to the line area of the triangle having the point for

PHILUPS AND MOORE. — ALGEBRA OF PROJECTIVE GEOMETRY. 785

vertex and the segment for base multiplied by the magnitude of the
point. Or dually, the product is equal to the angle area of the triangle
having the sector A for vertex and a for base line, multiplied by the
magnitude of a. If the line a passes through F, the above product be-
comes indeterminate since a = 0 and ^ = 00; this can be evaluated by

remembering the relation bA = aB. Both h and A are finite and the
product becomes determinate as before. From the above expression
for the product we see that

Aa = aA. (35)

44. The product of two unit points was defined as the segment join-
ing the two points. This segment we may now consider as represented
by the line joining the two points taken with a magnitude equal to the
length of the segment. Then making use of the definition of the prod-
uct of a point and a line we see at once

ABC = AB C==ABC. (36)

That is, the product is associative. Likewise the product of three lines
is associative.

45. The distributive law. The distributive law for points

(^B + C) = AB -f AC

(87)

follows from the definition of addition. Let the magnitudes of the
three points be X, ju, v respectively. Then (Figure 29)

AB = A/xC, AC = Avb.

VOL. XLVIL — 50

786

Let

PROCEEDINGS OF THE AMERICAN ACADEMY.

AD = A/ic, AE = \vb.

Then by definition AB + AC = 2h, where H is the harmonic of f with
respect to D, E and h joins A to H. It was shown that the line AH

divides the segment BC in the ratio and therefore the Hne must

pass through B + C. It is evident that the magnitude of A (B + C)

is equal to the magnitude of AB + AC, each being equal to A (yu + v),
and since these lines have two points in common they are then equal.
The distributive law for points and lines

a (C + D) = aC + aD

(38)

can be proved as follows : Let a = AB where A and B are unit points.
Then the left member can be written

AB (C + D),

or, since the products are associative,

A (BC + BD).
Let (Figure 30) H = i(C + D).

Then BH = ^B (C + D) = i(BC + BD)

PHILLIPS AND MOORE. — ALGEBRA OF PROJECTIVE GEOMETRY. 787

and A (BC + BD) = 2ABH

= 2(AB + BH + HA)

= 2AB + (BC + BD) + DA + CA

= (AB + BC + CA) + (AB + BD + DA)

= ABC + ABD

= aC + aD.

By duality the distributive law

A (b + c) = Ab + Ac (39)

is also true.

46. We have defined the product of two lines and have expressed it

in terms of three unit points when the segments representing the two

lines have an end point in common. This product can also be ex-
pressed in terms of unit points when the segments representing the
lines do not have an end point in common. That is, we know that the
product AB • CD is the sector determined by the two lines and we
seek to express this sector in terms of the four points A, B^ C, D. Grass-
mann has called such a product a regressive product. Let the two
lines be represented by segments thus

a = CD, b = AB

and let X be the unit point at the intersection of a, b.

Then we can express A in terms of B and X.

(A + 1) A = X + AB.

(40)

788 PROCEEDINGS OF THE AMERICAN ACADEMY.

Multiplying by B

(X + 1) AB = XB.

Multiplying by CD

(X + 1) AB • CD = XB CD

= XB (CX + XD)

= (XBD - XBC) X

= (BCD) X.

Again multiplying (40) by CD

(X + 1) ACD = X (BCD).

Using the last two relations with (40)

(X + 1) A = ^^^^- B + (X + l)-^cBDy

From which we get

AB CD = (CDA) B - (CDB) A. (41)

Starting with the relation

(X 4-1) C = X + XD

the following relation is obtained :

AB CD = (ABD) C - (ABC) D. (42)

These last two relations are the general formulae for Grassmann's
regressive product. Similar formulae can be obtained for the regres-
sive product

ab • cd.

Subtracting (41) from (42) we get

(ABC) D - (ABD) C + (ACD) B - (BCD) A = 0 (43)

for the identical relation connecting four points of the plane.

Scalar Products.

47. The point F was exceptional only in the addition of lines. It is
lines through this point that are exceptional and not the point itself.
The preceding product theory then holds when F is one of the quanti-
ties involved. If A, B and F are unit points not on f

(ABF)=AB + BF-fFA.

PHILLIPS AND MOORE. — ALGEBRA OF PROJECTIVE GEOMETRY. 789

Hence

(ABF) = AB (44)

since the distances from P to A and B are zero. A£ F is fixed through-
out the discussion we may consider (ABF) or AB as a product of A
and B. Since it is a number we call it the scalar product. If A and
B are not unit points we shall use the notation AB for the product
(ABF). It is then the distance from A to B multiplied by the product
of the magnitudes of A and B.

From the definition, if

B + C = D,

we have

AB + AC = (ABF) + (ACF)

= (ADF)
= AD.

The scalar product of two points has then the following properties :

AB = -BA

A (B + C) = AB + AC. (45)

These laws hold for both AB and AB. The two differ in the fact
that AB is a multiple quantity, AB a number. The first forms an as-
sociative product

AB C =z A BC,

while the second does not.

If a, b and f are unit lines not passing through F,

(abf ) = ^ -f bf + E

Since the angles bf and fa are zero

(abf) = ^. (46)

The angle between two lines may then be considered as a scalar product
of those lines. If a and b are not of unit magnitude, we define ab by
equation (45). This product dual to AB has the following properties:

ab = — ba (47)

a (b + c) = ab + ac.
Equations (45) together with the fact that AB is a number suggests

790 PROCEEDINGS OF THE AMERICAN ACADEMY.

geometry in one dimension. In fact, if a point xV is represented as a
linear function of three points, one of which is F, the multiple of F is
lost in the product

AB =: (ABF).

Thus, so far as concerns their values in products of the form AB,
points of the plane are linear functions of two points. In respect to
this multiplication the plane is then one dimensional. Thus any homo-
geneous identical relation between products AB along a line will hold
for distances AB in the plane. For example, along a line

AB CD = AC BD - AD BC.

Therefore

AB-CD = AC-BD-A5-BC (48)

where A, B, C, D are any four points in the plane. This can be proved
directly by using the equation

(ABF) C - (ABC) F -f (AFC) B - (BFC) A = 0

which is obtained from (43) by changing the notation. Multiplying
by DF and transposing we get

(ABF) (CDF) = (ACF) (BDF) - (ADF) (BCF)

which is equivalent to (48).

Massachusetts Institute op Technology.

Proceedings of the American Academy of Arts and Sciences.
Vol. XLVII. No. 21. — March, 1912.

CONTRIBUTIONS FROM THE JEFFERSON PHYSICAL
LABORATORY, HARVARD UNIVERSITY.

ON ELECTRICAL PROPERTIES OF CRYSTALS.

1. — STRATIFICATION AND CAPACITY OF CARBORUNDUM.

Bt G. W. Pierce and Rhys D. Evans.

With a Plate.

CONTRIBUTIONS FROM THE JEFFERSON PHYSICAL
LABORATORY, HARVARD UNIVERSITY.

ON ELECTRICAL PROPERTIES OF CRYSTALS.

I. STRATIFICATION AND CAPACITY OF CARBORUNDUM.

By Geoege W. Pierce and Rhys D. Evans.

Presented by G. W. Pierce, February 14, 1912. Received February 1, 1912.

This work is a continuation of some investigations by one of us on
Crystal Rectifiers for Alternating Currents. *

Capacity of Carborundum. — In the experiments that are described
in the present paper it has been found that a fragment of carborundum,
with certain attachments of the electrodes, shows a large electrostatic
capacity. Measurements are given of this capacity in two typical
cases.

Character of the Phenomenon. — The discussion of the measurements
is followed by an account of a microscopic and electrical investigation
of the carborundum, which shows that the carborundum crystal is made
up of an insulating mass permeated by fine layers of conducting ma-
terial. These conducting layers are nearly parallel, and, separated as
they are in the crystal by non-conducting sheets, form a natural elec-
trical condenser, provided electrical contacts are made to two conduct-
ing layers or sets of layers that do not happen to short-circuit within
the crystal.

Method of Measuring the Capacity of the Crystals.

Method of Charge and Discharge. — The capacity of the carborundum
crystals was measured directly by a method of charge and discharge.
A simplified diagram of the circuits employed is shown in Figure 1.
By means of a motor-driven commutator C the crystal Cr was con-

^ G. W. Pierce: "Crystal Rectifiers for Electric Currents," Part I, Physi-
cal Review, 25, pp. 31-60, 1907; Part II, ibid., 28, pp. 153-187, 1909, and
These Proceedings, 44, pp. 317-349, 1909; Part III, Physical Review, 29, pp.
478-484, 1909. See also " A Simple Method of Measuring the Intensity of
Sound," These Proceedings, 43, 1908, and " Principles of Wireless Telegraphy,"
McGraw-Hill, New York, 1910.

794

PROCEEDINGS OF THE AMERICAN ACADEMY.

nected alternately first ■with the charge circuit VG'Cr and then with
the discharge circuit CrG. A galvanometer, used for measuring the
current out of or into the crystal, could be placed either in the dis-
charge circuit at G or in the charge circuit at G'.

When the galvanometer was placed at G and allowed to come to a
steady reading, while the commutator C was in operation, the reading

^LnjU

A^-:dc::^B

FiGtJRE 1. Circuit employed
in capacity measurements.

Figure 2. Clamp for holding spe-
cimen between screws A and B.

of the galvanometer gave the discharge current made up of a series of
discharge impulses from the crystal. Placed at G', the steady deflec-
tion of the galvanometer, with the commutator in operation, gave the
charge current made up of charge impulses going into the crystal.

The Commutator. — The commutator was made of cold-rolled copper
and was used with brushes of the same material so as to avoid thermo-
electric currents in this part of the apparatus.

In order to minimize the leak current, the segments of the commu-
tator and the brushes pressing against them were so arranged as to
make the time of open circuit between charge and discharge as small
as possible.

In order to simplify the interpretation of results, the time of contact
for charge was made approximately equal to the time of contact for
discharge.

Measurement of Frequency of Commutation. — Various speeds of the
commutator were obtained by the use of a series of pulleys of different
sizes on the axle of the motor and a corresponding series of different-
sized pulleys on the axle of the commutator, which was driven by a

PIERCE AND EVANS. — CAPACITY OF CARBORUNDUM. 795

belt from the motor. The speed of the commutator was measured by-
putting a standard mica condenser in the place of the crystal Cr of
Figure 1, and reading the galvanometer at G with a known impressed
voltage. In practice, in order to eliminate any errors arising from lack
of proportionality of the galvanometer deflections, the impressed vol-
tage was varied so that the readings of the galvanometer in the speed
determinations were brought always to the same deflection (20 cm.),
under which condition the number of charges or discharges per second
was inversely proportional to the voltage required to give the standard
deflection.

While the galvanometer deflection and voltage were under observa-
tion, one of these speeds was found absolutely by means of a revolution-
counter attached to the shaft of the commutator, and the other speeds
were then known in terms of the speed given by the revolution counter.

The capacity method of measuring the frequency of charges or dis-
charges had the advantage of permitting instantaneous observations of
the constancy of the commutator speed before and after measurements
with the crystal as condenser.

Measurements Capable of Repetition. — Although the adjustment of
the electrodes upon the crystal so as to get the capacity eifects afforded
some difticulty, yet when the adjustments were once made, the galva-
nometer readings, under given conditions, were about as constant with
the crystal as capacity as with the standard mica condenser as capacity,
and all the observations, with ordinary precautions, were capable of
repetition with an error of about 1 per cent, which represented the
irregularities of the speed of the commutator.

Galvanometer. — A D'Arsonval Galvanometer of 2000 ohms resist-
ance was used. This galvanometer was provided with a heavy closed-
coil electromagnetic damper, so as to obtain steady deflections even
with comparatively slow speeds of the commutator. High resist-
ance or high inductance in the galvanometer used with this method of
determining capacity, if the capacity is large, is objectionable, because
of the danger of having incomplete charge or discharge. In the present
experiments attention was given to the matter of the completeness or
incompleteness of the charge or discharge. In one of the experiments
described below (Experiment II.) the charges and discharges were prob-
ably incomplete, but this was due not to the resistance or inductance
of the galvanometer, but to the high resistance of the conducting sheets
which served, in the crystal, as armatures of the condenser or else to the
high resistance of the contacts of the electrodes with these sheets.

796

PROCEEDINGS OF THE AMERICAN ACADEMY.

Experiment I.

Crystal held in a Clamp. — In this experiment a flat piece of carbo-
rundum, about 1 mm. thick, was clamped between two screws A and B
of Figure 2. These screws passed through brass supports P and Q in-
sulated from each other by a fibre block F. The screws had copper-
plated ends, and were screwed down upon the specimen with sufficient

1.0 1.2

Figure 3. Current vs. voltage. A
positive, n = 24.2.

Figure 4. Current vs. voltage. B
positive, n = 24.2.

pressure to cause the brass supporting strips (1 cm. wide and 1.5 mm.
thick) to spring apart perceptibly. Later experiments showed that the
amount of this pressure probably has no influence on the capacity, so
long as the increase or decrease of pressure does not change the posi-
tion of the contacts with respect to the conducting laminae.

Choice of Specimen. — The particular specimen used in this experi-
ment and the particular setting of the crystal between the supports was
obtained only by groping. It had been found accidentally that a speci-
men of carborundum used in temperature measurements of conductivity
showed a slight capacity effect. Incited by this observation, we selected
a large number of pieces of carborundum and put them one after the
other in the clamp and tested for capacity. Most of them showed no
capacity. Finally the piece used in this experiment was tried with the

PIERCE AND EVANS. — CAPACITY OF CARBORUNDUM. 797

adjustment that happened to give the capacity eflfect in a marked degree. ^
Then without changing the adjustment a complete set of data with dif-
ferent speeds and different applied voltages was taken. After the ex-
periment was completed, the specimen was examined with a microscope
and was explored electrically while under the microscope, and the exis-
tence of the conducting laminae separated by insulating sheets was dis-
covered. After the discovery of these laminae, other specimens could
be selected and, with a somewhat difficult adjustment of the electrodes
against the conducting laminae, could be shown to act as condensers
with larger capacity in some cases than that of the specimens with which
the present data were obtained.

Data ivith Specimen I. — Table I. following contains values of the
charge and discharge current obtained with Specimen I, in a circuit of
the form of Figure 1, under various impressed voltages and for various
numbers of charges and discharges per second. The crystal was con-
nected into the circuit so that one side should be positively charged (see
column headed "A positive") and then, without changing the adjust-
ment of the specimen in the clamp, the leads to the crystal were re-
versed so that it should be charged with the other side positive (see
column headed " B positive ").

Charge and Discharge Current not a Linear Function of the Voltage.
— From these data, sample curves of charge and discharge current
plotted as a function of the impressed voltage, with n = 24.2, are given,
in Figure 3, with the charge applied so that the side A was positive,
and in Figure 4 with the charge applied in the opposite direction. Along
with the "charge" and "discharge" curves there is plotted, in each
figure, a curve of steady current through the crystal obtained when the
various voltages were applied directly in circuit with the crystal and
galvanometer without the intermediation of the commutator. These
curves, which are marked "steady," are the current-voltage character-
istics of the crystal in the two opposite directions.

The curves of Figures 3 and 4 show that the charge and discharge

^ In his testimony, on May 22, 1911, in the case of the National Electric
Signaling Company vs. The United Wireless Telegraph Company, Equity
No. 643, District of Maine, Dr. Louis Cohen stated that a certain carborundum
detector had a capacity of about .004 microfarads. This result he obtained by
measurements with a high frequency generator of 72,500 cycles. So far as we
know, his result has not been published except in the Court Record. Dr. Cohen
gave no explanation of the phenomenon.

Our own discovery of the capacity was made before the date of Dr. Cohen's
experiments, and our delay in publication has been occasioned by a long and
tedious search for the explanation of the phenomenon, which we believe we
have now found.

798

PROCEEDINGS OF THE AMERICAN ACADEMY.

TABLE I.
Observations in Measurement of the Capacity of Specimen I.

Current in Amperes X lO"^

No. of Charges

Impressed Vol-

or Discharges

tage E in

A Positive.

B Positive. 1

per Second, n.

Volts.

Charge.

Discharge.

Charge.

Discharge.

11.43

.2

2.46

2.14

2.35

2.11

for A positive

.4

5.49

4.01

5.20

4.22

and

.6

10.00

5.80

8.87

6.36

.8

17.90

7.17

15.00

7.85

11.85

1.0

8.23

8.75

for B posi-

1.2

9.26

9.50

tive

1.4

10.22

10.27

16.60

.2

3.17

2.80

3.30

2.71

for A posi-

.4

6.80

5.54

6.85

5.60

tive

.6

11.70

8.05

11.33

8.72

and

.8

20.00

10.02

18.04

11.04

16.90

1.0

11.65

12.79

for B posi-

1.2

13.20

14.20

tive

1.4

14.25

15.55

20.0

.2

3.43

3.20

3.43

3.16

for A posi-

.4

7.25

6.34

7.40

6.62

tive

.6

12.40

9.00

12.13

10.00

and

.8

20.4

11.17

19.30

12.75

20.4

1.0

12.70

14.80

for B posi-

1.2

13.98

16.35

tive

1.4

14.80

17.84

24.3

.2

3.94

3.62

3.94

3.64

for A posi-

.4

8.36

7.34

8.21

7.47

tive

.6

14.00

10.73

13.35

11.50

and

.8

23.05

13.50

20.30

15.04

24.2

1.0

15.83

17.75

for B posi-

1.2

17.70

19.80

tive

1.4

19.50

21.60

29.1

.2

4.41

4.17

4.43

4.25

for A posi-

.4

9.21

8.23

9.22

8.71

tive

.6

15.10

12.10

14.80

13.30

and

.8

23.75

15.32

22.40

17.40

29.5

1.0

17.83

20.32

for B posi-

1.2

20.05

22.90

tive

1.4

21.90

24.40

32.7

.2

5.02

4.43

5.01

4.75

for A posi-

.4

10.30

9.25

10.56

9.75

tive

.6

16.85

13.70

16.77

15.25

and

.8

25.90

17.30

25.02

20.20

33.1

1.0

20.60

23.80

for B posi-

1.2

23.20

26.85

tive

1.4

25.65

29.60

39.80

,2

5.67

5.36

5.78

5.28

for A posi-

.4

11.80

10.77

11.96

11.12

tive

.6

19.10

15.91

19.33

17.16

and

.8

30.35

20.54

28.40

23.03

39.83

1.0

24.75

27.95

for B posi-

1.2

28.20

31.95

tive

1.4

31.45

35.10

PIERCE AND EVANS. — CAPACITY OF CARBORUNDUM.

799

current obtained with this specimen is not a linear function of the ap-
plied e. m. f. This might have been anticipated from the fact that the
leak current through the crystal which increases the charge current

TABLE II.
Equations of Current as Function of n.

Impressed
Voltage E.

Charge Equation.

Discharge Equation.

With A Positive.

.2

Ii X 10« = 1.3 + 1.12 n

I2 X 108 = .9 + 1.10 n

.4

3.0 + 2.25 n

1.8 -f 2.24 n

.6

6.3 + 3.33 n

1.8 + 3.46 n

.8

13.3 + 4.02 n

1.5 + 4.80 n

1.0

1.5 + 5.85 n

1.2

1.6 + 6.72 n

1.4

1.9 + 7.28 n

With B Positive.

.2

Ii X 108 = 1.0 + 1.20 n

I2 X 108 = .7 + 1.20 n

.4

2.3 + 2.45 n

1.4 + 2.46 n

.6

4.4 + 3.74 n

2.3 + 3.74 n

.8

9.3 + 4.82 n

1.7 + 5.44 n

1.0

1.4 + 6.66 n

1.2

.6 -f 7.87 n

1.4

- .1 + 8.35 n

and diminishes the discharge current is not a linear function of the
voltage.

Charge and Discharge Currents are Linear Functions of n. — If, in-
stead of being plotted against voltage, the charge and discharge current-
readings be plotted against the number of charges and discharges per
second, the curves of Figures 5, 6, 7, and 8 are obtained. These curves

800

PROCEEDINGS OF THE AMERICAN ACADEMY.

show that with either orientation of the crystal ("A positive" or "B
positive ") the current-reading of the galvanometer on charge or on dis-
charge is a linear function of the number of charges or discharges per
second.

40

Figure 5. A positive. Charge current vs. no. charges per second, for various
applied voltages v.

10 20 80 40

Figure 6. A positive. Discharge current vs. no. di^scharges per second, for
various applied voltages v.

The empirical equations of the curves of Figures 5 to 8, as taken from
the curves, are given in Table II. above.

The equations of Table II. agree closely with the data of Table I.
The simplicity of these equations indicates that we are dealing with an
orderly phenomenon. The linear relation between charge or discharge

PIERCE AND EVANS. — CAPACITY OF CARBORUNDUM.

801

current and number of charges or discharges per second, we have taken
to indicate that the charge and discharge were practically complete at
each commutation ; for it is apparent that if this charge or discharge
were not complete the incompleteness would be greater at the higher
frequencies of commutation and we should not have the linear relation.

10 20 30 40 eo

Figure 7. B positive. Charge current vs. no. charges per second.

10 20 30 40 eo

Figure 8. B positive. Discharge current vs. no. discharges per second.

There follows a mathematical investigation of the phenomenon with
the assumption of a complete charge and discharge at each cycle of the
commutator. The problem is an interesting one on account of the fact
that the leak current through the crystal is not proportional to the
voltage.

VOL. XLVII. — 51

802

PROCEEDINGS OF THE AMERICAN ACADEMY.

Theory of Action of Crystal as a Leaky Condenser on the
Assumption that Charge and Discharge are Complete.

R

I— VW\AA

Let us suppose an e. m. f. E (Figure 9) to be applied to a condenser

C through a resistance R, and suppose that
the condenser is shunted by a resistance r,
through which the leak occurs — the resis-
tances being of such a character that the
current through it is not proportional to
the voltage.

Let a- = the feed current in the main

lead R,

y = the leak current through r,

V = difference of potential between the

ends of the resistance r ; this is

a function of y, and is also the

FiGUBE 9.

p. d. between the plates of the condenser.

These quantities, .r, y, and v are functions of the time t.
Kirchhofifs laws give the following equations :

E=Rx-\-v,
obtained by taking the e. m. f. around the circuit ERCr. ; and

(x — y)dt = Cv,

/<

(1)

(2)

since [x — y) is the current charging the crystal capacity.
By integration of equation (2) from ^ = 0 to ^ = T, we have

xdt = C{vt — Vo) + / ydt,
0 Jo

(3)

in which qi is the quantity of electricity flowing through the charge
leads during the time T of one complete connection of the condenser
to the charging e. m. f.

If we suppose the previous discharge of the condenser to have been
complete

vq = 0. (4)

If also we suppose the charge of the condenser is complete in the time
T, the current x flowing through the leads at time T is Y, where Y is
the steady current through the crystal under the impressed e. m. f. E ;
therefore, by equation (1), we have

= E-RY.

(5)

PIERCE AND EVANS. — CAPACITY OF CARBORUNDUM. 803

Whence equation (3) becomes

<ii

= {E-RY)C+ Cydt. (6)

Jo

With n charges of the condenser per second, we have for the galva-
nometer current-reading Ii in the charge circuit Ii = nqi ; whence

/i = nC{E - BY) + n Cydt. (7)

In this equation R is the resistance of the charge circuit from the
source of e. m. f. up to the point at which the charge is deposited on
the condenser. This includes the resistance of the galvanometer, the
resistance of the contacts of the electrodes with the conducting laminae,
and the resistance of these laminae up to the point of leak.

Equation (7) is an exact expression for the current-reading of the
galvanometer in the charge circuit when the commutator is driven so
as not to exceed the speed at which the charge of the condenser at each
impulse is complete.

Equation (7), therefore, holds for

in which T is the time during which the condenser is in charge relation
to the circuit during one cycle of the commutator, and r is the interval
required for practically complete charging of the condenser. Let us
now break up the last term of equation (7) into two integrals, one from
zero to T and the other from t to T. During the first of these intervals
the leak current y =. y-^ (say) is variable, and during the second interval
the leak current y ^ Y (say) is constant. Then we have

/i = nC{E - nY)-\-n {\j^dt + n j Ydt,

in which yi is the variable leak current during the short interval for the
potential of the condenser to attain substantially its final value, and Y
is the steady current through the crystal and the leads under the steady
e. m. f £J during the remainder of its connection with the charge circuit.
The steady-leak term may be integrated, and we have after integration

804 PROCEEDINGS OF THE AMERICAN ACADEMY.

7i = nC{E - RY) + n Y{T - t) + nj\j^dt. (8)

Now it should be noted that the quantity nTh independent of the
speed, since the geometrical dimensions of the commutator, which is of
the rotating type, are fixed. The value oinT'i^ l/^j>, — this quantity
1/p being the part of the whole circumference of the commutator occu-
pied by the charge segment. Replacing nThj its value 1/p, we have

I, = — + n\CE-IlYC-Yr+f\j,dt}. , (9)

P Jo

In equation (9) r is arbitrarily defined as the time for a practically

complete charge. Let us be a little more specific and suppose that t

is of such value that when substituted for t in the exponential expres-
t

sion e "^ it reduces this exponential to .006. This would make the

charge complete so far as measurements of the accuracy of the present

experiment would show. If

T

g-Rc= 006,
T = 5BC (by tables of exponentials). (10)

With this definition of t equation (9) becomes

I^ = — -\-n\CE-^BYC+ / y^dt\. (11)

P I/O

This is the equation of current-reading of the galvanometer in the
leads to the crystal during charge.

Let us next examine briefly the theoretical problem of the discharge
of the crystal condenser.

A mathematical treatment similar to that of the charge shows that
the current-reading of the galvanometer in the discharge circuit, if
there are n discharges per second, is

J'^bRC
y^dt, (12)

0

in which y^ is the leak current during discharge and Eq is the poten-
tial of the condenser at the beginning of the discharge. The potential

PIERCE AND EVANS. — CAPACITY OF CARBORUNDUM. 805

of the condenser at the beginning of the discharge is less than E the
applied e. m. f. for two reasons ; first, because on account of the leak,
the crystal was not charged to the applied e. m. f. ; and second, because
there has been a small loss of charge during the insulation time while
the commutator was changing from charge to discharge.

As may be seen by reference to equation (5) the deficiency of poten-
tial due to the first of these causes is R Y. The fall of potential due

1 C^^
to the second of these causes is -^^ I y^dt, in which yz is the leak

current during insulation, and T^ is the length of time of the insulation
period during each cycle. Therefore the current reading of the galva-
nometer in the discharge circuit is

l2 = n\CE-RYC- / \j,dt - / y^dtl (13)

Jo Jo

This is the exact equation on discharge.

As an approximation let us suppose that the leak current during
insulation was constant and equal to its value at the end of the pre-
ceding charge. This is approximately true, because the insulation
time was short. With the approximation we have

S\dt = nYT^ (14)

Jo

Y . . 1 .

= — , in which — is the part of the com-
m m

mutator circumference occupied by the insulation segment. With this

approximation equation (13) becomes

/2 = - ^ + w {CE -EYC- j yodt} , (approx.) (15)

in which the first term Y/m is a little too large.

Examination of the Data of Experiment I.

In order to compare the data of Experiment I. with the theoretical
equations for charge and discharge current derived above, let us write
the charge equation (11) in the form

J, = ^-{-nEC\, (16)

n

806 PROCEEDINGS OF THE AMERICAN ACADEMY,

in which C\ is related to the capacity C by the equation

^=- 6i?F , 1 r^flc • (17)

Likewise writing the discharge equation (15) in the form

h = -- + nEC\, (18)

m

in which G'2 is related to the capacity C by the equation

C =

c\

BY 1 P«C ,^g)

Let us now tabulate the values of C\ and C'2 obtained from the ex-
perimental data. These quantities which we shall call approximate
values of capacity are obtained by dividing the coefficients of n of the
equations of Table IL by the corresponding values of E, and are col-
lected in Table III.

In the attempt to get a nearer approximation to the capacity in
terms of these coefficients C\ and C^, it should be noted that the in-
tegral terms of equations (17) and (19) are greater than would be ob-
tained by putting y^ and y^ respectively equal to zero, and are less than
would be obtained by setting yi and ?/2 equal to their greatest value
Y ; whence it may be seen from equation (17) and equation (19)
respectively that

^ E ^ E

and

Iry^^^ RY^ ^^^^

^ E ^ E

in which C is the capacity.

It is, therefore, evident that G, the capacity of the crystal, is greater
than the coefficients C\ or C'l of Table III.

In the attempt to ascertain whether or not the resistance terms
could influence the coefficients sufficiently to account for the large

PIERCE AND EVANS.

CAPACITY OF CARBORUNDUM.

807

excess of these coefficients with B positive over the corresponding
values of A positive, or whether on the other hand it is necessary to
assume different capacities in the two opposite directions, we have
computed approximate values of the integrals in the denominators of
equations (17) and (19). These computations were made by omitting

TABLE III.

Applied Voltage
E, Volts.

Approximate Value of Capacity of Specimen I. 1

With A Positive.

With B Positive.

C'l Farads
Charge.

C'j Farads
Discharge.

C'l Farads
Charge.

C'j Farads
Discharge.

.2

,4

.6

.8

1.0

1.2

1.4

.560 X 10-«
.562
.555
.503

.550 X 10-8

.560

.580

.600

.585

.560

.520

.600 X 10-8
.612
.623
.603

.600 X 10-8

.615

.623

.681

.666

.656

.632

average

.545

.565

.619

.639

second-order effects and assuming that the electromotive force on

t t

charge is -Vi = ^(1 — e *^), and on discharge V2 — Ee ^^. With these

values of the e. m. f, as functions of t/RC and with the steady

current-voltage curves of Figures 3 and 4, t/^ and 1/2 were plotted as

functions of t/EC and integrated by measuring areas, with the result,

which is only an approximation, that on charge ^

C

". = ^(1-^),

(22)

^ An independent investigation of the problem imposing the condition that

the leak resistance obey Ohm's law (i. e. is independent of voltage) leads also

exactly to equation (16) for charge and to equation (18) for discharge, with,

C f 27?\
however, C\ = C'2 = -, 5^ = C f 1 J , approximately.

(' - f )'

808 PROCEEDINGS OF THE AMERICAN ACADEMY.

and on discharge

C',= cf I -1.5^\

(23j

in which E, is the resistance from the impressed e. m. f. into the con-
denser, and p is equal to Y/ E and is the resistance to steady e. m. f.
of the circuit from the source of e. m. f. through the leads and through
the plates and dielectric of the condenser. The resistance p is a func-
tion of E and is smaller the greater E is.

These equations are consistent with the fact that the coefficient C'^
on discharge is greater than the coefficient C'l on charge. This is seen
from Table III. to be true both for A positive and for B positive.
Now the current-voltage curves of Figures 3 and 4 show that p is
smaller for A positive than for B positive. This would make the
coefficients for B positive smaller than those for A positive, whereas
the converse is the case. In order to explain this discrepancy it is
necessary to suppose either

(1) that the capacity of the crystal condenser is actually greater
in direction B positive than in the opposite direction, or

(2) that the resistance R is also a function of ^ and decreases with
increasing E more rapidly than p does.

The second of these propositions is entirely consistent with previous
experiments with carborundum crystals, which showed that if the
electrodes were plated to the specimen a large part of the dependence
of resistance on current disappeared.

We cannot, however, be sure that the apparent inequality of capacity
in the two opposite directions is entirely an effect of leak current ; for
we give next data obtained with another specimen with which the
leakage through the crystal is almost entirely absent, and yet the ca-
pacity given by the measurements is different in the two opposite
directions.

Experiment II. Specimen with very Small Leakage.

Mounting in Wood's Metal. — This specimen of carborundum was
mounted in a metallic cup in a matrix of Wood's metal. The Wood's
metal which served as a solder was placed in the cup and was melted.
The specimen was pushed into the molten solder and held with all but
its upper face submerged until the solder solidified, forming a close-
fitting mold about the specimen. The cup served as one electrode.
The other electrode was a pointed brass rod brought down upon the
crystal and held by a spring. The cup containing the specimen was

PIERCE AND EVANS. — CAPACITY OF CARBORUNDUM.

809

TABLE IV.
Data in Measuhement of the Capacity of Specimen II.

No. of

Charges or

Discharges

per Second, n.

Impressed

e. m. f. E.

in Volts.

Current in Amperes X 10"'.

Point Positive.

Point Negative.

Charge.

Discharge.

Charge.

Discharge.

11.0

.3

.6

.9

1.2

1.43

2.07

2.68

1.43
2.06
2.66

.787
1.66
2.71

4.48

.787
1.64
2.54
3.52

16.7

.3

.6

.9

1.2

2.14
3.18
4.05

2.14
3.17
4.03

1.16
2.46
3.98
6.20

1.16
2.43
3.81
5.34

22.5

.3

.6

.9

1.2

2.92
4.30
5.61

2.92
4.29
5.59

1.59
3.30
5.41
8.04

1.59
3.27
5.22
7.26

30.9

.3

.6

.9

1.2

3.97
5.92
7.64

3.97
5.89
7.60

2.16
4.42
7.17
10.7

2.16
4.39
7.02
10.0

38.3

.3

.6

.9

1.2

4.81
7.15
9.18

4.78
7.15
9.10

2.60
5.40

8.72
12.75

2.60

5.37

8.54

12.08

46.2

.3

.6

.9

1.2

5.67

8.30

10.67

5.67

8.34

10.67

6.37
10.17
14.76

6.33
10.00
14.10

54.6

.3

.6

.9

1.2

6.41

9.50

12..50

6.40

9..50

12.30

3.48

7.35

11.41

16.45

3.38

7.34

11.27

15.85

810

PROCEEDINGS OF THE AMERICAN ACADEMY.

carried by a mechanical microscope stage, so that the specimen could
be moved around under the point terminal until a point of contact
that gave the capacity effect was located by the capacity measurements.
The pressure of the point electrode was then increased so as to avoid
accidental disturbance of the connections during the measurements of
capacity.

Data. — Current-readings on charge and discharge were taken with
the crystal charged so that the point electrode was positive and then
with the point electrode negative. Table IV. contains the record.

2i-;;:u;

HH

i

rHi

al

n ■:..,:.:tt

P

ji

^i

D '■'■'v' -H

n ;::':::::?

m

ffiSi

W

-:!

Figure 10. Point negative. Discharge current vs. n, for various applied
voltages V.

By a reference to Table IV. it will be seen that with the crystal
charged so that the point was positive this specimen gives the same
current on discharge as on charge. With this direction of charging
the crystal condenser shows practically/ no leak. Table V., which con-
tains the steady current-voltage data for this specimen, shows also
that with this direction of application of the e. m. f the crystal lets
through only .09 X 10-'' amperes at 1.2 volts. With the e. m. f ap-
plied in the opposite direction (point negative) the charge and dis-

PIERCE AND EVANS. — CAPACITY OF CARBORUNDUM.

811

charge currents (Table IV.) differ by about 5 per cent, at the highest
voltage, 1.2 volts. At .9 volts, and lower, this difiference is one per
cent or less. With the point negative the steady current at 1.2 volts
amounts to 1.79 X 10 "^ amperes as is seen in Table V. Therefore
the crystal with the point charged negative is not non-leaky as with the
opposite direction of charging, but the leak is so small as to make the
analysis of the problem much more satisfactory than with Specimen I.

Figure 11. Point positive. Discharge current vs. n, for various applied
voltages V.

Figures 11 and 10 show the discharge current plotted against n, the
number of discharges per second, obtained with point positive and
point negative respectively. The corresponding charge curves depart
so slightly from the discharge curves that they are not here reproduced.

AU of the charge and discharge curves for this specimen pass
through the origin. This is a result such as one obtains with an
ordinary condenser possessing no leakage.

The curves all droop at higher values of n, but are nearly straight
for small values of n. Now this fact is in agreement with results
obtained with good condensers provided they possess such high resist-
ance in the charge or discharge circuit that the charge and discharge
are incomplete. It is interesting that the treatment of the experimen-
tal curves of Figures 10 and 11 as due to a condenser with incomplete

812 PROCEEDINGS OF THE AMERICAN ACADEMY.

charge and discharge leads to the result that the capacity is indepen-
dent of n but is dependent, as in Experiment I., upon the magnitude
and direction of the impressed e. m. f. We shall give a brief deriva-
tion of the formula for multiple incomplete charge and discharge.

Sketch of Theory of Multiple Incomplete Condenser

Discharge.

Let a condenser of capacity C be alternately charged and discharged
through a resistance R which is so great as to permit only a partial
charge or discharge in the time T of one connection of the condenser
into the charge or discharge circuit.

Let the applied e. m. f. on charge be E, and suppose that the charge
and discharge have been repeated until a final state is reached.

Let qi = quantity of electricity in the condenser at the end of a charge,
qo = the quantity in the condenser at the end of a discharge.

If we write down the differential equation for the quantity in the
condenser on charge and integrate it subject to the conditions of the

problem, we obtain

r T

q, = goe"^^ +CE{\- e"«^). (24)

Similarly from the differential equation for discharge we get

T

go = qii''''. (25)

Eliminating between equations (24) and (25) we have

■ CE

qi = -^^'

1 + e'"""

Qo

T

CEe''"''

1 + e

T
' RC

The quantity of electricity flowing into the condenser during one
charge, or out of the condenser during one discharge, is

T
' RC

q^q^-q,= CE- ^. (26)

1 -I- e"''^

PIERCE AND EVANS. — CAPACITY OF CARBORUNDUM. 813

This equation by expansion becomes

T T T

q=CE{\- 2e'^^ + 2 (^e'^y - 2 (/«^)« + ....). (27)

T

If we may neglect 2 {e-^^Y in comparison with unity, equation (27)

becomes

r

q=CE{l — 26'^^) approximation. (28)

If there are w charges per second, the current-reading of a galva-
nometer in the charge or discharge circuit is

I=nq,

and the time of charge or discharge is

pn

where \/p is the fraction of the circumference of the commutator oc-
cupied by the charge segment or discharge segment, the two being
equal.

With these substitutions equation (28) becomes

I=nCE{l-2e ^"^^). (29)

With the commutator used in these experiments \/p was .48, whence

a48

'nRC

I=7iCE{l-2e "«^). (30)

Examination of the Data of Experiment II.

The curves of discharge current of Figures 10 and 11 with current
plotted against number of discharges per second are accurately de-
scribed by equation (30), as may be seen by reference to Tables VI.
and VIL, which contain a comparison of observed and calculated
values.

The equations of Table VIII. were obtained as follows : Consistent
with the theoretical equation (30), the slope of each of the curves of
Figures 10 and 11 was taken at the origin. This slope is the coeffi-
cient of n in equation (30), and the corresponding coefficient in Table

814

PROCEEDINGS OF THE AMERICAN ACADEMY.

VIII. Having obtained the slope term, the exponential was next ob-
tained by assuming the upper end point of one of the experimental

TABLE V.

Steady Current-Voltage Characteristic of Specimen II.

E. m. f. Volts.

Current in 10-' Amperes.

Point Positive.

Point Negative.

.3
.6
.9

1.2

1.5

.004

.02

.04

.09
.165

.012
.083
.45
1.79
6.13

carves to satisfy equation (30). This gave the exponent — 165/w, and
by trial the same exponent was found to apply approximately to all of
the other curves. That is, all the equations of Table VIII. were ob-

t2 1.4

Figure 12. Capacity in microfarads of Specimen II. for different values of
applied e. m. f.

tained by employing the slope at the origin of each of the experimental
curves, and in addition assuming the exponential equation to be correct
for one other point of one of the curves. All of the points of all the
curves were then found to be closely given by the equations so derived.

PIERCE AND EVANS.

CAPACITY OF CARBORUNDUM.

815

The conclusion is that the droop of the several curves of Figures 10
and 1 1 may be reasonably explained as due to incompleteness of charge
and discharge. On this assumption it will be seen that the capacity of
the crystal, obtained by dividing the coefficients of the equations of
Table VIII. by the corresponding values of ^, are functions of the applied

TABLE VI.
Data of Experiment II. Compared with Equation (30).

No. of
Discharges

per
Second, n.

Point Positive. Discharge Current in 10"' Amperes.

E = .6.

E = .9.

E = 1.2.

Obs.

Calc.

Obs.

Calc.

Obs.

Calc.

11.0
16.7
22.5
30.9
38.3
46.2

1.43

2.14
2.94
3.97
4.78
6.40

1.43
2.15
2.94
3.99

4.85
6.42

2.06
3.17
4.29
5.89
7.15
9.50

2.11
3.17
4.32
5.90

7.18
9.50

2.66
4.03
5.59
7.60
9.10
12.30

2.73
4.09
5.58
7.62
9.26
12.30

e. m. f. and of the direction of charge, while the product of R by C, as
given by the exponent, is constant. These quantities are collected in
Table IX., and plotted in the curves of Figure 12.

The curves of Figure 12 show that the capacity, as given by equation
(30), is changed by a mere reversal of the direction' of charge. The
capacity is the greater when the point electrode is negative, and with
this orientation the capacity increases with increase of applied e. m. f.
With the opposite direction of application of e. m, f. the capacity is less
and decreases with increasing applied e. m. f.

Whether this result is evidence of a unilateral dielectric constant of
the carborundum — which seems improbable — or whether the result is
due to an imperfect comprehension of the various factors that may
enter into the phenomenon and appear in the final coefficient as capac-
ity, we are at present unable to say.

Among the various factors neglected in the mathematical discussion
of the data there is the possibility that heat effects may be important.
It looks at first glance as if a thermoelectromotive force at the junction

816

PROCEEDINGS OF THE AMERICAN ACADEMY.

of the electrode with one of the laminae of the crystal might aid the
charge in one direction of charge and hinder it with the opposite di-
rection of charge, and might, hence, cause differences in the capacity
coefficients in the two directions, and might also account for the form
of the curves of Figure 12. We have submitted the thermoelectric
hypothesis to a mathematical treatment, assuming that both Joulean

TABLE VII.
Data of Experiment II. Compared with Equation (30).

Point Negative.

Discharge Current

in 10"' Amperes.

No. of

Disch.

per Sec,

n.

E =

.3.

E =

.6.

E =

= .9.

E =

1.2.

Obs.

Calc.

Obs.

Calc.

Obs.

Calc.

Obs.

Calc.

11.0

.78

.77

1.64

1.59

2.54

2.52

3.52

3..52

16.7

1.16

1.17

2.43

2.42

3.81

3.80

5.34

5.35

22.5

1.59

1..58

3.27

3.26

5.22

5.11

7.26

7.20

30.9

2.16

2.22

4.39

4.58

7.02

7.17

10.00

10.10

38.3

2.60

2.61

5.37

5.38

8.54

8.45

12.08

11.92

46.2

6.33

6.32

10.00

9.95

14.10

14.30

54.6

3.38

3.48

7.34

7.18

11.27

11.25

15.85

15.85

heat and Peltier heat act at the junction of one of the electrodes with
the crystal, and have arrived at the result

(1) That the assumption of Joulean heat alone in combination with
capacity gives a capacity coefficient that is the same in the two opposite
directions, and for both directions the effect of the heat term is to make
the capacity coefficient diminish with increasing applied e. m. f.

(2) Peltier heat and Joulean heat, if both present in combination
with the capacity, would give different capacity coefficients in the two
opposite directions, but the effect of the heat would still manifest itself
as an apparent decrease of capacity with increase of applied e. m. f. for
both directions of application of the e. m.f.

Neither of these results is in complete accord with the experimental
facts.

Various other possible explanations of the apparent unilateral ca-
pacity of the crystal condenser have suggested themselves, but we have

PIERCE AND EVANS, — CAPACITY OF CARBORUNDUM.

817

decided to make further measurements before entering into an attempt
to consider more of the factors of the problem.

Specimen ivitk Soldered Attachment under Test. — We have suc-
ceeded in soldering on the electrodes to one specimen now under test,
and are able to preserve the condenser for a more extensive study of
its characteristics. Up to the present this study has not added any-

TABLE VIII.
Equations Used in Calciilating Values in Tables VI. and VII.

E.

Point Positive. Equation.

Point Negative. Equation.

165

.3

165

7 =

.0703 X 10-7 X n (1 - 2e » )

165

.6

/ =

.13XlO-7XK(l-2e ")

165

7 =

.144 X 10-7 Xn(l-2e ")

165

.9

7 =

.192XlO-'Xw(l-2e «)

165

7 =

.227 X 10-7 Xn{l-2e '^ )

165

1.2

7 =

.248 X 10-7 xn{\-2e « )

7 =

.320 X 10-7 X n (1 - 2e " )

thing to the results given above. The new condenser leaks badly in
one direction but very little in the opposite direction of charge. We
are putting it through an ageing process before submitting it to final
measurement.

Microscopic and Electrical Exploration of the Specimens.

Illumination and Magnification. — Plate I. contains some micro-
graphs of fragments of the crystals. These pictures — which are re-
produced with a magnification of 20 diameters — were obtained by
reflected light, with the aid of an illuminating objective. The light,
which entered the side of the objective, was reflected downward by a
prism so that it fell nearly perpendicularly upon the face of the crystal.
This vertical illumination from above is most favorable for showing the
stratifications in the crystals. Viewed by transmitted light the char-
acteristics are hardly discernible.

Micrograph a, Plate I, shows two of the crystallographic angles of
the carborundum crystal. The distance between these two vertices is
1.6 mm., and will serve as a convenient standard of reference for the
dimensions of the other pictures, which were magnified to the same
scale.

Conducting and Insulating Strata. — Micrograph c shows very clearly
the characteristic stratification, which we have found to be the founda-

VOL. XLVII. — 52

818

PROCEEDINGS OF THE AMERICAN ACADEMY.

tion of the electrostatic capacity of the carborundum. The black lines
running in a general horizontal direction across the surface of the
specimen are outcroppings of conducting dykes of the crystal ; while
the white spaces separating the black lines are outcroppings of the in-
sulating matrix in which these dykes are imbedded. The lines which

TABLE IX.
Values of C, RC, and R for Specimen II.

Applied e. m. f. E.

Capacity C, in
Micro-farads.

RC in Ohm-farads.

R in Ohms.

For Point Positive

.6

.0216

.0029

1.34 X 105

.9

.0213

.0029

1.36

1.2

.0207

.0029

1.40

For Point Negative

.3

.0234

.0029

1.24 X 105

.6

.0246

.0029

1.18

.9

.0252

.0029

1.14

1.2

.0267

.0029

1.08

are black and white in the pictures are really merely dlfferenthj colored
in the crystal. The white regions are generally a transparent blue in
the crystals, and the regions reproduced as black are usually seen as
brown or red in the specimen.

The difference in electrical conductivity of the dark and light strata
was discovered by mounting the specimen in the field of the micro-
scope, and exploring it with two pin-points serving as electrodes. The
pin-point electrodes were connected with a battery and galvanometer,
or telephone, and were moved about over the surface of the specimen
by means of two independent mechanical microscope stages insulated
from each other. By means of the slow motion of the mechanical
stages, the two pin-points could be put down upon the same dyke or
on two different dykes, or one pin could be placed on a dyke while the

PIERCE AND EVANS. — CAPACITY OF CARBORUNDUM. 819

other was placed on one of the lighter colored strata separating the
dykes.

It was found that the insulation resistance of a very thin layer of the
lighter colored material was so great that the current through it under
an impressed e. m, f. of 7 volts did not give a perceptible deflection on
the galvanometer, that is, the resistance was more than 7000 million
ohms, whereas the resistance of the circuit when both pins were upon
the same dark-colored dyke was only a few thousand ohms at this
voltage.

It was not possible with some of the specimens to get into electrical
contact with all of the dark-colored outcroppings, because in some
cases it was evident that the outcroppings were in depressions or were
coated over so that the electrodes could not be brought against them.
With other specimens and with the aid of a telephone receiver in the
exploring circuit, we could make attachment of one electrode to a
solder-bed in which the crystal was mounted and could draw the other
electrode across an exposed face of the crystal in the field of the micro-
scope and hear a click in the telephone as the moving electrode passed
over each of the dark-colored outcroppings.

Outcrop of Conducting Points. — In addition to the linear outcrop-
pings of the conducting dykes, there are also with some of the speci-
mens minute points of outcrop of conducting material. Some of these
points are visible in Micrograph d. They are the globular markings
near the left-hand side of the picture. Each globular marking is a
minute darker speck surrounded by a whitish circle. In some cases
we found an outcrop in the form of a minute speck, which evidently
communicated with one or more conducting layers within the crystal,
and which showed measurable capacity when one electrode was brought
into contact with the speck while the other electrode was in contact
with a distant corner of the crystal. In fact, with the specimen of d
many of the apparently linear outcroppings are made up of discrete
points of conducting material.

A Visible Condenser in Micrograph h. — As an illustration of a con-
denser completely visible, reference is made to Micrograph h. The left
half of the picture shows two nearly parallel lines running up through
the center and down along the left-hand side of the specimen. These
lines, which run out of the field at the bottom and top of the picture,
were seen, by moving the specimen in the original examination of this
specimen, to be really two closed curves, one inside of the other. They
are the outcroppings of two practically flat parallel strata nearly perpen-
dicular to the direction of vision. By exploration with the pin-point
electrodes these strata were found to be conducting, whereas the whitish

820 PROCEEDINGS OF THE AMERICAN ACADEMY.

band between the dark lines is the outcrop of an insulating layer sepa-
rating the two conducting strata. Thus we have a visible condenser in
the specimen. The capacity of this condenser was too small to be
measured by the method we were employing, and this specimen is kept
for future investigation.

Micrograph of Specimen I. — The pictures e and / of Plate I. show
micrographs of the two opposite sides, respectively, of Specimen I. The
electrical connection of the specimen into the test circuit was by means
of screws set up against the two sides of the crystal. The ends of the
screws were so large that the exact point of contact of the screws against
the crystal could not be accurately determined, but one of the screw
contacts was apparently against the ridge near the center of e ; the other
screw contact was near the center oif, which is opposite to e. Judging
from the large value of the capacity obtained, we are of the opinion that
more than one conducting dyke was in contact with each electrode, and
that we were dealing with a multiple -plate condenser. Of this, however,
we cannot at present be certain, as we have not as yet been able to
measure the dielectric constant of the insulating strata, and have not
yet been able to determine accurately the geometrical dimensions of the
crystal condensers.

Note on Relation of Stratification to Action of Carborundum
Crystals as Detectors for Electric Waves.

Not all points of a carborundum crystal are equally good detectors
for the electric waves of wireless telegraphy. After our discovery of the
existence of alternate conducting and insulating strata in the carborun-
dum crystal, we arranged circuits, with the crystal connected to a mul-
tiple-pole switch so that it could be thrown into a wireless telegraph
circuit and tested for its sensitiveness to electric waves produced by a
test buzzer ; then into a circuit of the form of Figure 1, and tested for
conductivity and capacity.

The crystal was mounted in the field of a microscope and was carried
by a mechanical stage with micrometer adjustment so that different
parts of the crystal, while under observation with the microscope, could
be brought into contact with the pin-point electrode.

It was found that

1. The crystal and its contact (i. e. the detector) did not respond to
electric waves, and did not conduct, and did not have capacity when the
point electrode was on one of the light- colored strata;

2. The crystal detector did respond whenever the contact was against
one of the darker strata. In general, however, no capacity was dis-

PIERCE AND EVANS. — CAPACITY OF CARBORUNDUM. 821

cernible with one of these random adjustments sensitive to electric
waves ;

3. In rare cases, obtainable only after numerous trials, the adjustment
of the contact upon the crystal would give a capacity ; in these cases the
system would also act as a detector for electric waves.

These observations show that the detection of electric waves occurs
for practically any conductive high-resistance contact of the electrode
with the crystal, whereas only a rarely attainable adj ustment of the con-
tact against a conducting stratum that happens to be pretty well insu-
lated from the other electrode gives the capacity effect measurable by
the method of charge and discharge. It is however apparent that if
the capacity measurements could be made with the high frequency
oscillations of wireless telegraphy, the capacity effect would appear
much more commonly.

Summary.

1. An electrostatic capacity is found in carborundum.

2. The capacity-measurements with two specimens are given for dif-
ferent voltage and different frequencies of charge and discharge. The
capacity of one of the specimens was about .006 microfarads; that of
the other about .022 microfarads.

3. With Specimen I. a leak, different in different directions of charge
and not obeying Ohm's law, made the measurements uncertain of accu-
rate interpretation.

4. Specimen II. was practically non-leaky but showed incompleteness
of charge and discharge such as would be obtained with a high resistance
(120,000 ohms) in the circuit. A reduction of the observation on the
assumption of incomplete charge and discharge gives a capacity, which
for voltages not zero, is different in the two opposite directions of
charge. In one direction of charge the capacity increases with increase
of applied voltage; while in the opposite direction of charge the capacity
decreases with increase of voltage.

5. The existence of capacity in the crystal was found to be due to the
existence of numerous alternate conducting and insulating strata within
the crystal. These strata are visible with vertical illumination and
moderate magnification.

6. Micrographs showing the stratification are given.

7. So far as the present experiments show, the action of the carborun-
dum as a detector for electric waves and as a rectifier for electric cur-
rents is independent of its action as a capacity. But it will detect
electric waves or rectify only provided contact is made to one or more of

822 PROCEEDINGS OF THE AMERICAN ACADEMY.

the conducting strata. It may detect electric waves with an adjustment
that shows no capacity by the present method of measuring capacity.
On the other hand, with every adjustment at which we found capacity,
we found also rectification and detection of electric waves.

Acknowledgment. — The authors gratefully acknowledge their indebt-
edness to the National Academy for an appropriation from the Bache
Fund, which was employed in defraying a part of the expenses of this
investigation.

Jefferson Physical Laboratory,

Harvard University,

Cambridge, Mass.

Pierce and Evans. — Capacity of Carborundum.

Proc. Amer. Acad. Arts and Sciences. Vol. XLVII.

Proceedings of the American Academy of Arts and Sciences.
Vol. XLVII. No. 22. — November, 1912.

RECORDS OF MEETINGS, 1911-1912.

OFFICERS AND COMMITTEES FOR 1912-1913.

LIST OF THE FELLOWS AND FOREIGN HONORARY
MEMBERS.

BIOGRAPHICAL NOTICES.

Thomas Wentworth Higginson. By Andrew McFarland

Davis.
Frederick Irving Knight. By Francis H. Williams.

STATUTES AND STANDING VOTES.

RUMFORD PREMIUM.

INDEX.

(Title Page and Table of Contents.)

RECORDS OF MEETINGS.

One thousand and seventli Meeting.

October 11, 1911. — Stated Meeting.

The Academy met in Ellis Hall, in the Massachusetts His-
torical Society's Building.

The President in the chair.

There were thirty-seven Fellows present.

The Corresponding Secretary presented the following letters
and circulars : — from the University of Minnesota, inviting
the Academy to be represented at the inauguration of George
Edgar Vincent as its President ; the preliminary announcement
of the eighth International Congress of Applied Chemistry ; a
notice of contest for the Elia de Cyon prize ; a request for sub-
scriptions for the purchase of the birthplace of Pasteur; from
the Naturforschende Gesellschaft zu Gorlitz, inviting the
Academy to be represented at the celebration of its centenary ;
a notice from the Surrogates' Court of New York regarding
the property of Catherine R. B. Griffith ; a notice regarding the
probating of the will of Mary H. Cooke.

The following deaths were announced by the Chair: —

Samuel Hubbard Scudder, Resident Fellow in Class II., Sec-
tion 3, Corresponding Secretar}"- and Chairman of the Publi-
cation Committee from 1896 to 1900, Librarian from 1877 to
1885; Cyrus Gurnsey Pringle, Associate Fellow in Class II.,
Section 2.

At the request of the C. M. Warren Committee it was

Voted, That the sum of two hundred dollars ($200) be ap-
propriated from the income of the C. M. Warren P^und for the
use of the Committee.

The following gentlemen were elected Fellows of the
Academy : —

826 PROCEEDINGS OF THE AMERICAN ACADEMY.

In Class I., Section 1 (Mathematics and Astronomy):-

Joel Hastings Metcalf, of Winchester ; Edwin Eidwell Wil-
son, of Cambridge ; Lewis Boss, of Albany.

In Class I., Section 2 (Physics) : —

Harvey Nathaniel Davis, of Cambridge ; Harry Wheeler
Alorse, of Cambridge ; Joseph Svveetman Ames, of Baltimore.

In Class I., Section 3 (Chemistry) : —

William Crowell Bray, of Boston ; Forris Jewett Moore, of
Boston ; Willis Rodney Whitney, of Schenectady.

In Class I., Section 4 (Technology and Engineering) : —

Dugald Caleb Jackson, of Boston ; Frederic Pike Stearns, of
Boston ; Charles Proteus Steinmetz, of Schenectady.

In Class II., Section 1 (Geology, Mineralogy, and Physics of
the Globe) : —

Herdraan Fitzgerald Cleland, of Williamstown ; Hervey
Woodburn Shimer, of Boston ; Charles Richard Van Hise, of
Madison.

In Class II., Section 2 (Botany) : —

Oakes Ames, of North Easton ; Edward Murray East, of
Jamaica Plain ; Robert Aimer Harper, of Madison.

In Class II,, Section 3 (Zoology and Physiology) : —

Henry Bryant Bigelow, of Concord ; Otto Knut Olof Folin,
of Brookline.

In Class II., Section 4 (Medicine and Surgery) : —

Milton Joseph Rosenau, of Boston ; Elmer Ernest Southard,
of Boston ; Simon Flexner, of New York.

In Class III., Section 1 (Philosophy and Jurisprudence) : —

Melville Madison Bigelow, of Cambridge ; Marcus Perrin
Knowlton, of Springfield ; George Vasmer Leverett, of Boston;
Roscoe Pound, of Belmont ; Woodrow Wilson, of Princeton.

In Class III., Section 2 (Philology and Archaeology) : —

Fred Norris Robinson, of Cambridge; Charles Cutler Tor-
rey, of New Haven.

In Class III., Section 8 (Political Economy and History) : —

Edward Channing, of Cambridge ; Frederick Jackson Turner,
of Cambridge ; John Franklin Jameson, of Washington.

In Class III., Section 4 (Literature and the Fine Arts): —

William Sturgis Bigelow, of Boston,

The following report of the Committee on the Revision of
the Statutes was read by the Chairman, Mr. Henry H. Edes: —

RECORDS OF MEETINGS. 827

At the Stated Meeting of the Academy in March, several amend-
ments to the Statutes were adopted upon the favorable report of
the Committee to which they had been duly referred. At the same
meeting, further important amendments were proposed, chiefly for the
purpose of defining some of the newly-created functions and powers of
the Council, of enlarging the functions of the Class Committees, and
of prescribing the procedure of both bodies with respect to the nomi-
nation and election of Fellows and Foreign Honorary Members. These
new amendments also proposed an increase in the number of Council-
lors from nine to twelve and of their terms of service from three years
to four years, thereby insuring always to each Section of each Class at
least one representative in the Council, which, with the eight ex-officio
members, elected annually for terms of one year, would then be com-
posed of twenty persons.

These amendments having been duly referred to a Committee for
consideration and report, it was suggested from the floor, that as the re-
cent adoption by the Academy of the several far-reaching recommenda-
tions of the Committee on Policy necessitated so many alterations in
the Statutes, other changes, doubtless, would, in consequence, suggest
themselves to the Committee ; and the hope was expressed that it
would feel warranted in incorporating in its report upon the amend-
ments then referred to it such further changes as it might deem ex-
pedient. Whereupon, it was unanimously voted by the Academy that
the Committee be authorized and requested to act accordingly.

The present Code of Statutes was adopted on the thirtieth of May,
1854. When the last printed edition appeared, in June, 1910, it had
been then amended twenty-one times. Among the inevitable results of
so many changes are tautology, repetition, and the distribution under
two or more heads of subjects which should be treated in a single
chapter. There are also strange omissions. For instance, there are
no Articles describing the Corporate Seal of the Academy or providing
for the attestation and delivery of the Academy's Diploma ; indeed,
the fact that the Society has a Common Seal is not even recognized,
save by a casual allusion to it in the Chapter defining the duties of
the President, while there is no mention whatever of a Diploma.

The new powers given to the Council by the amendments adopted
in March last necessitated the draughting of an entirely new Chapter ;
while a proper recognition of the Seal required another. On the other
hand, it was desirable that certain chapters should be consolidated, and
repetitions eliminated, especially in the Chapter on Standing Com-
mittees, where three lines of print are five times repeated, and three
other lines are four time repeated.

828 PROCEEDINGS OF THE AMERICAN ACADEMY.

From what has been already said, it will be readily seen that the
only way in which the problem before us could be satisfactorily dealt
with was by recasting and re-arranging the whole Code. This has been
done and the result submitted to the Academy in print during the
past few days.

The principal changes, beside those already referred to, are (i) the
fixing of the limit of the number of Fellows at Six hundred, — those
residing in Massachusetts not to exceed Four hundred, as provided in
the amended Charter ; (ii) raising the limit of the Annual Dues, to be
annually voted and determined by the Academy, from Ten dollars to
Fifteen dollars ; (iii) providing for a Commutation of the Annual Dues
by the payment at one time of Two hundred dollars ; (iv) restricting
elections to the Stated Meetings in January and May ; (v) providing
that the Annual Report of the Treasurer shall be submitted in print ;
(vi) establishing the date when the financial year of the Acad-
emy shall begin ; (vii) reducing the time in which delinquents may
pay their Annual Dues from two years to six months ; and (viii) the
incorporation of some Standing Votes with those Chapters of the Stat-
utes to which they pertain and in which they appear to your Com-
mittee to be more appropriately placed.

The new machinery for the nomination and election of Fellows and
Foreign Honorary Members, if adopted by the Academy, cannot fail to
result in a closer scrutiny by the Class Committees of the names pro-
posed, and a more careful and discriminating selection by the Council
of those presented to the Academy for its consideration.

Conciseness, concentration, comprehensiveness, and conformity were
the principal objects aimed at by your Committee in redraughting the
Code. Except in one or two unavoidable instances, no provision of
the Statutes affecting more than one officer, committee, or subject has
been repeated, such provisions being clearly indicated under their ap-
propriate secondary headings by cross-references to the Chapter and
Article where the text of the provision is printed.

Your Committee has given careful consideration to proposals for
rotation in office applying to the eight Officers and the Standing
Committees annually elected by the Academy, and for an increase in
the number of members of some of the other Committees ; but it is
unanimously of opinion that the adoption of these propositions would
not be Avise. Experience gained by long, continuous service on such a
committee, for instance, as that which administers the Rumford Fund,
is valuable to the Academy ; while for such service as is expected from
those committees which it was proposed to enlarge, small bodies are
generally more efficient than large ones.

RECORDS OF MEETINGS. 829

In conclusion, your Committee begs leave to present for consider-
ation the accompanying votes, intended to give effect to the new Code
if it shall prove acceptable to the Academy.

Respectfully submitted,

Henry H. Edes,
Elihu Thomson",
Henry Lefavour,

Committee.
Boston, October 11, 1911.

I. That the Report of the Committee on the Revision of the
Statutes and Standing Votes is hereby accepted and the Code
submitted therewith adopted.

II. That all previously adopted Statutes and Standing Votes
are hereby repealed,

III. That the places of those Councillors whose terras will ex-
pire in May, 1913, and May, 1914, are hereby declared vacated
at the Annual Meeting in May, 1912 ; and that the Councillors
affected by this vote shall be eligible for renomination and re-
election at that time.

This was followed by discussion. As the time was too lim-
ited to consider the whole subject, it was

Voted., To meet on adjournment, November 8th, when the
discussion would be continued.

The following papers were presented by title : —

" Water, in the Liquid and Five Solid E'orms, under Pressure."
By P. W. Bridgman. Presented by G. W. Pierce.

" Mercury, Liquid and Solid, under Pressure." By P. W.
Bridgman. Presented by G. W. Pierce.

" A New Method of Impact Excitation of Undamped Oscil-
lations and Analysis by Means of Braun Tube Oscillographs."
By E. L. Chaffee. Presented by G. W. Pierce.

" The Measurement of Hydrostatic Pressures up to 20,000
Kilograms per Square Centimeter." By P. W. Bridgman.
Presented by G. W. Pierce.

" Polycerella Zoobotryon (Smallwood). By W. M. Small-
wood. Presented by E. L. Mark.

Because of the lateness of the hour the communication an-
nounced was not presented.

830 PROCEEDINGS OF THE AMERICAN ACADEMY.

One thousand and eighth Meeting.

November 8, 1911. — Adjourned Stated Meeting.

The Academy met at Ellis Hall.

The President in the chair.

There were forty-four Fellows and one guest present.

The Corresponding Secretary read letters from the follow-
ing gentlemen, accepting Fellowship : — Joel H. Metcalf, Lewis
Boss, Harvey N. Davis, Harry W. Morse, Joseph S. Ames,
William C. Bray, Willis R. Whitney, Dugald C. Jackson, Fred-
eric P. Stearns, Herdraan F. Cleland, Hervej' W. Shimer, Charles
R. Van Hise, Oakes Ames, Edward M. East, Robert A. Harper,
Milton J. Rosenau, Melville M. Bigelow, Marcus P. Knowlton,
George V. Leverett, Woodrow Wilson, Fred N. Robinson,
Charles C. Torrey, Edward Channing, Frederick J. Turner,
William S. Bigelow; from John F. Jameson, declining Fellow-
ship; from the Executive Committee of the Eighth Interna-
tional Congress of Applied Chemistry, inviting the Academy to
join the Congress and to take part in its proceedings in Wash-
ington, September 4, 1912, and New York, September 5-13,
1912; from Wssewolod Tscheschichin, Riga, regarding a new
international language.

Mr. Charles P. Bowditch presented a subscription paper,
dated jNIarch, 1849, and signed by prominent members of the
Academy. This interesting paper, which gave the amounts
subscribed to a publication fund, was found among his father's
papers.

The President announced that the Boston Athenaeum had
consented to return to the Academy the bust of Franklin which
was given it by the American Philosophical Society in 1802,
and read the following letters : —

10 Appleton Street, Cambridge, October 23, 1911.

Mr. John Trowbridge, President.

Dear Sir : — I am authorized by the Trustees of the Boston Athe-
naeum to announce to you that the Athenaeum presents to the Acad-
emy, the bust of Franklin which has for many years stood in the
vestibule of the Athenaeum building. The circumstances under which
I have become an intermediary in this transaction are these —

RECORDS OF MEETINGS. 831

In 1800, the American Philosophical Society received by gift a
plaster cast of a bust of Franklin. In 1802, the same society received
another and probably a different bust. At any rate, the Philosophical
Society presented a bust of Franklin to the Academy, presumably one
of these, and to-day the Academy has no such bust.

On the other hand, the Athenaeum has no conclusive record as to
the source from which possession was derived by that society of the
bust in the vestibule.

It appears by our records that the gift by the Philosophical Society
was made in 1802, the same year that the second bust was given to
that society. The Athenaeum bust is said to be a replica of a bust by
Houdon. It is not a replica of the bust in possession of the Philosoph-
ical Society, but represents Franklin at the same period of life, and in
many respects there is a close resemblance between the two busts.

Believing that the Athenaeum bust was probably ours, yet feeling
that there was no method available for proving this, I requested per-
mission to have a replica made of that bust, either for us, or to replace
the Athenaeum bust, as the Trustees might prefer.

The application brought me a reply, a copy of which I enclose, in
which it will be seen that the Athenaeum presents the bust to the
Academy. I have the honor to be.

Yours very truly,

A. McF. Davis.

The following is a copy of the letter enclosed : —

Library of the Boston Athenaeum,
Charles Knowles Bolton, Librarian,

Boston, Mass., October 17, 1911.
Andrew McFarland Davis, Esq.,

10 Appleton Street, Cambridge, Mass.

Dear Sir : — Your letter addressed to me and dated October 14th was
brought before the Trustees of the Athenaeum at their meeting yester-
day. The Trustees wish me to say that, on account of the long and
friendly relation which has existed between the American Academy of
Arts and Sciences and the Proprietors of the Boston Athenaeum,
they welcome your letter as an opportunity to continue these evidences
of good will. They therefore instruct me to present through you to
the American Academy the plaster replica of the bust of Franklin men-
tioned in your letter.

•If at some time in the future the Athenaeum should desire a rep-

832 PROCEEDINGS OF THE AMERICAN ACADEMY.

lica of this bust, we have no doubt that the Academy would look with
favor upon our request ; but that may be left to the future.

Very truly yours,

Charles K. Bolton'.

It was

Voted, That the thanks of the Academy be extended to the
Boston Athenaeum for restoring to the Academy the replica of
the bust of Benjamin Franklin, and their courteous expression
of interest in the Academy. Also that the thanks of the Acad-
emy be extended to Mr. Davis for his efforts in securing this
bust for the Academy.

The consideration of the Report of the Committee on the
Revision of the Statutes continued from the October meeting
was resumed and the Code discussed at length, after which
the following votes were passed: —

1. Voted, That the Report of the Committee on the Revision
of the Statutes and Standing Votes is hereby accepted and the
Code submitted therewith, as amended, adopted.

2. Voted, That all previously adopted Statutes and Standing
Votes are hereby repealed.

3. Voted, That the places of those Councillors whose terms
will expire in May, 1913, and May, 1914, are hereby declared
vacated at the Annual Meeting in May, 1912 ; and that the
Councillors affected by this vote shall be eligible for renomina-
tion and re-election at that time.

On motion of Dr. G. F. Moore, it was also

Voted, That the Committee on the Revision of the Statutes
is hereby authorized to make such verbal changes in the code
just adopted as may be necessary or desirable to bring all its
provisions into harmony with the Academy's action at this
meeting, or to improve the style.

The final wording of the Statutes, here adopted, is as
follows :

STATUTES AND STANDING VOTES

STATUTES

Adopted November 8, 1911

CHAPTER I
The Corporate Seal

Article 1, The Corporate Seal of the Academy shall be as here
depicted :

Article 2. The Recording Secretary shall have the custody of the
Corporate Seal.

See Chap. v. art. 3 ; chap. vi. art. 2.

834 STATUTES OF THE AMERICAN ACADEMY^

CHAPTER II
Fellows and Foreign Honorary Members and Dues

Article 1. The Academy consists of Fellows, who are either citizens
or residents of the United States of America, and Foreign Honorary-
Members. They are arranged in three Classes, according to the Arts
and Sciences in which they are severally proficient, and each Class is
divided into four Sections, namely :

Class I. The Mathematical and Physical Sciences
Section 1. Mathematics and Astronomy
Section 2. Physics
Section 3. Chemistry
Section 4. Technology and Engineering

Class II. The Natural and Physiological Sciences
Section 1. Geology, Mineralogy, and Physics of the Globe
Section 2. Botany
Section 3. Zoology and Physiology
Section 4. Medicine and Surgery

Class HI. The Moral and Political Sciences
Section 1. Theology, Philosophy, and Jurisprudence
Section 2. Philology and Archaeology
Section 3. Political Economy and History
Section 4. Literature and the Fine Arts

Article 2. The number of Fellows shall not exceed Six hundred,
of whom not more than Four hundred shall be residents of Massachu-
setts, nor shall there be more than Two hundred in any one Class.

Article 3. The number of Foreign Honorary Members shall not
exceed Seventy-five. They shall be chosen from among citizens of
foreign countries most eminent for their discoveries and attainments
in any of the Classes above enumerated. There shall not be more
than Twenty-five in any one Class.

Article 4. If any person, after being notified of his election as
Fellow, shall neglect for two months to accept in writing and to pay
his Admission Fee (unless he be at that time absent from the Common-
wealth) his election shall be void ; and if any Fellow resident within
fifty miles of Boston shall neglect to pay his Annual Dues for twelve
months after they are due, provided his attention shall have been called

OF AETS AND SCIENCES. 835

to this Article of the Statutes in the meantime, he shall cease to be
a Fellow ; but the Council may suspend the provisions of this Article
for a reasonable time.

With the previous consent of the Council, the Treasurer may dis-
pense {sub silentio) with the payment of the Admission Fee or of the
Annual Dues or both whenever he shall deem it advisable. In the case
of officers of the Army or Navy who are out of the Commonwealth on
duty, payment of the Annual Dues may be waived during such absence
if continued during the whole financial year and if notification of such
expected absence be sent to the Treasurer. Upon similar notification
to the Treasurer, similar exemption may be accorded to Fellows sub-
ject to Annual Dues, who may temporarily remove their residence for
at least two years to a place more than fifty miles from Boston.

If any person elected a Foreign Honorary Member shall neglect for
six months after being notified of his election to accept in writing,
his election shall be void.

See Chap. vii. art. 2.

Article 5. Every Fellow hereafter elected shall pay an Admission
Fee of Ten dollars.

Every Fellow resident within fifty miles of Boston shall, and others
may, pay such Annual Dues, not exceeding Fifteen dollars, as shall
be voted by the Academy at each Annual Meeting, when they shall
become due ; but any Fellow shall be exempt from the annual pay-
ment if, at any time after his admission, he shall pay into the treas-
ury Two hundred dollars in addition to his previous payments.

All Commutations of the Annual Dues shall be and remain perma-
nently funded, the interest only to be used for current expenses.

Any Fellow not previously subject to Annral Dues who takes up his
residence within fifty miles of Boston, shall pay to the Treasurer within
three months thereafter Annual Dues for the current year, failing which
his Fellowship shall cease ; but the Council may suspend the provisions
of this Article for a reasonable time.

Only Fellows who pay Annual Dues or have commuted them may
hold office in the Academy or serve on the Standing Committees or
vote at meetings.

Article 6. Fellows who pay or have commuted the Annual Dues
and Foreign Honorary ]\Iembers shall be entitled to receive gratis one
copy of all Publications of the Academy issued after their election.

See Chap. x. art. 2.

836 STATUTES OF THE AMERICAN ACADEMY

Article 7. Diplomas signed by the President and the Vice-President
of the Class to which the member belongs, and countersigned by the
Secretaries, shall be given to all the Fellows and Foreign Honorary
Members.

Article 8. If, in the opinion of a majority of the entire Council,
any Fellow or Foreign Honorary Member shall have rendered himself
unworthy of a place in the Academy, the Council shall recommend to
the Academy the termination of his membership ; and if three fourths of
the Fellows present, out of a total attendance of not less than fifty, at a
Stated Meeting, or at a Special Meeting called for the purpose, shall
adopt this recommendation, his name shall be stricken from the Roll.

See Chap. iii. ; chap. vi. art. 1 ; chap. ix. art. 1, 7 ; chap. x. art. 2.

CHAPTER HI

Election of Fellows and Foreign Honorary Members

Article 1. Elections of Fellows and Foreign Honorary Members
shall be by ballot, and only at the Stated Meetings in January and
May. Three fourths of the ballots cast, and not less than twenty,
must be affirmative to effect an election.

Article 2. Candidates must be proposed in writing by two Fellows
of the Section for which the proposal is made. These signed nomina-
tions shall be sent to the Corresponding Secretary and shall be retained
by him until the fifteenth of the following October or February, as
the case may be, when all nominations then in his hands shall be imme-
diately sent in printed form to every Fellow having the right to vote,
with the names of the proposers in each case, and with a request to send
to the Corresponding Secretary written comments on these names not
later than the fifth of November or the fifth of March respectively.

All the signed nominations, with the comments thereon, received up
to the fifth of November or the fifth of March shall be sent at once to
the appropriate Class Committees, which shall report their decisions
to the Council at a special meeting to be called to consider nom-
inations, not later than two days before the meeting of the Academy in
December and April respectively.

Article 3. All nominations approved by the Council shall be read
to the Academy at a meeting in December or in April, or be sent to the

OF ARTS AND SCIENCES. 837

Fellows in print with the official notice of the meeting, and shall then
be posted in the Hall of the Academy until the balloting.

Not later than two weeks after any nomination is reported to the
Academy, the Corresponding Secretary shall send to every Fellow having
the right to vote a brief printed account of the nominee.

See Chap. ii. ; chap. vi. art. 1 ; chap. ix. art. 1.

CHAPTER IV

Officers

Article 1. The Officers of the Academy shall be a President (who
shall be Chairman of the Council), three Vice-Presidents (one from each
Class), a Corresponding Secretary (who shall be Secretary of the Coun-
cil), a Recording Secretary, a Treasurer, and a Librarian, all of whom
shall be elected by ballot at the Annual Meeting, and shall hold their
respective offices for one year, and until others are duly chosen and
installed.

There shall be also twelve Councillors, one from each Section of each
Class. At the Annual Meeting in 1912 three Councillors, one from
each Class, shall be elected by ballot to serve for one year, three for
two years, three for three years, and three for four years. At each
subsequent Annual Meeting three Councillors, one from each Class,
shall be elected by ballot to serve for the full term of four years and
until others are duly chosen and installed. The same Fellow shall
not be eligible for two successive terms.

The Councillors, with the other officers previously named, shall
constitute the Council.

See Chap. x. art. 1.

Article 2. If any office shall become vacant during the year, the
vacancy may be filled by the Council in its discretion for the unexpired
term.

Article 3. At the Stated Meeting in March, the President shall
appoint a Nominating Committee of three Fellows having the right
to vote, one from each Class. This Committee shall prepare a list of
nominees for the several offices to be filled, and for the Standing Com-
mittees, and cause it to be sent to the Recording Secretary not later
than four weeks before the Annual Meeting.

838 STATUTES OF THE AMERICAN ACADEMY

Article 4. Independent nominations for any office, if signed by
at least twenty Fellows having the right to vote, and received by the
Recording Secretary not less than ten days before the Annual Meet-
ing, shall be inserted, together with the list of nominees prepared by
the Nominating Committee, in the call therefor, and shall be mailed
to all the Fellows.

See Chap. vi. art. 2.

Article 5. The Recording Secretary shall prepare for use in voting
at the Annual Meeting a ballot containing the names of all persons
duly nominated for office.

CHAPTER V

The President

Article 1. The President, or in his absence the senior Vice-President
present (seniority to be determined by length of continuous fellowship
in the Academy), shall preside at all meetings of the Academy. In
the absence of all these officers, a Chairman of the meeting shall be
chosen by ballot.

Article 2. Unless otherwise ordered, all Committees which are not
elected by ballot shall be appointed by the presiding officer.

Article 3. Any deed or writing to which the Corporate Seal is to be
affixed, except leases of real estate, shall be executed in the name of the
Academy by the President or, in the event of his death, absence, or
inability, by one of the Vice-Presidents, when thereto duly authorized.

See Chap. ii. art. 7 ; chap. iv. art. 1, 3 ; chap. vi. art. 2 ; chap,
vii. art. 1 ; chap. ix. art. 6 ; chap. x. art. 1, 2 ; chap. xi. art. 1.

CHAPTER VI

The Secretaries

Article 1. The Corresponding Secretary shall conduct the corre-
spondence of the Academy and of the Council, recording or making an
entry of all letters written in its name, and preserving for the files all
official papers which may be received. At each meeting of the Council
he shall present the communications addressed to the Academy which

OF ARTS AND SCIENCES. 839

have been received since the previous meeting, and at the next meeting
of the Academy he shall present such as the Council may determine.

He shall notify all persons who may be elected Fellows or Foreign
Honorary Members, send to each a copy of the Statutes, and on their
acceptance issue the proper Diploma. He shall also notify all meet-
ings of the Council ; and in case of the death, absence, or inability of
the Recording Secretary he shall notify all meetings of the Academy.

Under the direction of the Council, he shall keep a List of the
Fellows and Foreign Honorary Members, arranged in their several
Classes and Sections. It shall be printed annually and issued as of the
first day of July.

See Chap. ii. art. 7; chap. iii. art. 2, 3 ; chap. iv. art. 1 ; chap,
ix. art. 6 ; chap. x. art. 1 ; chap. xi. art. 1.

Article 2. The Recording Secretary shall have the custody of the
Charter, Corporate Seal, Archives, Statute-Book, Journals, and all
literary papers belonging to the Academy.

Fellows borrowing such papers or docufnents shall receipt for them
to their custodian.

The Recording Secretary shall attend the meetings of the Academy
and keep a faithful record of the proceedings with the names of the
Fellows present ; and after each meeting is duly opened, he shall read
the record of the preceding meeting.

He shall notify the meetings of the Academy to each Fellow by mail
at least seven days beforehand, and in his discretion may also cause
the meetings to be advertised ; he shall apprise Officers and Commit-
tees of their election or appointment, and inform the Treasurer of
appropriations of money voted by the Academy.

He shall post in the Hall a list of the persons nominated for election
into the Academy ; and after all elections, he shall insert in the Rec-
ords the names of the Fellows by whom the successful candidates were
nominated.

In the absence of the President and of the Vice-Presidents he shall,
if present, call the meeting to order, and preside until a Chairman is
chosen.

See Chap. i. ; chap. ii. art. 7 ; chap. iv. art. 3, 4, 5 ; chap. ix.
art. 6 ; chap. x. art. 1, 2 ; chap. xi. art. 1, 3.

Article 3. The Secretaries, with the Chairman of the Committee
of Publication, shall have authority to publish such of the records of
the meetings of the Academy as may seem to them likely to promote
its interests.

840 STATUTES OF THE AMERICAN ACADEMY

CHAPTER VII
The Treasurer and the Treasury

Article 1. The Treasurer shall collect all money due or payable to
the Academy, and all gifts and bequests made to it. He shall pay all
bills due by the Academy, when approved by the proper officers, except
those of the Treasurer's office, which may be paid without such ap-
proval ; in the name of the Academy he shall sign all leases of real
estate ; and, with the written consent of a member of the Committee
on Finance, he shall make all transfers of stocks, bonds, and other
securities belonging to the Academy, all of which shall be in his official
custody.

He shall keep a faithful account of all receipts and expenditures,
submit his accounts annually to the Auditing Committee, and render
them at the expiration of his term of office, or whenever required to
do so by the Academy or the Council.

He shall keep separate accounts of the income of the Rumford Fund,
and of all other special Funds, and of the appropriation thereof, and
render them annually.

His accounts shall always be open to the inspection of the Council.

Article 2. He shall report annually to the Council at its March
meeting on the expected income of the various Funds and from all
other sources during the ensuing financial year. He shall also report
the names of all Fellows who may be then delinquent in the payment
of their Annual Dues.

Article 3. He shall give such security for the trust reposed in him
as the Academy may require.

Article 4. With the approval of a majority of the Committee on
Finance, he may appoint an Assistant Treasurer to perform his du-
ties, for whose acts, as such assistant, he shall be responsible ; or, with
like approval and responsibility, he may employ any Trust Company
doing business in Boston as his agent for the same purpose, the com-
pensation of such Assistant Treasurer or agent to be fixed by the
Committee on Finance and paid from the funds of the Academy.

Article 5. At the Annual Meeting he shall report in print all his
official doings for the preceding year, stating the amount and condition

OF ARTS AND SCIENCES. 841

of all the property of the Academy entrusted to him, and the character
of the investments.

Article 6. The Financial Year of the Academy shall begin with
the first day of April.

Article 7. No person or committee shall incur any debt or liability
in the name of the Academy, unless in accordance with a previous vote
and appropriation therefor by the Academy or the Council, or sell or
otherwise dispose of any property of the Academy, except cash or
invested funds, without the previous consent and approval of the
Council.

See Chap. ii. art. 4, 5 ; chap. vi. art. 2 ; chap. ix. art. 6 ; chap.
X. art. 1, 2, 3; chap. xi. art. 1.

CHAPTER VIII
The Librarian and the Library

Article 1. The Librarian shall have charge of the printed books,
keep a correct catalogue thereof, and provide for their delivery from
the Library.

At the Annual Meeting, as Chairman of the Committee on the Li-
brary, he shall make a Report on its condition.

Article 2. In conjunction with the Committee on the Library he
shall have authority to expend such sums as may be appropriated by
the Academy for the purchase of books, periodicals, etc., and for de-
fraying other necessary expenses connected with the Library.

Article 3. All books procured from the income of the Rumford
Fund or of other special Funds shall contain a book-plate expressing
the fact.

Article 4. Books taken from the Library shall be receipted for to
he Librarian or his assistant.

Article 5. Books shall be returned in good order, regard being had
to necessary wear with good usage. If any book shall be lost or
injured, the Fellow to whom it stands charged shall replace it by a new
volume or by a new set, if it belongs to a set, or pay the current price
thereof to the Librarian, whereupon the remainder of the set, if any,

842 STATUTES OF THE AMERICAN ACADEMY

shall be delivered to the Fellow so paying, unless such remainder be
valuable by reason of association.

Article 6. All books shall be returned to the Library for examina-
tion at least one week before the Annual Meeting.

Article 7. The Librarian shall have the custody of the Publications
of the Academy. With the advice and consent of the President, he
may effect exchanges with other associations.

See Chap. ii. art. 6 ; chap. x. art. 1, 2.

CHAPTER IX
The Council

Article 1. The Council shall exercise a discreet supervision over
all nominations and elections to membership, and in general supervise
all the affairs of the Academy not explicitly reserved to the Academy
as a whole or entrusted by it or by the Statutes to standing or special
committees.

It shall consider all nominations duly sent to it by any Class Com-
mittee, and present to the Academy for action such of these nomina-
tions as it may approve by a majority vote of the members present
at a meeting, of whom not less than seven shall have voted in the
affirmative.

With the consent of the Fellow interested, it shall have power to
make transfers between the several Sections of the same Class, reporting
its action to the Academy.

See Chap. iii. art. 2, 3 ; chap. x. art. 1.

Article 2. Seven members shall constitute a quorum.

Article 3. -It shall establish rules and regulations for the transac-
tion of its business, and provide all printed and engraved blanks and
books of record.

Article 4. It shall act upon all resignations of officers, and all
resignations and forfeitures of fellowship ; and cause the Statutes to
be faithfully executed.

It shall appoint all agents and subordinates not otherwise provided
for by the Statutes, prescribe their duties, and fix their compensation.

OF ARTS AND SCIENCES. 843

They shall hold their respective positions during the pleasure of the
Council.

Article 5. It may appoint, for terms not exceeding one year, and
prescribe the functions of, such committees of its number, or of the
Fellows of the Academy, as it may deem expedient, to facilitate the
administration of the affairs of the Academy or to promote its interests.

Article 6. At its March meeting it shall receive reports from the
President, the Secretaries, the Treasurer, and the Standing Committees,
on the appropriations severally needed for the ensuing financial year.
At the same meeting the Treasurer shall report on the expected income
of the various Funds and from all other sources during the same year.

At the Annual Meeting it shall submit to the Academy, for its ac-
tion, a report recommending the appropriations which in the opinion
of the Council should be made.

On the recommendation of the Council, special appropriations may
be made at any Stated Meeting of the Academy, or at a Special Meet-
ing called for the purpose.

See Chap. x. art. 3.

Article 7. After the death of a Fellow or Foreign Honorary Mem-
ber, it shall appoint a member of the Academy to prepare a Memoir for
publication in the Proceedings.

Article 8. It shall report at every meeting of the Academy such
business as it may deem advisable to present.

See Chap. ii. art. 4, 5, 8 ; chap. iv. art. 1, 2 ; chap. vi. art. 1 ;
chap. vii. art. 1 ; chap. xi. art. 1, 4.

CHAPTER X

Standing Committees

Article 1. The Class Committee of each Class shall consist of the
Vice-President, who shall be chairman, and the four Councillors of the
Class, together with such other officer or officers annually elected as
may belong to the Class. It shall consider nominations to Fellowship
in its own Class, and report in writing to the Council such as may
receive at a Class Committee Meeting a majority of the votes cast,
provided at least three shall have been in the affirmative.

See Chap. iii. art. 2.

844 STATUTES OF THE AMERICAN ACADEMY

Aeticle 2. At the Annual Meeting the following Standing Com-
mittees shall be elected by ballot to serve for the ensuing year :

(i) The Committee on Finance, to consist of three Fellows, who,
through the Treasurer, shall have full control and management of the
funds and trusts of the Academy, with the power of investing the funds
and of changing the investments thereof in their discretion.

See Chap. iv. art. 3 ; chap. vii. art. 1, 4 ; chap. ix. art. 6.

(ii) The Rumford Committee, to consist of seven Fellows, who shall
report to the Academy on all applications and claims for the Rumford
Premium. It alone shall authorize the purchase of books, publications
and apparatus at the charge of the income from the Rumford Fund,
and generally shall see to the proper execution of the trust.

See Chap. iv. art. 3 ; chap. ix. art. 6.

(iii) The Cyrus Moors Warren Committee, to consist of seven Fel-
lows, who shall consider all applications for appropriations from the
income of the Cyrus Moors Warren Fund, and generally shall see to
the proper execution of the trust.

See Chap. iv. art. 3 ; chap. ix. art. 6.

(iv) The Committee of Publication, to consist of three Fellows, one
from each Class, to whom all communications submitted to the Acad-
emy for publication shall be referred, and to whom the printing of the
Proceedings and the Memoirs shall be entrusted.

It shall fix the price at which the Publications shall be sold ; but
Fellows may be supplied at half price with volumes which may be
needed to complete their sets, but which they are not entitled to
receive gratis.

Two hundred extra copies of each paper accepted for publication in
the Proceedings or the Memoirs shall be placed at the disposal of the
author without charge.

See Chap. iv. art. 3 ; chap. vi. art. 1, 3 ; chap. ix. art. 6.

(v) The Committee on the Library, to consist of the Librarian, ex
officio, as Chairman, and three other Fellows, one from each Class, who
shall examine the Library and make an annual report on its condition
and management.

See Chap. iv. art. 3 ; chap. viii. art. 1, 2 ; chap. ix. art. 6.

OF ARTS AND SCIENCES. 845

(vi) The House Committee, to consist of three Fellows, who shall
have charge of all expenses connected with the House, including the
general expenses of the Academy not specifically assigned to the care
of other Committees or Officers.

See Chap. iv. art. 3 ; chap. ix. art. 6.

(vii) The Committee on Meetings, to consist of the President, the
Recording Secretary, and three other Fellows, who shall have charge of
plans for meetings of the Academy.

See Chap. iv. art. 3 ; chap. ix. art. 6.

(viii) The Auditing Committee, to consist of two Fellows, who shall
audit the accounts of the Treasurer, with power to employ an expert
and to approve his bill.

See Chap. iv. art. 3 ; chap. vii. art. 1 ; chap. ix. art. 6.

Article 3. The Standing Committees shall report annually to the
Council in March on the appropriations severally needed for the ensuing
financial year ; and all bills incurred on account of these Committees,
within the limits of the several appropriations made by the Academy,
shall be approved by their respective Chairmen.

In the absence of the Chairman of any Committee, bills may be ap-
proved by any member of the Committee whom he shall designate
for the purpose.

See Chap. vii. art. 1, 7 ; chap ix. art. 6.

CHAPTER XI

Meetings, Communications, and Amendments

Article 1. There shall be annually four Stated Meetings of the
Academy, namely, on the second Wednesday of January, March, May,
and October. Only at these meetings, or at adjournments thereof
regularly notified, or at Special Meetings called for the purpose, shall
appropriations of money be made, or amendments of the Statutes or
Standing Votes be effected.

The Stated Meeting in May shall be the Annual Meeting of the
Corporation.

Special Meetings shall be called by either of the Secretaries at the
request of the President, of a Vice-President, of the Council, or of ten

846 STATUTES OF THE AMERICAN ACADEMY.

Fellows having the right to vote ; and notifications thereof shall state
the purpose for which the meeting is called.

A meeting for receiving and discussing literary or scientific com-
munications may be held on the second or the fourth Wednesday,
or both, of each month not appointed for Stated Meetings, excepting
July, August, and September ; but no business shall be transacted at
any meeting which may be held on the fourth "Wednesday.

Article 2. Twenty Fellows having the right to vote shall constitute
a quorum for the transaction of business at Stated or Special Meet-
ings. Fifteen Fellows shall be sufficient to constitute a meeting for
literary or scientific communications and discussions.

Article 3. Upon the request of the presiding officer or the Record-
ing Secretary, any motion or resolution offered at any meeting shall
be submitted in writing.

Article 4. No report of any paper presented at a meeting of the
Academy shall be published by any Fellow without the consent of the
author ; and no report shall in any case be published by any Fellow in
a newspaper as an account of the proceedings of the Academy without
the previous consent and approval of the Council.

Article 5. No Fellow shall introduce a guest at any meeting of
the Academy until after the business has been transacted, and espe-
cially until after nominations to Fellowship have been read and the
result of the balloting for candidates has been declared.

Article 6. The Academy shall not express its judgment on literary
or scientific memoirs or performances submitted to it, or included in
its Publications.

Article 7. All proposed Amendments of the Statutes shall be re-
ferred to a committee, and on its report, at a subsequent Stated Meet-
ing or at a Special Meeting called for the purpose, two thirds of the
ballots cast, and not less than twenty, must be affirmative to eff'ect
enactment.

Article 8. Standing Votes may be passed, amended, or rescinded
at a Stated Meeting, or at a Special Meeting called for the purpose,
by a vote of two thirds of the members present. They may be
suspended by a unanimous vote.

See Chap. ii. art. 5, 8 ; chap. iii. ; chap. iv. art. 3, 4, 5 ; chap. v.
art. 1 ; chap. vi. art. 1, 2 ; chap. ix. art. 8.

RECORDS OF MEETINGS. 847

The following communication was given : —

" A biographical notice of Dr. Henry Pickering Bowditch,"
by Professor W. B. Cannon.

The following paper was presented by title: —

" An Electromagnetic Theory of Gravitation," by D. L.
Webster. Presented by B. O. Peirce.

One thousand and ninth Meeting;.

December 13, 1911.

The Academy met at the Museum of Fine Arts, Huntington
Avenue.

The President in the chair.

There were eighteen Fellows and three guests present.

The Corresponding Secretary read the following letters : —
from Henry B. Bigelow and Elmer E. Southard, accepting Fel-
lowship ; from the New Hampshire Historical Society, inviting
the Academy to be represented at the dedication of its Li-
brary building.

The President read the following letter from Mrs. George
R. Agassiz.

76 Mount Vernon Street, December 11, 1911.

To Professor John Trowbridge,

President of the American Academy of Sciences :
My dear Mr. Trowbridge,

May I offer the American Academy, through you, a bas-relief of Mr.
Alexander Agassiz by Bela Pratt ? It is life size, and most satisfac-
tory to us all, and I hope you will find it so.

If it is accepted by the Academy, I should consider it as a favor to
me, if Mr. Pratt may be allowed to confer with Mr, Page as to the
placing of this bas-rehef.

Yours very sincerely,

Mabel S. Agassiz.

It was

Votedy To accept the gift from INIrs. Agassiz, and the Secre-
tary was instructed to acknowledge it.

The following communication was given by Dr. Fairbanks : —
" Some Aspects of the Fine Arts."

848 PROCEEDINGS OF THE AMERICAN ACADEMY.

One thousand and tenth Meeting.

January 10, 1912.— Stated Meeting.

The Academy met in Ellis Hall.

The President in the chair.

There were twenty-eight Fellows present.

The following letters were presented by the Corresponding
Secretary: — from Edwin B. Wilson, accepting Fellowship;
notices of the deaths of Sir J. D. Hooker and J. B. E, Bornet ;
a preliminary notice of the International Congress of Anthro-
pology and Prehistoric Archaeology, to be held at Genoa, in
September, 1912.

The President announced the following deaths : — Dr. Al-
gernon Coolidge, Fellow in Class II., Section 1 ; Sir Joseph
D, Hooker, and J. B. E. Bornet, Foreign Honorary Members in
Class II., Section 2.

The following report of the Building Committee was read by
the chairman : —

At the Annual Meeting of the Academy, it was voted that the
President appoint a building committee composed of the chairman of
the house committee, the librarian, and such other persons as they
should add to their number to have oversight of the carrying on of the
building, and to decide such matters of detail in connection therewith,
as might come up. The President accordingly appointed Dr. Louis
Bell, in addition to the two officials above named, to whom was subse-
quently added Dr. H. M. Goodwin, who with the President consti-
tuted the committee. The committee held several meetings during
the summer, and considered a number of matters of detail. Several
conferences were held by representatives of the committee with the
architect, who seemed very averse to treating with the committee or
taking any of their suggestions. The Agassiz heirs were also con-
sulted and finally agreed to change the elevator which had been or-
dered to a self-acting one. The committee feel bound to state that
this is the chief tangible result that their labors have accomplished.
They have been unable until very recently to secure access to the
stack so that it has has been impossible to consult books or records,
and many of their recommendations have not been carried out. It
was the opinion of the committee that the reading room should have

RECORDS OF MEETINGS. 849

low book shelves entirely around it, which would permit placing in the
reading room the recent volumes of all the transactions of the learned
societies now in our book stack. It was also our opinion that conven-
ience required a door opening directly from the librarian's room into
the reading room. This, however, the Messrs. Agassiz refused to allow.
We do not think that the shelving should have glass doors nor that
five sofas are desirable, believing that the room should have the requi-
sites of a reading room rather than of a club room. The committee hope
that the members of the Academy may express their opinion on this
point, and that either the functions of the committee may be deter-
mined more definitely or that the committee may be discharged.

Respectfully submitted,

A. G. Webster.

After discussion, on the motion of A. C. Lane, it was'
Voted, 1. That the President notify the architects of the

names of the Building Committee, and that they are expected

to carry out the wishes of the same, so far as is compatible with

the wishes of the Agassiz heirs.

2. That the Building Committee be requested to continue.

It was also

Voted, That the Report of the Building Committee be

accepted.

The following communication was given : —

" The Fall of a Meteorite. " By Dr. Elihu Thomson.

The following paper was presented by title: —

" A Revision of the Atomic Weight of Phosphorus. Second

Paper. — The Analysis of Phosphorus Tribromide." By G. P.

Baxter, C. J. Moore, and A. C. Boylston.

One thousand and eleventh Meeting.

January 17, 1912. — Special Meeting.

The Academy met at Ellis Hall, called by the President to
consider the furnishing of the new building.

The President in the chair.

There were twenty-three Fellows present.

In the absence of the Recording Secretary, the Corresponding
Secretary acted in his place.

850 PROCEEDINGS OF THE AMERICAN ACADEMY.

The President stated the object of the meeting and gave his
views of the matter in question.

A representative of the firm of Page and Frothingham, the
architects of tlie new building, was present, and after discussion
the Academy took a recess of five minutes to examine the plan
of the Reading-room which he presented.

After business was resumed, on motion of the Treasurer, it was

Voted, That in the opinion of the Academy it is desirable
that the plan of furnishing the Academy building as suggested
by the Agassiz heirs through the architects be carried out.
This was passed by a vote of 13 to 6.

At 9.45 the meeting adjourned.

One thousand and t'welf th Meeting.

February 14, 1912.

The Academy met in Ellis Hall.

The President in the chair.

There were thirty-three Fellows and one guest present.

The Corresponding Secretary presented the following com-
munications:— letters from Forris Jewett Moore, accepting
Fellowship ; and from Heiurich Oscar Hofman, resigning Fel-
lowship ; an invitation from the Royal Society of London, to
send a delegate to the celebration of its 250th anniversary, in
July, 1912; an invitation from the American Philosophical
Society, to send a delegate to its Annual General Meeting,
April 18-20, 1912 ; an invitation from the Academy of Natural
Sciences of Philadelphia, to send a representative to the celebra-
tion of its centenary anniversary, March 19-21, 1912 ; a notice
of the eighth International Congress of Applied Chemistry, to
be held in Washington and New York, in September, 1912, en-
closing blanks for application for Membership.

The President announced the death of Dr. O. F. Wadsworth,
Fellow in Class XL, Section 4, and of Joseph Lister, Foreign
Honorary Member in Class H., Section 4.

The President was authorized to appoint a delegate to the
celebration of the "250th anniversary of the Royal Society,
London ; to the celebration of the centenary anniversary of the

RECORDS OF MEETINGS. 851

Academy of Natural Science of Philadelphia, and also to the
Annual General Meeting of the American Philosophical Society.

On motion of Mr. C. P. Bowditch, the following resolution
was passed, and the Corresponding Secretary requested to send
copies to the Carnegie Institution, the Smithsonian Institution,
and the Library of Congress : —

JVJiereas^ In 1908, the Carnegie Institution published the
" Handbook of Learned Societies and Institutions in America "
which had been compiled by Mr. J. D. Thompson, of the Li-
brary of Congress,

JVIiereas, This book is of inestimable value to Librarians and
to all interested in a knowledge of the history, or publications
of Societies, and

Whereas, Material has been collected for a Handbook relating
to Societies of the Old World, which is now kept on file in the
Library of Congress, it is therefore

Voted, That the American Academy of Arts and Sciences re-
quest that this unpublished material may be published with as
little delay as possible, if not by the Carnegie Institution, then
by the Library of Congress or the Smithsonian Institution.

On motion of Professor Lanman, it was

Voted, That the Chairman of the Committee of Publication
be requested to see that the bound volumes of the Proceedings
be lettered on the back with the date as well as the volume
number.

The Secretary of the Council announced that at his own re-
quest, Dr. Harold C. Ernst had been transferred from Class II.,
Section 3, to Class II., Section 4.

The following communications were given : — •

Dr. F. H. Williams. " A Biographical Notice of Dr. Fred-
erick I. Knight."

Mr. Charles P. Bowditch. " The Results of the American
Occupation of the Philippines."

The following papers were presented by titles : —

" Electrical Properties of Crystals. Capacity in Carborun-
dum." By G. W. Pierce and R. D. Evans.

" Pali Writing-machines — a Study for a Rational Kej'board."
By C. R. Lanman.

" An Algebra of Plane Projective Geometry." By H. B.
Phillips and C. L. E. Moore, Presented by H. W. Tyler.

852 PKOCEEDINGS OF THE AMERICAN ACADEMY.

One tliousand and thirteenth Meeting.

March 13, 1912. — Stated Meeting.

The Academy met at the X-ray department of the Boston
City Hospital, Harrison Avenue and Massachusetts Avenue.

The President in the chair.

There were present twenty-six Fellows and two guests.

The Corresponding Secretary presented the following com-
munications: from Otto Folin, Roscoe Pound, Charles P. Steiu-
metz accepting Fellowship ; from R. S. Woodward, of the
Carnegie Institution, Charles D. Walcott, of the Smithsonian
Institution, in reply to Resolution of the Academy sent to
them.

The following deaths were announced by the Chair: —

Charles Robert Sanger, Class I., Section 3 ; Edward Henry
Hall, Class III., Section 4 ; Henry Williamson Haynes, Class
III., Section 2, Librarian from 1886 to 1899.

The Corresponding Secretary reported that the Council had
voted to invite Doctor H. P. Walcott to deliver the dedicatory
address at the opening of the new Academy Building, and had
requested the President, with two other members to be selected
by himself, to serve as a Committee of Arrangements for the
opening of the new building.

On the recommendation of the Council it was

Voted, To appropriate five hundred (iSOO) dollars from the
income of the Publication Fund for use of the Publication
Committee.

On the recommendation of the Council it was

Voted, To appropriate two hundred (-1200) dollars from the
income of the General Fund for the use of the House Committee.

The Council proposed the following amendment to the
Statutes: —

Omit paragraph 2, of Article 6, of Chapter IX., and insert in
its place the following:

" A report from the Council shall be submitted to the Acad-
emy, for action at the March meeting, recommending the ap-
propriations which in the opinion of the Council should be
made."

RECORDS OF MEETINGS. 853

The above proposed amendment to the Statutes was referred
to a Committee consisting of Messrs. Bowditch and Edes, with a
request to report at the Annual meeting in May.

On the recommendation of the Council it was

Voted, That in the opinion of the Academy it is desirable
that twenty-five new Fellows, living within fifty miles of Bos-
ton, should be elected in May, in addition to such a number as
is needed to fill vacancies occasioned by deaths or resignations
since January 1, 1912.

The President appointed the following gentlemen to serve as
Nominating^ Committee : —

Henry Lefavour, of Class I.

William T. Sedgwick, of Class II. (Chairman).

George L. Kittredge, of Class III.

Professor Kittredge having declined service on the Com-
mittee, Mr. Worthington C. Ford was appointed by the Pres-
ident in his stead.

The following communication was given ; —

Dr. Francis H. Williams. "X-rays and Radium," with dem-
onstrations.

The following paper was presented by title : —

" On the Ultra Violet Radiation of Practical Illuminants."
By Louis Bell.

One thousand and fourteenth Meeting.

April 10, 1912.

The Academy met at Ellis Hall.

The President in the chair.

There were twenty-two Fellows present.

The Corresponding Secretary presented the following corre-
spondence:— an invitation from the Trustees and Faculty of
Princeton University requesting a delegate from the Academy
at the inauguration of John Grier Hibben, as President of the
University ; from the Secretary of the third International Con-
gress of Archaeology, to be held in Rome, October 9-16, 1912,
requesting delegates ; from the Organizing Committee of the
fourth International Congress of Religious, to be held Septem-
ber 9-13, 1912, at Leiden.

854 PROCEEDINGS OF THE AMERICAN ACADEMY.

The President was authorized to appoint delegates to repre-
sent the Academy at the inauguration of the new President at
Princeton, and at the Congresses to be held at Rome and
Leiden.

The President announced the death of A. Lawrence Rotch,
Class I., Section 1, Librarian of the Academy since 1899.

At the suggestion of the President, it was

Votedy To thank the Massachusetts Historical Society for
their very generous hospitality in allowing the Academy the use
of Ellis Hall during the year.

The following paper was presented by title : —

"New or Critical Laboulbeniales from the Argentine." By
Roland Thaxter.

The following communication was given : —

" Recent Applications of the Gyroscope," with lantern illus-
trations. By Arthur G. Webster.

One thousand and fifteenth Meeting.

May 8, 1912. — Annual Meeting.

The Academy met for the first time in its new building,
erected on the site of its former house and the adjoining lot.
Numbers 28 and 26 Newbury Street.

The President in the chair.

There were forty-four Fellows present.

The Corresponding Secretary presented the following corre-
spondence:— from the Regents and Secretary of the Smith-
sonian Institution, an invitation to view the art objects of
the Freer Collection ; from the chairman of the Organizing
Committee of the Eighteenth International Congress of Amer-
icanists, requesting a representative of the Academy to at-
tend the session in London, May 27-June 1 ; from the Presi-
dent of the Association des Ingenieurs Electriciens, giving
the conditions of the competition for the George Montefiore
prize.

The Chair announced the deaths of the following Fellows : —
George Davidson, Class I., Section 1 ; George Jarvis Brush,
Class II., Section 1.

RECORDS OF MEETINGS. 855

The following report of the Council was read : —

Since the last report of the Council, there have been reported
the deaths of ten Fellows: — Algernon Coolidge, O. F. Wads-
worth, S. H. Scudder, H. W. Haynes, C. R. Sanger, Edward H.
Hall, A. Lawrence Rotch, C. G. Pringle, G. J. Brush, and
George Davidson ; and of three Foreign Honorary Members : —
Sir Joseph Hooker, Lord Lister, and J. B. E. Bornet.

One Fellow has resigned : — H. O. Hofman.

Thirty-four Fellows have been elected, of which number
one declined Fellowship, and one has not yet accepted, as he is
out of the country.

The roll now includes (counting the one who has not yet ac-
cepted) 272 Fellows and 52 Foreign Honorary Members.

The annual report of the Treasurer was read, of which the
following is an abstract : —

General Fund.

Receipts.

Balance, May 1, 1911 $438.14

Investments 3,459.96

Assessments 2,110.00

Admission fees 230.00

Use of water 19.77 86,257.87

Expenditures.

Expense of House S815.14

Expense of Library 2,388.12

Expense of Meetings 171.69

Treasurer 143.57

General expenses of Society 473.96

Interest on bonds 2.91

Income transferred to principal .... 227.10 $4,222.49

Balance, April 1, 1912 2,035.38

$6,257.87

BuMFORD Fund.

Receipts.

Balance, May 1, 1911 $1,498.10

Investments 2,850.93

Sale of Publications 5.00 64,354.03

856 PROCEEDINGS OP THE AMERICAN ACADEMY.

Expenditures.

Research $1,400.00

Books, periodicals, and binding .... 221.70

Publication 756.53

Medals 400.00

Sundries 40.85

Income transferred to principal . . . . 147.03 $2,966.11

Balance, April 1, 1912 1,307.92

$4,354.03

C. M. Warren Fund.

Receipts.

Balance, May 1, 1911 $897.72

Investments 620.60 $1,518.32

Expenditures.

Research $750.00

Vault rent, part 4.00 '

Interest on bonds 70.14

Income transferred to principal .... 16.84

Charged to cancel premium on bonds . . 300.00 $1,140.98

Balance, April 1, 1912 . . . 377.34

$1,518.32

Publication Fund.

Receipts.

Balance, May 1, 1911 $1,066.18

Appleton Fund investments 665.56

Centennial Fund investments .... 2,076.41

Sale of Publications 49.04 $3,857.19

Expenditures.

Publication $2,981.08

Vault rent, part 12.50

Income transferred to principal .... 148.26 $3,141.84

Balance, April 1, 1912 '~. TT . . 715.35

$3,857.19
The following reports were also presented : —

Report of the Library Committee.

Owing to the death of Mr. A. Lawrence Rotch, the usual report of the
Librarian devolves upon the Library Committee ; and the Committee

RECORDS OF MEETINGS. 857

has also lost by death Mr. Henry W. Haynes. Mr. Rotch served as
Librarian from May 10, 1899, until his death, April 7, 1912. Mr.
Haynes died February 16, 1912 ; he had been a member of the Library
Committee since May, 1899, and had previously been the Librarian
of the Academy for thirteen years.

During the year the Library has been conducted at the rooms tem-
porarily occupied by the Academy at 711 Boylston Street. The New-
bury Street book stack was accessible only from November, 1911, and
during this time 62 books were borrowed by 10 persons.

Upon the completion of the new building in April, 1912, the cur-
rent numbers of serials and of the publications of institutions were re-
moved to the Librarian's room and the pamphlets to the gallery of the
same room ; the duplicate books have been placed in the stack room
on the fourth floor, and the stock of the publications of the Academy
in the stack room in the basement.

725 volumes have been placed on the shelves since the last report ;
this includes 626 volumes received by gift and exchange, 81 volumes
purchased from the income of the General Fund, and 18 volumes pur-
chased from the income of the Eumford Fund.

The number of volumes now in the library is 32,068.

578 volumes have been bound, 147 have been stamped and plated
at a cost of $656.25.

The expenses charged to the Library are : — Miscellaneous (includ-
ing 820.13 for cataloguing), 8382.29; Binding, $597.80 General, and
$58.45 Rumford, Funds ; Purchase of periodicals and books, $491.37
General, and $163.25 Rumford, Funds.

H. M. Goodwin of Class L,
Samuel Henshaw of Class H.,

Committee.
May 8, 1912.

Report of the Rumford Committee.

During the present year appropriations in aid of research have been
made by the Committee as follows : —

May 10, 1911 (evening meeting), to Professor Daniel F. Com-
stock, in aid of his research on the effect of motion of the source
on the velocity of light $150

Nov. 8, 1911, to Mr. Frank W. Very, in aid of his research on
the intensity of spectrum lines (additional) 150

To Professor John Trowbridge, in aid of the researches of Mr.
Harvey C Hayes in thermo-electricity 300

858 PROCEEDINGS OF THE AMERICAN ACADEMY.

To Professsor Robert W. Wood, in aid of his researches on the
optical properties of vapors and long heat waves (additional) . 150

Dec. 13, 1911, to Professor Arthur L. Clark, in aid of his re-
search on the physical properties of vapors in the neighborhood
of the critical point (additional) 250

Feb. 14, 1912, to Professor Gilbert N. Lewis, in furtherance of
his researches on the free-energy changes in chemical reactions
(additional) 250

Since the last annual meeting of the Academy, papers have been
published in the Proceedings at the expense of the Rumford Fund,
wholly or in part, as follows : —

Hayes, Harvey C. — An Investigation of the Errors in Cooling Curves
and Methods for Avoiding these Errors ; also, a new Form of Crucible.

Richards, Theodore W., and Kelley, George L. — The Transition
Temperatures of Sodium Chromate as Convenient Fixed Points in
Thermometry,

Bridgman, Percy W. — Mercury, Liquid and Solid, under Pressure.

Bridgman, Percy W. — Water, in the Liquid and Five Solid Forms,
under Pressure.

At the meeting of March 13, 1912, it was voted to authorize the
Chairman to proceed to the printing of the Supplement to the "Rum-
ford Fund " pamphlet, the copy for which is now complete.

The Committee has succeeded in locating all the Rumford medals
which have been awarded, and has procured casts or photographs from
which replicas can be made at any time.

At the meeting of Nov. 8, 1911, the Committee made a change in
the requirements as to the publication of papers embodying the re-
sults of researches aided from the Rumford Fund. The rule as modified
now reads, " Persons carrying on researches with the aid of the Rum-
ford Fund should submit to the Academy an account of their researches
not less complete than that published elsewhere. These researches
may be published in any place or form, with the proviso that due rec-
ognition be made of the grant."

At the meeting of the Committee held on February 14, 1912, it was
unanimously voted for the first time, and at the meeting held on
March 13 it was unanimously voted for the second time, to recommend
to the Academy the award of the Rumford Premium to Frederic Eu-
gene Ives for his Optical Inventions, particularly in Color Photogra-
phy and Photo-engraving.

Charles R. Cross, Chairman.

May 8, 1912.

records of meetings. 859

Report of the C. M. Warren Committee.

The C. M, Warren Committee beg to report that during the past
year grants have been made as follows : —

To Dr. S. F. Acree, Johns Hopkins University, for the study
of the physical and chemical properties of pure ethyl alcohol . $200

To Professor H. G. Byers, University of Washington, for work
upon passivity of metals 250

To Professor W. D. Harkins, University of Montana, for work
upon the energy relations in a surface between two liquid phases 300

To Dr. Latham Clark, Harvard University, for work on the
paraffin hydrocarbons 150

Reports have been received from the various recipients of the grants
from the Warren Fund, indicating the progress which is being made
upon the researches not yet completed.

The Committee has suffered a serious loss in the death of Professor

Charles R. Sanger, who has for many years taken a marked interest in

this work. The members of the Committee desire to record their

sense of personal loss which Professor Sanger's death occasions.

H. P. Talbot, Chairman.
May 8, 1912.

Report of the Publication Committee.

Between May 1, 1911, and April 1, 1912, there were published seven
numbers of Volume XL VI. (Nos. 19-25) and twenty-one numbers of
Volume XLVn. of the Proceedings. The total publication amounted
to 1001 pages. The expense of publishing five numbers and a part of
a sixth has been assumed by the Rumford Committee.

There was available for the use of the Publication Committee an
unexpended balance from last year of $375.72, an appropriation of
$2500 and an additional appropriation of $500, and an amount of
$33.99 from the sale of publications up to March 4th — in all $3409.71
from the Publication Fund and Sales. Bills against this appropriation
to the amount of $2981.08 have been approved by the Chairman of
the Publication Committee, and have been submitted to the Treasurer.
This leaves an unexpended balance of $428.63.

Bills aggregating .$756.53, incurred in publishing papers on light
and heat, have been referred to the Rumford Committee for payment
in accordance with their authorization.

G. W. Piebce, Chairman.

May 8, 1912.

860 proceedings of the american academy.

Report of the House Committee.

The rooms at 711 Boylston Street were occupied from March 25,
1911, to April 11, 1912. Out of an appropriation of $1004.93, the
sum of $858.89 has been spent, leaving a balance of $146.04.

A. G. Webster, Chairman.

May 8, 1912.

Financial Report of the Council.

Estimated Income — May 1, 1912, to April 1, 1913.
General Fund $3,846.84

Publication Fund \ ^PP^^*°^ ^"^^ ^^^^"^^

PUBLICATION rUND I ^^^^^^^.^^p^^^ ^ ^ _ ^Qgygg 2,775.72

RuMFORD Fund 2,754.18

Warren Fund 620.60

Available for Appropriation.

General Fund Unappropriated balance. . . $992.76
Cash for current expenses . . . 2,000.00
Income, less 5% added to capital 3,645.00 $6,637.76
Publication Fund " " " ... 2,636.93

RuMFORD Fund " " " ... 2,616.47

Warren Fund " " " ... 589.58

Appropriations recommended.

General Fund House expenses $1,540.00

Library expenses 1,466.67

Books, periodicals, and binding 1,100.00

Expenses of Meetings. . . . 183.33

Treasurer's Office 191.67

" Insurance. . 450.00

General expenses 366.67 $5,398.34

Publication Fund.

Publication $2,500

RuMFORD Fund.

Research $1,000

Periodicals, books, and binding . . . 200

Publication 600

To be used at discretion of Committee 800 $2,600

Warren Fund.

Research $500

RECORDS OF MEETINGS. 861

In accordance with the recommendation in the foregoing report it
was

Voted, To appropriate for the purposes named the following sums : —
From the General Fund, $5,398.34.
From the income of the Publication Fund, $2,500.
From the income of the Rumford Fund, $2,600.
From the income of the Warren Fund, $500.
On the recommendation of the Rumford Committee, it was
Voted, To award the Rumford Premium to Frederic Eugene Ives for
his Optical Inventions, particularly in Color Photography and Photo-
engraving.

The following report was read : —

Your Committee, appointed to consider and report on the Amend-
ment to the Statutes offered at the March meeting, respectfully
report, —

They advise the adoption of the Amendment, as follows : —
Omit Paragraph 2 of Article 6 of Chapter IX and insert the
following : —

" A Report from the Council shall be submitted to the Academy, for
action, at the March meeting, recommending the appropriations which
in the opinion of the Council should be made."

Charles P. Bowditch,
Henry H. Edes,

Committee.

On the motion of Mr. Bowditch, it was

Voted, To adopt the amendment as reported.

Upon motion of Mr. Lanman, it was

Voted, 1. That among the volumes kept upon the shelves of
the Reading Room there be included one set of the publications
of this Academy, complete from the beginning; and also any
other such volumes as throw light upon the history and activ>
ities of the Academy.

2. That the Librarian be requested to give efiPect to this vote
as soon as that may conveniently be done.

The annual election resulted in the choice of the following
officers and committees : —

John Trowrridge, President.
Elihu Thomson, Vice-President for Class I.
Henry P. Walcott, Vice-President for Class II.
A. Lawrence Lowell, Vice-President for Class III.

862 PROCEEDINGS OF THE AMERICAN ACADEMY.

Edwin H. Hall, Corresponding Secretary.
William Watson, Recording Secretary.
Charles P. Bowditch, Treasurer.
Harry W. Tyler, Librarian.

Councillors for One Year.

George F. Swain, of Class I.
Reginald H. Fitz, of Class H.
Henry H. Edes, of Class HI.

Councillors for Two Years.

Robert W. Willson, of Class I.
Thomas A. Jaggar, Jr., of Class H.
Joseph H. Beale, of Class III.

Councillors for Three Years.

Arthur G. Webster, of Class I.
Merritt L. Fernald, of Class II.
George F. Moore, of Class III.

Councillors for Four Years.

James F. Norris, of Class I.
George H. Parker, of Class II.
Frank W. Taussig, of Class HI.

Finance Committee.
John Trowbridge, Gardiner M. Lane,

John Collins Warren.

Rumford Committee.
Charles R. Cross, Erasmus D. Leavitt,

Edward C. Pickering, Elihu Thomson,

Arthur G. Webster, Louis Bell,

Arthur A. Noyes.

G. M. Warren Committee.
Henry P. Talbot, Walter L. Jennings,

Charles L. Jackson, Gregory P. Baxter,

Arthur A. Noyes, James F. NorriS;

William H. Walker.

RECORDS OF MEETINGS. 863

Publication Committee.

George W. Pierce, of Class I.
Walter B. Cannon, of Class II.
Albert A. Howard, of Class III.

Library Committee.

Harry W. Tyler,
Harry M. Goodwin, of Class I.
Samuel Henshaw, of Class II.
William C. Lane, of Class III.

House Committee.

Henry P. Talbot, Louis Derr,

Hammond V. Hayes.

Committee on Meetings.

The President, The Recording Secretary,

William M. Davis, Wallace C. Sabine,

Arthur Fairbanks.

Auditing Committee.
Elliot C. Clarke, Worthington C. Ford.

The following gentlemen were elected Fellows of the
Academy : —

In Class I., Section 1 (Mathematics and Astronomy) : —

George Russell Agassiz, of Boston ; Ernest William Brown,
of New Haven ; Frederick Shenstone Woods, of Newton,

In Class I., Section 2 (Physics) : —

Louis Agricola Bauer, of Washington; Percy Williams
Bridgman, of Cambridge ; Daniel Frost Comstock, of Boston ;
Arthur Louis Day, of Washington ; Charles Sheldon Hastings,
of New Haven ; Maurice deKay Thompson, of Boston.

In Class I., Section 3 (Chemistry) : —

Russell Henry Chittenden, of New Haven; Lawrence Joseph
Henderson, of Cambridge; Samuel Parsons Mulliken, of
Boston.

864 PROCEEDINGS OF THE AMERICAN ACADEMY.

In Class I„ Section 4 (Technology and Engineering) : —

William Herbert Bixby, of Washington ; Desmond FitzGer-
ald, of Brookline ; George Washington Goethals, of Culebra;
Canal Zone ; Lionel Simeon Marks, of Cambridge.

In Class II., Section 1 (Geology, Mineralogy, and Physics of
the Globe) : —

Waldemar Lindgren, of Washington; William Berryman
Scott, of Princeton.

In Class II., Section 2 (Botany) : —

Ezra Brainerd, of Middlebury; Vt. ; Alexander William
Evans, of New Haven.

In Class II., Section 3 (Zoology and Physiology) : —

William Healey Dall, of Washington; John Eliot Thayer,
of Lancaster, Mass.

In Class II., Section 4 (Medicine and Surgery): —

Elliott Proctor Joslin, of Boston ; Charles Pickering Putnam,
of Boston; Simeon Burt Wolbach, of Boston; James Homer
Wright, of Boston.

In Class III., Section 1 (Philosophy and Jurisprudence ) : —

John Adams Aiken, of Greenfield, Mass. ; Simeon Eben Bald-
win, of New Haven; Frederic Dodge, of Belmont; Richard
01ne3% of Boston; Elihu Root, of New York; Arthur Prentice
Rugg, of Worcester,

In Class III., Section 2 (Philology and Archaeology) : —

Franz Boas, of New York ; George Henry Chase, of Cam-
bridge ; Alfred Louis Kroeber, of Berkeley, Cal. ; Hanns Oertel,
of New Haven.

In Class III., Section 3 (Political Economy and History) : —

Irving Fisher, of New Haven.

In Class III., Section 4 (Literature and the Fine Arts) : —

Henry Leland Chapman, of Brunswick, Maine ; Wilberforce
Fames, of New York ; Henry Lee Higginson, of Boston ; Mark
Antony De Wolfe Howe, of Boston ; George Herbert Palmer,
of Cambridge ; Robert Swain Peabody of Boston ; William Jew-
ett Tucker, of Hanover, N. H. ; Williston Walker, of New
Haven.

The following gentlemen were elected Foreign Honorary
Members : —

In Class I., Section 2 (Physics) : —

RECORDS OF MEETINGS. 865

Svante August Arrhenius, of Stockholm ; Hendrik Antoon
Lorentz, of Leyden ; Augusto Righi, of Bologna.

In Class III., Section 4 (Literature and the Fine Arts) : —

Jean Adrien Aubin Jules Jusserand, of Paris.

Dr. C. S. Minot presented the following paper by Professor
Hugo Kronecker : —

" Unexpected Effects of Electrical Stimuli on the Human
Biceps."

The following paper was presented by title : —

" A Theory of Linear Distance and Angle." By Dr. H. B.
Phillips and Dr. C. L. E. Moore. Presented by H. W. Tyler.

BIOGEAPHICAL NOTICES.

FREDERICK IRVING KNIGHT.

Dr. Frederick Irving Knight was born in Newburyport, Massa-
chusetts, on May 18, 1841, was graduated at Yale College in 1862,
from which later he received the degree of A.M., and at the Harvard
Medical School in 1866. While studying in Europe he was made
Instructor in Percussion, Auscultation, and Laryngology in this school,
and in 1886 Clinical Professor of the last subject. He inaugurated a
clinic for diseases of the chest and throat at the Massachusetts Gen-
eral Hospital, was consulting physician there, as well as at the Free
Home for Consumptives, and the Sharon Sanatorium. A pioneer in
the movement against tuberculosis, he gave time and thought to its
furtherance, and it was largely through the advice given by him to
Governor Greenhalge that the Massachusetts Sanatorium at Rutland
was established. One of the founders of the Boston Medical Library,
he was a student, as well as a practitioner, of medicine, a frequent
contributor to the medical press, and a member of well-known medical
societies.

His knowledge of lar3aigology and diseases of the chest, founded
upon a broad knowledge of medicine as a whole, made him one of the
foremost authorities on these subjects in the country. Possessed of
every quality for which we respect the older physician, he was also
conspicuously cordial to what was new in medicine, spared no pains to
inform himself, and weighed the evidence critically before accepting
or rejecting the new remedy or method. No one in the profession
reached sounder conclusions or more quietly and courageously held
his secure ground.

In the care of his patients he took exceptional pains to have every-
thing done that might contribute to their welfare and recovery.

He was just, considerate, and generous, to the younger as well as to

868 THOMAS WENTWORTH HIGGINSON.

the older medical men, and it was a privilege to be counted among

his friends.

He was elected a Fellow of the Academy March 13, 1889. He

died February 20, 1909.

Francis H. Williams.

THOMAS WENTWORTH HIGGINSON.

Thomas "Wentworth Higginson, preacher, soldier, author, was
born in Cambridge, Massachusetts, December 22, 1823. His pre-
liminary education was obtained in a private school at Cambridge, and
he was graduated from Harvard College in 1841. After graduation
he taught for six months in a boarding-school at Jamaica Plain, and
then became private tutor to the sons of a cousin, who at that time
resided in Brookline. Here, domesticated in an affectionate and
interesting family, and having access to a library the shelves of which
were loaded with the works of French and German writers with which
for the first time he then came in contact, he led a happy life. The
beautiful country about Brookline fascinated him, and he spent hours
in rambling over the hills, watching the birds and animals and gath-
ering wild flowers. " We often had school," he says, " in the woods
adjoining the house, perhaps sitting in large trees, and interrupting
work occasionally to watch a weasel gliding over a rock or a squirrel
in the boughs."

The Brook Farm experiment was then in full career and Higginson
came in contact, while living in Brookline, with several of the young
men who were at that time giving practical proof of their faith in
communistic theories. Obviously these theories did not reach him,
although, so far as money matters were concerned, he at this time
deliberately renounced all thoughts of the accumulations that might
be had from the law as a profession, and under the influence of the
books that he was then reading, concluded that a life of extreme
economy was without terror for him. So minded, he became engaged
to be married, and returned to Cambridge in September, 1843, where
he entered college as a "resident graduate," having no clearly defined
purpose or intention as to the future, but attracted by the thought of
a purely literary life carried on in an unworldly spirit with the pos-
sible chance of an appointment as professor as a reward. The in-
fluences that surrounded him while in Cambridge are best told by
himself: "There were always public meetings in Boston to be at-
tended, there were social reform gatherings where I heard the robust
Orestes Brownson and my eloquent cousin, William Henry Channing ;

THOMAS WENllV'ORTH HIGGINSON. 869

there were anti-slavery conventions, with Garrison and Phillips ; then
on Sunday there were Theodore Parker and James Freeman Clarke,
to show that one might accomplish something and lead a manly life
even in the pulpit." Then, as ever after, manliness was with him an
essential feature of life, and it was with the thought that " even in
the pulpit" a man might lead a "manly life," that he gravitated
towards the "liberal ministry," and in preparation therefor entered
the Harvard Divinity School. He completed the regular course of
study there and graduated in 1847.

On the 30th of September of that year he married, in Boston, his
cousin, Mary Elizabeth, daughter of Dr. Walter Channing. Mrs.
Higginson, not long after her marriage, became a confirmed invalid,
but she survived until September 2, 1877, when she died at Newport,
Rhode Island. In the preface of "Malbone," Higginson makes the
statement that " Aunt Jane," a character in that novel, was studied
as closely as possible from real life, and the bright sayings of the
lady were the fruit of a long habit of jotting down her actual conver-
sation. We shall probably not be far out of the way if we conclude
that this statement points out where a clue to the character of Mrs.
Higginson may be found.

In 1847, the year that he graduated at the Divinity School, and
the year also in which he was married to his cousin, he received a
call from the First Religious Society at Newburyport, then ostensibly
Unitarian, which call he accepted. He was ordained, at his own
suggestion, by the Society itself without the intervention of an ordain-
ing council. In Newburyport he was drawn into the temperance
agitation, the peace movement, the woman's rights movement, and
the anti-slavery movement. He did, indeed, accept in 1848 — though
hopeless of election — the nomination for Congress from the Free Soil
party, a party defined by him as "political abolitionists," and, while
still a settled clergyman at Newburyport, he actually entered upon an
active campaign in that congressional district. His nomination was
due, partly at any rate, to Whittier. At Cambridge he had been a
friend and associate of Lowell. His life at Newburyport brought him
in contact with Whittier. The anti-slavery sentiments of both these
poets drew him into close and sympathetic touch with them, and
though he was strong enough to stand alone, he welcomed the support
of their influence.

His career as an anti-slavery candidate for Congress, stumping the
district in search of votes, or perhaps it would be better to say in an
effort to create public opinion and to identify himself with a cause,
naturally aroused hostility in his congregation. He himself says that

870 THOMAS WENTWORTH HIGGINSON.

he preached himself out of the pulpit. His sermons doubtless had to
do with his separation from this congregation, but his political speeches
must also be reckoned in the general accounting. For two years and
a half he retained connection with this parish, and during all that time
he had the cordial support of the younger members of his congrega-
tion. Then, for two years after the severance of this connection, he
continued to live in Newburyport, teaching private classes, serving on
the school committee, organizing public evening schools, and enlisting
the young ladies of the town in the instruction of factory girls, thus
making himself a living force in local affairs. As if all this were not
enough for one man, he was at the same time busily engaged in
writing editorials and communications for three or four newspapers.

In February, 1851, a fugitive slave, known as Shadrach, was rescued
by Boston negroes from the hands of the officers having him in custody,
while actually within the precincts of the Suffolk Court House. This
evasion of the enforcement of the fugitive-slave law caused a commotion
even in Washington, and it was not long before a second test was made
of the power of the federal government to enforce in Massachusetts an
obnoxious law in a community thoroughly loyal and obedient to law,
but hostile to the principles on wbich this particular law was based.

Following the rescue of the negro Shadrach in February, 1851, Hig-
ginson joined the Vigilance Committee in Boston, an organization the
purpose of which was apparently to be on the alert and ready to aid in
such cases, but without definite plans as to how assistance might be given.
The committee was divided in opinion on the question of forcible resist-
ance to the authorities. His official connection with this organization
soon caused him to be summoned to Boston, where in April of the same
year the arrest of Thomas Simms, another fugitive, brought the Vigilants
face to face with the question of what they should do. At the meeting
of the committee Higginson urged action in opposition to the enforce-
ment of the law, and at a crowded public meeting held subsequently in
Tremont Temple he spoke vehemently, his counsels on this occasion being
characterized as of a nature to bring the community to the verge of a
revolution. More moderate speeches at the same meeting had the effect
of counteracting the influence of his speech, and Higginson was left to
organize secretly, as best he could, a plan for the rescue of Simms. Pre-
cautions taken by the officers having the fugitive in charge prevented
the success of the plan for the rescue.

It happened that the United States Marshal having charge of the
fugitive was Charles Devens, a schoolmate and a friend of Higginson.
The relations of these two men to each other and to the subject under
discussion thoroughly illustrate the complexity of the political situa-

THOMAS WENTWORTH HIGGINSON. 871

tion in Massachusetts caused by the attempts at that time to enforce
the fugitive-slave law. Here were two men, both hostile to slavery,
both animated by a keen sense of honor, both striving to do their
duty. The one if he should perform the duties of the office which he
had accepted would be compelled to restore to slavery an individual,
entitled under local laws to his personal freedom. The other, should
the decision of the case have the effect of returning the fugitive to
his master, and should opportunity offer to attempt the rescue of the
fugitive, would be prompted by a sense of duty to violate the laws of
his country and in such event would himself become, in all probability,
either a fugitive from justice or a prisoner.

Higginson wrote to Devens imploring him to resign rather than to
be the instrument of sending a man into bondage. The answer was
courteous, but Devens considered that, however repugnant the perform-
ance of this service might be, the service was nevertheless inherent
upon his having accepted the office of marshal. Simms was returned to
servitude. The vigilance of the police prevented any attempt to release
him. Devens showed how deeply he felt the burden of rendering offi-
cial service which would perhaps cost a man his freedom, by making two
efforts at a later date to secure through purchase the liberty of the negro,
the first offer being refused by the master and the second attempt being
frustrated by the outbreak of the war. In the course of military
events Simms recovered his freedom, and Devens at a later period was
able to help him pecuniarily and otherwise.

In 1852 Higginson was invited to take charge of the Worcester Free
Church, an organization which sprang up under the influence of Theo-
dore Parker's society in Boston, in which there was no church member-
ship, which did not call itself specifically Christian, and which held no
communion service. This call he accepted and his evening lectures or
sermons soon became very popular. He retained connection with this
church for six years and in 1858 resigned in order to devote his life to
literary pursuits.

It will be seen at a glance that his relations with his followers here
were widely different from those which existed between himself and his
congregation at Newburyport. Fresh from the Divinity School, without
political record, he had assumed charge at Newburyport of a congrega-
tion having a history of two hundred years behind it and having as a
body no pronounced political opinions. There was, however, a certain
amount of denominational adherence and of pride in the old church.
On the other hand, he came to Worcester, a preacher without a congre-
gation and an open advocate of resistance to the government in all
attempts to enforce the fugitive -slave law. This move was made at the

872 THOMAS WENTWORTH HIGGINSON.

call of a body of active reformers, all abolitionists, baving no strong
element of cohesion ; a mere aggregation of extremely independ-
ent individuals ; leaders in public movements, wbose popular in-
fluence was restrained by the fact that they were combating local
prejudices and attacking opinions sustained by conservatism and social
power. Higginson says of Wendell Phillips that to abolitionism he
"sacrificed his social position, his early friendships, his professional
career," and of himself he says that he found himself in fashion in
Worcester, "at least with the unfashionable." The portals of society
could not have remained closed in that place to a Higginson married
to a Channing if he had cared to cause them to open, but the illness of
his wife and the gratification that he derived from social intercourse
with those who sympathized with his views prevented him from pene-
trating abodes where an abolitionist, a woman's rights man, and a
Parkerite would not have been altogether persona grata. He says in
one place, " I cannot dispense with the society which we call unculti-
vated." If he found any such in Worcester he did not rely upon it
altogether, for he discovered cultivated, genial friends, unknown to so-
ciety, with whom he had delightful intercourse. The home of a tailor,
for instance — of whom Higginson wrote that he had the freshest and
most original mind in Worcester — who stood at his cutting board all
day, and who at night read Browning with his charming wife, and this
too at a time when to be able to read Browning meant even more than
it does to-day, furnished one place of resort. In such families as this,
where the free interchange of opinions on all topics was permissible, he
found the sort of social intercourse that he wanted. His time was taken
up with outdoor exercise, writing for the papers, and at times in giving
a helping hand to some escaped slave. Naturally, fugitives from servi-
tude claimed assistance from such a body as his church, and it follows
of course that actual aid was freely given to help them on their way to
freedom.

He quotes in his " Cheerful Yesterdays " from a contemporary
journal, apparently his own, in illustration of that curious period, a
paragraph describing the impression of the writer on thus participating
in revolutionary work, in which the journalist states that it is strange
" to see law and order, police and military, on the wrong side and find
good citizenship a sin, and bad citizenship a duty. . . ."

On the 25th of May, 1854, there came to him a summons to
Boston to attend a public meeting to be held in Faneuil Hall in con-
sequence of the arrest of Anthony Burns, another fugitive. Higginson
found the Vigilance Committee inadequate for the situation through
the non-resistance element and through division of opinion. Those

THOAL\S WENTWORTU HIGGINSON. S73

who were willing to act personally in forcible resistance were, however,
left in charge of the situation, and of these Higgiuson was selected as
the leader. The fugitive was confined in the United States Court
room in the Sutfolk Court House, the jails of the state not being at
the behest of Federal officers for the confinement of persons who had not
violated any state law. A plan was devised to take advantage of the
Faneuil Hall meeting. An announcement was to be made, while the
meeting was in progress, that an attack on the Court House was being
made. This would break up the meeting and bring a mob up to Court
Square, under cover of which such an attack might be successful.
The various parts of this disjointed scheme did not fit very well to-
gether, and the attack resulted in a mere fiasco. The killing of one of
the deputies at an early stage of the affair seems to have paralyzed the
combatants, and out of it all the only visible result was that T. W.
Higginson, alone of all the clamorous abolitionists, had shown conspic-
uous courage, the only real contestant for supremacy in that timebeing an
unknown colored man. Then followed the consequences of the assault;
an inquest by the grand jury and the indictment of Theodore Parker,
Wendell Phillips, Thomas Wentworth Higginson, and others. The fact
that a man had been killed at the Court House gave to the proceedijigs
a solemnity and an importance which they might otherwise have
lacked. The distinguished men thus brought to the bar made no
efi"ort to escape their trial, but the issue was never fairly met by the
submission of the case to the jury. The indictment was quashed on a
technicality. This episode cost Higginson the good will of many
persons whose approval he would have enjoyed, but this fact did not
cause him to swerve a jot from his position. Neither then nor there-
after did he offer excuse or apology for what he had done. He was
actuated by principle, firm, unyielding, and unchangeable.

Serious as was the position of these men while under indictment, it
is evident that Higginson's family were not much disturbed by it, nor
had they much fear of the result. His mother, writing concerning it,
picked out a curious phrase in the indictment and referring to it face-
tiously informed her correspondent that she was not troubled at having
a son "riotously and riotously disposed," while on the occasion of a
suggestion made by his wife that her letters to him while he was in
prison might be read by the jailer, another member of the family re-
marked, "Not if he writes them in his usual handwriting."

In October, 1854, a deputy supposed to have come to Worcester in
search of evidence against the participants in the Burns riot was
recognized and was attacked by a mob of negroes. A number of abo-
litionists, among whom was Higginson, interposed, protected the deputj",

874 THOMAS WENTWORTH HIGGINSON.

and with much difficulty saved him from serious harm and succeeded in
getting him out of the city. Higginson rode with him in the vehicle
in which he was transported to safety, and, although his feelings of
hostility towards the man were not vile enough to permit his sacrifice
by the mob, he humorously tells us that while he thus had him at
his mercy he took an inhuman advantage of him and gave him a
discourse on the baseness of his career.

After the Burns affair all attempts to enforce the fugitive-slave law
in Massachusetts ceased, but the abolitionists made preparation for
active interference in case opportunity offered, and kept in com-
mission a yacht which was nominally for hire, but which was ready at
all times for several years to receive a fugitive or, as the case might
be, his master, and take him on a cruise while the excitement should
last. Higginson was a stockholder in this yacht.

As was the case when in Newburyport, he did not allow his crusade
against slavery to prevent his taking an active part in Worcester in
affairs of more immediate and local importance. He interested him-
self in the new question of a prohibitory law, was for a time secretary
of the state committee, and took a hand in the local enforcement of the
law. He, was deeply concerned with the problem of discharged convicts,
and at a later period he served as a delegate to a meeting of prison
reformers in Europe. He was firm in the conviction that the lives of
many of these convicts could be rescued.

The peculiar nature of his religious society led to a certain amount
of ostracism. Edward Everett Hale was for a time, at any rate, the
only clergyman in Worcester who would exchange with him. Later
he was brought into amicable relations with others. As was to be ex-
pected, he was put on the school committee, from which, however, he
was subsequently dropped for defending the right of a Roman Catholic
father to decide which version of the Scriptures his child should read
in school. Later he was reinstated. He had a hand in organizing
the Worcester Public Library. He, with others, organized a local
Natural History Society. His fondness for out-of-door exercise took
shape in tramps over the hills about Worcester and in boating on Lake
Quinsigamond and in the organization of a gymnastic club, a skating
club, and a cricket club, of each of which he was president.

He dates the beginning of his literary life from the publication of
" Saints and their Bodies " in the " Atlantic Monthly " in 1858. It is
true that the "North American Review," the "Christian Examiner,"
and " Putnam's Magazine " had already published articles from his pen,
and that numerous communications and short poems had found a
ready welcome in the columns of certain newspapers, but for such recog-

THOMAS WENTWORTH HIGGINSON. 875

nition as this he cared but little. The acceptance of an article by the
Atlantic was for him a baptism as a litterateur.

From November, 1855, to May, 1856, he was in Fayal. What he
found there worth observing is set forth in a paper entitled " Fayal and
the Portuguese," originally published in the "Atlantic Monthly" in
November, 1860, and reprinted in "Outdoor Papers."

The Kansas Nebraska Act was passed in 1854, and the struggle for
possession of the territory of Kansas between the free states and the
slave states began at once. In Massachusetts organized emigration
from that state to Kansas was effected through the agency of the
Emigrant Aid Society. This movement was at first of a peaceful
nature, but later such emigrants as went forth were better prepared
for emergencies. Higginson arrived in Boston from Fayal in May,
1856. A public meeting which was held in Worcester in honor of his
return was converted into a call for volunteer emigrants to Kansas.
A committee was appointed, of which he was secretary, under whose
auspices three parties of emigrants were sent forward armed with rifles
and pistols and prepared for camping out. He himself was first sent
to St. Louis to look out for a stray party of emigrants whose progress had
been hindered, and later, as agent of the National Kansas Committee,
having its headquarters at Chicago, he was sent to Kansas with a con-
voy of rifles to oversee a party of emigrants. On this expedition he
met the famous " Jim Lane " at the head of a party of mounted
followers, and was honored by an appointment on Lane's staff with the
rank of brigadier-general. He passed safely through Kansas, though
the trip was not without the fascination of actual peril. He speaks of
the " tonic life " of these weeks, and says that when they were over and
he arrived where he could call for help upon a policeman, he felt as if
"a despicable effeminacy had set in."

In January, 1857, he joined with a few other Republicans and
Garrisonian Abolitionists in calling and in holding a state disunion
convention. A call for a national disunion convention was also circu-
lated, Cleveland being the appointed place of meeting, but the financial
panic of 1857 prevented the meeting of this convention.

February 2, 1858, John Brown wrote to him, as "an abolitionist"
and " a true man," for pecuniary aid in perfecting what Brown con-
sidered the most important undertaking of his life. This celebrated
abolitionist was already famous, and Higginson says that there was but
one way of thinking among the Kansas Free State men as to the most
extreme act of John Brown's Kansas career, the so-called "Pottawa-
tomie Massacre." As one of them put it. Brown saw the necessity of
some such blow and had the nerve to strike it. " Personally," adds

876 THOMAS WENTWORTH HIGGINSON.

Higginson, " I have never fully reconciled myself to this vindication
of ' the blow,' " and he claims that Brown is to be judged as " a pure
enthusiast — fanatic, if you please."

Brown had developed a plan for penetrating Virginia with a few fol-
lowers, not with a view to an insurrection, but with intent to assemble
fugitives, and if unable to protect them in local fastnesses to send them
to Canada. In this plan Higginson, Theodore Parker, and others of
the anti-slavery leaders co-operated and raised money for its further-
ance. The details of the scheme were betrayed, and action on the part
of Brown was necessarily postponed. In October, 1859, came the
attack on Harper's Ferry, a proceeding on the part of Brown radically
different from the plan previously proposed by him, in aid of which the
money referred to above had been contributed, and further a proceed-
ing which was opposed by Brown's followers. For a time all those
who had been in touch with this fanatical leader and all those who had
furnished him with money were under suspicion and were in danger
of arrest. Some fled to Canada, but Higginson felt that it was his
duty to stand his ground and give Brown his moral support, and he
goes on to state that with Brown in confinement there was, of course,
an immediate impulse to rescue him from prison. " I do not know
how far this extended," he says, "and can only vouch for myself."
Brown, however, had absolutely prohibited any such attempt, and
unless he could be led to change his opinion any efforts to rescue the
inflexible old man would be thrown away. It occurred to Higginson
that Brown's wife might, in a personal interview, influence the prisoner
to recede from this position, and he went to North Elba and secured
her co-operation. The plan failed through the stubbornness of Brown,
who refused positively to see his wife. A harebrained effort was
shortly afterward started to rescue two of Brown's followers, but the
leader chosen for the purpose, after carefully inspecting the ground,
pronounced the scheme impracticable. When this proposition was
under consideration, Higginson went to Harrisburg to meet the leader
of the enterprise, to arrange details, and to take part in the rescue if
it should be attempted. On the abandonment of the expedition he
returned to his home.

At the outbreak of the war he visited Governor Andrew and volun-
teered, if provided with the necessary funds, to invade the Virginia
mountains with a small force of men selected from the Kansas Free
State men, and kindle a back fire there, with a view of distracting
attention from the national capital, then in peril. There was no con-
tingent fund in Massachusetts that could be used, but a small sum of
money was raised from private sources. Governor Curtin of Pennsyl-

THOIIAS WENTWORTH HIGGINSON. 877

vania was consulted, but events moved so rapidly that the proceeding
became unnecessary and even undesirable.

In the spring of 1861 he was offered the command of the 4th Bat-
talion of Infantry, then hastily raised for government service. Not-
withstandiug the fact that the impending collision had for some time
back induced him to turn his reading towards military works, so that
he had acquired an academic acquaintance with the theories of attack
and defense, he did not feel competent to assume charge in the field
of a battalion of troops. Moreover the state of his wife's health at
that time was precarious, and she was especially dependent upon him.
A third and probably a prevailing reason was the uncertainty of the
government position on the slavery question, and the fear that, as com-
manding officer, he might be compelled to return fugitive slaves to their
masters.

By the fall of that year the anti-slavery position of the government
had become more clearly defined, and he sought and obtained permis-
sion to raise a regiment of which he was to be second in command.
After three months of hard labor in raising companies in different
parts of the state, and after about half the necessary companies had
been raised, an order putting a stop to recruiting rendered all of this
preliminary work abortive. Recruiting was renewed in 1862, and he
then raised a company for the 51st regiment, of which company he was
commissioned as Captain, September 25, 1862, He quotes in his
" Cheerful Yesterdays " a popular nonsense rhyme made at his expense
about this time which ran as follows:

" There was a young curate of Worcester
Who could have a command if he 'd choose ter,
But he said each recruit
Must be blacker than soot,
Or else he 'd go preach where he used ter."

Very shortly after receiving his commission as Captain in the 51st
regiment he was offered by General Saxton, military commander of the
Department of the South, the command of a regiment of freed slaves.
This offer fulfilled, he says, the dream of a lifetime, and after investi-
gating the circumstances under which the offer was made, he accepted
it. November 10, 1862, he became Colonel of the 1st South Carolina
volunteers, afterwards the 33d United States colored troops, the first
regiment of freed slaves mustered into the United States service. The
regiment was stationed near Beaufort, South Carolina. During his
connection with it, whether on the march or in camp, he made a close,
analytical study of the negro as a soldier, the record of which is to be

878 THOMAS WENTWORTH HIGGINSON.

found in his " Army Life in a Black Regiment." It chanced that he
was not engaged in any large battle, but he went on expeditions up the
St. Mary's, the St. John's, and the Edisto. While up the St. John's
the city of Jacksonville was captured by his command and was held by
him until he was ordered back to head-quarters. On the Edisto raid
on the 10th of July, 1863, he was wounded. He was shortly thereafter
invalided and sent North and, although he thought at one time that
he was well enough to resume active service, he found on returning to
his regiment that he was not able to bear the exposure of camp life.
He resigned in October, 1864.

His wife had meantime, for the sake of her health, gone to Newport
to live. He joined her there and resumed literary work. Suggestions
as to his life in that place will be found in " Malbone " and in " Old Port
Days."

In 1878, shortly after the death of his wife, he took a trip to Europe,
where he was cordially received as a representative of American liter-
ature, and where he met Froude, Carlyle, Sir Frederick Pollock, Mat-
thew Arnold, Darwin, and many other distinguished Englishmen. On
his return to this country he settled at Cambridge, where in February,
1879, he married Mary P. Thacher, herself an authoress of some note.

The numerous services which he performed for the public in New-
buryport and at Worcester indicate his sense of civic responsibility
and his willingness to give to the public without reward what there
was that was available in his still vigorous body and his richly en-
dowed intellect. Though no longer able to endure as much as for-
merly, still he performed substantially the same roles at Newport and
at Cambridge, renewing his former experiences even to the extent of
being dropped from the Newport School Committee, serving as trustee
of public libraries, organizing social clubs, and patronizing Shakespeare
and Browning Societies. To his connection with the Colonial Club of
Cambridge we owe the preservation on canvas of an adequate repre-
sentation of his person. The picture of the first president of the club
graces the walls of the clubhouse. While in Newport and in Cam-
bridge he was for many consecutive years engaged in giving lectures
and in editorial works on the " Index " and the " Woman's Journal."

He was elected to the Legislature in 1880 and again in 1881. He
served one year as chief of the personal staff of Governor Long. He
was three years on the State Board of Education and served seven
years as state military and naval historian. He says, indeed, "Look-
ing back fifty years, I cannot put my finger on five years when I myself
was not performing some official service for the city or state or both
simultaneously." Reentered actively the Cleveland campaign in 1888

THOMAS WENTWORTH HIGGINSON. 879

and reluctantly ran for Congress on the democratic ticket. Although
not elected, he was gratified by the vote.

His old age in Cambridge and at his charming summer residence
at Dublin, New Hampshire, was peaceful, and his days were full of
happiness. The various reforms in which he had been interested were
either accomplished or in a fair way of being so. He no longer felt
estranged among his fellow Unitarians. They had so nearly reached
his own position on the question of religious freedom that he could
and did join the congregation of the First Parish in Cambridge. He
was blessed with offspring, and, indeed, before he died he was glad to
welcome in his household a new member of the family, of a generation
twice removed from his own.

With growing years and increasing fame he was accustomed to re-
ceive his friends on the recurrence of his birthday, and this custom he
kept up to the last whenever his health would permit. These recep-
tions were originally inaugurated on his seventieth birthday, and the
scores of persons who annually thereafter took advantage of them to
pay their respects to the Colonel bore testimony to the extent of his
fame and to the great change in the popular estimate of his character
since the days of his personal attack on the Suffolk Court House.
They were interrupted by a severe illness which kept him in the house
for nearly two years. It was during this period of physical suffering
that his " Cheerful Yesterdays " was written. Propped up in bed,
leaning against the pillows, he dictated the book, the spirit of which
shows that even under those circumstances his to-day as well as his
yesterday was cheerful.

He was honored by the Western Reserve and by Harvard Universi-
ties with the degree of LL.D. He was Vice-President of the Liberal
Congress of Heligion, Fellow of the American Academy of Arts and
Sciences, Corresponding Member of the Royal Society of Canada,
Member of the American Academy of Arts and Letters, and Member
of the Massachusetts Historical Society.

A chronological list of his publications was prepared and published
in 1906 by the Cambridge Public Library, and in this publication there
is also an alphabetical list of books and articles pertaining to his life
and career. The information contained therein will be found to be
very serviceable to the biographer of Colonel Higginson. It needs,
however, to be supplemented with the publications made after 1906.
His collected works were reprinted in 1900 in seven volumes. In 1906
a volume was put forth entitled " Part of a Man's Life."

Colonel Higginson died May 9, 1911. He was accorded a military
funeral by the Loyal Legion, of which he was a member, and was

880 THOMAS WENTWORTH HIGGINSON.

escorted to his last resting place by a guard of colored men, a fitting
tribute on their part to the devotion of his life to the cause of the
down -trodden of their race.

When the Colonel entered the field of active life he devoted his
energies to three causes : Freedom for the colored race ; freedom from
the trammels of the law, for women ; freedom in religions belief from
the restraints of dogma. To the first of these causes he sacrificed, in
his youth at least, social position and political ambition, and later the
chance of military promotion. To a certain extent the championship
of the second and third of these causes could only be prosecuted dur-
ing the same period under similar disadvantages. Coupled with these
three reforms, but holding a secondary position in his esteem, was the
open advocacy of Outdoor Exercise or Athletics, of Higher Education
for Women, and of Temperance for all.

He lived to see the slave released from bondage and to see Woman's
Suffrage adopted in several of our states. He attended services in
later life in a church where Theodore Parker would have been wel-
comed in the pulpit. He had but to cast his eyes across the Charles
to see, in the Stadium, the evidence of the extraordinary hold upon
modern collegiate life developed by athletics and intercollegiate
games. The group of buildings made use of by Radcliffe College for
the higher education of women in Cambridge he might daily see, and
he might also have heard that the preponderant number of women in
some of the Western State universities made it questionable in the
minds of some philosophic observers whether in the near future it
might not prove that there would be a body of highly educated females
in these states, while the bulk of the men, absorbed in business and
industries, would be found to have contented themselves with a high
school education. If in his latter days he had travelled from Maine to
the Mexican border he would have found that Prohibition had so far
prevailed that a thirsty man would often have to wait for entry into
an unprogressive state if he wanted anything stronger than water to
drink. There still remained fields in which, if strength had been
granted him, he might as a reformer have worked. International
arbitration, civil service reform, and the abolition of monopolies are to
be found in his list of what remains to be accomplished.

Any man who reads Colonel Higginson's accounts of his personal
experiences will realize not only that he was a courageous man, being
absolutely devoid of fear, but also that he actually thirsted for adven-
ture. He would have enjoyed being present at the liberation of
Shadrach, not alone because the rescue of the slave was in accord with
his moral convictions, but because of an impulse in his blood which he

THOMAS WENTWORTH HIGGINSON. 881

describes as " an intrinsic love of adventure." This love of adventure
doubtless had voice in all his after proceedings. The story of his army
life is tinctured with it. He knows " nothing in life more fascinating
than the nocturnal ascent of an unknown river leading far into an
enemy's country," or, again, " of going into a region where peril made
fascination." At any time, he says, by going into the outskirts at one
of his camps, one could have a skirmish which, he adds, was nothing
but fun. Such expressions as these betray the soldier rather than the
preacher, the lecturer, or the translator of Epictetus and the Sonnets
of Petrarch.

At the outset of his appeal to the public through the press he seemed
disposed to make use of poetry rather than prose. Twenty titles are
given in the chronological list published by the Cambridge Public Li-
brary of publications in newspapers in the years 1846-1849 inclusive.
Of these fifteen are sonnets, poems, or hymns. Thereafter the poem is
the exception, but his " Outdoor Papers " are filled with the aroma of
woods and the fragrance of flowers. The cadence of their sentences is
so beautifully adjusted that they might almost pass for poems. He
seldom ventured into the land of fiction, and once only tried his hand
at a novel. A competent critic says that " his writings show a deep
love of nature, art, and humanity, and are marked by vigor of thought,
sincerity of feeling, and a grace and finish of style."

In 1875 he published "Young Folks' History of the United States,"
which had a marvellous success in this country, new editions appearing
from time to time thereafter, while in Europe the volume was trans-
lated into the French, German, and Italian tongues. He also engaged
in other historical work, and published in 1885 a "Larger History of
the United States "; in 1893 "English History for American Readers,"
in collaboration with Professor Edward Channing ; and in 1905 a " His-
tory of the United States," in collaboration with Professor WiDiam
McDonald, this last being practically an enlarged edition of his "Larger
History of the United States."

In Colonel Higginson's sketch of Theodore Parker's life he says,
" There may be some whose fame is so ill established that one shrinks
from speaking of them precisely as one saw them ; but this man's place
is secure, and that friend best praises him who paints him just as he
seemed." No better suggestion could be made to the biographer of
Colonel Higginson than the words which he himself uses concerning
the task set for the biographer of Theodore Parker. So far as the
person engaged in the memoir of Colonel Higginson is concerned, he is
relieved from the necessity of explanation or apology for Higginson's
resistance to constituted authorities by the frankness of the Colonel

882 THOMAS WENTWORTH HIGGINSON.

himself, who has revealed his entire career to the world with a sincerity
which would permit one who differed from him as to the propriety of
the methods of which he at times made use, to appropriate freely ftom
the autobiographical writings which he has left behind him. To a
great extent this is what I have done, thus trying to do justice to a
friend whom I honored even when I did not agree with him. The
story herein given of the career of this aggressive reformer, this out-
spoken independent preacher, this courageous soldier and scholarly
author, this useful citizen and brilliant man, is practically told in his
own words. Should it seem that his social charms have been inad-
equately developed and that there is no sufficient picture of the gentle
urbanity of his later years, we must hope that this phase of the Col-
onel's character will be more forcibly portrayed in the forthcoming life
promised at the hand of Mrs. Higginson.

Andrew McFarland Davis.

Class I.

Elihu Thomson,

American Academy of Arts and Sciences

OFFICERS AND COMMITTEES FOR 191 2-13.
PRESIDENT.

John Trowbridge,
vice-presidents.

Class II.
Henry P. Walcott,

corresponding secretary.
Edwin H. Hall.

Class III.

A. Lawrence Lowell.

Class I.
George F. Swain,

Robert W. Willson,

Arthur G. Webster,

James F. Norris,

John Trowbridge,

Erasmus D. Leavitt,
Arthur G. Webster,

Walter L. Jennings,
Arthur A. Noyes,

Class III.

Henry H. Edes,
Joseph H. Beale,
George F. Moore,
Frank W. Taussig,

recording secretary.

William Watson.

TREASURER.

Charles P. Bowditch.

librarian.

Hakry W. Tyler.

COUNCILLORS.
Class II.
Reginald H. Fitz,

Terms expire 1913.
Thomas A. Jaggar,

Terfus expire 191 4.
Merritt L. Fernald,

Terms expire 191 5.
George H. Parker,

Terms expire X916.

committee of finance.
Gardiner M. Lane, John Collins Warren-

rumford committee.

Charles R. Cross, Chairman,
Edward C. Pickering,
Elihu Thomson,

C. M. WARREN COMMITTEE.

Henry P. Talbot, Chairman,

Charles L. Jackson, Gregory P. Baxter,

James F. Norris, William H. Walker.

COMMITTEE OF PUBLICATION.

George W. Pierce, of Class I, Chairman,

Walter B. Cannon, of Class II, Albert A. Howard, of Class III.

COMMITTEE ON THE LIBRARY.
Harry W. Tyler, Chairman,
Harry M. Goodwin, of Class I, Samuel Henshaw, of Class II,

William C. Lane, of Class III.

auditing committee.

Worthington C. Ford,

house committee.
Henry P. Talbot, Chairman, Hammond V. Hayes,

COMMITTEE ON MEETINGS.

The President,

The Recording Secretary,

William M. Davis, Wallace C. Sabine, Arthur Fairbanks.

Louis Bell,
Arthur A. Ncyes.

Eliot C. Clarke,
Louis Derr,

LIST

OF THE

FELLOWS AND FOREIGN HONORARY MEMBERS.

(Corrected to July 1, 1912.)

FELLOWS. — 323.

(Number limited to six hundred.)

Class I. — Mathematical and Physical Sciences. — 129.

Section I. — Mathematics and Astronomy. — 30.

Solon Irving Bailey Cambridge

Edward Emerson Barnard Williams Bay, Wis.

Lewis Boss Albany, N. Y.

Ernest W^illiam Brown New Haven, Ct.

Sherburne Wesley Burnham Williams Bay, Wis.

William Elwood Byerly Cambridge

William Wallace Campbell Mt. Hamilton, Cal.

Seth Carlo Chandler Wellesley Hills

Fabian Franklin New York

George William Hill West Nyack, N. Y.

Edward Singleton Holden West Point, N. Y,

Percival Lowell Boston

Emory McClintock New York

Joel Hastings Metcalf ... * Winchester

Eliakim Hastings Moore Chicago, 111.

Edward Charles Pickering Cambridge

William Henry Pickering Cambridge

Charles Lane Poor New York

Arthur Searle Cambridge

George Mary Searle Berkeley, Cal.

Vesto Melviu Slipher Flagstaff, Ariz.

886 FELLOWS.

John Nelson Stockwell Cleveland, O.

William Edward Story Worcester

Henry Taber Worcester

Harry Walter Tyler Boston

Oliver Clinton Wendell Cambridge

Eobert Wheeler Willson Cambridge

Edwin Bidwell Wilson Cambridge

Frederick Shenstone Woods Newton

Paul Sebastian Yendell Dorchester

Section II. — Physics. — 40.

Joseph Sweetman Ames Baltimore, Md.

Carl Barus Providence

Louis Agricola Bauer Washington

Alexander Graham Bell Washington

Louis Bell Boston

Clarence John Blake Boston

Francis Blake Weston

Percy Williams Bridgman Cambridge

George Ashley Campbell New York

Harry Ellsworth Clifford Newton

Daniel Frost Comstock Boston

Charles Eobert Cross Brookline

Harvey Nathaniel Davis Cambridge

Louis Derr Brookline

Alexander Wilmer Duff Worcester

Arthur Woolsey Ewell Worcester

Harry Manley Goodwin Brookline

George EUery Hale Pasadena, Cal.

Edwin Herbert Hall Cambridge

Hammond Vinton Hayes Cambridge

William Leslie Hooper Somerville

William White Jacques Boston

Frank Arthur Laws Boston

Henry Lefavour Boston

Theodore Lyman Brookline

Richard Cockburn Maclaurin Boston

Thomas Corwin Mendenhall , . . Ravenna, 0.

FELLOWS. 887

Albert Abraham Michelson Chicago, 111.

Harry Wheeler Morse Cambridge

Edward Leamington Nichols Ithaca, N. Y.

Charles Ladd Norton Boston

Benjamin Osgood Peirce Cambridge

George Washington Pierce Cambridge

Michael Idvorsky Pupin New York

Wallace Clement Sabine Boston

John Stone Stone Boston

Maurice deKay Thompson Boston

Elihu Thomson Swampscott

John Trowbridge Cambridge

Arthur Gordon Webster •. . . . Worcester

Section III. — Chemistry. — 32.

Gregory Paul Baxter Cambridge

William Crowell Bray Boston

Russell Henry Chittenden New Haven, Ct.

Arthur Messinger Comey Chester, Pa.

James Mason Crafts Boston

Charles William Eliot Cambridge

Henry Fay Boston

Frank Austin Gooch New Haven, Ct.

Lawrence Joseph Henderson Cambridge

Eugene Waldemar Hilgard Berkeley, Cal.

Charles Loring Jackson . Cambridge

Walter Louis Jennings Worcester

Gilbert Newton Lewis Boston

Charles Frederic Mabery Cleveland, O.

John William Mallet University, Va.

Forris Jewett Moore Boston

George Dunning Moore Worcester

Edward Williams Morley West Hartford, Ct.

Samuel Parsons Mulliken Boston

Charles Edward Munroe . . Washington, D. C.

John Ulric Nef Chicago, 111.

James Flack Norris Boston

Arthur Amos Noyea . . • Boston

Ira Remsen Baltimore, Md.

88S FELLOWS.

Robert Hallowell Richards Jamaica Plain

Theodore William Richards Cambridge

Stephen Paschall Sharpies Cambridge

Francis Humphreys Storer Boston

Henry Paul Talbot Newton

William Hultz Walker Newton

Willis Rodney Whitney Schenectady, N. Y.

Charles Hallet Wing Boston

Section IV. — Technology and Engineering. — 27.

Henry Larcom Abbot Cambridge

Comfort Avery Adams Cambridge

Alfred Edgar Burton Boston

Eliot Channing Clarke Boston

Desmond FitzGerald Brookline

John Fritz Bethlehem, Pa.

George Washington Goethals Culebra, Canal Zone

Ira Nelson HoUis Cambridge

Frederick Remseu Hutton New York

Dugald Caleb Jackson Boston

Lewis Jerome Johnson Cambridge

Arthur Edwin Kennelly Cambridge

Gaetano Lanza Philadelphia, Pa.

Erasmus Darwin Leavitt Cambridge

William Roscoe Livermore Boston

Lionel Simeon Marks Cambridge

Hiram Francis Mills Lowell

Cecil Hobart Peabody Brookline

Andrew Howland Russell Paris

Albert Sauveur Cambridge

Peter Schwamb Arlington

Henry Lloyd Smyth Cambridge

Frederic Pike Stearns Boston

Charles Proteus Steinmetz Schenectady, N. Y.

George Fillmore Swain Cambridge

William Watson Boston

Robert Simpson "\Yoodward Washington, D. C.

FELLOWS. 889

Class II. — Natural and Physiological Sciences. — 102.
Section I. — Geology, Mineralogy, and Physics of the Globe. — 27.

Cleveland Abbe Washington, D. C.

Thomas Chrowder Chamberlin Chicago, 111.

Henry Helm Clayton Canton

Herd man Fitzgerald Clelaud AVilliamstown

William Otis Crosby Jamaica Plain

Reginald Aldworth Daly Cambridge

Edward Salisbury Dana New Haven, Ct.

Walter Gould Davis Cordova, Arg.

William Morris Davis Cambridge

Benjamin Kendall Emerson Amherst

Grove Karl Gilbert Washington, D. C.

Oliver Whipple Huntington Newport, R. I.

Robert Tracy Jackson Cambridge

Thomas Augustus Jaggar, Jr Brookline

Douglas Wilson Johnson Cambridge

Alfred Church Lane Cambridge

Charles Palache Cambridge

John Elliott Pillsbury Washington, D. C.

Raphael Pumpelly Newport, R. I.

William Berryman Scott Princeton, N. J.

Hervey Woodburn Shimer Boston

Charles Richard Van Hise Madison, Wis.

Charles Doolittle Walcott Washington, D. C.

Robert DeCourcy Ward Cambridge

Charles Hyde Warren Auburndale

John Eliot Wolff Cambridge

Jay Backus Woodworth Cambridge

Section II. — Botany. — 21.

Oakes Ames North Easton

Liberty Hyde Bailey Ithaca, N. Y.

Douglas Houghton Campbell Stanford Univ., Cal.

Frank Shipley Collins Maiden

John Merle Coulter Chicago

890 FELLOWS.

Edward Murray East Jamaica Plain

Alexander William Evans New Haven, Ct.

William Gilson Farlow Cambridge

Charles Edward Faxon Jamaica Plain

Merritt Lyndon Fernald Cambridge

George Lincoln Goodale Cambridge

Robert Aimer Harper New York

John George Jack Jamaica Plain

Edward Charles Jeffrey Cambridge

Winthrop John Vanleuven Osterhout Cambridge

Benjamin Lincoln Robinson Cambridge

Charles Sprague Sargent _ Brookline

Arthur Bliss Seymour ' Cambridge

John Donnell Smith Baltimore

Roland Thaxter Cambridge

"William Trelease St. Louis, Mo.

Section UI. — Zoology and Physiology. — 29.

Joel Asaph Allen » New York

Francis Gano Benedict Boston

Henry Bryant Bigelow Concord

William Brewster Cambridge

Louis Cabot BrooKline

Walter Bradford Cannon Cambridge

William Ernest Castle Cambridge

Samuel Fessenden Clarke Williamstown

William Thomas Councilman Boston

William Healey Dall Washington, D. C.

Charles Benedict Davenport . . . Cold Spring Harbor, N. Y.

Otto Knut Olof Foliu Brookline

Samuel Henshaw Cambridge

Franklin Paine Mall Baltimore, Md.

Edward Laurens Mark Cambridge

Charles Sedgwick Minot Milton

Silas Weir Mitchell Philadelphia, Pa

Edward Sylvester Morse Salem

Henry Fairfield Osborn New York

Geoi'ge Howard Parker Cambridge

FELLOWS. 891

James Jackson Putnam Boston

Herbert Wilbur Rand Cambridge

William Thompson Sedgwick Boston

John Eliot Thayer Lancaster

Addison Emory Verrill New Haven, Ct.

William Morton Wheeler Boston

James Clarke White Boston

Harris Hawthorne Wilder Northampton

Edmund Beecher Wilson New York

Section IV. — Medicine and Surgery. — 25.

John Shaw Billings New York

Edward Hickling Bradford Boston

Arthur Tracy Cabot Boston

Harold Clarence Ernst Jamaica Plain

Reginald Heber Fitz Boston

Simon Flexner New York

William Stewart Halsted Baltimore, Md.

Abraham Jacobi New York

Elliott Proctor Joslin Boston

William Williams Keen Philadelphia, Pa.

Samuel Jason Mixter Boston

William Osier Oxford, Eug.

Theophil Mitchell Prudden New York

Charles Pickering Putnam Boston

William Lambert Richardson Boston

Milton Joseph Rosenau Boston

Theobald Smith Jamaica Plain

Elmer Ernest Southard Boston

Henry Pickering Walcott Cambridge

John Collins Warren Boston

William Henry Welch Baltimore, Md.

Francis Henry Williams Boston

Simeon Burt Wolbach Boston

Horatio Curtis Wood Philadelphia, Pa.

James Homer Wright Boston

892 FELLOWS.

Class III. — Moral and Political Sciences. — 92.
Section I. — Philosophy and Jurisprudence. — 16.

Simeon Eben Baldwin New Haven, Ct.

Joseph Henry Beale Cambridge

Melville Madison Bigelow Cambridge

Joseph Hodges Choate New York

Frederic Dodge Belmont

John Chipman Gray Boston

Marcus Perrin Knowlton Springfield

George Vasmer Leverett Boston

Hugo Mlinsterberg Cambridge

Charles Sanders Peirce Milford, Pa.

George Wharton Pepper Philadelphia, Pa.

Roscoe Pound Belmont

Josiah Royce Cambridge

Arthur Prentice Rugg Worcester

Samuel Williston Belmont

Woodrow Wilson Princeton, N. J.

Section II. — Philology and Archceclogy. — 28.

Charles Pickering Bowditch . Jamaica Plain

Franklin Carter Williamstown

George Henry Chase Cambridge

Roland Burrage Dixon Cambridge

Timothy Dwight New Haven, Ct.

William Curtis Farabee Cambridge

Jesse Walter Fewkes Washington, D. C.

Basil Lanneau Gildersleeve Baltimore, Md.

William Arthur Heidel Middletown, Ct.

Albert Andrew Howard Cambridge

Charles Rockwell Lanman Cambridge

Thomas Raynesford Lounsbury New Haven, Ct.

David Gordon Lyon Cambridge

Clifford Herschel Moore Cambridge

George Foot Moore Cambridge

Hanns Oertel New Haven, Ct

FELLOWS. 893

Charles Pomeroy Parker Cambridge

Frederick Ward Putnam Cambridge

Eufus Byam Eichardson Woodstock, Ct.

Edward Robinson New York

Fred Norris Robinson Cambridge

Edward Stevens Sheldon Cambridge

Herbert Weir Smyth Cambridge

Franklin Bache Stephenson Pittsfield

Charles Cutler Torrey New Haven, Ct.

Alfred Marston Tozzer Cambridge

Andrew Dickson White Ithaca, N. Y,

John Williams White Cambridge

'E5''

Section III. — Political Economy and History. — 19.

Charles Francis Adams Lincoln

Henry Adams , . . . Washington, D. C.

Thomas Nixon Carver Cambridge

Edward Channiug Cambridge

Archibald Cary Coolidge Boston

Andrew McFarland Davis Cambridge

Ephraim Emerton Cambridge

Irving Fisher New Haven, Ct.

Worthington Chauncey Ford Boston

Abner Cheney Goodell Salem

Arthur Twining Hadley New Haven, Ct.

Henry Cabot Lodge Nahaut

Abbott Lawrence Lowell Cambridge

Alfred Thayer Mahan New York

James Ford Rhodes Boston

Charles Card Smith Boston

Henry Morae Stephens Berkeley, Cal.

Frank William Taussig Cambridge

Frederick Jackson Turner Cambridge

Section IV. — Literature and the Fine Arts. — 29.

James Burrill Angell Ann Arbor, Mich.

Francis Bartlett Boston

894 FELLOWS.

Arlo Bates Boston

William Sturgis Bigelow Boston

Le Baron Russell Briggs Cambridge

Henry Leland Chapman Brunswick, Me.

"Wilberforce Eames New York

Henry Herbert Edes Cambridge

Arthur Fairbanks Boston

William Wallace Fenn Cambridge

Kudo Francke Cambridge

Horace Howard Furness Wallingford, Pa.

Mark Antony De Wolfe Howe Boston

George Lyman Kittredge Cambridge

Gardiner Martin Lane Boston

William Coolidge Lane Cambridge

Albert Matthews Boston

Edward Caldwell Moore Cambridge

George Herbert Palmer Cambridge

Robert Swain Peabody Boston

Herbert Putnam Washington, D. C.

James Hardy Ropes Cambridge

Denman Waldo Ross Cambridge

John Singer Sargent London, Eng.

William Jewett Tucker Hanover, N. H.

Willistou Walker New Haven, Ct.

William Robert Ware Milton

Herbert Langford Warren Cambridge

Barrett Wendell Boston

FOREIGN HONORARY MEMBERS. 89i

FOREIGN" HONORARY MEMBERS. — 54.

(Number limited to seventy-five.)

Class I. — Mathematical and Physical Sciences. — 16.
Section I. — Mathematics and Astronomy. — 5.

Arthur Auwers Berlin

Sir George Howard Darwin Cambridge

Sir David Gill London

Felix Klein G -ttingen

Emile Picard Paris

Section II. — Physics. — 5.

Oliver Heaviside , Torquay

Sir Joseph Larmor Cambridge

Augusto Righi Bologna

John William Strutt, Baron Rayleigh "Witham

Sir Joseph John Thomson Cambridge

Section III. — Chemistry. — 4.

Adolf, Ritter von Baeyer Munich

Emil Fischer Berlin

Wilhelm Ostwald Leipsic

Sir Henry Enfield Roscoe London

Section IV. — Technology and Engineering. — 2.

Heinrich Mliller-Breslau Berlin

William Cawthorne Unwin London

S96 rOREIGN HONORARY MEMBERS.

Class II. — Natural and Physiological Sciences. — 17.
Section I. — Geology, Mineralogy, and Physics of the Globe. — 4.

Sir Archibald Geikie Hasleraere, Surrey

Julius Hann Vienna

Albert Heim Zurich

Sir John Murray Edinburgh

Section II. — Botany. —4.

Adolf Engler Berlin

Wilhelm Pfeffer Leipsic

Hermann, Graf zu Solms-Laubach Strassburg

Eduard Strasburger Bonn

Section III. — Zoology and Physiology. — 5.

Ludimar Hermann Konigsberg

Hugo Kronecker Bern

Sir Edwin Ray Lankester London

Elie Metchnikoff Paris

Magnus Gustav Retzius Stockholm

D

Section IV. — Medicine and Surgery. — 4.

Emil von Behring Marburg

Sir Thomas Lauder Brunton, Bart London

Angelo Celli Rome

Sir Victor Alexander Haden Horsley Loudon

Class III. — Moral and Political Sciences. — 19.
Section I. — Philosophy and Jurisprudence. — 4.

Arthur James Balfour Prestonkirk

Heinrich Brunner Berlin

Albert Venn Dicey Oxford

Sir Frederick Pollock, Bart London

FOREIGN HONORARY MEMBERS. 897

Section II. — Philology and Archceolojy. — 7.

Ingram Bywater London

Friedrich Delitzsch Berlin

Hermann Diels , Berlin

Wilhelm Dorpfeld Athens

Henry Jackson . . . , Cambridge

Hermann Georg Jacobi Bonn

Sir Gaston Camille Charles Maspero Paris

Section ITT. — Political Economy and History. — 5.

James Bryce London

Adolf Harnack Berlin

John Morley, Viscount Morley of Blackburn London

Sir George Otto Trevelyan, Bart London

Pasquale Villari Florenco

Section IV. — Literature and the Fine Arts. — 3.

Georg Brandes Copenhagen

Jean Adrien Aubin Jules Jusserand Paris

Rudyard Kipling Burwash

STATUTES AND STA;N^DING VOTES

STATUTES

Adopted November 8, 1911 : amended May 8, 1912

CHAPTER I

The Corporate Seal

Article 1. The Corporate Seal of the Academy shall be as here
depicted :

Article 2, The Recording Secretary shall have the custody of the
Corporate Seal.

See Chap. v. art. 3 ; chap. vi. art. 2.

900 STATUTES OF THE AMERICAN ACADEMY

CHAPTER II
Fellows and Foreign Honorary Members and Dues

Article 1. The Academy consists of Fellows, who are either citizens
or residents of the United States of America, and Foreign Honorary
Members. They are arranged in three Classes, according to the Arts
and Sciences in which they are severally proficient, and each Class is
divided into four Sections, namely :

Class I. The Mathematical and Physical Sciences
Section 1. Mathematics and Astronomy
Section 2. Physics
Section 3. Chemistry
Section 4. Technology and Engineering

Class II. The Natural and Physiological Sciences
Section 1. Geology, Mineralogy, and Physics of the Globe
Section 2. Botany
Section 3. Zoology and Physiology
Section 4. Medicine and Surgery

Class III. The Moral and Political Sciences
Section 1. Theology, Philosophy, and Jurisprudence
Section 2. Philology and Archaeology
Section 3. Political Economy and History
Section 4. Literature and the Fine Arts

Article 2. The number of Fellows shall not exceed Six hundred,
of whom not more than Four hundred shall be residents of Massachu-
setts, nor shall there be more than Two hundred in any one Class.

Article 3. The number of Foreign Honorary Members shall not
exceed Seventy-five. They shall be chosen from among citizens of
foreign countries most eminent for their discoveries and attainments
in any of the Classes above enumerated. There shall not be more
than Twenty-five in any one Class.

Article 4. If any person, after being notified of his election as
Fellow, shall neglect for two months to accept in writing and to pay
his Admission Fee (unless he be at that time absent fi-om the Common-
wealth) his election shall be void ; and if any Fellow resident within
fifty miles of Boston shall neglect to pay his Annual Dues for twelve
months after they are due, provided his attention shall have been called

OF ARTS AND SCIENCES 901

to this Article of the Statutes in °the meantime, he shall cease to be
a Fellow; but the Council may suspend the provisions of this Article
for a reasonable time.

With the previous consent of the Council, the Treasurer may dis-
pense (si(b silentio) with the payment of the Admission Fee or of the
Annual Dues or both whenever he shall deem it advisable. In the case
of officers of the Army or Navy who are out of the Commonwealth on
duty, payment of the Annual Dues may be waived during such absence
if continued during the whole financial year and if notification of such
expected absence be sent to the Treasurer. Upon similar notification
to the Treasurer, similar exemption may be accorded to Fellows sub-
ject to Annual Dues, who may temporarily remove their residence for
at least two years to a place more than fifty miles from Boston.

If any person elected a Foreign Honorary Member shall neglect for
six months after being notified of his election to accept in writing,
his election shall be void.

See Chap. vii. art. 2.

Article 5. Every Fellow hereafter elected shall pay an Admission
Fee of Ten dollars.

Every Fellow resident within fifty miles of Boston shall, and others
may, pay such Annual Dues, not exceeding Fifteen dollars, as shall
be voted by the Academy at each Annual Meeting, when they shall
become due ; but any Fellow shall be exempt from the annual pay-
ment if, at any time after his admission, he shall pay into the treas-
ury Two hundred dollars in addition to his previous payments.

All Commutations of the Annual Dues shall be and remain perma-
nently funded, the interest only to be used for current expenses.

Any Fellow not previously subject to Annual Dues who takes up his
residence within fifty miles of Boston, shall pay to the Treasurer within
three months thereafter Annual Dues for the current year, failing which
his Fellowship shall cease ; but the Council may suspend the provisions
of this Article for a reasonable time.

Only Fellows who pay Annual Dues or have commuted them may
hold office in the Academy or serve on the Standing Committees or
vote at meetings.

Article 6. Fellows who pay or have commuted the Annual Dues
and Foreign Honorary Members shall be entitled to receive gratis one
copy of all Publications of the Academy issued after their election.

See Chap. x. art. 2.

902 STATUTES OF THE AMERICAN ACADEMY

Article 7. Diplomas signed by the President and the Vice-President
of the Class to which the member belongs, and countersigned by the
Secretaries, shall be given to all the Fellows and Foreign Honorary
Members.

Article 8. If, in the opinion of a majority of the entire Council,
any Fellow or Foreign Honorary Member shall have rendered himself
unworthy of a place in the Academy, the Council shall recommend to
the Academy the termination of his membership ; and if three fourths of
the Fellows present, out of a total attendance of not less than fifty, at a
Stated Meeting, or at a Special Meeting called for the purpose, shall
adopt this recommendation, his name shall be stricken irom the Roll.

See Chap. iii. ; chap. vi. art. 1 ; chap. ix. art. 1, 7 ; chap. x. art. 2.

CHAPTER HI

Election of Fellows and Foreign Honorary Members

Article 1. Elections of Fellows and Foreign Honorary Members
shall be by ballot, and only at the Stated Meetings in January and
May. Three fourths of the ballots cast, and not less than twenty,
must be affirmative to effect an election.

Article 2. Candidates must be proposed in writing by two Fellows
of the Section for which the proposal is made. These signed nomina-
tions shall be sent to the Corresponding Secretary and shall be retained
by him until the fifteenth of the following October or February, as
the case may be, when all nominations then in his hands shall be imme-
diately sent in printed form to every Fellow having the right to vote,
with the names of the proposers in each case, and with a request to send
to the Corresponding Secretary written comments on these names not
later than the fifth of November or the fifth of March respectively.

All the signed nominations, with the comments thereon, received up
to the fifth of November or the fifth of March shall be sent at once to
the appropriate Class Committees, which shall report their decisions
to the Council at a special meeting to be called to consider nom-
inations, not later than two days before the meeting of the Academy in
December and April respectively.

Article 3. All nominations approved by the Council shall be read
to the Academy at a meeting in December or in April, or be sent to the

OF ARTS AND SCIENCES 903

Fellows in print with the official notice of the meeting, and shall then
be posted in the Hall of the Academy until the balloting.

Not later than two weeks after any nomination is reported to the
Academy, the Corresponding Secretary shall send to every Fellow having
the right to vote a brief printed account of the nominee.

See Chap. ii. ; chap. vi. art. 1 ; chap. ix. art. 1.

CHAPTER IV

Officers

Article 1. The Officers of the Academy shall be a President (who
shall be Chairman of the Council), three Vice-Presidents (one from each
Class), a Corresponding Secretary (who shall be Secretary of the Coun-
cil), a Recording Secretary, a Treasurer, and a Librarian, all of whom
shall be elected by ballot at the Annual Meeting, and shall hold their
respective offices for one year, and until others are duly chosen and
installed.

There shall be also twelve Councillors, one from each Section of each
Class. At the Annual Meeting in 1912 three Councillors, one from
each Class, shall be elected by ballot to serve for one year, three for
two years, three for three years, and three for four years. At each
subsequent Annual Meeting three Councillors, one from each Class,
shall be elected by ballot to serve for the full term of four years and
until others are duly chosen and installed. The same Fellow shall
not be eligible for two successive terms.

The Councillors, with the other officers previously named, shall
constitute the Council.

See Chap. x. art. 1.

Article 2. If any office shall become vacant during the year, the
vacancy may be filled by the Council in its discretion for the unexpired
term.

Article 3. At the Stated Meeting in March, the President shall
appoint a Nominating Committee of three Fellows having the right
to vote, one from each Class. This Committee shall prepare a list of
nominees for the several offices to be filled, and for tlie Standing Com-
mittees, and cause it to be sent to the Recording Secretary not later
than four weeks before the Annual Meeting.

904 STATUTES OF THE AMERICAN ACADEMY

Article 4. Independent nominations for any office, if signed by
at least twenty Fellows having the right to vote, and received by the
Recording Secretary not less than ten days before the Annual Meet-
ing, shall be inserted, together with the list of nominees prepared by
the Nominating Committee, in the call therefor, and shall be mailed
to all the Fellows.

'See Chap. vi. art. 2.

Article 5. The Recording Secretary shall prepare for use in voting
at the Annual Meeting a ballot containing the names of all persons
duly nominated for office.

CHAPTER V

The President

Article 1. The President, or in his absence the senior Vice-President
present (seniority to be determined by length of continuous fellowship
in the Academy), shall preside at all meetings of the Academy. In
the absence of all these officers, a Chairman of the meeting shall be
chosen by ballot.

Article 2. Unless otherwise ordered, all Committees which are not
elected by ballot shall be appointed by the presiding officer.

Article 3. Any deed or writing to which the Corporate Seal is to be
affixed, except leases of real estate, shall be executed in the name of the
Academy by the President or, in the event of his death, absence, or
inability, by one of the Vice-Presidents, when thereto duly authorized.

See Chap. ii. art. 7 ; chap. iv. art. 1, 3 ; chap. vi. art. 2 ; chap,
vii. art. 1 ; chap, ix. art. 6 ; chap. x. art. 1, 2 ; chap. xi. art. 1.

CHAPTER VI

The Secretaries

Article 1. The Corresponding Secretary shall conduct the corre-
spondence of the Academy and of the Council, recording or making an
entry of all letters written in its name, and preserving for the files all
official papers which may be received. At each meeting of the Council
he shall present the communications addressed to the Academy which

OF ARTS AND SCIENCES 905

have been received since the previous meeting, and at the next meeting
of the Academy he shall present such as the Council may determine.

He shall notify all persons who may be elected Fellows or Foreign
Honorary Members, send to each a copy of the Statutes, and on their
acceptance issue the proper Diploma. He shall also notify all meet-
ings of the Council ; and in case of the death, absence, or inability of
the Recording Secretary he shall notify all meetings of the Academy.

Under the direction of the Council, he shall keep a List of the
Fellows and Foreign Honorary Members, arranged in their several
Classes and Sections. It shall be printed annually and issued as of the
first day of July.

See Chap. ii. art. 7; chap. iiL art. 2, 3 ; chap. iv. art. 1 ; chap.
ix. art. 6 ; chap. x. art. 1 ; chap. xi. art. 1.

Article 2. The Recording Secretary shall "have the custody of the
Charter, Corporate Seal, Archives, Statute-Book, Journals, and all
literary papers belonging to the Academy.

Fellows borrowing such papers or documents shall receipt for them
to their custodian.

The Recording Secretary shall attend the meetings of the Academy
and keep a faithful record of the proceedings with the names of the
Fellows present ; and after each meeting is duly opened, he shall read
the record of the preceding meeting.

He shall notify the meetings of the Academy to each Fellow by mail
at least seven days beforehand, and in his discretion may also cause
the meetings to be advertised ; he shall apprise Officers and Commit-
tees of their election or appointment, and inform the Treasurer of
appropriations of money voted by the Academy.

He shall post in the Hall a list of the persons nominated for election
into the Academy ; and after all elections, he shall insert in the Rec-
ords the names of the Fellows by whom the successful candidates were
nominated.

In the absence of the President and of the Vice-Presidents he shall,
if present, call the meeting to order, and preside until a Chairman is
chosen.

See Chap. i. ; chap. ii. art. 7 ; chap. iv. art. 3, 4, 5 ; chap. ix.
art. 6 ; chap. x. art. 1, 2 ; chap, xi, art, 1, 3.

Article 3, The Secretaries, with the Chairman of the Committee
of Publication, shall have authority to publish such of the records of
the meetings of the Academy as may seem to them likely to promote
its interests.

906 STATUTES OF THE AMERICAN ACADEMY

CHAPTER VII
The Teeasurer and the Treasury

Article 1. The Treasurer shall collect all money due or payable to
the Academy, and all gifts and bequests made to it. He shall pay all
bills due by the Academy, when approved by the proper officers, except
those of the Treasurer's office, which may be paid without such ap-
proval ; in the name of the Academy he shall sign all leases of real
estate ; and, with the written consent of a member of the Committee
on Finance, he shall make all transfers of stocks, bonds, and other
securities belonging to the Academy, all of which shall be in his official
custody.

He shall keep a faithful account of all receipts and expenditures,
submit his accounts annually to the Auditing Committee, and render
them at the expiration of his term of office, or whenever required to
do so by the Academy or the Council.

He shall keep separate accounts of the income of the Rumford Fund,
and of all other special Funds, and of the appropriation thereof, and
render them annually.

His accounts shall always be open to the inspection of the Council.

Article 2. He shall report annually to the Council at its March
meeting on the expected income of the various Funds and from all
other sources during the ensuing financial year. He shall also report
the names of all Fellows who may be then delinquent in the payment
of their Annual Dues.

Article 3. He shall give such security for the trust reposed in him
as the Academy may require.

Article 4. With the approval of a majority of the Committee on
Finance, he may appoint an Assistant Treasurer to perform his du-
ties, for whose acts, as such assistant, he shall be responsible ; or, with
like approval and responsibility, he may employ any Trust Company
doing business in Boston as his agent for the same purpose, the com-
pensation of such Assistant Treasurer or agent to be fixed by the
Committee on Finance and paid from the funds of the Academy.

Article 5. At the Annual Meeting he shall report in print all his
official doings for the preceding year, stating the amount and condition

OF ARTS AND SCIENCES 907

of all the property of the Academy entrusted to him, and the character
of the investments.

Article 6. The Financial Year of the Academy shall begin with
the first day of April.

Article 7. No person or committee shall incur any debt or liability
in the name of the Academy, unless in accordance with a previous vote
and appropriation therefor by the Academy or the Council, or sell or
otherwise dispose of any property of the Academy, except cash or
invested funds, without the previous consent and approval of the
Council.

See Chap. ii. art. 4, 5 ; chap. vi. art. 2 ; chap. ix. art. 6 ; chap.
X. art. 1, 2, 3; chap. xi. art. 1.

CHAPTER VIII
The Librarian and the Library

Article 1. The Librarian shall have charge of the printed books,
keep a correct catalogue thereof, and provide for their delivery fi-om
the Library.

At the Annual Meeting, as Chairman of the Committee on the Li-
brary, he shall make a Keport on its condition.

Article 2. In conjunction with the Committee on the Library he
shall have authority to expend such sums as may be appropriated by
the Academy for the purchase of books, periodicals, etc., and for de-
fraying other necessary expenses connected with the Library.

Article 3. All books procured from the income of the Rumford
Fund or of other special Funds shall contain a book-plate expressing
the fact.

Article 4. Books taken from the Library shall be receipted for to
the Librarian or his assistant.

Article 5. Books shall be returned in good order, regard being had
to necessary wear with good usage. If any book shall be lost or
injured, the Fellow to whom it stands charged shall replace it by a new
volume or by a new set, if it belongs to a set, or pay the current price
thereof to the Librarian, whereupon the remainder of the set, if any,

908 STATUTES OF THE AMERICAN ACADEMY

shall be delivered to the Fellow so paying, unless such remainder be
valuable by reason of association.

Article 6. All books shall be returned to the Library for examina-
tion at least one week before the Annual Meeting.

Article 7. The Librarian shall have the custody of the Publications
of the Academy. With the advice and consent of the President, he
may effect exchanges with other associations.

See Chap. ii. art. 6 ; chap. x. art. 1, 2.

CHAPTER IX

The Council

Article 1. The Council shall exercise a discreet supervision over
all nominations and elections to membership, and in general supervise
all the affairs of the Academy not explicitly reserved to the Academy
as a whole or entrusted by it or by the Statutes to standing or special
committees.

It shall consider all nominations duly sent to it by any Class Com-
mittee, and present to the Academy for action such of these nomina-
tions as it may approve by a majority vote of the members present
at a meeting, of whom not less than seven shall have voted in the
affirmative.

With the consent of the Fellow interested, it shall have power to
make transfers between the several Sections of the same Class, reporting
- action to the Academy.

See Chap. iii. art. 2, 3 ; chap. x. art. 1.

Article 2. Seven members shall constitute a quorum.

Article 3. It shall establish rules and regulations for the transac-
tion of its business, and provide all printed and engraved blanks and
books of record.

Article, 4. It shall act upon all resignations of officers, and all
resignations and forfeitures of fellowship ; and cause the Statutes to
be faithfully executed.

It shall appoint all agents and subordinates not otherwise provided
for by the Statutes, prescribe their duties, and fix their compensatioa

OF AETS AND SCIENCES 909

They shall hold their respective positions during the pleasure of the
Council.

Article 5. It may appoint, for terms not exceeding one year, and
prescribe the functions of, such committees of its number, or of the
Fellows of the Academy, as it may deem expedient, to facilitate the
administration of the affairs of the Academy or to promote its interests.

Article 6. At its March meeting it shall receive reports from the
President, the Secretaries, the Treasurer, and the Standing Committees,
on the appropriations severally needed for the ensuing financial year.
At the same meeting the Treasurer shall report on the expected income
of the various Funds and fi-om all other sources during the same year.

A report from the Council shall be submitted to the Academy, for
action, at the March meeting, recommending the appropriation which
in the opinion of the Council should be made.

On the recommendation of the Council, special appropriations may
be made at any Stated Meeting of the Academy, or at a Special Meet-
ing called for the purpose.

See Chap. x. art. 3.

Article 7. After the death of a Fellow or Foreign Honorary Mem-
ber, it shall appoint a member of the Academy to prepare a Memoir for
publication in the Proceedings.

Article 8. It shall report at every meeting of the Academy such
business as it may deem advisable to present.

See Chap. ii. art. 4, 5, 8 ; chap. iv. art. 1, 2 ; chap. vi. art. 1 ;
chap. vii. art. 1 ; chap. xi. art. 1, 4.

CHAPTER X

Standing Committees

Article 1. The Class Committee of each Class shall consist of the
Vice-President, who shall be chairman, and the four Councillors of the
Class, together with such other officer or officers annually elected as
may belong to the Class. It shall consider nominations to Fellowship
in its own Class, and report in writing to the Council such as may
receive at a Class Committee Meeting a majority of the votes cast,
provided at least three shall have been in the affirmative.

See Chap. iii. art. 2.

910 STATUTES OF THE AMERICAN ACADEMY

Article 2. At the Annual Meeting the following Standing Com-
mittees shall be elected by ballot to serve for the ensuing year :

(i) The Committee on Finance, to consist of three Fellows, who,
through the Treasurer, shall have full control and management of the
funds and trusts of the Academy, with the power of investing the funds
and of changing the investments thereof in their discretion.

See Chap. iv. art. 3 ; chap. vii. art. 1, 4 ; chap. ix. art. 6.

(ii) The Rumford Committee, to consist of seven Fellows, who shall
report to the Academy on all applications and claims for the Rumford
Premium. It alone shall authorize the purchase of books, publications
and apparatus at the charge of the income from the Rumford Fund,
and generally shall see to the proper execution of the trust.

See Chap. iv. art. 3 ; chap. ix. art. 6.

(iii) The Cyrus Moors Warren Committee, to consist of seven Fel-
lows, who shall consider all applications for appropriations from the
income of the C)t:us Moors Warren Fund, and generally shall see to
the proper execution of the trust.

See Chap. iv. art. 3 ; chap. ix. art. 6.

(iv) The Committee of Publication, to consist of three Fellows, one
from each Class, to whom all communications submitted to the Acad-
emy for publication shall be referred, and to whom the printing of the
Proceedings and the Memoirs shall be entrusted.

It shall fix the price at which the Publications shall be sold ; but
Fellows may be supplied at half price with volumes which may be
needed to complete their sets, but which they are not entitled to
receive gratis.

Two hundred extra copies of each paper accepted for publication in
the Proceedings or the Memoirs shall be placed at the disposal of the
author without charge.

See Chap. iv. art. 3 ; chap. vi. art. 1, 3 ; chap. ix. art. 6.

(v) The Committee on the Library, to consist of the Librarian, ex
officio, as Chairman, and three other Fellows, one from each Class, who
shall examine the Library and make an annual report on its condition
and management.

See Chap. iv. art. 3 ; chap. viii. art. 1, 2 ; chap. ix. art. 6.

OF ARTS AND SCIENCES 911

(vi) The House Committee, to consist of three Fellows, who shall
have charge of all expenses connected with the House, including the
general expenses of the Academy not specifically assigned to the care
of other Committees or Officers.

See Chap. iv. art. 3 ; chap. ix. art. 6.

(vii) The Committee on Meetings, to consist of the President, the
Recording Secretary, and three other Fellows, who shall have charge of
plans for meetings of the Academy.

See Chap. iv. art. 3 ; chap. ix. art. 6.

(viii) The Auditing Committee, to consist of two Fellows, who shall
audit the accounts of the Treasurer, with power to employ an expert
and to approve his bill.

See Chap. iv. art. 3 ; chap. vii. art. 1 ; chap. ix. art. 6.

Article 3. The Standing Committees shall report annually to the
Council in March on the appropriations severally needed for the ensuing
financial year ; and all bills incurred on account of these Committees,
within the limits of the several appropriations made by the Academy,
shall be approved by their respective Chairmen.

In the absence of the Chairman of any Committee, bills may be ap-
proved by any member of the Committee whom he shall designate
for the purpose.

See Chap. vii. art. 1, 7 ; chap ix. art. 6.

CHAPTER XI

Meetings, Communications, and Amendments

Article 1. There shall be annually four Stated Meetings of the
Academy, namely, on the second Wednesday of January, March, May,
and October. Only at these meetings, or at adjournments thereof
regularly notified, or at Special Meetings called for the purpose, shall
appropriations of money be made, or amendments of the Statutes or
Standing Votes be effected.

The Stated Meeting in May shall be the Annual Meeting of the
Corporation.

Special Meetings shall be called by either of the Secretaries at the
request of the President, of a Vice-President, of the Council, or often

912 STATUTES OF THE AMERICAN ACADEMY

Fellows having the right to vote ; and notifications thereof shall state
the purpose for which the meeting is called.

A meeting for receiving and discussing literary or scientific com-
munications may be held on the second or the fourth Wednesday,
or both, of each month not appointed for Stated Meetings, excepting
July, August, and September ; but no business shall be transacted at
any meeting which may be held on the fourth Wednesday.

Article 2. Twenty Fellows having the right to vote shall constitute
a quorum for the transaction of business at Stated or Special Meet-
ings. Fifteen Fellows shall be sufficient to constitute a meeting for
literary or scientific communications and discussions.

Article 3. Upon the request of the presiding officer or the Record-
ing Secretary, any motion or resolution offered at any meeting shall
be submitted in writing.

Article 4. No report of any paper presented at a meeting of the
Academy shall be published by any Fellow without the consent of the
author ; and no report shall in any case be published by any Fellow in
a newspaper as an account of the proceedings of the Academy without
the previous consent and approval of the Council.

Article 5. No Fellow shall introduce a guest at any meeting of
the Academy until after the business has been transacted, and espe-
cially until after nominations to Fellowship have been read and the
result of the balloting for candidates has been declared.

Article 6. The Academy shall not express its judgment on literary
or scientific memoirs or performances submitted to it, or included in
its Publications.

Article 7. All proposed Amendments of the Statutes shall be re-
ferred to a committee, and on its report, at a subsequent Stated Meet-
ing or at a Special Meeting called for the purpose, two thirds of the
ballots cast, and not less than twenty, must be affirmative to effect
enactment.

Article 8. Standing Votes may be passed, amended, or rescinded
at a Stated Meeting, or at a Special Meeting called for the purpose,
by a vote of two thirds of the members present. They may be
suspended by a unanimous vote.

See Chap. ii. art. 5, 8 ; chap. iii. ; chap. iv. art. 3, 4, 5 ; chap. v.
art. 1 ; chap. vi. art. 1, 2 ; chap. ix. art. 8.

OF ARTS AND SCIENCES 913

STANDING VOTES

1. Communications of which notice has been given to either of the
Secretaries shall take precedence of those not so notified.

2. Fellows may take from the Library six volumes at any one time,
and may retain them for three months, and no longer. Upon special
application, and for adequate reasons assigned, the Librarian may
permit a larger number of volumes, not exceeding twelve, to be drawn
from the Library for a limited period.

3. Works published in numbers, when unbound, shall not be taken
from the Hall of the Academy without the leave of the Librarian.

RUMFORD PREMIUM

In conformity with the terms of the gift of Sir Benjamin Thompson,
Count Rumford, of a certain Fund to the American Academy of Arts
and Sciences, and with a decree of the Supreme Judicial Court of
Massachusetts for carrying into effect the general charitable intent and
purpose of Count Rumford, as expressed in his letter of gift, the Acad-
emy is empowered to make from the income of the Rumford Fund, as
it now exists, at any Annual Meeting, an award of a gold and a silver
medal, being together of the intrinsic value of three hundred dollars,
as a Premium to the author of any important discovery or useful
improvement in light or heat, which shall have been made and pub-
lished by printing, or in any way made known to the public, in any
part of the continent of America, or any of the American Islands ;
preference always being given to such discoveries as, in the opinion of
the Academy, shall tend most to promote the good of mankind ; and,
if the Academy sees fit, to add to such medals, as a further Premium
for such discovery and improvement, a sum of money not exceeding
three hundred dollars.

INDEX.

Academy of Natural Sciences of
Philadelphia, centenary aniver-
sary, 850.

Aeroplanes, Determination of the Al-
titude of, 23.

Agassiz, G. R., elected Fellow, 863.

Agassiz, Mrs. G. R., Letter from, 847.

Aiken, J. A., elected Fellow, 864.

Algebra, An, of Plane Projective
Geometry, 735, 851.

Altitude of Aeroplanes, Determina-
tion of the, 23.

American Philosophical Society, An-
nual General Meeting, 850;
Bust of Franklin presented by,
830.

Ames, J. S., elected Fellow, 826;
accepts Fellowship, 830.

Ames, Cakes, Elected Fellow, 826;
accepts Fellowship, 830.

Angle, A Theory of Linear Distance
and, 865.

Argentine, New or Critical Laboul-
beniales from, 854.

Arrhenius, S. A., Elected Foreign
Honorary Member, 865.

Association des Ingenieurs Electri-
ciens, 854.

Atomic Weight of Phosphorus, A
Revision of, 583, 849.

Babbitt, L. A., The von Waltenhofen
Phenomenon in Soft Iron Rings,
227.

Baldwin, S. E., elected Fellow, 864.

Barroetea, Revision of the Genus, 202.

Bauer, L. A., elected Fellow, 863.

Baxter, G. P., INIoore, C. J., and
Boylston, A. C., A Revision of
the Atomic Weight of Phos-
phorus, 583, 849.

Bell, Louis, On the Ultra Violet
Radiation of Practical Illumi-
nants, 853.

Bermuda Islands, Calanoid Copep-
oda from, 217.

Biceps, Human, Unexpected Effects
of Electrical Stimuli on, 865.

Bigelow, H. B., elected Fellow, 826;
accepts Fellowship, 847.

Bigelow, M. M., elected Fellow, 826;
accepts Fellowship, 830.

Bigelow, W. S., elected Fellow, 826;
accepts Fellowship, 830.

Bixby, W. H., elected Fellow, 864.

Boas, Franz, elected Fellow, 864.

Bolton, C. K., Letter from, 831.

Bornet, J. B. E., Death of, 848.

Boss, Lewis, elected Fellow, 826;
accepts Fellowship, 830.

Boston Athenaeum, Bust of Frank-
lin presented by, 830. Vote of
thanks to, 832.

Bowditch, C. P., Report of Commit-
tee on Amendment of the Stat-
utes, 861; Report of Treasurer,
855; Results of the American
Occupation of the Philippines,
851; Subscription Paper pre-
sented by, 830.

Bowditch, H. P., Notice of, 847.

Boylston, A. C. See Baxter, G. P.,
Moore, C. J., and Boylston, A. C.

Brainerd, Ezra, elected Fellow, 864.

Braun Tube Oscillographs, A New
Method of Impact Excitation of
Undamped Oscillations and their
Analysis by Means of, 265, 829.

Bray, W. C, elected Follow, 826;
accepts Fellowship, 830.

Bridgman, P. W., elected Fellow,
863; The Measurement of Hy-

916

INDEX.

drostatic Pressures up to 20,000
Kilograms per Square Centi-
meter, 319, 829; Mercury, Liq-
uid and Solid, under Pressure,
345, 829; Water, in the Liquid
and Five Solid Forms, under
Pressure, 439, 829.

Bro^vTi, E. W., elected Fellow, 863.

Brush, G. J., Death of, 854.

Building Committee, Report of, 848.

Gannon, W. B., Biographical notice
of Dr. H. P. Bowditch, 847.

Capacity, Electrical, of Carborundum
Crystals, 791, 85 L

Carborundum, Stratification and Ca-
pacity of, 791, 851.

Chaffee, E. L., A New Method of
Impact Excitation of Undamped
Oscillations and their Analysis
by Means of Braun Tube Oscil-
lographs, 265, 829.

Channing, Edward, elected Fellow,
826; accepts Fellowship, 830.

Chapman, H. L., elected Fellow, 864.

Chase, G. H., elected Fellow, 864.

Chemical Laboratory of Harvard
College, Contributions from, 169,
583, 671.

Chittenden, R. H., elected Fellow,
863.

Chloride, Pyrosulphuryl, and Chlor-
sulphonic Acid, 671.

Chlorsulphonic Acid, Phrosulphuryl
Chloride and, 671.

Chromate, Sodium, The Transition
Temperatures of, as Convenient
Fixed Points in Thermometry,
169.

Cleland, H. F., elected Fellow, 826;
accepts Fellowship, 830.

Committees, Standing, elected, 862.

Compositae, On some hitherto unde-
scribed or misplaced, 206.

Comstock, D. F., elected Fellow, 863.

Cooke, Mary H., Notice of will of, 825.

Coolidge, Algernon, Death of, 848.

Cooling Curves, An Investigation of
the Errors in, and Methods for
Avoiding these Errors; also a
New Form of Crucible, 1.

Copepoda, Calanoid, from the Ber-
muda Islands, 217.

Council, Report of, 855; Financial
Report of, 860.

Cross, C. R., Report of the Rumford
Committee, 857.

Crucible, A New Form of, 1.

Crystals, On Electrical Properties of,
791, 851.

Curves, Cooling, An Investigation of
the Errors in, and Methods for
Avoiding these Errors; also a
New Form of Crucible, 1.

Dall, W. H., elected Fellow, 864.
Daly, R. A., The Nature of Volcanic

Action, 45.
Davidson, George, Death of, 854.
Davis, A. McF., Letter from, 831.
Davis, H. N., elected Fellow, 826;

accepts Fellowship, 830.
Day, A. L., elected Fellow, 863.
Distance, Linear, and Angle, A

Theory of, 865.
Dodge, Frederic, elected Fellow, 864.

Eames, Wilberforce, elected Fellow,
864.

East, E. M., elected Fellow, 826;
accepts Fellowship, 830.

Edes, H. H., Report of Committee
on Revision of the Statutes, 826.

Electrical Stimuli, Unexpected Effects
of, on the Human Biceps, 865.

Electromagnetic Theory of Gravi-
tation, On an, 559, 847.

Elia de CyOn prize, 825.

Ernst, H. C, transferred to Class II.,
Section 4, 851.

Errors in Cooling Curves, An Inves-
tigation of, and Methods for
Avoiding these Errors; also a
New Form of Crucible, 1.

Esterly, C. O., Calanoid Copepoda
from the Bermuda Islands,
217.

Eupatorieae, On the Classification of
certain, 189.

Evans, A. W., elected Fellow, 864.

Evans, R. D. See Pierce, G. W.,
and Evans, R. D.

INDEX.

917

Fairbanks, Arthur, Some Aspects of

the Fine Arts, 847.
Fellows, deceased, —

G. J. Brush, 854.

Algernon Coolidge, 848.

George Davidson, 854.

Edward H. Hall, 852.

H. W. Haynes, 852.

C. G. Pringle, 825.

A. L. Rotch, 854.

C. R. Sanger, 852.
S. H. Scudder, 825.
O. F. Wadsworth, 850.

Fellows, elected, —
G. R. Agassiz, 863.
J. A. Aiken, 864.
J. S. Ames, 826.
Oakes Ames, 826.
S. E. Baldwin, 864.
L. A. Bauer, 863.
H. B. Bigelow, 826.
M. M. Bigelow, 826.
W. S. Bigelow, 826.
. W. H. Bixby, 864.
Franz Boas, 864.
Lewis Boss, 826.
Ezra Brainerd, 864."]
W. C. Bray, 826.
P. W. Bridgman, 863.
E. W. Brown, 863.
Edward Channing, 826.
H. L. Chapman, 864.
G. H. Chase, 864.
R. H. Chittenden, 863.
H. F. Cleland, 826.

D. F. Comstock, 863.
W. H. Dall, 864.
H. N. Davis, 826.
A. L. Day, 863.
Frederic Dodge, 864.
In/ing Fisher, 864.
Desmond FitzGerald, 864.
Simon Flexner, 826.
O. K. O. Folin, 826.
G. W. Goethals, 864.
R. A. Harper, 826.

C. S. Hastings, 863.
L. J. Henderson, 863.
H. L. Higginson, 864.
M. A. DeW. Howe, 864.

D. C. Jackson, 826.

J. F. Jameson, 826.

E. P. Joslin, 864.

M. P. Knowlton, 826.
A. L. Kroeber, 864.
G. V. Leverett, 826.
Waldemar Lindgren, 864.
L. S. Marks, 864.
J. H. Metcalf, 826.

F. J. Moore, 826.
H. W. Morse, 826.
S. P. MuUiken, 863.
Hanns Oertel, 864.
Richard Olney, 864.

G. H. Palmer, 864.
R. S. Peabody, 864.
Roscoe Pound, 826.
C. P. Putnam, 864.
F. N. Robinson, 826.
Elihu Root, 864.

M. J. Rosenau, 826.
A. P. Rugg, 864.
W. B. Scott, 864.
H. W. Shimer, 826.

E. E. Southard, 826.

F. P. Steams, 826.
C. P. Steinmetz, 826.
J. E. Thayer, 864.

M. deK. Thompson, 863.
C. C. Torrey, 826.
W. J. Tucker, 864.
F. J. Turner, 826.
C. R. Van Hise, 826.
Williston Walker, 864.
W. R. Whitnev, 826.

E. B. Wilson, 826.
Woodrow Wilson, 826.
S. B. Wolbach, 864.

F. S. Woods, 863.
J. H. Wright, 864,

Fellows, List of, 885.

Fisher, Irving, elected Fellow, 864.

FitzGerald, Desmond, elected Fel-
low, 864.

Flexner, Simon, elected Fellow, 826.

Folin, O. K. O., elected Fellow, 826;
accepts Fellowship, 852.

Foreign Honorary Members, de-
ceased, —
J. B. E. Bornet, 848.
Sir Joseph D. Hooker, 848.
Lord Lister, 850.

918

INDEX.

Foreign Honorary Members,
elected, —

S. A. Arrhenius, 865.

J. A. A. J. Jusserand, 865.

H. A. Lorentz, 865.

Augusto Righi, 865.
Foreign Honorary Members, List of,

895.

General Fund, 855; Appropriations
from the Income of, 852, 861.

Geometry, Plane Projective, An
Algebra of, 735, 851.

George Montefiore Prize, 854.

Goethals, G. W., elected Fellow, 864.

Goodwin, H. M., Report of the
Library Committee, 856.

Granite, The Pegmatites of the
Riebeckite-Aegirite, of Quincy,
Mass.; their Structure, Miner-
als and Origin, 123.

Gravitation, On an Electromagnetic
Theory of, 559, 847.

Gray Herbarium of Harvard Uni-
versity, Contributions from, 189.

Griffith, Catherine R. B., Notice of
property of, 825.

Gyroscope, Recent Applications of
the, 854.

Hall, Edward H., Death of, 852.

Handbook of Learned Societies and
Institutions in America, 851.

Harper, R. A., elected Fellow 826;
accepts Fellowship, 830.

Harvard College. See Harvard Uni-
versity.

Harvard University. See Chemical
Laboratory, Jefferson Physical
Laboratory, Gray Herbarium.

Hastings, C. S., elected Fellow, 863.

Hayes, H. C, An Investigation of
the Errors in Cooling Curves and
Methods for Avoiding these
Errors; also a New Form of
Crucible, 1.

HajTies, H. W., Death of, 852.

Henderson, L. J., elected Fellow, 863.

Higginson, H. L., elected Fellow, 864.

Higginson, T. W., Notice of, 868.

Hofman,H.O.,resignsFeIlowship,850.

Hooker, Sir J. D. Death of, 848.
House Committee, Report of, 860.
House Expenses, Appropriations for,

860.
Howe, M. A. DeW., elected Fellow,

864.

Illuminants, Practical, On the Ultra
Violet Radiation of, 853.

Impact Excitation of Undamped
Oscillations, A New Method of,
265, 829.

International Congress of Ameri-
canists (Eighteenth), 854.

International Congress of Anthro-
pology and Prehistoric Archae-
ology, 848.

International Congress of Applied
Chemistry (Eighth), 825, 830,
850.

International Congress of Archae-
ology (Third), 853.

International Congress of Religions
(Fourth), 853.

Iron and Steel, The Anomalous Mag-
netization of, 631.

Iron Rings, Soft, On the von Walten-
hofen Phenomenon in, 227.

Ives, Frederic Eugene, Award of
Rumford Premium to, 861.

Jackson, D. C, elected Fellow, 826;
accepts Fellowship, 830.

Jameson, J. F., elected Fellow, 826,
dechnes Fellowship, 830.

Jefferson Physical Laboratorj^ Con-
tributions from, 1, 227, 265, 319,
345, 439, 559, 631, 791.

JosUn, E. P., elected Fellow, 864.

Jusserand, J. A. A. J., elected For-
eign Honorary Member, 865.

Kelley, G. L. See Richards, T. W.,
and Kelley, G. L.

Knight, F. I., Notice of, 851, 867.

Knowlton, M. P., elected Fellow,
826; accepts Fellowship, 830.

Kroeber, A. L., elected Fellow, 864.

Kronecker, Hugo, Unexpected Effects
of Electrical Stimuli on the Hu-
man Biceps, 865.

INDEX.

919

Laboulbeniales, New or Critical, from
the Argentine, 854.

Lanman, C. R., Pali Writing-ma-
chines — a Study for a Rational
Keyboard, 851.

Leverett, G. V., elected Fellow, 826;
accepts Fellowship, 830.

Library, Appropriation for, 860.

Library Committee, Report of, 856.

Lindgren, Waldemar, elected Fellow,
864.

Lister, Joseph, Death of, 850.

Lorentz, H. A., elected Foreign Hon-
orary Member, 865.

Magnetization, The Anomalous, of
Iron and Steel, 631.

Marks, L. S., elected Fellow, 864.

Measurement of Hydrostatic Pres-
sures up to 20,000 Kilograms
per Square Centimeter, 319, 829.

Mercury, Liquid and Solid, under
Pressure, 345, 829.

Metcalf, J. H., elected Fellow, 826;
accepts Fellowship, 830.

Meteorite, The Fall of a, 719, 849.

Moore, C. J. See Baxter, G. P.,
Moore, C. J., and Boylston, A. C.

Moore, C. L. E. See Phillips, H. B.,
and Moore, C. L. E.

Moore, F. J., elected Fellow, 826;
accepts Fellowship, 850.

Morse, H. W., elected Fellow, 826;
accepts Fellowship, 830.

Mulliken, S. P., elected Fellow, 863.

Naturforschende Gesellschaft zu

Gorlitz, 825.
New Hampshire Historical Society

Library, Dedication of, 847.
Nominating Committee, appointed,

853.

Oertel, Hanns, elected Fellow, 864.

Officers elected, 861; List of, 883.

Olney, Richard, elected Fellow, 864.

Oscillations, Undamped, A New
Method of Impact Excitation of,
and their Analysis by means of
Braun Tube Oscillographs, 265,
829.

Oscillographs, Braun Tube, A New
Method of Impact Excitation of
Undamped Oscillations and their
Analysis by Means of, 265, 829.

Palache, Charles. See Warren, C.
H., and Palache, Charles.

Pali Writing-machines — a Study
for a Rational Keyboard, 851.

Palmer, G. H., elected Fellow, 864.

Pasteur, Purchase of birthplace of,
825.

Peabody, R. S., elected Fellow,
864.

Pegmatites of the Riebeckite-Aegi-
rite Granite of Quincy, Mass.;
their Structure, Minerals and
Origin, 123.

Peirce, B. O., The Anomalous Mag-
netization of Iron and Steel,
631.

Philippines, The Results of the Amer-
ican Occupation of the, 851.

Phillips, H. B., and Moore, C. L. E.,
An Algebra of Plane Projective
Geometry, 735, 851; A Theory
of Linear Distance and Angle,
865.

Phosphorus, A Revision of the
Atomic Weight of, 583, 849.

Pierce, G. W., Report of Publica-
tion Committee, 859.

Pierce, G. W., and Evans, R. D.,
On Electrical Properties of
Crystals.
I. Stratification and Capacity of
Carborundum, 791, 851.

Polycerella Zoobotryon, 607, 829.

Potential, The Wave, of a Circular
Line of Sources, 313.

Pound, Roscoe, elected Fellow, 826;
accepts Fellowship, 852.

Pressure, Mercury, Liquid and Solid,
under, 345, 829.

Pressure, Water, in the Liquid and
Five Solid Forms, under, 439,
829.

Pressures, Hydrostatic, up to 20,000
Kilograms per Square Centi-
meter, The Measurement of,
319, 829.

920

INDEX.

Princeton University, Invitation from,
853.

Pringle, C. G., Death of, 825.

Publication, Appropriation for, 860.

Publication Committee, Report of,
859.

Publication Fund, 856; Appropria-
tion from the Income of, 852,
861.

Putnam, C. P., elected Fellow, 864.

Pyrosulphuryl Chloride and Chlor-
sulphonic Acid, 671.

Quincy, Mass., U. S. A., The Peg-
matites of the Riebeckite-Aegi-
rite Granite of; their Structure,
Minerals and Origin, 123.

Radium, X-rays and, 853.

Records of Meetings, 825.

Riebeckite-Aegirite Granite of
Quincy, Mass., The Pegmatites
of the, 123.

Riegel, E. R. See Sanger, C. R., and
Riegel, E. R.

Righi, Augusto, elected Foreign
Honorary Member, 865.

Richards, T. W., and Kelley, G. L.,
The Transition Temperatures of
Soduim Chromate as Conven-
ient Fixed Points in Thermom-
etry, 169.

Robinson, B. L., (I.) On the Classi-
fication of certain Eupatorieae,
189. (II.) Revision of the Gen-
us Barroetea, 202. (III.) On
some hitherto undescribed or
misplaced Compositae, 206.

Robinson, F. N., elected Fellow, 826;
accepts Fellowship, 830.

Root, Elihu, elected Fellow, 864.

Rosenau, M. J., elected Fellow, 826;
accepts Fellowship, 830.

Rotch, A. L., Death of, 854.

Royal Society, London, 250th anni-
versary of, 850.

Rugg, A. P., elected Fellow, 864.

Rumford Committee, Report of,
857.

Rumford Fund, 855; Appropria-
tions from the Income of, 861;

Papers published by aid of, 1,
169, 345, 439.
Rumford Premium, 913; Award of,
861.

Sanger, C. R., Death of, 852.

Sanger, C. R., and Riegel, E. R.,
Pyrosulphuryl Chloride and
Chlorsulphonic Acid, 671.

Scott, W. B., elected Fellow, 864.

Scudder, S. H., Death of, 825.

Shimer, H. W., elected Fellow, 826;
accepts Fellowship, 840.

Small wood, W. M., Polycerella Zoo-
botryon, 607, 829.

Smithsonian Institution, Invitation
from, 854.

Sodium Chromate, The Transition
Temperatures of, as Convenient
Fixed Points in Thermometry,
169.

Southard, E. E., elected Fellow, 826;
accepts Fellowship, 847.

Standing Committees elected, 862;
List of, 883.

Standing Votes, 913.

Statutes, as adopted Nov. 8, 1911,
833; as amended May 8, 1912,
899; adopted, 832; Amendment
of, 861, 852; Report of Com-
mittee on Revision of, 826,
861.

Steams, F. P., elected Fellow, 826;
accepts Fellowship, 830.

Steel, The Anomalous Magnetiza-
tion of, 631.

Steinmetz, C. P., elected Fellow, 826;
accepts Fellowship, 852.

Talbot, H. P., Report of C. M. War-
ren Committee, 859.

Temperatures, The Transition, of
Sodium Chromate as Conven-
ient Fixed Points in Thermome^
try, 169.

Thaxter, Roland, New or Critical
Laboulbeniales from the Argen-
tine, 854.

Thayer, J. E., elected Fellow, 864.

Thermometry, The Transition Tem-
peratures of Sodium Chromate

INDEX.

921

as Convenient Fixed Points in,

169.
Thompson, M. deK., elected Fellow,

863.
Thomson, Elihu, The Fall of a

Meteorite, 719, 849.
Torrey, C. C, elected Fellow, 826;

accepts Fellowship, 830.
Treasurer, Report of, 855.
Tscheschichin, Wssewolod, Letter

from, 830.
Tucker, W. J., elected Fellow, 864.
Turner, F. J., elected Fellow, 826;

accepts Fellowship, 830.

Ultra Violet Radiation of Practical

Illuminants, 853.
University of Minnesota, Invitation

from, 825.

Van Hise, C. R., elected Fellow, 826;

accepts Fellowship, 830.
Vincent, G. E., Inauguration of,

825.
Volcanic Action, The Nature of, 45.

Wadsworth, O. F., Death of, 850.

Walcott, C. D., Letter from, 852.

Walker, Williston, elected Fellow,
864.

von Waltenhofen Phenomenon in
Soft Iron Rings, 227.

Warren, C. H., and Palache, Charles,
The Pegmatites of the Rie-
beckite-Aegirite Granite of
Quincy, Mass., U. S. A.; their

Structure, Minerals, and Origin,

123.
Warren (C. M.) Committee, Report

of, 859.
Warren (CM.) Fund, 856; Appro-
priations from the Income of,

825, 861.
Water, in the Liquid and Five Solid

Forms, under Pressure, 439, 829.
Wave Potential of a Circular Line

of Sources, 313.
Webster, A. G., Recent Applications

of the Gyroscope, 854; Report

of House Committee, 860; The

Wave Potential of a Circular

Line of Sources, 313.
Webster, D. L., On an Electromag-
netic Theory of Gravitation,

559, 847.
Whitney, W. R., elected Fellow, 826;

accepts Fellowship, 830.
Williams, F. H., Biographical Notice

of Dr. F. I. Knight, 851, 867;

X-rays and Radium, 853.
Willson, R. W., Determination of the

Altitude of Aeroplanes. 23.
Wilson, E. B., elected Fellow, 826;

accepts Fellowship, 848.
Wilson, Woodrow, elected Fellow,

826; accepts Fellowship, 830.
Wolbach, S. B., elected Fellow, 864.
Woods, F. S.r elected Fellow, 863.
Woodward, R. S., Letter from, 852.
Wright, J. H., elected Fellow, 864.

X-rays and Radium, 853.

^}.Sh ^'"OI LIBRARY

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