Vol. 37
PROCEEDINGS
OF THE
AMERICAN ACADEMY
OF
ARTS AND SCIENCES.
Vol. XXXVII.
FROM MAY, 1901, TO MAY, 1902.
BOSTON:
PUBLISHED BY THE ACADEMY.
1902.
SSttibrrsitg $3rcss:
John Wilson and Son, Cambridge, U.S.A.
CONTENTS.
j
€i
Page
I. The Possible Significance of Changing Atomic Volume. By
Theodore William Richards 1
II. Preliminary Diagnoses of Neiv Species of Laboulbeniacae. — IV.
By Roland Thaxter 19
III. The Law of Physico- Chemical Change. By Gilbert Newton
Lewis 47
IV. The Visible Radiation from Carbon. By Edward L. Nichols . 71
V. On Ruled Loci in n-Fold Space. By Halcott C. Moreno . 119
VI. The Arc Spectrum of Hydrogen. By O. II. Basquin .... 159
VII. The Standard of Atomic Weights. By Theodore William
Richards 175
VIII. Stuilies on the Reactions of Limax maximus to Directive Stimuli.
By Peter Frandsen 183
IX. The Algae of Jamaica. By Frank Shipley Collins . . . 229
X. Modifications of HempeVs Gas-Apparatus. By Theodore Wil-
liam Richards 271
XI. The Parametric Representation of the Neighborhoo<l of a Singular
Point of an Analytic Surface. By C. W. M. Black . . . 279
XII. A Preliminary Enumeration of the Sorophorcae, By Edgar W.
Olive 331
XIII. The Decomposition of Mercurous Chloride by Dissolved Chlorides :
A Contribution to the Study of Concentrated Solutions. By
Theodore William Richards and Ebenezer Henry
Archibald 345
XIV. A New Investigation Concerning the Atomic Weight of Uranium.
By Theodore William Richards and Benjamin Shores
Merigold .... 363
XV. The Significance of Changing Atomic Volume. II. — The Prob-
able Source of the Heat of Chemical Combination, and a New
Atomic Hypothesis. By Theodore William Richards . ;>!»7
i
CM
IV CONTENTS.
Page
XVI. On the Accuracy of the Improved Voltameter. By Theodore
William Richards and George W. Heimrod . . . 413
XVII. 1. The Northern Carices of the Section Hyparrhenae.
2. The Variation of Some Boreal Carices. By M. L. Fernald 445
XVIII. Apatite from Minot, Maine. By John E. Wolff and
Charles Palache 515
XIX. A Description of Epidote Crystals from Alaska. By Charles
Palache . 529
XX. On the Specific Heats and the Heat of Vaporization of the Par-
affine and Methylene Hydrocarbons. By Charles F.
Mabery and Albert H. Goldstein 537
XXI. Certain Sense Organs of the Proboscis of the Polychaetous A nne-
lid Rhynchobolus dibranchiatus. By Adele Oppenheimer 551
XXII. The Composition of Petroleum. By Charles F. Mabery . 563
Records of Meetings 599
A Table of Atomic Weights. By Theodore William Richards . . 630
Report of the Council 635
Biographical Notices 635
Augustus Lowell 635
Truman Henry Safford 654
Horace Elisha Scudder 657
Joseph Henry Thayer 661
John Fiske 665
James Bradley Thayer 679
Officers and Committees for 1902-1903 683
List of the Fellows and Foreign Honorary Members . . . 685
Statutes and Standing Votes 693
Rumford Premium • 703
Index 705
Proceedings of the American Academy of Arts and Sciences.
Vol. XXXVII. No. 1. —Jink, 1901.
THE POSSIBLE SIGNIFICANCE OF CHANGING
ATOMIC VOLUME.
By Theodore William Richards.
THE POSSIBLE SIGNIFICANCE OF CHANGING
ATOMIC VOLUME.
By Theodore William Richards.
Presented May 8, 1901. Received April 16, 1901.
Compressibility is a universal property of matter. It is so essential
an attribute of the experimental universe that it is ascribed even to the
imponderable and imaginary ether as well as to " material." The three
states of matter are compressible in very varying degrees, dilute gases
being compressible to a great extent, highly compressed gases and liquids
to a far less extent, and solids to an extent usually even less than liquids.
The first case has been studied in great detail, the last two scarcely at all.
Compressibility is simply an evidence of work done upon a system by
a given pressure. It' the application of considerable pressure in a system
causes only a slight change of volume, it is evident that there must be
other powerful influences at work. Clearly a clue as to the variation in
these influences can be found in the quantitative study of the phenomena.
In all reversible cases which may be studied directly, an increase in
pressure is accompanied by an increase of resistance to pressure and a
diminution of volume. This depends upon the fundamental idea of
equilibrium, and is a special case of the general principle sometimes
named after Le Chatelier. Working backwards from this idea, one may
infer with regard to any given substance at a given temperature, that it
is under the influence of great pressure if its volume-change is unusually
small under addition of a given pressure.
There are two conceivable causes of great compression in a substance.
The pressure may be applied from the outside, or it may be due to the
mutual internal attraction or affinity of the smallest particles of the
substance for one another. That is, the substance may be compressed
either by an outside pressure, or by the intensity of its own cohesion.
The first may be typified by highly compressed gases, the second by
liquids, whose small compressibility may be taken as evidence of great
compression.
4 PROCEEDINGS OP THE AMERICAN ACADEMY.
In solids one must consider also the directive agency which manifests
itself in crystalline form and optical structure. In a few cases the
" crystallogenic force" seems to be rather directive than attractive; in
other cases it seems to have both properties, for considerable diminution
in volume may occur. The presence of the crystal-making force compli-
cates the phenomena and is a considerable stumbling-block in the way
of the study of the internal tension of solids.
In view of these facts, it seemed to me possible that the study of com-
pression as manifested by atomic volume under different circumstances, as
well as of atomic compressibility, might afford some light as to the
affinities at work. The attempt, while only just begun, has not been
wholly unsuccessful.
Evidently the liquid is the most suitable state in which to study the
effects of molecular and atomic compressibility. It is most suitable
because the irregularities in the behavior of liquids are very great, indi-
cating various internal stresses, and because they are nevertheless not at
the mercy of the directive crystal-making tendency which superposes its own
influence upon that of cohesion. The great difficulty in the subject lies
in the fact that the total compressibility of a substance is usually made
up of a number of parts ; the molecular compressibility might be due
partly to a diminishing of the so-called " free-space" between the mole-
cules, as well as to a diminishing of the distance between the atomic
centres. In words free from hypothesis, we may say that the compressi-
bility may be made up of a chemical and a physical compressibility.
When one comes to compute from compressibility the probable affinities,
one is still more at a loss, — for each affinity is a mutual affair, concern-
ing two specific substances. The immense number of variables thus
introduced has discouraged most investigators, and I can find little if any
hint of the significance of chemical compressibility in the literature
familiar to me.*
In a case of this kind, one naturally seeks at first cases as simple as
possible. A study of the volume changes which take place on mixing
liquids reveals at first no apparent regularity. In some cases an expan-
sion occurs, but more usually a contraction ; sometimes heat is evolved,
and at other times heat is absorbed. One law may, I think, be detected
in the midst of the confusion, namely : Similar liquids exhibit less
change of volume on mixing than dissimilar ones do. That is, where the
* The considerations of NordenskjiJld are too seriously complicated by uncer-
tain assumptions to liave much value. (See Ostwald's Lehrbuch, I. 850 (1891), for
these and similar considerations.)
RICHARDS.
SIGNIFICANCE OF CHANGING ATOMIC VOLUME.
affinity of a substance for itself is not unlike that of the substance for
another, no great contraction or expansion occurs on mixing. Thus
benzol and tuluol when mixed scarcely change in volume at all, while
alcohol and water contract considerably. That is just what would be
expected if affinity is the cause of contraction.
In order to use such facts it is not necessary to imagine an atomic
theory adapted to them. Such a theory is ventured upon at the end of
this paper, but the facts are significant without it. One only has to bear
in mind that liquid and solid substances resist compression, and hence
that when we find them compressed we have reason to believe that
pressure has been applied upon them. It is rather a matter of common
sense than a hypothetical abstract conception.
In order to present in a clear light the complications iuvolved in the
study of even a simple series of cases of chemical compression, the facts
concerning the molecular volumes of several metals and their oxides are
recorded and discussed below.
Molecular Volumes of Oxides.
Substance.
Weight of
metal com-
bined with
16 grains
oxygen.
Density
of
metal.
Density
of
oxide.
Space oc-
cupied by
giveu weight
of metal.
Space oc-
cupied by
corresponding
weight of
oxide.
Excess of
volume
of oxide.
2 Ag . . .
215.86
10.56
7.521
20.55
31.55
+11.00
Hg
200.00
13.59
11.130
14.71
19.4
+ 4.7
Cu . . . .
63.6
8.95
6.40
7.10
12.4
+ 5.3
Ni ....
58.7
8.9
6.39
6.60
11.75
+ 5.15
Cd . . . .
112.3
8.67
6.5
12.95
19.7
+ 6.75
Zn . . . .
65.4
6.9
5.6
9.5
14.5
+ 5.0
Mg ....
24.36
1.74
3.4
14.0
12.0
- 2.0
2Na ...
46.1
0.973
2.80
47.4
22.6
-24.8
2 II ...
2.0
0.07
1.00
28.2
18.0
-10.0
Si ....
14.2
2.00
2.30
7.1
13.14
+ 6.0
In compounds of carbon, accon
ing to posi
... 4.'
' to 12.0
In liquid oxygen at —119° and i
)0 atm. (s]
). gr. = 0.6,
5). . • O
= 24.5 c.c.
In liquid oxygen at —181° and ]
. . . O:
= 14.1 c.c.
6 PROCEEDINGS OP THE AMERICAN ACADEMY.
While in the first part of this paper no atomic hypothesis is assumed,
the words atomic volume, atomic weight, and atomic heat will be used in
a purely material sense, as the actual constants pertaining to quantities
chemically consistent.
The results recorded in this table are typical of the variety of degrees
of contraction which take place when substances combine with oxygen.
It is evident that in some cases the product occupies considerably more
space thau the metal from which it was formed, and that in others
(typified by magnesium and sodium above) the oxide occupies consid-
erably less space than the metal. This last remarkable circumstance
at once emphasizes the absurdity of estimating the atomic volume of an
element in a compound by discovering the volume-change which takes
place when that element is replaced by another. Oxygen cannot be
said to occupy a minus quantity of space, — the only possible outcome
of the false assumption in this particular case. The false method gives
fairly consistent results among carbon compounds only because of the
great similarity of their composition. This consideration leads to the
first law underlying the change of volume in chemical or physical
change, namely, The atomic volume is not a constant, but is dependent
upon the environment. This law was first suggested by Horstmann,*
but he looked upon it rather as the absence of a law than as the
presence of one.
If the affinity of oxygen for the metal were the only variable entering
into the figures given above, it is obvious that the total contraction,
the difference between the volumes of factors and product, would be at
once a comparative measure of the attractive forces which produce the
compression. This reasoning of course rests upon the plausible ground
that a state of being which resists pressure, such as liquid oxygen or
solid metal, may be compressed only by the application of pressure.
In this case pressure may be supposed to be applied by the mutual
affinity. But unfortunately the case is not so simple.
It is clear that in each case recorded above at least three affinities are
concerned : first, the affinity of the metal for itself; second, the
affinity of oxygen for itself ; and third, affinity of the metal for
oxygen. The second of these is constant throughout the series, hence
for the present comparison it may be considered as a known quantity.
Therefore each change of volume may concern at least two unknown
quantities. Hence if it were possible to measure either of the two
* Horstmann, Ostwald's Lehrbuch, I. 389 (1891).
RICHARDS. — SIGNIFICANCE OF CHANGING ATOMIC VOLUME. 7
variable affinities, an approximate idea could be obtained concerning
the other from these data concerning atomic and molecular volume.
A slight uncertainty is caused also by the possible varying intensity
of the u crystal-making tendency " which determines the structure of
solids. The small differences caused by this uncertainty may be seen
from the following typical calculation. If solid rather than liquid
mercury had been chosen above, the atomic volume of the mercury
would have become — — — = 14.2 instead of 14.7, and the excess of
14.1
volume of the oxide would have been 5.2 instead of 4.7. These
differences are unimportant compared with the larger values under
consideration ; the precise state of the solids or liquids makes less
difference than one would have supposed.
Is there any direct method of determining either the mutual affinity of
the two elements or the affinity of the metal for itself?
Countless attempts to measure the former have so continually resulted
in failure that many chemists are inclined to deny the existence of
chemical affinity. The electrometric method suggested by Ostwald *
clearly measures one of the ways in which chemical affinity may accom-
plish work, but it is limited in application and only represents a small
fraction of the possibilities. The thermal relations are complicated by
well-known thermodynamic irregularities, and would be fully significant
only at the imaginary absolute zero.
The direct determination of the affinity of a substance for itself is an
easier matter, for many of the properties of a single substance, such as
volume, compressibility, tenacity, must be associated with this affinity.
Let us seek to study these relationships more closely.
If one could only be sure that all substances, when relieved of their
self-affinity, would occupy the same volume, the atomic volume itself
would be the simplest and most direct means of comparing this property
in different substances. The smaller the actual atomic volume,- the
greater must be the self-affinity. Such an assumption would at first
sight seem to be justified, for those elements which have the largest
atomic volumes have the least inclination to remain in the elementary
states. Deserting the elementary state means introducing other affini-
ties, however ; hence the assumption would be unsafe.
It has been already pointed out that compressibility, if measured over
a wide range of pressures, might afford a clue to the extent of compres-
I tstwald, The Chemometer, Z. phys. Cheni. 15, 399 (1894).
8 PROCEEDINGS OF THE AMERICAN ACADEMY.
sion already existing in any given substance. But the comparison of
different substances involves the dangerous assumption that all substances
would be alike compressible if freed from self-affinity, — an assumption
which seems more probable than the last, but which nevertheless must
be rejected. A much safer measure of the stress under which a single
substance rests is the work which heat is able to do upon it. The
changing of a simple substance from t° to t° + dt° Centigrade must
involve the addition to it of an amount of internal work which is
represented by the rise of temperature multiplied by the heat capacity
of the substance, or C dt. In a simple elementary substance, when this
work does not involve the alteration of crystalline form or any other
apparent change except increase in size, it seems reasonable to consider
no other variables, at least as a working hypothesis. If this is the case,
we may write C dt = P dc, in which P is the internal stress against
which the heat-energy is doing work, G the molecular heat capacity, t
temperature, and v volume. The stress against which this work is
being done is due only to the internal stress and to atmospheric pressure
(which latter may be neglected by comparison with the very large value
G dt
of the former), hence the stress = P =— — ■• This can apply precisely
only to infinitesimal changes, because in all probability P will vary with
the volume. While it cannot be claimed that the expression just given
certainly expresses a single pressure pitted against temperature-work, the
expression certainly represents a resultant tendency which opposes
expansion by heat, and therefore, by inference, opposes all other forms of
expansion.* It is the inward tendency, the opposite to the driving
tendency f or fugacity.J
While then this stress, represented by the quotient of energy divided
by change of volume, can hardly represent anything very definite, it
must nevertheless be supposed in a general way to increase when the
self-affinity increases. Hence, while giving no certain knowledge, its
study may give an indication of affinity.
A typical comparison may be made of the two elements zinc and
mercury. They are simple, similar, and yet widely different as to their
power of holding oxygen. In each case the atomic contraction on union
with oxygen is about the same. If we take as the atomic volume of
* All the slight data which we possess upon compressibility seem to run
parallel with the coefficients of expansion.
1- Richards, These Proceedings, 35, 471.
% Lewis.
RICHARDS. — SIGNIFICANCE OP CHANGING ATOMIC VOLUME. 9
oxygen the atomic critical volume, the contractions are as follows :
14.7 -f 24.5 — 19.4 = 19.8, in the case of mercury, and 9.5 + 24.5 —
14.5 = 19.5, in the case of zinc. If the metals were originally subject
to the same internal stress, we should infer from the similarity of con-
tractions that the affinities concerned in the two cases were about equal.
This inference is, however, overthrown by other facts. Both elements
have about the same atomic heat capacity, hence no internal rearrange-
ment takes place in one which is not approximated in the other. On
the other hand, the increase in atomic volume for a rise of 1° of tem-
perature exhibited by one is much greater than that exhibited by the
other.
If a gram atom of one element increases more rapidly in size than
the gram atom of another, it is only reasonable to suppose that the
heat energy is finding less opposition in the former case. The co-
efficient of cubic expansion of mercury is 0.000179 at 0°C. and the
heat required to raise a gram through 1° is 0.139 joule. With zinc
the corresponding numbers are 0.000087 and 0.392. * The respective
atomic volumes are 14.7 and 9.5. Substituting these values in the
equation we obtain.
p (200X0.139) _... ,
" = (14.7 X 0.000179) = 106'000 megadynes Per square cm.
(65 4x0 392)
Pzn = (9.5 x 0.000087) = 310'000 megadynes per square cm.
Both these pressures are very large, for a megadyne exerts on a
square centimeter a pressure of almost an atmosphere. As has been
said, they signify a resultant tendency which resists expansion.
It is interesting to note that these stresses agree in their indications
with the comparison of boiling points and latent heats of evaporation.
The boiling point of mercury is 357° C. and that of zinc about 930° C.
The latent heat of evaporation of zinc is not known, but there is no
reason for believing that in its case Trouton's rule is broken. Hence
the criteria all indicate that zinc is harder to dissociate from itself than
mercury is.
A comparison of the energy-quotients of several metals, measured in
this way, may be of interest.
* All figures not otherwise designated were taken from the tables of Landolt
and Burnstein, 1894.
10
PROCEEDINGS OP THE AMERICAN ACADEMY.
Metal
(in order of
boiling point).
Boiling point
700 rn.ni.
Heat capacity
(,mayers per
gram)
C
Cubic
coefficient
of expansion.
Energy quotieut
P_ cat
atom, expan.
megadynes
mol. weight.
Mercury . .
Cadmium .
Sodium . .
Zinc ....
Copper . . .
Magnesium
Lead ....
357° C = 630° A
770° C = 1043° A
860° C = 1133° A
930° C = 1203° A
unknown
1100°^ = 1400° A
1400°-!- = 1700° A
0.139
0.23
1.21
0.392
0.375
1.02
0.120
0.00018
0.000093
0.00022
0.000087
0.000050
0.000081
0.000088
106,000
214,000
53,700
310,000
672,000
224,000
162,000
Silicon . .
Diamond .
unknown
unknown
0.7
0.5
0.0000230
0.0000036
755,000
4,900,000
In these figures one may find traces of many properties associated
with firmness of structure or intensity of self-affinity. For example,
the order of sequence of the energy-quotients agrees essentially with
that of tenacity and of hardness. There is some relationship also to
boiling points and melting-points, although here there are more ex-
ceptions. " Chemical affinity " is so much affected by electrical relations
and by atomic volume that one would expect to find regularity only on
comparing similar elements. Such comparison (zinc with cadmium, or
carbon with silicon) seems to show that the energy-quotient tends to
increase with diminishing atomic weight.
Having thus plausible inference, from independent sources, as to the
relative values of the compressing agencies existing in metals at the
ordinary temperature, it is worth while to study the correction which
must be applied to the volume-change exhibited in chemical combina-
tion with another element. In zinc the self-affinity is so great (boiling
point = 1200° A), and the metal is hence already so compressed, that
a given further pressure causes less change in its volume than it would
cause in the case of mercury. That is, the mercury contracts more
than zinc when it is oxidized. Hence the difference between the
volume of the oxide and the volume of the metal gives too low a
value for the volume of the combined oxygen in the case of mercury.
KICHAliDS. SIGNIFICANCE OF CHANGING ATOMIC VOLUME. 11
Thus the contraction of the oxygen is really less in the case of
mercuric oxide, although it appears to be the same.
Without going further, one can explain by means of these considera-
tions the behavior of zincic and mercuric oxides when subjected to high
temperatures. The sixteen grams of oxygen in mercuric oxide occupies
a larger space than an equal weight in the case of zinc, hence one
infers that it is less compressed by its affinity, hence the affinity must be
less. This smaller affinity should be more easily overcome by rising
temperature, a prediction which agrees with facts. Thus there appears
to be in this case a connection between the compression of substances
and their tendency to combine one with another.
The case under consideration is typical. In the case of sodium and
magnesium, the affinity of the metal for oxygen is so enormous as to
overcome easily the large affinity of the metal for itself, and besides this
to compress both metal and oxygen together into a space smaller than
that previously occupied by the metal. This fact corresponds with the
great difficulty of decomposing sodic and magnesic oxides. Metallic
magnesium probably has as energy-quotient a stress more than four times
as great as sodium (see table on p. 10) ; hence the total contraction on
combination with oxygen is less than in the case of sodium. Compari-
son with the cases of mercury and zinc will show that this small con-
traction does not necessarily conflict with the fact that magnesium
decomposes sodic oxide at high temperatures. Again, the contraction
involved in the formation of argentic oxide is very slight. In this case
the large volume of oxygen is not concealed by the contraction of the
metallic element, as it was in the case of mercury, for silver is not par-
ticularly compressible. Hence one can infer that the affinity of silver for
oxygen is smaller than that of magnesium for oxygen, — an inference
which agrees with fact. Moreover, since the relation is nearly additive,
that is, neither silver nor oxygen change much in volume on com-
bination, their combination is easily shifted, that is to say, silver oxide
is easily decomposed by heat.
Of course many tables comparing the molecular volumes of solids and
liquids might be drawn up, since a very great number of specific gravi-
ties have been determined. A table containing chlorides of the metals
already considered may be of interest.
Here the variations in contraction are less than they were before.
Chlorine evidently possesses more equally distributed affinities than
oxygen does, and apparently somewhat weaker ones. The two most
interesting features of this table, which may be seen without the eliini-
12
PROCEEDINGS OF THE AMERICAN ACADEMY.
Molecular Volumes of Chlorides.
Substance.
Weight of
metal com-
bined with
35.5 grams
of chlorine.
Density
of
metal.
Density
of
chloride.
Volume of
given weight
of metal.
Volume of
corresponding
weight of
chloride.
Excess
of volume
of chloride
above metal.
Ag . .
108.
10.56
5.53
10.27
45.90
+15.63
|Hg.
.
100.
14.00 .
5.42
7.30
25.5
+18.2
Hg..
200.
14.00
7.10
14.00
33.2
+19.2
|Cu .
•
31.8
8.95
3.05
7.10
25.4
+18.3
iCo . .
.
28.5
9.00
2.94
3.16
21.8
18.64
iCd .
.
56.2
8.67
3.7
6.47
24.8
18.33
i Zn .
■
32.7
6.9
2.753
4.75
25.0
+20.25
Mg. .
•
12.2
1.74
2.177
7.0
21.95
+15.00
Na . .
. .
23.05
0.973
2.15
23.7
27.2
+ 4.2
K. . .
.
39.14
0.875
1.995
45.7
37.3
- 8.4
Rb . .
.
85.44
1.52
2.21
56.1
55.0
- 1.0
II . .
• •
1.01
0.07
1.27
14.1 (?)
28.9
fl4.7
Combined with ca
Liquid chlorine at
22.8
-80° (boili
ng point, 1
60 mm.) (s]
a. gr. = 1.66
21.5
+80° (sp. |
;r. = 1.20;
29.6
nation of the self-affinities of the several metals, are the small excess in
the case of silver, and the larger excess in the case of mercurous chloride.
This is quite in accord with the facts; for argentic chloride is more
stable than the oxide, and mercurous chloride easily splits into mercuric
chloride and mercury.*
The case of the hydroxides is especially interesting.
The density of the hydroxide of zinc has not been accurately deter-
mined ; indeed the data concerning cobalt, cadmium, and magnesium are
not very trustworthy on account of the amorphous condition of most hy-
droxides. It is interesting to note that in this table, where the substances
are arranged in the order of the contraction which ensues when hydroxyl
combines with the metal, should also be arranged in the electro-chemical
* Richards, These Proceedings, 33, 9 (1897).
RICHARDS. — SIGNIFICANCE OF CHANGING ATOMIC VOLUME. 13
Molecular Volumes or Hydroxides.
Substance.
Weight of
metal com-
bined with
17 grams
hydroxyl.
Density
of
metal.
Density
of
hydroxide.
Volume of
given weight
of metal.
Volume of
hydroxide
corresponding.
Excess of
volume of
hydroxide
above metal.
Ag
1 Hg . . .
\ Cu . . .
Tlie hydroxide is exceedingly unstable.
It is doubtful if the hydroxide exists.
The hydroxide cannot be dried without decomposition.
\ Co . . .
\ Cd . . .
\ Mg . . .
\ Sr ...
Na . . . .
K
28.5
56.2
12.2
43.83
23.05
39.14
9.
2.54
0.973
0.875
3.597
4.79
2.36
3.62
2.13
2.044
3.16
6.47
7.0
17.3
23.7
45.7
12.67
15.25
12.90
17.0
18.80
27.5
+ 9.51
+ 8.78
+ 5.90
- 0.3
- 4.9
-18.2
Hvdroxvl i" nrcranin nomnoiinds
+12 (
I
Hy
droxyl in I13
'drogen di
oxide (sp.
gr. = 1.50) . . 11.4
[
order. That is to say, the solution tension of a metal appears to be
associated with the excess of affinity of the metal for hydroxyl over its
affinity for itself, and intensity of potential seems to be associated with
intensity of atomic compression. The inference to be drawn from this
comparison is of course that the formation of the metallic ion in water is
connected with the affinity of the metal for water, — an affinity
which manifests itself even when both of the " bonds" of oxygen are
filled.* Similar attraction for nitrogen or sulphur would explain cases
in which the solvent does not contain oxygen.
If this is true, contraction should take place when salts are dissolved
in water. This inference is amply verified by facts. In some cases the
solution occupies even less space than the water alone, involving a total
contraction greater than the volume of the salt itself. The best known
of these cases are those of lithic, sodic, and baric hydroxides, and
* Briihl has suggested that oxygen is the cause of dissociation, but he ascribes
it rather to quadrivalence than to a general affinity.
14 PROCEEDINGS OP THE AMERICAN ACADEMY.
cobalt, nickel, zinc, and magnesium sulphates,* but undoubtedly others
exist. In a large majority of cases when an electrolyte is dissolved in
water, the sum of the volumes of salt and of the solvent taken together
considerably exceeds the volume of the solution. This contraction is
usually ascribed wholly to the dissolved substance in dilute solutions,!
but it seems to me that the behavior of the salts named above proves the
falsity of this method of calculation. The water as well as the salt must
contract ivhen a salt is dissolved. So many complications are concerned
in the act of the solution of an electrolyte that it is difficult to unravel
the tangled clues ; but the wide deviations exhibited by different sub-
stances seem to indicate that there are present overlapping contractions
and expansions, the resultant of which is a smaller quantity than some
of the individual influences. Such contractions and expansions are just
what one would expect to find in a readjustment of affinities.
In considering the simpler case of solid non-electrolytes, one usually
finds here also a contraction upon solution, although less marked than in
the extreme cases named above. For this reason, one is inclined to
ascribe the act of solution of all kinds primarily to the affinity of the
solvent for the dissolved substance. The solution tension of a metal or
salt becomes simply a balance or ratio of attractions, — the sejiarating
tendency of heat upon the dissolving phase is much assisted by the
attraction from outside. This is of course no new idea. The possible
method of treating mathematically these balanced influences is suggested
in a recent paper on the "driving tendency" of reaction. $
That electrolytic separation also should be assisted by the outside
attraction for the solvent is almost a foregone conclusion. This may be
inferred from the contraction shown by most electrolytes on dissolving.
Hence may arise the various contact-potentials exhibited by the same
substance in different solvents ; for different solvents must possess differ-
ent affinities. Hence also one would expect to find a much greater
potential needed for the dissociation of gases than for that of dissolved
substances.
The mechanism of electrolytic dissociation in gases is now usually
* Thonisen, Thermoehemische Untersuchungen, I. 45 (1882). MacGregor,
Trans. Roy. Soc. Canada, 1890, p. 19; 1891, p. 15; Trans. Nova Scotia Inst. Nat.
Sc, 7, 368 (1890).
t Van't Hoff, Vorlesung. phys. theoret. Cliem., III. p. 41 (1900). Drude and
Nernst (Z. phys. Cliem., 15, 79 (1896)) ascribe this contraction to "Electro-
striction."
t Richards, Jour. Phys. Chem., 4, 385 (1900). See specially p. 391.
RICHARDS. SIGNIFICANCE OF CHANGING ATOMIC VOLUME. 15
explained by the aid of the ingenious hypothesis of "electrons," as
amplified by J. J. Thomson and his students in the brilliant experimental
researches published in the recent volumes of the Philosophical Magazine.
This daring hypothesis must not be accepted without reservation, how-
ever. Some physical objections to it have been suggested by Ernest
Merritt in his interesting address to the American Association for the
Advancement of Science ; * and other objections arise when one tries
with its aid to unravel the tangle of influences involved in purely
chemical action. The rejected alternative of imagining the atom as
indivisible, but as capable of receiving widely varying electric charges
under widely different conditions, has some advantages which the opposite
hypothesis does not possess. The subject is much too large for discus-
sion here, however. One phase of it, which bears directly upon the sub-
ject of the present paper, may receive brief notice.
The results of Thomson, Townsend, Zeleny f and others seem to indi-
cate that the bearer of the negative electricity not only carries the high
charge referred to above, but that it is very small, while the bearer of the
positive electricity is very large. May it not be the atom itself which thus
expands and contracts ? This agrees with the verdict of the results of
atomic compression given above. Change of atomic volume seems to be
associated with electric stress. This assignment of electric expansibility
to the atomic sphere of influence might explain other phenomena con-
cerning the behavior of electrified gases, for example, the increase of
pressure which is observed when a gas is highly charged.^ Again, the
great conductivity of a gas with adequate potential and quantity of
electrical discharge § seems to indicate that then the situation must
resemble that in a metal, where the spheres of stress fill the whole
volume occupied by the substance. The temperature must be so high
under these circumstances that the gas is probably in a condition of
thermal dissociation. Hence one is inclined to refer the great conduc-
tivity to the electrical susceptibility of evenly compressed or undistorted
atoms. The fact that pure metals conduct electricity better than alloys or
compounds seems to support this conclusion. The permeability of solids
to cathode rays might be explained by supposing that the smallest particles
of both solid and gas are much contracted by the negative charge.
* Proc. Am. As. Adv. Soc, 1900, p. 49.
t Phil. Mag. [5] 46, 120, (1898). See also Am. Chem. Journ., 25, 340 (1901),
for a resume' of this work.
X De la Rue and Miiller, Phil. Trans., 1880, SG.
§ Trowbridge and Richards, Phil. Mag. [5] 43, 349 (1897).
16 PROCEEDINGS OF THE AMERICAN ACADEMY.
It is with some diffidence that this paper attempts to reconcile the facts
with any hypothesis, for hypotheses sometimes lead to dangerous delu-
sions. If, however, one never forgets the essential difference between
fact and hypothetical inference, a theory may afford useful suggestions
for further research. The facts under discussion in the present paper
seem to me to be adequately connected by none of the current concep-
tions concerning atoms, hence it has seemed not wholly pointless to
postulate a theory which might serve better. The essential elements of
this theory must be evident from the trend of the hypothetical discussion
above ; they are not wholly new. Since changes of atomic volume seem
to be so closely associated with the most intimate properties of substance,
it seems necessary to assign more importance to the atomic " sphere of
influence " or the " free space " around the atomic centres than is cus-
tomary. Indeed, the properties of material seem to be as much concerned
with the " atomic shell " as with the " atomic centre." The two hypothet-
ical conceptions are so closely related as to be inseparable.
Such a point of view leads to the conception of an atom as a compres-
sible field of force possessing two attractive attributes, chemical affinity
and gravitation, both of which may be concerned in chemical action.
Mass may be supposed to be causally connected with gravitation. The
fact that in many cases affinity diminishes with increasing atomic weight,*
taken together with the Laws of Faraday and of Dulong and Petit,
suggests that the two attractive forces in the atom may bear some
sort of reciprocal or additive relationship to one another, — that the
product or sum of the two may afford a constant basis for the vibrations
of heat and electricity. This relation is often hidden by electrical attrac-
tion, which plays so important a role in chemical action that it is some-
times hard to distinguish the intensity of chemical affinity proper. In
such an atom one can imagine that either thermal or electrical vibration
might cause distention. The phenomena of electricity suggest that
electricity plays around the atomic surface, while heat seems to be
concerned with a more fundamental or central agitation. Light-vibra-
tion, which seems also to be intimately concerned with atomic structure,
would be assumed to be a surface effect like electrical vibration.
Such an atom would be compressible under the influence of its own
affinities as well as under the influence of external pressure. Permanent
* Van't Hoff, Vorl. th. phys. Chem., III. 87 (1900). Compare also the relation
of the energy-quotients of similar metals referred to on p. 10 of the present
paper.
RICHARDS. — SIGNIFICANCE OP CHANGING ATOMIC VOLUME. 17
atomic distortion would accompany chemical union, and the heat of the
reaction would be the outcome of the resulting decrease of internal
energy. Atomic volume and atomic compressibility might limit the
possibility of distortion ; hence would arise a possible explanation for
quantivalence, stereochemistry, and crystal form. Many other proper-
ties of material, too numerous to mention, seem to be explicable in a
similar way.
It would be unreasonable to expect the hypothesis thus briefly de-
scribed to correspond to all known facts. No hypothesis has ever been
proposed which is wholly satisfactory ; our knowledge is incommensurate
with the possibilities involved. If, however, a given theory is found to
explain some relationships better than other hypotheses, it may be of
service in suggesting new experimental research. Such a service is of
course the best one which a hypothesis can perform.
The idea discussed above has been already applied in plausible fashion
to a wide range of chemical and physical phenomena. If future experi-
mentation to be carried on here seems to warrant it, these applications
may form the subject of another communication.
The object of the present paper may be summed up in a few words, as
follows : It is pointed out that changing atomic volume may be used as
an approximate measure of the pressure which causes it, and therefore
of the affinity which causes the pressure. Some of the difficulties in
the way of exact interpretation are pointed out, and hints are given
as to possible modes of overcoming the difficulties.
The chief outcome of the paper is the following postulate : The atomic
volume is not constant, but a function of pressure and temperature, and
probably of electric stress.
In this connection it is pointed out that chemical affinity is possibly a
reciprocal function of mass.
To explain these and many other facts, a modification of the atomic
hypothesis is tentatively proposed which contends that we have no right
to disregard the compressible environments around the centres of gravity
and affinity.
Cambridge, Mass.
Proceedings of the American Academy of Arts and Sciences.
Vol. XXXVII. No. 2. — June, 1901.
CONTRIBUTIONS FROM THE CRYPTOGAMIC LABORATORY OF
HARVARD UNIVERSITY. — XLVII.
PRELIMINARY DIAGNOSES OF NEW SPECIES OF
LABO ULBENIA CEAE. — IV.
By Roland Thaxter.
CONTRIBUTIONS FROM THE CRYPTOGAMIC LABORATORY OF
HARVARD UNIVERSITY. — XL VII.
PRELIMINARY DIAGNOSES OF NEW SPECIES OF
LABOULBENIACEAE. — IV.
By Roland Thaxter.
Received May 6, 1901. Presented May 8, 1901.
Additional material illustrating the well-marked generic type de-
scribed in a former paper as Mbnoicomyces renders necessary some
modification of the original diagnosis, as well as the separation of several
species in a second nearly allied genus, which I have called Eumonoico-
myces (E. Papuamis being taken as the type), that is well characterized
not only by constant differences in the structure of the peculiar anther-
idium, but also by reason of certain differences in gross habit which are
constant in normal forms of all three of the known species, one of which,
E. invisibilis, was formerly placed by me in Mbnoicomyces.
EUMONOICOMYCES nov. gen.
Receptacle consisting of a basal and subbasal cell ; the latter producing
terminally a sterile appendage and laterally a fertile branch (abnormally
more than one) the axis of which is coincident with that of the receptacle
from which it is not distinguished and consists of a series of superposed
cells which may bear a sterile appendage, an antheridium, or an anther-
idium and a perithecium ; the three terminal cells usually bearing these
organs in the order mentioned. The antheridia consisting of a single
stalk-cell, and a single, often obscure, basal cell; the body of the antherid-
ium consisting of a series of numerous antheridial cells in four (?) vertical
rows which extend obliquely inward and upward, emptying into a com-
mon cavity, and replace entirely the two tiers of wall-cells and the anther-
idia of Monoicomyces ; the terminal cells growing upward directly to
form four unequal sterile terminal appendages, similar to those of
Monoicomyces.
22 PROCEEDINGS OF THE AMERICAN ACADEMY.
Eumonoicomyces Papuanus nov. sp.
Nearly or quite hyaline. Basal cell of the receptacle small, usually
triangular ; the subbasal cell terminating in a short appendage distin-
guished by a dark basal septum, and sometimes once branched. The
fertile branch not differentiated from the receptacle, consisting of three,
rarely two cells similar to the subbasal cell, obliquely superposed; the
lowest bearing normally a short, hyaline or faintly brownish, erect, sterile
appendage, similar to that of the subbasal cell ; the middle cell bearing a
single antheridium, and the upper an antheridium and a stalked perithe-
cium. The autheridia rather stout, broader distally ; the stalk-cell small
and short; the antheridial cells very numerous — thirteen to fifteen
usually visible in optical section — the terminal appendages of the usual
type, short or seldom longer than the antheridium. Perithecium rather
long and sometimes slender ; the venter inflated ; the distal portion
tapering gradually and symmetrically to the blunt, nearly truncate apex ;
the rather short tip hardly distinguished above a slight elevation ; the
stalk-cell variable in length, rather slender, seldom more than half as
long as the perithecium ; the basal cells rather large and broad, not dis-
tinguished from the venter. Spores about 35 X 3/x. Perithecia 80-
120 X 32-40^, the stalk-cell 35-75 x 15^. Antheridia including
stalk-cell and without appendages 35 X 18 fi. Total length to tip of
perithecium 150-290^.
On all parts of a small pale species of Oxytelus. Ralum, New Pome-
rania. Berlin Museum, No. 1011.
Eumonoicomyces Californicus nov. sp.
Resembling E. Papuanus in general habit. Basal cell of the recep-
tacle short, stout, geniculate, with a dark brown suffusion extending from
the foot half-way up its convex margin ; the subbasal cell bearing distally
a long appendage consisting of a short hyaline basal cell, separated by a
dark septum from a second cell above it, which is dark brown and bears
two long, slender, one-celled, erect branches, brown below, becoming
hyaline distally. The fertile branch not distinguished from the receptacle
and consisting of three, sometimes more, very obliquely superposed cells
similar to the subbasal cell : the lowest bearing a sterile appendage like
that which terminates the receptacle; the middle cell usually bearing an
antheridium, and the npper an antheridium and a perithecium. Anther-
idium short-stalked, with a more or less well-defined median constriction,
resulting from an inflation of the cells which bear the terminal append-
THAXTER. NEW LABOULBENIACEAE. 23
ages. The latter very long, brown, extending beyond the tip of the
peritheciura. Perithecium short and stout, the venter inflated, the much
shorter neck-like distal portion abruptly distinguished, the apex blunt,
the stalk-cell usually rather short and stout. Perithecia 75 X 25 ix, the
stalk-cell 20 X 18 fx. Sterile appendages, longest 150 ^u. Appendages of
antheridium 100^. Total length to tip of perithecium 150 p.
On Oxylelus sp. Berkeley, California.
MONOICOMYCES Thaxter.
The characters which may be considered to separate this genus from
Eumonoicomyces are as follows : — The stalk of the antheridium consists
of two cells placed side by side ; the body of the antheridium consists of
two tiers of wall-cells, from each of which an inner antheridial cell is
separated ; the subbasal cell of the receptacle bears normally more than
one heterogeneous fertile branch.
o ■
Monoicomyces Echidnoglossae nov. sp.
Subbasal cell of the receptacle somewhat smaller than the basal cell,
bearing a terminal appendage the basal cell of which is as long, or nearly
as long as the receptacle and often distally enlarged ; the axis above it
consisting of a curved series of several cells, externally opaque, black,
hyaline along the inner margin, each cell giving rise from its inner side
to a hyaline simple branchlet, much as in the appendage of Laboulbenia
cristata. Fertile branches usually two, sometimes one or three, arising
from the subbasal cell of the receptacle, and consisting of a single short
basal cell which bears directly a perithecium (in some cases more than
one) and an antheridium. Antheridium relatively large, the stalk-cells
somewhat longer and narrower than the basal cells ; the cells of each of
the middle tiers distally more or less prominent, the rounded, almost
papillate elevations thus formed from the upper tier more prominent than
those from the lower tier : the distal cells proliferous externally and dis-
tally, thus forming an outer crown of shorter appendages of very unequal
length, which surround the usual inner series. Perithecium becoming
greatly and asymmetrically inflated below, and tapering rather abruptly
to the slightly distinguished, rather short, bluntly pointed tip ; the stalk-
cell variably developed. Perithecia 100-125 X 45-55^, the stalk-
cells 40-80 x 15 ft. Antheridia 75-100 /j, the sterile appendages
50-75 li. Total length to tip of perithecium 220-250 fx.
On the inferior surface of the thorax of Echidnoglossa Americana Fau-
vel. Vera Pass, Colorado. Leconte Collection.
24 PROCEEDINGS OF THE AMERICAN ACADEMY.
Monoicomyces furcillatus nov. sp.
Receptacle consisting of two small cells which are hardly distinguish-
able owing to a general blackish brown suffusion ; producing on either
side a stout blackened prolongation, the two forming a nearly symmetri-
cal fork-like structure, the prongs of which are slightly curved inward,
and slightly divergent. From near the base of these outgrowths and
between them arise, apparently from single basal cells on both sides,
single stalked perithecia and antheridia. The antheridia rather long
and slender, their detailed structure not determinable in the types. The
perithecia long and slender, straight, symmetrical, pale yellowish, slightly
inflated toward the base, tapering gradually to the blunt apex. Spores
about 40 X 3 ^. Perithecia 135 X 27^. Outgrowths from the recep-
tacle 110 X 12 fi.
Near the tip of the abdomen of Aleochara repetita Sharp. Panama.
Sharp Collection, No. 1095. Of the three individuals obtained one only
is in fair condition, and none have antheridia in which the details of
structure can be made out. Owing to the suffusion and great reduction
of the receptacle it is further impossible to determine the exact origin of
the remarkable fork-like outgrowths, or the other structures which arise
from it. The form is a most peculiar one and recognizable without diffi-
culty ; yet, until further data are obtained concerning it, its generic
position cannot be certainly determined, although it seems at least more
closely allied to Monoicomyces, in which it is provisionally placed, than
to any other known type.
Monoicomyces Aleocharae nov. sp.
Pale amber, shading to amber brown. Receptacle, together with the
foot and the basal cell of the terminal appendage, forming a heart-shaped
body, blackened below, bearing terminally a median, rigid, slender, almost
wholly opaque, black branch, abruptly distinguished from its broad basal
cell : the subbasal cell of the receptacle small, triangular when viewed
side wise, giving rise to two fertile branches, the short small basal cells
of which give rise at once each to two secondary branches and an anther-
idium ; the branchlets proliferous and forming an axis of usually three
cells, the lower bearing an antheridium, and each of the two upper an
antheridium and a perithecium ; there being thus sixteen antheridia and
eight perithecia, in fully and symmetrically developed specimens, which
form a dense, spreading, fan-like tuft, the antheridia being in general
posterior in position, overlapping one another between the black sterile
THAXTER. NEW LABOULBENIACEAE. 25
appendage and the perithecia. Antheridium distally broadened and
truncate, elongate ; the stalk-cells about equal and about one half the
length of the body of the antheridium or somewhat longer than this ; the
basal cells unequal ; the cells of the two middle tiers, and their antheridia,
clearly distinguishable ; the terminal cells forming four unequal, rounded
prominences, the upper inner angle of each cell separated by an almost
vertical septum to form the four " guard cells," that terminate in papillate
prominences just below which they proliferate to form the characteristic,
erect, sterile appendages, all four of which do not always develop; the
sterile appendages relatively short, two to three-septate, tapering to a
blunt point, distinctly inflated above the slightly constricted base. Peri-
thecium relatively large, straight or slightly curved, somewhat inflated
below, tapering gradually to the rather short, moderately well distin-
guished tip ; the apex bluntly rounded, the basal cells relatively small ;
the stalk-cell variably developed, its distal end usually somewhat broader
than the basal cells collectively, sometimes more than half as long as the
body of the perithecium. Spores about 50-55 X 4-5 ft. Perithecia
130-185 x 35-55 ^ the stalk-cell 35-100 X 18-25^. Antheridia 70-
75 x 22 /j, its appendages 45-50 p. Receptacle about 35 x 28 p.
Greatest general length and width of largest individual 350 X 300 ^.
On Aleochara rujipes Boh. Derema, Usambara, East Africa. Berlin
Museum, Nos. 844 and 845.
EUHAPLOMYCBS nov. gen.
Receptacle consisting of two cells, the upper bearing a free stalked
antheridium and a stalked perithecium. Antheridium conical, consisting
of a single stalk-cell followed by a basal cell from which is separated
a group of smaller cells some of which (two or four ?) extend upward
and inward to form antheridial cells : above these follow three external
marginal cells, the lowest of which lies beside the antheridial cells; the
uppermost succeeded by a conical chamber terminating in a pore, and
extending downward along the inner sides of the marginal cells to form
a cavity into which the antheridial cells empty. Perithecium resembling
that of Haplomyces and having two ascogenic cells.
Euhaplomyces Ancyrophori nov. sp.
Receptacle small, the basal cell somewhat longer, nearly hyaline,
tapering to the relatively small foot; the subbasal cell becoming pale
amber brown. Antheridium, including its short stalk-cell, about as long
26 PROCEEDINGS OF THE AMERICAN ACADEMY.
as the receptacle, becoming pale amber brown, tapering to a pointed
apex. Perithecium becoming pale amber brown, relatively large, thick
walled, considerably and abruptly inflated above the basal cells, somewhat
asymmetrical, tapering rather evenly to the blunt apex; the stalk-cell
long, thick walled, slightly curved, nearly hyaline, distally somewhat
broader, not distinguished from the basal cells. Spores about 40-45
X 3.5 fi. Perithecia 180-200 X 72-82 /* ; the stalk-cell 110-120 X
28-30 /a. Antheridium including the stalk-cell 55-65 /x. Total length
to tip of perithecium 360 fi.
On the superior surface of the abdomen of Aneyrophorus aureus.
Dumfriesshire, Scotland. Sharp Collection, No. 1091.
Eucantharomyces Xanthophaeae nov. sp.
Perithecium (not fully mature) straw colored, somewhat asymmetrical,
almost symmetrically and but slightly inflated from base to apex; the
tip short, well distinguished ; the lip-cells rounded, and slightly inflated,
forming a knob-like termination, one of them protruding in the form of
a slight tongue-like projection beyond the others : the stalk-cell about
as long as the receptacle, from which it projects at an angle, being more-
over turned at the same time a little to one side. The cells of the recep-
tacle subequal, lying side by side, the basal one extending to the base of
the stalk-cell of the perithecium, with which it is in contact. Appendage
relatively large, the stalk-cell subtriangular, somewhat larger than the
basal cell which is wholly overlapped externally by the well defined and
distally somewhat inflated marginal cell; the antheridial cells in four
tiers of seven, six, five and four cells respectively; the discharge-tube
long and curved outward. Spores about 36 x4ju. Perithecia 165 X
50 fj., the stalk-cell 46 X 20 p. The appendage to tip of discharge tube
120 fj., the antheridium proper 55 X 30 /x. Total length to tip of peri-
thecium 290 fx.
On the right inferior margin of the prothorax of Xanthophaea vittata
Dej., Australia. Berlin Museum, No 973.
Dichomyces bifidus nov. sp.
Basal cell slightly enlarged, pellucid, tinged with brown, about as long
as broad : the lower tier, and more or less of the middle tier, opaque ;
the marginal cells of the latter forming a bluntly rounded, sometimes
almost obsolete projection on either side, hardly extending above the
THAXTER. — NEW LABOULBENIACEAE. 27
venter of the short, stout, short-necked antheridia : the upper tier
relatively large, more or less crescent-shaped according to the degree of
lateral development, edged externally with blackish brown, more broadly
below, the brown area punctate ; the cells about thirty-one in the larger
individuals, the marginal ones forming a rather slender series, which
may curve abruptly upward nearly to the middle of the perithecia, or
assume a more divergent* habit ; the perithecigerous area horizontal, pro-
ducing normally four perithecia, three appendages arising between the
two middle ones and one between each of the others, the external cells
bearing appendages as usual which vary in length. Perithecia rather
long and slender, hyaline or faintly yellowish brown, conspicuously
tinged with purplish brown below the perfectly hyaline tip, the anterior
lip-cells forming a pointed projection, the posterior ones forming each a
relatively large ear-like appendage which tapers to a pointed apex, and
is slightly curved, the two diverging from one another at an angle of
about 50°. Spores about 38 X 2.5 fx. Perithecium without appendages
126 X 25/x.; the appendages 14^. Receptacle 220-350 X 120-165 /a.
Total length to tip of perithecium 300-330 /x. Appendages 20-80 fx.
Ou the abdomen of (?) Philonthus sp. Ralum, New Pomerauia.
Berlin Museum, No. 1013.
Dichomyces Belonuchi nov. sp.
Receptacle relatively large and long : the distal tier relatively small,
consisting of from eleven to thirteen short cells, slightly suffused, the
median cells little longer than the rest, the series forming slight, rounded,
sometimes almost obsolete lateral projections on either side of the peri-
thecia : the basal cell small, partly transparent : the lower and middle
tiers not distinguished, uniformly opaque • a portion of the middle cell,
and sometimes the tips of other cells in the middle tier, more or less
translucent, the marginal cells ending in a slight rounded prominence
below the base of the antheridium. Perithecia normally two, evenly
suffused with pale reddish brown, rather long and slender, tapering
throughout, the conformation of the lip-cells much as in D. furciferus.
Spores about 30 X 3 ll. Perithecia 75-80 X 18-20 /x. Receptacle
108-126 X 54-58,1/. Total length to tips of perithecia 185-200 /x.
On the abdomen of Belonuchus fuscipes Fauvel. New Guinea.
Sharp collection, No. 1090.
28 PROCEEDINGS OP THE AMERICAN ACADEMY.
Dichomyces Australiensis nov. sp.
Receptacle usually rather loug and narrow, the basal cell relatively
large, hyaline or slightly suffused; the margins of the lower tier usually
continuous with those of the middle one, the marginal cells deep blackish
brown or quite opaque, the middle cell hyaline or translucent throughout,
its lower third often punctate : the middle tier consisting of about nine
cells, slightly suffused with pale reddish brown externally, more or less
edged with deep blackish brown; the terminal cells forming a free
rounded projection on either side, extending as high as about the middle
of the rather large antheridia, the tips of which may reach to the bases
of the perithecia : the upper tier nearly hyaline, consisting normally of
from eleven to thirteen subequal cells, the terminal ones extending but
slightly higher than the bases of the perithecia, which are normally two
in number, rather deeply suffused with purplish brown throughout ; the
apex hyaline, the posterior lip-cells producing each a relatively large
bluntly pointed appendage, the two diverging nearly at right angles to
the axis of the perithecium, becoming slightly recurved, the distance from
tip to tip about twice the diameter of the perithecium. Appendages
nearly as long as the perithecia. Perithecium 60-70 X 16-20/*, its
appendages 18/*. Receptacle 90-100 X 42-48/*. Total length to tip
of perithecium 160-170 /*.
On the superior surface of the abdomen of Quedius riificollis Grav.
Sharp Collection, No. 1102.
Dichomyces Mexicanus nov. sp.
General habit much like that of D. prhiceps, generally rather long and
slender. Basal cell hyaline, the lower tier relatively long and narrow,
broadly edged externally with black ; the median cell hyaline, or only the
marginal cells slightly suffused with smoky brown : the middle tier dis-
tinguished from the lower by a slight prominence, hyaline, seven to nine
celled; the marginal cells protruding but slightly on either side; the
antheridia brownish, short, stout, blunt pointed : the upper tier relatively
very long, sometimes twice as long as the middle tier, consisting of from
nine to eleven cells ; the marginal cells protruding but slightly on either
side, very much as in the middle tier. Perithecia normally two, about
as long as the distal tier and concolorous with it, or somewhat darker,
rather stout, tapering but slightly; the tip rather abruptly distinguished,
broadly truncate with a slight median projection ; the posterior lip-cells
giving rise each to a long horizontal appendage, which becomes recurved,
THAXTER. NEW LABOULBENIACEAE. 29
is bluntly pointed and somewhat narrower toward the base, the distance
from tip to tip often twice the diameter of the perithecium. In a few
specimens the receptacle and perithecia are somewhat evenly suffused
with smoky brown. Perithecia 75-85 X 25-30 jx, the appendages 18-
22 ix. Receptacle 165-200 X 55-70 /x. Total length 235-275 fx.
On the inferior surface of the abdomen of Philonthus atriceps Sharp.
Jalapa, Mexico. Sharp Collection, No. 1112. Specimens, apparently
normal, sometimes occur in which the tips of the perithecia are blunt
and unmodified.
Dichomyces Homalotae nov. sp.
Form short and stout. Basal cell geniculate, more or less suffused :
the lower tier more or less, sometimes wholly, suffused with reddish
brown ; the margins darker, more or less translucent, without contrasts,
the outline somewhat uneven, the transition to the middle tier indicated
by a distinct prominence: the middle tier consisting of from nine to
(rarely) thirteen cells, hyaline or subhyaline, with slight lateral suf-
fusions ; the marginal cells ending in a slight hyaline rounded projection,
seldom extending higher than the venter of the somewhat suffused
curved antheridia : the upper tier relatively small, the cells subequal,
hyaline, asymmetrical, owing to the development of but one perithecium ;
the appendages often equalling, or exceeding the perithecium in length.
Perithecium characteristically short and stout, inflated below, sometimes
oval, tapering somewhat abruptly distally, to the rather broadly truncate,
or slightly rounded unmodified apex. Spores 33 X 3 /x. Perithecia
65-75 X 25-30 /a. Receptacle 70-90 X 40-55/1. Total length 125-
165 fx.
On all parts of Homalota sordida Marsh. Fresh Pond, Cambridge.
First observed by Mr. Bullard.
Peyritschiella Xanthopygi nov. sp.
Basal cell of the receptacle very small, or hardly distinguished from the
foot : the first tier consisting of three subequal cells without appendages,
the middle one somewhat shorter than those on either side of it : the
second tier asymmetrical, consisting of three subequal median cells, the
margins of the two outer free below for nearly half their length and
coincident with the margins of the tier below, the appendiculate " margi-
nal " cells, about three to five on either side, separated from them as
usual by oblique septa ; the first on the right bearing the large, slender,
pointed, nearly straight purplish antheridium : the upper tier consisting
30 PROCEEDINGS OF THE AMERICAN ACADEMY.
of about fifteen or more cells, the series distally concave, rising abruptly
upward on either side above the base of the perithecium and bearing the
usual appendages. Perithecium solitary at the right of the median
(primary) appendage, almost symmetrically inflated from base to apex,
dull purplish ; the tip slightly darker, hardly distinguished ; the apex
truncate, sometimes slightly spreading; the lip-cells hardly projecting.
Perithecia 115-150x34-42^. Receptacle 200 X 65-70 p. Total
length to tip of perithecium 310-360 /x.
On the abdomen of Xanthopyyus Solskyi Sharp. Sharp Collection, No.
1158. Nearly allied to P. Amazonica, from which it differs principally
in the form of the perithecium.
Chitonomyces occultus nov. sp.
Short and stout, becoming suffused with somewhat smoky amber
brown. Lower portion of the receptacle deeper brown, the basal cell
relatively large, broad distally ; the subbasal cell broad and flattened ;
the lower cell of the distal portion rather large and but slightly over-
lapped by the subterminal cell, which may bulge slightly below the
terminal cell, the latter being thus turned so as slightly to overlap the
perithecium. Perithecium short and stout, its upper third or less free,
darker brownish externally ; the tip bent outward, tapering rather
abruptly to the slightly irregular apex, its outer half or less suffused
with dark brown. Spores about 22 X 2.5 xi. Perithecium 60 X 20 xi.
Receptacle to tip of distal cell 90 /x. Total length to tip of perithecium
100 ft.
In the median marginal depression of the right elytron of Onemidotus
sp. Lake Eustis, Florida.
Chitonomyces psittacopsis nov. sp.
Nearly hyaline. Receptacle rather slender, the basal cell several times
as long as the squarish subbasal cell ; the cell above the latter nearly
equalling it in size and separated by an oblique septum from the lowest
of the marginal cells, which are all subequal ; the terminal appendiculate
cell of the usual form, relatively large and long, without any distinct
basal enlargement; the tip of the lower appendiculate cell curved slightly
outward. Perithecium relatively very large, long, slender, usually
curved sidewise throughout, the upper half tapering very slightly to the
curiously modified, clear black contrasting tip, which resembles the
partly open beak of a parrot ; a larger upper recurved mandible-like pro-
THAXTER. — NEW LABOULBENIACEAE. 31
cess being separated from a second, that resembles a lower mandible,
by a hyaline area which includes, and extends back from, the pore ; the
lower lip-cells translucent, but suffused with brown in such a way as to
suggest a tongue-like process projecting slightly between the " mandi-
bles." Spores very numerous, completely filling the cavity of the
perithecium, greatly attenuated, 85 X 2.5 /a. Perithecium 200 X 30 jx.
Receptacle to tip of distal cell 140 /a. Total length to tip of perithe-
cium 290-300 fi.
On the posterior legs of Laccophilus sp. Lake Eustis, Florida.
Chitonomyces Bullardi nov. sp.
Straw colored becoming tinged with pale amber brown. Basal cell of
the receptacle monstrously developed, about as long, sometimes twice as
long, as the remainder of the plant, its axis coincident with that of a distal,
variably developed, blunt, tooth-like, free posterior projection, near the
base of which the subbasal cell and the remainder of the plant project
backward at an angle of about 45° , or less, to the axis of the basal cell,
the separating septum being vertical or nearly so ; the subbasal cell small
and flattened : the lower marginal cell of the distal portion of the recep-
tacle subtriangular, short and broad ; the lower appendiculate cell above
it relatively large ; the subterminal cell larger than the lower marginal
cell, curved inward so that the terminal appendiculate cell projects from
it obliquely inward against the perithecium. Perithecium four fifths
or more free, relatively large and stout, distinctly inflated below, taper-
ing to the tip, which is characteristically modified through the presence
of a large claw-like subterminal dark amber brown external projection,
the distal half of which is somewhat abruptly recurved, like the upper
mandible of a parrot, over the small hyaline incurved 4-papillate apex,
which is immediately subtended on the inner side by a small, erect,
dark amber brown, tooth-like process, the blunt tip of which alone is
free. Appendages slender and extending to or beyond the tip of the
perithecium. Spores about 20 X 2.5 /x. Perithecium average 70-75 x
30-32 ft not including the hook-like appendage, which is 25 /x to its upper
margin. Receptacle : basal cell to tip of prolongation 90-220 X 15-
22 fx, the portion above to tip of distal cell 48 /x.
On the right inferior anterior margin of the prothorax of Cnemidotus
12-punctatus Say. Glacialis Pond, Cambridge. The most singular
species of the genus, discovered by Mr. Charles Bullard, to whom I take
pleasure in dedicating the species.
32 PROCEEDINGS OF THE AMERICAN ACADEMY.
Chitonomyces Hydropori nov. sp.
Receptacle nearly hyaline, the subbasal cell flattened, many times
smaller than the basal cell, slightly inflated and distinguished from the
cells above and below by slight constrictions ; the two cells above sub-
equal, the posterior somewhat broader, and separated from the lower
marginal cell of the distal portion by an oblique curved septum, which
overlaps its upper fourth ; the subterminal marginal cell often nearly as
long as the lower, the narrow upper half or more of which it overlaps.
The lower appendiculate cell rather small, the upper terminal one of the
typical form, relatively rather long, distinguished by a slight constriction,
the appendage extending beyond the tip of the perithecium. Perithecium
relatively large, its upper half or more free, distally broader, the outer
margin nearly straight with a slight subterminal rounded elevation below
the abruptly rounded projecting outer brownish lip-cells ; the apex other-
wise flat, broad, bent outward so as to be slightly oblique, the inner
margin below it bulging and curved throughout. Spores 55 X 4/*.
Perithecium 98-108 X 25 /a. Receptacle to base of perithecium 80 //, to
tip of terminal cell 150 /a. Total length to tip of perithecium 185 yu,.
On the mid-elytron of Hydroporus modesties Aube. Cape Neddock,
Maine. Mr. Bullard.
Chitonomyces Orectogyri nov. sp.
Dull purplish, the cells thick walled and marked by faint transverse
striations. The basal cell of the receptacle very small and hardly dis-
tinguishable, owing to an abrupt curvature just above the foot ; the sub-
basal cell relatively large, distally narrowed, nearly the whole upper half
of its posterior margin covered by a relatively large triangular cell, from
which it is separated by a nearly vertical septum ; this triangular cell is
in contact distally with the ascigerous cavity and the base of the lowest
marginal cell ; the latter is very long, extending upward, its narrow
extremity ending without enlargement opposite the blackened base of the
inner appendage, lying between the latter and the tip of the perithecium;
the lower appendiculate cell well defined, about two thirds as long as the
subterminal cell, which projects slightly above and bears the free terminal
appendiculate cell, which is hyaline, about equal to the lower in length,
its inner margin nearly straight, its outer margin curved abruptly inward
to the base of the obliquely distinguished, blackened, narrow, erect ter-
minal portion, from which the appendage has been broken in the types.
Perithecium relatively large, of nearly equal diameter throughout ; the
THAXTER. NEW LABOULBENIACEAE. 83
tip broad with a bluntly rounded apex ; a short erect contrasting brown
prominence formed by the left posterior lip-cell, toward the base of which
the inner (anterior) lip-cells are curved iu a characteristic fashion, so as
partly to overlap it. Spores about 75 X 5 \x. Perithecium 125 x oG ft.
Receptacle 250-270 /*. Total length to tip of perithecium 255 jx.
On the superior surface of the tip of the abdomen of Orectogyrus
specular is Aube. Africa. Berlin Museum, No. 606.
DIOICOMYCES nov. geu.
Male individual consisting of four superposed cells, the upper of
which is a simple antheridium bearing a subterrainal discharge tube.
Female individual. Receptacle ending distally in a peculiarly modi-
fied sterile cell, corresponding to the upper spore-segment: the subbasal
cell producing a single perithecium laterally, and separated from the
sterile terminal cell by a second small cell. Perithecium free, stalked ;
the ascogenic cell single, the spores more or less obliquely once-septate,
and of two kinds corresponding to the sexes.
Dioicomyces Floridanus, formerly referred provisionally to Amor-
pkomyces, must be transferred to this genus ; since, although the male
is unknown, the female has the typical characters which distinguish the
genus very clearly from its near ally. D. obliqueseptatus on Myrmed&nia
(?) sp. must also be removed from Amorphomyces, on account of its
obliquely septate spores, and should with little doubt be included in the
present genus; although it is evident, from comparison with abundant
material of the species described below, that the specimens, both females,
from which the original description was made, are more imperfect than
was at first supposed, and should not have been used as types. The
peculiar sterile cell is present in neither of these ; but, since they corres-
pond in all other respects to the generic type, may be assumed to have
been broken off. No free spores are available in either, although an ex-
amination of the spore mass within the ascus seems to show that they
present the same variation in size which characterizes the species described
below.
Dioicomyces Anthici nov. sp.
Male individual. Form slender, of nearly the same diameter through-
out, the basal cell half the total length of the individual to the tip of the
discharge tube ; the third cell nearly square, the subbasal about as large
as the terminal antheridial cell, which ends in a distal blunt projection ;
the discharge-tube arising laterally below the tip, projecting upward from
VOL. XXXVII. 3
34 PROCEEDINGS OF THE AMERICAN ACADEMY.
a broadened base, slightly divergent from the main axis, slender, about
as long, or a little longer than, the body of the antheridial cell. Length
to tip of antheridial cell, including foot, 50 fx : to tip of discharge-tube
GO^c. Width 8 fi.
Female individual. Often more or less strongly curved, the terminal
sterile cell bluntly pointed, slightly curved, brownish ; the basal cell
becoming narrower below, the upper septum convex ; tinged with brown
posteriorly as is the rest of the receptacle : the subbasal cell very small,
subtriangular ; separated from the terminal sterile cell by a somewhat
smaller triangular cell. Stalk-cell of the perithecium hyaline, long, often
about the same diameter throughout; the thick wall becoming gradually
thicker distally : the perithecium slightly inflated, faintly brownish ; the
short, stout, broad, blunt tip slightly distinguished, and nearly symmetri-
cal ; the lip-cells forming an unbroken outline, without protrusions.
Spores (male) 40x4/i, (female) 60 X 6 jx. Perithecium 100-110 X
35-45 /a, the stalk-cell 75-115 x 18 /x. Receptacle including foot 35 x
1*2 /a, the sterile terminal cell 18-25 X 7-9 fx. Total length to tip of
perithecium 185-220 /x.
On Anthicus fioralis Linu. Fresh Pond, Cambridge. On A. Califor-
nicus Laf. California (Lecoute Collection).
Dioicomyces onchophorus nov. sp.
Male individual similar to that of D. Ant hid, slightly smaller.
Female individual. Usually strongly curved, especially at the base
of the stalk-cell ; similar to D. Anthid ; the receptacle, sterile cell, and
the stalk of the perithecium, relatively smaller. Perithecium dirty
brown, one of the lip-cells protruding in the form of a well defined,
lateral, finger-like, erect, straight, or slightly curved, blunt-tipped, cou-
colorous process ; an irregular anterior elevation or angular prominence
is also more or less well defined above the middle of the perithecium.
Spores (male) 35 x 4/x, (female) 45 X 5 /x. Perithecia to tip of pro-
jection 125-140 X 40-45 fx, the stalk-cell 90 p. Total length to tip of
perithecium 210-230 fx.
Usually on the basal half or at the base of the left elytron of Anthicus
floralis Linn. Fresh Pond, Cambridge.
Dioicomyces spinigerus nov. sp.
Male individual similar to that of D. Anthici, much smaller, the ex-
tremity less prominent, or almost horizontal, the discharge tube some-
THAXTER. NEW LABOULBENIACEAE. 85
what more slender, and more often erect. Total length including foot
40 X 6.5 fx; to tip of discharge-tube 47 /x.
Female individual. Receptacle relatively small, tinged with dirty
yellowish, edged with brown to the tip of the small terminal sterile cell.
Perithecium dirty yellowish and relatively large, considerably and more
or less symmetrically inflated, above and including its basal cells, to the
base of the tip, which is bent abruptly outward at right angles to the axis
of the perithecium; the apex broad, blunt, the lip-cells hardly projecting:
a unicellular brown, straight or slightly curved, spine-like process, which
tapers to a blunt point, projects upward at an angle of about 45° from
the middle of the outer (anterior) .margin of the perithecium ; and a
slight elevation is also more or less distinct between its base and that of
the tip ; the stalk-cell relatively short, becoming rapidly narrower toward
its base. Spores (male) 26 X 4 /x, (female) 40 X 6 /x. Perithecia
including basal cells 125 X 50 fx, the spinous process 55 /x, the stalk-cell
36-40^. Receptacle to tip of sterile cell about 45 [x. Total length to
tip of perithecium about 185 fx.
On Anthicus Jloralis Linn., with the last two species, more commonly
on the inferior surface of the abdomen. Fresh Pond, Cambridge.
Teratomyces Zealandica nov. sp.
Receptacle with a distinct distal obliquity, opaque with the exception
of a hyaline area just above the foot, the margins straight, the distal por-
tion relatively narrow, the base relatively broad, the suffusion involving
the bases of the appendiculate cells which are relatively numerous and
narrow and more or less suffused with brownish yellow. Appendages
sometimes scanty, but slightly divergent, concolorous throughout, nearly
hyaline or pale yellowish ; the basal cells of the larger branches rela-
tively slender, the external branchlets and numerous beak-like cells hardly
more deeply colored. Perithecia relatively large, long, rather slender,
slightly inflated throughout, the blunt tip more or less abruptly distin-
guished ; the stalk-cell very short or almost obsolete, hidden by the
appendages; the basal cells relatively small and not distinguished from
the body of the perithecium. Spores about 50 X 2.5-3 fi. Perithecia
150-180 X 20-28 fx, basal and stalk-cells together about 35 /x. Longest
appendage 180 /^. Receptacle 75-125 X 15-18 (base) 22-30 /x (distally).
On Quedius insolitus Sharp. Dunedin, New Zealand. Sharp Collec-
tion, No. 1099.
36 PROCEEDINGS OF THE AMERICAN ACADEMY.
Teratomyces petiolatus nov. sp.
Receptacle nearly symmetrical, almost wholly black, slender below,
expanding rather abruptly distally ; the appendiculate cells relatively
large and long, translucent, brownish yellow, subtended by a slight en-
largement. Appendages numerous, spreading, the larger ones consisting
of a very large colorless or brownish basal cell, which bears a series of
branchlets externally and several branches terminally ; the branchlets
usually short, and two-celled, the distal cell usually long, beak-like and
clear purplish brown, the lower cell hyaline or light brown and in the
lower branchlets usually bearing long-necked antheridia: the terminal
branches with several short branchlets of a similar character. The
smaller shorter appendages ahout the bases of the larger ones, mostly
dark purplish brown, with many beak-like cells. Perithecia usually
several, large, symmetrical, purplish brown ; the tip short, rather narrow
and abruptly distinguished ; the basal cells relatively very large, forming
a portion of the stalk sometimes half as long as the perithecium proper ;
the stalk-cell stout and elongate. Perithecia 185-225 X 45-50 /a, the
basal cell 100-150 x 10//., the stalk-cells 180-300 /*.. Receptacle about
150 /a. Appendage, longest 175, longest basal cells 110 //..
On Quedius sp. Greymouth, New Zealand. Sharp Collection,
No. 1103.
Teratomyces insignis nov. sp.
Receptacle usually quite opaque, long, slender ; the outline unbroken
and nearly straight, tapering evenly to the slightly geniculate base, which
is nearly hyaline just above the foot: the margin of the suffused area
distally strongly oblique, especially before maturity ; the appendiculate
cells small, becoming brownish. The appendages numerous, spreading,
the larger ones hyaline or nearly so, consisting of a large elongate basal
cell, which bears two or ihree small remote antheridial branches exter-
nally ; and terminally, as a rule, two large branches placed side by side
(one of which may be wanting) sometimes associated with one or two sub-
terminal smaller branchlets, the basal cells of which are dark contrasting
brown : the terminal branches hyaline with branchlets like those of the
basal cell ; the branchlets, however, more numerous, contrasting, brown,
simple or branched, many having characteristic beak-like terminations,
while others are blunt tipped, with oblique septa. The smaller peripheral
appendages more or less crowded around the bases of the larger ones,
with conspicuous and numerous beak-like terminations. The antheridia
with long curved necks. Perithecia usually several, brown, long and
THAXTER. — NEW LABOULBENIACEAE. 37
slender, straight, very slightly inflated near the base, with a slight sub-
median enlargement ; tapering throughout to the short, truncate, well
distinguished tip : the basal cells rather small, concolorous ; the group
narrower than the stalk-cell and separated from it by a horizontal sep-
tum : the stalk-cell very large, usually elongate, often inflated and thick
walled. Spores about 50 X 4 jx. Perithecia including basal cells 240-
275 x 40 (u, the stalk-cell 150-325 X 25-85 /x. Appendages, longest
225,0.. Receptacle 100-185 X 14 (base) X 55 (distal end). Total
length to tip of perithecium largest, 800 /x.
On abdomen of Qaedius nov. sp. New Zealand. Sharp Collection,
No. 1159.
ACOMPSOMYCES nov. gen.
Receptacle two-celled, bearing an antheridial branch terminally and
a single perithecium laterally. Antheridium consisting of several super-
posed cells from which single simple antheridia are borne directly. The
perithecium borne on a stalk, the lumen of which becomes continuous
with that of the ascigerous cavity.
Acompsomyces Corticariae nov. sp.
Receptacle narrow below, distally enlarged, hyaline ; the subbasal cell
• small. Basal cell of the appendage brown, distally narrowed to the base
of the appendage proper, which is brown, and consists of three sym-
metrical cells, the upper smaller, becoming a terminal antheridium, the
lower bearing several antheridia somewhat irregularly. Perithecium
brown, rather abruptly distinguished from the short hyaline stalk ; the
tip very broad and darker ; the lip-cells forming four hyaline-tipped,
nearly symmetrical papillae, which terminate four corresponding ridges.
Spores about 30 X 2 u. Perithecia 90 x 26 jx, the stalk 15 /x. Recep-
tacle 25 /x. Antheridial appendage, above stalk-cell, and including
terminal antheridium, 40 «.
On elytron of Corticaria sp. Berkeley, California.
STICHOMYCES nov. gen.
Receptacle consisting of two cells, the upper bearing one or more
stalked perithecia laterally, and an antheridial appendage terminally.
The appendage consisting of several superposed cells, the lowest sterile, or
having one or two opposite lateral perithecia; those above it bearing
opposite lateral branchlets distally, the series ending in a terminal sterile
88 PROCEEDINGS OP THE AMERICAN ACADEMY.
branch. Antheridia simple, flask-shaped, free, borne in small groups on
short branchlets.
Stichomyces Conosorriae nov. sp.
Dull amber brown. Receptacle and appendage undifferentiated, the
basal cell of the former small, triangular in outliue ; the subbasal cell
about as broad as long, and similar to the cells of the appendage, bearing
distally and laterally a single perithecium, sometimes two, which are then
paired on opposite sides of the cell, like the antheridial branchlets. Ap-
pendage consisting of five superposed subequal cells slightly longer than
broad, the basal one sterile, or rarely (abnormally) producing one or two
perithecia as in the subbasal cell below it : the three cells above slightly
larger, the upper angles separated by oblique septa to form small cells
on either side, which bear short one or few celled antheridial branchlets ;
the terminal cell somewhat smaller, bearing a simple terminal several-
celled branch in addition to the lateral branchlets, all of which appear to
be sterile. Antheridia with broad necks grouped in twos or threes.
Perithecium darker brown, more or less symmetrically inflated ; the tip
hardly modified; the basal cells collectively broader and nearly as long
as the stalk-cell. Spores 35 X 2.5 fx. Perithecia 85 X 25 /x, the stalk-
cell 36 x 1 t /x. Total length to tip of the appendage proper 150 «, the
terminal branch 150 fx, the antheridial branchlets about 20 /x. Total
length to tip of perithecium 185-200 ft.
On Conosoma pubescens Payk. Belmont and Waverly, Mass. First
observed by Mr. Dullard.
Rhachomyces Oedichiri nov. sp.
Receptacle strongly curved, rather short, the lower cells especially
more or less suffused with clear brown, the basal cell slender, the cells of
the main axis above it successively larger, about ten to twelve in all.
Appendage hardly ever reaching to the tip of the perithecium; the shorter
margin alone subulate and straight, the rest appressed, denser toward the
base of the perithecium, where they form a tuft which does not wholly
surround it, curved slightly outward, somewhat attenuated; tips abruptly
recurved or subhelicoid. Perithecium somewhat inflated, hyaline, with
the exception of several longitudinal dark brown marks at the tip, the
base concealed by the appendages. Spores 36 X 4 m. Perithecia 90-
1 10 X 30-35 (i. Total length to tip of perithecium 220-250 /x. Long-
est appendages about 90 u.
On Oedichirus nov. sp. Rio de Janeiro, Brazil. Sharp Collection,
No. 1154.
'I Hi XTKIi. — NEW LA BOULBENIACEAE. 39
Rhachomyces Glyptomeri nov. gp.
Receptacle slender, dirty translucent brown, the main axis coi
of about seven cells (below the lower of the two perithecia which are
present in the type; : the appendages -lightly divergent, large and long,
opaque brown, flexed inward near their hyaline, somewhat more Blender
extremities, and extending beyond the tips of the perithelia. Perithecinm
short-stalked, -trongly curved, slightly inflated, hyaline, -oiled with brown-
ish, the dps well distinguished, blackish brown and obliquely truncate.
Perithecia, including basal and stalk-cells, about 185 / 41 /v.. Receptacle
to base of lower perithecinm 100 / 15 /*. Appendage-, long 60/*
or more.
On tip of abdomen of Glyptomerta cavicolus MulL Carniola, Austria.
Sharp Collection. No. 1111.
Rhachomyces Dolicaontis nov. sp.
Form elongate. Cells of the main axis of the receptacle- twenty to
thirty-five, more or less dirty brownish, banded with dark blackish br<
below, while the more slender proximal cells are usually opaque ; the axis
of nearly equal diameter throughout and nearly -traight above about the
eighth cell; each cell containing distally one, the axis cells two, roundish
or oblong brown bodies ''possibly thickenings of the walls; which
the stigmata of an insect larva. The appenda* .hat divergent,
opaque, except a narrow upper hyaline margin, short, stiff and numerous ;
those external more slender, slightly curved and sharply pointed ; th
between somewhat stouter and longer, with -lightly recurved tips; th
about the base of the perithecium, which they do not conceal, but slightly
longer and few in number. Perithecinm -hort-stalked, slightly more
or less symmetrically inflated, dull brown, minutely punctate or irrarmlar,
not uniformly suffused ; the tip with darker shades, the blunt apex
hyaline. Spores 66 / 5 a. Perithecia 150-200 X 42-60/*, including
the basal and stalk-cells. Larger appendages 90-110 /t, smaller about
7o/y.. Total length 600-1100/*, the- average diameter about 30-35//.
On all parts of Dolicaon Lathrobioidei Casteln. Cape of Good If
Africa. Sharp Collection. No. 1146. Berlin Museum, No- 833 and
842.
Sphaleromyces Quedionuchi nov-
Perithecium relatively small, translucent, tinged with amber brown,
straight, very slightly almcrst symmetrically inflated ; the tip hardly dis-
40 PROCEEDINGS OF THE AMERICAN ACADEMY.
tinguished ; one of the lip-cells forming a blunt, terminal, irregularly
curved, hyaline, sometimes abruptly distinguished projection, below the
base of which arises on the inner side a tongue-like outgrowth externally
and basally blackish brown, the broad rounded hyaline end of which is
curved against or across the base of the terminal outgrowth; the stalk-
cell small, the basal cells collectively larger, and separated from it by a
very oblique septum. Basal cell of the receptacle long, black, obconical,
the narrow base translucent ; the subbasal cell small, nearly triangular.
Appendage consisting of five very obliquely superposed cells, the two
lower nearly equal, the cells ahove successively smaller, but equal in
length ; the branches which are once or twice branched and extend about
to the middle of the perithecium, arising from the whole surface of their
inner margins, the terminal cell soon destroyed. Spores 55 X S /x.
Perithecia 135 X 36/a. Basal cell of receptacle 120 fx. Appendage
without branches 55 //.. Total length to tip of perithecium 290-310 jx.
On the abdomen of Quedionuchus impunctus Sharp. San Andres,
Vera Cruz. Sharp Collection, No. 1105.
Sphaleromyces Chiriquensis nov. sp.
Almost uniformly translucent dirty amber brown. Perithecium very
large and crowded with spores, long, with a very slight general inflation,
the base narrower, tapering abruptly at the short tip : one of the lip-cells
forming an erect, median, straight, hyaline, cylindrical or slightly in-
flated, nearly truncate terminal projection, which is subtended by a
posterior or partly lateral, somewhat larger, spine-like, slightly diver-
gent, deep black brown, nearly straight or slightly outcurved pointed
outgrowth, its tip nearly on a level with that of the median projection :
the basal cells collectively slightly larger than the short stalk-cell, and
not distinguished from the base of the perithecium. Basal cell of the
receptacle very large, tapering throughout from the broad distal to the
narrow basal end, paler than the small, flattened, deeper brown subbasal
cell. The appendage consisting of a relatively large basal stalk-cell,
which is slightly longer than broad, and partly united to the stalk-cell
of the perithecium; above are four short successively smaller cells, their
septa slightly oblique, the three lower bearing branches as usual, which
may branch once above their basal cells, the branchlets brown, erect,
rigid, closely aggregated ; the uppermost cell paler, with a terminal
branch. Spores 50 X 2 /x. Perithecia 220-250 X 40-48 fx, to tip of
median projection, the subterminal process 25 X 7 p; the stalk-cell 35
X 25 p. Receptacle 240 X 40 jx, the basal cell 220 fx. Total length to
THAXTER. NEW LABOULBENIACEAE. 41
tip of perithecium 500-600 //.. Appendage without branches, including
stalk-cell, 75 p.
On the tip of the abdomen of Quedius flavicaudus Sharp. Volcan
de Chiriqui, Panama. Sharp Collection, No. 1157.
Sphaleroniyces Indicus now sp.
Perithecium relatively very long and large, yellowish, very slightly
inflated toward the base, tapering very gradually to the broad, blunt tip
which is subtended by a truncate, conical lateral projection ; the stalk-
cell relatively short. Receptacle relatively small, the two cells nearly
equal, the upper bearing the stalk-cell of the perithecium terminally and
the basal cell of the appendage laterally ; the latter overlapping it to its
base. Appendage consisting of four superposed cells, the basal (stalk-
cell) small, triangular ; the two cells above it larger and longer, bearing
short antheridial branches from the upper inner angles ; the terminal
cell smaller, subcorneal, bearing a small terminal branchlet. Spores
about 44 X 4 /a. Perithecium 290-340 X 45 ft, the stalk-cell 72 /x.
Receptacle 55^. The appendage 125 /a.
On the upper surface of the tip of the abdomen of Pinophilus (near
"P. rufipennis"). Malabar, India. Sharp Collection, No. 1151.
Corethromyces Latonae nov. sp.
Perithecium reddish brown with a purplish tinge, often straight, or
externally concave, slightly inflated ; the lip-cells forming a small short,
slightly bent, nearly cylindrical, truncate, or papillate terminal projection,
which is rather abruptly distinguished ; the secondary stalk-cell, and the
basal cell above it, bulging outward more or less prominently, and
separated by a rather conspicuous irregular indentation : the stalk-cell
small and squarish. The basal cell of the receptacle asymmetrical ; its
anterior margin straight and perpendicular, the posterior slightly curved
and oblique ; its distal margin oblique with a posterior protrusion ; its
slender base translucent, but otherwise opaque, the opacity involving a
portion of the small flattened subtriangular subbasal cell. The appendage
consisting of a series of about five successively smaller hyaline cells, the
lowest greatly flattened ; the series above, the distal cells of which soon
disappear, often turned outward so as to become almost horizontal in
position, giving rise from their inner sides to numerous hyaline branches,
which may be more or less copiously branched. Spores about 35 X 2 fx.
Perithecium 90-105 X 20-25 ^, the stalk and basal cells together 20-
42 PROCEEDINGS OF THE AMERICAN ACADEMY.
25 fj.. Receptacle 110 X 50 (distal end) X 10 /x (base). Total length
to tip of perithecium 225-250 /x.
On the legs and abdomen of Latona Spinolae Guer. Bogota, Colum-
bia. Berlin Museum, No. 834.
Corethromyces Stilici nov. sp.
Perithecium amber colored, with a faint brownish or reddish tinge,
somewhat irregular in outline through a spiral twist in the wall-cells,
which are distinguished from one another by slight furrows ; slightly
inflated toward the base, tapering to the broad blunt apex ; the tip not
at all distinguished ; the basal and stalk-cells well developed, hyaline, the
latter bent abruptly upward from its insertion. Basal cell of the re-
ceptacle small, hyaline on the anterior side just above the foot, but
otherwise blackish brown or opaque, bulging posteriorly above the foot ;
distally and posteriorly pi'oliferous to form a straight, black, blunt finger-
like outgrowth, which lies external to the appendage ; the subbasal cell
nearly hyaline, subtriangular, separated from the basal cell by a very
oblique septum. Appendage hyaline, consisting of a nearly free and
nearly isodiametric stalk-cell, above which are three or four cells which
produce a close tuft of hyaline brauches on the inner side. Spores about
30x3^. Perithecia 80-85 x 22 /x, its stalk-cell 30 X 18 p. Recep-
tacle 25 fx, the outgrowth 55 X 7 /x. Appendage, including branches,
50 /x. Total length to tip of perithecium 150 ai.
On the abdomen of Stilicus sp., Interlaken, Switzerland. On Stilicus
ruftpes Germ., Berlin Museum, No. 836. Europe.
Ceratomyces spinigerus nov. sp.
Bright amber brown. Perithecium paler anteriorly, about twenty-
eight wall-cells in each row; narrower at the base, the lower half
bulging anteriorly, tapering distally where it is rather strongly curved
away from the antheridial appendage : the tip hyaline, prominent, obtuse,
about half as long as the curved tooth- or spine-like one-celled deep
amber brown appendage, which arises below and beside it. Basal cell
of the receptacle large, long, mostly curved, broader distally, opaque ;
the portion above it relatively small and narrow, concolorous with the
perithecium. The appendage erect, slightly divergent, stiff, long, slender,
rather remotely septate, but the basal cell often broader than long, about
seven-celled, tapering distally. Spores 90 X 4 /x, in one small specimen
165 x 4.5 /x. Perithecia 425-500 X 70-95^, the appendage 45-50 tt.
THAXTER. — NEW LABOULBENIACEAE. 43
Receptacle 1 75-220 /x, the basal cell 150-170 /*. Antheridial appendage
200-325 fx.
On the inferior anterior margin of the thorax near the base of the right
elytron of Tropisternus apicipalpis Cast. Jalapa, Mexico. Sharp Col-
lection, No. 1178.
Ceratomyces procerus nov. sp.
Rather pale amber brown. Perithecium very elongate, of nearly
equal diameter throughout, the wall-cells in each row more than sixty
in number ; the conformation at the tip similar to that in O. confusus ;
the perithecial appendage erect, short and stout, consisting of about ten
cells, distally curved outward, tapering from its broad base to the bluntly
pointed tip. Appendages (broken) and receptacle much as in C. con-
fusus. Perithecium 800-850 X 65 /x, its appendage 125 /x. Total length
to tip of perithecium more than one millimeter.
On the inferior surface of the abdomen (near the middle) of Tro-
pisternus sp. San Fidelio, Brazil. Museum of Comparative Zoology,
Cambridge, No. 1338.
Ceratomyces curvatus nov. sp.
Amber brown. Perithecium relatively large, inflated toward the base;
the distal half up to the perithecial appendage of about equal diameter
throughout ; about forty cells, more or less, in each row of wall-cells ;
the configuration at the tip very similar to that in C. confusus, the tip
itself more prominent, the apex more pointed ; the perithecial appen-
dage about nine-celled, the distal half pale, curved or recurved, broader
below, shorter and stouter. Receptacle much as in C. confusus, the basal
cell black, the further suffusion somewhat less extensive. Appendage
consisting of about six or seven cells, tapering distally, rather short.
Spores about 70 X 4 /x. Perithecia 500-615 X 75 [x (below) X 60 /x
(distally), the appendage 150^. Total length to tip of perithecium
600-700 (i, to tip of antheridial appendage about 250 /x.
On Tropisternus Caracinus N. on inferior surface of abdomen near
the tip. Caracas? Berlin Museum, No. 1057.
Ceratomyces Mexicanus nov. sp.
Dark amber brown. Perithecium with a slight submedian inflation ;
distally broad, the outer margin turning abruptly inward distally to the
inconspicuous retracted tip, which lies close at the base of the perithecial
appendage, and is externally subtended by irregular inconspicuous papil-
44 PROCEEDINGS OF THE AMERICAN ACADEMY.
late protrusions : the basal cell of the appendage slightly divergent,
several times as long as broad ; the external margin straight, the inner
strongly concave with a median blackish suffusion; the rest of the appen-
dage slightly curved, about eight or nine-celled, tapering slightly and
diverging strongly above the basal cell. The antheridial appendage and
the receptacle much as in C. mirabilis. Spores 85 X 5 fi. Perithecia
400-175 x 110-125 fi, the appendage about 290 //, its basal cell 70 X 26
and 36^. Total length to tip of perithecium 550-640 p.
On the left inferior margin of the abdomen of Tropistemus nitidus
Sharp, Sharp Collection, No. 1177, and of T. chalybeus Cast., British
Museum, No. 772, Oaxaca, Mexico.
Ceratomyces Braziliensis nov. sp.
Dark amber brown. Perithecium somewhat inflated just above the
constricted base, the upper two-thirds broad and of about the same
diameter throughout; about forty-five wall-cells in each row, the tip
small, short, rather narrow, abruptly hunched externally, the hyaline
lips turned abruptly toward the base of the perithecial appendage, which
consists of a basal cell hardly differentiated from the wall-cell below it,
though somewhat longer, the portion above it erect, slender, stiff, slightly
curved outward, tapering but little, the subbasal cell bearing a charac-
teristic basal enlargement which projects toward the lip-cells and lies
just above them. The appendage and receptacle much as in C. mira-
bilis. Perithecium 650 X 95 ju (basal) X 87 ^ (distal). Appendage
185 ix, or more. Total length to tip of perithecium 800 p.
On inferior thorax of Tropistemus nitens Cast. var. Rio de Janeiro.
Sharp Collection, No. 1181.
KAINOMYCES nov. gen.
"Receptacle much as in Zodiomyces, broad and flattened ; consisting of
a single basal cell and typical foot, above which the successive cells
become variably divided by longitudinal septa into transverse cell-rows
or tiers : the distal portion more or less definitely distinguished and con-
sisting of superposed cells, the lowest of which alone become longitu-
dinally divided, all producing laterally antheridial (?) branches : several
of the tiers immediately below this appendiculate portion growing out
laterally at right angles to the main axis of the receptacle on one or
both sides to form "perithecial branches" consisting of superposed cells
and terminated by solitary perithecia. The perithecium of peculiar
THAXTER. — NEW LABOULBENIACEAE. 45
form, with six wall-cells in each row in addition to the lip-cells ; the
base of the trichogyne persistent in the tbrui of a peculiarly modified
unicellular appendage.
It has proved impossible from an examination of the available material
of this extraordinary form, to determine the character of the antheridia;
yet there can hardly be any doubt as to its true position among the
" Exogenae " near Zodiomyces, Euzodiom^ces, and Ceratomyces, its dis-
tal appendiculate portion being evidently homologous with the "appen-
dage " of the last-mentioned genus.
Kainomyces Isomali nov. sp.
Receptacle variably developed below the distal appendiculate portion,
sometimes very broad, often much narrower : the cells above the basal
cell becoming broader and flattened, and soon divided longitudinally by
one or more septa, nearly hyaline and broadly edged wholly or in part
below, especially on the posterior side, with contrasting brownish black,
which may involve the whole of the cell, except the transverse septa;
the blackened area usually characteristically indented above, and some-
times involving all but the uppermost tiers. Perithecial branches vari-
ably developed, the free portion curving upward, and consisting of from
about twelve to thirty-five superposed hyaline cells, which are more or
less flattened, usually separated by slight constrictions, the distal one
similar to the others and followed directly by the basal cells of the
perithecium. Perithecium becoming tinged with pale amber brown,
usually short, stout and suboblong, often not distinguished from its
basal cells ; the distal end abruptly rounded, the pore subtended by a
tooth-like outgrowth, half as long as and paler than the trichogynic
appendage, which bears a slight resemblance to a duck's bill, is dark
clear brown, somewhat narrower distally and pale tipped, broader toward
the base, where it is abruptly constricted and hyaline. Spores about
30 X 3.5 jte. Perithecia 72-80 X 40-50 ^ exclusive of trichogynic ap-
pendage, which measures 28-32 X 11 fi. Perithecial branch 100-253 p.
Receptacle 150-220 X 40 60 p. Antheridial branches about 50 p.
Total length to tip of perithecium 250-460 ft.
On Isomalus Conradti Fauvel. Derema, Usambara, East Africa.
Berlin Museum, Nos. 847-848.
Proceedings of the American Academy of Arts and Sciences.
Vol. XXXVII. No. 3. —Junk, 1901.
THE LAW OF PHTSICO-CHEMICAL CHANGE.
By Gilbert Newton Lewis.
THE LAW OF PHYSICO-CHEMICAL CHANGE.
By Gilbert Newton Lewis.
Received April G, 1901. Presented by T. W. Richards, April 10, 1901.
Introduction.
The many-sided application of thermodynamics to physical chemistry
in recent years has led to a maze of mathematical expressions which is
bewildering to the beginner and confusing even to the initiated. The
great majority of these physico-chemical formula; arc based not only
upon the two laws of thermodynamics but also upon some empirical law
or approximation, and are as a rule not rigorously true, but are useful in
so far as the system considered does not deviate too widely from certain
ideal conditions. The difficulty of treating mathematically equations
which are not strictly exact is probably the chief reason for the con-
tinued separate existence of the large number of formulae which, though
not identical, are tantalizingly similar in form. It seemed probable that
if the present formulae could in any way be replaced by rigorously exact
ones, without sacrificing concreteness or immediate applicability, then
these exact equations might be so systematized that one might serve
where a number of isolated equations are now in use, with a great gain
in simplification. With this object in view the present investigation has
been carried on, and with the unexpected success of finding a single law
which is simple, exact, general enough to comprise in itself many laws
and yet concrete enough to be immediately applicable to specific cases.
The following development will be based upon four laws of nature and
upon no other hypothesis or assumption of any kind. These laws are
the following : —
1. The first law of thermodynamics.
2. The second law of thermodynamics.
3. Every gas, when rarefied indefinitely, approaches a limiting condi-
tion in which
Pv = RT, (1)
if P represents pressure; v, molecular volume; R, the gas constant; T,
the absolute temperature.
VOL. XXXVII. — 4
50 PROCEEDINGS OF THE AMERICAN ACADEMY.
4. Every solution diluted indefinitely approaches a limiting condition
in which
n v = R T, (2)
if II represents osmotic pressure.
The present paper will discuss the laws which govern systems com-
posed of a single, chemically simple, substance, and will be followed by a
second paper in which the laws governing mixtures will be studied.
I.
Clausius' Formula Simplified. •
Clausius showed that if Q represents the heat change in a reversible
change, the second law of thermodynamics may be expressed by the
equation
Q _dQ
which is valid for every cyclic process ; moreover, that since in a cycle
there is no change in internal energy, d Q represents the work of the
cycle, and that when the process is one in which the system undergoes a
finite change of volume at constant pressure, and no other work is done,
dQ = dP(V1-V2),
where P represents the pressure and Vl and V.2 the original and final
volumes. In the specific case in which the system is composed of a
liquid and its vapor we obtain the equation
Q _ pi — vt) dp
' T~ dT '
in which p represents vapor pressure ; Q, the total heat of vaporization
of one gram-molecule ; and vx and v2, the molecular volumes of vapor and
liquid respectively. Transposing the equation gives an expression for
the change of vapor pressure with change of temperature,
d T (», - v2) T W
This equation of Clausius is both general and exact, but in practice it
is replaced by a simpler equation, which is derived from it if two
assumptions are made : First, that r2 is negligible compared with vu and
therefore approximately,
t'i — V2 = Vi.
LEWIS. — THE LAW OP PHYSICO-CHEMICAL CHANGE. 51
Second, that the vapor obeys the gas law,
RT
i\ —
P
These two equations substituted in (4) give the familiar equation,
d In p _ Q
dT ~ RTZ
(5)
While neither of the two assumptions made above is in any case
strictly true, they differ in that the second represents a true limit as the
vapor approaches the perfect gas in its behavior, but the first is always
mathematically absurd, for the volume of a liquid cannot be made to
approach zero even as a limit. For an exact equation, therefore, we
must return to equation (4), notwithstanding its rather complicated form.
There is in fact a lack of simplicity in this equation which does not
appear in certain analogous expressions that will be developed in this
paper. That this lack of simplicity is, however, not inherent in every
exact equation for the influence of temperature on vapor pressure, but is
due rather to the complex conditions for which equation (4) is proved,
will be evident from the following considerations.
It is well known that at constant temperature the vapor pressure of
any substance is changed by a change in the total pressure on its surface,
according to the equation first obtained by Poyntiug,*
i£ = % (6)
dP vx
in which p represents vapor pressure ; P, total pressure ; v.2 and vh mo-
lecular volumes of liquid and vapor respectively. When, therefore, the
temperature of a liquid is raised, the resulting increase in vapor pressure
brings an increase in the total pressure on the surface, and this in itself is
a cause of further change in vapor pressure. The observed change in
vapor pressure is the sum of the change due merely to temperature
change and the change due to the change in total pressure upon the
surface. Let us therefore determine the change in vapor pressure with
change of temperature when the total pressure on the surface is kept
constant by artificial means. Figure 1 represents such an arrangement.
The space E D contains liquid kept at constant pressure by a piston, F.
B D contains an inert insoluble gas. B C is a membrane impermeable
to this gas, but permeable to the vapor of the liquid used. A B contains
* Phil. Mag., (5) XII. 32 (1881).
52
PROCEEDINGS OF THE AMERICAN ACADEMY.
this vapor alone. A change of temperature will change the vapor pres-
sure in A B without changing the total pressure on the liquid, which
is always equal to the outside pressure on F. We may simplify this
arrangement by making the layer of inert gas so thin that it may be
regarded together with the membrane B C merely as a single membrane,
which is impermeable to the liquid but permeable to the vapor. In
A
C
D
5
Figure 1.
Figure 2.
Figure 2 it is represented by the dotted line B. The spaces B C and A B
are filled with liquid and vapor respectively, and the pistons A and C can
be moved up and down so as to distribute the substance between the
liquid and gaseous phases as desired. The whole is removed from the
influence of gravity. Let us start with one gram-molecule of the sub-
stance, all in the liquid state, and pass through the following reversible
cycle, during which the pressure, P, upon the piston, C, remains constant,
while the pressure upon A is always kept equal to the vapor pressure.
At first the piston A is at B ; the space B C has the volume v2. (1) The
temperature is raised from T to T + d T, the pressure on A being raised
at the same time from p, the original vapor pressure, to p + dp, so that
none of the liquid evaporates. The piston C moves down on account of
the expansion, dv2, of the liquid. (2) All the liquid is evaporated at
temperature T -f d T, C moving to B, and A moving up to furnish the
volume, vv (3) The temperature is again brought to T; the pressure
on A to p. A moves down on account of the contraction di\. (4) All
the vapor is condensed and the original condition is restored. The
amounts of work done by the system in the several steps are : —
Wl = Pdv2,
W2 = -P(v2 + dv2) + (p + dp) Oi + dvj,
W3 = — p dvu
Wi = Pv2 — pvv
LEWIS. — THE LAW OF PHYSICO-CIIEMICAL CHANGE. 53
The total amount of work gained, the sum of these terms, is equal to
the total amount of heat transformed into work, that is,
Wt+ IF2+ Wz + Wi = dQ = ^dT,
from equation (3). Adding the terms we obtain,
vidP = j.dT>
or writing so as to express the constancy of P,
9TjP~VlT'
(
(7)
This important result may be derived directly from equations (4) and
(6) and for solids as well as liquids. Since the vapor pressure is a func-
tion of the temperature, T, and the pressure on the surface, P, we may
write
Now, in general, when only a pure substance and its vapor are present,
the change in pressure on the surface of the substance is merely the
change in vapor pressure, that is,
dP=dp.
Moreover, ( y^ j = — , from equation (6), therefore,
it 7)
Substituting for -r— from equation (4),
Tfr-vjy vJ-\9TjP'0T \9TJP vxTy
which is equation (7). "We have in this equation a marked simplifica-
tion of the Clausius formula with no loss of exactness. We could now,
by making the single assumption that the vapor obeys the gas law, throw
equation (7) into the form analogous to (5), namely,
Q
\9T )P-
RT2
54 PROCEEDINGS OF THE AMERICAN ACADEMY.
Instead of using this equation we may introduce here a quantity with the
aid of which it is possible to substitute for approximate equations of the
type of (7) other entirely exact equations of the same form. This
quantity is one whose utility I have shown in a recent paper.* It
may be well to repeat and amplify the definition there given.
II.
FUGACITY.
If any phase containing a given molecular species is brought in contact
with any other phase not containing that species, a certain quantity will
pass from the first phase to the second. Every molecular species may
be considered, therefore, to have a tendency to escape from the phase in
which it is. In order to express this tendency quantitatively for any
particular state, an infinite number of quantities could be used, such, for
example, as the thermodynamic potential of the species, its vapor pres-
sure, its solubility in water, etc. The quantity which we shall choose is
one which seems at first sight more abstruse than any of these, but is in
fact simpler, more general, and easier to manipulate. It will be called
the fugacity.f represented by the symbol if/ and defined by the following
conditions : —
1. The fugacity of a molecular species is the same in two phases when
these phases are in equilibrium as regards the distribution of that species.
2. The fugacity of a gas approaches the gas pressure as a limiting
value if the gas is indefinitely rarefied. In other words, the escaping
tendency of a perfect gas is equal to its gas pressure.
That these two conditions are sufficient to define a property of every
substance which is not a mathematical, fictitious quantity, but a real
physical quantity, capable of experimental determination in every case,
must now be shown. It is obvious from the above conditions that in any
case where our present methods of measurement are unable to show a
deviation of the vapor of a substance from the gas law then the vapor
pressure is the nearest approximation to the fugacity. In all cases the
vapor pressure is an approximation to the fugacity, the approximation
being nearer the nearer the vapor is to a perfect gas. When the
* Proc. Amer. Acad., XXXVI. 145 (1900) ; Zeit. Phys. Chem., XXXV. 343 (1900).
t In the earlier paper this quantity was called the escaping tendency and repre-
sented by the same symbol. For the sake of brevity I have chosen to substitute
the word " fugacity " for " escaping tendency " without the slightest change in the
meaning of the function.
LEWIS. — THE LAW OF PIIYSICO-CHEMICAL CHANGE. 55
behavior of the vapor deviates perceptibly from that of the perfect gas
the exact value of the fugacity may be found as follows : —
From the four laws stated in the introduction it is easy to derive the
following, which is a rigorous statement of Henry's law, namely : The
coefficient of distribution between a gas and its solution at constant tem-
perature approaches a constant with increasing dilution. This constant
will be designated by p. At infinite dilution,
P _
where p is the gas pressure and II the osmotic pressure in solution.
Now p, at infinite dilution, is equal to the fugacity of the substance in
the gaseous phase, and also in the solution, since the two phases are in
equilibrium. Therefore,
if/ = P n. (8)
That is, the fugacity of the solute in an ideal solution is equal to its
osmotic pressure multiplied by p. If now it is desired to find the
fugacity of any molecular species X in any given phase, that phase may
be brought in contact with a chosen solvent and the osmotic pressure
Ili of the saturated solution determined. Then by diluting this solution
in contact with vapor of X the limit px of the distribution ratio may be
found and so the product px IIx. So for another solvent we may find the
product p2 n2 ; for a third, ps H3, etc. These will all be equal except in
as far as the saturated solutions deviate from the ideal solution. Prac-
tically, the product will be the same for all solvents in which X is only
slightly soluble and will be the fugacity of X. Theoretically, the exact
value of the fugacity is the limit approached by the product, p II, as sol-
vents are successively chosen in which X is less and less soluble.
We see, therefore, that fugacity is a real physical quantity capable in
all cases of experimental determination. A complete appreciation of the
meaning of this quantity is essential for the understanding of the follow-
ing pages. In order, however, not to distract attention further from our
main object, a further discussion of fugacity will be postponed to the last
section of this paper, in which another independent method for the
determination of if/ will be offered, using only such quantities as have
already been determined in many cases.
The great utility of this new quantity will be shown to lie in the fact
that the approximate equations containing the vapor pressure and
developed rigorously except for the assumption that the vapor pressure
obeys the gas law, may be replaced by exact equations of the same form
56 PROCEEDINGS OF THE AMERICAN ACADEMY.
or of equal simplicity containing the fugacity instead of the vapor
pressure. Let us proceed to the determination of the laws according
to which fugacity changes with changes in the variables upon which
the condition of a substance depends, considering in the present paper
only those systems which are composed of a single chemically simple
substance.
III.
Influence of Temperature and Pressure on the Fugacity.
Let us consider two' phases of a substance at the same temperature
and pressure, but not necessarily in equilibrium with each other. A
solvent may be chosen in which both phases are soluble without molecu-
lar change, and to so slight an extent that the saturated solutions may
be regarded as infinitely dilute. In such a case the solubility of each
phase is governed by the following equation, which may be obtained
directly from equations (2) and (3),
/cHn_n\ _Q_
\ 9T )P R T2'
in which II is the osmotic pressure of the saturated solution and Q the
reversible heat of solution (that is, inclusive of the osmotic work). We
may write for the two phases,
{-JT-)P = RT* aud VJT-)P = RT» °r COmbimng>
Qx - Q, (9)
1t no
91au2
9T
RT1
Qx — Q2 may be conveniently replaced in the following way. Let one
gram-molecule of the first phase be dissolved in the solvent, this solution
then diluted or concentrated to the osmotic pressure II2, and then the
gram-molecule removed as the second phase. If these three steps be
done reversibly the heat absorbed in each will be respectively
&, RT\u^, -<?2.
The total heat change is a function only of the conditions of the two
phases, not of the path by which one passes into the other, and may be
designated by Qh2, thus,
LEWIS. — THE LAW OF PHYSICO-CHEMICAL CHANGE.
57
Qi,2 = <?i + R Tin -+ [- - <?.,, or Q, - Q, = Qlfi -RTln^-
"2 II9
We may therefore write equation (9) as
n,
9 In
[L
3 7'
<?i,2
In
n,
i2 T* T
Since we are dealing with infinitely dilute solutions in the same solvent,
ij/l = pUi and $2. = p n2, therefore
— = — - , and the above equation becomes
«A2 n2
9 In
«/o
_}h I
P?1 J,
Q1.2
Infe
^2
(10)
This is the desired equation connecting temperature and escaping
tendency. Its form can be simplified by a slight rearrangement.
Considering the quantity yin — we notice that
$2
9Tln^
1A2
T
d In —
+ ln^,or
31n^i
<A2
Combining this equation with (10) gives
1
T5
Prin^1
1^2
jr
^2
3 Tin
1A2
3T7
(ii)
Leaving in this form for the present the equation connecting tempera-
ture and fugacity at constant pressure, let us determine the influence of
pressure on the fugacity at constant temperature. I have already dis-
cussed this question in a previous paper,* but instead of using the
general equation there derived it has seemed preferable to base all
the reasoning of this paper directly upon the four laws stated in the
introduction.
Let us consider any simple substance and a solvent, so arranged t
that the pressure upon the substance in question may be altered without
* Loc, cit.
t Several such arrangements are described in the paper just mentioned.
58 PROCEEDINGS OF THE AMERICAN ACADEMY.
changing the pressure on the solvent and without preventing the sub-
stance from passing freely into or out of the solvent. The osmotic
pressure of the saturated solution depends upon the pressure on the
substance. If the latter is represented by P and the former by II, then
for P -f d P the osmotic pressure will be II + d II. We may moreover
represent the molecular volume of the substance by v at pressure P,
by v — d v at pressure P + dP; the molecular volume in the solution
by v' at osmotic pressure II, by v' — d v' at II + d II. If a gram-mole-
cule of the substance at pressure Pis (1) dissolved against the osmotic
pressure II, (2) its solution concentrated to II -f d II, (3) removed from
solution against the pressure P + d P and (4) allowed to expand from
P + d P to P, an isothermal cycle is formed, and if each step is made
reversible the total work of the cycle is zero. The work obtained in the
several steps may be represented by Wx, W2, etc.
Wx = 1TV - Pv,
Wz = -Ildv>,
w3 = (P + d P) (v - dv) - (n + d n) 0' - dv<),
Wi = Pdv.
Writing the sum equal to zero,
vdP— v'dU = 0,
or expressing in the equation the constancy of T,
(3n\ v_
\dPJT~ v<'
(12)
This is an exact general equation connecting the osmotic pressure of a
saturated solution and the pressure upon the pure solute. It is entirely
analogous to equation (6). Since we may choose a solvent in which the
solute is as slightly soluble as desired we will choose one in which the
solution may be regarded as infinitely dilute. Then,
n
v'
from equation (2). Combining this equation with (12) we obtain
From equation (8), t/r = p II. Therefore In \p = In II + In p, and
\JP~)*~~ \9P Jt
LEWIS. — THE LAW OF PHYSICO-CHEMICAL CHANGE.
59
since p is constant at constant temperature. Hence equation (13)
becomes
/9 In i/A v
\~9~p~ )T=ln
(14)
Subtracting two such equations we obtain an equation for two phases,
r
Sln^
*H
9P
Vl — Vj
RT
(15)
IV.
The General Law of Fugacity.
Equations (11) and (15) show a similarity which may be made more
striking by a few simple transformations. In equation (11) Qlfi> the
heat absorbed in any reversible transformation of the substance from
the first to the second state is equal to the difference in entropy
between the second state and the first, multiplied by the absolute tem-
perature ; that is, —p~ = — (Si — S2),
where St and S2 represent the entropy of the first and second states
respectively.
Substituting in equation (11) and transposing the constant R, we
obtain,
9RTln
^2
9T
= _ (Sl _ S.2).
(1G)
In equation (15) R T is constant, and may be transposed, bringing
the equation into the form,
*»
9RT\n*r±
«^2
9P
J T
= vi — y2-
(17)
The symmetry of equations (16) and (17) with regard to the quan-
tities T and — S on the one hand, and P and v on the other hand, is
perfect. This similarity is peculiarly interesting in the light of the
brilliant theory of Helm, according to which two quantities are funda-
mentally connected with each kind of energy, the one its intensity, the
60 PROCEEDINGS OP THE AMERICAN ACADEMY.
other its capacity.* Thus, for example, pressure, surface tension, elec-
trical, potential, and temperature are considered to be the intensities
concerned in energy changes in which the corresponding capacities are
respectively volume, surface, quantity of electricity, and entropy. We
may denote in general the intensity of any energy by /and its capacity
by H. If we substitute / and H for /and S in equation (16) and for
Pand v in (17), the equations become identical except for the minus sign
in (16). We are thus led to suspect the existence of a general equation
of the form
{dR Tin &
^2
I 91
J r,r>
F7 H <18>
and further, of the equation for a single phase,
This equation would mean that if the fugacity is a function of a number
of energy intensities, I, /', /", etc., the rate of change in the quantity
.R Tlu.il/, with a change in one of the intensities alone, is equal to the
corresponding capacity. In other words, this equation, if true, expresses
a law so far reaching that it embraces every possibility of the change of
state of any simple substance under all conceivable conditions. Let us
examine the validity of this equation for all cases in which the escaping
tendency can be shown to be influenced by the intensities of various
energies.
The influence of pressure is given in equation (14), which may be
written,
and therefore conforms to equation (19).
* These quantities have been hitherto called the factors of energy, and their
product has been written equal to the quantity of energy concerned. I believe
that this part of the theory is absolutely unjustified by the facts, and that it has
been the chief cause of the hostility which has been shown to a conception which
is valuable in research and has proved a veritable boon in the pedagogical treat-
ment of energetics. I hope soon in another paper to discuss this whole question,
especially in the light of the results of the present paper. Meanwhile we may
speak of intensity and capacity as the dimensions of energy, signifying that their
product has the dimensions of energy.
LEWIS. — THE LAW OP PHYSICO-CHEMICAL CHANGE. 61
The influence of temperature is expressed for two states simultane-
ously in equation (1G), which conforms to equation (18) except for the
minus sign. This slight difference might be explained away, but a much
weightier difficulty confronts us when we attempt to split equation (1G)
into two equations, each expressing the influence of temperature upon
the fugacity for a single phase, in the form,
(9R Tlnif,\
v 9 T /
= -&
This equation is in general not true, notwithstanding the fact that we
may choose arbitrarily the zero of entropy. If for each temperature
this zero could be chosen arbitrarily it could be so chosen that the equa-
tion would be true, but as a matter of fact the entropy is in all cases a
determinate function of the temperature, and the zero chosen for one tem-
perature must be retained for all. We must conclude, therefore, either
that the general equation (19) is false, or that entropy is not the capacity
dimension of heat. To make the latter conclusion would appear too
arbitrary were it not that other considerations lead also to the suspicion
that entropy has been too hastily chosen as the capacity in question. In
fact, the equation, d Q = TdS, for the heat absorbed in a reversible
process, corresponding to the general equation for change of energy,
dE — Id H, is the only argument for the consideration of entropy as
the capacity dimension of heat. This argument would apply equally
well to any other quantity, h, such that d Q = ± Td h ; in other words,
such that dh = ± d S. It is interesting, therefore, to determine whether
there is, in fact, a quantity which fulfils this condition and also the
condition
If a simple function can be found which satisfies these two require-
ments it may, I think, be accepted, at least provisionally, as the true
capacity of heat energy.
The entropy of every body is a very complex function of its other
variables, and even the entropy of a perfect gas is represented by the
complicated equation,*
S=S0 f- GP\n^-R\n^.
* See Clausius, Warmetheorie, I. p. 214, third edition.
62 PROCEEDINGS OF THE AMERICAN ACADEMY.
The value of h for a perfect gas may be found from the second of the
above conditions, equation (21). For a perfect gas, according to the
definition of fugacity,
\p = P, and therefore
, (9RT\u^\ {9RT\nP\
h = \~-rr^)P = \--^T-)rRlxlP' (22)
We see, therefore, that the value of /* which satisfies the condition of
equation (21) is expressed by a far simpler function than entropy is.
Let us see whether this value for the perfect gas is consistent with the
other condition that,
dh= ± dS.
For a perfect gas the following equations for isothermal change are
familiar :
dQ Pdv vdP RdP __1 _
and from equation (22),
d h = R d In P, hence, for constant temperature,
dh = — dS, (23)
and the condition is satisfied. The value R In P satisfies both the above
conditions for h in the case of a single state, the perfect gas. Moreover,
every substance is capable of being brought into the state of a perfect
gas isothermally by evaporation and indefinite expansion. Consequently
it is easy to show that for any state of a substance either of the two
conditions will define a value of h which is consistent with the other
condition. Thus by the first condition, expressed now by equation (23),
the difference in value of h between two states of a substance is equal to
the difference in entropy and opposite in sign, that is,
h, — /?2 == iJ-2 — *^1*
If we choose as the second state the vapor of the substance at such a
low pressure, P2, that the vapor may be regarded as a perfect gas,
h2 = R In P2, from equation (22), and the last two equations give,
h1 = Ss-Si + BlnP* (24)
in which *^2 represents the entropy of the vapor at pressure P2. This
equation furnishes a complete definition of the value of h for any state.
Let us see whether this value satisfies the other condition of equation
(21).
LEWIS. — THE LAW OP PHYSICO-CHEMICAL CHANGE. 63
Equation (16), namely,
9T
02 — Oj,
holds true for the two states which we have just considered, one of
which is the vapor in the state of a perfect gas at the low pressure P2.
By the aid of equation (24) we may therefore write
*p2
~\
hi-fi In P2.
According to (22)
9T
and the last two equations give by addition
\ 9T )rK
which is equation (21).
I think, therefore, that we are justified in considering h the true
capacity dimension of heat, and in considering equation (21) the special
form of equation (19) applied to heat energy. The replacement of
entropy in general energy equations by the quantity h will have a
further advantage on account of the much greater simplicity of the
latter, the approximate value of which may be in all cases very easily
determined by assuming that the vapor of the substance in question may
be regarded as a perfect gas, in which case equation (24) evidently
becomes
h = ^ + E]np, (25)
where Q is the total heat absorbed in the evaporation of one gram-
molecule and p is the vapor pressure.*
We have now obtained equations of the form of (19) for two of the
* This approximate equation is a special form of a general and rigorously exact
equation,
& = ^ + fllnf, (25a)
in which i|/ is the escaping tendency of the substance and Q' is the heat absorbed
when one gram-molecule is allowed to evaporate irreversibly against an infini-
tesimal vapor pressure. Since this equation will not be used in this paper its
demonstration may be postponed.
64 PROCEEDINGS OF THE AMERICAN ACADEMY.
most important kinds of energy. The fugacity is also known to be a
function of a third energy-intensity, namely, surface tension. Let us
consider a drop of liquid containing n gram-molecules with a surface o-
and a surface tension t. The change in surface of the drop with a
change in its content expressed in gram-molecules, that is, — — , has been
an
called the molecular surface, and we may designate it by s. If the
quantity dn is taken from the drop and added to a large mass of the
liquid the process is capable of yielding work. The amount has, I
think, always hitherto been written equal to tela, the change in surface
energy. This is not strictly true. The molecular volume in the drop is
not exactly equal to but always slightly less than the molecular volume
in the large mass. There is therefore always a small amount of work
done against the atmosphere, and the total work capable of being done by
the transference of dn gram-molecules is equal to t d cr + P (d v0 — d v),
where dv0 represents the increase in the volume of the large mass, dv
the decrease in the volume of the drop. If the transfer be made reversi-
bly in any way the total amount of work obtained must be equal to the
above. The transfer may be actually carried out reversibly as follows :
Let a solvent be chosen in which the liquid in question is so slightly
soluble that the solution may be regarded as an ideal one. The drop
and the large mass of liquid will be in equilibrium * with the solution at
two different osmotic pressures, II and II0, respectively. We may now
take the following steps reversibly: (1) dn gram-molecules of the drop
dissolve into its saturated solution, (2) the same amount is diluted to the
osmotic pressure II0, and (3) passes out of solution into the large mass.
The three steps yield the following amounts of work, in which d vj and
d v' represent the volumes occupied by the amount d n in solution at the
osmotic pressures II0 and II, respectively.
Wi = Udv' - Pdv,
W2 = dnRT\n^>
W3 = Pdv0-Il0dv>.
The sum of these terms, written equal to the amount of work given
above, gives
* In order not to affect the surface tension of the drop, it may be separated
from the solvent by its own vapor and thus pass into solution through the vapor
phase.
LEWIS. — THE LAW OF PHYSICO-CHEMICAL CHANGE. 65
P{dv0-dv) + Udv'-U0dv0' + dnRTln — =
tda+ P(dv0-dr).
Now from equation (2), II0 d vj = II d v',
U^ if/
and, as on page 55,
Therefore
RTlu^ = t^ = ts. (26)
This is the general equation connecting fugacity and surface tension at
constant temperature and pressure. If t is variable we may differentiate,
\p0 and s being constant, obtaining
dR Tlnif/ = sdt,
or expressing the constancy of T and P,
fdRT\xxxb\
C-srf )„...=* (27)
This equation completely confirms the validity of equation (19) as
applied to surface energy and corresponds to equations (20) and (21).
An important form of energy which we have not yet discussed is
electrical energy, whose dimensions are potential, and quantity of elec-
tricity. If these be represented by i? and e, respectively, in any case
where the fugacity is influenced by the electrical potential, we should
have the equation,
(-^L.=* (28)
There are in fact a number of cases in which the potential may be
shown to have an effect upon the escaping tendency, the most important
being that in which the potential influences the fugacity of the ions. The
following equation has been amply proved experimentally, and thermo-
dynamically is shown to be rigorously exact on the assumption that the
ions form an ideal solution.
e 77 = R T In n + K,
in which tt is the potential at which equilibrium is established between
an electrode and its ions at the osmotic pressure II, if e is the charge of
one gram-ion and K is at constant temperature and pressure a character-
istic constant of the electrode. In other words, II is the osmotic pressure
of the ions which will be in equilibrium with the electrode when the
VOL. XXXVII. — 5
66 PROCEEDINGS OF THE AMERICAN ACADEMY.
potential ir is established. Since we are discussing an ideal solution this
osmotic pressure is proportional to the fugacity of the ions. That is,
from equation (8), \p = p II, and
€ 77 = R T In ijf - R Tin p + K.
Differentiating at constant temperature and pressure we obtain the
equation,
(9RT\nxp\
V Sir Jt,p,...
which is equation (28).
Equations (20), (21), (27), and (28) comprise all cases in which
fugacity is known to depend upon the intensity of any form of energy.
The identity of these equations with equation (19) gives the highest
degree of probability to the supposition that the latter equation expresses
an exact law of nature and one possessing such universality as few
others possess. For this equation expresses the condition for any con-
ceivable change of state of any simple substance. Moreover, it will be
shown in the paper which is to follow this, that equation (19) not only
applies to chemically simple substances but, with a slight generalization
in the meaning of the symbols which it contains, applies to mixtures as
well, and further that it applies not merely to physical processes but also
to all chemical processes,* so that this law becomes the general law of
physico-chemical change.
Finally, it will be shown that the adoption of the two functions \p and
R Tlnif/, which possess such peculiar importance, will remove many
obstacles in the search for the fundamental principles of energetics, in
which already so much progress has been made by the work of Helm, of
Ostwald, and of other investigators. I shall therefore offer in the last
section of this paper a further explanation of fugacity as a tangible,
physical quantity.
V.
The Fugacity of Imperfect Gases.
The vapor pressure is determined for many substances and capable of
direct or indirect determination for all. Moreover the fugacity of a sub-
* In the further extension of this theory, analogy will be seen between the
conception of fugacity and the driving tendency of chemical reaction as used by
T. W. Richards (These Proceedings, 35, 471 ; Jour. Phys. Chem., 4, 385 (1900)).
It is a pleasure to recall how much I owe to the many conversations full of assist-
ance and encouragement which I had with Professor Richards during the early
development of the theory of fugacity or escaping tendency.
LEWIS. — THE LAW OF PHYSICO-CHEMICAL CHANGE.
67
stance is the same as that of the vapor in equilibrium with it. It is
important therefore to know what relation exists in general between thi
fugacity of any gas or vapor and its pressure.
Figure 3.
If a section of the isothermal of any vapor is plotted on the P V dia-
gram (Figure 3) we obtain a curve such as M M', which, according
the third law stated in the introduction, approaches asymptotically I
hyperbola N N', whose equation is,
P v = RT.
Let us determine the value of if/ for any point M of the curve. Tl
variation of if/ with P is given by equation (20), which may be written
for constant temperature,
d R T In if/ = v d P.
Between the two points M and M' we find by integration
RT
V J M
I- d p.
Now if the lines of constant pressure L M N and L' M' N' are drawn,
I v dP is equal to the area M M' L' L, and this is equal to the area
68 PROCEEDINGS OF THE AMERICAN ACADEMY.
L N N' L' minus the area M M' N' N. The former area is equal to
P
R Tin—, and if the latter be designated by A we have the equation,
RT\n^ = RTln^- A. (29)
Now if the point M' is moved in the direction of greater volume, equa-
tion (29) holds true continuously, and therefore is true if M' is taken at
infinite volume. But at infinite volume
*' = P',
and therefore
R T\m}, = R TlnP-A^, (30)
if Am represents the total area bounded by the line M N and the curves
M M' and N N', each produced to infinity. This equation may be
written,
RTln^ = -Aa,OT\*^ = -^i,oT $ = Pe=£, (31a)
where e is the base of natural logarithms.
The deviation of the fugacity from the gas pressure is, therefore,
dependent upon the area A^. The case that has been chosen in which
the curve M M' lies within N N' is of course the common one. For
gases of the opposite type, hydrogen and helium, the formulae will be,
R Tln^ = + A„ andi/, = Pe^ (31b)
We see at once that for all known gases and vapors except hydrogen
and helium the escaping tendency is less than the gas pressure ; for
these two, greater. The determination of the value of the fugacity at
any pressure involves the estimation of the area Av . This must be
done by integrating the most exact empirical equation of the isotherm of
a s;as between the pressure in question and the pressure zero. This
method has the disadvantage of all extrapolation, but the value thus
obtained may be checked by using a second empirical equation of
another form and recalculating A^. If the two results coincide the
value obtained will in all probability be very near the true value of A^.
In conclusion it may be remarked that equation (29) applies to the
isothermal of all substances, not merely to gases, and can be frequently
of use. For example, if it is possible to pass continuously from vapor to
liquid along an isothermal, it is evident that in passing from a saturated
vapor to its liquid,
LEWIS. THE LAW OF PHYSICO-CHEMICAL CHANGE. 60
<// = «//, and P= P'
in equation (29). Therefore the total area A reckoned algebraically
must equal zero. That is, the two areas on the two sides of the line of
constant pressure P must be equal. This is the well-known principle
of Maxwell.
Summary.
(1) The equation of Clausius for vapor pressure is simplified.
(2) The meaning and utility of a new quantity, the escaping tendency,
or fugacity, are explained.
(3) The influence of temperature and pressure upon fugacity is ex-
pressed in simple equations.
(4) A simple, general equation, which embraces every possibility of
the change of state of any simple substance, is proposed.
(5) This equation rests upon the conception of the intensity and
capacity dimensions of energy.
(6) This equation is verified as applied to the influence of pressure on
fugacity.
(7) This equation is verified as applied to the influence of temperature,
if a new quantity, instead of entropy, is regarded as the capacity dimen-
sion of heat.
(8) This equation is verified for the influence of surface tension.
(9) This equation is verified for the influence of electrical potential.
(10) A method is offered by which the fugacity may be found from
the vapor pressure.
Proceedings of the American Academy of Arts and Sciences.
Vox. XXXVII. No. 4. — August, 1901.
THE VISIBLE RADIATION FROM CAR HON.
By Edward L. Nichols.
hsatioss os Light A5i> Heat, mai»e ahtj published wholly oa ra part with Appropriation-*
PROM THE Bl -U.
THE VISIBLE RADIATION FROM CARBON.*
By Edward L. Nichols.
Presented May 8, 1901. Received May 15, 1901.
The law of radiation has for a long time been considered by physicists
as a subject of high interest, and numerous investigations looking to the
establishment of a general relation between radiation and temperature
have been made both from the theoretical and the experimental stand-
point. The earliest attempts to determine incandescence in its relation
to temperature were made with platinum. Draper f in 1847 made
observations upon a wire of that metal heated by an electric current.
The temperatures were determined from the expansion of the wire.
ZolIner$ in 1839 compared the light emitted by incandescent platinum
with the heat evolved. E. Becquerel,§ who made an extensive study of
visible radiation from various solids at high temperatures, used thermo-
elements of platinum and palladium, calibrated by reference to melting
points with the air thermometer. A partial separation of the rays was
effected by means of colored screens.
Becquerel found that opaque bodies, such as lime, magnesia, platinum,
and carbon, at the same temperature had very nearly equal emissive
powers, a conclusion vigorously contested by his contemporaries, but ex-
plained, in the light of later work, by the fact that the -lowing bodies
were enclosed in a long earthen tube. The conditions for ideal blackness
were thus approximately fulfilled. He likewise made photometric obser-
vations upon wires electrically heated and found the' light to increase
much more rapidly than the emitted heat.
Although some of Becquerel's results were at fault, particularly his
estimation of temperature above the melting point of gold, his work is
especially noteworthy in that he employed many of the methods to which.
* An investigation carried on in part by means of an appropriation from the
Rumford Fund. Read at the meeting of the American Association for the Advance-
ment of Science in New York, June 27, 1900.
t Draper, Philosophical .Magazine, XXX. 345 (1847).
| Zollner, Photometrische Untersuchungen (1859).
§ Becquerel, Annales de Chimie et de Physique, (3), LXYII. 17 (1863).
74 PROCEEDINGS OF THE AMERICAN ACADEMY.
iti the hands of later investigators, our knowledge of the laws of incan-
descence is due. He established the direct proportionality of the loga-
rithm of the intensity of radiation to the temperature and pointed out the
possibility of optical pyrometry.
In 1878 Crova* used the Glan spectrophotometer in the comparison
of various sources of light, such as candles, gas flames, the lime light, the
arc light, and sunlight, and proposed au optical method for the measure-
ment of temperatures.
In 1879 f I published the results of a series of measurements made in
this manner upon the visible radiation from platinum at various tempera-
tures. At that time, the measurement of high temperatures by means
of thermo-elements, of platinum and platinum-rhodium, or platinum-ind-
ium, had not been developed, audj the determination of the temperature
from the change of resistance of the metal was, as has been previously
pointed out by Siemens, a matter of great uncertainty on account of the
varying performance of different samples of platinum. This difficulty,
which was due to the impurities contained in the metal, has since been
largely overcome, and platinum thermometry has, through the study of
Callendar and others, been advanced to the position of au operation of
precision, but at that time I was forced to content myself in the investi-
gation just referred to with an expression of temperature of the glowing
platinum in terms of its increase of length.
Work upon the incandescence of carbon was first taken up in a serious
manner after the development of the incandescent lamp.
Schneebeli,$ in 1884, made some observations upon the total radiation
and candle power of the Swan lamp. He made no estimation of tem-
peratures.
In the same year Schumann § published his very complete spectro-
photometric comparison of the various incandescent lamps in use in
Germany. Lucas, || in 1885, heated arc-light carbons in vacuo, estimated
their temperature from the current employed, and measured the light
given in carcels. I shall refer to his work in some detail later.
In 1887 H. F. Weber U began his studies of the spectrum of the in-
* Crova, Comptes Rendus, LVII. 497 (1878).
t Nichols, Ueber das von gliihendem Platin ausgestrahlte Licht. Gottingen,
1879 ; also American Journal of Science, XVIII. 446 (1879).
t Schneebeli, Wiedemann's Annalen, XXII. 430 (1884).
§ Schumann, Elektrotechnische Zeitschrift, V. 220 (1884).
|| Lucas, Comptes Rendus, C. 1451 (1885).
IT Weber, Wiedemann's Annalen, XXXII. 256 (1887;.
NICHOLS. THE VISIBLE RADIATION FROM CARBON. 7.',
candescent lamp. He found that the first light to appear was not that of
the region nearest the red end of the spectrum, but corresponded in wave
length to the region of maximum lumiuosity, and that at these low tem-
peratures the spectrum was devoid of color. Stenger* in the same year
corroborated Weber's observations and offered what has since b<
received as the proper explanation of the phenomenon.
In 1889 I published in collaboration with W. S. Franklin f a series of
spectrometric comparisons of incandescent lamps maintained at various
degrees of brightness. No attempt was made to determine temperatures.
In 1891 II. F. Weber t read a paper at the Electrotechnical Congress
in Frankfurt on the general theory of the glow-lamp. By means of
numerous measurements through a wide range of incandescence made
upon lamps with treated and untreated filaments, constants were estab-
lished for his empirical formula for the relation of radiation and tempera-
ture.
The infra-red spectrum of carbon has, since the appearance of the
incandescent lamp, likewise been subjected to measurement. Abney and
Festing § in 1883 published curves for the distribution of energy in the
spectrum of such lamps from measurements male with the thermopile.
In 1894 I compared, with the help of the same instrument and a highly
sensitive galvanometer, the infra-red spectra of lamps with black and gray
filaments. ||
Of late years attention has been devoted especially to the problem of
the law of radiation from an ideal black body, and various formulae have
been proposed by means of which the rise of radiation of any single wave
length upon the one hand, and of the total radiation on the other, may be
expressed as a function of the temperature. Interesting as this phase of
the problem is from the point of view of theoretical physics, it is perhaps
even more important to know the relation between temperature and
radiation for actual surfaces.
Apparatus and Outline of Method.
I propose in the present paper to describe an attempt to measure the
temperature of carbon rods rendered incandescent by the passage of an
* Stenger, Wiedemann's Annalen, XXXII. 271 (1887).
t Nichols and Franklin, Am. Jour, of Science, XXXVIII. 100 (1880).
| Weber, Bericht des internationalen Flektroteehniker-congresscs zu Frankfurt
am Main, p. 49 (1891); also Physical Review, II. 112.
§ Abney & Festing, Philosophical Magazine, (5) XVI. 224 (1833); also Pro-
ceedings of the Royal Society, XXXVII. 157 (1884).
II Nichols, Physical Review, II 260 (1894).
76
PROCEEDINGS OF THE AMERICAN ACADEMY.
electric current, and to make spectropliotometric comparisons of the
visible radiation from their surfaces with the corresponding wave lengths
m the spectrum of an acetylene flame.
The carbons used for this purpose were produced by the well-known
process of squirting a semi-fluid carbonaceous paste through a cylindrical
opening. They were straight cylindrical rods 10 cm. in length, and 2 mm.
in diameter. Still larger rods would have been preferable, but I was
unable to obtain any of greater diameter than the above that were capa-
ble of withstanding the temperatures to which it was necessary to heat
thetn. The rods were mounted horizontally in a massive metal box
40 cm. in length, 20 cm. wide, and 20 cm. in height. This box, which was
made especially for this investigation, had openings at the ends, through
which, by means of air-tight plugs, the terminals of the carbon could be
introduced. Through one of these plugs, likewise, the platinum and
platinum-rhodium wires of the thermo-element, by means of which the
temperature measurements were made, entered the box. In one of the
vertical sides of the box was a row of five circular plate-glass windows,
which could be removed for cleaning, through which the carbon could be
seen and the spectropliotometric observations couM be made. Other
openings in the top of the box and through the opposite sides served to
connect it with a mercury air pump of the Geissler type and for the
introduction of manometers for the measurement of pressure. A vertical
cross-section of this part of the apparatus is shown in Figure 1. Attempts
7o jnanom&tci- To fiumjo
Figure 1.
NICHOLS. — THE VISIBLE RADIATION FROM CARBON
i i
to locate, by a variety of methods, the hot junction of the thermo-element,
by means of which the temperature of the surface of the roils was to be
measured, in such manner that it would assume the temperature of that
surface, made it only too clear that herein lay one of the chief difficulties
of the investigation. It was found that such a junction, however small
its size, and however carefully it might be brought into contact with the
surface of the rod, would not take even approximately the temperature of
that surface ; and recourse, after the failure of numerous other expedients,
was had to the following plan, which although far from being free from
objection, was found to be upon the whole the most reliable, and to give,
when properly carried out, the most definite and satisfactory result.
By means of a drill made for the purpose from the smallest obtainable
size of steel sewing-needle, a minute hole was bored radially at a point
upon the surface of the rod lying within the field of view of the spectro-
photometer. This hole had an approximate diameter of 0.03 cm. It
extended to a depth equal to about one half the radius of the rod and was
conical in form. Platinum and platinum-rhodium wires to he used for
the thermo-element were drawn to a diameter of 0.0 1G cm., and their
free ends having been. laid together side by side, were fused in the flame
of the oxyhydrogen blowpipe so as to form a junction. This junction,
which after the action of the blowpipe took the shape of a small bead of
the combined metals, was trimmed down into conical form, until it would
just enter the hole in the side of the rod, care being taken that the
entire junction was beneath the surface. The wires leading from this
junction were next sealed into a glass tube of about 2 mm. bore, through
the interior of which they were carried from end to end, care being
taken that they should be nowhere in contact. They were held in place
by fusing the glass around them at either end of the tube. This tube
was inserted through an opening in the plug a
(Figure 1) carrying one terminal of the rod,
and there made air tight by means of cement.
One end of the carbon rod was then inserted
in a clamp attached to the inner face of the
plu"-, and the wires at a distance of about
1 cm. from the junction were bent downward
at right-angles, so as to bring the junction
into position for insertion into the hole in the
rod, and to hold it there when inserted by
the slight but sufficient spring-action of the
wires themselves. This arrangement of the junction and rod is indicated
in Figure 2.
Figure 2.
78 PROCEEDINGS OF THE AMERICAN ACADEMY.
The introduction of the thermo-element having been successfully car-
ried out by the method just described, it was possible to insert the plug,
carrying the rod and thermo-junction with it, into the end of the box
and to secure it in place ; after which the free terminal of the rod was
introduced between the jaws of a strong clip attached to the opposite
plug (b, Figure 1). This operation had to be performed through the open
windows in the side of the box. These were then screwed rightly iuto
place, and the box was ready for the exhaustion of the air.
This method of measuring the temperature of the surface, to be suc-
cessful, involved the fulfilling of several rather difficult conditions and
the application of an important correction. To bore into the material of
a carbon rod carrying a current in the manner described, necessarily dis-
turbs more or less the flow of the current ; and the changes of resistance
thus introduced are likely to bring about decided changes of tempera-
ture in that neighborhood. In some instances this became obvious when
the rod was heated, the temperature being higher near the hole than else-
where. Indeed, it was often possible to note this effect with the eye on
account of the increased incandescence of the region in question. In all
such cases the mounting was rejected. It was found possible, however,
to so nearly compensate for this loss of carbon by the introduction of the
platinum junction that no difference in the incandescence of the surface
could be detected by the closest observation ; and since differences of
temperature which cannot be detected by the eye will be negligible in
spectrophotometric work, this was taken as the criterion of a satisfactory
mounting of the thermo-junction. Measurements were attempted only
when this condition was fulfilled. It is likewise obvious that there is
danger from the contact of the two wires of the thermo-junction with the
sides of the hole in the rod. A branch circuit for the passage of the
current is thus formed which includes the galvanometer coils, thus im-
perilling the integrity of the readings of the electromotive force. This
could be obviated only by having the wires touch the rod at points in an
equipotential surface, and the fulfilment of this condition was determined
by the reversal of the current through the rod and the absence of any
effect of such reversal upon the galvanometer.
Another and more serious objection to the method, and one which
could only be met by the introduction of a correction, lay in the fact that
even with the smallest wires which could be used for a thermo-element a
certain amount of heat would be carried away by conduction through the
metal ; so that the junction would never reach the full temperature of
the surfaces with which it was in contact. I was at first inclined to think
NICHOLS.
THE VISIBLE RADIATION FROM CARBON.
79
that this correction would be a small one, but attempts to measure in a
similar manner the temperature of the acetylene flame indicated that the
loss of heat from this source was by no means to be neglected. These
attempts are described in a subsequent section of this paper.
The numerical value of this correction was accordingly determined
by direct experiment in the following manner. Thermo-elements
drawn from the same pieces of wire but differing considerably in
diameter were prepared. These were inserted two at a time in holes
on opposite sides of a carbon rod and the rod was brought to incandes-
cence by means of the current. The temperatures reached by these
junctions were compared by means of the potentiometer, and a curve
was plotted showing the relation between the cross-section of the wire
in the thermo-element and the temperature of the junction. This curve,
extended in the direction of decreasing cross-section, served to indicate
l*oo°
/loo0
'
00 1
oo J
oo *
oo
Relative Cross-sections.
Figure 3.
with at least a fair degree of accuracy the temperature which would
have been reached by a thermo-element of zero cross-section placed in
contact with the surface to be measured. The difference between this
temperature and that reached by a junction of any desired size gave the
correction which was to be applied. The correction, as will be seen by
inspection of the curve, Figure 3, is a very large one, amounting, even in
the case of the smallest wires which it was found practicable to use, to
80 PROCEEDINGS OF THE AMERICAN ACADEMY.
about 85°. The result of the calibration agreed, however, so well with
similar experiments made by placing thermo-j unctions of various sizes in
the non luminous outer envelopes of the acetylene flame, of the ordinary
gas flame, and of the flame of the candle, that I feel warranted in placing
much dependence upon them.
The correction is not of the same size in the various cases, but the
differences are such as one would expect from the nature of the flames.
This method of correcting for the loss of heat in a thermo-junction
was first employed by Waggener * in his investigation of the temperature
of the flame of the Bunsen burner. I became acquainted with his
research only after the completion of my experiments.
Calibration of the Thermo-Elements.
All our estimates of very high temperatures may be said to rest in
one way or another upon extrapolation. Tne upper limit of usefulness
of the air thermometer has been found to lie in the neighborhood of
1.300.° At this temperature Erhardt and Schertel, t in their admirable
but little known research upon the melting-points of alloys of silver,
gold, and platinum, were obliged to abandon direct determination ; and,
at about the same temperature, Holborn and Wien and Holborn and
Day I in their latest studies upon thermo-electric thermometry found that
the indications of the air thermometer, even when constructed of the
most refractory of modern porcelain, began to be erratic. We have, it
is true, the investigations of Violle § upon the melting-points of the
metals of the platinum group; but these, it must not be forgotten, are
based upon an assumed value for the specific heat, and this assumption is
equivalent to the extrapolation of the curve of the variation of the
specific heat with temperature. The observed values, by means of
which this value was determined, all lie far below those of the melting-
points of the metals in question. It is necessary, therefore, in spite of
the accumulation of indirect evidence of their approximate accuracy, to
hold in reserve the assignment of absolute values of these melting-points
until by some means as yet unthought of we shall be able to obtain
direct experimental data. In the meantime, they afford us the best
present available basis for a temporary scale, our confidence in the
* Waggener, Wiedemann's Annalen, LVIII. 579 (1896).
t Erhardt and Schertel, Jahrbuch fur das Hiittenwesen in Sachsen, 1879, p.
154.
\ Holborn and Day, American Journal of Science, VIII. 1G5 (1899).
§ Violle, Comptes Rend us, LXXXIX 702, 1879.
NICHOLS. — THE VISIBLE RADIATION FROM CARBON. 81
approximate accuracy of which must rest upon the fact that the melting-
points for palladium, platinum, etc., as given by Violle arc found to lie
upon what may reasonably be supposed to be an extension of the curves
experimentally determined for lower temperatures by means of the air
thermometer. As for the various formulae for the variation of electro-
motive forces of thermo-elemeuts with the temperature, we must not lo
si'dit of the fact that they are simply analytical expressions for experi-
mentally determined relations, and that the extension of them to temper-
atures lying far beyond the experimental range is not to be regarded as
more trustworthy than the extention of a curve by graphical methods.
Under these circumstances I decided to content myself with the pro-
visional acceptance of the following values for the melting-points
gold, palladium, and platinum, namely : —
Gold, 1075° C
Palladium, 1500° C
Platinum, 1775°C,
and to ascertain as accurately as possible the electromotive force given
by the thermo-elements used at these points. It was thought that b\
drawing a curve through them, and reading intermediate temperatures
from this' curve, the values obtained would be as close as our present
knowledge of the subject will admit. The platinum, platinum-rhodium
wire used for my elements was obtained, as has already been state I.
from Heraeus in Hanau and was supposed to be of the same stock as
that employed by Ilolboru and Wien. The fact that the electromotive
force given by these thermo-elements when exposed to the temperature
of melting platinum agreed very closely indeed with that obtained 1»\
extrapolation of their data seems to indicate that the metals were identi-
cal with those used by them.
Exhaustive studies at the hands of Le Chatelier,* of Barus,t and ol
Holborn and Wien. t and others have led to the conclusion that whenevei
thermo-elements consisting of platinum on the one hand, and ol the
alloys of that metal with iridium, rhodium, or any other metals of
platinum group on the other, are to be used in the measurements of
* Le Chatelier, Comptes Rendus. CII. (1860) 819; Journal de IV
VI. 26 (1887) ; also Mesure des Temperatures fclevees [Paris, 1000), Chapter VI.
t Barus, Bulletin of the U. S. Geological Survey No. 54 ; also American -lour
nal of Science, XLVIII. 336.
t Holborn and Wien, Wiedemann's Annalen, XLVIT. 107 (1892); LV1
560 (1895).
VOL. XXXVII. — 6
82
PROCEEDINGS OF THE AMERICAN ACADEMY.
high temperatures, it is necessary to make a thorough calibration of the
individual thermo-elements involved, or at least of the set of elements
manufactured from any given sample of metal. How important it is to
perform such a calibration for one's self may be seen from the fact that
Ilolman, Lawrence, and Barr* obtained an electromotive force of .0303
volts from a platinum, platinum-rhodium (10%) element at the tempera-
ture of melting platinum, whereas a similar element constructed of wire
from Heraeus gave in the hands of the present writer .0182 volts at the
same temperature.
Numerous more or less complicated methods of calibration involving
the use of various forms of the gas thermometer have been proposed,
the carrying out of which involves the use of special apparatus which
is difficult of construction and laborious in operation. Fortunately it was
possible in the present investigation to substitute for these a new and
easy method in which the acetylene flame itself was the source of heat.
This method t possesses the advantage of extreme simplicity, and it
affords indications the accuracy of which leaves little to be desired.
The acetylene flame em pi »yed was of the usual flat form produced by the
union of two impinging jets. There are three distinct stages observable
in the form of such a flame, depending upon the pressure at which the gas
is supplied to the burner. In the first, we have two separate cylindrical
jets of small size (Figure 4 a), which, with increasing gas pressure meet
without uniting, each being deflected, by impinging upon the other, into
a vertical plane (Figure 4 b). At still higher pressures the actual union
of the two jets takes place, giving the flame the structure shown in (Fig-
* Holman, Lawrence, and Barr, J. Am Acad, of Arts and Sciences (1895),
p. 218.
t This method of calibration has been separately described in a contribution to
the Lorentz Jubilee Volume. The Ha cue, 1900.
NICHOLS. — THE VISIBLE RADIATION FROM CARBON.
83
ure 4 c), in which the two cylindrical jets of gas in the process of combus-
tion unite to form a single flat vein or envelope which constitutes the
luminous portion of the flame. When this third stage is readied, there
is oreat stability of form and position. Such a flame responds with a
sharp lateral motion to air waves such as are produced by the slamming
of a door, but is comparatively unaffected by slight drafts. Even in a
room not essentially free from air currents the lateral motions of the
flame, which may be accurately observed by throwing an enlarged
ima^e of it, viewed edgewise, upon a screen, rarely amount to more
than .1 mm., and in an especially protected place, these lateral move-
ments become entirely imperceptible. The temperature gradient in the
layer of air bordering upon the luminous envelope of such a flame is
very steep, but it is capable of definite deter-
mination by exploration with suitable thermo-
elements, and so long as the flame remains
undisturbed by lateral drafts its stability is
surprising.
The burner used is of a well-known form
(Figure 5), and is made from a single block of
steatite. It is mounted upon a horizontal bar
of steel (Figure G), along which it may be Figure 5.
moved by means of a micrometer screw.
The bar is set up in an inner room without windows, being opposite a
circular opening in the wall through which the flame may be observed
from without. In this opening is placed the lens of a micro-camera,
«C~J
Figure G.
upon the ground-glass screen of which instrument, at a distance of abut
two meters, an enlarged image of the flame is focussed. The platinum
and platinum-rhodium wires to be tested are drawn down to a
84
PROCEEDINGS OF THE AMERICAN ACADEMY.
Figure 7.
size (diameter about 0.01 cm.), and a thermo-element is formed by cut-
ting pieces of the platinum wire, and of the wire of the alloy to be used,
about 70 cm. in length, and binding these to the opposite faces of a
rectangular block of wood about 1 cm. in thickness. Beyond this block
the wires project about o cm. They are bent
toward each other until the free ends are in
contact, forming a V, and these ends are then
fused in the oxyhydrogen flame, forming a
junction, which is subsequently trimmed down
to the form shown in Figure 7. The apex of
the V is cut away until the arch of fused metal
joining the two wires is considerably less in
thickness than the diameter of the wires them-
selves, the face of the junction forming a smooth plane surface.
The formation of such a junction becomes, with practice, a simple
matter, and can be performed, as it is necessary to do after each obser-
vation, in a few moments. The junction is rigidly mounted upon the
steel bar with the plane passing through the wires of the V vertical and
the plane surface of the metal which forms the face of the junction
parallel to the flat face of the acetylene flame. To the free ends of the
wires are soldered the copper terminals of the galvanometer circuit, and
the junctions are placed in a bath of meking ice. The support carrying
the thermo-element is mounted in such a position as to bring the face
of the hot junction as nearly as possible into the centre of the field of
view of the camera, where it is clearly visible under the illumination of
the acetylene flame, which should, at the beginning of the operation, be
about 1 cm. from the junction. The micrometer screw, by means of
which the flame is moved along the bar, is operated by means of a long
handle with a universal joint; so that the flame can be shifted by an
observer sitting opposite the ground-glass screen. For the measure-
ment of the electromotive forces produced by the heating of the junction
a potentiometer of the usual form is used. The metals the melting
temperatures of which are to form points upon the calibration curve, are
worked into thin foil, and from this foil strips about .03 cm. in width are
out. Such a strip is looped into the angle of the V and drawn snugly into
place, the free ends being cut away until they project only about 1 mm.
beyond the face of the junction. To hold this minute loop of metal
in its place, it is only necessary to press the foil carefully together
arouud the junction. The thermo-junction carrying the loop having
been mounted, in the manner described, in the focus of the camera,
NICHOLS. THE VISIBLE RADIATION FROM CARBON. 85
will be clearly seen upon the ground-glass screen, the ends of the loop
of metal projecting towards the flame.
The determination of the electromotive force corresponding to the
melting-point is made as follows. The observer seats himself in a
position where he can watch closely the image of the flame and of the
thermo-element and moves the former gradually toward the junction,
balancing the potentiometer approximately from time to time as the
electromotive force rises with the increasing temperature.
At a definite distance from the luminous envelope of the flame, which
distance depends upon the character of the metal under investigation,
the projecting ends of the loop will be seen to melt. So quiet is the
flame, and so well fixed the temperature gradient from its surface out-
ward when a proper burner is used, and when the flame is placed in a
locality reasonably free from air currents, that the fusion of the succes-
sive portions of the metal loop may be brought about from the end in-
ward with the greatest nicety; and the electromotive force may be
determined at each stage until the fusion has progressed to the plane
coinciding with the face of the junction. Even then, in many cases,
those portions of the loop of metal which lie within the angle of the
junction will remain unfused, although their distance from the melted
portion of the loop is only a fraction of a millimeter.
The delicacy of this operation under favorable conditions is very great,
and the agreement of the successive readings of the melting-points of a
fiven sample of metal is excellent. It is desirable to make a series of
readings, leading up to the true melting-point, for the reason that when
the fusion of the metal loop has progressed to that portion which lies in
contact with the platinum, an alloy is almost immediately formed bet urn
the fused metal and the junction itself, which affects the thermo-electric
indications of the couple. For this reason it is not possible to get con-
sistent readings by repeating observations with a given junction. The
proper procedure is to cut the wires back 2 or 3 mm. from the apex of
the V after each set of readings, ami to make a new junction of tin; proper
form from the free ends thus produced. This requires but little time
after the operator has gained a reasonable degree of familiarity with the
method.
When the metal, the melting-point of which is desired, is platinum
itself, the platinum wire of the junction begins to fuse at the same time
as the loop, the platinum rhodium or platinum-iridium side remaining
unmelted. The precise point at which this fusion of the platinum occurs
is, however, quite as definite as in the case of metals of lower meltiDg
86
PROCEEDINGS OF THE AMERICAN ACADEMY.
temperature. This method has the advantage of avoiding the use of the
air thermometer and of furnaces in which fusion of the metals takes
place. The amount of metal which it is necessary to melt is almost
infinitesimal. The loops used in each observation weigh only a fraction
of a milligram, and the operation may be repeated time after time at the
will of the observer with the greatest ease. On the other hand it should
be noted that the method is applicable only to such metals as will fuse
before oxidation in the hot layers of the acetylene flame. It is not prac-
ticable with magnesium, aluminium, zinc, or iron, since these oxidize
under the conditions of the experiment instead of fusing. For ouch of
the metals of the platinum group as have melting-points below that of the
junction itself, and for gold, silver, and copper, the method is a convenient
one, and its accuracy is, I believe, fully equal to that of any other method
which has thus far been employed. To guard against the deleterious
influence upon the thermo-junction of the vapors of the flame, it is impor-
tant to bring the latter up gradually by the slow action of the micrometer
screw in the manner which I have already described. The atmosphere
with which the junction is surrounded under these conditions contains an
/too0
^^ 0
/*:
0
L 0
r 0
0
IZ^O*
^r 0
^r 0
*r *
^ 0
^ 0
^ 0
*
too0
dp /
s f
/4*
f
0
V
+00*
r
*
60
00 10
ooo 1 *■
OOO It
OOO
Figure 8.
NICHOLS. — THE VISIBLE RADIATION FROM CARBON. 87
excess of oxygen, and even where the metal to be melted is platinum
itself, fusion occurs before the luminous portion of the flame, the action
of which upon the thermo-electric properties of the junction is to be
feared, has been reached. It is well-known that a junction, the perform-
ance of which has been vitiated by exposure to the vapors of a thane or
furnace, can be restored to its original condition by immersion in an
oxydizing flame. In this method of calibration the junction is continually
subject to such oxidation as is necessary to preserve it. Thus one of the
sources of error which it has been found most difficult to guard against
in the use of the furnace is altogether avoided.
Figure 8 contains the calibration curve of the thermo-elements used in
this investigation, and likewise, for purpose of comparison, a curve repro-
duced from Waggener's paper and extrapolated by him from data given
by Holborn and Wien. It will be seen that while the curves are not
identical they are of the same character, and that the differences are not
greater than experience would lead us to expect in the case of different
thermo-elements, even where these are from metals of the same manufac-
ture. It is not a question of absolute electro-motive forces, but of the
form of the curves, since what we need is a criterion by means of which
to determine whether temperature readings based upon Violle's values for
palladium and platinum are in reasonable accord with those obtained by
the extension of the curve of Holborn and Wien.
The Spectrophotometer .
The spectrophotometer used was a copy of the instrument designed
by Lummer and Brodhun for the Imperial Institute in Charlotteuburg.
It consists of a one-prism spectroscope with two collimator tubes, placed
at right-angles to each other, as shown in Figure 9. Each of these tubes
carries a slit the width of which is regulated by means of an accurate
micrometer screw with a drum head divided into one hundred parts. By
estimating tenths of a scale division, the width of the slits could be esti-
mated to one one-thousandth of a revolution.
The essential feature of this photometer consists in the Lummer-Brod-
hun prism D, placed between the objective lenses of the two collimators,
and the dispersing prism in such a position that the beam of light from
one of the tubes is transmitted directly to the latter, while that from the
other tube is bent to 90° by total reflection. The instrument was set up
with collimator A in such a position that a portion of the surface of the
incandescent rod lying nearest to the point at which the thermo-eleinent
had been inserted formed a field of illumination for the slit at a distance
88
PROCEEDINGS OP THE AMERICAN ACADEMY.
of about 25 cm.
Tod
r-id,
Kct
A
The region under observation was limited by means of
a vertical diaphragm d, 5 mm. in width, which was
mounted in a tube in front of a window of the metal
vacuum box. The comparison source was the spec-
trum of the brightest part of an acetylene flame set
up in the axis of the other collimator at a corre-
sponding distance, and viewed through a circular
aperture c, 5 mm. in diameter, cut in a metal screen
interposed between the flame and the slit and as
near the former as practicable.
The acetylene flame was adopted as a comparison
standard for the fol-
D
l
c
A
1I>
the less refrangible
lowing reasons : —
1. It possesses
a continuous spec-
trum, brighter in
regions than that of
^
Figure 9.
any other controllable source of light.
2. The radiating material is finely di-
vided carbon, presumably of a character
not unlike that of the surface of the
untreated rod.
3. The acetylene fl ime is the result of the combustion of a definite
fuel (C2rl2) burning under reasonably constant conditions. It is prefer-
able in this regard to any of the ordinary gas or candle flames in which
the fuel is of an undetermined and more or less variable character.
4. When supplied with gas under constant pressure, an acetylene
flame of the type used in these experiments, that, namely, obtained by
means of a burner composed of a single block of steatite, is more nearly
constaut in its intensity and color than any other fkime with which I am
acquainted, with the exception of that of the Hefner lamp. It is indeed
questionable whether the latter is superior to acetylene in this respect,
and its comparative weakness in the blue and violet renders it very un-
desirable as a comparison source in spectrophotometry.
Determination of the Temperature of the Acetylene Flame*
Concerning the temperature of the acetylene flame, varying and in-
compatible statements are in existence. The temperature of combustion
* The results of these experiments on the temperature of the comparison flame
were separately communicated to the American Physical Society on February 24,
1900, and were published in the Physical Review, X. 234.
NICHOLS. — THE VISIBLE RADIATION FROM CARBON. 89
of this gas, according to Le Chatelier,* would be, when burned in air,
2100° to 24200. Measurements with Le Chatelier's pyrometer, on the
other hand, made by V. B. Lewes, f give temperatures lower than those
of ordinary gas flames. Lewes found for the obscure zone 459,° for the
edge of the luminous zone 1411,° and for the region near the summit of
the luminous zone 1517°. Smithells, $ upon the appearance of the data
given by Lewes, described a series of experiments for the purpose of
showing that the temperature of the flame reaches, in point of fact, very
much higher values than those given by that author, and that in many
portions it is higher than the melting point of platinum.
It can be easily shown by inserting wires of platinum into the flat
acetylene flame obtained from any one of the forms of burner usually
employed, that while the thicker wires remain unmelted, those of very
small diameter are readily fused. I found, for example, that a wire
having a diameter of 0.0082 cm. became fused at the end with the for-
mation of a distinct globule, before the metal had penetrated the outer
luminous layer of the flame, whereas wires of 0.01 cm. or of larger
diameter remained unmelted. The experiments of Waggener § show
that there are portions of the flame of the Bunsen burner in which it is
possible to melt platinum, while MacCrae, || working with a platinum-
rhodium element, found for the hottest region in the Bunsen flame 1725°.
It will be seen from the experiments to be described in this paper, that
MacCrae's determination, which was made with wires having a diameter
of 0.02 cm., is not incompatible with the observations of Waggener and
others. Smithells, in the paper just cited, describes the melting of
platinum wires having a diameter of 0.01 cm., in various parts of the
outer sheath of a flat flame of illuminating gas. Pellissier, If in com-
menting upon Lewes's measurements, refers to experiments in which
minute wires of platinum, made by Wollaston's method of silver
plating, drawing, and subsequent dissolving of the silver coating, when
thrust into the flame of a candle, melted instantly. I have not been able
to find other printed reference to these observations and do not know
with whom they originated. An attempt to repeat the experiment with
a Wollaston wire having a diameter of 0.0011 cm. resulted in the ready
* Le Chatelier, Comptes Rendus CXXI. 1144 (1895).
t Lewes, Chem. News, LXXI. 181 (1895).
\ Smithells, Journal of the Chemical Society, LXIX. 1050 (1895).
§ Waggener, 1. c.
|| MacCrae, Wiedemann's Annalen, LV. 97.
If Pellissier, L'ftclairage a l'acetylene (Paris, 1897), p. 186.
90
PROCEEDINGS OF THE AMERICAN ACADEMY.
fusion of the wire by the flame. An examination of the remaining
portions under the microscope showed that the metal had been melted
down into clean, well-rounded beads, and had not been consumed by
oxidation or any other chemical reaction.
Smithells's contention that the temperature of flames cannot be
obtained directly from the indications of a thermo-element because of
the loss of heat by conduction and by dispersion from the surface of the
latter, so that the portions submerged in the flame never arrive at the
temperature of the surrounding gases, is well founded. Lewes and
likewise Waggener recognized this fact, and in their measurements
made use of wires of different sizes.
The apparatus which I employed for the determination of the temper-
ature of the acetylene flame has already been described (see Figure 6).
The method was similar to that used in the calibration of the thermo-
elements. The electromotive force of the elements, as these were
gradually brought into the flame, was measured by means of the
potentiometer previously employed in the calibration of the thermo-
elements and subsequently in the determination of the temperature
of the carbon rods. It consisted of a sensitive galvanometer of the
d'Arsonval type and au accurately adjusted resistance box containing
coils ranging from 50,000 ohms to 1 ohm. A large Clark cell of the
old Feussner type was mounted in series with the resistance box. The
thermo-element, the galvan-
ometer, and a subsidiary re-
sistance of 10,000 ohms were
looped around a portion of
the resistance box, the ratios
being varied until complete
balance was secured. The
electrical connections are
shown in Figure 10. The
type of standard cell selected
for this work is subject to
considerable errors from diffu-
sion lag. It has, however, the
advantage of being capable
of furnishing a much larger
amount of current than the small types of cell, in which diffusion lag
is avoided, without appreciable loss of electromotive force. Two of
these cells were placed side by side in a thick-walled inner room which
THERMO JUNCTION
10,000
OHMS.
110,000 OHM8.
CELL
Figure 10.
NICHOLS. — THE VISIBLE RADIATION FROM CARBON.
91
had been constructed for the purpose of securing uniform temperature
for the standard clock of the physical laboratory, and other similar
apparatus. The range of temperature in this room fluctuated through-
out the entire investigation be-
tween 18°C. and 19°C. The
range was so small and the
variations occurred so gradu-
ally that no changes of electro-
motive force of a size which
it was necessary to consider in
these measurements could have
arisen other than those included
in the usual correction for
temperature.
The two cells were compared
with each other from time to
time by setting them in opposi-
tion to one another in circuit
with a sensitive galvanometer
and noting the deflection pro-
duced. It was found that
although one of them was sup-
plying current to the 100,000
ohm circuit of the potentiome-
ter, during the times when it
was necessary to close the key
of that circuit, the difference
of electromotive force between
the used and unused cell was
always very small, never more
than a few hundred thousandths
of a volt. At the end of the
entire set of measurements, the
difference was 0.00006 volts.
The absolute electromotive
force of these cells was checked by comparison with Clark cells of the
II form and of the test-tube form, constructed in this department in 1898.
As a result of these comparisons it was found that the electromotive
force of the cell used in the potentiometer might be taken at 1.430 volts
at 18.°
1600°
MELTING
PT. OF PT.
iff''
1
1400°
11/ ^
1200°
iff '
1000°
800°
o
600
400°
200°
6 mm
4 mm
Figure 11.
92
PROCEEDINGS OF THE AMERICAN ACADEMY.
The wires selected for the four junctions to be used in the experiment
upon the acetylene flame were measured under a microscope with
micrometer stage. Their diameters were as follows : —
Junction I.
" II.
" III.
" IV.
Diameter 0.0199G cm.
" 0.01598 cm.
" 0.01089 cm.
" 0.00821 cm.
Readings were first made with junction I. (diameter 0.01996 cm.).
The flame was set at a distance of 6 mm. from the face of the junction,
and the potentiometer was balanced. The flame was then moved step-
wise nearer and nearer, and the potentiometer rebalanced at each step
until the face of the junction coincided with the edge of the luminous
mantle at a point just above the apex of the inner nonduminous zone.
The rise of temperature indicated by the potentiometer readings is
shown in curve a (Fig. 11), the data for which as well as for the other
curves in that figure are contained in Table II.
TABLE II.
Temperatures indicated by thermo-junctions I., II., III., and IV. at various
DISTANCES FROM THE MEDIAN PLANE OF THE ACETYLENE FLAME.
Junction I.
J
unction II.
Junction III.
Junction IV.
Distance.
Temp.
Distance.
Temp.
Distance.
Temp.
Distance.
Temp.
5.62
mm.
185°
. . .
5.42 mm.
165°
4.63 mm.
233°
3.91
mm.
370°
3.65
mm.
353°
4.82 mm.
183°
4.11 mm.
406°
2.85
mm.
760°
3.33
mm.
508°
3.21 mm.
657°
2.55 mm.
1168°
2.09
mm.
1128°
2.90
mm.
595°
2.03 mm.
1278°
2.12 mm.
1411°
1.66
mm.
1229°
2.30
mm.
989°
1.50 mm.
1598°
1.86 mm.
1613°
1.30
mm.
1367°
1.93
mm.
1322°
118 mm.
1685°
1.70 mm.
1667°
1.07
mm.
1382°
1.68
mm.
1385°
0.894 mm.
1724°
1.54 mm.
1705°
0.85C
mm.
1467°
1.40
mm.
1513°
0.566 mm.
1747°
1.30 mm.
1738°
1.09
mm.
1617°
0.238 mm.
1759°
1.025 mm.
1771°
0.320
mm.
1715°
0.00 mm.
- 0.29 mm.
1775°
Molten.
0.780 mm.
0.300 mm.
Molten.
Molten.
NICHOLS. — THE VISIBLE RADIATION FROM CARBON. 93
The iucrease of temperature as the flame approaches the junction is
gradual at first: but at a distance of about 0.4 cm. from the median
plane, the curve suddenly becomes steep. It is probable that this
distance measures the thickness of the layer of non-luminous gas which
surrounds the visible flame. Outside of this region, the junction is
heated almost altogether by radiation. As soon as it penetrates the
column of moving gas, however, heat is brought to it principally by
convection. Before the surface of the luminous mantle is reached the
curve shows indications of approaching a maximum.
Upon pushing the flame still nearer to the junction so that the latter
penetrated the luminous region, an accumulation of lampblack began to
form upon the wire, with fall of temperature ; a process so rapid that at
the end of two minutes a button of carbon several millimeters in diameter
is formed. This is finally torn loose from the wire by its own weight;
whereupon the deposition of a new mass begins. I attempted by watch-
ing the breaking away of the carbon from the wire, which occurred at
regular intervals, to determine the temperature of the wire before the
coating of carbon had begun to show itself again. The highest temper-
ature which it was possible to observe in this way was nearly one hundred
decrees below that in the luminous layer, and it was obvious from the
movement of the galvanometer needle that the junction was being rapidly
cooled by the deposition.
Junction II. (diameter 0.01598 cm.) was now substituted for Junction
I., and a similar set of readings were made. This junction, as had been
anticipated, showed higher temperatures. It was found possible, owing
to the small diameter and consequently high temperature of the wire, to
penetrate further into the flame before the deposition of carbon began,
so that measurements with the junction actually within the luminous
layer could be made. The general form of the curve, as will be seen by
inspection of the figure (curve b) is the same as that obtained with Junc-
tion I. After penetrating the luminous mantle to a small fraction of a
millimeter, carbon began to gather upon this junction likewise, wilh
lowering of temperature, as in the case of Junction I. The attempt to
read temperatures immediately after the dropping of the accumulated
carbon showed that the highest temperature which could thus be ob-
served was again about one hundred degrees below the temperature of
the luminous mantle. It was clear in this case, as before, from the rapid
fall of temperature already going on, that this reading has no significance.
Similar readings with Junction III. (diameter 0.0108 cm.) gave a third
curve of the same type as those plotted from the reading made with I.
94 PROCEEDINGS OF THE AMERICAN ACADEMY.
and II., but the temperatures were higher throughout. With this junc-
tion it was found possible to penetrate to the centre of the flame without
the deposition of carbon, the temperature of the wire being apparently
too high to permit the formation of soot. Upon pushing through the
median plane of the flame to the second luminous mautle, the junction
was melted. This result was not unexpected, since the temperature of
the junction at the first luminous mantle reached 1750°, so that a rise of
twenty-five degrees of temperature would suffice to produce fusion. The
wire when pushed through the flame in the manner just described is
heated for greater and greater distances back from the junction until the
losses of heat at the junction are sufficiently diminished to raise the tips
of the wires to the melting-point.
With Junction IV. (diameter 0.0082 cm.), a fourth curve, similar iu
form to the preceding ones and with still higher temperatures, was ob-
tained. This junction was fused at a distance of 0.075 cm. from the
core of the flame, and of 0.037 cm. from the edge of the first luminous
mantle. It was easy to observe in the enlarged image upon the plate of
the microcamera the melting away of the platinum wire, while the
platinum-rhodium alloy was still unaffected, and while contact was still
unbroken. A satisfactory observation of the electromotive force of the
thermoelement at the melting-point of platinum was thus obtained. This
reading (0.018236 volts) differs from the value found in my calibration
of the thermo-junctions used in this investigation (0.0182G2 volts) by a
quantity of (0.000026 volts) less than the errors due to changes in the
electromotive force of the standard cell. If the latter reading be taken
to correspond to 1775°, the former indicates 1773°.
Beyond this point, it was impossible to make direct observations of
temperature ; but the form of this and the preceding curves were so
closely allied that I felt no hesitation in extending the curve d to the
core of the flame. This has been done by means of dotted lines in the
figure. Curves a and b have been extended in the same manner. In
order to form an estimate of the temperature which would have been
reached by a thermo- junction of negligible cross-section, provided such a
junction could have been obtained which was capable of registering tem-
peratures above that of the melting-point of platinum, the ordinates of the
four curves, a, b, c, and d were taken for the core of the flame, for the
plane of the luminous mantle, for a plane distant 0.07 cm. from the core,
and for a plane 0.10 cm. from the core. These readings were plotted
and curves were drawn through them as shown in Figure 12; relative
cross-sections of the wires being taken as abscissae, the temperatures as
NICHOLS. — THE VISIBLE RADIATION FROM CARBOX. 95
1800
1600
1400
1200
V
^C^
■4^
100 200 300
CROS8-SECTION OF WISES
FlGDRE 12.
400
ordinates. If these curves could be extended to the Hue representing zero
cross-section, the temperatures indicated by the points in which each of
them cuts that line would give the temperature of the portion of the
flame to which the curve corresponds. There is a considerable element
of uncertainty in extrapolation even over so short a range as this ; but it
is obvious from the character of the curves lying within the limits of
observation, that each of them trends upward, and it seems highly prob-
able that they all meet the line of zero cross-section at a temperature not
far from 1900°. The fact that the curves cut this line at nearly the
same temperature would seem to indicate that the distribution of tempera-
tures from the centre of the flame outward for a distance of about 1 mm.
is a nearly uniform one.
It would perhaps be unwise to attempt to draw any more definite con-
clusion from the probable trend of these curves; but I have ventured to
extend them in the manner shown in the figure, so that the curve for the
region 1 mm. from the centre of the flame reaches the zero of abscissae
about twenty degrees above that for the centre of the flume, i. e. at 1920°,
and the. intermediate curves at temperatures lying between them. I
regard this as an extreme treatment of the case, and allude to it only to
indicate that, in accordance with common belief, the highest temperature
96 PROCEEDINGS OP THE AMERICAN ACADEMY.
may be found in the outer non-luminous layer of the flame, but that it
is unlikely that the difference amounts to more than twenty degrees.
The point of intersection referred to above lies nearly one hundred
degrees above the highest temperature recorded by even the smallest
of the thermo-elements, and it is safe to infer that nearly all previous
attempts at the measurement of flame temperatures must, for lack of
correction of the error, due to loss of heat through the wire, be regarded
as much too low. The junction IV. is, so far as I am aware, the smallest
in cross-section that has been used in such work. With larger wires,
the correction for loss of heat would be even greater, except in case3
where, as in the observations made by Smithells, and by Waggener, the
precaution was taken to immerse an extended portion of the wires within
the flame.
Temperature of Other Flames.
For the purpose of comparison, I measured in a manner analogous to
that just described, the temperature of the luminous flame of ordinary
illuminating gas and the flame of a candle. The gas flame employed
for this purpose was obtained from a lava tip rated at one cubic foot and
giving a Hat flame of the usual form. The image of this flame, when
viewed upon the ground-glass screen of my
camera, was found to be comparatively ill-
defined and unsteady ; but although the outlines
of the luminous sheath were much less clearly
marked than in the case of the acetylene flame,
they were discernible. Owing to the continual
motion of the flame, due to the small velocity
of the gas i-suing from the jet, no attempts
were made to plot curves of temperatures outside
the flame. All readings were made with the
Figure 13. . . , .
junction as nearly as possible in contact with
the outer surface of the luminous sheath, at a point in the brightest por-
tion of the flame. This position is approximately indicated by the letter
x in Figure 13. The four junctions already described were mounted,
one after another, in such a position that the flame could be moved up
until they came into contact with the sheath at the point indicated. The
temperatures of the junctions when in that position are given in tic
following table : —
TABLE III.
Junction I.
1385°
Junction III.
1009°
II.
1484°
IV.
1070°
NICHOLS. — THE VISIBLE RADIATION FROM CARBON.
'••7
These values having been plotted with relative cross-sections of the
ires as abscissae, and temperatures as ordinates, were found to lie
1800°
\
1600
n \
X
^V£j«
(£}
1400
K
X(o;
1200
\
— ^
100 200 300 400
cross-section of wire
Figure 14.
upon a smooth curve (g) as shown in Figure 14. This curve, when ex-
tended to the line corresponding to zero cross-section, gave for the tem-
perature of the flame 1780°, a temperature sufficient to account for the
success of Smithells's experiment, already described, in which platinum
wires of small diameter were melted in the outer sheath of such a flame.
I found it easy, by holding a wire of the size used in junction IV. in a
plane parallel to that of the flame, and moving it gradually toward the
latter to verify his statement. The wire was readily melted.
It was not thought necessary to make further experiments upon this
flame. The region selected was, so far as one could judge from the
brightness of the luminous sheath, the hottest portion of flame. My
measurements upon this region would lead to the conclusion that the
luminous sheath of ordinary gas flumes is at least one hundred and twenty
degrees lower than the corresponding region in the acetylene /lame.
Luminous flames of ordinary illuminating gas would perhaps repay
further study, but owing to the fact that such gas is an ever varying
mixture and that it is burned under conditions of pressure, etc.. such as
to give a fluctuating character to the flame, the problem would have
VOL. XXXVII. — 7
98 PROCEEDINGS OF THE AMERICAN ACADEMY.
best an indefinite character from which studies of acetylene are free. In
the latter case we have to deal with a definite fuel, and the velocity of
the jets of gas from the burner is sufficient to give a high degree of sta-
bility to the flame.
The caudle would seem an even less satisfactory subject of study in
these respects than illuminating gas, but the fact of the melting down
of Wollaston wire, the verification of which I have briefly described in
an earlier paragraph of this paper, seemed to discredit so completely the
low values commonly given that I decided to redetermine its tempera-
ture by the method already described.
The fact that the flame of a candle, mounted upon a fixed stand,
would move steadily downward as the material of which it was com-
posed burned away, made it convenient, without any serious modifications
of my apparatus, to explore the temperature of the luminous sheath
throughout the entire length of the flame. It was only necessary for
this purpose to mount a candle upon the steel bar in the position previ-
ously occupied by the acetylene flame, and when it had reached such a
length that the level of the rim of the cup lay below the level of the
junction, to move the candle toward the latter by means of the microm-
eter screw until the junction began to be submerged in the luminous
sheath of the flame. It was then easy by a series of slight adjustments
of the flame to explore with the junction the eutire surface of the lumi-
nous sheath from base to tip, measuriug temperatures from time to
time, and determining the position by means of the height of the junc-
tion above the rim of the candle cup. The latter observations were
readily made by means of the image of the candle upon the ground
glass of the camera. Explorations of the candle flame in the manner
described were made with Junctions II. and IV., and the results obtained
showed a degree of consistency much greater than the fluctuating char-
acter of the source under observation had led me to expect. Both sets
of observations showed a maximum of temperature in the same region :
that lying just above the tip of the interior dark zone of the flame.
Readings were made by watching the movements of the candle flame
and securing a balance of the potentiometer at times when the face of
the junction was as nearly as possible in contact with, but not deeply
submerged within, the luminous layer. Whenever the wire plunged to
any considerable depth beyond the luminous surface, deposition of soot
occurred with lowering temperature, and it was necessary to withdraw
the junction into the non-luminous regions outside and to wait until the
deposit had been burned off, before proceeding with the readings. In
NICHOLS. THE VISIBLE RADIATION FROM CARBON. 99
computing the actual temperatures of the luminous sheath of the flame
from these readings, I contented myself with the following rough ap-
proximation. The maximum temperatures shown by Junctions II. and
IV. were plotted upon the same diagram used for the luminous »as
flame. These temperatures were 1281° and 154G0; values which, as
will be seen by inspection of -Figure 14 (c), lie much below those of the
corresponding readings for the luminous gas flame, but in such position?
as to make it easily possible to draw through them a curve analogous
in form to that obtained for the latter. Such a curve would cut the
line of zero cross-section at about 1670°, which may, I believe, be taken
as the approximate temperature of the hottest portions of the luminous
sheath of the candle flame. Estimates of this temperature by the prob-
ably less accurate methods of drawing a straight line through the points
in question and taking the point in which this line cut the line of zero
cross-section to be the temperature of the flame, and estimates based
upon the assumption that the true temperature is as many degrees above
the temperature indicated by Junction IV. for the candle as it is for the
gas flame, would lead to values respectively twenty-four degrees and
forty degrees lower than that obtained by the method which I have
adopted. I believe that the temperature just given (1670°) is much
closer to the truth than that obtained under either of the other assump-
tions. Estimated temperatures for other portions of the luminous sheath
were made by assuming that the correction to be applied to the readings
obtained with Junction IV. would be the same in all positions. TIi
values are given in Figure 14 which may serve in place of an ordinary
table. The portions of the flame to which each reading refers are
more readily indicated by giving such a diagram of the flame than in
any other way.
The fact that, in the case of the acetylene flame and the ordinary gas
flame, this method gives values high enough to account, for the melting
of platinum, but leads to an estimate of the temperature of the candle
flame which is about one hundred degrees below the melting-point of that
metal, would seem, at first sight, to throw the procedure into serious
doubt. My experience with the method has, however, been such as to
make an error of one hundred degrees in the estimation of the candle-
flame'temperature seem highly improbable. Messrs. Lurnmer and Pring-
sheim, in a recent communication to the German Physical Society,* give
an estimate of the temperature of candle flames based upon a relation
* Lummer and Pringsheim, Verhandlungen der deutschen pliysikalischen
Gesellschaft, 1899, p. 214.
100
PROCEEDINGS OF THE AMERICAN ACADEMY.
which they have established between the position of the maximum in the
energy curve of the spectrum of a source of light and its temperature.
Assuming the radiating substance in the flame to have the properties of
a black body, they find this temperature in the case of the candle flame to
be 1687°, a value seventeen degrees above that which I have given.
To account for the fusion of Wollaston wire in the flame of a candle,
one might consider the possibility of the existence in such a flame of
layers of gas the temperature of which is much above the surrounding
regions, and that these layers may be so thin that it would not be possi-
ble to submerge the thermo-junction completely in them. In such a case
the junction would give a value approximate to the average of the tem-
peratures of the gases with which it was brought into contact. Before
assuming this structure of the flame, which really has nothing to support
it save the necessity of accounting for the apparent discrepancy which I
have just pointed out, it seemed wise to consider, on the other hand,
whether the melting-point of the Wollaston wire was necessarily that of
pure platinum. Such wires would naturally be made of ordinary com-
mercial metal, the melting-point of which might vary considerably from
that of the purer platinum used in the determination of melting-points.
It is likewise readily conceivable that in the process of drawing within
the silver coating, a certain amount of silver might be worked into the
pores of the platinum and not be removed by the subsequent action of
the nitric acid. The determination of the melting-point of even such
minute wires is fortunately a simple matter
by means of the form of thermo-element
used in the calibration experiments already
described. It is only necessary to wrap a
piece of the wire to be tested around the
junction, as shown in Figure 15, to cut it off
so that the end of the loop extends slightly
(about 0.05 cm.) beyond the face of the
junction ; and having mounted the juuction
in the usual manner, to move the acetylene
up to it by means of a micrometer screw. I
performed this experiment with a piece of the same Wollaston wire
which I had succeeded in melting in the candle flame, and found its
melting-point, as indicated by the electro-motive force of the junction, to
be 1674°. To test the question whether this very low melting-point
was due to the presence of silver undissolved by the nitric acid, a piece
of the same wire was left in the acid for twelve hours, after which the
Figure 15.
NICHOLS.
THE VISIBLE RADIATION FROM CARBON.
101
melting-point was again tested in the manner just described. The result
of this determination was 1687°. The latter reading was, I think, too
high, since subsequent examination under the microscope showed that
the loop of the wire behind the junction had been melted so that the
junction was probably a few degrees too hot. It may safely be conclude 1
from these determinations that the melting-point of the Wollaston wire
was at least one hundred degrees lower than that of pure platinum.
Method of Checking the Constancy of the Acetylene Flame.
To secure as complete a check as possible upon the constancy of the
flame, the following method, based upon the assumption that so long as
the radiation from the flame remained constant, its light-giving power
dd
Ifll
Figure 16.
would not vary, wras employed. A diaphragm (d, Figure 16) similar to
that interposed between the slit and the flame, and having an aperture of
the same size, and mounted on the opposite side of the latter and a thermo-
pile p, was placed at a distance of about 15 cm. from this opening. A
second diaphragm, d' , with an intervening air space, served to cut off, in
large part, the radiation from the heated metal. Two thin sheets of
glass forming the sides of an empty cell c, of the kind used in the study
of absorption spectra, etc., were placed between the cone of the thermo-
pile and the second diaphragm ; so that only those rays from the (lame
which were transmitted by the glass fell upon the face of the pile.
The thermopile was connected with a sensitive d'Arsonval galvano-
meter g, the circuit being kept permanently closed ; and a double metallic
shutter s, which could be raised or lowered so as to open or close the
opening in the diaphragm next to the flame, was so mounted that it could
be readily operated by an observer at the telescope of the galvanometer.
When a reading of the radiation from the flame was to be made, the
zero point of the galvanometer was noted, and this shutter was raised
during the short interval of time necessary to bring the needle, which
was Dot strongly damped, to its first turning point. The shutter was
102 PROCEEDINGS OF THE AMERICAN ACADEMY.
then immediately closed in order to prevent further heatiug of the face
of the thermopile. This throw of the galvanometer was taken as an
indication of the intensity of the flame.
It was found that the thermopile would cool sufficiently within two
minutes to admit of the repetition of the reading. These observations
were taken by an assistant simultaneously with each setting of the
spectrophotometer, the intention being to reject any spectrophotometry
readings made at a time when the flame showed marked deviation from
its standard intensity, and to reduce the readings to a uniform flame
intensity under the assumption that for the small range of variation
occurring from reading to reading, the change in the brightness of the
flame would be proportional to the variations of this galvanometer read-
ing from the mean of the whole set. In point of fact it was found that
the flame rarely varied from the mean in the course of a set of observa-
tions by more than one per cent. From day to day, indeed, its intensity
was usually within the limits stated above. Occasionally a larger varia-
tion was detected. None of these variations in the course of the present
investigation reached values so great as to lead me to hesitate to apply
the correction already referred to, and all the observations described in
this paper have been reduced to a constant flame intensity by means of a
correction factor obtained from the readings of the galvanometer.
Control and Measurement of the Temperature of the Carbon Rod.
The carbon rod, having been brought to the desired degree of incan-
descence by means of the current from a storage battery, was held at a
constant temperature by varying the resistance placed in the battery
circuit. The indications of the thermo-element inserted in the rod were
noted by means of the potentiometer. The cells used in the measure-
ment of the temperature of the carbon rod were the same as those em-
ployed in the calibration pf the thermo-elements and in the study of the
temperature of the acetylene flame.
The potentiometer having been balanced by looping the circuit con-
taining the thermo-element around a sufficient portion of the resistance
box to balance its current against that of the Clark cells, a condition
which was indicated by the reduction of the galvanometer deflection to
zero, the current was maintained at such a value as to hold the carbon
at a constant temperature during the time necessary to complete meas-
urements of the intensity of eight different portions of the spectrum,
ranging from the extreme red to violet, with the corresponding portions
of the spectrum of the flame. In order to insure the maintenance of this
NICHOLS. — THE VISIBLE RADIATION FROM CARBON. 103
constant temperature in the rod, an assistant made repeated observa-
tions with the potentiometer and readjusted the resistance in the
battery circuit whenever necessary. Excepting at very high tempera-
tures, where the rod was subject to rapid disintegration, it was rarely
necessary to make any adjustment during the progress of a single set
of observations. Readings of the current flowing through the carbon
and of the fall of potential between its ends were made at the beginning
and end of each experiment.
Spectrophotometry Observations.
It was my expectation, in planning this research, that whatever might
prove true as to the character of the radiation from gray carbon, Lhe
distribution of energy in the spectrum from black carbon would change
in such a manner with increasing incandescence as to become nearly or
quite identical with that of the various luminous gas flames at tempera-
tures corresponding to the temperature of the glowing carbon in those
flames. I had also hoped, among other things, to be able to bring about
a degree of incandescence approaching that of the acetylene flame itself,
before the usefulness of the thermo-element as a means of measuring
the temperature failed because of the melting of the platinum wire, and
in this way to obtain a check upon my previous measurements of that
flame ; and at the same time to be aide to determine the temperature of
any given luminous flame in which the incandescent material consists
of carbon particles by ascertaining the temperature of the carbon rod
for which its surface had a spectrum corresponding in distribution of
energy to that of the flame.
It will be seen from inspection of the curves to be discussed in a
subsequent paragraph that this expectation was far from being realized,
and that the distribution of energy in the spectrum of the carbon rod.
instead of approaching that of the acetylene flame as the temperature of
the rod increased, took on an entirely unexpected character. Even at
low temperatures, that is to say up to about 1100°, the change in the
spectrum was not of the comparatively simple character which had been
anticipated, and shortly after passing the temperature of 1100°, unlooked
for complications in the results arose. The energy in the yellow of the
spectrum which from the beginning had been increasing at a relatively
more rapid rate than either in the red or at the blue end, became so
great as to give the distribution curve a form entirely contrary to
expectation.
I was very slow to believe in the integrity of these results, and nearly
104 PROCEEDINGS OF THE AMERICAN ACADEMY.
a year was spent in repetitions of the measurements before I could con-
vince myself that the phenomenon was a genuine one. Measurements
taken upon a great number of different rods and at different times
showed the same result, however, and I was finally forced to the con-
clusion that the radiation from the carbon rods showed a much more
complicated law of distribution than had been anticipated, and that a
sort of selective radiation occurred such as to render the establishing
of any simple relationship between the curve of distribution and tem-
perature out of the questiou.
The hope of being able to make direct temperature measurements up
to the melting-point of platinum was also disappointed. While the
carbon rods at comparatively low temperatures showed a fair degree of
stability under the action of the current, they appeared to undergo a
decided change of behavior at about 1400°, and before that temperature
a rather rapid disintegration, showing itself by a change of resistance,
manifested itself. This effect appeared to be similar to that which
shortens the life of the filaments of incandescent lamps when these are
subjected to a large amount of current. It appears, moreover, that at
these high temperatures the carbon tends to combine with the metals
of the thermo-element, affecting the electromotive force very much as
the vapors in a furnace have been found to do. The thermo-elements
inserted in the rod begin, in consequence of this action, to fail of their
purpose. It was found that after exposure to temperatures much above
1400°, the electromotive force corresponding to even lower temperatures
was considerably below the normal. I svas consequently compelled to
abandon the attempt to measure directly temperatures above this point,
although it was possible to bring the rods to a higher degree of incan-
descence for a length of time sufficient to perform the spectrophotometric
observations. In order to obtain at least an approximate estimate of
these temperatures, T made use of the fall of potential between the
terminals of the rod, and also of the current of the heating circuit ; and
by extending these curves, which, throughout the range of measured
temperatures were found to be nearly straight, to the high temperatures
which I wished to estimate, to obtain some idea, even if not an exact
one, of the latter.
In expressing the results of the photometric measurements already
described, I have made use of two forms of curve. One set of curves,
in accordance with the nomenclature proposed in my original paper on
the visible radiation from platinum, and later adopted by Paschen and
other writers, I may call isotherms. These curves give in terms of the
NICHOLS. — THE VISIBLE RADIATION FROM CARBON.
105
^oTfu*-u*4
<f- t**vtrea*
5oL ca*-£
so,.
i
r
4
frt£*n*r- / 1
•iS"
C^H^ ao rf-
{<Z**t-cLasr-BL
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1
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f
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1
1
•*■
/
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,?f
/
/
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•
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' /
f
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f
t
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>
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•
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r« ?J0°
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•
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— — •
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•
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^. poo'
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Figure 17.
•7/*-
corresponding wave lengths of the comparison source (in this case the
acetylene flame), the relative distribution of energy in the visible
sprctrum from the carbon rods. The other curves, which I have termed
tsochroms, indicate the rise in the energy of any particular wave length of
the visible spectrum, with increase of temperature. Each of these curves,
taken by itself, is entirely independent of the nature of the light of the
comparison source, but the absolute relation of such curves to one another
can only be obtained when we know the distribution of energy in the
spectrum of that source. By means of the isochroms, it is, however,
possible even without this knowledge to compare the rise in intensity
of any single wave length of the spectrum with increasing temperature.
The set of curves shown in Figure 17 are plotted directly from obser-
106
PROCEEDINGS OF THE AMERICAN ACADEMY.
vations upon a black (untreated) carbon at temperatures ranging between
795° C and 1055° C. In tbis diagram abscissae are wave lengths and
-*f-
Zoo" /r //oo"
''It-
I
•fo-
\7af*
T
! i
i
~/ T
/ /
K /
/ /
/ /
1 L.
/ /
/ /
L
I I
I I
I I
i I
— 7 — T
>s.
ji
>A
—t
I
I
I
I'tOto
!
+■
/
$00'
fooe /ooo°
Figure 18.
IIOO'
ordinates are ratios of the brigbtness of the spectrum of tbe carbon rod
in each region to that of the corresponding region in the spectrum of
NICHOLS. — THE VISIBLE RADIATION FROM CARBON.
107
the acetylene flame. A noteworthy fact exhibited by means of these
curves is the relatively rapid increase of intensity in the middle of the
spectrum. In passing from 930° to 1055° the brightness of wave
length .7C p, increases 5.3 times ; that of .70 p, 7.2 times ; that of .60 p,
13.5 times, and that of .50 p o>dy 9 times. We have here the beginnings
of a process which becomes more marked in its effects as higher temper-
faocA
£*7**<7
(frca^ca
c ce*>.
■^xn+4
(.0
(cvuy
U&J
aM. ,
*ua*&<~
-CjHu+iA
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t
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' /
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t
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i
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i
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¥0
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1 1
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i '
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i
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/ /
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■ss-^.
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y-
■JfS-f*.
IOOO" nOQa /lOO° /ZOO'
Figure 19.
atures are attained. From 1100° upwards it was found much more
difficult to obtain satisfactory readings. The carbon rods which I had
brought from Paris for this investigation would not stand prolonged
heating and it was necessary to replace them frequently.
108 PROCEEDINGS OF THE AMERICAN ACADEMY.
In order to bring the observations upon the various rods to a common
scale, isochroms from the readings for each rod were plotted. The gen-
eral character of these curves is shown in Figure 18, in which the isochroms
corresponding to the isotherms of Figure 17 are given. From the ordinate
at 1000° of the isochrom for .G/.i, which for convenience was taken as
unity for the entire set, a reduction factor was obtained by means of which
all the curves for all the carbons were brought to the same scale. A new
set of isochroms was then plotted for each of the wave lengths .75^, .70^,
.65^, .60^, .55//, .50(i, and .45^, in the drawing of which all the obser-
vations upon the rods were used. While this method did not bring the
various sets of observations into perfect agreement, the results were
sufficiently definite to indicate with a close degree of approximation the
trend of these curves for temperatures up to 1400°. The result of this
compilation for the wave lengths just mentioned is shown graphically in
Figure 19. From these curves in turn, isotherms for the temperatures
900°, 1000°, 1100°, 1200°, 1300°, and 1400° were plotted. These curves
are given in Figure 20. Had the law of increasing intensities throughout
the spectrum with rising temperature been that anticipated at the begin-
ning of this investigation, the trend of the isochroms would necessarily
have been such as to bring all the curves together at a common point
corresponding to the temperature of the acetylene flame. In other words,
if the spectrum of the acetylene flame were identical throughout with that
of the carbon rod at the same temperature, the isotherm of the spectrum
of the rod at that temperature would be a horizontal line. It is obvious,
however, that if the wave lengths of the middle of the spectrum should
continue to increase faster than the red and the violet, a condition would
presently be attained in which the ordinate of the isotherm would be
greater in the yellow or green than at either end of the spectrum. We
see indications of the approach of this condition in the diagram of iso-
chroms (Figure 19), from which it is evident that the curves for .65/i and
.60/i would cut each other and would cut the curve for ,70ft at some tem-
perature not far above 1400° ? whereas the isochroms for the shorter
wave lengths would not be likely to cut the curves for the red until some
much higher temperature had been reached.
The curves in Figure 20 show the nature of this unexpected development
of the spectrum in a somewhat different aspect. It will be seen from
this figure that the growth in the extreme red so far lags behind that of the
full red, and this in turn behind that of the orange, and this in turn
behind that of the wave length .6^, that at 1400° the isotherm, instead of
being convex to the base line throughout, actually becomes convex. 1
NICHOLS. — THE VISIBLE RADIATION FROM CARBON.
109
have indicated by means of lighter lines the form of curve which might
have been expected had the type of isotherm which exists at lower tem-
peratures been maintained.
Ahove 1400° it was found impossible to obtain consistent readings on
account of the rapid disintegration of the carbon rods ; but I was ahle to
satisfy myself after repeated trials that at temperatures not far above
1500° this change in the character of the isotherms had progressed to the
y^O fac^~<! firr
<A±
6o
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f+m.fa&a2LcC £&A.lri
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S
s
/
/
: /
V
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s
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lOoa"
9oom
9-
FlGURE 20.
/A
point at which the yellow regions of the spectrum possess an ordinate
greater than that of the extreme red or of the blue or violet. At a tem-
perature about 300° below that of the acetylene flame, then, the spectrum
of the carbon rod was relatively weaker in the red, stronger in the yellow,
and weaker again in the shorter wave lengths than the spectrum of the
Maine. There is no reason to suppose that had it been possible to heat
the rods to the temperature of the flame itself the law of increase of
intensity for the various wave lengths would have undergone such radical
modifications to bring the two spectra at that temperature into identity.
110
PROCEEDINGS OF THE AMERICAN ACADEMY.
Spectrophotometric Measurements upon Rods with Treated Surfaces.
In order to compare the radiation of rods of black surface with those
the surfaces of which have acquired a gray coating by treatment in
hydrocarbon vapor, rods were mounted in the usual manner, and after
the exhaustion of the air from the metal box, gasoline vapor was allowed
to enter until the atmosphere surrounding the rod was saturated. The
Figure 21.
rod was then brought several times to a high state of incandescence for
a few seconds at a time, by which means the entire surface became coated
with a gray deposit of carbon similar to that obtained by the treatment
of incandescent lamp filaments. The metal box was then again pumped
out and spectrophotometric measurements similar to those already de-
scribed were made upon the radiation from the treated surface. It was
thought that as the result of this treatment the carbon rods would stand
NICHOLS. — THE VISIBLE RADIATION FROM CARBON. Ill
a more prolonged exposure at high temperatures, and that thus it might
be possible to extend the measurements beyond the point reached with
the rods of black surface. This was found to be the case.
As has already been indicated in a previous paragraph, the indications
of a thermo-junction at these high temperatures was subject to serious
suspicion. I was obliged to content myself, therefore, with estimations ol
/
i
•/
-^
•
/¥Q
/ /
1
1
1 /
1 J
/
/
t
©
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t
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i
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60
i
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/
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f
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S
/
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s
r
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= -:::
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.6 ii.
Figure 22.
./ ix
the temperature based upon the difference of potential between the ter-
minals of the rod. Fortunately the relation between the electromotive
force and the temperature up to 1400° was of such a character that but
little error was to be feared in extrapolating. The relation between
electromotive force in volts and temperature is shown in Figure 21.
From this curve temperatures above 1400° were determined.
112 PROCEEDINGS OF THE AMERICAN ACADEMY.
The work upon treated carbons was confined chiefly to high tempera-
tures, a sufficient number of readings within the range already explored
with the untreated carbons being taken to show that the distribution of
intensities at the lower temperatures did not differ materially from that
in the spectrum of the former. The set of isotherms given in Figure 22
will suffice to indicate the general character of the results. It will be
seen that in this case, as in that of the untreated carbon, the concavity of
the curve between .6^ and the red end of the spectrum is well marked
at 1365° ; and that at 1515° there was a well-pronounced maximum at
about .65^. The greater stability of the treated carbon made it possible
to obtain consistent measurements on a number of rods at temperatures
above 1500° and to establish beyond doubt the form of the curves. It
is obvious that for the study of the spectrum of incandescent carbon at
this and higher temperatures the conditions would be much more
favorable in the case of the incandescent lamp than with rods mounted
in a large vacuum chamber like that used in the present investigation.
Lamp filaments in the process of manufacture are brought by thorough
carbonization into a condition to withstand permanently much higher
temperatures than the rods at my disposal were capable of doing.
There is as yet, it is true, no direct means of determining the tempera-
ture of the lamp filament ; but the curve for the relation of electromotive
force to temperature (Figure 11) is of such a character as to lead us to
expect that comparisons of the spectra of incandescent lamps, in which
electromotive forces were used as a criterion of the decree of incan-
descence, would at least enable us to confirm the existence of the
remarkable phenomenon brought out by the present experiments and to
extend observations of it to still higher temperatures.
Mr. Ernest Blaker has, since the completion of the measurements
described in this paper, compared the visible spectrum of lamps with
treated filaments, and of lamps the filaments of which before exhaustion
had been coated with lampblack, with the spectrum of the acetylene
flame. His measurements confirm very completely those which I have
described in this paper, and contribute important evidence in favor of the
existence of this anomaly in the law of distribution of intensities in the
spectrum of glowing carbon.
Theoretical Aspects of the Foregoing Data.
The efforts of students of radiation have of late years been directed
particularly to the testing of the various formulae by means of which
the mathematical physicists have attempted to express the intensity of
NICHOLS. — THE VISIBLE RADIATION FROM CARBON. 113
radiation as a function of wave length and temperature. The equation
reached from quite different points of view by Wien * and by Planck, f
/= Cl A-5 e-Ar'
in particular, has been the subject of exhaustive discussion and of
experimental tests. To this end Paschen $ determined with the bolo-
meter the distribution of energy in the infra-red spectra of various
bodies from 15° C to 1300°. The materials thus subjected to measure-
ment were oxide of copper, platinum, lampblack, and graphitic carbon.
The range of wave lengths explored extended from 9.2/t to 0.7(«.
Luiumer and Pringsheim § made similar determinations upon the ideal
black hotly, and Lummer and Jahnke || finally repeated these measure-
ments in the case of the black body and of platinum. Wanner,! working
with Paschen, made careful spectrophotometric measurements of the
visible radiation from the ideal black body. To test the applicability of
the Wien-Planck formula to these measurements, the equation is given
the form, —
log 7= -vi — y» y>
in which
yi = log (<?! A-5),
72 = ^ log e.
The isochromatic curves are then plotted with the logarithm of the
intensities as ordinates and the reciprocal of the absolute temperature as
abscissae. The agreement of the equation with the observations is
found in the fact that isochroms thus plotted, at least as far as the work
of Paschen and Wanner is concerned, always take the form of straight
lines, and that the quantity r2 computed for various wave lengths is
found to be a constant. Lummer and Pringsheim, on the contrary, find
in the discussion of their measurements that the constant, c2 increases
steadily with the wave length from 13,500 at 1.2 p to 16,500 at 5 p, and
18,500 at 0.3 p. The value of c2 computed by measurements from
* Wien, Wiedemann's Annalen, LVIII. 662 (1896).
t Planck, Drude's Annalen, I. 69 (1900).
t Paschen, Wiedemann's Annalen, LVIII. 455 (1896); also LX. 662 (1897).
§ Lummer and Pring-sheim, Deutsche phys. Gesellsehaft, I. 23, II. 16o (1900).
|| Lummer and Jahnke, Drude's Annalen, III. 283 (1900).
1 Wanner, Drude's Annalen, II. 141 (1900).
VOL. XXXVII. — 8
114 PROCEEDINGS OF THE AMERICAN ACADEMY.
Beckman at wave length 24 was found to be 24,250. Lumraer and
Pringsheim find, moreover, that the logarithmic isochroms, especially
when extended to higher temperatures, are not straight lines, but show a
, . 1
slight convexity towards the — axis.
Exception has also been taken to the Wien-Planck formula on the
ground that it gives for infinite temperatures a finite limit to the value of
the intensity, a result which Rayleigh * in a recent paper has character-
ized as physically improbable.
Rayleigh proposes the form
. — 4 —
ft
2
I=Cl T\~% e~^T
but Lummer and Pringsheim find that this likewise fails to properly express
their experimental results. Lummer and Jahnke propose, in view of
these discrepancies, to give the equation the general form
/= CT5 (XT)-* e-(^)v'
an expression which coincides with Wien's formula for ft = 5 and with
Rayleigh's for [i = 4. They find the measurements of Lummer and
Pringsheim satisfied when p lies between 4.5 and 5, and v lies between
.9 and 1.0. If we accept the value /< = 5 and v — 0.9, this equation
always leads to a finite value of intensity for infinite temperature. All
other values of these quantities give infinity as the limit of intensity.
Whether logarithmic isochroms or the value of the quantity c2, computed
from measurements upon carbon rods, would aid in deciding between the
various equations under discussion is a question. The data given in this
paper would not lead us to class the carbon rods studied as black bodies.
The emissive power of various forms of carbon is well-known to be
smaller than that of the ideal black body, and there is no reason to
suppose that it is independent of the temperature. The relative lagging
behind of the intensities in the red might perhaps be taken a3 an indica-
tion of a tendency to approach the infinite maximum demanded by the
Wien-Planck formula ; but the isochrom for .76 shows that the effect, if
it exists, must be looked for at some much higher temperature than that
covered by these measurements. In spite of these doubts as to the
applicability of the measurements on carbon rods to the problem of the
* Philosophical Mag., XLIX. 539 (1900).
NICHOLS.
THE VISIBLE RADIATION FROM CARBON.
115
law of radiation of the ideal black body, I have plotted the various iso-
chroms obtained in the course of this investigation in logarithmic form ;
absolute temperatures being taken as abscissae and the logarithm of the
intensity as ordinates. These logarithmic isochroms, as will be seen from
/Sao'
Iffoai
/Soa°
/to**
Figure 23.
Figure 23, in which three curves from Figure 19 are reproduced, are
straight lines. The range of temperatures is doubtless much too small
to bring out the curvature found by Lummer and Pringsheim, but the
curves show clearly the change of direction with the wave length men-
116
PROCEEDINGS OF THE AMERICAN ACADEMY.
tioned by those writers on page 222 of their paper before the German
Physical Society.*
For very high temperatures no experimental data for the radiation
from carbon exist excepting the measurements described by Lucas, f It
has been rather the fashion to leave Lucas's work altogether out of
account as being hopelessly at variance with more recent results. Kay-
ser, $ for example, after giving Lucas's data, says, —
4-oo
.-»-•-
Joo
/
/ /
/ /
/ /
/ *
2-o
200 i
e/
m/
/
/
/
*
1
•
IS
0
•/
f
1
1
1
/
/
*
10
1-J»'
s
Jcroo" 2ooo° 3ooo'
Figure 24.
y-ooo*
Zu jahchen Schliissen gelangt audi Lucas, durch Versucke welche das
Verdampfen der Kohle in Frage zu stellen scheinen.
His results, nevertheless, which I have given graphically in Figure 24,
appear to me to be of significance. His formula for the relation of tem-
perature to current, t = 25 i, must of course be regarded as only ap-
proximately correct even at moderate temperatures. The curve for the
relation between the current in a carbon and the temperature, up to about
* Lummer and Pringsheim, Verhandl. d. Deutschen Physikal. Gesellscli (1899)
p. 222.
t Lucas, Comptes Rendus, 0. 1454 (1884).
% Kayser, Handbuch der Spectroscopic, I. 157.
NICHOLS. — THE VISIBLE RADIATION FROM CARBON. 117
1500°, does however not vary widely from a straight line. Beyond these
temperatures it is a matter of extrapolation, but the same thing is true
of all other attempts to estimate very high temperatures. The curve /,
for the relation of the logarithm of the intensities and the temperatures,
which I have also given in Figure 24 (between 1500° and 3750°), is in
the case of Lucas's measurements nearly straight ; so that in so far as
this is a criterion, his curve up to this point may be said to conform to
the Wien -Planck equation. It is significant that Lucas's curve shows an
inflection point between 3.300° and 4000°, becoming concave to the
axis of temperatures. This is the temperature at which, according to
nearly all the newer determinations, carbon, as in the crater of the arc,
approaches its maximum condition of incandescence. At about 3750°
the electrical energy developed in the rod is doubtless largely expended
in the disintegration or vaporization of the carbon, so that a maximum
degree of incandescence is approached. At the point at which this process
begins current can no longer betaken as a measure of the temperature.
The very slight falling off in the photometric measurement of intensity
does not appear to me to warrant the conclusion drawn by the author that
a maximum has been passed at the current value to which he assigns
the temperature 4750°. The difficulty of obtaining consistent readings
under conditions existing in such work would amply account for so slight
a discrepancy.
Lucas's work appears, in a word, to warrant the following rather
important conclusions. First, that up to about 3750° current and
temperature in the case of carbon rods heated electrically are nearly
proportional. We have in favor of this point two checks, — the straight-
ness of the logarithmic curve and the fact that the inflection of Lucas's
curve corresponds, as has already been pointed out, to the recognized tem-
perature of the crater of the arc. Secondly, that for a wide range of
temperatures photometric intensity, like the intensity of total radiation,
follows the logarithmic law of iucrease. Third, that after the tempera-
ture of the crater has been attained a considerable additional increase in
incandescence results from the application of further current before the
maximum is finally attained. This agrees with the observations of
Moissan,* that many reductions in the electric furnace which do not
occur with moderate currents become possible by increase of the current
strength. If, as seems proper, we ascribe the rapid approach of Lucas's
curve to a finite maximum to the utilization of the energy of the cur-
* Moissan, Comptes Kendus, CIX. 776 (1894).
118 PROCEEDINGS OF THE AMERICAN ACADEMY.
rent in disintegration of the carbon, it follows that no definite tempera-
tures can be given above the point of inflection. Lucas's measurements,
therefore, cannot be said to throw any light upon the question whether
the intensity of radiation of incandescent bodies reaches a finite limit as
demanded by the Wien-Planck formula. The lower portion of the
curve shows no approach to such a maximum. Whether the study of
radiation, wave length by wave length, up to the temperature of the
crater will be found to do so remains to be seen. Far beyond that tem-
perature experiments with carbon can probably never be carried ; so
that the final determination of this point must probably be reached by
experiments on some more refractory material.
In the prosecution of portions of this investigation I have received
valuable aid from Drs. C. H. Sharp and Leopold Kann and from Mr.
L. W. Hartman, to all of whom I desire to express my obligations and
extend my hearty thanks.
Phtsical Laboratory of Cornell University,
April 24, 1901.
Proceedings of the American Academy of Arts and Sciences.
Vol. XXXVII. No. 5. — September, 1901.
ON RULED LOCI IN n-FOLD SPACE.
By Halcott C. Moreno.
ON RULED LOCI IN w-FOLD SPACE.
By Halcott C. Moreno.
Presented by W. E. Story, May 8, 1901. Received June 1, 1901.
The present paper is a discussion of those loci in n-fold space that
can be generated by flats whose equations involve a single arbitrary
parameter. The ruled loci of space of three dimensions can be repre-
sented in this way.
I. Loci derived from an (n — 1)-flat whose Equation involves
a Single Arbitrary Parameter; Developables.
1. Description of the derived loci.
Let us consider the loci derived from the equation
A = 0,
the equation of an (n — l)-flat involving a single arbitrary parameter A.
If the parameter enters rationally, we suppose it to enter to as high a
degree as n, the number of ways of the space. If the parameter enters
rationally to the degree m where m < ?i, the locus is of a special kind to
be discussed later. As the parameter varies continuously we have a
1-fold infinite system of (11 — l)-flats.
Two consecutive (« — l)-flats of the system intersect in an (n — 2)-flat
whose equations are
If from these equations we eliminate the parameter there remains a
single equation of an (n — l)-spread, Sn_^ which is ruled by the 1-fold
infinite system of (n — 2)-flats.
Three consecutive (n — l)-flats of the system intersect in an (n — 3)-
flat whose equations are
a a ^ A 9-A
122 PROCEEDINGS OF THE AMERICAN ACADEMY.
These (ft — 3)-flats may be considered as arising from the intersection
of two consecutive (ft — 2)-flats of the system of (ft — 2) -flats. The
elimination of the parameter from these equations gives a restricted sys-
tem equivalent to two independent equations. The system represents an
(n — 2)-spread, Sn_2, which is ruled by the (ft — 3)-flats.
In like manner r consecutive (ft — l)-flats of the system intersect in
an (n — r)-flat whose equations are
A 9 A n 9r~2A
A = 0, _ = „,... ^ = o.
Any of these (n — r)-flats may be considered as arising from the inter-
section of two consecutive (ft — r + l)-flats of the system of (n — r + 1)-
flats that are the intersections of r — 1 consecutive (ft — l)-flats of the
system. The elimination of the parameter from these equations gives
a restricted system equivalent to r — 1 independent equations. These
equations represent an (n — r -f l)-spread, Sn_r + l, which is ruled by the
1-fold infinite system of (ft — r)-flats.
The locus of the intersections of n consecutive (ft — l)-flats of the
system is a curve, while n + 1 consecutive (ft — 1) -flats do not in
general have any common intersection.
We will use Sk to denote that one of the related spreads of this system
that is of k ways. It is geometrically evident that each one of these
spreads is a developable spread.*
Considered in this light we see that the (ft — 2)-spread is a double
spread on Sn_i corresponding to the cuspidal edge or edge of regression
in ordinary threefold space."}-
The Sn_s is a double spread on Sn_2, etc., and S: on S»> We see also
that $„_g is a triple spread on *S',i_1 ; Killing calls it doubly stationary.
Finally, St is an (ft — l)-tuple curve on £„_! ; it is a multiple curve on
all the other spreads of the system. J
If the equation
A = 0
contains k arbitrary parameters connected by k — 1 equations
<£ = 0, x = 0, ^ = o,
* Killing, Nicht-Euklidische Raumformen, p. 195 et seq.
t Puchta calls the S„—i the most general developable spread in w-fold space.
Puchta, Ueber die allgemeinsten abwickelbaren Riiume, ein Beitrag zur mehrdi-
mensionalen Geometric Wien. Berichte, CI.
% Killing, loc. cit.
MORENO. — ON RULED LOCI IN 71-FOLD SPACE.
123
we can, theoretically, solve these equations for k — 1 of the parameters
in terms of the remaining one, so that this case is the same as the previ-
ous one.
The actual elimination may be avoided. Let the parameters be A,
fjL, .... v. Differentiate totally all the equations,
9 A
9A^ JAr1
-7TT- « A + -pr- dfl +
a A <y fx
+
9 <f>
9 <f>
9 v
4>
dv = 0
d\ + ^dfJL + + -^ dv = 0
From these we may eliminate the differentials,
9 A 9 A 9 A
B =
9 A 9 (i
9 <f> 9 <f>
9 A 9 (i
9 v
9 I
9 v
9 i[/ 9 ^
c/A 9 [i
9 $
9 v
= 0
This is the equation of an (n — l)-flat. The equation involves k
parameters but they are connected by k — 1 equations. Two consecutive
(n — l)-flats of the system intersect in an (n — 2)-flat whose equations
are A = 0, B = 0.
Three consecutive (re — l)-flats of the system intersect in the (re — 3)-
flat,
A = 0, B = 0, C=0,
where 0 is the determinant B, with A replaced by B. The equation of
the £„_! is found by eliminating the parameters between the equations
of the (n — 2)-flats and the equations connecting the parameters. The
equations of the other spreads are derived in a similar manner. The
system of related spreads is of the same character as before.
2. Mutual relations of connected loci.
Let us consider more in detail these connected loci. We will use Fk
to denote a &-flat of the 1-fold infinite system of £-flats. Two consecu-
124 PROCEEDINGS OF THE AMERICAN ACADEMY.
rive i'Vi's intersect in an Fn_s, three in an Fn_3, r in an Fn_r, n — 2
in an F.2 or plane, n — 1 in an F1 or line, n in an F0 or point. There
is a 1-fold infinite system of these i^,_2's which are generators of £„_!,
a 1-fold infinite system of Fn_3s, generators of Sn_2, a 1-fold infinite
system of lines generators of S2, the developable surface.
Through any Fn_2 there pass two consecutive F^s, through any F„_3
there pass three consecutive -F„_i's, through any F0, n consecutive F^s.
Tlirough any Fn_z there pass two consecutive F„_2's, through any F„_4
there pass two consecutive -Fn_3's and three consecutive F„_2S,&nd so on.
"We may then reverse this process and start with the curve of the
system. Through any two consecutive points of the curve there passes
a line, an Fu through any three consecutive points an osculating plane,
an F2, through any four consecutive points an osculating 3-flat, an F3,
through any n — consecutive points an osculating (n — l)-flat, an Fn_v*
That these operations may give unique results this curve must lie in
the n-fold space and in no flat space of a less number of ways. If the
curve lie in a £-flat, where k < n — 1, all the £-flats through h + 1 con-
secutive points coincide and definite (k -f l)-flats are not determined at
all. By a theorem of Clifford, such a curve must be of an order as
great as ra.f
This theorem has been generalized by Veronese.^
Let us consider any curve in n-foh\ space whose equations are,
0 = 0, x = 0, . . . . if, = 03
a restricted system equivalent to n — 1 independent equations. The
equations of the tangent at any point P' of this curve are linear equa-
tions whose coefficients are functions of the n non-homogeneous co-
ordinates, x', y', . . . . v'. The same thing is true of the equations of
any of the osculating flats at the point P. The osculating (n — l)-flat
is given by a single equation, the coefficients of which are functions of
these n quantities x', y', . . . v'. If we regard these as n parameters
they are connected by the equations,
^ = 0, x' = 0, . . . . ip' = o,§
* We shall say a /t-flat osculates a curve if it contains k + 1 consecutive
points of it. Killing, loc. cit.
t Clifford, Classification of Loci; Mathematical Papers, pp. 305-331.
i Veronese, Behandlung der projectivischen Verhaltnisse der Baume von ver-
schiedenen Dimensionen durch das Princip des Projicirens und Schneidens,
Mathematische Annalen XIX.
§ <p' = <p (x>, y', . . . v>), etc.
MORENO. — ON RULED LOCI IN W-FOLD SPACE. 125
a restricted system equivalent to n — 1 independent equations. "We
have then the case of an (n — l)-flat whose equation involves n para-
meters connected by n — 1 independent relations ; this is equivalent to
the case of a single equation containing one arbitrary parameter. We
may, in general, consider the system of developables as given by an
(» — l)-flat whose equation contains a single arbitrary parameter or
k parameters connected by k — 1 equations.*
3. The tangent (n — \)-flats that are common to n — 1 (n — V)-spreads
envelop a developable.
The equation in homogeneous coordinates of any (n — l)-fiat may be
written
x = ay-\-j3z-\-....J!-yw.
This equation involves n independent parameters; if we connect them
by any n — 1 independent equations we shall have the equation of an
(n — l)-flat that contains but a single independent parameter, so that
the 1-fold infinite system of (n — 1) -flats represented by it envelop a
developable. The tangent (n — l)-flat at any non-singular point of a
developable S,^ contains the generating Fn_2 through that point and
touches the *S'„_1 all over this flat, t We may speak of this developable
Sn_! as enveloped by its tangent i^-i's. If then we impose on an
arbitrary (n — l)-flat any conditions that give rise to n — 1 independent
equations between the coefficients in its equation, the (n — l)-flat will
envelop a developable Sn_i.
Let IT= 0
be the equation of an (n — 1) -spread. The equation of the tangent
(n — l)-flat at any ordinary point P' is
9U< 3U> 9U> A
If we impose on the equation of the arbitrary (n — l)-flat the condi-
tions that it shall be this tangent (n — l)-flat, the coefficients in the two
equations must be proportional. We must have then
9U[ 9U[ 9U<
9 x' = 9 y' = . . . . 9 w'
— la y
From these equations by means of the equation
W = Q,
* Salmon, Geometry of Three Dimensions, p. 286. t Killing, loc. cit.
126 PROCEEDINGS OF THE AMERICAN ACADEMY.
we may eliminate the coordinates of P' leaving a single equation in
a, (5, .... y. For an (n — l)-flat to be tangent to an (?i — l)-spread,
one relation between the coefficients that enter into their equations must
be satisfied. We conclude then that the (n — l)-flats that touch n — 1
(n — l)-spreads envelop an Sn_1.
Let us consider only those tangent (n — l)-flats to an (n — 1)-
spread that touch it at the point of an (n — 2) -spread that lies on it.
Let £7=0
be the equation of the (n — l)-spread and let
U=0, V=0, ...,
a restricted system equivalent to two independent equations, be the equa-
tions of the (n — 2) -spread on it. We derive now the equations
9U' 9 IP 9U'
9x' =. 9 y' = . . . . 9 to'
— la y
and IP = 0, V = 0, ...
If we eliminate the parameters from these equations there remains
a restricted system equivalent to two independent equations in the
coefficients a, (3, ... y. For an (n — l)-flat to be tangent to an
(n — l)-spread at a point of an (n — 2)-spread on it requires two con-
ditions between the coefficients in the equation of the (n — l)-flat.
These two conditions may be used as part of the n — 1 conditions that
connect the coefficients of an (n — l)-flat that envelops a developable
S„-v We have then the theorem that the (n — l)-flats that are tangent
to p (n — l)-spreads at the points of p (n — 2)-spreads that lie one on
each (n — l)-spread, and are tangent to cr other (n — l)-flats, where
n — 1 = 2 p -\- cr, envelop a developable.
In a similar manner for an (n — l)-flat to be tangent to an (n — 1)-
spread at a point of an (n — 3) -spread that lies on it imposes three con-
ditions on the coefficients that enter into the equation of the (w — l)-flat.
To be tangent to the (n — l)-flat at a point of an (n — 4) -flat on it
requires four conditions, etc. To be tangent to an (n — l)-spread at a
point of a curve that lies on it requires n — 1 conditions between the
coefficients, which is just sufficient to make the {n — l)-flat envelop a
developable.
We have then the general theorem that the (n — l)-flats that are
tangent to p (n — l)-spreads at points of p (n — &) -spreads that lie one
MORENO. — ON RULED LOCI IN W-FOLD SPACE. 127
on each, tangent to o- (n — l)-spreads at points of cr (n — k -f l)-spreads
that lie one on each, tangent to t (n — l)-spreads at points of t (n — 2)-
spreads that lie one on each, and finally tangent to v other (n — 1)-
spreads, where p, cr, . . . t, v, are non-negative integers connected by
the relation
n — 1 = k. p + (k — 1) o- + •••• + 2 t + v,
envelop a developable Sn_v
Similar cases occur in three-fold space where we have the tangent
planes that are common to two surfaces enveloping a developable surface
as do the tangent planes to a surface at the points of a curve on that
surface*
4. Some additional properties of devehpables ; sections.
Other properties of an Sn_x may be deduced by regarding it as the
envelope of an (n — l)-flat whose equation involves a single parameter.!
Through any point in space can be drawn a definite number of tangent
i^n-j's to the Sn_v For substitute the coordinates of the point in the
equation of the variable (n — l)-flat and there is a certain finite number
of values of the parameter that satisfy the equation.
Any Fn_x of the system meets its consecutive F„-\ in a definite Fn_2, a
generator of Sn_t whose equations are,
„ = o,fi = <,
Any three consecutive i^-^s meet in a definite Fn_z, a generator of *^„_2,
whose equations are,
. 9 A PA .
A==0>9X=°>W=0-
Any n — 1 consecutive 2?TB_1's meet in a definite line Fx, a generator of
$2, whose equations are,
. n 9A 9->A
^ = 0,_=:0,. ..^=0-
Finally, any n consecutive i^_1's meet in a definite point of the curve of
regression of S2. The equations of the F0 are,
. . 9A 9^A
* Salmon, Geometry of Three Dimensions, p. 547.
t Salmon, Geometry of Three Dimensions, p. 289 et seq.
128 PROCEEDINGS OP THE AMERICAN ACADEMY.
In general n + 1 consecutive Fn_^s do not have any common inter-
section, for the n + 1 equations,
have no common solutions. If we regard these equations as homo-
geneous in the n -f 1 coordinates we may form their resultant, and the
values of the parameter that cause this determinant to vanish, give
special points where n + 1 consecutive F^s intersect. These points
are cusps on the curve Si.
Reciprocally there will, in general, be a finite number of Fn_^a that go
through n + 1 consecutive points of S^
Veronese has shown that a curve in n-fold space has 3 n singularities
which are connected by 3 (n — 1) relations, an extension of the Pluecker-
Cayleyan characteristics of a twisted curve in three-fold space.*
In this we have assumed that the variables that enter into the equation
of the enveloping (n — l)-flat cannot be expressed in terms of fewer
than n + 1 independent linear functions of the variables alone. If they
could be expressed in terms of v such linear functions, where v < n, the
developable »Sn_1 is a conoid with an (n — v)-way head, a case to be con-
sidered later.
The developable Skoi the series is ruled by (k — l)-flats, Fk_r'a. The
Su, where 2 < k ^ n — 1 can be given by means of its enveloping Fk
whose equations involve a single parameter. The n — k equations of the
Fk must however be of the form
, n 9A n dn~k~xA n
as we have previously seen. Even the Sx may be represented in this
manner.
Any (n — l)-flat B = 0
cuts the £„_, in a developable (n — 2)-spread, for it cuts the system of
Fn_i& in a system of (n — 2)-flats that intersect consecutively in (n — 3)-
flats. We may see this in another way. By means of this new equa-
tion we can eliminate one variable from the equation of the enveloping
(n — l)-flat. The resulting equation in n variables may evidently be
considered as the envelope of an (?i — 2)-spread in a new (n — l)-fold
space. The (n — l)-flat cuts any Sk of the system in a (i — l)-way
* Veronese, Ioc. cit. ; Killing, loc. cit. p. 197 et seq.
MORENO. — ON RULED LOCI IN W-FOLD SPACE. 129
developable. In general any r-flat where r > n — k + 1 cuts any Sk in
a developable (k + r — w)-spread.
Any Fn_x of the system cuts the Sn_x in an (ft — 2) -spread, and the
Fn_2 that it has in common with the consecutive Fn_l appears twice in the
intersection, so that the proper (ft — 2)-spread is of order less by two
than the order of Sn_v This (ft — 2)-spread is also a developable.
An Fn_o is met by the consecutive Fn_2 in an Fn_^ ; it is met by any
other Fn_2 in an (n — 4)-flat. In general, where 4 < n, there are a
2-fold infinite system of these (ft — 4)-flats and their locus is an (n — 2)-
spread which is a double spread on Sn_v In the case of cones and
conoids this double spread may be of fewer than n — 2 ways. Thus in
four-fold space the planes which join a line to the successive points of an
irreducible conic form a three-way developable. This developable is a
conoid and the one-way head is the only multiple locus on the conoid.
In three-fold space cones are the only developable surfaces that do not
possess a proper double curve, if we call the cuspidal curve a double
curve. In general there is a double curve distinct from the cuspidal
curve. We will assume that we have the general case of a developable
and not a cone or conoid. The total double spread on S,^ consists in
general of two parts, Sn_2 and 2„_2, where 2„_2 is the locus of the
2-fold infinite system of (ft — 4)-flats arising from the intersection of
non-consecutive F^s, while Sn_2 is the locus of the 1-fold infinite
system of (ft — 3)-flats arising from the intersection of consecutive F„_2s.
Any three non-consecutive Fn_2s intersect in an (n — 6)-flat ; there
are in general a 3-fold infinite system of such (n — 6) -flats whose locus
is an (n — 3)-spread, a triple spread on Sn_2. Any (ft — G)-flat is the
intersection of three (ft — 4)-flats of 2„_2 and any such (n — 4)-flat con-
tains a 1-fold infinite system of such (ft — 6)-flats. This 1-fold infinite
system of (ft — 6)-flats does not, in general, fill out the (ft — 4)-flat, for
this would require a 1-fold infinite system of them. The total triple
spread on S,,^ consists in general of two parts *S,(_3 and 2„_3 where 2„_o
is the locus of the 3-fold infinite system of (ft — 6)-flats. We can supply,
a similar mode of reasoning to the spreads of higher multiplicities on
Sn_v The spreads Sn_2, Sn^, . . . are developable, but 2„_2, 2„_^, . . . arc
not developable.
5. Special case where the parameter enters rationally.
Let us illustrate this theory by the case of the developable which is
the envelope of the (« — l)-flat,
a tm + mb r-1 + i m (m — 1 ) c P~\ -f . . . . = 0,
9
130 PROCEEDINGS OF THE AMERICAN ACADEMY.
where t is a variable parameter, a, b, c, . . . are linear functions of the
coordinates that are not expressible in terms of any v linear functions of
the coordinates where v < n, and m is an integer which is not less than n,
the number of ways of the space. Two consecutive F^s intersect in
the Fn_2,
ar-i+ (m _ j) br-2+ O-1) ' |m~2)cr-8+ . . . . + e = 0,
- 1
bfa~1+ (m — 1) ctm~2+ . . . + et +f= 0.
The elimination of the parameter from these equations gives the equa-
tion of Sn_v The result is the discriminant of the original equation
placed equal to zero ; the order of *S'„_1 is then 2 (m — 1).*
Three consecutive Fn_^s intersect in the Fn_&
a r~2 + (m — 2)b tm-3 +.... = 0,
btm~2 + (m — 2) c tm-' +.... + 0 = 0,
ctm~2+ + et +/= 0.
The equations of Sn_2 are found by eliminating the parameter from these
equations. The result is a restricted system equivalent to two inde-
pendent equations ; the order of the system, i. e., the order of Sn_2 is
3 (m- 2).f
Similarly k consecutive Fn_^s intersect in the Fk, given by the k
equations,
a fn-*+i + (m — k+ 1) b tm~k +....= 0
b r-&+1 + (m — h + 1) c r~* +.... = 0
+ 0*+/=O.
The elimination of the parameter from these equations gives a
restricted system equivalent to k — 1 independent equations, the equa-
tions of Sn_k+y The order of Sn_k+l is seen to be (k + 1) (m — k).
Lastly the intersection of n consecutive Fn_^s is the point, F0, given
by the equations,
a r-"+1 + (m — n + l)b tm'n +.... = 0
b r-n+1 + (m — ii+l)c tm~n +.... = 0
+ et+f=0.
* Salmon, Higher Algebra, art. 105.
t This is the condition that the three equations have a common root ; Salmon,
Higher Algebra, art. 277.
MORENO. — ON RULED LOCI IN W-FOLD SPACE.
131
The elimination of the parameter from these equations gives a re-
stricted system equivalent to n — 1 independent equations, the equation
of Sx whose order is n (m — n -f 1).
We can find the equations of those exceptional points where n -f- 1
consecutive Fn_xs intersect in a point, if we eliminate the parameter from
the n + 1 equations
a tm~n + (m — n) bm~n-1 +.... = 0
b t"1-" + O — n) c'"-"-1 + .... = 0
+ et + f=0.
The result is a restricted system equivalent to n independent equa-
tions; it is of order (n + 1) (m — n), which is the number of such
points, cusps on Si. We may verify this result by forming the resultant
of these (« + 1) equations. If we eliminate the variables from these
equations we have a determinant of order n + 1. If we expand this
result t enters to the degree (n + 1) (m — n) so that there are (n + 1)
(m — n) values of t tnat cause this resultant to vanish. These values of
t give the special points in question.*
Any double point on Sn_x must lie on two i^_2's. We may find the
equations of the total double spread on £„_!, by expressing the conditions
that the equations of an Fn_2 regarded as equations in the parameter,
have two roots in common. These conditions are t
a, (m - 1) b, i ^j '- c,
(I)
a,
('» - 1)
6,
b, (m — 1)
h,
(m — \)e,f
* For n — 3, these results agree with those of Salmon, Geometry of Three
Dimensions, p. 296. Neither the results there nor these hold when the system has
stationary (n — l)-flats.
t Salmon, Higher Algebra, art. 275.
132 PROCEEDINGS OP THE AMERICAN ACADEMY.
where there are 2 (m ■— 2) rows and 2 m — 3 columns. This restricted
system is of order | (2w — 3) (2 m — 4). The double spread repre-
sented by these equations consists of two distinct parts, Sn_2 and 2n_2.
The order of 2n_2 must be,
J (2 m — 3) (2 m — 4) — 3 (m — 2) = 2 (m — 2) (m — 3).
A triple point on Sn_i must lie on three Fn_2's. We may find the equa-
tions of the total triple spread on Sn_1 by expressing the conditions that
the equations of the Fn_2 have three common roots. These conditions
are expressed by means of a rectangular system similar in form to (I),
in which however there are only 2 (m — 3) rows and 2 m — 4 columns.
The order of the restricted system is
~ (2 m - 4) (2 m-b) (2 m- 6).
This triple spread consists of two distinct parts, Sn_3 and 2n_3. The order
of 2„_3 must be
1 2
-^(2m-4) (2m-5)(2m-6)-4(m-3)=-(m-3)(m-4)(2m-l).
o I o
In like manner we can find the equations of the total &-tuple spread
on Sn_u by expressing the conditions that the equations of the JFn_i have
Jc roots in common. These conditions are expressed by means of a
rectangular system similar to (I), in which, however, there are only
2 (m — k) rows and 2 m — h — 1 columns. This is a restricted system
equivalent to k independent equations, of order -r~j (2 m — k — 1)
(2 m — h — 2) . . . . (2 m — 2 k). This spread consists of two parts,
Sn_k and %n_k\ the order of the latter is
JL (2 m — k—\)(2m-k-2) (2 m — 2 k)- (k + 1) (m — k).
The total (n — l)-tuple curve on #„_! is given by means of a restricted
system similar to (I), in which, however, there are only 2 (m — n + 1)
rows and 2 m — n columns. We have then a restricted system equiv-
alent to n — 1 independent equations whose order is
(2 m — n) (2 m - n — 1) . . . (2 m - 2 n + 2).
(n - 1)
MORENO. — ON RULED LOCI IN W-FOLD SPACE. 133
The order of the curve 2 is,
— - (2 m — n) (2m — n — 1) (2 m-2n + 2) — n(m — n+ 1).*
(n — 1)1
The equations of all the w-tuple points on Sn_x are given by means of
a rectangular system similar to (I), in which, however, there are only
2 (jn — n) rows and 2 m — n — 1 columns. They form a restricted
system equivalent to n independent equations, whose order is
—. (2 m — n — 1) (2 m — n — 2) . . . . (2 m — 2 m) ;
n !
this is the number of w-tuple points. The number of the rc-tuple points
other than the cusps on Sx, are
— (2 m — n — 1) (2 m — n — 2) . . . . (2 m — 2 n) — (n + 1) (w — n).
These points necessarily lie on Si ; they are either n-tuple points on 2i,
or else they are n-tuple points on the combined curves Si and 2i. In
three-fold space the double curve on the developable may have tripl
points on it ; it can have no double points off of the cuspidal curve.
If m = n, then the order of Sx is n, and there are no cuspidal points
on the curve ; this is the rational normal curve of Veronese. f The
order of Sn_x in this case is 2 (n — 1) ; no developable Sn_x can be of
lower order unless it is a cone or conoid, for no curve of lower order
than n can lie in the n-fold space without at the same time lying in a
space of fewer than n ways.
Let us consider the case where m = p < n, where p is an integer.
Any p -\- 1 consecutive Fn_i& intersect in an Fn_p_i whose equations are
. A 9 A n 9pA .
If we use two homogeneous parameters X and /x instead of the single
parameter t, these equations may be written
* For n = 3, this result agrees with that in Salmon, Geometry of Three Dimen-
sions, p. 296.
t Veronese, loc. cit.
134 PROCEEDINGS OF THE AMERICAN ACADEMY.
in which form the parameter do longer appears. Any p -f 1 consecutive
i^_i's intersect in the same Fn_p_1 as any other consecutive p -f 1 ;
i. e., all the -Fn_i's of the system contain the same Fn_p_x. Any p-flat
that does not meet this Fn_p_l cuts S^_x in a developable (p — l)-spread
of order 2 (p — 1). This developable (p — l)-spread of order 2 (p — 1)
lying in a p-flat is exactly similar to the case in n-fold space where
m = n. The curve at the base of this system is of order p ; it is the
rational normal curve of p-fold space. Hence we may derive this system
by joining by lines all points of a developable (p — l)-spread of order
2 (p — 1) in a p-fold space, to all points of an (n — p — l)-flat that does
not meet the p-flat that contains the (p — l)-spread. Sn_1 is a conoid
of (n — 2)-flats with an (n — p — l)-way head. The generating Fn_2's
of Sn_i arise from the junction of the (« — p — l)-way head with the
generating (p — 2) -flats of the (p — 1) -spread. The generating Fn_s's
of Sn_2 arise from the junction of the (n — p — l)-way head with the
system of generating (p — 3)-flats of the (p — 2)-spread, and so on.
Any conoid ruled by a 1-fold infinite system of <?-flats with a (q — l)-way
head is a developable spread, but not so if it has only an r-way head
where r < q — 2. The latter spread is a developable only when the
consecutive ^-flats have (q — l)-way intersection. Any conoid ruled
by a 1-fold infinite system of (n — 2)-flats that have an (n — 3) -flat in
common is a developable, but if they have only an (n — £)-flat in com-
mon where k < 4, the conoid may or may not be developable. The
cones and conoids with a 2-fold infinite system of generators are not
developables at all.
The points of intersection of two consecutive generators are not in
general points of intersection of three generators. The equations of
a generator may be written
e+(m-1)d+(*'-iy™-2>c+ — o,
/+(m-1)c + ("-1H°'-2)rf+.,.. = o.
The points of intersection of three generators of the system are given
by the equations
MORENO. — ON RULED LOCI IN tt-FOLD SPACE.
135
(m-l) (m-2)
e, (m — 1) d, c,
e, (in — 1) of,
Q - 1) Qi» - 2)
/, (m — l)e, g- -f/,
= 0.
/, O - 1) «f •
where there are 2 (m — 2) rows and 2 m — 2 columns
For t = 0 we have the particular (n — 2)-flat
e = 0,f=0.
The next consecutive generator has for its equations,
e + 8t . d= 0
f+8t.e=0
The intersection of the two consecutive generators is the (n — 3)-flat
whose equations are
e = 0, /= 0, d= 0.
This Fn^ does not generally lie on the total triple spread for one of the
equations of that system, namely
(m — 1) (m — 2) c
(m — 1) d,
(m — 1) (m - 2) d,
(m — 1) e,
f,
= 0.
is not generally satisfied when the equations of the i^,_3 are satisfied.
The points that satisfy both these systems of equations are evidently
points on two consecutive generators and at the same time points on
three generators.
136
PROCEEDINGS OF THE AMERICAN ACADEMY.
If there is a linear relation between f, e, and d, then these two consec-
utive generators intersect in an (n — 2)-flat, i. e., they are coincident
and we have a stationary generator of the system. If
then
« = 0,
/=0
is the equation of a stationary generator of the system. The equation
of the developable Sn_i in this case is
(— 1H—2),
2!
/,
0,
0>d,(B>-l)(w-2)c
2!
0,
d,
0,
0.
"We see that / is a factor of the left member of this equation. When
this factor is thrown out, the residual or proper developable is of a
degree less by one than before. The orders of the multiple loci pre-
viously given are also reduced, they only holding when there are no
stationary ^_1,s in the system. By means of Veronese's formulae we
see that when there are /3 stationary F„_,'s the order of the A-way
developable is reduced from (m — X + 1) (m — n -\- X) to (?i — A -f- 1)
(m — n + X) — (n — X) (3.
6. Tangent flats to a ^-spread where 2 < p.
a. Definitions.
We have treated up to this point the various developables that arise
from a curve in ra-fold space. We shall show now that similar develop-
ables do not arise from the consideration of the tangent flats of spreads
of more than one way.
MORENO. ON RULED LOCI IN W-FOLD SPACE. 137
Let
£7=0
be the equation of an (n — 1) spread of order m. We shall use the
points (1), (2), A (1) + fi (2) to denote the points whose coordinates
are xx, yx, . . . wx, x2, y2, . . . w2, and \ xx -{- p x2, \yx -\- py., , . . .,
Xwx -j- \iw2, respectively, so that A (1) + ft (2) represents a point on the
line (12), i. e., the line joining (1) and (2). We denote the result of
substituting the coordinates of the points (1) or (2) in U by Ux, and U2
respectively. We use the symbols
( 9 9 9 \ Tt
A2 Ux = x, - h y, -, h • • • + »i n — Ux,
V 9 Xi 9xx die J
( 9 9 9 \
A U = [x2 — + y2 7r- + . . . + w2 ^—) Uj
\ a x 9 y dw)
f 9 9 9 \ rT
A U2=[X yr— + ^ h • . • + «> ^ Us,
\ 9x2 9y2 9w2J
(9 9 9 \k
^k2Ux~(x2^ h y2 ■= h • • • + «>2 s — tfi-
\ 9xx J 9yx <9wv
In the last case the operator is to be applied h times to f^. Now
A (1) + /i (2) is a point on the line (12), if it is also a point of the
(n — l)-spread, it must satisfy the equation of the spread. Substitute
the coordinates of A (1) + p (2) in Z7and we have
A"' Ux + A-1 M A2 Ux + ^T/i- A22 0i + . . .
u"1
. . . + —. A2ra Ux = 0.
m I
The m values of A: /u that satisfy this equation determine the m points
where the line (12) meets the (n — l)-spread. If the point (1) lies on
the spread then
t71==0.
If the line (12) meets the spread twice at the point (1), then
Ux = 0, A2 Ux = 0.
138 PROCEEDINGS OF THE AMERICAN ACADEMY.
The equation of the locus of all the Hues that meet the spread twice at
(1) is A Ux = 0.
From the analogy of three-fold space, this locus of lines is called the
tangent (n — l)-flat to the (n — 1) -spread, at the point (1).* At each
point of an (n — l)-spread there is in general a unique tangent (n — 1)-
flat.
A ^-spread is given by the equations,
V=0,
W=Q,
a restricted system equivalent to n — p independent equations. In a
similar manner the equations of the locus of all lines that meet the
jo-spread twice at any non-singular point (1) are,
A Ux = 0,
AV1=0)
A Wl = 0,
Since these equations are linear we may select any n — p that are inde-
pendent and the rest are superfluous. t We have then a ^?-flat which
from analogy is called the tangent p-flat to the p-spread at the point (1).
At any point of a ^-spread there is in general a unique tangent p-fl&t.t
We define a tangent r-flat at a given poiut of the jo-spread where
r < p as an r-flat that Jies in the tangent />-flat at that point and con-
tains the point. If r > p, we define a tangent r-flat at a given point
as an r-flat that contains the tangent ;>flat at that point. The locus of
tangent lines then to a ^-spread is simply the locus of tangent p-flats to
the spread. The locus of tangent planes, 3-flats, ...,(/> — l)-flats is
this same locus. If then there are developables that arise from a
jo-spread, where 1 < p their number is not so great as n — p — 1, for
* This proof is given in Dr. Story's Lectures on Hyperspace.
t Some of these equations may be satisfied identically ; this will be the case
when (1) is a multiple point on any of the {n — l)-spreads, but not a multiple point
on the p-spread.
t Dr. Story, Lectures on Hyperspace.
MORENO. ON RULED LOCI IN W-FOLD SPACE. 139
the tangent lines, tangent planes, tangent 3-flats, . . . , tangent jo-flats all
have the same locus. The planes through two consecutive lines, the
3-flats through two consecutive planes, etc., the ^>-flats through two
consecutive (p — l)-flats all have this same locus possihly of a certain
multiplicity.
b. Intersections of consecutive tangent flats.
We shall show further that (p -f l)-flats cannot in general be passed
through two consecutive tangent p-flats, for such p-^&ts do not in general
have (p — 1) -flats in common. Tangent ^o-flats at consecutive points
fi
of a j9-spread where 1 < p < - do intersect in points at least. Let
ft
v=o,
a restricted system equivalent to n — p independent equations be the
equations of the p-spread. Let
P' = (x1, y', . . . ) and P" = (xr + dx', y' + dy', . . . )
be consecutive points of the spread. The tangent jo-flats at these
points are
9 x' 9 y'
9 V 9 V
dx dy
and
A U" = A U< + x
/<?2 U' 92 U' \
\j* dx' + w*jsd' + ■■■■)= "•
{92 V 92 V \
All of these equations being linear, only n — p equations in each set can
be independent. In general, 2 (n — p) equations for such a value of p
have no common intersection. In the present case the resultant of any
n + 1 equations of the combined systems vanishes for any consecutive
points P' and P" on the ^-spread, so that no more than n equations of the
combined systems can be independent. Hence tangent ja-flats at con-
140 PROCEEDINGS OP THE AMERICAN ACADEMY.
secutive points of a ^-spread intersect in a point at least. Tangent
planes at consecutive points of a surface in w-fold space intersect at least
in points. These tangent planes do not generally intersect in lines
unless the surface lies in a space of three ways. Let us take p to repre-
sent the tangent plane at any point P of the surface and take p', p",
p'", ... to represent the tangent planes at the points P', P", P'", . . .
consecutive points of an infinitesimal closed curve about P. If p and p'
intersect in a line they determine a three-flat. If the consecutive tan-
gent planes intersect in lines, then p" has a line in common with both p
and p' and so p" lies in this three-flat. In a similar manner it can be
shown that p', p", p'" . . . , all the tangent planes consecutive, to p lie in
the same three-flat with it, i. e. a unicpue three-flat is determined at each
point of the surface that contains the tangent plane at the point and all
the tangent planes consecutive to it. Since however this three-flat is
determined by any two of these tangent planes, the three-flats corre-
sponding to P and P' any two consecutive points are the same. Take
now any curve through P that lies on the surface. Since the three-flats
corresponding to any two consecutive points of the curve are the same, it
follows that the three-flats corresponding to all the points of this curve
are the same. If we take a different curve through P the same thing is
true of the points of it. The three-flats corresponding to all the points
of these two curves are the same since they are all the same as the
three-flat corresponding to P. From this it follows that the whole sur-
face and all of its tangent planes lie in the same three-flat. Hence if in
general all the tangent planes consecutive to any tangent plane of a
surface lie in the same three-flat with it, then the whole surface lies in
this three-flat.
In the same way it may be shown that if in general all the tangent
planes consecutive to the tangent plane at any point of a surface lie
in the same four-flat with it that the whole surface lies in this four-flat.
Hence in w-fold space not only do the consecutive tangent planes of
a surface not intersect in lines, but all the tangent planes consecutive
to any tangent plane do not lie in the same four-flat with it.
c. The locus of the intersections of the tangent plane at any point
of a surface with the consecutive tangent planes.
In a four-fold space let the surface be given by
ry=o,
v=o,
MORENO. — ON RULED LOCI IN W-FOLD SPACE. 1-11
a restricted system equivalent to two independent equations. The
tangent planes at P' and P", any two consecutive points, have for their
equations
9W 9U>
9 x 9 y'
9 V 9 V
9x' dy'
and
LW, = AU, + x(^dxl + J^LiW + . ..) + .. .. = <>,
(9'2 V 92 V \
A V" = A V + x ~ dx> + ^-p^ dy' + ....+.... = 0
\9 x'~ 9 x' d y' I
Let us take the first two equations in each set to be independent, then
the rest are superfluous. Since P' and P" are points of the surface,
U' = 0
V =0
U"= U' + ^jdx' + = 0,
d x
9 V
V" = V + %^dx> + = 0,
dx
From these three sets of equations we derive
(92 U' 9'2 U' \
x[jx^ dx' + 9*9y-< dy' + ' ' ' 'J + * * • ' = °'
(d2 V 92 V \
x\9^dx' + d*w?d* + • • • ■) +■ • • • = °'
9J^dx> + .... = 0,
9x'
9 V
?rTrfar' + .... = 0.
dx'
These four equations are homogeneous in the five differentials dx',
d i/', . . . We may take one of these differentials to be zero and
eliminate the other four. We have
142
PROCEEDINGS OF THE AMERICAN ACADEMY.
92U>
;^^ + y
9x12
92V
X
X
1 + 9
92W
9 x' 9 y'
92V>
+
9x' 9y
9U'
9x>
9V<
Jx1
7 +
x
X
92U<
9 x' 9 y'
92V
9 x' 9 y'
92U>
9y'2
92V>
9U>
9y>
9 V
9y>
= 0.
This determinant and its derivatives vanish for the point P', therefore
the locus is a quadratic three-way cone with its vertex at PL This
cone is intersected by the tangent plane at P' in a pair of straight lines
which is the required locus. If a point x, y, . . . , be taken on either of
these lines, we have three independent equations just sufficient to deter-
mine the ratios of the four differentials ; i. e., just sufficient to determine
the consecutive point P", so that the tangent plane at this consecutive
point will intersect the tangent plane at P' in the point selected. That
these two consecutive tangent planes have no further intersection may
be further shown by forming the equation of the plane that goes through
their common intersection and through both the points P' and P". The
equations of this plane are
A" V .&U> - A" U' . A V = 0,
A' V" .AU"- A' U" .AV" = 0.
These equations in general represent a definite plane so long as P' and
P" are not coincident.
It would be of interest to examine the motion of the point of inter-
section along these lines as the point P" circles about the point P', and
to see whether at any time the consecutive tangent planes intersect in
one of these lines.
These lines are not inflexional tangents to the surface ; lines meeting
the surface in three consecutive points do not generally exist in a space
of more than three ways. For such lines would have to satisfy both
A U> = 0,
A V = 0,
and
A2 U> = 0,
A2 V = 0,
MORENO. — ON RULED LOCI IN W-FOLD SPACE. 143
These equations, however, in general have only the point P' counted
a multiple number of times in common. In general, then, in a space
of more than three ways a surface is so twisted that there are no lines
that meet the surface three times at a given point. This proof is easily
extended to a surface in a space of more than four ways.
d. The spreads that arise by considering the junctions of the
consecutive tangent flats.
Consider now any surface in rc-fold space. Draw the 2-fold infinite
system of tangent planes. Pass a four-flat through every two consec-
utive planes and there is a 3-fold infinite system of four-flats, form-
ing in general a seven-spread. Each four-flat is met by the infinity
of consecutive four-flats in the same plane. We may pass six-flats
through every two consecutive four-flats. There is a 4-fold infinite
system of six-flats constituting a ten-spread. This system of ruled loci
in no wise resembles the system of developables we derived from a
curve. Starting with a surface we cannot derive a system of develop-
ables in the same manner as when we start with a curve. The same
is true if we start with any ^-spread where 2 < p. Only in case the
©-spread lies in a (p + l)-flat do consecutive tangent p-flats intersect
generally in (p — l)-flats; the only exception is in the case the w-spread
is a curve.
II. Loci derived from an (n — 2)-flat whose Equation
involves a Single Arbitrary Parameter.
7. Description of the loci.
Let us consider next the system of loci represented by an {n — 2)-
flat whose equations involve a single arbitrary parameter. The parame-
ter may enter rationally or irrationally. If it enters rationally we
n
suppose it to enter to as high a degree as - iu each equation. Let the
equations of the flat be
.4 = 0, .5=0.
In these equations we suppose further that the linear function of the
coordinates that appear as coefficients of the various powers of the param-
eter cannot be expressed in terms of fewer than n + 1 linear functions
of the coordinates. Eliminate the parameter from these equations and
144 PROCEEDINGS OF THE AMERICAN ACADEMY.
we derive the equation of an (ti — l)-spread Sn_v which is ruled by the
system of (n — 2)-flats, F n_2s.*
Two consecutive Fn_2's intersect in an (?i — 4)-flat, whose equations
are,
^ = 0,^ = 0^=0,^ = 0.
The elimination of the parameter from these equations gives a re-
stricted system equivalent to three independent equations. The locus is
an (n — 3)-spread ruled by the Fn_f&. Sn_s is a double spread on S^_x.
Three consecutive Fn_2's intersect in an (ti — G)-flat Fn_6, whose equa-
tions are,
. 9 A 9" A
A = °>-9^ = °> 9X>=°>
9B_ 9*B_
If we elimiuate the parameter from these equations we derive a
restricted system equivalent to five independent equations. The locus
is an (n — 5)-spread S„_5, ruled by the F„^s. Sn_5 is a triple spread
on Sn_1 and a double spread on Sn_s .
Similarly r consecutive FH_2s intersect in an (n — 2 r)-flat Fn_2r, whose
equations are,
A A 5 A A 9r~1A A
„ A 9B A 9r-xB A
On the elimination of the parameter we derive a restricted system equiv-
alent to 2 r — 1 independent equations. The locus is an (« — 2 r + 1)-
spread, Sn_2r + V ruled by the Fn_2r,s. S„_2r + i is an r-tuple spread on
aS^j ; it is a multiple spread on other spreads of the system.
Two distinct cases arise according as n is odd or even. If n is odd,
n — 1
then — - — consecutive Fn_2s intersect in a line, F1} whose equations are,
* From now on we shall use Sk to denote the ^-spread of this system.
MORENO. — ON RULED LOCI IN W-FOLD SPACE. 145
. . 9 A 9^'A n
^ = 0,^ = 0,.. .-==,= 0,
B ft 3B-a ^B ft
B-0'ax-0'---s-T¥-°-
If we eliminate the parameter from these equations we derive a
restricted system equivalent to n — 2 independent equations. The locus
is a surface S2 ruled by the Fx's ; it is an ( — - — j-tuple surface on aS^.
Consecutive i^'s do not in general intersect for the n -\- 1 equations
0,
^ = o,|i = o;.
n— 1
9'*'A
9\2
B=0,3,f=0,.
a A
n—l
9* B
a— i
5 A"2"
o,
have not in general any common solutions. If we regard these n -f 1
equations as homogeneous in the n + 1 coordinates and form their result-
aut, the values of the parameter that cause it to vanish will give points
where consecutive lines meet. The equations of these points may be
formed by eliminating the parameter from the n + 1 equations, which
gives a restricted system equivalent to n independent equations. These
points are double points on S2 and ( — - — j-tuple points on Sn_x.
If n is even then — consecutive Fn_2'$ intersect in a point F0, whose
equations are,
. n 9 A 9**A A
A = 0, -=- = 0, . . . , — -j= 0,
2a
5 A"
n=2
2"
5 = 0,^ = 0,. ..,^=0.
° A 9 A 2-
The elimination of the parameter from these equations gives a restricted
system equivalent to n — 1 independent equations. The locus is a curve
10
146 PROCEEDINGS OF THE AMERICAN ACADEMY.
Si, which is an [ - J-tuple curve on Sn_i. There are not in general sta-
tionary points on >$i, for the n + 2 equations
n+l
.9 A 9'2'A
A = 0, ^— = 0, . . . , — ^r= 0,
<?A
9 A"2
3 i? 5~2 i?
R— 0 -— — 0 - — — 0
9\
9 A
have not in general any common solutions at all.
If the equation of the (u — 2) -flat involve k parameters connected by
h — 1 equations, the properties of the derived system of loci is the same
as in the case just discussed.
8. Mutual relations of the derived loci.
Two consecutive Fn_2s intersect in an Fn_v three in an Fn_$, r in an
71 • 1 71
Fn-o_ri — 5 — m aD -^ij ^ n 's odd, or - in an F0 if n is even. There is a
1-fold infinite system of each kind of flats. The Fn_2s are generators
of Sn_i, the F^s of *S„_3, the Fn__2rJs of «S^_2r+1. Let us consider the
case where rc is odd. Through any Fn_4 pass two consecutive Fn_2s,
n — 1
through any i?T„_2r pass r consecutive Fn_2's, through any Fx pass — - — ■
consecutive F„_2s. Any Fn_2 contains two consecutive i^n_4's, three con-
n — 1
secutive Fn_QS, — - — consecutive i^'s. Any Fn_2r contains two consecu-
Li
tive Fn_2{r+1),s, any two consecutive i^_2r's determine one -^,_2(r_i)'s. We
may then reverse the process and start with S.2, which lies in the space
of n ways but in no flat space of a less number of ways. Through each
two consecutive FiS of this surface pass three-fiats Fs's, these F3's will
generate a four-spread S„_4. Through each two consecutive F3's pass
five-flats ; this can be done as the i^_3's intersect consecutively in i^'s.
These five-flats will generate a six-spread S6. Finally, through each two
consecutive FH_Js> pass Fn_2s ; these Fn_2s generate an (n — l)-spread
Sn_i. If we start with the system of (n — 2)-flats we come down finally
to the surface, or starting with the surface we may work back to the
system of (ti — 2)-flats.
If n is even, through any Fn_± pass two consecutive Fn_2s, through any
71
Fn_2r pass r consecutive Fn_2s, through any F0 pass - consecutive F^_2s.
MORENO. — ON RULED LOCI IN W-FOLD SPACE. 147
Any Fn_o contains two consecutive F„_4's, three consecutive i^„_6's> o con-
secutive FqS. Any F„__2r contains two consecutive -^fTn_2(r+i)'s and any
two consecutive I,n_2r,s determine one FH_2{r_i) except in the case that
r = -. We cannot then start with a curve and retrace our steps ; two
consecutive points of the curve Si do not determine uniquely a plane of
the system. The i'Vs of the system in general intersect consecutively
in the points of Sv Starting with such a system of planes we may
retrace our steps. Through any two consecutive planes of the Sa we
may pass a four-flat. These four-flats are generators of S5. Through
any two consecutive B^s we may pass six-flats ; they are the generators
of S7. Finally through any two consecutive i^_4's pass (n — 2)-flats ;
they are generators of Sn_t. We may retrace our steps only in case we
do not begin with Sv
9. Director curves of the ruled (n — \)-spread.
Let the equation of such a ruled (n — l)-spread Sn_x be
0 = 0.
"We shall show that the equations of the generating flats of the spread
may be represented by linear equations involving a single parameter.
The equation in homogeneous coordinate of an arbitrary (?i — 2)-rlat in
n-fold space may be written
x = ax z + fix «+.... + 71 w
y — a2 z + /?2 s + . . . . + 72 w-
In this form the equations of the (n — 2)-flat, which we may call the
(n — 2)-flat AB, involve 2 {n — 1) independent arbitrary parameters.
These parameters must be connected by 2 (n — 1) — 1 equation to make
A B a generator of such an (n — 1) -spread. We wish to connect these
parameters in such a way that A B will be a generator of the Sn_i in
question. The equations of a curve on <£ are
<£ = 0, Ui = 0, u2 = o,... un_2=o.
If we eliminate the coordinates between these equations and the equa-
tions of A B we derive a single equation in the 2 (n — 1) parameters.
This resulting equation is the necessary and sufficient condition for A B
to meet the curve. In a similar way we may derive 2 (« — 1) — 1
such conditions and make -A B meet 2 (n — 1) — 1 curves on </>. If
from these 2 (n — 1) — 1 equations and the equations of A B we elimi-
148 PROCEEDINGS OP THE AMERICAN ACADEMY.
nate the parameters, we derive a single equation in the variables alone.
It is the locus of all the (n — 2) -flats that can be drawn to meet the
curves in question, and so it necessarily includes all the generating flats
of <jf>. It includes possibly other flats besides the generators of <j>, but in
this case the general locus will break up into several components, and one
component is <£. This is the case in three-fold space.
The spreads U^ U2, . . . Un_2 may in each case be taken to be flats ;
then the director curves are plane curves. These are the director curves
of <£; any or all of these curves may be plane, or they may be twisted to
any extent permitted by the space. Any 2 n — 3 curves in w-fold space
may be taken as the director curves of a ruled (n — l)-spread. In three-
fold space any three curves plane or twisted may be taken as the director
curves of a ruled surface. In four-fold space, any five curves plane or
twisted may be taken as the director curves of a ruled three-spread. In
this case the generating planes intersect consecutively in the points of a
sixth curve; so in four-fold space any five curves completely determine a
sixth. In five-fold space seven curves plane or twisted may be taken as
the director curves of a four-spread ruled by three flats. In six-fold
space nine curves determine a five-spread ruled by four-flats. Consecu-
tive four-flats intersect in planes and these in turn intersect consecutively
in points. So in six-fold space nine curves determine a tenth.
10. Multiple loci on the ruled (n — V)-spread.
Any generator of the (ii — l)-spread is an (n — 2)-flat Fn_2\ it is met
by any other generating Fn_2 in an (n — 4)-flat. If then 4 < n every
generator is met by every other generator. If n = 3, any generator is
met by only m — 2 other generators, m being the order of the surface.*
For 4 < n, any Fn_2 contains a single infinity of (n — 4)-flats where it
is met by the other Fn_2s. These are evidently double flats on &„_!• On
&„_! there are in general a 2-fold infinite system of such (n — 4)-flats
constituting a double (?i — 2)-spread, 2„_2 on Sn_x. In general, then, any
(n — l)-spread Sn_x ruled by (n — 2)-flats Fn_2s has on it such a double
(n — 2)-spread 2„_2 ruled by the 2-fold infinite system of (n — 4)-flats.
2„_4 has on it all those (n — 4)-flats, F^s that arise from the intersec-
tion of consecutive i^,_2's- These i^./s generate Sn_s, which therefore
lies on 2n_2 and forms but an infinitesimal part of it.
Any three Fn_2s intersect in an (n — 6)-flat; there are in general
a 3-fold infinite system of such (n — 6) -flats constituting an (?i — 3)-
* Salmon, Geometry of Three Dimensions, p. 427.
MORENO. — ON RULED LOCI IN W-FOLD SPACE. 149
spread 2„_3, a triple spread on S,^. Sn_5 lies on 2„_3, and constitutes
but an infinitesimal part of it. If n is sufficiently great there is a quad-
ruple (n — 4) -spread 2„_4 ruled by the 4-fold infinite system of (n — 8)-
fhits arising from the intersections of four Fn_2's. Sa_7 lies on Sn_5.
We can go on in this manner until we reach a limit due to the narrowness
of the space. If n is odd we have finally an f — - — j-tuple ( — - — )-
spread ruled by the f — - — Wold infinite system of lines that arise from
n — 1
the intersection of — - — generating i^4_2's. There may be further an
( — - — j-tuple ( — - — j-spread made up of the ( — - — j-fold infinite
system of points that are the intersection of — - — generating F^s, an
fn + 3\ , fn — 3\ , , , , n — 3 , , , . „ .
I — - — j-tuple I — - — j-spread made up of the — - — fold infinite
system of points that are the intersections of — - — generating -F„_2's,
etc., but these spreads do not always occur. In special cases the 2„_2,
or some component of it, may be of greater multiplicity than — - — •
M
In three-fold space a ruled surface generally has on it a double curve.
This double curve, or some component of it, may, however, be of
greater multiplicity than two. It is to be observed that Sn^ lies on
2„_2. In three-fold space this means that consecutive generators of a
ruled surface, if they intersect at all, must intersect in points of the
double curve. If n is even we have finally an ( - j-tuple ( - j-spread
2n that is made up of the ( - j-fold infinite system of points that
n
arise from the intersection of - generating Fn_.?s. There may be an
I - + 1 j-tuple f - — 1 j-spread 2„ whose points are points of inter-
section of - + 1 generating i^,_2's, an ( - + 2 j-tuple ( - — 2 j-spread
n
2n whose points are points of intersection of - + 2 generating Fn_2's,
etc., though these spreads may not always be present.
150 PROCEEDINGS OF THE AMERICAN ACADEMY.
11. Special case where the parameter enters rationally.
Let us consider the special case where the parameter enters rationally.
Let the equation of the generating (n — 2)-flat Fn_2 be
A = a tl + b t1'1 + c tl~2 + = 0,
B = a' r + b' r_1 + c> r~2 + .... = o,
where a, b, c, . . . , a', b', c', . . . , are linear functions of the coordinates
that cannot be expressed linearly in terms of fewer than n + 1 linear
functions of the coordinates. If we eliminate the parameter from these
equations, we have the equation of the £„_! ruled by the -F„_2's ; it is of
order I -\- m. It is more convenient in what follows to use two param-
eters, A and fx, that enter homogeneously into the equations.
Two consecutive generators intersect in the Fn_4 whose equations are
9 X 9 jx 9 X 9 /x
The elimination of the parameter from these equations gives a re-
stricted system equivalent to three independent equations the locus is
£n_3, whose order is
2 {I— 1) + 2 (m— 1) = 2 (Z+m — 2).
The order is found by expressing the conditions that the four equations
have a common root. The locus of the intersections of three consecu-
tive Fn_2's is a locus of F„_e's ; the equations of this locus are found
by eliminating the parameters from the equations,
3"-A 0^L_03M_0
ix a [x
9 A2 ' ' 9X9fx ' 9r2
92B _ 92B 92 B _
9X2 ~ ' 9\9fi~ ' 9fx2 ~
This gives a restricted system equivalent to five independent equations ;
it represents Sn_s, whose order is 3 (I + m — 4).
The r-tuple spread Sn_2r+i on £„_! is represented by the equations that
result from eliminating the parameters from the equations,
9" A r*A 3^
ir-1 — U> CI vr-2 Cl .. — U' * • * ' O ..r-1 U>
9X"'1 " ' 9kr~29fx ' ' * "'5
/•
9r~'B 9r^B 9r~1]3-o
9X^ ~ ' 9xr~29,x - u' • • • ' ^ "
MORENO. — ON RULED LOCI IN W-FOLD SPACE. 151
The equations then are of Sn_or+1 form a restricted system equivalent
to 2 r — 1 independent equations whose order is r (/ -f- m — 2r + 2).
As we have seen, there are two cases according as n is odd or even.
If n is odd we come down finally to an f — - — J-tuple surface S.
The equations of S2 are found by eliminating the parameters from the
equations
n-3 n-3 n-3
9~*'A_ 9'*' A 9~*'A
n=3 — ^' n-5 — O, . . . , n_3 — 0,
9X'2' QK'V'Qfi d/ir
n-3 n-3 n-3
n-3 — ^, n-S — "»•••} n-3 — 0.
2 A"2"" , 9\'* dp 9fiY
The equations of $2 form a restricted system equivalent to n — 2 inde-
n — 1
pendent equations, whose order is — - — (I + m — n 4-3).
Li
There are also f — — J-tuple points jP0's on Sn_u though in general
n 4- 1
— - — consecutive Fn^2's do not intersect. If we form the resultant of
the n -f- 1 equations
n-l n— 1
52~J rt 9^'A
—^i = 0, — ^ = 0, .
3 A 2 9 k 2 9 ft
n—l n—1
5A.2 3 A. 2 5 //.
n-l
J w-l -
= 0,
n-l
9'^ B
3/x 2
= 0,
we have a determinant of the (w + l)-st order, in which the parame-
ters e
n + 1
n 4- 1
ters enter to the degree — — — (l 4- m — n -\- 1). There are then
(I + m — n -\- 1) valujs of the parameters that cause this
Ld
determinant to vanish, and so this is the number of points F0. We
can find the equations of these points by eliminating the parame-
ters from these «4 1 equations. The result is a restricted system
equivalent to ii independent equations. The order of the system is
ii 4- 1
— - — (I 4- m — ii 4- 1). This is another proof of the number of
points F0 on Sn_i.
152
PROCEEDINGS OF THE AMERICAN ACADEMY.
In case n is even we have finally the f — J-tuple curve whose equations
are found by eliminating the parameters from the equations,
n-2
3-~ A
n-2 —
2 A"2
n-2
9^'A
o» -^— = o, .
9\2'9/x
n-2
ST A
• • 5 n-2 — UJ
5 fX.'2
n-2
9^'B
n-2
9 k2'
n 9^' B
o, n< = o, .
5a2 9 /ji.
n-2
9 ft 2
«
The order of the restricted system is - (I + m — n + 2), the order
of 8V.
We find the equation of the double spread 2„_2 on *S'„_1, by imposing
on the equations of the generating Fn_2 the conditions that they have two
common roots in the parameter. These conditions are,*
a, b, c =0
b, ....
(")
a,
a'
b', e',
< V,
where there are I -\- m — 2 rows and I -\- m — \ columns. This is a
restricted system equivalent to two independent equations ; the order of
the system is \ (J + m — 1) (I -\- m — 2). On 2„_2 must be Sn_o. We
find the equations of 2„_g by expressing the conditions that the equations
of the generating flat have three common roots in the parameter.! The
result is a restricted system similar in form to (II), in which, however,
there are only I + m — 4 rows and / + m — 2 columns. This restricted
system is equivalent to three independent equations, and its order is \
(I + m — 2) (/ + m -3) (1+ m — 4).
The equations of 2„_r are found by expressing the conditions that the
equations of the generating (n — r)-flat have r roots in common. By an
extension of the previous method we derive a restricted system of the
same form as (II), in which, however, there are only I + m — 2 (r — 1)
rows and I -\- m — (r — 1) columns. This is a restricted system equiva-
* Salmon, Higher Algebra, Art. 275.
tlbid., Art. 285.
MORENO. — ON RULED LOCI IN W-FOLD SPACE. 153
lent to r independent equations, the order of the system is — - (I + m —
r !
r + 1) (Z + m — r) . . . . (Z -f m — 2 r -f- 2).
Whether n is odd or even we have finally a curve 2i of multiplicity
n — 1, whose equations are found by expressing the conditions that
the equations of the generating (n — 2) -flat have n — 1 roots in the
parameter in common. We derive a restricted system of the same
form as (II) in which however there are I + m — 2 (n — 2) rows and
I + m — (n — 2) columns. The order of this system is —
V ; * (n - 1)1
(Z+ m — n + 2) (Z + m — n + 1) . . . . (I + m — 2 n + 4). This curve
has M-tuple points on it whose equations are fouud by expressing the con-
ditions that the equations of the generating (n — 2)-flat have n roots in
common. We again have a restricted system of the same form as (II),
in which, however, there are I -\- m — 2 (« — 1) rows and I -f- m — n + 1
columns. The order of this system is — - (I -\- m — n -\- 1) (I + m — n)
. . . . (I + m . 2 n + 2), which is the number of points in question. For
n = 3 these formulae for the order agree with those given in Salmon.*
A very special case is where the parameter enters only linearly in one
of the equations of the generating (n — 2)-flat. Let the equations of the
flat be
A = a t + b = 0,
B = a' tm + V r-1 + . . . . = 0,
where we make the same suppositions regarding a, b, a', b', . . . , as
before. The Sa_t in this case is a ruled spread with m sheets through
the (n — 2)-flat, whose equations are
a = 0, b = 0 ;
it has no other multiple locus on it at all. Consecutive generating -F„_2's
of the system intersect in the flat, whose equations are,
9 B
a = Q,b = 0,B= 0, V- = 0.
at
All the F^s of the system lie in the same (« — 2)-flat ; they generate a
developable (n — 3)-spread «S'„_3 in this flat. S'n^> is the section by this
flat of the developable (n — l)-spread enveloped by the (n — l)-fl;it B.
Consecutive generating F^'a of Sn^ intersect in generating -F„_4's of
* Salmon, Geometry of Three Dimensions, p. 428.
154 PROCEEDINGS OF THE AMERICAN ACADEMY.
<S'„_3. By means of an (n — 3)-way developable lying in an (n — 2)-flat
and two arbitrary curves we can generate a ruled (a — l)-spread by
taking all the (n — 2)-flats that can be drawn through the enveloping
(n — 3)-flats of the developable so as to meet both curves.
We have seen that the section of an (n — l)-way developable by an
(n — l)-flat gave an (?i — 2) -way developable of the same nature, so
here the section of an (n — l)-spread ruled by (n — 2)-flats by an
(n — l)-flat gives an (n — 2)-spread of the same nature as the (n — 1)-
spread.
III. Loci derived from an (?i — &)-flat whose Equations
involve a Single Arbitrary Parameter.
12. Description of the derived loci.
We shall complete the general theory by considering the locus of the
1-fold infinite system of (n — &)-flats, where 2 < £ whose equations all
contain a single arbitrary parameter. Let the k equations of the flat be
A = 0, B = 0, . . . , G = 0.
The equations of the locus of these i^^'s are found by eliminating the
parameter from these equations. The result is a restricted system
equivalent to k — 1 independent equations.
The locus is an (n — k + l)-spread 5„_HI ruled by the F„_k'a. Any
two consecutive i^'s intersect in an (n — 2 £)-flat Fn_2k whose equa-
tions are
A-O.g-O.B-O.g-O,
If we eliminate the parameter from these equations, we derive a restricted
system equivalent to 2 k — 1 independent equations. The locus is an
(n — 2 k + l)-spread *S,„_2i+i ruled by the Fn^2ks ; it is a double spread
on S„_k.
Any three consecutive Fn_2k'a intersect in an (n — 3 £)-flat Fn_3k whose
equations are,
The elimination of the parameter from these equations gives a restricted
system equivalent to 3 k — 1 independent equations. Their locus is an
(,a _ 3 h -}- l)-spread ruled by the F^-^s. Sn_ok+l is a triple spread on
MORENO. — ON RULED LOCI IN W-FOLD SPACE. 155
The equations of the locus of the intersections of r consecutive Fn_ks
are found by eliminating the parameter from the equations
9 A 9^ A
*=o>ff=o>
case we come
This gives a restricted system equivalent to r k — I independent equa-
tions. The locus is an (n — rk -f l)-spread ruled by the Ftl_rk%, it is an
r-tuple spread on Sn_k+1.
There are k cases according as n = 0 (mod k), n = 1 (mod £), . . . ,
n = k — 1 (mod k). In the first case we come finally to a curve St
which is an ( y- j-tuple curve on S„_k+l. In the second
down finally to a system of lines F^s which are generators of a ruled
surface S2. In the last case we come down finally to a ^-spread ruled by
(k — l)-flats. There are on Sk in general special points where two con-
secutive Fk_i's intersect.
13. Multiple loci on the spread; mutual relations of the system of
spreads.
Sn-k+\ nas on it m general multiple loci that arise from the intersection
of non-consecutive Fn_ks. Any Fn_k intersects every other Fn_k in an
(n — 2 £)-flat ; there is in general a 2-fold infinite system of such
(« — 2 £)-flats constituting a double (n — 2 k + 2)-spread 2„_24+2 on
Sn-k+i- Evidently Sn_2k+1 lies on 2n_2fcf2- Any three Fn_k'B intersect in
an (n — 3 £)-flat ; there is a 3-fold infinite system of such (n — 3 k)-
flats, they constitute in general a triple (n — 3 k + 3)-spread 2n_3A.+3 on
'S'n-A+i- Sn_Sk+1 nes on %n-sw Any r consecutive Fn_k's intersect in an
(n — r k)-i\at ; there is an r-fold infinite system of such (n — r£)-flats
in general, constituting an r-tuple (n — r k + r)-spread 2„_rjbfr on S„_k+U
on which lies Sa^rk+V
Finally the locus of the intersection of any a Fn_k's where a is the
n
greatest integer in T is an a-tuple [n — a (k — l)]-spread ln_a ll_1) on
<Stl-k+i ; it is ruled by the a-fold infinite system of (n — a £)-flats.
The question arises, When, in general, do these double loci cease to
exist? The double spread is in general an (n — 2 k -f- 2)-spread 2n_2it+2.
To have a continuous locus of double points we must generally have
156 PROCEEDINGS OF THE AMERICAN ACADEMY.
n + 1
n
2 k + 2% 1 or £ ^
For values of k that satisfy this condition there is in general a continuous
locus of double points. If
rc-2&+2 = 0, ov k = ^i-=
there is in general only a finite number of double points on the locus. If
n — 2k+2<0,ork> n^^-
there are in general no double points on the locus.
If there enter into the equations of the generating (n — £)-flat p
parameters connected by p — 1 equations the properties of the system of
related loci will be similar to those of the system just described.
Any two consecutive Fn_k's intersect in an Fn^2k while through any
Fn__<2k pass two consecutive F„_^a. Any three consecutive Fn_ks intersect
in an Fn^,k while through any F„_ok pass two consecutive Fn_2ks and
three consecutive Fn_ks. Any two consecutive Fn_rks determine in
general one Fll_k(r_l). An exception may occur if r = a the greatest
n
integer in -=• • Thus, if n = 0 ^mod k), two consecutive points of ^ do
rC
not determine a (k + l)-flat where 2 < k.
If n = 1 (mod k), two consecutive lines of S-2 do not determine a
(k + l)-flat, except in the case k — 2. In the last case, however, where
n EE k — 1 (mod k), two non-intersecting (k — l)-flats do determine a
(2 k — l)-flat. Only in this last case can we retrace the steps if we
come down to the last spread. We can always retrace the steps if we
do not come down to this last case.
14. Director spreads of the ruled spread.
The equation in homogeneous coordinates of any (n — £)-flat, 2 < k,
may be written
x = ai s + & t + . . . . + yx w,
y = a2 * + (3o t + . . . . -f y2 w,
z = akS + (3kt +.... + ykW.
In this form the equations of the flat contain k (n — k -f 1) independent
parameters. These parameters must be connected hy k(n — k + 1)— 1
equations for this (n — £)-flat to be a generator of such a ruled
(n — k -f- l)-spread. Any curve is given by the equations
MORENO. — ON RULED LOCI IN W-FOLD SPACE. 157
x = °,
• t • •
a restricted system equivalent to n — 1 independent equations. If we
eliminate the coordinates between the equations of the flat and curve, we
derive a restricted system equivalent to k — 1 independent equations in
the parameters alone. These are the conditions that must be satisfied
for the (n — &)-flat to meet the curve. In a similar way we may derive
a restricted system equivalent to k — p independent equations in the
parameters alone which are the necessary and sufficient conditions for
the (n — &)-flat to meet a certain ^-spread where 1 < p < k — 1. We
may have then curves, surfaces, . . . , or ^-spreads where 1 < jt> < & — 1
for the director loci of a ruled (« — k + l)-spread. The numbers of loci
of each kind that must be taken are A, p., ... v, p, namely, non-negative
integers chosen to satisfy the equation
A (k — 1) + ix (k — 2) + . . . . + v . 2 + p ■ 1 = k (n — k + 1) — 1.
If we consider a group of one or more points as a director locus of the
spread, we have to select integers to satisfy
k . k + A (k — 1) + . . . . + p ■ 1 = k (n — k + 1) — 1.
We may apply this to special cases. The director loci of a ruled surface
in three-fold space are three curves. We may take one curve and a
group of k points, in which case the ruled surface is reducible and has for
its components k cones whose vertices are the k points and whose
common base is the curve in question. In four-fold space the director
loci of a ruled surface may be five surfaces, three surfaces and one curve,
or one surface and two curves. The ruled surface in each case consist-
ing of all the lines that can be drawn to meet all the director loci. In
the same space the director loci of a three-spread ruled by planes may
be taken to be five curves.
If the director loci be all taken on any Sn_k+1, then the locus of all the
(n — £)-flats that can be drawn to meet these director loci will include
as one of its components the Sn_k+i in question ; it may or may not
have other components.
There are several special cases illustrative of these methods that can
be worked out in still greater detail. Some of these I hope to make the
subject of another paper.
Proceedings of the American Academy of Arts and Sciences.
Vol. XXXVU. No. 6. — September, 1901.
THE ARC SPECTRUM OF HYDROGEN.
By O. II. Basquin
With Two Plates.
Investigations on Light and Heat made and published wholly oe in part with Appropriations
FROM THE RllMFORD FUND.
THE ARC SPECTRUM OF HYDROGEN.
By O. H. Basquix.
Presented by C. R. Cross. Received June 8, 1901.
The Problem.
The arc spectra of those elements which are gases at ordinary tem-
peratures and pressures have not been extensively studied. Their spark
spectra, however, are easily obtained, and were among the first to be in-
vestigated. The general impression prevails, therefore, that these ele-
ments do not possess arc spectra. On the other hand practically all the
so-called "hot stars" and all the "new stars" possess the more impor-
tant lines of the hydrogen spectrum. Although our knowledge of what
is going on in the arc and in the spark is very crude and unsatisfactory,
yet it is, to the average mind, much easier to imagine a star as being in
a condition similiar to that of the arc, rather than in one similar to that
of the electric spark. It has seemed worth while, therefore, to search for
the more important lines of hydrogen in the arc spectrum. This is the
problem of the following investigation.
Historical.
Liveing and Dewar* examined the carbon arc in an atmosphere of
hydrogen and saw "the fairly bright" C line of hydrogen, also "a faiut
diffuse band " at the position of the F line of hydrogen. They obtained
these two lines also by allowing small drops of water to fall into the arc
in air.f They found the F line usually obscured by continuous spectrum,
becoming visible at intervals only, when, from some variation in the work-
ing of the arc, the continuous spectrum was less brilliant. Crew and
Basquin t incidentally noticed these two lines of hydrogen while work-
ing with the rotating metallic arc in an atmosphere of this gas.
* Proc. Roy. Society, 30, 156 (1880). t Ibid., 35, 75 (1883).
t Proc. Amer. Acad., 33, 18 (1898).
VOL. XXXVII. 11
162 PROCEEDINGS OF THE AMERICAN ACADEMY.
Apparatus.
In searching for these lines I have employed the rotating metallic arc »
wh"h s'one to nse chemically pnre electrodes having httle or no
rhemical reaction with the gas employed. In this arc, then, one my
exne the gas to give off its characteristic radiations with greater m-
ensi v han "n one where the gas may enter into chemtcal compounds
W re a temperatnre is reached at which it becomes lum.nou. Tins ar
enables one also to select snch metals as do not have strong hues m the
neighborhood of the lines sought for, while in the spectrum of the carbon
arc there arc few spaces not already ocenpied by lines of carbon or of an
Tie rotating arc, one electrode, either a disc or a rod of meUjl
rotates npon an axis, making abont 700 rotations per minute, while the
o her electrode has a slow movement of translation toward U-».. f
rotation The rotation not only prevents the excessive heating and
weTdtng together of the electrodes, bat it throws the hot gases to one
Tide o° thai the arc has the appearance of a small fan. The part of the
tne tl separated from the poles is very free from continuous
SPTnTe apparatus used in these experiments the arc is enclosed in a
brass box or ■ « hood," having a volume of about 1* litres and being corn-
el ivly .as-tight. The light from the arc issues through a long bras
LTdosed with a lens at the outer end ; the lens thus forms part of the
S of the hood, but is so far removed from the arc that it receives »m-
parativel, little of the deposit sometimes formed inside the hood, and
hence remains clean. lnnT,0[! -f _t
A stream of gas enters the hood at one stop-cock and leaves ,t at
another- a third cock is provided for nttachment to a manometer A -
1th the hood is not absolutely gas-tight, the purity of the gas inside
preserved in these experiments, partly by the small excess of pres-
Tre i id tie hood above that outside, and partly by the fresh supply of
;ue gas constantly running through the hood. The hydrogen used w
generated electrolytically, and varied in quantity from 10 to lo hues
^ThTspectra have been examined both visually and P»bical,y
by means of a small plane grating spectroscope and by means of a large
concave grating spectroscope.
* Crew and Tatnall, Phil. Mag., 38, 379 (1894).
BASQUIN. — THE ARC SPECTRUM OP HYDROGEN. 163
Observations of Hydrogen Lines.
The arc spectra of the following metals in hydrogen have been ex-
amined : Aluminium, copper, magnesium, coin-silver, sodium, tin, and
zinc. With the exception of sodium the arc of each metal shows to the
eye very clearly the Ha and ILj lines of hydrogen, and in most of them
the H? line comes out with the small instrument very clearly, and in-
distinctly with the large one. The H5 line shows only rarely, and then
to the eye rather indistinctly. The IIa line is quite sharp and well de-
fined, unless the electric current through the arc is unusually great ; it
has much the same appearance as the zinc line at 6363. The other three
are always broad, hazy, and ill-defined.
On the photographs taken with the large spectroscope H^ and IIV
usually show very plainly, always excepting the spectrum of metallic
sodium, while H5 shows in spectra of tin, silver, and copper. On
photographs taken with the small spectroscope -these lines show more
sharply, on account of the very much smaller dispersion, and the photo-
graphs of tin show the next hydrogen line, He quite clearly. Not hav-
ing found the hydrogen lines in the metallic sodium arc (using copper as
stationary electrode), I tried it in dry hydrogen also, thinking that in
some way the water vapor might have affected the appearance of the
hydrogen lines, but I have been unable to detect any of the hydrogen
lines in that arc in any way.
None of these lines excepting Ha is sharply defined. A wide space
in the middle of each line has fairly uniform intensity, shading off gradu-
ally and uniformly to each side. The following table gives a rough
estimate of widths, in Angstrom units, of these lines as they appear on
the photographic plates, the middle of the shading being taken as the
edfre of the line.
Line.
Ha
Hy
Hs
IIe faint, same general width.
It will be noticed that these lines, with the exception of TTai are exces-
sively wide, and I think it is for this reason alone that I have been
unable to photograph the still weaker hydrogen lines of Balmer's series.
imum width.
Minimum
width.
Mean width
6
4
5
65
13
31
44
14
26
32
12
20
164 PROCEEDINGS OF THE AMERICAN ACADEMY.
They may appear upon the plates, but are so wide and so faint that they
cannot be detected upon the general shading of the plates.
That these lines are not merely spark lines introduced into these arc
spectra by the supposed spark at the breaking of tbe current through the
rotating arc is shown, first, by the fact that they were first observed in
the carbon arc, and, second, by the fact that I have seen Ha and Hp quite
clearly in the magnesium metallic arc, when the poles were not rotating.
The lines produced in the stationary arc have much the same character
as in the rotating arc, but there is a large amount of continuous spectrum,
appearing as a background, in the case of the stationary arc, so that it
would be difficult to photograph the hydrogen lines in this way.
These lines in the arc seem to be due to hydrogen, and not to water
vapor coming from the hydrogen generators.* This is shown by the fol-
lowing two experiments : (1) I passed the stream of hydrogen through
concentrated sulphuric acid and phosphorus pentoxide ; and even after the
stream of dry gas had. been running through the hood for three hours, I
found the Ha line as bright as it was in the damp hydrogen coming
directly from the generators. (2) In place of the current of dry hydro-
gen, I passed through the hood a stream of air bubbling through warm
water, so that this air was charged with moisture to about the same
degree as the moist hydrogen coming directly from the generators. In
this case I was not able to detect the faintest trace of the Ha line.
Magnesium poles were used in both the above experiments.
Other Methods.
I have examined some of these metals in commercial ammonia gas,
such as is used in refrigeration. In this gas the hydrogen lines come out
with nearly the same intensity as in hydrogen when copper or aluminium
electrodes are used; no hydrogen lines are seen in the sodium arc in
ammonia, although the arc works well, and when tin electrodes are used
in ammonia a black dust collects in the atmosphere about the arc to such
an extent as to shut off practically all the light within thirty seconds after
starting the arc. From the standpoint of convenience and safety, the
ammonia gas is much to be preferred to hydrogen.
The copper arc in coal gas shows the Ha line very clearly, but the
other hydrogen lines are not distinguishable on account of the multitude
of comparatively strong carbon lines which the coal gas furnishes in this
part of the spectrum.
* Trowbridge, Phil. Mag., 50, 338 (1900).
BASQUIN. THE ARC SPECTRUM OP HYDROGEN. 165
Following the suggestion of Liveing and Dewar, above referred to, I
have tried the rotating metallic arc in air, playing a very small jet of
water upon the rotating electrode. In this manner the silver arc works
rather more poorly than usual, and resembles a rapid series of small
explosions. The hydrogen lines come out clearly, but are rather weaker
and more diffuse than in the hydrogen atmosphere.
The copper arc works well in an atmosphere of steam, much better
than in hydrogen. The hydrogen lines are nearly, if not quite, as strong
in steam as in hydrogen. The electrodes of the arc are slightly oxidized
and have very beautiful colors. In making this experiment a slight
alteration was necessary in the hood of the arc. The window through
which the light issues is usually as far away from the arc as possible, but
it was moved for this experiment so as to be as close to the arc as pos-
sible. It was placed at the inner eud of a brass tube projecting into the
hood, in order that the heat of the surrounding steam and hot air, as well
as that of the arc itself, might prevent condensation of steam upon the
surface of the window.
CHEMICAL ACTION IN THE ARC IN HYDROGEN.
Historical.
Crew and Basquin * have sought to eliminate the radiations due to
chemical causes in the electric arc by using chemically pure metallic
electrodes and enclosing the arc in an atmosphere of hydrogen or nitro-
gen. They interrupted the current through the arc about 110 times per
second and examined the light of the arc while the current was null.
They found in the rotating metallic arc in air " a luminous cloud " per-
sisting for several thousandths of a second after the current through the
arc had ceased, but they found no such luminous effect in an atmosphere
of hydrogen or nitrogen. This seems to show that the cloud is due to
chemical action going on in the gases after the electric current has
stopped, and that in hydrogen the chemical action is too feeble to be
noticed in this way.
Liveing and Dewarf found a magnesium "line" at 5210, making its
appearance in the arc spectrum only upon the introduction of hydrogen
or coal gas into the arc. Professor Crew t gives a number of lines ap-
pearing in the iron arc in hydrogen and not appearing in the arc in air.
* Proc. Amer. Acad., 33, 18 (1808).
t Proc. Roy. Society, 30, 96 (1880).
t Phil. Mag., 50, 497 (1900).
1G6 PROCEEDINGS OF THE AMERICAN ACADEMY.
Hydrogen-metal Flutings.
With the exception of tin, every metal thus far examined in the
rotating metallic arc in hydrogen gives a characteristic set of spectrum
Hues which are not found in the arc in air. Inasmuch as compounds of
hydrogen with some metals are known, I have, in lieu of a better hypoth-
esis, supposed that these lines are due to such compounds formed in the
arc. No new isolated lines, surely due to hydrogen, have been found.
The following description takes up the metals in the order of the relative
intensities of these flutings.
Tin.
No fluting has been discovered due to a combination of tin and hydro-
gen. There are four lines of intensity \ on Rowland's scale, at ap-
proximately 3715, 3841, 4245, and 4386, which have not yet been
identified. These may be weak tin lines not listed, or weak impurity
lines. The deposit which is formed in the hood enclosing the arc is very
small in amount and of a greenish color, and consists of very small
globules. If this deposit is heated upon platinum foil in a Bunsen flame
it quickly glows, and thereafter has a slate color ; and if this powder is
placed in hydrochloric acid it dissolves when heat is applied and gives
off bubbles of gas. If the dark powder, after the first heating, is reheated
on foil in the flame, it glows again, apparently at a higher temperature
than before, and then becomes a very white powder, both of which ex-
periments go to show that the original powder is not metallic tin but is
possibly some combination of tin and hydrogen.
Coin Silver.
This metal gives a delicate fluting with first head at 3333.86 and run-
ning toward longer wave lengths. There are only about fifty lines in
this fluting, and they have an average intensity rather less than h on
Rowland's scale.
Copper.
This metal gives a rather open fluting, having the head at 4279.77 and
running toward the longer wave lengths. The number of lines in this
fluting is about sixty, and they are individually stronger than those of the
coin-silver fluting. This fluting makes its appearance also when an
atmosphere of ammonia or of steam is used. The deposit formed inside
the hood is rather small in amount and of a brown color. The following
table gives the wave lengths of the hydrogen-copper flutings : —
BASQUIN. — THE ARC SPECTRUM OF HYDROGEN.
167
Wave
lengths.
4279.77
4280.72
4281.25
4281.85
4282.48
4283.38
4284.15
4285.26
4287.58
4290.25
4293.45
4294.86
4296.98
4298.55
4300.92
4302.63
4305.24
4307.07
4309.98
4311.89
4315.12
4317.07
4820.68
4322.74
4324.59
4320.61
4328.77
4331.38
Intensity.
Remarks.
>vave
lengths.
Intensity. Remarks.
2
head.
4332.98
1-
1
4335.20
1+
1+
ghost of 4275?
4339.80
1-
1+
4341.98
1+
i
2
4347.06
1-
1+
4349.13
1+
\
4354.59
1-
1+
4356.73
1+
1 +
4364.68
1+
1 +
4373.01
1+
1+
4381.70
1 +
1-
4382.92
2 hazy
1+
4384.74
1-
1-
4390.
very indistinct,
1+
4390.85
1+
1 +
4400.30
1+
1+
4405.04
1-
1 +
4410.12
1+
1
4413.09
1
2
1 +
4420.42
1+
1
4421.59
1-
2
slight shading toward
4430.94
1
1-
[blue.
4436.48
1
1
4447.18
i
1+
4453.30
i
1
4158.03
i
1+
4465.01
i
i
j
hazy.
4477.15
i
Aluminium.
The aluminium arc in hydrogen gives a beautiful fluting with first head
at 4241.26 and running toward longer wave lengths. This fluting ap-
pears equally well in an atmosphere of ammonia. The following table
gives the wave lengths and intensities of the principal lines : —
lengths, ^tensities.
Remarks.
lengths. Intensities.
Remarks.
4241.26
3
1st head.
4218.09
2
4241.75
3
4249.68
2
4242.41
2
4250.34
1
4243.10
2
4251.44
2
4243.94
3
wide.
4253.26
2
4245.32
4
4255 22
2
4246 58
3
4257.35
1+
4217.58
1
4259.71
3
wide, 2d head
1C8
PROCEEDINGS OF THE AMERICAN ACADEMY.
■\Vave
lengths Intensities- Remarks.
lecths Intensities. Remarks.
4261.18
3
4315.57
3
4261.77
3
4320.63
3
42G2.59
3
4326.00
5
4263.50
3
4331.91
2
4264.58
3
4338.37
2
4265.80
3
4345.34
1
4267.24
3
4353.38
2
4268.86
3
4354.13
4270.68
3
4355.17
4272.72
3
4356.64
4274.98
5
impurity here.
4361.30
4277.70
4
impurity here.
4362.21
4280.67
4
4363.50
4283.94
4
436518
2
4287.30
2
3d head?
4367.21
2
4287.75
3
4368.
i
2
4289.91
3
4369.67
2
4290.68
2
4371.49
i
2
4292.01
2
4372.54 •
1
4294.31
3
4375.18
\
4296.99
2
4375.97
1
4298.10
3
4379.19
1
"2
4302.08
3
4379.90
i
4302.65
1
4388.23
1
4306.34
3
4393.42
1
4310.82
3
M
4399.19
&.GNESITJM.
1
impurity superposed.
4th head.
The magnesium arc in hydrogen gives the three flutings discovered by
Liveing and Dewar * in the magnesium-hydrogen spark, with first heads
at 5618, 5210, and 4849, and running toward the shorter wave lengths.
The fluting at 5210, which is the cme showing the plainest on my photo-
graphs, is made up of such very fine lines near the heads that the princi-
pal head appears like a line by itself; but farther away from the heads the
lines seem to become stronger and to overlap one another, so that many of
these lines are much stronger than the head itself and their distribution
seems quite irregular. I mention this more particularly because it is
characteristic of the hydrogen-zinc and hydrogen-sodium flutings de-
scribed below. I have noticed that in the spark, the intensity of the
magnesium flutings is greatly increased with respect to that of the "b"
group by the introduction of inductance in series with the capacity
* Proc. Roy. Society, 32, 189 (1881).
BASQUIN. — THE ARC SPECTRUM OP HYDROGEN. 169
shunted about the induction coil. The deposit iu the hood enclosing
the magnesium arc in hydrogen is quite plentiful, has a dark slate
color, decomposes water at ordinary temperature, giving alkaline reaction,
and oxidizes rapidly on heated platinum.
Zinc.
The zinc arc in hydrogen gives a collection of lines between 4300 and
4050, having an average intensity from 2 to 4, and not found in the arc
in air. This appears to be a set of flutiugs of complicated structure
having heads less distinctly marked than usual and running toward the
shorter wave lengths. The semi-opaque deposit formed in the atmos-
phere of the hood is so considerable that a current of not more than
about four amperes can be used. This deposit is dark brown in color,
gives alkaline reaction in water, but does not decompose it enough to
form bubbles even when heated. It dissolves completely in sulphuric
acid, forming a clear solution, and rapidly oxidizes on heated platinum.
Sodium.
The sodium spectrum was obtained by using metallic sodium as the
cooler rotating electrode and copper as the stationary one. As above
mentioned, there is not the slightest trace of any of the hydrogen lines to
be detected in this spectrum either visually or on the photographs, but
there is a strong series of lines between 5000 and 3800, resembling the
hydrogen-magnesium series in character. This is probably a complicated
fluting of heads less clearly marked than usual and running toward the
shorter wave lengths. A compound of sodium and hydrogen is already
well known. The formation of the semi-opaque deposit in the atmos-
phere of the hood is so considerable that the arc can be run only about
five minutes at a time. I have not tried the sodium arc in air.
The sodium spectrum obtained in hydrogen is itself quite interesting.
All the sodium lines given by Kayser and Runge* come out very clearly,
but the principal interest centres about the D lines, which are very in-
tense, and so wide as to cover all the region between them. "When
observed visually their reversals change in width quite rapidly. At first
these reversals may be quite narrow black lines, and then they quickly
widen and blot out the whole of the bright field between them. The
width of the two lines taken together is about 150 Angstrom units,
though the photographic plates are stained for a much greater width.
* Kayser & Runge, Weld. Ann., 41, 302 (1890).
170 PROCEEDINGS OF THE AMERICAN ACADEMY.
The strongest copper lines show only very faintly, the weaker ones not
at all.
Correlation of Effects.
In the metals arranged in the order given above (tin, silver, copper,
magnesium, aluminium, zinc, and sodium) the following relations hold
roughly : —
(1) The set of lines characteristic of the spectrum of each metal in an
atmosphere of hydrogen is stronger than that of the preceding metal of
the series ; (2) the hydrogen lines appearing in the spectrum of the me-
tallic arc of each metal are stronger than in that of the succeeding metal
of the series ; (3) the general working of the metallic arc is worse for the
metals at the first of the series than for those at the end. Briefly stated,
the intensities of the hydrogen lines coming out in the spectra of various
metals are roughly inversely proportional to the intensities of the char-
acteristic flutings of those metals.
GENERAL EFFECTS OF THE HYDROGEN ATMOSPHERE.
Historical.
Liveing and Dewar * found the carbon arc to work badly in hydrogen,
and to give spectral lines of different relative intensities than in air.
Professor Crew | has given quantitative measurements of the changes of
intensities for the metallic arc spectra of magnesium, zinc, and iron.
The general effects of the hydrogen atmosphere may be summarized
thus : —
(1) The arc works poorly in hydrogen. (2) The intensity of the
whole spectrum is greatly reduced in hydrogen. (3) Those metallic lines
which belong to the series of Kayser and Eunge are uniformly reduced
in intensity. (4) Other lines are reduced in intensity but not uniformly.
(5) Certain lines supposed to belong to the spark spectrum make their
appearance in the arc in hydrogen.
Discussion.
The radiations of the electric arc are generally admitted to be due to
three causes, — electrical, chemical, and thermal. The chemical cause
must depend upon the electrical cause in some way, for the chemical cause
* Proc. Roy. Society, 33, 430 (1882).
t Phil. Mag., 50, 497 (1900).
BASQUIN. — THE ARC SPECTRUM OF HYDROGEN. 171
cannot originate the arc, and the chemical cause follows the electrical in
point of time, as is shown by the " luminous cloud " of Crew and Basquin
above referred to. The thermal cause also must depend upon the electri-
cal cause in some way. It probably depends upon it directly, but in any
event, it is a function of it through the chemical cause, for all chemical
reactions either take in heat or give off heat.
Let us consider two arcs which are alike except that a larger current
runs through the first than through the second. Since the secondary
causes of radiation go hand in hand with the electrical cause we may
expect the first arc to have a spectrum which is uniformly brighter from
one end to the other than that of the second arc. With the exception of
a slight variation probably clue to conduction losses, this is just what is
always observed and confirms the secondary character of the chemical and
thermal causes of radiation. If these causes were not dependent upon
the electrical cause, we might possibly get an arc which would give only
a flame spectrum or an arc which would give only a spark spectrum.
Let us now suppose that we run the same current through both the
similar arcs, and suppose that in some way we reduce the chemical action
going on in the second arc. What difference may we expect to observe
in them ?
A reduction of the chemical action necessarily involves a reduction of
the temperature of the arc, because the chemical reaction in the arc in air
is exothermic, We have then an arc of lower temperature. If it is a
stationary arc it will be shorter and will go out more frequently. If it
is rotating it will have a smaller flame and work more poorly. All of
which is amply verified by experiments in hydrogen.
But we may expect this reduction of chemical action to have certain
effects upon the spectrum. If all the lines of the spectrum of this arc
were functions of the electrical cause alone, then there would be no re-
duction in intensity of any part of the spectrum when the chemical action
is reduced. Professor Crew estimates from 5 to 100 times as the reduc-
tion in intensity caused by the hydrogen atmosphere. The electrical
cause alone can account, then, for only a small part of the radiation.
The secondary causes play very important parts.
If all the lines of the spectrum of this arc were the same function of
the causes of radiation, then all the lines of the spectrum would be
uniformly reduced in intensity upon the reduction of chemical action.
Experiment shows this hypothesis to be too broad, but the lines belong-
ing to the series of Kayser and Runge are uniformly reduced in intensity,
so that it is probable that these lines are all the same function of the
causes of radiation.
172 PROCEEDINGS OF THE AMERICAN ACADEMY.
Of the other lines, those which are reduced more in intensity than the
series lines, must be less intimately related to the electrical or thermal
causes of radiation than are the series lines.
Let us agree that the average intensity of the spectrum of the arc in
hydrogen is only one fifth of its intensity in air, and let us agree that
the electrical cause of radiation remains practically constant with constant
current and voltage although the general intensity of the arc is greatly
reduced by the hydrogen atmosphere, then it follows that of the total
radiation, that fraction which must be attributed to the electrical cause
alone, is relatively five times as great in hydrogen as it is in air. Any
line, therefore, which is a function of the electrical cause alone, should
have in hydrogen five times the relative intensity that it has in air. It
seems quite likely that this may account for the appearance in hydrogen
of numerous strong spark lines, not found in the arc in air.
The appearance of the spark lines in hydrogen is not confined to the
rotating arc; the magnesium spark line at 4481 appears clearly in the
stationary metallic arc in hydrogen but not in air. The above explana-
tion for the appearance of these lines makes it probable that the electri-
cal cause of radiation is not zero in either atmosphere.
In the rotating arc the current is interrupted about twenty-five times
per second when the rotating electrode is a rod, instead of a disc, of
metal, and this spark at the breaking of the current may account, in part,
for the appearance of these spark lines in hydrogen. But we may in-
quire why this spark should partake any more of the nature of the true
spark in hydrogen than in air. The reduction of the chemical action in
the arc reduces the temperature and conductivity of the gases between the
poles in hydrogen, and it occurred to me that this action may affect the
appearance of the spark lines in either of two ways : —
1 . It may be that a gas which is in the hot condition of the arc in
air cannot give off spark lines; the arc spectrum may be characteristic
of this condition of the gas and may have nothing to do with electrical
action, and so, in this state, would give off only arc lines if a spark were
passed through it.
2. It may be that the conductivity of the gases in air is reduced so
slowly at the breaking of the current in the rotating arc that the voltage
of break never rises high enough to make a true spark.
In either of these cases, in hydrogen, the hot gases are largely absent,
owing to reduction of chemical action, and give opportunity for the spark
to appear.
In order to test the first suggestion I arranged an electrical circuit as
BASQUIN. — THE ARC SPECTRUM OF HYDROGEN.
173
shown in the diagram. The dynamo furnishes a direct current of 110
volts, and when the switch was closed the current simply passed through
the arc and the resistance in series. The arc was stationary, one
electrode was carbon and the other a zinc rod. The induction coil used
is a duplicate of the one designed by Professor Rowland to give a short
SWITCH
SPARK
Figure 1.
spark but a very powerful discharge ; an alternating current of 110 volts,
6 amperes, was run through the primary, without an interrupter. The
condenser used has a capacity of fa microfarad. It will be noticed that
the spark can take place only by passing in succession the two gaps
marked "arc" and "spark." The spectroscope is adjusted to observe
phenomena at "arc" gap.
In performing this experiment I first turned on the spark and set the
cross-hairs of the eyepiece of the 10-ft. concave grating upon the zinc
spark line at 5895, between the D lines of sodium. The spark was
turned off and the arc turned on. The spark lines no longer appeared, but
came out instantly when the spark was again started along with the arc ;
both arc and spark were now running through the gap marked " arc "
and the spectroscope showed both arc and spark lines. Now while both
currents were on, the arc current was turned off ; the arc spectrum dis-
appeared, but the spark spectrum persisted with apparently the same
intensity as before and without an interval of darkness.
This experiment shows that the first suggestion is not true ; that the
arc spectrum is not characteristic of the condition of the gases in the arc,
and makes it highly probable that the electrical cause of radiation is
not zero.
In order to test my second suggestion above, I short-circuited the
spark gap shown in Figure 1. The spark line appeared as before in the
spark, but disappeared as soon as the arc current was made ; the arc and
the spark discharges were both passing through the arc as before ; I had
174 PROCEEDINGS OF THE AMERICAN ACADEMY.
simply cut out the " spark " gap, but the spark line could not be seen
when both currents were on. Now when both currents were on I broke
the arc circuit, and nothing at all could be seen in the spectroscope ;
neither the arc nor the spark lines remained, although the spark current
was still passing. After remaining at the eyepiece of the spectroscope
about one second I began to see traces of the spark lines, and then they
soon came out with their usual brightness, and the spark discharge which
had been silent during that second of darkness assumed its usual noisy
character.
This experiment shows that the gases of the arc do not furnish enough
resistance to the passage of a high voltage alternating current to cause
the discharge to assume the character of a spark for a full second after
the breaking of the arc current. This seems to confirm the second
suggestion above, to the effect that the conductivity of the gases de-
creases so slowly on the breaking of the arc current in air as to give rise
to no very high voltage, and so accounts for the non-appearance of the
spark lines in the rotating arc in air.
These two experiments throw an interesting light upon the nature of
the spark. The spark at the arc gap in these experiments seems to be
due to neither the current nor to the voltage, but to some kind of an im-
pulse furnished by the sudden rush of electricity across the auxiliary
" spark " gap.
In the second experiment, above described, the spark lines do not all
seem to come out at the same time. I hope in the near future to be
able to arrange an automatic apparatus for making and breaking the
currents and an adjustable occul ting-screen which will enable one to
photograph the spectrum of the spark at definite intervals of time after
the arc current is broken. A series of these photographs will probably
furnish an interesting story of the development of the spark spectrum.
Physical Laboratory,
Northwestern University.
INDEX TO PLATES.
Plate I, Figure 1. Tin arc in hydrogen, 1st order.
Plate I, Figure 2. Upper part, copper arc in hydrogen, 1st order. Lower part,
copper arc in air.
Plate I, Figure 3. Tin arc in hydrogen, 1st order. All lines are second order
except Ha at 6563.
Plate I, Figure 4. Copper arc in hydrogen, 2d order, showing hydrogen-copper
fluting and the Hy line.
Plate II, Fig ore 1. Aluminium arc in ammonia, 2d order, showing hydrogen-
aluminium fluting.
Plate II, Figure 2. Middle, magnesium arc in hydrogen, showing hydrogen-
magnesium fluting at 5210, 1st order. Outside, magnesium arc in air.
Plate II, Figure 3. Upper part, zinc arc in hydrogen, 1st order, showing hydro-
gen-zinc lines. Lower part, zinc arc in air.
Plate II, Figure 4. Sodium (and copper) arc in hydrogen, 1st order, showing
hydrogen-sodium lines.
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Proceedings of the American Academy of Arts and Sciences.
Vol. XXXVII. No. 7. — August, 1901.
CONTRIBUTIONS FROM THE CHEMICAL LABORATORY OF
HARVARD COLLEGE.
THE STANDARD OF ATOMIC WEIGHTS.
By Theodore William Richards.
CONTRIBUTIONS FROM THE CHEMICAL LABORATORY OF
HARVARD COLLEGE.
THE STANDARD OF ATOMIC WEIGHTS.
By Theodore William Richards.
Received July 27, 1901.
The long continued discussion concerning the relative advantages of
hydrogen and oxygen as standards of the numerical values of chemical
combining weights seems to need yet another word. In spite of the
fact that an international committee has decided by a large majority
in favor of oxygen, the opposing arguments have not been put to rest.
The latest paper on this subject is by Erdmauu,* the well known
champion of the old unit value for hydrogen and the new value for
every other atomic weight. The paper consists mainly of a partial
reply to an earlier paper by Brauner.f The weight of the argument
in these papers seems to be distinctly on Brauner's side, but it is not
my purpose to recapitulate all the arguments which these gentlemen
and others have advanced. | I wish rather to call attention to a few
points wliich do not seem to have received the attention which they
deserve.
The first of these concerns the question of fact. What element has
served as the actual standard of comparison in a plurality of cases?
The question is easily answered by referring to Clarke's valuable
compilation. §
Evidently hydrogen in combination has been weighed accurately only
in the cases of water and the ammonium salts. The atomic weights of
zinc, aluminum, iron, nickel, cobalt, and gold have been determined by
* Zeitschrift fur anorg. Chem., 27, 127 (1901 ).
t Zeitschrift fur anorg. Cliem., 26, ISO (1901).
J A recent recapitulation of many of the arguments on each side may bo
found in the report of the American Chemical Society's branch of the International
Committee, published in the Journal of the American Chemical Society, February,
1901, p. 44 of the Proceedings.
§ F. W. Clarke, A Recalc. of the At. Weights, Smithson. Misc. Coll., The Con-
stants of Nature, Part V. (1807).
178 PROCEEDINGS OF THE AMERICAN ACADEMY.
measuring or weighing the hydrogen which they displace or to which
they correspond, but the results of different experimenters are far from
concordant. All other elements beside these eight have been referred
to hydrogen only with the assistance of oxygen.
On the other hand, oxygen has been used as the direct standard of
reference in countless cases. The determination of oxygen in the chlo-
rates, bromates, and iodates may be considered as the starting-point for
the calculation of Ag, K, Na, CI, Br, and I, and through them of very
many others. Into this remarkable series of experiments, executed in
great measure by Stas, the value of hydrogen enters only in the case
of amnionic salts. If the atomic weight of nitrogen were certain, we
should indeed have here a direct basis of comparison, but unfortunately
the value for this element may be as much as 0.05 per cent, or even
more, in error. The direct practical determination of the exact com-
position of ammonia gas, either by analysis or synthesis, has not yet
been accomplished. The value for nitrogen depends largely upon the
analysis or synthesis of nitrates, thus making oxygen the essential stand-
ard of reference in this case also. The other elements which have
been determined more or less accurately by reference to oxygen are as
follows : H, C, Cu, Ca (through the carbonate), Pb (through the
nitrate), Zn, Cd, Hg, Tl (through the nitrate), Sn, P, As, Sb, Bi, Mo,
U, W, Se, Te, Mn, Fe, Ni, Co. If one adds to these all those which
are connected less directly with oxygen through the halogen and silver
values and the sulphates, all the chemical elements are included in the
list. Thus an overwhelming majority of elements is referred more
directly to oxygen than to hydrogen.
Erdmann points out in his recent paper that there are possible causes
of error in some of the methods used by Stas for the analysis of chlo-
rates. Unfortunately he does not touch upon the very important ques-
tion of the percentage effect of these causes of error. It is undoubtedly
true that in these cases, as well as iu every other case, absolute accuracy
was not attained. No analytical method is wholly free from the possi-
bility of error, and hence it is vain to expect that any table of atomic
weights should be perfectlv trustworthy. When the accuracy of Stas
has been exceeded in actual fact, it will be time to forsake his results
for the newer values.
Erdmann su<rgrests that silver be chosen as the standard of reference,
and the suggestion is one which has some advantages. On the other
hand the tendency which this metal has to absorb oxygen has cast a sus-
picion over some of the work in which it was used. A further objection
RICHARDS. — THE STANDARD OF ATOMIC WEIGHTS. 179
to silver lies in the fact that it cannot be directly used in the demonstra-
tion of Avogadro's rule. Moreover, one is in doubt as to the value to
assign to this element, supposing that it should be selected as the stand-
ard. According to Erdmann's earlier arguments, logically followed out,
one should make silver 100.000, but this would cause hydrogen to be less
than unity. If silver is taken as 107.11, hydrogen would be 1.000 at
the present time, but what it might be in the future no one can predict,
since hydrogen is compared with silver at present only in a roundabout
fashion. Hence each of these assumptions would bring with it a further
disadvantage besides that attending the immediate inconvenience of using
new values.
The most important argument used by the minority is the pedagogic
one. It is contended that the uneven value for hydrogen, 1.0075, com-
plicates the explanation of the very important rule of Avogadro. If
this were true, it would indeed be worthy of consideration, but according
to my experience there is no difficulty in the matter.
For some time I have abandoned the comparison of specific gravities
as a means of demonstrating Avogadro's rule. I have used instead the
densities of gases and vapors, — that is, the actual weights of a litre of
the several substances at 0°C, or at 273° C or at 546°C. This seems
to be a more successful method, probably because density has concrete
dimensions, and is not a numerical abstraction as specific gravity is.
1.97 x
The student at once comprehends the equation of ratios -^— - = •
If the exact experimental values for the densities of the two gases arc*
given, the solution of this equation gives the student not only the ob-
served molecular weight of carbon dioxide, but also an insight into the
extent of the actual deviations from Avogadro's rule. Since the intro-
duction of this method of presentation, I have had far less trouble, and
far more successful examination results, than were formerly obtained.
The student usually learned by heart the old rule, "The molecular
weight equals twice the specific gravity," without understanding it.
Because the density-method would serve equally well with any gas
used as a standard, the pedagogic argument against II = 1.0075 seems
to me illusory.
The argument just discussed has led the Committee of the German
Chemical Society to an action which seems to me exceedingly unfortu-
nate,— namely, the publication of two tables of atomic weights. This
action has already been criticised by Krister and others. Either table
alone, supported by suitable weight of opinion, would have been vastly
180 PROCEEDINGS OF THE AMERICAN ACADEMY.
better than two. The mistake is especially to be regretted because the
eminent committee in question has previously acted with so' much wisdom
and ability.
It seems to me that by far the most important questions which have
been raised in the whole discussion are the questions of uniformity and
permanence of usage. These were indeed the prime objects of the foun-
dation of the German Committee in the first place. Nothing could be
more destructive to accurate calculation than a changeable standard of
measurement ; and yet this very uncertainty marks the present state of
affairs.
I cannot but think that every one should accept the standard of refer-
ence upon which any considerable majority of representative chemists
agree, since the matter is rather a question of convenience than a ques-
tion of principle. In the first place I preferred O = 16.000 primarily
because so much valuable work, both in analytical and in physical chem-
istry, has already been calculated upon this basis, and because of the
effect of a possible change in the oxygen-hydrogen ratio. At pres-
ent a still more important reason for preferring this standard exists,
namely the action of the International Committee, consisting of some of
the most prominent chemists of many countries, appointed for the ex-
press purpose of voting upon this question. This Committee, by a large
majority, decided to call oxygen exactly 16.000. I cannot avoid the
belief that until a yet more representative body of chemists is appointed
by international co-operation, or until the present committee reconsiders
its vote in parliamentary fashion, the present verdict of this committee
should rule the chemical world. Unless chemists are prepared to ac-
cept such a ruling, the appointment of an international committee is a
waste of time.
Representative government in civil affairs would be impossible if the
minority refused to act in accordance with the decision of the majority.
Does not the same principle apply to scientific rulings ? Of course
intelligent discussion is always desirable — the restriction applies to
action and not to speech. Before the action of the International Com-
mittee the situation might have been called one of scientific barbarism.
but at present it may be called one of scientific rebellion.
Formerly new determinations of atomic weights made at Harvard
were expressed in publication both upon the basis O = 16.000 and
upon the basis O = 15.879, because the question had not been decided
by representative vote. In future, out of respect to the action of the
International Committee, only the former standard will be used iu this
RICHARDS. — THE STANDARD OF ATOMIC WEIGHTS, 181
Laboratory. If an adequate internationally representative body of
chemists should in the future decide that some other standard is better,
immediate change of practise will be made to suit the new decision.
One regrets that so much time should have been spent in discussing a
matter which involves no fundamental principle, but is simply a question
of form and of convenience.
The subject matter of the present paper may be summed up in the
following sentences. It is pointed out that oxygen has actually served
as the experimental standard of reference in a great majority of cases,
that a great bulk of valuable work has already been published on the
basis O = 16.000, and that the use of this standard involves no impor-
tant didactic difficulties. It is further contended that the decision of
the representative International Committee is in itself an important rea-
son for adopting this standard, and that uniformity of usage is more
important than any of the special advantages claimed by either side in
the discussion.
Seal Haruor, Mt. Desert, Maine,
July 22, 1901.
Proceedings of the American Academy of Arts and Sciences.
Vol. XXXVII. No. 8.— October, 1901.
CONTRIBUTIONS FROM THE ZOOLOGICAL LABORATORY OF THE
MUSEUM OF COMPARATIVE ZOOLOGY AT HARVARD COLLEGE.
E. L. MARK, DIRECTOR. — No. 127.
STUDIES ON THE REACTIONS OF LIMAX MAXIMUS
TO DIRECTIVE STIMULI.
By Peter Frandsen.
CONTRIBUTIONS FROM THE ZOOLOGICAL LABORATORY OF THE
MUSEUM OF COMPARATIVE ZOOLOGY AT HARVARD COLLEGE.
E. L. MARK, DIRECTOR. — No. 127.
STUDIES ON THE REACTIONS OF LIMAX
MAXIMUS TO DIRECTIVE STIMULI.
By Peter Frandsen.
Presented by E. L. Mark. Received September 3, 1901.
II.
Introduction ....
Tliigmotaxis ....
Material and Methods
Results
Geotaxis
Methods ...
Operations and Results
CONTENTS.
Page
185
187
187
188
190
190
191
Summary of Part II .
III. Pliototaxis
Methods
Operations and Results
Summary of Part III
Bibliography . . .
Page
205
206
208
209
225
22G
Introduction.
The following studies were made at Harvard University during the
fall and winter of 1898-99. The problem was proposed by Dr. C. B.
Davenport and the investigation carried on under his immediate direc-
tion. I wish here to acknowledge my indebtedness to his many sugges-
tions and helpful criticisms throughout the year. In connection with the
preparation of the manuscript for publication, I am under obligation to
Dr. E. L. Mark for many kindnesses.
The behavior of any organism toward artificial stimulation is prob-
ably always largely dependent on its normal environmental condi-
tions. The long action of those conditions, assisted, perhaps, by the
animal's own efforts, conscious or unconscious, to adapt itself to them,
finally results in certain habits and instincts. The process of adaptation
being extremely slow, organisms are strongly averse to great or sudden
changes in their environment and incapable of adjusting themselves to
them. As a rule, then, we should expect animals to seek those condi-
tions of light, heat, moisture, and other physical and chemical influences
which are most in accordance with those to which they are normally
subjected.
186 PROCEEDINGS OP THE AMERICAN ACADEMY.
The most easily observed responses of animals are naturally those
which find their expression in locomotion. The number of stimuli which
may influence locomotion are, of course, numerous, but of these a certain
limited number play much the larger part. If we had an accurate
knowledge of the relative weight of these different forces, we might pre-
dict with certainty the path any animal would follow under certain given
conditions. An experimental study of the different stimuli ought at least
to enable us to find out which ones do operate, and perhaps to establish
certain general laws regarding them and the biological tendencies which
impel the animal to respond.
The present paper is a study of the locomotor responses of the slug
Limax maximus to three kinds of stimuli, — those of touch, gravity, and
light. In connection with these studies new problems have constantly
arisen, some of which have been cursorily considered, many others
merely alluded to, so that the work is far from being complete.
The term " geotaxis " has been used to designate the influence of gravity
on locomotion. Interesting and careful studies have been made on the
geotaxis of numerous Protista by Schwarz ('84), Aderhold ('88),
Massart ('91), and Jensen ('93). These investigations clearly show a
geotactic response in the unicellular organisms studied. The kind of
response varies according to other conditions, such as those of light, heat,
density of medium, chemical influences, etc., and may also differ in indi-
viduals of the same genus under apparently like conditions. Massart
('91, pp. 161-162) found that, when a number of Spirilla were put into
a vertical tube, one group collected in the upper part and another at the
lower part. He also found (p. 164) that Chromulina woroniniana was
negatively geotactic — that is, moved upward, or in a direction opposite to
that of the pull of gravity — at 15° to 20° C, but positively geotactic at
5° to 7° C. Jensen's work also showed the important influence of other
agents in modifying geotaxis. Loeb ('88, pp. 7-8) found that cock-
roaches preferred the steepest side of a box whose four sides were inclined
at different angles ; that is, they are negatively geotactic. He also dis-
covered that a number of other Metazoa were geotactic.
In a certain way, the present paper is a continuation of a recent study
made by Dr. C. B. Davenport and Miss Helen Perkins on geotaxis in
the slug. Davenport and Perkins ('97, p. 105) discovered that the
intensity of the animal's geotactic response was directly proportional to
the sine of the angle of deviation from the vertical, and hence " varied
directly as the active component of gravity." In the third section of
their paper, the question, " What determines whether the head end of
FRANDSEN. REACTIONS OF LIMAX MAXIMUS. 187
the slug shall be directed up or down ? " was raised and considered. The
results showed that certain individuals appeared to have a fairly marked
positive geotaxis, for, when placed on an inclined glass plate, such
animals swung the head-pole of the axis toward the earth ; but others
showed as strongly marked a tendency to move away from the earth, and
a few seemed indifferent as to whether they went up or down. Their
experiments showed further that there was, apparently, no inherent
tendency in individual animals to move either to the right or to the left,
so that the difference in geotactic response could not be explained as due
to differences of an inherent tendency of this kind. The effect of a slight
initial impulse given to the head of the animal indicated that the thigcno-
tactic, or contact, stimulus imparted to the animal in handling might, to
some extent, modify its response to the stimulus of gravity. But
Davenport and Perkins did not reach any definite, satisfactory answer to
the main question.
It was to test their observations by a larger number of experiments,
and, if confirmed, to explain them by further experimentation, that the
present investigation was undertaken. In the first place, I wished to
find out whether certain individuals, if put on an inclined glass plate,
always responded to the pull of gravity by directing the head end up and
moving away from the earth, and whether certain other individuals
always did the contrary. If this proved to be true, then it was my main
problem to seek the reason for it. Is the force which makes some slugs
go up, others down, and still others indifferent to the attraction of gravity,
a purely accidental one, — is it a physical force, or is it what we may call
a psychical peculiarity, which varies in different individuals and in the same
individual at different times ? As a preliminary to the main problem,
I first made a series of experiments on the animal's thigmotaxis, — its
response to contact- and pressure-stimuli. By virtue of its thigmotaxis, an
animal moves either toward or away from the agent which comes in
contact with it, just as its geotaxis is expressed in a movement toward or
away from the earth, in response to the attraction of gravity.
I. Thigmotaxis.
Material and Methods. — The animal used in all the following experi-
ments was Limax maximus, which is fairly abundant in the greenhouses
about Cambridge. Material was obtained from several different green-
houses and kept in a large closed tin box, the bottom of which was
covered with moss kept moist, so as to afford an environment as much like
the customary one as possible. Fresh cabbage leaves constituted the
188
PROCEEDINGS OF THE AMERICAN ACADEMY.
animal's main food. The cannibalistic tendencies of the slug, together
with an unavoidable deterioration due to repeated handling, necessitated
a frequent renewal of the animals.
The methods used in the experiments were simple. The slug was
placed on a circular glass plate set horizontally in the bottom of a
cuboidal wooden box which was made impervious to light and covered
with a thick, black cloth. Precautions were taken to avoid thermal and
chemical influences by keeping the box at as equable a temperature as
possible and by wiping the plate free from slime before each test. The
tests were made only when the animal had definitely oriented itself and
was moving ahead in a straight line. Two series were made. In the
first series the dorsal tentacle was touched gently with the forefinger.
The box was then immediately covered with the black cloth. Observa-
tions were made after the lapse of 20 to 30 seconds and the position of
the animal noted. The right and left tentacles were touched alternately.
Results. — The following Table (I.) gives the results of a number of
experiments on ten different animals.
TABLE I.
Response to Thigmotactic Stimulation of the Tentacles.
Number of Trials.
Animal
No.
Total Number
of Trials.
—
+
0
1
7
2
3
12
2
11
3
3
17
O
8
Q
1
12
4
4
3
3
10
5
7
2
0
9
6
6
0
2
8
7
10
2
2
14
8
10
4
2
22
9
18
1
5
24
10
22
1
4
17
Totals . .
99
21
25
145
FRANDSEN. — REACTIONS OP UMAX MAXIMUS. 189
The column headed with the minus sign shows the number of times the
animal responded by moving away from the source of stimulus; the one
headed with the plus sign, the number of times it moved towards that
source ; and the zero column, the number of times there was no response.
I found that the animal would respond very definitely and precisely to
stimuli two or three times in succession by immediately retracting the
tentacle touched and moving away from the stimulating influence. After
the third trial, however, it either refused to change its direction of loco-
motion or else moved directly towards the source of the stimulus. If a
respite of a few seconds before the next stimulation was then permitted,
the animal would again give a precise negative response for two or three
trials, and then, as before, it desisted. Out of the total 145 tests, there
was a negative response in two thirds of the trials. The remaining
trials — one third of the whole — were about equally divided between
the positive responses and refusals to respond at all. Sometimes five or
six tests were made in quick succession, so that the total negative
response is rather less than it would have been if a rest had been given
in each case after three tests. Out of the 21 cases of direct positive
response, 15 were cases where the right tentacle was touched, and the
remaining 6 were due to stimulation of the left tentacle. Similar, but
more marked, differences between the results of stimulating the right and
the left tentacles were observed in other experiments. This suggests that
either the right tentacle may be less sensitive to stimuli, or that its coun-
terirritancy may be more readily aroused. There is, however, a third
possible cause. The animal may have an innate tendency to go to the
right, and, if so, this tendency may diminish to some extent the force of
the stimulating agent when it impinges on the right side of the animal,
and correspondingly increase the response when the stimulus is directed
upon the left side of the animal. Something further will be said about
this point in a later part of the paper.
A few thigmotactic experiments were next made on the sides of the
animal posterior to the head. The right and left sides were touched
alternately. The results are given in Table IT.
Phenomena like those observed in stimulating the tentacles are seen
here, and they also agree with similar observations by Davenport and
Perkins ('97, p. 109.) After two or three trials, the animal begins to
show resistance, and if the finger is held against its side, will sometimes
try to displace the finger by pushing against and curling the body around
it. The frequency of the negative response is here somewhat less marked
than in the preceding experiments, which is as we should expect, owing
190
PROCEEDINGS OF THE AMERICAN ACADEMY.
to the greater sensitiveness of the tentacles as special tactile organs. In
these experiments every one of the minus and zero results was due to
stimulation of the right tentacle.
TABLE II.
Response to Thigmotactic Stimulation of the Sides of the Body.
Animal
No.
Number of Trials.
Total Number
of Trials.
—
+
0
1
2
3
11
8
17
3
6
5
3
2
4
17
16
26
Totals . .
36
14
9
59
These facts clearly prove that, under ordinary circumstances, the slug
is negatively thigmotactic. In our consideration of the animal's responses
to other stimuli, we shall have to take this into account, as causing
occasional vagaries, and therefore endeavor to eliminate it as much as
possible from the experiments.
II. Geotaxis.
What determines whether the head end of the slug shall be directed
up or down ?
Methods. — The same apparatus was used as in the preceding experi-
ment. A circular glass plate was employed so that the animal could be
rotated into any desired position without the necessity of its being
handled. The plate was set in a box at an augle of about 45° with the
horizon. In each test the animal was so placed on the plate that the
long axis was horizontal, different sides being directed downward in
different trials. At first the experimentation consisted mostly of watching
the animals in order to obtain some clue for further work. Later, rough
sketches of the pigment patterns of the individual animals were made, so
that it was possible to identify individuals with certainty ; the same
animal could then be subjected to experiments at different times and the
difference in results noted. The methods used in working out particular
FRANDSEN. REACTIONS OF LIMAX MAXIMUS. 191
questions will appear as these questions are considered. As the same
number of experiments were not made on each animal studied, I have,
for the sake of comparison, estimated in each case the geotaxis in per
cents. This percentage is obtained by dividing the number of positive
or negative responses by the total number of responses. The nearer the
geotaxis percentage approaches 100 the more precise has been the kind
of response. No fixed time was allowed to elapse between successive
tests, but in'each test the observation was made at an interval of from 30
to 60 seconds after covering the box.
Operations and Results. — The first question investigated was whether
particular animals exhibited a decisive positive or negative geotaxis. A
number of tests were, therefore, made on each of several selected indi-
viduals. The results obtained were like those of Davenport and Perkins
('97, p. 108) ; that is, certain animals showed a very marked positive geo-
taxis ; others, an equally decided negative tendency ; and a few, perhaps
one animal out of 12 or 15 where' 10 or more tests were made, were
apparently geotactically indifferent. The occasional irregularities in the
responses of individual animals were easily seen to be due to influences
other than pure gravity, such as jarrings of the plate, influence of contact
in putting the animal on the plate, and to the influence of light admitted
in lifting the cover of the box. Frequently, upon the raising of the
cloth to make an observation, the animal would retract its tentacles, as
if dazzled by the sudden inflow of light, and at the next observation
it would be seen to have altered its response.
Naturally, this question next arose, Is the response the same on
different days? In Table IV. (p. 195) are given the results with a num-
ber of animals experimented on to test this point. These are numbers
2, 7, 8, 22-25, 27. Number 2 was positively geotactic on two days
and negative on another day. A similar variation is seen in the case
of slugs 7 and 22. In the case of all the rest, however, there is a very
marked constancy. The ninth (last) column in the table indicates the
condition of the animals at the time of experimentation. We see from
this that on the days of different response, the animals were in somewhat
unlike conditions, which may account for the irregularity of response.
The significance of this will be dealt with later. The important matter
here is, that the animals, when in the same condition and under the
same circumstances, have a fairly constant geotaxis from day to day.
One of the most marked cases is that of number 24. This animal was
experimented on at different times for a period of three weeks. During
this period, it was always active and in good condition, and, as the
192
PROCEEDINGS OF THE AMERICAN ACADEMY.
table shows, at all times, exhibited nearly the same percentage nega-
tive geotaxis. At the last trial made, it responded irregularly, and so
slowly, — at one time not changing its position for thirty minutes, —
that I had to give up the attempt to obtain a series. This was often
the case with other individuals after a few definite responses.
Tests were then made on the geotaxis of the same individuals at
different times of the same day. Considering the slug's normal en-
vironment, it would not be surprising if, for instance, it should show an
upward tendency in the evening and a downward geotaxis in the day-
time. Its nocturnal habits and dislike of daylight might give it a dif-
ferent geotactic instinct at night from that of the daytime. I insert here
a table (III.) giving the results of a few experiments bearing on this
point. As the table shows, the response is pretty constant at different
TABLE III.
Geotaxis of three Individuals at Different Times in the Day.
Number of Trials.
Animal
No.
Time of Day.
% Geotaxis.
Condition
of Mucus.
+
—
1
8.00 A.M.
5
2
+71.4
Good
1.30 p.m.
6
3
+6G.6
Rather Dry
8.30 p.m.
7
4
+63.6
Tail Dry
2
1.30 p.m.
16
1
+94.1
Good
7.00 p.m.
9
18
-60.0
Rather Dry
7.00 p.m.
12
5
+70.5
Fair
10.00 p.m.
6
o
•J
+GG.6
Fair
3
7.00 A.M.
3
8
-72.7
Fair
1.30 p.m.
0
5
-100.
Fair
times of the same day. The one exception is number 2. That it
was negative on one evening at 7 p. m., may be explained by the fact
that its condition was not good. Moreover, on another evening at the
same time the animal had become positively geotactic.
From the observations recorded in Tables III. and IV., it is plain that
the geotactic response is not due to purely accidental factors, but can
FRANDSEN. — REACTIONS OF LIMAX MAXIMUS. 193
be explained only by some marked difference between the individual
animals. The first thought is that differences in response are due to a
difference in size, and the facts seem to give some support to that ex-
planation. Most of the positively geotactic individuals were found
among the small and medium-sized animals, and nearly all the negative
animals were of large size. Moreover, the few indifferent individuals
were of medium size. This, however, was not an invariable rule.
Small animals were sometimes negatively geotactic and, occasionally, a
large slug would migrate earthward.
A second, clearly important, factor is the condition of the animal's
mucus. As shown by the preceding experiments, animals, positively
geotactic when normal, became negatively geotactic when lacking in
an abundance of sticky slime ; e. g. animal 2, Table III., and animals 2
and 7, Table IV. On the other hand, in one instance (22 b), a nega-
tive animal, when extremely sticky, went downwards. Abundant, sticky
mucus is evidently connected with a downward migration, and dryness
seems to force the animal to take an upward direction. But these facts
are not enough to explain all responses. For sometimes two animals
of nearly the same size and in equally good condition gave different
geotactic responses. We must look for other differences. It will,
however, be necessary first to refer briefly to the form and external
appearance of the slug. t
mtlp. ofpul. m(ia // l¥
"■tav.
Figure 1.
Outline of Limax maximus. mtl. a., anterior edge of mantle ; mtl. p., posterior
edge of mantle ; a. to mtl. />., anterior region of body ; mtl. p. to p., posterior region ;
oc, eye ; ta. d., dorsal tentacle ; ta. v., ventral tentacle ; of. pul., pulmonary orifice.
The slug, if we except the respiratory opening on the right side of
the body, is externally bilaterally symmetrical. It has no external
shell. There are two pairs of tentacles, — a dorsal pair bearing the
eyes and a smaller ventral pair. The mantle extends from the neck,
ventrally, to near the edge of the foot. Posteriorly, it forms a prominent
fold, as indicated in the figure, which may be used to separate the body
into an anterior and a posterior region. Observations of the animal
vol. xxxvii. — 13
194 PROCEEDINGS OP THE AMERICAN ACADEMY.
reveal that it has very different degrees of control over these two
regions of the body. In locomotion, the head end of the body, back
as far as the respiratory opening, is freely swung about from side to
side and determines the axis of orientation of the animal. Over the
posterior region, the animal seems ordinarily to have very imperfect
control. The relation between the two regions is crudely that of a
span of horses to a chain of wagons which they are pulling. When the
horses change direction, the wagons come only slowly around into posi-
tion one after the other, and there is likely to be some slipping in the
process, especially if it takes place on a down grade. In watching the
slug, I saw that the adhesion of the anterior region appeared consider-
ably greater than that of the posterior. When the animal gets dry, it
does so first at the posterior region. The tip of the tail is the part first
to lose its clinging power, and it may curl up dorsally as a result of the
drying process. If an animal which is thus beginning to deteriorate in
its supply of mucus be put on a glass plate and the plate raised into a
vertical position, the slug will move along and desperately cling to the
plate with the anterior part of its body. The posterior region will
gradually swing downward as a result of the pull of gravity, and, in
consequence, the animal's head will eventually be directed upward.
From this, we are justified in concluding that the same principle will
operate, although to a considerably, less degree, in the animal's normal
condition. A hasty examination showed that there was a good deal of
variation in the proportions of the two regions in different individuals.
As a crude and easy way of estimating these proportions, I measured
the length in millimeters of the anterior region from the tip of the head
to the posterior fold of the mantle, and similarly the length of the pos-
terior region from that fold to the tip of the tail.*
The results from 27 animals thus measured are given in Table IV.
The individuals (Table IV.) are arranged in a series, beginning with
those in which the two regions are most nearly of the same length
and ending with those in which the disproportion is greatest. In animal
No. 1, the length of the anterior region is 83.3 per cent (column 8) of
the posterior ; that is, the ratio is almost one to one. In No. 25, the
anterior region is only 45 per cent as long as the posterior, or less than
half its length.
The fifth column in the table gives the geotaxis of individuals in per
* The measurements were made when the animal was extended and moving
across the plate. The amount of elongation varies a good deal, but the regions
retain pretty closely their relative proportions.
FRANDSEN. — REACTIONS OP LTMAX MAXIMUS.
195
TABLE IV.
StJMMART OF GeOTACTIC RESULTS.
Sei
Animal se
No. oi
ei
•iesof (
rvatioi
)b- Number of Trials,
is
taxis.
Length of
Anterior
Region in
mm.
Length of
Posterior
Region in
mm.
Ratio of Ant.
to Post. Re-
gion in per
cents.
Condition of Animal.
) Diffe
it Days
r- "
+
—
1
,
10
0
+100.
20
24
83.3
Good.
2
a
6
3
4- 0(5.0
18
22
82.
Fair.
2
b
5
13
- 72.2
18
22
82,
Dry.
2
c
12
5
+ 70.5
18
22
82.
Good.
3
6
0
+100.
6.5
8
81.
Good.
4
6
1
+ 85.7
17
21
81.
Good.
5
.
5
2
+ 71.4
24
30
80.
Good.
0
7
1
+ 87.5
11
15
73.
Good.
7
a
0
4
-100.
26
40
65.
7
7
b
9
6
+ 60.
26
40
65.
Rather dry.
7
c
7
3
+ 70.
26
40
65.
Slow.
7
d
0
2
-100.
26
40
65.
Tail slips.
8
a
12
6
+ 66.6
t
7
7
Good.
8
b
17
1
+ 94.4
i
7
1
Good.
9
0
6
-100.
21
33
63.6
Tail slips.
10
2
8
- 80.
20
32
62.
Mucus watery.
11
.
14
3
+ 82.3
21
34
61.8
Good.
12
6
0
+100.
27
44
61.
Good.
13
a
5
12
- 70.5
17
25
61.
Active.
13
b
• >
8
- 72.7
17
25
61.
Active.
14
9
3
+ 75.
20
33
60.5
Good.
15
1
8
- 88.8
24
40
60.
Fair.
16
0
10
-100.
28
50
56.
Good.
17
6
14
- 70.
30
55
54.5
Good.
18
8
3
+ 72.7
30
56
53.5
Extrem'ly sticky.
19
0
8
-100.
23
43
53.5
Fair.
20
1
' 5
-83.3
17
32
53.
Good.
21
4
12
- 75.
21
40
52.5
Good.
22
a
7
8
- 53.3
41
79
52.
Sticky.
22
b
8
5
+ 61.5
41
79
52.
Very sticky.
23
a
5
9
- 64.2
18
36
50.
Good.
23
b
6
10
- 62.5
18
36
50.
Good.
23
c
0
5
-100.
18
36
50.
Good.
23
d
0
4
-100.
18
36
50.
Good.
24
a
3
15
- 83.3
27
54
50.
Good.
24
b
3
14
- 82.3
27
54
50.
Good.
24
c
2
19
- 90.5
27
54
50.
Good.
24
(1
4
19
- 82.6
27
54
50.
Goo.l.
24
e
3
14
- 82.3
27
54
50.
Good.
25
a
7
17
- 70.8
21
44
48.8
Good.
25
b
4
14
- 77.7
21
44
48.8
Good.
25
c
0
12
-100.
21
44
48.8
Dry.
20
3
15 ■
- 83.3
7
■2
45.
Good.
27
a
0
14
-100.
32
71
45.
Good.
27
b
1
5
- 83.3
32
71
45.
Good.
19G PROCEEDINGS OF THE AMERICAN ACADEMY.
cents. The table includes those animals which were fairly active in
response but does not give individuals obviously unable to respond
because of a lack of slime secretion. The positively geo tactic animals,
with two exceptions, are all found in the upper half of the table and
almost all the negative animals in the lower half. Supposing other
conditions the same, we can say that those animals in which the ratio
of anterior to posterior regions is as 2 : 3, or greater, will be positively
geotactic. Those between the ratios of 2 : 3 and 3 : 5 will be more
uncertain in their geotaxis, which will depend largely on the combina-
tion of other conditions. Finally, those in which the ratio is less than
3 : 5 will almost invariably be negatively geotactic. The nearer one
gets to the extremes, the greater the accuracy of prediction. This pre-
diction, it is understood, applies only to animals tested on the glass plate.
An examination of the ninth column shows that the few cases of nega-
tive geotaxis occurring in the positive half of the table are probably due
to a deficiency in the second most important factor affecting the geotaxis ;
namely, the condition of the slime secretion of the animal. This
secretion may be deficient either (1) in quantity, as in the case of slug
2 b ; or (2) in quality, as was the case with slug 10. Of the two cases
of positive geotaxis occurring in the negative half of the table, the first,
that of slug 18, is easily explained as due to an extraordinary tenacity
of the mucus. Moreover in this, and more markedly in the case of
slug 22 b, the slugs were very large and rather slow in their movements.
Slug 22 b, instead of moving ahead actively, like most slugs when in
good condition, often swung its head toward the earth without any fore-
ward movement, and hence did not give the pull of gravity the most
favorable opportunity to work on the posterior region of its body. This
connects itself with a general observation on all the animals. When
active, they are usually very precise and uniform in their responses.
If stupid, slow, and averse to movement, — a condition in which the
best of them sometimes get, — they will either obstinately refuse to
move, or else, keeping the posterior region firmly fixed, will swing the
head end toward the earth. Sometimes such a slug will slowly move
in a circle, first down then up, and finally curl itself up, like a dog by
the fireplace, and apparently go to sleep. This peculiarity may be
connected with the food conditions of the animals, as will be shown in
a set of experiments to be given later on.
The two most important factors in determining the geotaxis of indi-
vidual slugs are, therefore : first, the proportion of the anterior (mantle-
covered) and posterior (uncovered) regions of the body ; secondly, the
FRANDSEN. — REACTIONS OF LIMAX MAXIMUS. 197
character of the slime secretion of the animal. If accurate measure-
ments were made of the two regions of the body, we might obtain ex-
actly the relative weights of these two factors. By means of a spring
balance, the effectiveness of the mucus in counteracting gravity could be
ascertained with a fair degree of accuracy. A large number of such
observations in connection with geotactic tests might, finally, enable us
to state precisely what combination of the two factors — weight of
regions and strength of mucus — would be necessary to make an
animal positively or negatively geotactic. I have made no such calcu-
lations, and it would perhaps not be worth the trouble. The suggestion
is instructive, however, as indicating the possibilities of predicting, with
a certain degree of exactness, a phenomenon which seems at first sight
to be entirely haphazard. Perhaps perfect mathematical exactness
would, however, never be possible in this case, for, as I shall show a
little later, other factors of importance probably enter in to modify
the results. However, these too are not out of the reach of precise
definition.
Certain slugs are negatively geotactic because gravity pulls the pos-
terior region of the body down faster than it does the anterior region.
Since in all slugs the posterior region somewhat exceeds in length the
anterior, we should expect all animals to respond in the same way, pro-
vided gravity acted in only a mechanical way. But about the same
number of slugs go down as go up. Therefore, there must be some
other factor, such as an inherent tendency, impelling these positive
slugs to seek the earth. But if so, is it not probable that all slugs
have this inherent tendency to move towards the earth, the tendency
being obscured in the negative slug by the superior force of the me-
chanical difficulties to be overcome ? The fact that positive slugs,
when deficient iu means of resisting the pull of gravity, — that is, when
dry, — assume a negative geotaxis, shows that the inherent tendency is
sometimes obscured. If this hypothesis is true, then we ought to be
able, by diminishing the force of gravity, or better, by increasing the
animal's powers of resisting the disproportionate pull on the posterior
region, to make the negative animals become positive. Similarly, if
this mechanical difficulty of adhesion is the cause of negative geotaxis,
we ought, by increasing it, to be able to compel positive animals to be-
come negative. The first end may be attained by substituting for the
glass plate a wooden one, which will presumably offer the animal a
better chance of adhesion. The second end may be reached by substi-
tuting for the glass plate one which has been coated with vaseline or
198
PROCEEDINGS OF THE AMERICAN ACADEMY.
a similar substance. Both ends may also be attained, to a certain extent,
by increasing or decreasing the angle of inclination of the plate. An
examination of the tables given by Davenport and Perkins ('97, p. 103)
shows that the largest average number of negative responses occurred
when the glass plate was vertical ; that is, when the mechanical diffi-
culties were greatest. There is a gradual decrease in this average
(and a corresponding increase in the average number of positive re-
sponses), as the angles of inclination of the plate with the horizon were
diminished from 90° to 60°, 45°, and 80° successively. At the still
smaller inclinations of 22^°, 15°, 7°, and 0° (i.e., horizontal), however,
there is on the whole an increase in the average number of negative
responses, though this is quite irregular. Since the proportion of anterior
to posterior region of the animals experimented on is not known, we
cannot tell how far this factor may have been the cause of this irregu-
larity in the sense of the response.
I have made a few experiments by varying for the same individual the
angle of inclination of the plate. The animals were all in good condi-
tion throughout the experiments. The results — given in Table V. —
show a decided increase in negative geotaxis with increase in the angle
of inclination.
TABLE V.
Per Cent of Geotaxis at Different Angles of Inclination of the
Support.
Number of Trials.
Animal
No.
Angle of
Inclination.
% Geotaxis.
Condition
of Animal.
+
1
45°
8
2
+ 80.
Good.
1
90°
0
14
-100.
Good.
2
45°
7
1
+ 87.5
Good.
2
70°
8
3
+ 72.7
Good.
3
45°
2
8
- 80.
Good.
3
90°
0
10
-100.
Good.
The most striking case is the complete reversal of geotaxis, seen in the
first animal experimented on.
FRANDSEN. — REACTIONS OF LIMAX MAXIMUS.
199
Still more conclusive results were obtained by the substitution of wood
or vaselined glass surfaces for the clean glass plate. In order to make
sure that the animal's power to hold on varied with different surfaces,
and to determine approximately the relative strength of the adhesion, Dr.
Davenport suggested the use of a delicate spring balance, such as are used
in weighing letters. The animal was placed on a horizontal glass plate.
When it had oriented itself, and was moving forward, the pan of a letter
balance was held against the side of the animal and gradually increased
pressure exerted until the animal was made to slip along the plate. The
maximum reading (in ounces) on the indicator was noted. Then the same
animal was placed on a wooden plate and a similar test made under
like conditions of movement and activity. The same was done on the
vaselined plate. A number of such tests were made on each individual.
In order to avoid possible differences in results due to a gradual de-
terioration in the condition of the animal, the sequence of the surfaces
was varied in the successive sets (three) of trials so that each surface was
once employed for the first experiment of a set. This method proved
fairly satisfactory and gave in some instances very striking results.
TABLE VI.
Amount of Tricssure required to dislodge the Slug from Different
Horizontal Surfaces.
Animal No.
Wood.
Glass.
Vaselined Glass.
1
1.8 ounces
1.5 ounces
.23 ounces
2
1.25 ounces
.67 ounces
.34 ounces
3
3.16 ounces
2.16 ounces
1.55 ounces
4
4.33 ounces
2.55 ounces
1.55 ounces
5
3. ounces
1.16 ounces
.50 ounces
6
5.7 ounces
3 50 ounces
1.52 ounces
The results recorded for each individual are the averages of three
trials on each of the surfaces used. The table shows a considerable differ-
ence in the degree of adhesion to the different surfaces. In the last four
cases the animals were all very large. They were in excellent condition,
having just been captured, and secreted a sticky slime in large quantities.
200
PROCEEDINGS OF THE AMERICAN ACADEMY.
After being ou the vaselined surface, there was a noticeable decrease in
the power to hold on to the glass or wood, due probably to the vaseline
which still adhered to the animal. Regarding these cases as typical of all
slugs, we can say that the wooden surface affords a condition nearly
twice as favorable as that of the glass plate for the exhibition of an inter-
nal tendency. The vaselined surface, on the contrary, is only about half
as favorable as the glass plate ; that is, it doubles the obstacles. As a
general rule, owing to the irregularities of other influences, the differ-
ence between the different surfaces would be, probably, somewhat less.
For active, well-conditioned animals, however, we have no hesitation
in concluding that the ratios obtained from these cases are fairly
representative.
Having thus established the fact that the character of the surface does
modify the animal's power to attach itself, I next give a table (VII.)
showing the results of a series of experiments on twelve different individ-
TABLE VII.
Geotaxis of the Slug on Different Surfaces.
Animal
No.
Ratio of
Anterior to
Posterior
Parts in %.
Plate at Inclination of 45 D.
Wooden Plate.
Glass Plate.
Vaselined Glass Plate.
No. of Trials.
%
Geotaxis.
No. of Trials.
n % ■
Geotaxis.
No. of Trials.
%.
Geotaxis.
+
—
+
—
+
—
1
61.
9
8
+ 53.
0
5
-100.
0
5
-100.
2
7
5
0
+100.
6
5
+ 54.5
0
9
-100.
3
52.
5
0
+100.
1
3
- 75.
0
5
-100.
4
47.
7
0
+100.
1
8
- 88.8
0
slips
0
5
76.
5
2
+ 71.4
5
1
+ 83.3
1
3
- 75.
6
50.
7
3
+ 70.
2
8
- 80.
0
slips
0
7
66.6
9
1
+ 90.
1
9
- 90.
0
slips
0
8
83.3
5
0
+100.
10
0
+100.
4
6
- 60.
9
56.
9
1
+ 90.
0
10
-100.
0
0
0
10
61.
5
1
+ 83.3
5
1
+ 83.3
1
5
- 83.3
11
53.
8
0
+100.
1
5
QO O
— oo.o
0
slips
0
12
53.5
6
0
+100.
7
2
+ 77.7
2
slips
0
FRANDSEN. — REACTIONS OF LIMAX MAXIMUS. 201
uals. The geotaxis of each animal was tested on three different sur-
faces, — the glass plate, a circular wooden plate, and a glass plate coated
with vaseline. Care was taken to have other conditions as nearly as possi-
ble the same. Circular plates were employed so that the animal could be
rotated into a horizontal position without being touched by the hand. In
several cases a series was made on an animal using the glass surface ;
the animal was then transferred to a wooden plate and the same number
of trials made ; the same individual was then put back on the glass plate
and as many more tests were made ; finally, it was returned to the wooden
plate and an equal number of observations made. The same thing was
tried alternating between glass and vaselined surfaces.
The second column shows what per cent of the length of the posterior
region of the animal's body its anterior region is, as previously defined.
A comparison of the columns " % Geotaxis" under the different con-
ditions at once shows, in nearly every case, a marked difference in the
geotactic response with the three kinds of surfaces. The same number
of trials was not always made on a given animal under the different con-
ditions, so that the comparisons are not always on exactly the same basis.
The results, however, prove pretty conclusively that all animals have an
inherent tendency to move toward the earth. On the glass plate, the
animals moving upward and downward are about equal in number, the
rea-ons for which we have already given. On the wooden plate, which
affords the best of the three surfaces for adhesion, all the animals have
become positive. A vaselined surface offers still greater difficulties to
positively geotactic responses; it compels the positively geotactic animals
to become negative (Nos. 2,5, 8, 10). Some animals are utterly unable
to adjust themselves to this extraordinary condition, especially if not en-
dowed with the power of secreting excellent mucus. These animals either
vainly cling with the anterior end of the body to the plate, while the poste-
rior region slips downward, thus directing the animal up, or they roll off the
plate altogether as soon as it is placed in an inclined position. For this
reason some of the animals negatively geotactic on the glass plate gave
no geotactic response when they were placed on the vaselined surface.
These facts, then, conclusively answer in the affirmative our second ques-
tion. All slugs have a tendency to move toward the earth.
Now the question naturally comes up, Can we not assist this tendency
in those animals which are negatively geotactic on a glass surface by
bringing some other stimulus — light, for example — to bear upon them ?
This slug is negatively phototactic to strong light, as the third part of
this investigation will show. By exposing the animals to strong light, can
202
PROCEEDINGS OF THE AMERICAN ACADEMY.
we not make the desire for darkness cooperate with the inherent positive
geotactic tendency to such an extent that the two together will over-
come all mechanical difficulties and cause the animal to move downward ?
The following table (VIII.) answers this question in the affirmative.
TABLE VIII.
Geotaxis of Slug on Glass Plate at an Angle of 45° influenced (1) by
Gravity alone, and (2) by Gravity and Strong Light.
Animal
No.
Size.
Gravity alone.
Gravity -f- Influence of Strong Light.
No. of Trials.
% Geotaxis.
No. of Trials.
»j0 Geotaxis.
+
—
+
-
1
2
3
4
5
6
Big
Big
Big
Big
Medium
Small
0
0
1
0
3
0
17
14
7
5
9
5
-100.
-100.
- 87.5
-100.
— 75.
-100.
8
7
2
2
4
0
8
5
2
4
4
5
+ 50.
+ 58.3
± 50.
+ 66 6
± 50.
-100.
These experiments were carried on in the evening. The animal was
first tested on a glass plate at an angle of 45° in the dark, in the ordinary
way. Then it was placed on a horizontal glass plate and strong lamp
light thrown directly upon it for a few seconds. In most cases it imme-
diately gave a negative response to the light. When definitely oriented,
the plate was again placed in the box at an angle of 45° and the box*
covered with a black cloth. Two or three geotactic observations were
then taken, and the animal again exposed to strong light. The expo-
sure to light was repeated about three times in the course of ten observa-
tions. The table shows that the influence of light has been to change a
condition of strong negative geotaxis to one of indifference. The only
exception is No. 6, which seemed little affected by the light. I hope to
make a fuller study of the combined action of light and gravity later.
It has been said that all slugs have an innate tendency to move toward
the earth. Now, this tendency is probably due to the environment and
habits of the animal. The slug, we know, is nocturnal in its habits. In
the nighttime, it is actively moving about in search of food. In the day-
time, it is inactive and seeks concealment, which is of course accom-
FRANDSEN. — REACTIONS OF LIMAX MAXIMUS. 203
plished by moving toward the earth. In hunting for food, it must
naturally do some climbing. These facts lead us to expect a possible
difference between the geotactic response of the nighttime and that of
the daytime. My experiments in this matter, however, gave inconclusive
results. But the animals experimented on were not in their normal en-
vironment. There was no light and little change in temperature to assist
the instinct, if it exists, in divining night from day. Moreover they did
not have to seek food, for it was constantly supplied them. Such being
the case, the instinct of concealment would be the main environmental
influence on the animal, and this impels it toward the earth.
These experiments have shown, then, that when the mechanical con-
ditions are favorable, most animals exhibit a positive geotaxis. This is
as we should expect. There were, however, a few exceptions. A few
animals went up when all the factors enumerated seemed to point to the
probability of a downward movement, and there were also a few animals
which went down when the mechanical difficulties were such as should
have impelled them upward. As previously noted, the upward-moving
animals sometimes displayed an unusual amount of activity, and the ex-
ceptional cases of positive geotaxis in the negative group were those of
animals usually slow and stupid. As the effort was constantly made to
select only fairly active animals in good condition for producing mucus,
there were not many of these exceptions. Knowing the habits of the
animal, we may naturally associate its activity with its food condition.
The question then comes up, Does the state of the animal's nutrition
affect its tendency to move toward the earth ? Does a poorly nourished
animal respond to the stimulus of gravity differently from a well-nour-
ished individual ? To get an answer to this question, four animals were
put into a small box which contained nothing but moist earth. The slugs
were kept there for three days, and a series of geotactic tests was then
made upon them. Two of the four individuals were inactive, aud so un-
satisfactory in response that no series was obtained. The other two were
rather restless, but precise in response. All the animals were then
returned to the box and supplied with fresh cabbage leaves. The next
morning another series of geotactic stimuli was given. The rather
meagre results given in Table IX. are perhaps not worth very much, since
only one individual (No. 1) out of the four responded well in both cases.
The ratios given in the second column (Table IX ) indicate that
slugs Nos. 1 and 2 belong with those of the positive half of Col. 8,
Table IV. I unfortunately neglected to control these experiments by
observing the geotaxis before the animals were deprived of food. In
204
PROCEEDINGS OF THE AMERICAN ACADEMY.
TABLE IX.
Comparison of Kesponses of Individuals when poobly nourished and
when well nourished.
Animal
No.
Proportionate
Ratio of Anterior
to Posterior
Region.
Poorly nourished.
Well nourished.
No. of Trials.
% Geotaxis.
No. of Trials.
°10 Geotaxis.
+
—
+
-
1
2
3
70.
60.
56.
3
1
0
9
8
0
-75.
-88.8
0
7
4
12
2
1
6
+77.7
+80.
+66.6
both instances (Nos. 1 and 2) the animals were rather dry, and they
were not noticeably different in this respect after being well fed. No. 2
was less active and less precise in response after it had had plenty of
food. I think these experiments too few to warrant laying much stress
upon them, but I have given them here because they at least point in the
direction of what we might reasonably expect, since the natural desire of
the animal to escape from its narrow prison and the impulse to seek
food would both tend to make it go up, if given the opportunity.
Another element which may alter the slug's inherent geotaxis is
probably the state of fear. This element may be combined with the
impulse to seek food, as is perhaps the case in the instances just given, or
it may operate by itself. Animals which had just been captured were al-
ways kept in a small tin box. The captured animals would thrust them-
selves between the box and lid, which was not perfectly tight, in their
endeavors to escape, and they had to be frequently pushed back. When
they were transferred to the large box mentioned at page 187, it was
always found that they had all collected in the upper part of the smaller
box. This may have been solely for the purpose of getting air, but such
animals put on a glass plate were exceedingly active and restless, and
usually exhibited a decided negative geotaxis. I have not made any care-
ful set of experiments to find out whether these negatively geotactic
animals afterwards became positive. In one instance, I confined over
night in a small flower-jar a slug (not a freshly captured one) which had
shown a very decided positive geotaxis. In the morning it was found at
the top of the jar, and, when placed on a glass plate, showed great activ-
ity, as though it sought to escape. In every one of the tests which I
then made, it responded negatively. From these few observations, it
FRANDSEN. — REACTIONS OF LIMAX MAXIMUS. 205
would seem that fear, by impelling the animal to escape from captivity,
may alter its geotatic response. Such freshly captured slugs, moreover,
which seem unusually restless and excited, respond more capriciously
to the stimulation of light, as some later experiments will show.
Summary of Part II.
The results of the foregoing experiments warrant the following con-
clusions : —
1. On an inclined glass plate, all slugs give a geotactic response.
2. Certain slugs give a decided positive, others a markedly negative
geotactic response; a few are somewhat indifferent.
3. The geotaxis of animals kept in confinement does not vary much
on different days, nor at different times on the same day.
4. The occasional vagaries in the responses of individual animals are
to some extent due to thigmotactic and phototactic influences.
5. The different geotactic response, on a glass plate, of different indi-
viduals is due mainly to two factors : (a) The quantity and quality of the
slime secreted, which is a very important factor ; (b) the relative pro-
portions of the length of the anterior and the posterior regions of the
animal's body. All the conditions being the same, it is this factor
which " determines whether the head end will be directed up or down."
6. If the ratio of length of anterior to posterior region of body is 2:3,
or more, and the mucus is of good quality and sufficient quantity, the
slug will be positively geotactic.
7. If the ratio is 3 : 5, or less, the animal will usually migrate upward,
and the nearer the ratio approaches 1 : 2 the more apt is the slug to
respond negatively.
8. In a small number of individuals, in which the ratio lies between
2 : 3 and 3 : 5, the response will depend largely on the condition of the
mucus and cooperation of other factors.
9. All slugs have a natural tendency to move towards the earth.
This tendency is masked in the animals which are negatively geotactic
on a glass plate by the greater pull of gravity on the disproportionately
larger and heavier posterior region of the animal.
10. The general downward tendency may vary normally at different
times of the day, owing to the animal's habit of remaining in concealment
in the daytime and feeding at night.
206 PROCEEDINGS OP THE AMERICAN ACADEMY.
III. Phototaxis.
The influence of light on the direction of locomotion has been very
generally noticed among organisms, even the mostly widely separated.
The swarm spores of many algae, desmids, and other lowly organized
plants, are as truly responsive to light stimuli as are crustaceans or verte-
brates. According to the character and direction of the stimulating
light rays, two kinds of light responses have been distinguished. Photo-
taxis is the response with reference to the direction of the rays of light.
The organism moves in the path of the ray, either positively (toward)
or negatively (away from it). The response to different intensities of light
from which the directive force of the rays has been eliminated is known
as photopathy. A photopathic animal is one that selects, out of a series
of uniformly increasing intensities of light, a limited field of a certain
intensity.
Some animals, like butterflies and fresh-water Entomostraca, are
strikingly positively phototactic to diffuse daylight ; others, such as the
earthworm and the leech, are as pronouncedly negative. The kind of re-
sponse (positive or negative) may be different in closely allied forms and
in different stages of development of the same species. For example,
butterflies are attracted by strong sunlight, while moths are repelled
by it. The adult house fly is positively phototactic to daylight ; its
larva, negatively (Loeb, '90, pp. 69-77, 81-83).
The phototactic sense has been shown in some forms to change with
different intensities of light. Thus, Famintzin ('67) found that swarm
spores positively phototactic to a certain intensity of light became
negative to a light of greater intensity. The same phenomenon has
been found true of various flagellates, desmids, diatoms, oscillariae, etc.
Wilson ('91, p. 414) found that Hydra fusca was attracted by diffuse
daylight and repelled by strong sunlight. Finally, the moth's liking
for candlelight and aversion to daylight is well known. The fact
that many organisms are photopathic — that is, have a preference
for light of a certain intensity — makes it probable, in connection with
these observed variations in phototactic responses, that, for most organ-
isms, there is an optimum intensity to which they will respond posi-
tively. This optimum will vary widely in different species, probably
according to the habits and the usual environment of the species. In-
habitants of sunny pools or the open air will have an optimum of rela-
tively high intensity ; those which dwell in the ground or in shady places
FRANDSEN. — REACTIONS OP LIMAX MAXIMOS. 207
will have a correspondingly lower optimum. May it not be that every
organism will respond positively to a certain range of light intensities and
negatively to another range of intensities which is greater ? The nature
of the phototaxis may sometimes be gradually changed by organisms
becoming acclimated to new conditions. Verworn ('89, pp. 47-49) found
that a culture of the diatom Navicula brevis, which ordinarily is negatively
phototactic to very weak light, became positively phototactic when reared
for several weeks near a window. Groom und Loeb ('90, pp. 166-167)
found that young Nauplius larvae of Balanus which were at first positively
phototactic to daylight became negatively phototactic later in the day,
probably as the result of the accumulated effects of this exposure.
The character of the light responses, as was the case with geotaxis,
depends also to a certain extent on other external conditions, such as
those of temperature, the states of density and pressure, and various
chemical influences. Polygordius larvae, when gradually cooled from
16.5° C. to 6° C, were found by Loeb ('93, pp. 90-96), to change from
a negative to a positive phototaxis. Like results were obtained by him
from Copepoda. When the temperature was raised from 6° C. to 16° C,
the animals again became negative. Increasing the density of sea-water
by the addition of sodium chloride produced a change from a negative to
a positive response, thus acting like diminished temperature. Engelmann
('82, pp. 391-392) showed the apparent phototactic response of chlor-
ophyllaceous ciliates to be really a chemotactic attraction for oxygen,
which chlorophyll can produce only in the light. These facts make it
important in any study of light response to consider other possible influ-
ences, and above all to take account of the strength of the stimuli used.
Davenport and Perkins ('97) found that the slug (Limax maximus)
responded with marked precision to the varying stimuli of gravity at
different angles of inclination of the glass plate. The precision of re-
sponse varied correlatively with the force of gravity. In fact, the paral-
lelism was almost perfect. The question naturally rises, Is there a
similar parallelism between other stimuli and their responses ?
A very little experimentation shows that the slug is extremely sensi-
tive to light. We have already seen how light may enter in to modify
the action of gravity. Casual observation shows that the response is in
most cases negative, — the animal moves away from the source of
light. Owing to its method of locomotion, the slug is easily experi-
mented on. It moves slowly and deliberately. In regard to its responses
to light, the following questions suggest themselves : (1) Are all indi-
viduals negatively phototactic to artificial light? (2) Does the precision
208 PROCEEDINGS OF THE AMERICAN ACADEMY.
of response vary correlatively with the intensity ? (3) Within what
limits of intensity is the animal responsive ? (4) Does the kind of
response vary at different intensities ? (5) Is there a difference in the
sensitiveness to light of the two sides of the animal's body ? (6) In what
part, or parts, of the animal's body does the sensitiveness reside? (7)
How does the animal move when in the dark and deprived of all stimu-
lating influences ? These various problems came up gradually as the
work progressed and were considered in turn. Other interesting studies
have suggested themselves in the course of the investigation, but there
has not been time to go much beyond a consideration of the questions
above proposed. The experiments performed were all phototactic ; that
is, they were studies of the response of the slug to the direct rays of
light.
Methods. — The methods used were simple. For light, the standard
candle and the ordinary small Christmas candle, of a one fourth candle
power, were employed. The candle was placed in a box 50 cm. (20
inches) high and having a bottom 12.5 cm. (5 inches) wide and 20 cm.
(8 inches) long. It could be raised or lowered to any desired position by
means of an adjustable stage inside the box. A circular opening in the
middle of one of the broad sides of the box 2 cm. (£ inches) in diameter
permitted the light to pass out. This opening was covered by a piece of
oiled paper, so as to give a well-defined uniform source of light. During
the experiment the box was closed by a lid. The intensity of the light
was varied by altering the distance between the box and the animal.
Additional thicknesses of paraffined paper were also employed when it
was desired to greatly diminish the intensity of the light. The animal
was put on a circular glass plate which rested horizontally on a support,
and the box was raised so that the centre of the light opening was in the
same horizontal plane as the body of the animal. The movement of the
slug from its original position was measured in degrees in the following
manner. A circle of the same size as the glass plate was described on a
sheet of thin paper and divided by radii into 72 sectors of 5° each. This
sheet was pasted to the under side of a second circular glass plate (of the
same size as the first), on which also a heavy base line was drawn, corre-
sponding with a diameter of the circle. This second plate was so placed that
the centre of the source of light was on a line perpendicular to the base
line at its middle point. The slug was put on the first glass plate, which
could be rotated so as to bring the animal into any desired position with
reference to the base line. The experiments were carried on in a dark
room provided at one end with a hinged window which could be easily
FRANDSEN. — REACTIONS OF LIMAX MAXIMUS. 209
and quickly thrown open. The window was covered with a thick, black
cloth, so that, when closed, external light was almost completely shut off.
Unfortunately, it was impossible, owing to the position and nature of the
room used, entirely to equalize all conditions. The temperature was not
the same from day to day and varied somewhat in different, parts of the
room. Generally, it was so hot and close that it was necessary to leave
an opening between the sashes, and this of course created a slight draft
and produced irregularities of temperature. No account was taken of
the varying humidity of the atmosphere, a factor which may have some-
what influenced the animal's locomotion. Moreover, as the room was
not perfectly light-tight, there were feeble light stimuli in addition to the
artificial ones used. However, all these imperfections were but slight,
and, since they entered more or less into all the experiments, could not
greatly alter the relation between the results, which was the main thing
sought in the investigation. Other unestimated possible influences were
the nutrition of the animal and such slight thigmotactic stimuli as could
not well be avoided.
The strength of the different intensities of light used was measured by
moving a piece of paper, the centre of which was oiled, between a light
of known intensity and the light whose intensity it was desired to know,
until the oiled spot on the paper was not distinguishable from the rest of
the paper. The distance from this point to each source of light was then
measured. Since the intensity varies inversely as the square of the dis-
tances, it is an easy matter to calculate the relative strengths. This
method is accurate enough for all ordinary purposes.
Operations and Results. — In beginning any experiment, the slug, as
soon as it had definitely orieuted itself, was rotated into such a position
that the axis of its body coincided with the base line, and its head was at
the centre of the disk. The window was then immediately closed and
the time noted. At the expiration of 45 seconds, the window was thrown
open and the animal's position instantly noted. The extent of positive
or negative migration was at first ascertained by finding the length of the
arc stretching from the base line to the radius which was parallel tvith
the axis of the slug's body. Any movement into the half of the circle
toward the source of light was called positive ; any movement into the
other half, negative. It would occasionally happen that an animal would
at first move into the positive half of the circle and then turn away from
the light. In this case the axis of orientation made a negative angle
with the base line, although the animal itself lay in the positive half of
the circle. Later, in the course of the experiments, the positive or
vol. XXXVII. — 14
210 PROCEEDINGS OF THE AMERICAN ACADEMY.
negative movement of the animal was measured by taking the radius
which passed midway between the two tentacles, without regard to the
position of the body axis. A comparison of the two methods showed but
little difference in the results. The animals only occasionally made these
irregular responses, first in a plus and then a minus direction. As a rule,
the migration was unequivocal after the head end had oriented itself to
the stimulus. Experiments were made with 18 different intensities of
light, each constituting a " series." Six successive observations were
made on each individual (3 with the right side exposed ; 3 with the left),
and from 8 to 14 animals were employed in each "series." i.e., at each
intensity of light, making a total of from 48 to 84 observations at each
candle power used. A summary of the results for each of 18 such
" series " is given in Table X.
The first column gives the number of the series ; the second, the
intensities of light. This intensity is expressed in terms of the standard
candle power at a distance of one meter. The next column (3) shows
the total positive migration of the (8 to 14) animals experimented with.
Column 4 similarly gives the total negative migration. Column 5 repre-
sents the average arithmetical angular deviation from the original posi-
tion due to phototactic stimuli, effected in a period of 45 seconds by all
the slugs, without regard to the positive or negative character of the
individual phototaxis. This average was obtained by adding together the
average phototactic responses (whether plus or minus) of each individual
of the series and dividing the result by the number of animals. The
average plus or minus phototactic response (algebraic average) for each
series (column 6) was obtained by getting the difference between the
sums of all the plus and all the minus movements of each series and
dividing this difference by the number of tests (observations) made.
Column 7 gives the number of positively phototactic animals in each
series; column 8, the number of negative animals; column 9, the num-
ber of indifferent animals ; and column 10, the total number of individ-
uals employed in each series. The sequence of the series is not the
same as that of the experiments, but is based on gradually diminishing
light intensities. I did not determine the possible influence of the heat
of the candle for each of the series, but in one series of experiments in
the dark (186), a candle, covered (to shut out the light) with an opaque
paper of the same thickness as the paraffined paper, was left burning at
a distance of 30 cm. (intensity .676 C. P.).
A casual glance at the table at once answers the first of the questions
proposed in the statement of the problems (pp. 207-208). All slugs are
FRANDSEN.
REACTIONS OP LIMAX MAXIMUS.
211
not negatively phototactic. At the strongest intensity of light used, two
animals exhibited a positive phototaxis, — they moved toward the stiinu-
TABLE X.
Responses of the Slug to Light.
1
2
3
4
5
6
7
8
9
10
No. of
Series.
Intensity of
Light.
Total Pho
gration i
;otactic Mi-
i Degrees.
Average Response
in Degrees in a Period
of 45 Minutes.
No. of Animals.
Arithmet-
rical .Sum.
Algebraic
Sum.
+
—
+
2
6
0
0
Total.
1
.676
330
2155
45.5
-38.
8
2
.382
625
2772
40.
-25.5
2
12
0
14
3
.169
440
2430
27.5
-25.5
2
11
0
13
4
.042,4
625
1330
26.
-11.7
2
8
0
10
5
.010,5
250
1165
17.6
-15.
2
8
0
10
6
.004,7
830
1140
16.1
- 5.1
o
7
0
10
7
.001,09
405
7G0
9.1
- 6.
3
6
1
10
8
.000,754
695
595
13.
+ 1.4
7
5
0
12
9
.000,424
1145
895
17.
+ 3.5
6
4
2
12
10
.000,260
823
345
14.5
+ 7.9
7
3
0
10
la
.001,69
365
480
4.6
+ 1-7
4
7
0
11
8a
.000,754
845
345
11.8
+ 8.3
7
3
0
10
9«
.000,424
985
130
14.7
+14.2
9
1
0
10
10a
.000,260
740
435
11.
+ 4.2
8
4
0
12
11
.000,022
1395
55
22.3
+22.3
10
0
0
10
12
.000,009,6
030
515
8.6
+ 2.
7
o
o
0
10
13
.000,003,35
865
255
13.
+10.
8
2
0
10
14
.000,002,00
800
170
10.5
+10.5
9
0
1
10
15
.000,001,26
850
415
11.1
+ 7.2
7
3
0
10
16
.000,000,185
1375
145
24.
+20.5
7
3
0
10
17
.000,000,018,8
445
370
8.9
+ 1.
6
4
0
10
18a
Darkness.
1440
1290
3.6
+ 1-2
10
8
2
20
186
" with
candle heat.
475
635
8.7
- 3.
3
6
0
10
212 PROCEEDINGS OF THE AMERICAN ACADEMY.
lating light rays. Here, then, arises another problem, similar to the
one treated of in the first part of this paper, viz., What determines
whether a particular slug shall be positively or negatively phototactic ?
In the first series of experiments — in fact throughout this whole set —
the animals used were about equally divided between large, small, and
medium-sized individuals. The two positive animals in series 1 were both
of large size. They were very active. The only peculiarity wherein
they seemed to differ from other individuals was in the unusually
sticky character of the slime. Whether there is any correlation between
this fact and the liking for strong light, I am not prepared to say; It
is possible — and certain observations seem to indicate that it is highly
probable — that the food conditions of the animals have some influence
on their responses to light, as they were shown to have on their responses
to gravity. The psychic state of the animal is also to some extent, I
think, a factor. Freshly caught slugs when put on a glass plate some-
times acted as if in great fear. They displayed unusual activity and
were very erratic in their movements. If forcibly checked or held,
they made strenuous efforts to escape. The great activity of the posi-
tive individuals indicates a possible state of fear. One animal in par-
ticular seemed highly abnormal. Several times it moved directly toward
the circular field of light and even placed its tentacles against the oiled
paper which covered the opening. This was the only individual in the
whole course of the experiments which exhibited a response like that of
moths. No definite set of experiments was planned or carried out in
regard to this matter.
As we run down column 5, we see that the average arithmetical
response varies quite strikingly at the different intensities. The first
seven series show a gradual decrease in the average response as the
strength of the light is diminished. Although not so regular, there is
also a gradual decrease in the degree of negative response on the part
of these seven groups of animals, as shown by the average algebraic sums
of their responses (column 6).
Owing to the constant dying off and deterioration of the stock, it was
found impossible to use the same set of animals in all the different series
of experiments. Moreover, this was not desirable, for the reason that
an animal which is constantly experimented on gradually loses its sensi-
tiveness, and thus its responses become untrustworthy. Not knowing
the factors which determine the kind of phototaxis, it was of course
impossible to make a uniform selection in this respect. We see, how-
ever, that the number of negative animals (column 8) is less at the
FRANDSEN. — REACTIONS OF LIMAX MAXIMUS. 213
weaker intensities than at the stronger. When we come to series 8 of
the table, we meet with a new condition of affairs. Instead of a still
further decrease in the amount of deviation, there is a sudden slight in-
crease, from 9.1° to 13°, and a reversal in phototaxis for the series from
an average response of — 6° to + 1-4°. The number of positive indi-
viduals has increased from 3 to 7. It was because of this striking
change that it was thought best to repeat this series and the three suc-
ceeding ones on another set of animals. The absolute positive or nega-
tive migration was this time taken without regard to the position of the
body axis. Series 7a, 8a, 9a, and 10a are hence taken at the same
intensities as 7, 8, 9, and 10 respectively. These repeated series indi-
cate as strongly as the first set that an intensity of .001,69 C. P. very
nearly marks the lower limit of negative phototaxis in the slug. Some-
where near a candle power of .000,754, lies an intensity which attracts
about as many animals as it repels and in about the same degree. That
is, the average phototaxis (algebraic sum) is zero. Below this intensity,
there is more attraction than repulsion, and hence there is an average in-
crease of migration toward the light. The table shows that the average
positive response increases to some extent correlatively with the diminution
of the light intensity, up to a certain point. This point, according to
the results here obtained, is the intensity of .000,022 C. P., where
the average movement toward the light, in a period of 45 seconds, was
through an angle of 22.3°. As we go below this intensity, there is
again a falling off in the strength of the positive response, which dimin-
ishes, however, with a good deal of irregularity until absolute darkness
is reached. These facts will become more apparent from the study of
their graphic portrayal in the curve here given.
The continuous line represents the curve as plotted from the results of
Table X., column 6 ; the dotted line, the curve of responses as one may
assume theoretically it would have been, could all of the conditions
other than intensity of light have been equalized. The abscissae here
represent the logarithms of the intensities of light + 10. Beginning
with darkness on the left end, there is a constant increase of intensity
as we move toward the right. The sines of the angles of response are
marked off on the ordinates. Remembering that the left represents a
region of weak intensity and the right a region of strong light, that all
points above the line x x' are points of positive response and all points
below it of negative response, we can understand the significance of
the curve. In the region of strong light, the curve lies far below the
line x x', but gradually rises toward and finally crosses it, as the light
214
PROCEEDINGS OF THE AMERICAN ACADEMY.
CURVE OF RESPONSES TO LIGHT.
*■**"
*-.
'{
1
6S
y
\
s
/ /
\
\
\
*
/
\
'
\
h
/
/
\
\
\
\
\
.
/
\
\
\ ?
a
/
\
\
\/
►
/
/
\
'(
2
/
t
/
14.
\
/
\
1
t
1
1
> 1 :
V
J
\
3 a
t
1
\
U.
VI
1
?\
D
1
\
J
1
I
1
i
1
\
\
1
/
/
/
I
If
)a* J
\
/
i
7 a
/
1
, 7
i
i
1 1\
--
\
2
3
4
5
5
7
8
3
10
--1
,
7
'
\
i \
\
i
\
i
\
4
2
^
■^ /
\
5
\
\
3
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\ *
\
\
\
4
\\
:
?*
\
i
5
\
\
i l
i 1
6
ii
7
Figure 2.
Curve of Responses to Light Abscissae are logarithms of light intensities plus
10 ; ordinates are sines of angles of responses multiplied by 10.
PRANDSEN. — REACTIONS OF UMAX MAXIMUS. 215
diminishes in strength. Then there is a gradual increase in positive
reaction, which reaches its height in a response of +22. °3 at a .000,022
C. P., and then falls toward the zero line as we approach darkness.
There is some irregularity in the negative region, but on the whole the
rise is gradual. In the region of positive response, there is a consider-
able lack of regularity, especially marked by the interpolation of one
series (12) of very low response between the two series of greatest
response. These series intermediate between Nos. 11 and 16 represent
later experiments than the two series bearing those numbers. Having
obtained such a marked positive response at two widely separated in-
tensities of light, it was thought desirable to get other intermediate
series. Hence, the order of the series as arranged in the table, on the
basis of gradually diminishing light intensities, does not, as already stated,
represent the order in which the series were obtained in my experiments.
While the slugs, thus far, had, on the whole, been in good active condi-
tion, they were not so in these intermediate series. Although a fresh
supply was obtained, all the animals seemed much more stupid and
irresponsive than usual. Some of them refused to move, when put on
a plate, and many of those that did, responded in a very half-hearted
way. The cause of this unusual lack of activity, I could not discover.
It may be that a slight change in the food of the animals, which I made
at this time, was partly responsible. At any rate, instead of obtaining
responses intermediate in amount between those of series 11 and 16 as
might have been expected, the results were as have beeu given. Series
12 was the last one taken. In this, the animals were noticeably more
stupid and irresponsive than in any of the preceding experiments. It is
very evident from these results, I think, that the precision of response
will vary to some slight extent from day to day. The negative responses —
those to strong intensities of light — will not be as variable at different
times as the positive responses — those to weaker stimuli — as the curve
shows. The varying thermal conditions of the room, already mentioned,
may have been in part a cause of this irregularity. Furthermore, an
animal that has had plenty of food is likely to be stupid and slow in
movement and is more apt than a hungry one to seek darkness and
concealment. On the other hand, a hungry, active slug will probably ex-
hibit positive phototaxis in a most marked and sometimes abnormal degree,
as was the case occasionally with the positive animals at the strongest
light intensities. Besides this individual variation, there is, I think, a
general variation for all slugs from time to time, for reasons imperfectly
known, which will find its expression in curves of different heights.
216 PROCEEDINGS OF THE AMERICAN ACADEMY.
Thus the less responsive animals of the intermediate but later series
mentioned fall into a less prominent curve, as is indicated by the shorter
dotted line in the diagram. The curve of positive response approaches,
but never actually reaches, the zero line. Even in darkness there is a
slight positive migration. This series (No. 18a) represents the average
of two series of experiments, one of 54 and the other of 66 deter-
minations, each taken at different times during the investigation. This
slight positive response — speaking of it as positive with reference to the
position of the source of light in the preceding series (17) — may be inde-
pendent of conditions of light and due to several causes. As mentioned
before, the thermal conditions of the room were not uniform, conse-
quently the positive response may have been a response to heat. The
movement was away from the window and hence might be ex-
plained as a negative response to the repeated inflowing of daylight,
when the window was thrown open to make observations. In the last
few experiments an opaque screen was put up between the animal and
the window. In these cases the average of the responses was slightly
negative, so there is some reason to suppose that it was in part the posi-
tion of the window in the previous experiment that determined the slight
positive migration. The actual phototactic responses to the caudle light
in the positive half of Table X. would then be the observed responses
minus this small positive movement in the dark. The actual negative
responses to the strong intensities would be the observed responses plus
this increment. In series 18b the box was placed at a distance of
30 cm. (C. P. 0.676) with the light burning, but the opening was cov-
ered with a piece of black paper to shut out the influence of the light
while leaving that of heat. The small average response of —3.0 may
possibly be regarded as a thermotactic one, and, if so, will have to be
deducted from the negatively phototactic response to this intensity of
light. For intensities less than the 0.676 C. P., the response to the heat
would be correspondingly less.
We can now answer the second and fourth questions (pp. 207-208) by
saving, — that the precision of the phototactic response does, on the
whole, vary correlatively with the intensity of the light, and that the kind
of phototaxis (positive or negative) is not the same for different intensi-
ties of light. The slug gives a negative phototactic response to strong
light, a positive one to weak intensities, and is neutral to an intensity
somewhere between the extremes.
A few individuals were tested successively at different light intensities
in order to find out with what precision an individual's phototaxis might
vary with a change of intensity.
FRANDSEN. — REACTIONS OV LIMAX MAXIMUS.
217
TABLE XI.
Responses of Individuals to Different Intensities of Light.
Animal No.
Intensity.
Response.
Intensity.
Response.
Intensity.
Response.
1
2
3
.382 C. P.
.382 C. P.
.382 C. P.
-36.°
-39.°
-42°
.169 C. P.
.169 C. P.
.169 C. P.
-34.°
-14.6°
::i.°
.067 C. P.
.067 C. P.
.067 0.1'.
-27.°5
- 10°
-23.°
In all these cases, there if seen to be a gradual diminution in the degree
of response as the intensity of light diminishes. Again, from an animal
which responded negatively to a certain intensity of light, a positive
response could be got by weakening the light sufficiently (Nos. 2 and 3,
Table XII.), and a positive animal could be made to give a negative
response by using stronger light (No. 1, Table XII.), as the following
instances show.
TABLE XII.
Responses of Individuals to Different Intensities of Light.
No.
Intensity.
Response.
Intensity.
Response.
Intensity.
Response.
Intensity.
Response.
1
.382 C. P.
+41.°
Strong
Light.
-22.°
o
.676 C.P.
-15.°
.0424 C.P.
+35.°
3
.169 C.P.
-37.°
•0188C.P.
- 2.°5
.0067 C.P.
-32.°
.0047 C.P.
+30.°
No. 3, Table XII., shows a less regular response than any of the other
animals. From a response of — 37° it drops to one of — 2.5°, and, under
the influence of a still lower intensity of light, it again rises to a marked
negative response of —32.° At a still lower intensity, it gives a striking
positive response of +36°. Here, however, we have well illustrated in
particular individuals the law laid down for all slugs, — that they are
negatively phototaetic to strong intensities of light, the precision of re-
sponse varying correlatively with the intensity of the stimulus ; that to
weak intensities they are positive ; and that to a certain intermediate
intensity they are neutral.
A glance at the intensity column (Table X.) shows that the slugs are
218
PROCEEDINGS OP THE AMERICAN ACADEMY.
responsive to a very wide range of intensities. They would probably
continue to respond negatively to still stronger light, until the light
became strong enough to kill the animal. They respond positively to a
light (series 16) less than one three millionth part as intense as the
strongest intensity experimented with. The response to the weakest
intensity used (series 17) is less than the positive migration in the dark.
Hence we cannot speak of this as a phototactic response. This attenua-
tion of light was so weak that I could not be sure I saw it myself, and
had constantly to reassure myself by approaching it. The slug is evi-
dently sensitive to a very minute degree of light.
Where does the slug's sensitiveness reside? The first and most
natural answer is, that the eyes are the important organs. The matter
was tested on five different individuals. The normal phototactic response
was first taken with a .676 candle power. Then the dorsal tentacles,
bearing the eyes, were snipped off with scissors and the animal again
experimented on. The results are given in Table XIII.
TABLE XIII.
Effect of Amputation of Tentacles.
Animal
No.
Normal Phototactic
Response.
Response after Amputation
of Dorsal Tentacles.
Ventral Tentacles also
Amputated.
1
-70.°
+41.°
2
-26.°
- 3.°
o
o
-44.°
-29.°
+7.°
4
-53.°
+16.°
5
-65.°
+ G.°
As soon as the operation was performed, the stumps were retracted, as
the tentacles are when stimulated by touching, or by strong light. After
a moment or two, the animal again rolled out the stumps and began
moving forward in perfectly normal fashion, as though nothing had
happened. The only observable difference was a perhaps slightly in-
creased activity. This table (XIII.) shows a striking effect of the
amputation on the phototactic response. In some cases, the animal
deviated but very little either positively or negatively from its original
position, but kept on moving ahead in a straight line. In other cases,
the amputation seemed to cause a change from a strongly negative to a
FRANDSEN. — REACTIONS OF LIMAX MAXTMUS.
219
more or less positive response. In the case of animal No. 3, removal of
the eyes did not seem to altogether prevent, though it considerably
reduced, the negative response. Thereupon, the ventral tentacles were
also amputated and the result then was a slight positive response. Since
there is probahly some shock to the nervous system by the amputation,
these results ought to be corroborated by other experiments where the
eyes are covered over with some substance to shut off the rays of light.
This, I have not yet succeeded in doing satisfactorily.
The experiment of removing only one of the ocular tentacles was tried
on two different animals with the following interesting results.
TABLE XIV.
Comparison of Effect of Amputation of Right and Left Dorsal
Tentacles.
Animal
No.
Normal Phototactic
Response.
Response after Amputation of
Right Tentacle.
Left Tentacle.
1
2
-70.°
-55.°
—27.°
+3.°
In the case where the right tentacle was removed, the animal still
responded negatively with considerable precision. Amputation of the
left tentacle, in the case of No. 2, on the other hand, resulted in a slight
positive phototaxis. While these two cases by themselves have little, if
any, significance, taken in connection with facts now to be discussed, they
seem to indicate a greater degree of sensitiveness to strong light on the
part of the left side of the animal's body than the right.
It will be remembered that our thigmotactic experiments pointed to a
possible asymmetry in the sensitiveness of the right and left tentacles of
the slug. Do we find a similar asymmetry in the responses to light?
Table XV. gives the responses of right and left sides respectively for the
18 series. Column 1 gives the number of the series, column 2 the in-
tensities of light, columns 3 and 4 the total angular migrations in a positive
and negative direction for the series when the right side was exposed to the
light, and the fifth column the algebraic average (positive or negative)
phototactic response of the right side. Similarly, the next three columns,
6, 7, and 8, give the responses of the left side. Column 9 represents
the total movement of the series in degrees to the right. This result was
obtained by adding the total positive responses of the right side (column 3)
220
PROCEEDINGS OF THE AMERICAN ACADEMY.
TABLE XV.
Comparison of Responses of Right and Left Sides to Light.
1
CO
JV
0)
o
6
m
l
2
o
O
4
5
6
7
8
9
10
11
<
°i
& s
a
o
H
Intensity of
Light.
Responses of Right
Side in Degrees.
Responses of Left
Side in Degrees.
Total Movement
in Degrees to
+
—
Average
Photo-
taxis
+ or —
+
—
Average
Photo-
taxis
+ or —
Right.
Left.
.676
305
770
-19.
25
1385
-57.
1690
795
8
2
.382
250
1056
-19.
375
1716
-32.
1966
1431
14
3
.169
425
595
- 4.3
15
1835
-46.8
2260
610
13
4
.042,4
255
355
- 3.3
370
975
-20.
1230
725
10
5
.010,5
65
730
-22.
185
435
- 8.
500
915
10
6
.004,7
295
805
-17.
535
335
+ 6.7
630
1340
10
7
.001,69
250
500
- 8.3
155
260
- 3.9
510
655
10
8
.000,754
280
330
- 1.4
415
265
+ 4.1
545
745
12
9
.000,424
530
645
- 3.
615
250
-10.
780
1260
12
10
.000,200
435
245
+ 6.3
388
100
+ 9.6
535
633
10
la
.001,69
250
210
+ 12
115
270
- 5.
520
325
11
8a
000,754
410
165
+ 8.1
435
180
+ 8.5
590
600
10
9a
.000,424
380
75
+10.
005
55
+17.
435
680
10
10«
.000,200
560
230
+ 9.
180
205
- 0.7
765
410
12
11
.000,022
955
0
+31.7
440
55
+12.7
1010
440
10
12
.000,009,6
160
275
- 3.8
470
240
+ 7.6
400
745
10
13
.000,003,35
460
120
+11.7
405
135
+ 9.
595
525
10
14
.000,002,0
410
90
+10.7
390
80
+10.3
490
480
10
15
.000,001,26
395
320
+ 2.5
455
95
+12.
490
775
10
16
.000,000,185
915
40
+29.
460
105
+12.
1020
500
10
17
.000,000,018,8
210
215
- 0.2
235
155
+ 2.6
365
450
10
18a
186
Darkness
" with
candle heat
1220
155
240
495
+16.
-10.
220
320
1050
140
-13.8
+ 7.
2270
295
460
815
20
10
Totals
9570
8506
7808
10321
19891
16314
" less 18a & 186
8195
7771
7268
9131
17326
15039
FRANDSEN. — REACTIONS OF LIMAX MAXIMUS.
221
and the total negative responses of the left side (column 7), — these
responses being necessarily right-hand movements. The total movement
in degrees to the left (column 10) was likewise obtained by adding the
total negative responses of the right side and the positive responses of the
left side. Column 1 1 gives the total number of animals used in each series.
In the region of negative phototaxis, the total positive and negative
angular migrations, and the average negative phototaxis of all the series
(1-7, inclusive) when the riglit and left sides respectively were turned
toward the light, were as follows.
TABLE XVI.
Sum of the Responses of Right and Left Sides when Phototaxis
is Negative.
Side turned
toward Light.
Total Angular Migration.
Average Negative
Phototaxis.
+
—
Right.
Left.
1815°
1660.°
4811.°
6941.°
13.°1
23.°4
This shows on the whole a less sensitive right side, or, to put it differently,
a more marked negative phototaxis of the left side. How is it when the
animals become positively phototactic ? Table XVII. gives the average
positive response of the right and left sides for series 8 to 18, including
series la, 8a, da, and 10a.
TABLE XVII.
Sum of Responses of Right and Left Sides when Phototaxis
is Positive.
Side turned
toward Light.
Total Angular Migration.
Average Positive
Phototaxis.
+
—
Right.
Left.
6350°
5608°
2960.°
2190.°
7.°68
7°75
Here an asymmetrical response is less strongly marked. The left side,
however, appears on the average to be somewhat more strongly attracted
toward the light. The results prove that the asymmetry in response of the
right and left sides cannot be wholly due to a tendency to move toward
222 PROCEEDINGS OF THE AMERICAN ACADEMY.
the right, for, if this were so, we should expect an average positive
response of the right side as much greater than that of the left side, as the
average negative response of the left is greater than that of the right side,
for both these would mean a greater movement to the right. These
facts curiously suggest that the right and left sides are attuned to slightly
different intensities of light. Is this possibly due to ancestral habits of
life in which environment, acting unequally on the two sides, produced
this difference ?
The results obtained for the right and left sides from the experiments
in darkness (series 18a) are rather puzzling. If the responses are due
to some uncontrolled directive stimuli of the kind already suggested, it
would seem that the two sides had given opposite responses. As these
experiments represent two series taken at different periods, it is the
more surprising that they should both show this peculiarity. Again, in
the responses to weak candle heat (series 18b) the left seems to have
been positively, and the right side negatively affected. So far as is known,
there was no unequal operation of stimuli on the two sides.
Related to this matter is the question, — Is there any tendency on the
part of all slugs to move either to the right or to the left? Individuals
were noticed which seemed to have a marked tendency to continue
moving toward the right, and there were others which seemed to be as
strongly biassed toward the left. Not many seemed entirely indifferent.
The total movement of all the slugs in the region of negative response
(series 1-8, Table XV.) toward the right side was 8786° (col. 9), and to
the left G471° (col 10). In the positive region (series 8-18, Table XV.),
the total migration toward the right side was 8540° (col. 9), and to-
ward the left 8568° (col. 10). Thus, there seems to have been con-
siderably less migration toward the left in the range of negative
responses, but only a slightly greater movement toward the left in
the region of positive response. In all the 17 series, there was a mi-
gration towards the right of 17,326°, and towards the left of 15,039°.
That is, there appears on the whole to have been a slightly greater
average movement for all slugs toward the right than there has been
toward the left. What do we find to be the case with the animals experi-
mented on in the dark? Out of the 120 determinations made on 20
animals in the dark (series 18a), the amount of right-hand movement
was 2270° and the left-hand movement only 4 G0°. That is, there was
nearly five times more migration toward the right than there was toward
the left. In series 18b, however, there seems to have been a marked pre-
ponderance of movement toward the left. From the foregoing experi-
FRANDSEN. — REACTIONS OF LIMAX MAXIMUS. 223
ments, it seems pretty clear that there is a difference in the sensitiveness
of the right and left sides. There is also some indication of a slightly
greater average tendency to move to the right. But a further study of
the undirected movements of slugs in the dark is needed.
Studies have been made by several observers on the undirected move-
ments of a number of different animals, chiefly ants and other insects.
In all animals experimented on, there appears to be a tendency to travel
in loops or constantly widening spirals. Man, when he loses his way,
travels in a circle. Some interesting observations have been made bv
George and Elizabeth Peckham ('98, pp. 211-219) on the sense of
direction in the solitary wasps. When the wasp starts out from its nest,
it flies quite around it and gradually circles farther and farther away in a
constantly enlarging spiral, sometimes recrossing its path a number of
times. The authors' observations show that this action is to enable the
wasp to familiarize itself with its surroundings, so that it can find its way
home when it so desires. The similar phenomenon observed in other
insects, such as ants, is, no doubt, for the same purpose. Davenport
('97, pp. 278-279) in his experiments on Amoebae found that, when
their movement was undirected by any external stimulus, they tended to
travel in curious spiral loops. Pouchet ('72, pp. 227-228) made obser-
vations on the movement of larvae of Musca (Lucilia) caesar in the dark.
There is a striking contrast between the paths given by him of the un-
directed movements and those made in response to the stimulus of light.
The tendency to travel in a gradually widening spiral has also been
observed by the writer in young frog and toad larvae — before the develop-
ment of mouth and eyes — when they are dislodged from the support to
which they are clinging.
Most of the following experiments on the slug were made in a room
about 12 feet square. The floor was sometimes covered with cardboard
or paper, but in other experiments was left bare. Heavy curtains were
hung in front of the windows and light shut out as completely as possible.
The experiments were conducted at night, and the temperature of the.
room was nearly, if not quite, constant. A slug was put on the floor in
the centre of the room and left to itself for two or three hours, sometimes
longer. By means of the mucous secretion, which hardened into white,
shiny flakes, the exact path of the animal could, in most cases, be easily
followed. This path was roughly reproduced by pencil on paper. A num-
ber of these paths are given in Figures 3-22, much reduced from the
actual space covered. The series here given includes all the animals
experimented on, with the exception of three individuals which did not
224
PROCEEDINGS OP THE AMERICAN ACADEMY.
Figttres 3-22.
Much reduced copies of the tracks made by slugs (Limax maximus) in the dark.
dx., right-hauded loops ; s., left-handed loops.
FRANDSEN. — REACTIONS OF UMAX MAXIMUS. 225
give any characteristic paths. Two of the three moved only a short dis-
tance in wavy lines without recrossing their paths, and were in poor condi-
tion, for they did not go far, and shortly died. One extremely active little
individual moved ahead in a straight line quite across the floor, a distance
of eight or ten feet. With these few exceptions, it will be seen that
there is a very marked tendency to travel in loops. In general, the
loops varied in size from a couple of inches in diameter to two feet and
sometimes more. The animal generally makes a circle soon after starting
out, and then may travel for some distance before again recrossing its
tracks. The individuals which did the most looping also showed a
tendency, by gradually swinging away from the starting point, to make
larger and larger circles. Nos. 7, 8, 11, 13, 14, 16, 17, 19, and 22 all
showed this tendency. The smaller individuals usually make the
smaller loops, but this is not always the case. Although the paths made
by different animals have a very different appearance, they all show the
same general looping tendency. It will at once be noticed that all curves
are not in the same direction. Some are right-handed loops, others are
left-handed, and two cases, Nos. 10 and 12, contain loops of both right and
left hand character, or at least indicate a tendency to the formation of
such loops. As a rule, however, the individual shows a marked con-
stancy in the character of the loops made. Disregarding the two cases
in which there were both right and left hand loops, we have ten individuals
with a tendency to circle to the right and eight individuals with just as
marked a tendency to circle to the left. This does not indicate a very
great preponderance of individuals travelling to the right. If the total
space travelled over by all individuals be considered, I think it might
show, on the average, a more marked swerving to the right than does a
counting of right and left circling individuals, but I have not measured
the distances carefully enough to speak confidently on this point. The
evidence thus far accumulated in regard to an asymmetrical response of
the right and left sides to artificial stimuli points to a greater sensitive-
ness of the left side, which is perhaps correlated with a slight average
tendency to move toward the right side more than to the left.
Summary of Part III.
These studies on the light responses of Limax maximus seem to estab-
lish the following points: —
(1) The animals are markedly phototactic.
(2) There are individual differences in phototaxis, as there are in
geotaxis.
vol. xxxvn. — 15
226 PROCEEDINGS OF THE AMERICAN ACADEMY.
(3) To strong light, slugs, on the average, give a strong negative
response.
(4) The degree of response gradually diminishes with the reduction
in the strength of the stimulus.
(5) There is a certain strength of light which appears neither to repel
nor attract the slug. This may be said to be a neutral stimulus.
(6) Reduction of the intensity of the light beyond the neutral point
changes the phototaxis from negative to positive.
(7) The positive response becomes stronger up to a certain degree of
intensity.
(8) It then gradually diminishes with decreasing intensity until abso-
lute darkness accompanied by no response is reached.
(9) Slugs are responsive to light stimuli covering a wide range of
intensities.
(10) The principal organ of response is probably the eye.
(11) The response is unsymmetrical on the part of the right and left
sides of the animal's body. The right side is not as sensitive to stimuli
as is the left. On the whole the right side moves through a slightly greater
arc in a period of 45 seconds than does the left.
(12) In the dark, other directive stimuli being eliminated, the slug
tends to travel in a spiral of gradually increasing radius, though almost
invariably producing one or more loops. Some slugs make right-hand
loops, others left-hand ones ; there is a slightly greater tendency to
right-hand circling.
These responses of the slug to touch, gravity, and light-stimuli empha-
size the fact that it is an animal's normal environmental conditions which
chiefly determine its general response to artificial stimuli. The variations
in precision and character of this general response are mainly dependent
on certain internal factors, such as the food conditions of the animal, its
fear of an enemy, and desire to escape captivity.
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"88. Beitrag zur Kenntnis rich tender Krafte bei der Bewegung niederer Or-
ganismen. Jena. Zeit. Bd. 22, pp. 310-342.
Davenport, C. B.
'97. Experimental Morphology. Part I. pp. xiv. + 280. New York.
Davenport. C. B., and Perkins, Helen.
'97. A Contribution to the Study of Geotaxis in the Higher Animals. Jour.
of Physiol. Vol. 22, pp. 99-110.
FRANDSEN. — REACTIONS OF LIMAX MAXIMUS. 227
Engelmann, T. W.
'82. Ueber Liclit- unci Farbenperception niederster Organismen. Arch. f.
ges. Physiol. Bd. 29, pp. 387-400.
Famintzin, A.
'67. Die Wirkung des Lichtes und der Dunkelheit auf die Vertheilung der
Chlorophyllkorner in den Bliittern von Mnium sp. (?) Jahrb. f. wiss.
Bot. Bd. 6, pp. 49-54.
Groom, T. T., und Loeb, J.
'90. Der Heliotropismus der Nauplien von Balanus perforatus und die peri-
odischen Tiefenwanderuiigen pelagischer Tiere. Biol. Ceutralbl. Bd. 10,
pp. 160-177-
Jensen, P.
'93. Ueber den Geotropismus niederer Organismen. Arch. f. ges. Physiol. Bd.
53, pp. 428-480.
Loeb, J.
'88. Die Orientierung der Thiere gegen die Schwerkraft der Erde (Thierischer
Geotropismus). Sitzber. phys.-med. Gesell. Wiirzburg. Jahrg. 1888.
pp. 5-10.
Loeb, J.
'90. Der Heliotropismus der Thiere und seine Uebereiustimmung mit dem
Heliotropismus der Pflanzen. 118 pp. Wiirzburg : G. Hertz.
Loeb, J.
'93. Ueber kiinstliche Umwandlung positiv heliotropischer Thiere in uegativ
heliotropische und umgekehrt. Arch. f. ges. Physiol. Bd. 54,
pp. 81-107.
Massart, J.
'91. Recherches sur les organismes inferieurs. III. La sensibility a la gravita-
tion. Bull. Acad. roy. Belg., ser. 3, torn. 22, pp. 158-167-
Peckham, G. W., and Elizabeth G.
'98. On the Instincts and Habits of the Solitary Wasps. Wisconsin Geol.
and Nat. Hist. Survey, Bull. No. 2 (Sci. ser., No. 1), 1898, pp. iv.
+ 245. 14 pis.
Fouchet, G.
'72. De l'influence de la lumiere sur les larves de dipteres privees d'organes
exterieurs de la vision. Rev. et Mag. de Zool., ser 2, torn. 23,
pp. 110-117,129-138, 183-186,225-231,261-264, 312-316, pis. 12-17-
Schwarz, F.
'84. Der Einfluss der Schwerkraft auf die Bewegungsrichtung von Chlamido-
monas und Euglena. Ber. deutsch. bot. Gesell. Bd. 2, Heft 2,
pp. 51-72.
Verworn, M.
'89. Psycho-physiologische Protisten-studien. viii. -f- 218 pp. 6 Taf. Jena:
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'91. The Heliotropism of Hydra. Amer. Nat., Vol. 25, pp. 413-433.
Proceedings of the American Academy of Arts and Sciences.
Vol. XXXVII. No. 9. — November, 1901.
THE ALGAE OF JAMAICA.
By Frank Shipley Collins.
THE ALGAE OF JAMAICA.
By Frank Shipley Collins.
Presented October 9, 1901. Received October 15, 1901.
The earliest reference to the algae of Jamaica, and very nearly the
earliest reference to the algae of America, appears to be by Sloane ; * in
the chapter on submarine plants 43 species are named and described,
among which, however, are a few aquatic phanerogams, and a considerable
number of corals ; of the remainder most are too vaguely described to be
now identified, but by the help of the plates, we can give with fair cer-
tainty the modern names for four.
Vol. I. p. 57, PI. XX. Fig. 2, Corallina opuntioides, ramidis den-
sioribus, et Jills magls sinuatis atque corrugatis, is Halimeda Opuntia.
P. 58, PI. XX. Fig. 3, Corallina major, nervo crassiore fuciformi, inter-
nodla breviora nectente, White Bead Bandstring dicta, is Cymopolia bar-
bata. P. 61, PI. XX. Fig. 9, Fucus minimus denticulalus triangularis, is
Bryothamnion triangulare. P. 58, PI. XX. Fig. 6, Fucus marlnus vesi-
culas habens membranis extantlbus alatas, is Turbinaria trialata.
P. 58, PI. XX., Corallina minima capillacea, is probably our present
Corallina capillacea, but neither plate nor description is characteristic
enough to make this certain. P. 51, PI. XVIII. , Corallium album pumi-
lum nostras, seems to be some species of Lithothamnion. The other de-
scriptions are too uncertain to hazard any identifications.
A few algae are mentioned by Browne,! apparently mostly copied from
Sloane ; some plants undoubtedly belonging to the genus Sargassum are
mentioned, and from the description of the great floating masses, S.
bacciferum is undoubtedly meant, but it is probable that other species are
included under this name.
Lunan % gives seven species of algae, as follows, p. 157-158:
* A voyage to the Islands Madera, Barbados, Nieves, S. Cristophers and
Jamaica, by Hans Sloane, M.D., London, 1707.
t The Civil and Natural History of Jamaica, by Patrick Browne, M.D., 1756.
t Hortus Jamaicensis, by John Lunan, 1814.
232 PROCEEDINGS OF THE AMERICAN ACADEMY.
Fucus turbinatus = Turbinaria trialata.
" natans = Sargassum bacciferum, at least in part.
" acinarius.
" vesiculosus.
" triqueter.
Ulva pavonia = Padina sp.
" Lactuca.
After this date, except for an occasional reference in some general
work, we find nothing until Murray's West India list.* In this are in-
cluded references to Sloane and Browne, and several species are added
from specimens in the British Museum, collected by Chitty ; in a few
cases, however, these are species so little to be expected in tropical
regions, that it seems as if there must have been some displacement
of labels. The total number of Jamaica species mentioned in Murray's
list is surprisingly small, if we consider the size of the island, and that
it has been so long a comparatively thickly settled English colony. It
would be hardly fair to compare it with the Maze & Schramm Guade-
loupe list, f for it is not improbable that half the species in the latter,
certainly more than half the new species, will ultimately be relegated
to synonymy or to the catalogue of indeterminables. As an instance
of this, see the genus Gracilaria; 57 species are given by Maze
and Schramm under Gracilaria and Plocaria ; 15 of these are species
whose previously known distribution would lead one to expect them in
Guadeloupe ; of 5, the previous record would make their occurrence here
unlikely ; the remaining 37 are new species, with scanty description or
none at all. Any one at all familiar with Gracilaria will recognize what
this means.
But as compared with Puerto Rico, for which Hauck's list t gives 92
species against 31 Jamaica species in Murray's list, the disproportion is
so great that it might seem as if there must be some special conditions at
Jamaica to impoverish the marine flora.
Within the past few years the writer has had the opportunity of ex-
amining three collections of algae from this island, that show quite con-
clusively that this is not the case, and that there is every reason to
* Catalogue of the Marine Algae of the West Indian Region, by George Murray.
Journal of Botany, Vol. XXVII. p. 224. 1889.
t Algues de la Guadeloupe. 2d Edition. Maze & Schramm, Basse Terre,
1870-77.
| Meeresalgen von Puerto-Rico, von F. Hauck. Engler's Botanische Jahrbiicher,
Vol. IX. p. 30, 1888.
COLLINS. THE ALGAE OF JAMAICA. 233
suppose that the flora of the islaud is in no way inferior to similar
regions.
The first collection was made by Mrs. Cora E. Pease of Maiden, Mass.,
and her sister, Miss Eloise Butler of Minneapolis, Minn. In July, 1891,
they collected at Port Antonio and points in its vicinity ; and some
collecting was done at other ports, where the steamer touched for a few
hours. In 1894 Mo rant Bay was visited in July, with a visit to Borden
and Annotto Bay the first of August, followed by Orange and Hope Bays
and Port Antonio, where the greater part of August was spent. In
June, 1900, short visits were made to Ora Cabessa, Rio Novo, Runaway
Bay, and Rio Bono; June 21 to 27 was spent at Montego Bay; June 29
to July 1 at Kingston ; and the time to July 18 was spent at Manchioueal,
Port Morant, Hope Bay, Port Antonio, St. Ann's Bay, and Port Maria,
in the order named.
The second collection was made by the late Dr. J. E. Humphrey, in
March and April, 1893, mostly at or near Kingston, but also near Port
Antonio ; a few specimens in Dr. Humphrey's herbarium were collected
by R. P. Bigelow at Kingston in July, 1891. In 1897 Dr. Humphrey
made a second visit to Jamaica ; on August 16 he was attacked by the
island fever, and died two days later. Among the collections made that
year is a large amount of material of shell boring algae, of which he
hoped to make a thorough study on his return ; unfortunately no one
has been able to take up this task, and only such notes as Dr. Humphrey
made at the time of collecting have been available for this list.
Tlie third collection, received when this paper was practically ready
for publication, was made near Kingston, May 3, 1901, by Dr. J. E.
Duerden, who at that time was collecting corals for the Museum at
Kingston. By the kindness of Dr. William Fawcett, Director of the
Museum, arrangements were made whereby two large cans of algae pre-
served in formalin were forwarded to the writer. Of the 47 species
which were included, six were not represented in the other and larger
collections.
In the following list the abbreviation P. & B. has been used for the
first named collection, H. for the second ; where the specimens had a
number in the Humphrey herbarium, the number is given here ; notes on
station, depth of water, etc., have been copied; and Dr. Duerden's name
is given for the third collection. Of one species, not included in either
of these collections, I have received specimens from F. Borgesen, col-
lected by O. Hansen.
Many Jamaica algae have been distributed in the two sets of exsiccatae,
234 PROCEEDINGS OF THE AMERICAN ACADEMY.
Phycotheca Boreali-Americana, issued by Collins, Holden and Setchell,
and Phykotheka Universalis, issued by Hauck and Richter : references
to these are given under the respective species, with the abbreviations
P. B.-A. and P. IL, and the numbers.
The Humphrey collection includes 25 fresh water algae, the Pease and
Butler collection 9 ; only two species are common to both. If we com-
pare the marine -species * in these two collections, we find that of the
whole number, 215, only 72 occur in both; 143 are found in one and
not in the other. A natural inference from this would be that the field
was by no means exhausted, and that more species might be expected.
In Murray's list four species are given, which are omitted here :
Gyrnuogongrus furcellatus, Phyllophora Brodiaei, Liagora viscida, and
Plocamium coccineum, the first on the authority of Wright, the others of
Chitty. Probably a misplacement of labels has occurred.
Tables have been prepared, comparing the marine flora of Jamaica
with the floras of New England, Great Britain, the northern coast of
Spain, the coast of Morocco, the Canary Islands, aud Puerto Rico, lists
having been published of these regions of sufficient extent to make a
comparison of interest.!
Some of these regions having been more thoroughly explored than
others, too much importance should not be given to the total number of
species in any region ; the relative proportion of the different classes is
of more weight, while the number of species common to two regions
* In making up these statistics, named varieties and forms have been counted
the same as species.
t The data of these tables are from the following works : —
Preliminary List of New England Marine Algae, by F. S. Collins, Rhodora, Vol.
II. p. 41, 1900.
A Revised List of the British Marine Algae, by E. M. Holmes andE. A. L. Bat-
ters, Annals of Botany, Vol. V. p. 63, 1892.
Note Pre'liminaire sur les Algues Marines du Golfe de Gascogne, par C. Sauva-
geau, Journal de Botanique, Vol. XL, 1897.
Les Algues de P.-K.-A. Schousboe, par E. Bornet, Memoires de la Socie'te Na-
tionale des Sciences Naturelles de Cherbourg, Vol. XXVIII. p. 165, 1892.
Plantes Cellulaires des lies Canaries, par C Montagne, Paris, 1840.
Crociera del Corsaro alle Isole Madera e Canarie ; Alghe, per Antonio Piccone,
Genova, 1884.
Contributions a la Flore Algologique des Canaries, par Mile. A. Vickers, An-
nates des Sciences Naturelles, Series 8, Botany, Vol. IV., 1897.
Meeresalgen von Puerto-Rico, von F. Hauck, Engler's Botanische Jahrbiicher,
Vol. IX. p. 30, 1888.
In addition to the published lists of the Canary Islands, some species have been
included from the collection of the author.
COLLINS. — THE ALGAE OF JAMAICA. 235
indicates the affinities of the floras. The tables are useful merely as
showing general tendencies, not exact relations. Exactness would be
possible only when the districts compared had been explored and studied
to the same extent, with the same care and under the same conditions,
a thing practically impossible.
Table No. I. shows the distribution, in the districts named, of each
species found in Jamaica ; Table No. II. summarizes by classes the total
number of species for each of the seven regions, — it represents less the
probable richness of each region, than the extent to which it has been
explored. A tolerable test of thoroughness of exploration is often found
in the proportion which the Schizophyceae bear to the whole number.
Being insignificant, usually microscopic plants, they are quite overlooked
by the non-scientific collector. Where the knowledge of a region de-
pends on collections made by a non-scientific collector, or by a collector
who, however competent in other departments, is not specially an algolo-
gist, the red algae constitute a larger, the blue-green a smaller proportion
of the whole.
Tbe Puerto Rico collection, and in great y>art the Canary collection,
were made by non-algologists ; the Morocco was made by a skilled al-
gologist, but before much was known of the lower algae, or microscopes
perfected so that they could be suitably studied. The Biscay collection
was the work of one man, a trained algologist, studying the plants on the
spot; while the lists for New England and Great Britain cover the most
thoroughly studied parts of the world, and the work of generations of
botanists. The proportion of Schizophyceae, as shown by Table No. III.,
follows these conditions fairly well. In the New England list it is ex-
ceptionally large, as that list included a number of species, normally
fresh water, which were found growing with marine forms, but which
usually would not be included in a marine flora. The totals in all parts
of the Great Britain list are increased by the fact that in that list the
naming of forms is carried out more fully than in any of the others ; the
percentage, however, is but little affected by this.
It is noticeable that in the first five floras, which might be grouped as
warm water floras, the red algae constitute over half the whole list, while
in the two northern they are less than half, New England, the most
arctic in character though not in latitude, having only 37 per cent.
Puerto Rico and Jamaica, the most southern, have the highest percentage
of green algae, 27 and 28, respectively, they being in the region of the
Siphonaceous plants. The Canaries have less of this element, but
more than the region farther north. The low percentage of green algae
236 PROCEEDINGS OF THE AMERICAN ACADEMY.
iii the Biscay region is noticeable, but not easy to account for. Tbe
high percentage of brown algae in New England and Great Britain is
due to their northern latitude, these plants becoming increasingly preva-
lent as we go from tbe equator to the poles ; in actual arctic waters they
constitute the most conspicuous element of the flora.
Table No. IV. shows the number of species common to the flora of
Jamaica and the other floras respectively ; No. V. shows the per cent of
each class of the Jamaica flora which is found in each of the other floras ;
No. VI. the per cent of each of the others found in Jamaica. A thor-
oughly explored country shows a larger per cent in No. V., a smaller per
cent in No. VI. than a region less known, but certain general deductions
can be made. The Puerto Rican flora is closely allied to the Jamaican,
69 percent being common to the latter ; further exploration would proba-
bly increase rather than reduce this. The Canaries come next, and it is
noticeable that the percentage in Table No. V. is nearly the same in green,
brown, and red algae. In Table VI., which is perhaps the one best show-
ing the relationships, the common elements in the European floras grow
regularly less as the distance increases, only 8 per cent of the flora of
Great Britain being found in Jamaica.
, The Schizophyceae seem to vary least in different regions, the other
classes coming, Chlorophyceae, Rhodophyceae, Phaeophyceae, the com-
mon per cent of the latter being surprisingly small outside of Puerto Rico
and the Canaries.
It is worth noting that Jamaica and the Canaries have 66 species in
common, being 30 per cent of the former and 24 per cent of the latter;
while New England and Great Britain, at about the same distance, have
258 in common, being 60 per cent for the former, 35 for the latter.
This merely illustrates the general rule that beginning almost identical,
in the Arctic Ocean, the floras of the two shores of the Atlantic diverge
increasingly as we go south. There are, however, a few species common
to Jamaica and the Canaries which have not apparently been found on
the mainland of either continent ; these probably represent an actual
communication between the two.
Of the 34 fresh water algae, all but 2 are found in Europe, quite in
conformity with the rule that the fresh water algae of the two continents,
though separated by salt water, in which they cannot exist, are much
more alike than the marine algae, inhabiting the two shores of the
Atlantic.
COLLINS. THE ALGAE OP JAMAICA. 237
The island of Jamaica is situated in the Caribbean Sea, between lat.
17.40 and 18.30 N. and between long. 76.10 and 78.28 W. from Green-
wich. The land vegetation is distinctly tropical in character, though the
high land of the interior, and the steady sea breezes of the eastern coast,
make the climate more comfortable than might be expected from the
latitude. The marine flora is also of a tropical character, as is showu
by the number of species of the Dictyotales, and of green algae of the
Caulerpaceae, Codiaceae, Valoniaceae, and Dasycladaceae, as also by the
absence of any representative of the Lamiuariuceae. Coral abounds all
along the shore, and the coral reefs are often richly overgrown with
algae.
The following notes by Mrs. Pease give an idea of the character of the
shore and the conditions for collecting algae ; occasionally throughout the
list that follows similar notes by Mrs. Pease on special localities or forms
will be inserted, enclosed, like this, in quotation marks.
" The island of Jamaica is scalloped with beautiful little bays or har-
bors, and a description of one will apply to nearly all of them. The semi-
circular shores of these bays, about which the little villages cluster, are
usually low for only a very short distance back from the water ; then they
rise abruptly into steep hills or mountains. From one to several small
rivers empty into each of these bays; the shores are often of 'tufa,'
a porous rock, very trying to a pedestrian, but sometimes relieved by
little stretches of sandy beach. . . .
" At Port Antonio, which was visited at each of our trips, the harbor
is varied by having a small island lying at its entrance, and by a bold
point of land running out to break the shore into two little scallops
instead of one, one of the bays being barred by a coral reef, the other
having a very narrow channel for the entrance of vessels. This reef was
the best collecting ground at this place; the water was shallow for quite
a distance, and on jagged rocky bottom, the water about waist deep,
we found a very luxuriant growth. Caulerpa clavifera grew like little
clusters of green grapes, in big soggy masses; there were great clumps
of the encrusted algae, Halimedas, Amphiroas, Galaxauras, Cymopolias,
etc. ; these continued up towards the shore, and with them upon the
rocks were those green, warty, potato-ball-like Dictyosphaerias, Padina,
Colpomenia sinuosa, and Anadyomene stellata. Still nearer the shore,
the water flattened out to nothing, and the bottom was sand, like pow-
dered shell. Corallina still grew here, but the others dropped out, and
Caulerpa ericifolia and C. plumaris covered the bottom, as club mosses
grow in the woods. We searched here in vain for a long time for Peni-
238 PROCEEDINGS OF THE AMERICAN ACADEMY.
cillus, and only at our last visit I noticed, in water barely deep enough
to cover them, peculiar little mounds in the sand ; brushing off the tops
of these revealed the Penicillus capitatus, as abundant as seedling ever-
greens in a neglected Maine pasture lot. Not far from here, on a stone
wall at the edge of a gentleman's garden, the ribbon Ulva, U. fasciata,
streamed out into the water, quite filling it for a distance of about a
meter. It grew here, on a very limited area, on each of our visits, but
we found it nowhere else on the island. . . .
" Morant Bay is larger, and has a comparatively long stretch of sandy
beach, but the surf comes in so heavily that seaweeding is very difficult.
Annotto Bay is somewhat unusual, the land for some distance from the
sea being low and swampy, with sluggish rivers entering the sea by
several mouths, but the sandy pebbly shores retained the usual beautiful
curve. Montego Bay has a group of small atolls overgrown with man-
grove trees, surrounded with shallow water. Kingston has a fine large
harbor, enclosed by a long, narrow, sandy arm. On the outside of this,
deep water species were often washed ashore. . . .
" The conditions under which one must collect algae in the tropics are
somewhat different from those for collecting in the North, where we
have the rise and fall of the tide at intervals of a few hours, alternately
laying bare and covering the algae on the rocks. At Jamaica many
weeds grow on rocks so situated as to be alternately bared and covered
by the wash of the waves at intervals of a few minutes. Many of the
Polysiphonias, Gelidiums, Gracilarias, etc., are generally found under
these conditions. Padina and the Galaxauras occur at these stations,
but the finest growth of Padina that we saw was at Montego Bay, from a
road passing over a bluff, directly on the edge of the sea^jdown into which
one could look and see Padina growing like a field of gray morning-
glory blossoms set upon stones in the shallow, rather quiet water. Near
by were patches of Zonaria variegata, like red-brown morning glories.
" Much of our collecting was done from boats, rowed by two or three
strong, experienced boatmen. We would be rowed out to the shallow
places overgrown with grass, the water even there being to our waists,
then jump from the boat into the water, and fish about for seaweeds.
We always wore bathing suits and boys' thick hip rubber boots. On the
reefs or by the ledges the waves were often strong enough to take us off
our feet. Then we would cling closely together, one holding on to the
other, while the latter plunged for the seaweeds. Even then we would
sometimes be washed away from our footing. The boatmen would be
busy keeping the boat from the rocks, and stood ready to assist us back
COLLINS. — THE ALGAE OP JAMAICA. 239
into the boat, often with great difficulty. Most of the Caulerpas were
collected in this way, at places some distance from the shore. Even when
the plants grew near land, often the shores were so precipitous that one to
reach them must use a boat."
In the list that follows, the arrangement practically follows that of Die
Natiirlichen Pflanzenfarnilien of Engler and Prantl, but the names of
orders, families, etc., are not given ; these are shown later in Table I.,
giving the comparison of the marine flora of Jamaica with the floras of
other regions ; the few fresh water algae are included in their appropriate
positious in the general list, and the fact of their being fresh water plants
is noted by a star prefixed to the name.
General List.
Chroococcus turgidus (Kuetz.) Naeg. Among various fresh water
algae, forming a scum on a small roadside brook at the base of a cliff,
near the baths, Bath, July, 1900, P. & B. P. B.-A., No. 751. Among
marine algae, near Kingston, Duerden.
*Gloeocapsa quaternata (Breb.) Kuetz. Roadside, Bath, July, 1900,
P. &B.
Chroothece Richteriana Hansg. Among other algae, in small quantity,
Montego Bay, P. & B.
Xenococcus Schousboei Thuret. On Spermothamnion Gorgoneum,
Kingston, July, 1900, P. & B.
*Oscillatoria anguina Bory. In still water, Roaring River, near St.
Aun's Bay, March, 1893, H.
O. Corallinae (Kuetz.) Gomont. In a pellicle on coral rock, Port An-
tonio, March 27, 1893, II. Among other algae, near Kingston, Duerden.
*0. formosa Bory. In still water, Roaring River, near St. Ann's
Bay, March, 1893; Castleton, April, 1893, II.
*0. princeps Vauch. In mats in stream, St. Ann's Bay, March, 1893,
H; Bath, July, 1900, P. & B.
*0. princeps forma purpurea n. f. Trichomes and stratum a
bright purple, otherwise like type. Forming a stratum on a roadside
brook, near the baths, July, 19.00, P. & B. P. B.-A., No. 753.
*0. proboscidea Gomont. In a pool by " Wag Water," and in stream
from reservoir, Castleton, April, 1893, H.
*0. tenuis Ag. In company with O. princeps forma purpurea, Bath,
July, 1900, P. & B.
*Phormidium Retzii (Ag.) Gomont. In tufts on plants, Rio Cobre,
Bog Walk, April, 1893, H.
240 PROCEEDINGS OF THE AMERICAN ACADEMY.
Lyngbya aestuarii (Mert.) Liebm. In mats on stones, Kingston, April,
1893, H ; Port Antonio, July, 1891, P. & B. Near Kingston, Duerden.
L. confervoid.es forma violacea n. f. In company with L. ma-
juscula, Manchioneal Bay, July, 1900, P. & B. Differing from the type
only in color.
L. majuscula Harv. Forming a film on marine algae, Port Antonio,
March, 1893, H. Same locality, July, 1891, P. & B. Forming exten-
sive tufts on muddy bottom, near the mouth of a small stream, Manchio-
neal Bay, July, 1900, P*. & B.
*L. putalis Mont. Morant Bay, July, 1900, P. & B.
*L. versicolor (Wartm.) Gomont. Marine Garden, Kingston, II.
P. B.-A., No. 54.
Symploca hydnoides Kuetz. var genuina Gomont. On rocks in shallow
water, in small patches, not abundant, Montego Bay and Manchioneal
Bay, 1900, P. & B.
S. hydnoides var. fasciculata (Kuetz.) Gomont. With var. genuina,
P. & B.
*Plectonema Nostocorum Bornet. Among Gloeocapsa quaternata,
Bath, July, 1900, P. & B.
*P. Wollei Farlow. Morant Bay, Aug., 1894, P. & B. Roaring
River, H. P. B.-A., No. 55.
*Schizothrix coriacea (Kuetz.) Gomont. In tufts on sides of lily
tanks, Botanic Garden, Castleton, April, 1893, H.
*S. Mexicana Gomont. On rock in " AVag Water," Castleton, April,
1893, No. 399, H.
Microcoleus chtbonoplastes (Fl. Dan.) Thuret. In turfs of algae, St.
Ann's Bay, March, 1893, H.
M. tenerrimus Gomont. In company with M. chthonoplastes, March,
1893, H.
*M. vaginatus (Vaucb.) Gomont. On moist rock, Rio Cobre, Bog
Walk, April, 1893, II.
*Nostoc commune Vauch. In crusts on sandy soil, Constant Spring,
April, 1893, No. 365, H.
*N. microscopicum Carm. On steps into reservoir, Constant Spring,
April, 1893, No. 361, H. The specimens are sterile, so that the deter-
mination is somewhat in doubt.
*N. verrucosum Vauch. On rocks in "Wag Water," Castleton, April,
1893, H. No. 362, H., from trough in running water, Castleton, April,
1893, is probably the same species.
*Cylindrospermum muscicola Kuetz. On sides of basin, Constant
COLLINS. — THE ALGAE OP JAMAICA. 241
Spring; on sand at edge of river, Castleton, April, 1893, No.
364, H.
Hormothamnion enteroraorphoides Grunow. In shallow water, St.
Ann's Bay ; on coral reef, Navy Island, July 25, 1897, H. P. B.-A.,
No. 56. Near Kingston, Duerden.
*Scytonema Arcangelii Born. & Flah. On moist rocks by spring,
Castleton, April, 1893, H.
S. conchophilum Humphrey ms. In old conch shell, Port Antouio,
March, 1893, H. Kingston, June, 1897,11; Producing slight, gray,
pustular roughenings of outside of shell, Mastigocoleus testarum occur-
ring on inside of same shell.
Filaments 5-8 /x diam., irregularly branched, branches single or gemi-
nate, tips rounded, cells two thirds to two times as long as broad, 2.7-
4.5 fx diam., pale bluish when separate. Heterocysts globose or slightly
elongated, 5 /x diam., rarely two or three together, intercalary. Sheath
rather thin, deep yellow, homogeneous ; when old, rough outside, hyaline
and thin at growing tips. J. E. Humphrey.
*S. crispum (Ag.) Bornet. On sides of trough, Constant Spring; in
basin, Kingston, April, 1893, H. P. B.-A., No. 60.
*S. densum (A. Br.) Bornet. In turfs, moist places, Port Antonio,
April, 1893, H.
*S. Hofmanni Ag. On steps of Court House, Port Antonio, April,
1893, H.
*S. Javanicum (Kuetz.) Bornet. On flower-pot in garden, Castleton,
April, 1893, H.
*S. ocellatum (Dillw.) Thuret. On old palm stems, Castleton, April,
1S93, H.
*Hapalosiphon fontinalis (Ag.) Bornet. • On rock, " Wag Water,"
Castleton, April, 1 893, H.
Mastigocoleus testarum Lagerh. In old shells, Kingston, 1897, H.
Calothrix aeruginea (Kuetz.) Thuret. On Dasya arbuscula, Montego
Bay, June, 1900, P. & B.
C. confervicola (Roth) Ag. On various algae, Port Antonio, March,
1893, H.
C. Contarenii (Zan.) Born. & Flah. On wreck on beach, Port Mo-
rant, March, 1893, H.
*C. fusca (Kuetz.) Born. & Flah. Among Gloeocapsa quaternata,
Bath, 1900, P. & B.
*C. Juliana (Meneg.) Born. & Flah. On stones in stream, Roaring
River, St. Ann's Bay, March, 1893, H.
VOL. XXXVII. — 16
242 PROCEEDINGS OP THE AMERICAN ACADEMY.
C. pilosa Harv. On Bostrychia tenella, Port Antonio, Aug., 1894,
P. & B.
Dichothrix penicillata Zan. On Cymopolia barbata, Port Maria, H.
On Dictyota dichotomy P. & B. P. B.-A., No. 62.
*Gloeotricbia natans (Hedw.) Rab. Under Nymphaea leaves, Botanic
Garden, Castleton, April, 1893, H.
*Spirogyra decimina (Muell.) Kuetz. Mauchioneal, July, 1900,
P. & B. "
The spores agree with this species, and as far as can be judged from
dried specimens, the vegetative characters. A sterile Spirogyra from
Bath has the same dimensions of cells, but cannot be specifically deter-
mined.
Ulva fasciata Delile. In dense masses just below water mark, but
only in one limited locality, Port Antonio, July, 1891, P. & B.
P. B.-A., No. 221. Near Kingston, Duerden.
U. Lactuca var. rigida (Ag.) Le Jobs. Port Antonio, Aug., 1894;
Kingston, Montego Bay, June, 1900, P. & B. Near Kingston, Duerden.
Enteromorpha erecta (Lyng.) J. Ag. Port Antonio, April, 1892,
P. & B.
E. flexuosa (Wulf.) J. Ag. Port Antonio, July, 1891 ; Runaway
Bay, July, 1900; washed ashore, Mauchioneal Bay, July, 1900, P. & B.
Near Kingston, Duerden.
E. intestinalis (L.) Link. Port Antonio, washed ashore, July, 1894,
P. & B.
E. prolifera (Muell.) J. Ag. Runaway Bay, Montego Bay, Manchi-
oneal, on stones; also in fresh water at Bath, on stones in river, 1900,
P. & B.
*Stigeoclonium tenue (Ag.) Rab. No. 366, H., locality not given.
Diplochaete solitaria n. g. & sp. Frond epiphytic, consisting of
a single cell, with thick, transparent wall, and bright green contents,
spherical or flattened, the outline as seen from above round or slightly
oval ; two hairs arising from each cell, usually opposite, and from points
on the under surface quite near the edge. Cell 25-30^ diameter,
half this diameter being occupied by the wall ; hairs 4-6/* diameter,
slightly tapering, straight. On Laurencia obtusa, near Kingston,
Duerden.
This minute plant was observed on a specimen of Laurencia, after it
had been mounted for the herbarium, so that nothing is known as to its
development, but it seems so distinct from any described genus of the
Chaetophoraceae as to require a new name.
COLLINS. — THE ALGAE OF JAMAICA. 243
Pringsheimia scutata Reinke. On Laurencia obtusa, near Kingston,
Duerden.
*Mycoidea parasitica Cunningham. On leaves of various plants,
Roaring River, March, 1893, Nos. 324 & 325 ; Bath, 1897, II.
P. B.-A., No. 763.
Chaetomorpha brachygona Harv. Port Antonio, July, 1891 ; Man-
chioneal Bay, Rio Bono, 1900, P. & B. Forming dense mats on bottom
of Kingston Harbor, April, 1893, No. 369, H. Near Kingston,
Duerden. Hardly distinct from C. cannabina of Europe.
C. clavata (Ag.) Kuetz. Washed ashore, Port Antonio, P. & B. St.
Ann's Bay, March, 1893, No. 329, H. A rather slender form.
C. aerea (Dillw.) Kuetz. Washed ashore, Port Antonio, Aug., 1894,
P. &B.
C. Linum (Fl. Dan.) Kuetz. Kingston Harbor, Aug., 1891, R. P.
Bigelow. Mauchioneal, in company with C. brachygona, Morant Bay,
June, 1900, P. & B.
The plant from Morant Bay has very moniliform filaments, up to
.4 mm. diameter, the cell wall thin, color light green, articulations one to
two diameters ; perhaps a distinct species.
C. Linum var. brachyarthra Kuetz. Port Antonio, July, 1891, P. & B.
C. Melagonium (Web. & Mohr.) Kuetz. ? Growing in mud near the
mouth of a river, Mauchioneal, July, 1900, P. & B. Quite like the
northern form usually known as C. Picquotiana, but possibly not distinct
from C. Linum.
Cladophora fascicularis Kuetz. Port Antonio, July, 1891 ; Montego
Bay, Mauchioneal, 1900, P. & B. ; Port Antonio, Feb., 1893, No.
179, H. Generally distributed, usually growing on pebbles in mud in
shallow water.
C. crystallina (Roth) Kuetz. Ora Cabessa, June, 1900, P. & B.
C. fuliginosa Kuetz. In turfs, Port Maria, No. 298, H. Morant
Bay, Annotto Bay, etc., P. & B. Apparently common everywhere ;
usually known as Blodgettia confervoides.
C. Hutchinsiae (Dillw.) Kuetz. Port Antonio, July, 1891, P. & B.
C- intertexta n. sp. Filaments 200-350^ diam., articulations one to
three diameters, usually one and one half to two ; sparingly branched,
branches naked or with short, usually secund ramuli ; terminal cells
blunt, rounded. Tufts densely matted, prostrate.
The plant forms dense masses on the bottom of pools, creeping over
the coral sand and broken shells ; the upright branches are usually sim-
ple, and the plant resembles an entangled mass of some coarse Chaeto-
244 PROCEEDINGS OP THE AMERICAN ACADEMY.
morpha rather than a Cladophora, but occasionally the free branches
have a series of secund, two or three-celled ramuli, issuing one from each
articulation. In the entangled mass more branching of this character
will be found, also long normal branches in no definite order. The habit
of C. intertexta is much like that of C. repens (J. Ag.) Harv., but the
filaments are two or three times as large as in that species, and the color
is a light green, somewhat whitish in drying, instead of the dull olive
green of C. repens ; the latter has, moreover, a vaguely dichotomous
branching, and articulations many times — according to Harvey, even
twenty times — the diameter. C. herpestica (Mont.) Kuetz. has fila-
ments of about the same size as C. intertexta, but it has long articula-
tions, up to fifteen diameters, and irregular branching, with the upper
branches fasciculate.
Found along the shore near Manchioneal, July, 1900, P. & B.
P. B.-A., No. 818.
C. trichocoma Kuetz. Manchioneal, July, 1900, P. & B.
Gomontia polyrhiza (Lagerh.) Born. & Flah. In old shells, coral and
bones, Kingston, 1897, H.
Bryopsis Harveyana J. Ag. In tufts on stones, Kingston Harbor,
April, 1893, No. 367, H.
B. pennata Lamour. In tufts on rocks, Apostles' Battery, Kingston
Harbor, April, 1893; Port Maria, March, 1893, No. 297, H. A single
specimen, Port Morant, July, 1900, P. & B.
Caulerpa cupressoides var. typica Weber. On sandy bottom, Navy
Island, Port Antonio, March, 1893, No. 188, H. ; Port Antonio,
P. & B. P. B.-A., No. 79.
C. cupressoides var. Turneri Weber. Port Antonio, P. & B.
P. B.-A., No. 765.
C. cupressoides var. mamillosa (Mont.) Weber. Among eel-grass, at
about one meter depth, Montego Bay, July, 1900, P. & B. Including
forma typica and forma nuda. P. B.-A. No. 765. Near Kingston,
Duerden.
C. cupressoides var. ericifolia (Turn.) Weber. Port Antonio, July,
1891, P. & B.
C. pinnata forma Mexicana (Sond.) Weber. Montego Bay, July,
1900, P. &B.
C. plumaris forma longiseta (J. Ag.) Weber. Forming dense mats in
mud in shallow water, Port Antonio, July, 1891, P. & B. P. B.-A.,
No. 27. Near Kingston, Duerden ; very luxuraint, the erect fronds
20 cm. hi<rh.
COLLINS. THE ALGAE OF JAMAICA. 245
C. plurnaris forma brevipes (J. Ag.) "Weber. Port Antouio, July,
1891; Montego Bay, July, 1900, among eel-grass at about one meter
depth, P. & B. P. B.-A., No. 766. P. U., No. 672. Near King-
ston, Duerden.
C. prolifera (Forsk.) Lamour. Washed ashore, not common, Port
Morant, July, 1900, P. & B.
C. racemosa var. clavifera (Turn.) Ag. Port Antonio; Port Morant,
at about one meter depth, July, 1900, P. & B. In tufts on rocks,
Kingston, April 8, 1893, No. 370, H. P. B.-A., No. 707.
C. racemosa var. clavifera forma macrophysa (Kuetz.) Weber. On
coral reef, Port Antonio, 1894 & 1900, P. & B. Near Kingston,
Duerden, passing insensibly into var. clavifera. P. B.-A., No. 870.
C. taxifolia (Vahl) Ag. Washed ashore, Port Morant, July, 1900.
Annotto Bay, 1894, P. & B. Chitty. P. B.-A., No. 768.
C. verticillata J. Ag. In tufts on coral rocks, Port Antonio, Feb. 27,
1893, No. 181, II. Near Kingston, Duerden.
C. verticillata forma charoides (Harv.) Weber. Kingston, June,
1900, P. & B. Forming fine moss-like mats in soft mud near Man-
grove swamp, at depth of about one meter. Near Kingston, Duerden.
Peuicillus capitatus Lam. Port Antonio, Montego Bay, Manchioneal,
nearly buried in coral sand, 1900, P. & B. Port Maria, No. 294, H.
Sloane. P. B.-A., No. 271. P. U., No. 523. Near Kingston,
Duerden.
P. dumetosus (Lamour.) Decsne. Annotto Bay, washed ashore,
Manchioneal, July, 1900, P. & B. Specimen without locality, H.
P. B.-A., No. 769.
" Penicillus dumetosus grew in some abundance in a pool near Man-
chioneal. The pool was narrow, with precipitous tufa walls, which
towards the sea closed over the pool in an arch, through which the waves
broke heavily. The Penicillus grew among eel-grass, in muddy soil,
covered by a coating of powdered shell and coral. With it were P.
capitatus, Avrainvillea longicaulis, and Halimedas. The P. dumetosus
looked like miniature groves of carefully trimmed evergreen trees, gray
green in color."
Rhipocephalus Phoenix (Ell. & Sol.) Kuetz. Port Morant, a single
specimen washed ashore, July, 1900, P. & B.
Avrainvillea longicaulis (Kuetz.) Murray & Boodle. Montego Bay,
June, Manchioneal, July, 1900, P. & B. P. B.-A., No. 770.
Avrainvillea nigricans Decsne. Singly in shallows, Port Maria,
March 17, 1893, No. 270, H. Manchioneal, July, 1900, P. & B.
P. B.-A., No. 771.
246 PROCEEDINGS OF THE AMERICAN ACADEMY.
" Avrainvillea longicaulis at Montego Bay grew imbedded in mud
among eel-grass in shallow water, near a small island consisting of man-
grove swamp. It was discovered by the sense of feeling as we were
dredging in the mud among the eel-grass roots for Caulerpa. We were
continually feeling through the thick soles of our rubber boots a sensa-
tion as of stepping on drowned kittens. It proved to be the curious
fleshy fronds of Avrainvillea, somewhat resembling a downy, dirty,
swollen Udotea, often full of worms and other small animals. Avrain-
villea grew also at Manchioneal, in an enclosed salt water pool, in eel-
grass with Penicillus dumetosus, rooted in a clean bottom of powdered
shells and coral ; but on the rocks bordering the pool was another species,
A. nigricans, with short stems, and tops not so flabellate, resembling in
shape our stemmed puff-balls."
Udotea conglutinata (Sol.) Lamour. Closely set on bottom, Port
Maria, March 17, 1893, No. 269, H.
U. flabellata Lamour. On sandy bottom, Port Antonio, March 3,
1893, No. 202 ; Port Maria, March 17, 1893, No. 268, H. On muddy
bottom, Port Antonio, July, 1894; washed ashore, Moraut Bay, P. & B.
Halimeda Opuntia (L.) Lamour. In dense tufts, Port Maria, March,
1893, II. Port Antonio, July, 1891, P. & B. Near Kingston, Duerden.
Sloane. Growing similarly to the preceding species.
H. tridens (Ell. & Sol.) Lamour. In tufts, St. Ann's Bay, March 23,
1893; Port Maria, March 17, 1893, II. Port Antonio, July, 1891,
growing in shallow water, in soil composed of broken shells and coral.
Near Kingston, Duerden.
It is impossible to distinguish II. incrassata (Ell.) Lamour from H.
tridens. In any considerable collection typical forms of each and a
series of intermediate forms are to be found.
II. Tuna (Ell. & Sol.) Lamour. In dense tufts, shallows, Port An-
tonio, March 10, 1893, No. 235, H.
Codium adhaerens (Cabr.) Ag. Port Antonio, Aug., 1894, P. & B.
Specimen without locality, No. 293, H.
C. tomentosum (Huds.) Stack. In immense tufts, Port Maria, March
17, 1893, No. 266, H. Port Antonio, July, 1891 ; Kingston, July,
1900, P. & B. Near Kingston, Duerden. Washed ashore in large
quantities, nearly everywhere. P. B.-A., No. 168.
Valonia aegagropila Ag. On rocks in shallows, Port Maria, March
20, 1893, No. 296, H. Montego Bay, July, 1900, on rocks in shallow
water, P. & B. P. B.-A., No. 772.
V. ventricosa J. Ag. On rocks in shallows, Port Antonio, March 11,
COLLINS. — THE ALGAE OF JAMAICA. 247
1893 ; Port Maria, March 20, 1893, No. 295, H. On rocks in shallow
rough water, Mont ego Bay, June, 1900, P. & B. "Fronds smooth and
transparent, as if made of thin green glass."
V. verticillata Kuetz. On rocks in shallow water, Port Morant,
Manchioneal, July, 1900, P. & B.
Siphonocladus membranaceus (Ag.) Bornet. Growing in mats on
rocks, near shore, Port Antonio, Aug., 1894 ; Runaway Bay, June,
1900, P. & B. Near Kingston, Duerden.
S. tropicus (Crouau) J. Ag. Washed ashore, Morant Bay, July,
1894, P. & B.
Dictyosphaeria favulosa (Ag.) Decsne. On rocks in shallows, Port
Antonio, March 3, 1893, Nos. 205 & 271, H. On coral reef, Port
Antonio, July, 1891, P. & B. P. B.-A., No. 124.
Chamaedoris anuulata (Lam.) Mont. Washed ashore, Morant Bay,
July, 1894, P. & B.
Microdictyon umbilicatum (Velley) Zan. In dense tufts, Port Anto-
nio, Feb. 27, 1893, No. 174, H.
Anadyomene stellata (Wulf.) Ag. In tufts on rocks, Port Antonio,
Feb. 27, 1893, H. Similar localities. Port Antonio, July, 1891; Kings-
ton, Port Morant, July, 1900, P. & B. P. B.-A., No. 169.
Acetabularia crenulata Lamour. Port Antonio, Annotto Bay, Au°\,
1894 ; Rio Novo, June, 1900, P. & B. Near Kingston, Duerden. P.
B.-A., No. 125.
" At Annotto Bay Acetabularia and Dasycladus grew in water nearly
to our shoulders, not very rough, on cobble stones, the two species grow-
ing together like minute forests covering the stones."
Dasycladus clavaeformis (Roth) Ag. In tufts on rocks, Port Maria,
Apr. 19, 1893, No. 285, H; Annotto Bay, with the preceding species ;
on pebbles washed ashore, St. Ann's Bay, 1900, P. & B. P. B.-A.,
No. 170.
Botryophora occidentalis (Harv.) J. Ag. In salt pools, Palisadoes,
Kingston Harbor, April 10, 1893, No. 386, H. Port Antonio, Aug.,
1894, P. & B.
Neomeris dumetosa Lamour. Kingston Harbor, on mangrove roots,
July, 1900, P. & B. "Looking like small green worms."
Cymopolia barbata (L.) Lamour. In tufts on stones, St. Ann's Bay
and Port Maria, March. 1893, H. On coral reef. Port Antonio, Annotto
Bay, 1891 & 1894, washed ashore; Kingston, Port Morant, 1900, P. &
B. Near Kingston, Duerden. P. B.-A., No. 28. P. U., No. 674.
Sloane.
248 PROCEEDINGS OF THE AMERICAN ACADEMY.
Maii}r specimens agree with the description of C. Mexicana J. Ag., but
all intermediate forms occur, and often the same individual will agree with
one species in one part of the frond, with the other in other parts.
E. Mitchellae Harv. ? Kingston, March, 1893, Nos. 141, 142, 372,
H. Not exactly like the type of this species, the plurilocular sporangia
being longer and sometimes clavate. Possibly E. Duchassaingianus
Grunow.
Striaria attenuata (Ag.) Grev. Montego Bay, June, 1900, washed
ashore on sandy beach, P. & B.
S. attenuata var. ramosissima (Kuetz.) Hauck. With the type, June,
1900, P. & B.
Colpomenia sinuosa (Roth) Derb. & Sol. On coral rocks, Port Anto-
nio, March 8 and 23, 1893, Nos. 153 and 212; Port Maria, March 17,
1893, No. 273, H. Annotto Bay to Port Antonio, in shallow water,
Aug., 1894, P. & B.
Hydroclathrus cancellatus Bory. On coral rocks, Port Antonio, Feb.
10, 1893, No. 234, H.
Cutleria sp. A single specimen, attached to a frond of Udotea flabel-
lata, seems to be the Aglaozouia form of some Cutleria, but in the absence
of fruit it is indeterminable. The frond consists of radiating articulate
filaments, united laterally, and varying much in diameter.
Turbinaria trialata Kuetz. Washed ashore, Port Antonio, March 8,
1893, No. 211 ; in tide pools, Port Maria, March 16, 1893, No. 249, H.
Washed ashore, Port Antonio, July, 1891; Montego Bay, July, 1900,
P. & B. P. B.-A., No. 774. T. vulgare, Sloane, is undoubtedly this
species.
Sargassum bacciferum (Turn.) Ag. Washed ashore, Port Maria,
March 18, No. 248, H. Sloane, Chitty.
S. lendigerum (L.) Kuetz. Washed ashore, Port Antonio, July,
1891, P. & B. In tufts in tide pools, Port Maria, March 17, 1893, No.
292, H.
S. platycarpum Mont. Washed ashore, Port Antonio, July, 1891, P.
& B. Same locality, March 8, 1893, No. 210, H. P. B.-A., No. 775.
S. vulgare Ag. Washed ashore, Port Maria, March 18, 1893, No.
247, H. The references to Sloane and Chitty are doubtful, and some
other form may have been referred to under this name.
S. vulgare forma ovata n. f. Washed ashore, Montego Bay, June,
1900, P. & B. P. B.-A., No. 776. Leaves thick, dark, ovate to subor-
biculate, coarsely and sharply, sometimes doubly toothed, usually slightly
oblique at the base. The branching is dense, the leaves numerous and
COLLINS. — THE ALGAE OF JAMAICA. 249
of form and thickness mentioned above ; otherwise it agrees with typical
S. vulgare.
S. vulgare var. foliosissimum (Lamour.) J. Ag. Washed ashore, Port
Antonio, July, 1891, P. & B.
Spatoglossum Schroederi (Mert.) J. Ag. Two specimens only, washed
ashore on sandy beach with high surf, near lighthouse, Kingston harbor,
July, 1900, P. & B. Chitty.
Stypopodium lobatum (Ag.) Kuetz. Washed ashore, Port Maria,
March 10 and 19, Nos. 231 and 286; St. Ann's Bay, March 23, 1893,
No. 311, II. Annotto Bay, July, 1891 ; Montego Bay, June, 1900, P.
& B. P. B.-A., No. 777.
"Stypopodium lobatum grew in magnificent clumps of two sorts, one
with the frond narrowly divided and heavily marked with dark bars, mak-
ing the plant resemble bunches of turkey feathers ; the other with fronds
of broader divisions and not so prominently barred. The first mentioned
form grew deeper down in the water, so deep as to have to be pulled off
by the boatmen by means of a long handled boat-hook. The two forms
were plainly distinguished as they grew in the water."
Gymnosorus variegatus (Lamour.) J. Ag. Kingston, Montego Bay,
1900, P. & B. P. B.-A., No. 778.
" Gymnosorus variegatus grew with Padina, which it resembled in
manner of growth, being in shape like clusters of short-stemmed morning
glory flowers. It formed a covering to the rocks nearer shore than the
Stypopodium, the water being about knee deep. G. variegatus is reddish
brown in color, Padina gray, Sargassum and Turbinaria rich yellow
brown ; Dictyota a darker brown with less yellow ; Stypopodium gen-
erally grayish brown with dark markings. The contrasting colors were
very rich in the water."
Padina Durvillaei Bory. On rocks, Port Antonio, Feb. 28, 1893, No.
173, H. Port Antonio, July, 1891 ; Ora Cabessa, Montego Bay, 1900,
P. & B. Near Kingston, Duerden. The P. Pavonia of Murray and
earlier lists is probably this species.
Dictyopteris delicatula Lamour. In tufts on rocks, Port Maria, March
19, 1893, II. Washed ashore, Annotto Bay, Aug., 1894; Hope Bay,
Kingston, 1900, P. & B. P. B.-A., No. 485.
D. Justii Lamour. Washed ashore, Port Antonio, July, 1891 ; Morant
Bay, Annotto Bay, Aug., 1894; Kingston, 1900, P. & B. In tufts on
rocks, Port Maria, March 17, 1893, No. 264, H. Chitty.
D. plagiogramma Mont. Annotto Bay, July, 1894, washed ashore,
P. & B. Chitty.
250 PROCEEDINGS OF THE AMERICAN ACADEMY.
Dictyota Bartayresiana Larnour. Washed ashore in mats, Port Anto-
nio, March, 1893, Nos. 154, 194, 229, H. Port Antonio, July, 1891 ;
on rocks in shallow water, Kingston, Montego Bay, Manchioneal, 1900,
P. & B. Near Kingston, Duerden. P. B.-A., No. 579. Found in both
broad and narrow forms, at nearly all the localities, often appearing like
two distinct species.
D. cervicornis Kuetz. "Washed ashore, Port Antonio, Aug., 1894, P.
& B. Near Kingston, Duerden.
D. ciliata Ag. In tufts on rocks, Port Maria, March 16, 1893, Nos.
246 and 287; Port Antonio, March 10, 1893, No. 230, H. Washed
ashore, Montego Bay, Ora Cabessa, Manchioneal, 1900, P. & B. P. B.-A.,
No. 779. All three kinds of fruit are represented in the specimens dis-
tributed in the Phycotheca Boreali-Americana, the plants being collected
at the same time. All are similarly arranged, occupying the whole of
the fertile segments, except a narrow strip at the margin. The male
plants are mostly old and battered, as if the antheridia were produced
somewhat earlier in the season than the other kinds of fruit.
"Dictyota ciliata at Montego Bay, June 23, 1900, grew on boulders
near a precipitous rocky shore in water more than waist deep. It formed
large round clumps. The water being very clear here, the hairs on the
edge of the frond were so conspicuous as to easily distinguish in the water
this form from other Dictyotas. The rocks in this locality were beauti-
fully draped with the Dictyota, robust plants of Turbinaria in large thick
masses, a Sargassum with rounded leaves, and Stypopodium in magnifi-
cent clumps."
D. dentata Lamour. Washed ashore, Port Maria, March 17, 1893,
No. 265, H. Port Antonio, July, 1891, P. & B. On rocks in rough
water, one meter or more deep. P. U., No. 669. Some specimens have
the tips of the branches so finely divided as to seem ciliate.
D. dichotoma (Huds.) Lamour. Kingston Harbor, July, 1891, R. P.
Bigelow. On rocks, Port Antonio, July, 1891 ; Montego Bay, June,
1900, P. & B. Chitty.
D. divaricata Lamour. In various places, 1900, P. & B. Near Kings-
ton, Duerden. Connected by intermediate forms with D. Bartayresiana.
D. fasciola (Roth) Lamour. Washed ashore, Port Antonio, July,
1891 ; Rio Novo, June, 1900, P. & B.
Dilophus alternans J. Ag. Port Antonio, July, 1894, P. & B.
D. Guineensis (Kuetz.) J. Ag. On flat rocks washed by the waves,
in company with Gelidium rigidum, Montego Bay, Rio Novo, June, 1900,
P. & B.
COLLINS. THE ALGAE OF JAMAICA. 251
Dictyerpa Jamaicensis n. g. & sp. Frond filiform, 1-3 mm. diam.
up to 2 dm. long ; consisting of two layers of cells, an inner layer of large,
colorless, cylindrical cells, about three diameters long, symmetrically
arranged; an external monostromatic layer of brown rectangular cells
from one to three diameters long, in distinct longitudinal series. Branch-
ing di- or trichotomous, with occasional irregularly placed lateral branches,
mostly at wide angles, each branch ending in a large, depressed-hemi
spherical cell, by whose division the growth of the branch proceeds.
Tufts of very fine, rust-colored or colorless confervoid rhizoidal filaments
at irregular intervals on the frond. Fructification ? Washed ashore,
Manchioneal, July, 1900. P. B.-A., No. 780.
Though evidently belonging to the Dictyotaeeae, this plant differs
from any genus of the family yet described, in having the frond terete
throughout. Many Dictyotaeeae have prostrate rooting filaments from
which the erect fronds arise, but in all species found in Jamaica this pros-
trate growth is quite insignificant in comparison with the plant in ques-
tion. It was found washed ashore in two places, in considerable quantity,
and in no case shows any indication of fructification, or of producing
erect flattened fronds. It may seem hazardous to give it a generic name,
but as it is a plant of quite distinct habit, and cannot be now identified
with any named form, it seems to require at least a provisional name.
As washed up on the beach, it appeared like rolled and twisted strings.
The dried plant is quite black in color, and under a hand lens shows
closely set constrictions, probably due to the large interior cells being of
uniform length, and terminating at the same level, as in the frond of
Polysiphonia. These constrictions are lost when the frond is remoistened.
Goniotrichum Humphrey! Collins. On woodwork of wreck, St.
Ann's Bay, March 24, 1893, No. 31G, II. P. B.-A, No. 421.
" Frond filamentous, solid, gelatinous, occasionally forking or dividing
into several branches, the terminal portion consisting of a single series of
cells ; the older part containing numerous cells, irregularly placed near
the surface of the filament ; lateral branches abundant, simple, issuing
nearly at a right angle, composed of a single series of cells." This de-
scription is copied from the label of P. B.-A., No. 421.
G. elegans (Chauv.) Le Jolis. Among other algae, on Laurencia
obtusa, near Kingston, Duerden.
Chantransia Saviana (Menegh.) Ardiss. Among other algae, on
Laurencia obtusa, near Kingston, Duerden.
Liagora Cheyneana Harv. Washed ashore, Port Maria, March 17,
1893, No. 281 ; Port Antonio, March, 1893, No. 186, II.
252 PROCEEDINGS OF THE AMERICAN ACADEMY.
L. decussata Mont. Washed ashore, Hope Bay, July, 1891, and Aug.,
1894, P. & B. Very abundant in 1894. P. B.-A., No. 89. The finest
species of the genus, with fronds in shape of a fir tree, sometimes over a
meter in length. Apparently confined to the islands on the two sides of
the Atlantic.
L. elongata Zan. Hope Bay, July, 1891 ; Montego Bay, July, 1900,
P. & B.
L. pulverulenta Ag. Washed ashore, Manchioneal, July, 1900, P.
& B.
L. valida Harv. In large tufts, Port Maria, March 17, 1893, No.
283; Port Antonio, March 10, 1893, No. 240, H. Hope Bay, Orange
Bay, Montego Bay, 1891 and 1900, P. & B. Under No. 687, P. B.-A.,
a form was distributed as L. tenuis, which it now seems better to regard
as L. valida. It is difficult to see how the two species can be distin-
guished, when one has a large number of specimens. Harvey's name,
being the older, must be maintained.
Galaxaura cylindrica (Sol.) Decsne. Port Antonio, Morant Bay,
Manchioneal and elsewhere, common, P. & B. Near Kingston, Duerden.
Sloane. Chitty. P. B.-A., No. 134.
G. lapidescens (Sol.) Lamour. In large tufts, Port Antonio, March
10, 1893, No. 239, H. Annotto Bay, Port Antonio, July, 1891 ; Mon-
tego Bay, on rocks, June, 1900, P. & B. Chitty. Not so common as
other species of the genus.
G. marginata (Ell. & Sol.) Lamour. On stones at tide-mark, Port An-
tonio, March 10, No. 145 ; March 21, No. 241, H. Port Antonio, An-
notto Bay, Montego Bay, Manchioneal, 1900, P. & B. Common,
growing very densely on rocks.
G. obtusata (Ell. & Sol.) Lamour. Port Antonio, July, 1891 ; Port
Maria, July, 1900, P. & B., in company with other species of the genus.
G. rugosa (Sol.) Lamour. In large tufts, Port Antonio, March, 1893,
No. 131, H. Port Antonio, July, 1891 ; Rio Novo, Rio Bono, Montego
Bay, 1900, P. & B. Near Kingston, Duerden. P. B.-A., No. 133.
P. U., No. 510. Sloane. Usually washed ashore on beaches.
Wrangelia Argus Mont. Montego Bay, June, 1900, forming soft
mats on rocks, P. & B. Specimen without locality, H.
Gelidium coerulescens Crouan. Port Antonio, July, 1891 ; July,
1900, P. & B. P. B.-A., No. 783.
By the kindness of Dr. Bornet this plant has been compared with
authentic specimens from Guadeloupe, and it is the plant referred to by
Maze & Schramm, Algues de Guadeloupe, p. 199. Whether it is the
COLLINS. — THE ALGAE OF JAMAICA. 253
plant of Kuetzing, Tab. Phyc, Vol. XVIII. PI. 56, from New Caledo-
nia, is not certain.
G. crinale (Turn.) J. Ag. Port Antonio, July, 1900, with G. coeru-
lescens, P. & B.
G. rigidum (Vahl) Ag. Port Antonio, July, 1891 ; Montego Bay,
June, 1900, P. & B. P. B.-A., No. 784. Appears to be the form
known as var. radicans (Bory) J. Ag.
G. supradecompositum Kuetz. Mo rant Bay, July, 1894, P. & B.
No. 227, no locality, H.
The identification of this form is from a specimen from Fajardo, Puerto
Rico, received from Hauck. If G. crinale were taken in a broad sense,
it might include this form.
Catenella Opuntia var. pinnata (Harv.) J. Ag. Manchioneal, July,
1900, P. & B. Forming a thin greenish coating on small stones in shal-
low water, on muddy bottom near the mouth of a small river. P. B.-A.,
No. 792.
Agardhiella tenera (J. Ag.) Schmitz. Morant Bay, July, 1894; Mon-
tego Bay, June, 1900, P. & B.
Solieria chordalis (Ag. ) J. Ag. Washed ashore, Port Antonio, July,
1891. P. & B.
Eucheuma echinocarpum Aresch. Montego Bay, a few small plants,
June, 1900, P. & B.
Gracilaria Blodgettii Harv. Washed ashore, Montego Bay, June, 1900,
P. & B. ; only a few specimens, some of which show a tendency to pass
into G. confervoides.
G. caudata J. Ag. Port Antonio, Aug., 1894, P. & B.
G. cervicornis (Kuetz.) J. Ag. Washed ashore, Morant Bay, July,
1894; Manchioneal, July, 1900, P. & B. Near Kingston, Duerden.
P. B.-A., No. 787. Some of the plants are quite like Mediterranean
specimens of G. armata. The Florida plant described as G. armata by
Harvey in the Nereis Boreali-Americana seems to be different, and has
not been found in Jamaica.
G. compressa (Ag.) Grev. Annotto Bay, Aug., 1894, P. & B.
G. confervoides (L.) Grev. On small stones, St. Ann's Bay, March
23, 1893, No. 312, H. Washed ashore, Borden, July, 1894; Montego
Bay, Manchioneal, 1900, P. & B. Near Kingston, Duerden. Common
and variable.
G. cornea J. Ag. Washed ashore, Rio Bono, June, 1900, P. & B.
G. Curtissiae J. Ag. Washed ashore, Annotto Bay, Aug., 1894,
P. & B.
254 PROCEEDINGS OP THE AMERICAN ACADEMY.
G. damaecornis J. Ag. Annotto Bay, Aug., 1894; Mauchioneal,
July, 1900, P. & B. P. B.-A., No. 788.
G. divaricata Harv. In short tufts, Navy Island, Port Antonio, March,
1893, Nos. 155 and 228, H. Port Antonio, July, 1891 ; Port Morant,
Kio Bono, June, 1900, P. & B. P. B.-A., No. 789. Generally dis-
tributed but nowhere common.
G. Domingensis Sond. Mauchioneal, June, 1900, P. & B. Found
only in a very limited station, in large tufts on rocks about one meter
depth, in rough water; very luxuriant plants, showing beautiful shades
of violet.
By J. G. Agardh this is considered as merely a form of G. multipartita
var. polycarpa. Imperfectly developed specimens have some resemblance
to that variety, but well developed plants are quite different; the habit
reminds one rather of Laurencia pinnatifida. All three kinds of fruit
were found in the Mauchioneal specimens, the cystocarps and tetraspores
as usual in this genus, the antheridia in crypts, as described by Thuret
for G. confervoides. The description of G. Krugiaua in Hauck's Puerto
Rico list is quite suggestive of some of these specimens.
G. ferox J. Ag. AVashed ashore, Morant Buy, July, 1894, P. & B.
G. multipartita (Clem.) J. Ag. Port Antonio, July, 1891 ; Port Mo-
rant. Montego Bay, Ora Cabessa, Mauchioneal, 1900, P. & B. No.
380, no locality, H. Near Kingston, Duerden. Chitty. P. B.-A.,
No. 885.
G. Wrightii (Turn.) J. Ag. Annotto Bay, Aug., 1894; Montego
Bay, June, 1900, P. & B. A few plants only.
The fresh frond is very stout and densely branched, and not at all
compressed ; it shrinks much in drying, and herbarium specimens give
the idea of a flattened frond.
Hypuea divaricata Grev. In large tufts on rocks in shallow water,
Montego Bay, Manchioneal, 1900, P. & B.
H. musciformis (Wulf.) Lamour. On stones at tide mark, Port An-
tonio, March, 1893, Nos. 147 and 223 ; St. Ann's Bay, March 24, 1893,
No. 320, H. Near Kingston, Duerden. Common everywhere, P. & B.
Chitty.
H. Valentiae (Turn.) Mont. Annotto Bay, Aug., 1894, P. & B.
The species is here taken in the same sense as by Hauck, Hedwigia,
1887, Heftl, to include H. nidifica J. Ag. and H. fruticulosa Kuetz. ;
forms corresponding to both of these occur at Annotto Bay.
Cordylecladia irregularis Harv. Annotto Bay, Aug., 1894, P. & B.
Near Kingston, Duerden.
COLLINS. — THE ALGAE OP JAMAICA. 255
Some of the plants from each locality have tetraspores, which appear
not to have been previously reported. They are arranged much as in C.
erecta, except that they are at the ends of short lateral branches, instead
of terminal on the larger branches ; the modified portions of the branches
being ovate or subspherical rather than lanceolate. One of the Kingston
specimens has cystocarps, which are spherical and external on the
branches, as in other species of the genus.
Cordylecladia Peasiae n. sp. Fronds slender, filiform, arising from
a more or less distinct crustaceous base, dichotomously divided, with oc-
casional scattered or secund ramuli, usually quite short. Tetraspores
cruciate, in the somewhat swollen and darkened tips of the branches and
ramuli, immersed in the cortical layer. Cystocarps globular, sessile
along the main branches. Color purplish brown, changing into whitish
or greenish ; substance rigid.
Somewhat resembles C. erecta, which is, however, a smaller plant,
much less branched, and having the receptacles for tetraspores larger and
of different shape. C. conferta and C. Andersoniana have the tetra-
spores in densely tufted special lateral branches. C. irregularis is stouter,
with hollow steins and with oval or subspherical lateral branches for the
tetraspores. In C. furcellata the tetraspores are borne in branches resem-
bling the vesicles of Chrysymenia uvaria. C. heteroclada has a flat
frond, and C. Huntii is unrecognizable from the description of Harvey.
Manchioneal, July, 1900, P. & B. P. B.-A., No. 791.
Chrysymenia halymeuioides Harv. Washed ashore, Morant Bay,
July, 1894, P. & B.
Champia parvula (Ag.) Harv. Montego Bay, Port Maria, 1900,
P. & B.
Caloglossa Leprieurii (Mont.) J. Ag. Among Bostrychia, just above
water level, Port Antonio, July, 1900, P. & B.
Asparagopsis Delilei (Ag.) Lamour. In tree-like tufts, Navy Island,
March 10, 1893, II.
Laurencia cervicornis Harv. Annotto Bay, Aug., 1894; washed
ashore, Kingston, July, 1900, P. & B.
L. implicata J. Ag. Morant Bay, July, 1900, P. & B.
L. obtusa (Huds.) Lamour. In tufts on rocks, Kingston Harbor,
Apr. 8, 1893, No. 376 ; no locality, No. 224, H. Port Antonio, July,
1891; on rocks, Montego Bay, June, 1900, P. & B. Near Kingston,
Duerden. Chitty.
L. papillosa (Forsk.) Grev. In tufts on rocks, Kingston Harbor, Apr.
8, 1893, II. Port Antonio, Kingston, Montego Bay. Manchioneal, Port
256 PROCEEDINGS OF THE AMERICAN ACADEMY.
Maria, P. & B. Near Kingston, Duerden. Closely covering ledges in
rather shallow water, also washed ashore. Chitty.
L. perforata Mont. Densely carpeting rocks in shallow water, Mon-
tego Bay, July, 1900, P. & B. P. B.-A., No. 794.
L. tuberculosa var. gemmifera (Harv.) J. Ag. Washed ashore, Mo-
rant Bay, Annotto Bay, 1894 ; Ora Cabessa, July, 1900, P. & B.
Choudria Baileyana Harv. Hope Bay, July, 1900, P. & B. No.
336, no locality, H.
C. dasyphylla (Woodw.) Ag. Washed ashore, Port Antonio, July,
1891 ; Montego Bay, June, 1900, P. & B.
C. teuuissima (Good. & Woodw.) Ag. Washed ashore, on sandy
beach, Montego Bay, June, 1900, P. & B.
Acanthophora Thierii Lamour. Common on rocks in Kingston Har-
bor, Port Maria, Nos. 176, 195, 278, 377, H. Port Antonio, July,
1891, P. & B. Near Kingston, Duerden.
Digenea simplex (Wulf.) Ag. In tufts on rocks, Port Maria, March
16, 1893, No. 252 ; on stones in shallows, St. Ann's Bay, March 30,
1893, No. 334, H. Washed ashore, Orange Bay, 1894; Manchioneal,
July, 1900, P. & B. Near Kingston, Duerden.
Polysiphonia cuspidata J. Ag. In tufts on piles at beach, Port Maria,
March 16, 1893, No. 251 ; on stones in shallow water, St. Ann's Bay,
March 30, 1893, No. 335, H. Port Antonio, Aug., 1894, covering
rocks in shallow water; Manchioneal, Port Morant, 1900, P. & B.
P. ferulacea Suhr. In dense tufts on rocks and eel-grass, Rio Novo,
June, 1900, P. & B. Near Kingston, Duerden, a slender, long-jointed
form.
P. Havanensis Mont. On mangrove roots, Port Antonio, March 8,
1893, No. 214; on other algae, Kingston Harbor, Apr. 8, 1893, Nos.
374b, 375, H. Washed ashore, Montego Bay, Port Antonio, 1900,
P. & B. Near Kingston, Duerden.
P. Havanensis var. Binneyi (Harv.) J. Ag. Port Antonio, July,
1891, P. &B.
P. Pecten- Veneris Harv. On other Florideae, Port Maria, March 17,
1893, No. 276, H.
P. secunda (Ag.) Zan. On other algae, Kingston Harbor, Apr. 8,
1893, No. 374, H. Washed ashore, Borden, Morant Bay, 1894,
P. & B.
P. subulata (Duel.) J. Ag. Washed ashore, Montego Bay, June,
1900, P. & B.
Only two specimens collected of this species, which has not before
COLLINS. THE ALGAE OF JAMAICA. 257
been reported from America. These agree well with specimens from
the Mediterranean. The range of this species, as previously known, lias
been from the English Channel to Spain, the northern shore of the
Mediterranean and the Adriatic.
Lophosiphonia obscura (Ag.) Falk. Covering stones in shallow water,
Manchioneal, July, 1900, P. & B.
Bryothamnion triangulare (Gmel.) Kuetz. In great tufts in pools,
Port Maria, March 16, 1893, Nos. 254 and 277, H. Washed ashore,
Annotto Bay, Aug., 1894; Ora Cabessa, June, 1900, P. & B. Chitty.
P. B.-A., No. 95.
B. Seaforthii (Turn.) Kuetz. Washed ashore, Port Antonio, July,
•1891 ; Kingston, July, 1900, P. & B.
Bostrychia tenella (Vahl) J. Ag. Port Antonio, on rocks reached
only by spray, July, 1891, and 1894 ; Manchioneal, similar locality, July,
1900, P. & B. P. B.-A., No. 796.
B. Mazei Crouan. In dense tufts on rock, Port Antonio, Feb. 23,
1893, No. 158, H.
B. Moritziana var. intermedia J. Ag. On rocks, shore of island,
Port Antonio, Aug., 1894, P. & B.
" The Bostrychias grew upon rocks and ledges, usually above water,
but dashed by spray."
Murrayella periclados (Ag.) Schmitz. On mangrove roots, Port An-
tonio, March 8, 1893, No. 215; in dense tufts on wood, St. Ann's Bay,
March 24, 1893, H. Manchioneal, July, 1900, P. & B. P. B.-A.,
No. 795.
Amansia multifida Lamour. Washed ashore, Morant Bay, Annotto
Bay, July, 1894; Rio Bono, Rio Novo, Kingston, 1900, P. & B.
P. B.-A., No. 94. P. U., No. 708.
Dasya arbuscula (Dillw.) Ag. Washed ashore, Montego Bay, July,
1900, P. & B.
D. Gibbesii Harv. Washed ashore, Port Antonio, Aug., 1894, P. &
B.
D. mucronata Harv. Washed ashore, Morant Bay, July, 1894, P.
&B.
Heterosiphonia Wurdemanni (Bailey) Falk. On Gelidium rigiduni,
No. 276, H. Annotto Bay, Aug., 1894, P. & B.
Dictyurus occidentalis J. Ag. Annotto Bay, Aug., 1894; Kingston,
near the lighthouse, July, 1900, P. & B. Always washed ashore, never
in large quantity, usually only a fragment here and there. P. B.-A.,
No. 797.
VOL. XXXVII. — 17
258 PROCEEDINGS OF THE AMERICAN ACADEMY.
Halodictyon mirabile Zan. Washed ashore, St. Ann's Bay, March 30,
1893, H.
Spermotharanion Gorgoneum (Mont.) Bornet. On Codium tomento-
siim. Port Antonio, Aug., 1894; Kingston, July, 1900, P. & B. Port
Antonio, Feb. 27, 1893, No. 175 a, H. P. B.-A., No. 441.
" Both cystocarps and polyspores have been found in Jamaica speci-
mens ; in the former the spores have thick cell walls and are arranged
as in Spermothamnion ; the involucre is only slightly developed. The
polyspores are quite numerous, in an ovate or subspherical mass, occu-
pying not more than half the diameter of the large, hyaline sporangium."
Note from label of P. B.-A., No. 441.
S. Turneri var. variabile J. Ag. On Bryothamnion Seaforthii, Kings--
ton, July, 1900, P. & B.
Callithamnion byssoideum var. Jamaicensis Collins. In dense
tufts on rocks, Port Antonio, Feb. 27, No. 170, H. P. B.-A., No. 443.
" This plant has the divided cystocarps, with conical lobes, characteris-
tic of C. byssoideum ; antheridia and tetraspores also agree ; but the
habit is strikingly different, everything being condensed, the branches
relatively shorter and stouter, and very densely set, the terminal ramuli
often arranged more like C. corymbosum. It may possibly be the same
as C. Hypneae Crouau in Maze & Schramm, Algues de Guadeloupe ;
the name must be considered as provisional, awaiting comparison with
authentic specimens of the latter." Note from the label of P. B.-A.,
No. 443.
C. corymbosum (Eng. Bot.) Lyng. On Codium tomentosum, Port
Antonio, Aug., 1894, P. & B.
Haloplegma Duperryi Mont. Washed ashore, Morant Bay, Annotto
Bay, Orange Bay, 1894; Kingston, July, 1900, P. & B. Only a few
fragments at each place.
Crouania attenuata (Bonnem.) J. Ag. On Cryptonemia crenulata,
Morant Bay, July, 1894, P. & B. In small tufts, Navy Island, March
10, 1893, H.
Antithamnion Butleriae n. sp. Fronds erect, ecorticate, simple or
with a few branches, which may be dichotomous, alternate, or occasion-
ally opposite, diameter near base about 30//,, cells 3-6 diameters, walls
thick. The lower portion of the frond or branch is naked; above that
each cell bears normally a pair of ramuli, issuing at about two-thirds the
height of the cell ; the lowest ramuli are simple, subulate, of from two to
six cells about as long as broad; sometimes by the suppression of a
ramulus the branching is apparently alternate ; farther up the frond these
COLLINS. — THE ALGAE OP JAMAICA. 259
ramuli are compounded with similar smaller subulate ramelli, appearing
first on the lower side of the ramulus. The upper pinnae have from
each cell of the rachis a pair of ramelli which touch each other laterally,
so that the pinna forms a continuous triangle. At the tips of the
branches the cells are much shorter than those below, and the triangular
compound pinnae are in contact, giving a linear outline to the whole.
Color a rich rose. On Bryothamuion Seaforthii, Kingston, July, 1900,
P. & B.
From A. pteroton (Schousb.) Bornet it differs in the more densely
branched pinnae, with ramelli on both sides, or on the lower only. From
Ptilothamnion micropterum (Mont.) Bornet it differs by the absence of
the apparent bifurcation of the pinua. Callithamnion microptilum Gru-
now has much shorter articulations in the main branches, and less dense
pinnules, which also are alternately more and less developed, as in some
species of Ptilota. In the absence of fruit it is impossible to determine
that the plant in question may not, when fruit is found, have to rather
bear the name of Ptilothamnion Butleriae.
Spyridia aculeata Kuetz. Washed ashore, St. Ann's Bay, March SO,
1893, No. 337; in tufts, Port Antonio, March 10, 1893, No. 228, H.
S. filamentosa (Wulf.) Ilarv. In dense tufts, Port Antonio, March
10, 1893, No. 222, H. Port Morant, Kingston, Montego Bay, Man-
chioneal, P. & B. Probably common everywhere. Chitty.
Ceramium byssoideum Harv. Washed ashore, Port Antonio, July,
1891, P. & B.
C. clavulatum Ag. Port Maria, Nos. 275 and 301 ; Port Antonio,
No. 183, H. Morant Bay, Manchioneal, Kingston, Montego Bay, P. &
B. Common everywhere and very variable.
C. fastigiatum Ilarv. Washed ashore, Port Antonio, July, 1891 ; Ora
Cabessa, Rio Bono, Rio Novo, June, 1900.
C. gracillimum Ilarv. On rocks, Apostles Battery, Kingston Harbor,
Apr. 10, 1893. H.
C. nitens (Ag.) J. Ag. Washed ashore, Port Antonio, July, 1891 ;
Manchioneal, Montego Bay, 1900, P. & B.
C. tenuissimum (Lyng.) J. Ag. On eel-grass, St. Ann's Bay. March
24, 1893, No. 318, H. Port Antonio, July, 1891; Manchioneal, Mon-
tego Bay, 1900, P. & B. P. B.-A., No. 798. The Montego Bay speci-
mens are small, connecting the type with the following variety.
C. tenuissimum var. pygmaeum (Kuetz.) Ilauck. On Laurencia
obtusa, near Kingston, Duerden. P. B.-A., No. 890. A very small
form, hardly visible to the naked eye, but in full tetrasporic fruit.
260 PROCEEDINGS OP THE AMERICAN ACADEMY.
Halymenia Floresia (Clem.) Ag. Washed ashore, Montego Bay,
June, 1900, P. & B.
Grateloupia filicina (Wulf.) Ag. Morant Bay, on rocks washed by the
waves, but not really under water, July, 1894; Rio Bono, Rio Novo,
July, 1900, P. & B. In tufts on wood, St. Ann's Bay, March 24, No.
419; Kingston Harbor, Apr. 8, 1893, No. 381, H.
"The Grateloupia gathered in 1900 was lying in coarse, black, dry,
rigid tangle on the beach, totally unlike the Grateloupia found in 1894
at Morant Bay, growing on a big boulder on shore washed by heavy surf.
At the latter locality, when the water was over the plants they floated
out like fine, greenish-brown hair; as the water receded the plants fell
back on to the rock, covering it like a soft jelly. From the habit of the
two forms, one would never suspect that they were the same species."
G. dichotoma J. Ag. Near Kingston, Duerden. Fronds broader
than usual in this species as found in the Mediterranean or at the Cana-
ries, but otherwise the same.
G. prolongata J. Ag. Near Kingston, Duerden. Agreeing well with
Agardh's description, and with the form from California which passes
under this name.
Cryptonemia crenulata J. Ag. Morant Bay, Annotto Bay, and coast
towards Port Antonio, washed ashore and growing on '' sea-fans," July
and Aug., 1894; Kingston, July, 1900, P. & B.
Cruoriella Armorica Crouan. On stones and shells, Annotto Bay,
July, 1891, P. & B.
Peysonnellia Dubyi Crouan. On corals, Port Maria, March 17, No.
283 ; Port Antonio, Feb. 23, 1893, No. 161, H.
P. rubra (Grev.) J. Ag. On rocks, Port Maria, March 19, 1893, No.
291, H.
Hildenbrantia Prototypus Nardo. On coral rock, Port Antonio, Feb.
23, 1893, No. 161 ; Port Maria, March 20, 1893, No. 300, H.
Melobesia farinosa Lamour. On Dictyota, etc., Port Antonio, July,
1891, P. & B. On various algae, near Kingston, Duerden.
M. Lejolisii Rosanoff. On various algae and eel-grass, P. & B.
M. membranacea Lamour. On various algae, P. & B.
M. pustulata Lamour. On Gracilaria Domingensis, P. & B.
Lithothamniou incrustans Phil. On rocks, Port Maria, March 16,
1893, No. 258, H. Montego Bay, July, 1900, P. & B.
L. Lenormandi (Aresch.) Foslie. On shells, Port Antonio, P. & B.
Amphiroa charoides, Lamour. Port Antonio, July, 1891, P. & B.
In tufts on bottom, Port Antonio, March 2, 1893, H.
COLLINS. THE ALGAE OF JAMAICA. 261
A. debilis Kuetz. Port Antonio, July, 1891, P. & B. In tufts on
rocks, Port Antonio, Feb. 27, No. 177 ; Kingston Harbor, Apr. 8, 1893,
No. 382, H. Near Kingston, Duerdeu.
A. fragilissima Laraour. Growing like a moss on coral reef and sand
near shore, in shallow water, Port Antonio, July, 1891, P. & B.
Murray gives this species on authority of a specimen by Sloane, but as
he also refers to Farlow, Anderson & Eaton, No. 15, it is probable that
Sloane's specimen is rather A. debilis. The plant distributed under No.
15 was originally labelled A. fragilissima, but a revised label was after-
wards issued, as A. debilis.
Corallina capillacea Harv. Annotto Bay, Aug., 1894, P. & B. In
dense tufts, Kingston Harbor, Apr. 8, No. 383 ; Port Maria, March 17,
1893, H. P. B.-A., No. 150.
C. Cubensis Mont. Annotto Bay, Aug., 1894, P. & B. In dense
tufts, Port Maria, March 16, 1893, No. 250, H.
C. pumila (Latnour.) Kuetz. On Turbinaria trialata, Port .Antonio,
July, 1891 ; on Stypopodium lobatum, Montego Bay, June, 1900, P. &
B. P. B.-A., No. 799.
C. rubens L. In dense tufts, Port Maria, March 1G, 1893, No. 257,
II. On rocks, Port Morant, July, 1900, P. & B. P. B.-A., No. 800.
Sloane. Chitty.
C. subulata Ell. & Sol. Kingston, Feb., 1896, O. Hansen. Sloane.
262
PROCEEDINGS OF THE AMERICAN ACADEMY.
TABLE I.
Comparison of Marine Floras of Jamaica and Other Regions.
CLASS SCHIZOPHYCEAE.
Family Chroococcaceae.
Chrooeoccus turgidus
Chroothece Richteriana
Family Chamaesiphonaceae.
Xenococcus Schousboei
Family Hormogoneae.
Oscillatoria Corallinae
Lyngbya aestuarii
confervoides f. violacea ....
majuscula
Symploca hydnoides
" var. fasciculata . .
Microcoleus chthonoplastcs
tenerrimus
Hormothamnion enteromorphoides . .
Scytonema conchophihini
Mastigocoleus testarum
Calothrix aeruginea
confervicola
Contarenii
pilosa
Dichotlirix penicillata
CLASS CHLOROPHYCEAE.
Family Ulvaceae.
Ulva fasciata
Lactuca var. rigida
Enteromorpha erecta
flexuosa
intestinalis
prolifera
Family Chaetophoraceae.
Diplochaete solitaria
Family Mycoideaceae.
Pringslieimia scutata
-
3
Ah
+
+
+
a
o
+
+
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+
+
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+
+
+
+
+
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+
+
+
+
+
+
+
+
+
+
M
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S
"3:
CD
+
+
+
+
+
+
+
+
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+
+
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+
+
+
+
+
+
+
+
+
+
+
+
+
-t"
+
+
COLLINS. — THE ALGAE OP JAMAICA. 263
TABLE I. — continued.
Family Cladophoraceae.
Chaetomorpha brachygona
clavata
aerea
Linum
" var. brachyarthra ....
Melagonium f. typica
Cladophora crystallina
fascieularis
fuliginosa
Hutchinsiae
intertexta
trichocoraa
Family Gomontiaceae.
Gomontia polyrhiza
Family Bryopsidaceae.
Bryopsis Harveyana
pennata
Family Caulerpaceae.
Caulerpa cupressoides var. typica . . . .
var, Turned . . .
var. mamillosa . .
var. ericifolia . . .
pinnata f. Mexicana
plumaris f. longiseta
" f . brevipes
prolifera
racemosa var. clavifera
f. macrophysa
taxifolia .
verticillata
f . charoides
Family Codiaceae.
Penicillus capitatus
dumetosus
Rbipocephalus Phoenix
Avrainvillea longieaulis
nigricans
Udotea conglutinata
flabellata
Halimeda Opuntia
tridens
Tuna
Codium adhaerens
tomentosum
3
+
+
+
«
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
c
+
+
+
+
+
+
+
+
+
+
+
+
+
+
264
PROCEEDINGS OF THE AMERICAN ACADEMY.
TABLE I. — continued.
Family Valoniaceae.
Valonia aegagropila
ventricosa
verticillata
Siphonocladus membranaeeus . . . .
tropicus
Dictyosphaeria favulosa
Chamaedoris annulata
Microdictyon umbilicatum
Anadyomene stellata
Family Dasycladaceae.
Acetabularia crenulata
Dasycladus clavaeformis
Botryophora occidentalis
Neomeris dumetosa
Cymopolia barbata
CLASS PHAEOPHYCEAE.
Family Ectocarpaceae.
Ectocarpus Mitcliellae
Family Striariaceae.
Striaria attenuata
" var. ramosissima . .
Family Encoeliaceae.
Colpomenia sinuosa
Hydroclatbrus caiicellatus
Family Fucaceae.
Turbinaria trialata
Sargassum bacciferum
lendigerum
platycarpum
vulgare
" var. foliosissimum . . .
" f. ovata
CLASS DICTYOTALES.
Family Dictyotaceae.
Spatoglossum Schroederi
Stypopodium lobatum
Gymnosorus variegatus
Padina Durvillaei
Dictyopteris delicatula
3
+
+
+
+
+
+
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+
+
+
C3
P
C3
+
+
+
+
+
+
+
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o
+
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+
+
+
+
+
+
+
+
+
+
+
COLLINS. — THE ALGAE OF JAMAICA. 2G5
TABLE I. — continued.
Family Dictyotaceae. — continued.
Dictyopteris plagiogramma
Justii
Dictyota Bartayresiana
cervicornis
ciliata
dentata
dichotoma
divaricata
fasciola
Dilophus alternans
Guineensis
Dictyerpa Jamaicensis
CLASS RHODOPHYCEAE.
Family Bangiaceae.
Goniotriehum Ilumphreyi
elegans
Family Helminthocladiaceae.
Cliantransia Saviana
Liagora Cheyneana
decussata
elongata
pulverulenta
valida
Family Chaetangiaceae.
Galaxaura cylindrica
laj)idescens
marginaia
obtusata
rugosa
Family Gelidiaceae.
Wrangelia Argus .
Gelidium coerulescens
crinalt!
rigidum
supradecompositum
Catenella Opuntia var. pinnata
Family Rhodophyllidaceae.
Agardhiella tonera
Solieria chordalis
Eucheuma echinocarpum
«
3
Pi
+
+
+
:
+
+
+
+
a
o
+
+
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+
+
+
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+
+
+
+
+
+
+
+
+
5?
+
+
+
+
+
+
+
+
26G
PROCEEDINGS OF THE AMERICAN ACADEMY.
TABLE I. — continued.
Family Sphaerococcaceae.
Gracilaria Blodgettii
caudata
cervicornis
compressa
confervoides
cornea
Curtissiae
damaecornis
divaricata
Domingensis
ferox
multipartita
Wrightii
Hypnea divaricata
musciformis
Valentine
Family Rhodyrneniaceae.
Champia parvula
Cordylecladia irregularis
Peasiae
Chrysymenia halymenioides ....
Family Delesseriaceae.
Caloglossa Leprieurii
Family Bonnemaisoniaceae.
Asparagopsis Delilei
Family Rhodomelaceae.
Laurencia cervicornis
implicata
obtusa
perforata
papillosa
tuberculosa var gemmifera . . .
Chondria Baileyana
dasyphylla
tenuissima
Acanthophora Thierii
Digenia simplex
Polysiphonia cuspidata
ferulacea
Havanensis
" var. Binneyi ....
Pecten- Veneris
d
(3
o
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+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
a
+
+
+
+
+
+
+
COLLINS. THE ALGAE OF JAMAICA.
2G7
TABLE I. — continued.
Family Rhodomelaceae. — continued.
Polysiphonia secunda
subulata
Lopbosiplionia obscura
Bryothamnion Seaforthii
triangulare
Bostryehia tenella
Mazei
Moritziana var. intermedia ....
Murrayella perielados
Amansia multifida
Dasya arbuscula
Gibbesii
mucronata
Heterosiphonia Wurdemanni
Dictyurus occidentalia
Halodictyon mirabile
Family Ceramiaceae.
Spermoth amnion Gorgoneum
Turneri var. variabile
Callithamnion byssoideum var. Jamaicensis
corymbosum
Haloplegma Dnperryi
Crouania attenuata
Antithamnion Butleriae
Spyridia aculeata
filamentosa
Ceramium byssoideum
clavulatum
fastigiatum
gracillimum
nitens
tenuissimum
" var. pygmaeum ....
Family Grateloupiaceae.
Halymenia Floresia
Grateloupia filicina , .
dieliotoma
prolongata
Cryptonemia erenulata
Family Squamariaceae.
Cruoriella Armorica
Peysonnellia Dubyi
rubra
0)
3
+
+
+
+
+
+
+
+
<8
a
+
+
+
+
+
+
+
+
o
-
+
+
+
+
+
+
+
+
+
+
+
+
+
M
+
+
+
+
+
+
+
+
+
+
m
o
+
+
+
+
+
+
+
+
+
+
+
+
a
is
<v
+
+
+
+
+
268
PROCEEDINGS OF THE AMERICAN ACADEMY.
TABLE I. — continued.
Family Corallinaceae.
Hildenbrantia Prototypus . . . ,
Melobesia farinosa
Lejolisii
membranacea
pustulata
Lithothamnion incrustans . . . .
Lenormandi
Corallina capillacea
Cubensis
pumila
rubens
subulata
Amphiroa charoides
debilis
fragilissima
s
•6
o
'(3
o
G>
43
C8
o
DQ
.2
o
o
>>
Eh
n
s
o
FH
o
C8
Eh
a
Pm
u
a
s
o
fc
+
+
+
+
+
+
+
+
1
T
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
TABLE II.
Summary of Marine Floras, arranged by Classes.
Jamaica.
Puerto
Rico.
Canaries.
Morocco.
Biscay.
Great
Britain.
60
130
193
346
New
England.
Scbizophyceae
Chlorophyceae
Phaeopbyceae )
Dictyotales )
Khodopli3'cene
19
02
29
114
2
25
10
49
7
62
61
156
286
24
59
75
237
34
oo
80
173
75
88
118
153
Total
224
92
395
320
735
434
COLLINS. — THE ALGAE OF JAMAICA.
269
TABLE III.
Percentage by Classes in each Flora.
Jamaica.
Puerto
Rico.
Canaries.
Morocco.
Biscay.
Great
Britain.
New
England.
Scliizophyceae
8
2
3
6
11
9
17
Chlorophyceae
28
27
21
15
10
18
20
Phaeophyceae )
Dictyotales )
13
17
21
19
25
20
26
Rhodophyceae
51
54
55
60
54
47
37
TABLE IV.
Common to Jamaica in other Floras.
Puerto
Rico.
Canaries.
Morocco.
Biscay.
Great
Britain.
New
Englaud.
Scliizophyceae
Chlorophyceae
Phaeophyceae )
Dictyotales ;
Rhodophyceae
2
17
11
33
4
17
8
36
5
13
2
31
6
7
2
27
9
14
3
29
10
10
3
21
Total
63
65
51
42
55
44
TABLE V.
Percentage of Jamaica Flora common to other Floras.
Puerto
Rico.
Canaries.
Morocco.
Biscay.
Great
Britain.
New
England.
Scliizophyceae
Chlorophyceae
Phaeophyceae )
Dictyotales )
Rhodophyceae
11
28
38
29
28
22
29
27
31
26
22
7
27
32
12
7
23
47
23
10
25
53
10
10
18
Total
30
23
19
25
19
270
PROCEEDINGS OF THE AMERICAN ACADEMY.
TABLE VI.
Percentage of other Floras common to Jamaica.
Puerto
Rico.
Canaries.
Morocco.
Biscay.
Great
Britain.
New
England.
Schizophyceae
Chlorophyceae
Phaeophyceae )
Dictyotales )
Rliodophyceae
100
68
69
72
57
29
13
22
21
23
3
13
18
21
3
15
14
11
2
9
11
3
14
Total
69
24
14
11
8
10
Proceedings of the American Academy of Arts and Sciences.
Vol. XXXVII. Xo. 10. — Xovembek, IDOL
CONTRIBUTIONS FROM THE CHEMICAL LABORATORY
OF HARVARD COLLEGE.
MODIFICATIONS OF HEMPEVS GAS-APPARATUS.
By Theodore William Richards.
CONTRIBUTIONS FROM THE CHEMICAL LABORATORY
OF HARVARD COLLEGE.
MODIFICATIONS OF HEMPEL'S GAS-APPARATUS.
By Theodore William Richards.
Received October 26, 1901. Presented November 13, 1901.
The object of this paper is the description of some simple devices which
make possible the accurate analysis of gases with a minimum of special
apparatus.
I. Absorbing Pipette.
The essential feature of Hempel's method is the use of simply con-
structed vessels distinct from the measuring burette for the purpose of ab-
sorbing successively the various constituents of a gaseous mixture. Hempel
used for this end a modification of Ettling's gas pipette, which answers the
purpose admirably ; but of course many other combinations of apparatus
might be used. The simplest is perhaps a bulb or wide tube inserted
over liquid contained in a bottle. In order to prevent the access of air
into this bulb from below, it is well to make the lower part of the tube
somewhat narrow, and to bend it upward. If desired, the capillary serv-
ing to admit the gas may be bent downwards and then upwards, as it is
in the Hempel pipette; but with intelligent use of the pinchcock this pre-
caution is not necessary. A satisfactory form of the apparatus is illus-
trated in Figure 1.
Fifty cubic centimeters is quite enough gas for analysis, if a suitably
narrow burette is used for measurement, hence the receiving bulb of the
pipette (A) need not exceed seventy-five cubic centimeters in capacity.
The bottle (C) should be capable of holding one hundred and fifty cubic
centimetres in this case.
The " compound pipette " of Hempel may be imitated by the addition
at B of another bottle containing water and a levelling funnel, or the
same object may be attained merely by connecting to the outlet B a flex
ible rubber bulb, such as a child's toy balloon.
vol. xxxvii. — 18
274
PROCEEDINGS OF THE AMERICAN ACADEMY.
For solids, the stem D of the pipette may be made of wider tubing,
closed at the bottom with a perforated stopper. A small tube bent
upwards may be inserted in this per-
foration, if especial precaution against
incoming air is desired.
An explosion-pipette could be made
of similar apparatus, with the addition
of a stopcock just below the bulb A and
the usual conducting wires.
The pipette for fuming acid might be
made with a ground-glass joint instead
of a stopper to connect bulb with bottle.
In that case the bottle should be pro-
vided with a suitable side tube on the
neck, bent upwards.
The method of using these pipettes
will be understood without difficulty by
any one familiar with the Hempel
apparatus.
II. Measuring Apparatus.
The most serious cause of error in
Hempel's ordinary apparatus is due to
the possible change of temperature.
This is considerably greater than the
probable error in reading ; for a single
degree Celsius causes an error of 0.5
per cent of the total volume of gas
measured under ordinary conditions,
while the volume is easily read within
0.05 per cent. Hence, unless much
greater care than usual is taken to pre-
serve constant temperature, the reading
of the volume is unnecessarily precise.
But Hempel's ingenious arrangements
for maintaining constant conditions in a 100 c.c. burette are so large as
to be inconvenient for students' use in cramped quarters.
For these reasons I have often used somewhat smaller volumes, which
may be surrounded with an envelope of water without producing thereby
an unwieldy combination. An ordinary 50 c. c. burette, inverted and pro-
Figure 1.
RICHARDS. — MODIFICATIONS OF HEMPEL's GAS-APPARATUS. 275
vided with a levelling bulb or funnel, answers very well as a measuring
instrument. The burette may even be used in its usual position, if it is
provided above with a smooth rubber stopper with a single hole for the
capillary connecting-tube. Of course the stopper is always pushed pre-
cisely into a definite position, indicated by a carefully made mark on the
burette. There is little risk of displacing this stopper if it is firmly wired
into place. In any case of course the ungraduated space at the upper
extremity must be carefully calibrated. Au especially made 50 c. c. in-
strument, graduated all the way to the capillary tube at the top, is more
convenient, although no more accurate than the inverted burette. For
convenience in cleaning, it is well not to have both ends of the burette
drawn down to small diameter. The small size of the burette makes it
easily possible to provide the water jacket which is so essential for accu-
rate work, and both burette and pipette may be supported upon the ordi-
nary iron ring stand.
III. Practical Operation.
Of course the precautions usually necessary in gas analysis must be
used in all the operations with this apparatus. For example, due time
must be allowed for the running dowu
of the liquid from the moistened walls.
Again, care must be taken that the same Hvf
amount of gas, at definite pressure (as
small an amount as possible) is always
left in the connecting capillary tubes.
In order to make sure that no air-
bubbles are caught, it is well to draw
out the ends of the tubes in the manner
illustrated in the diagram, which indi-
cates two successive stages of the glass
blowing, as well as the finished and con-
nected nipple. The object of blowing
the small bulbs is to render the bore of
the portions drawn out as large as that
of the rest of the tube.
While the apparatus thus constituted
was devised primarily for use in an emer-
gency, it has several advantages over Figure 2.
the Hempel apparatus. It dispenses
with the necessity of calibrating the whole length of a new burette, it
UkJ
lU
276
PROCEEDINGS OP THE AMERICAN ACADEMY.
is very inexpensive, aud it occupies but little space. Each student may
possess a complete set of apparatus, and every one knows the value from
a pedagogic standpoint of such a possibility. A further advantage lies
in the fact that the pipette is easy to fill and to clean ; and a precipitate
in the liquid is not apt to clog its working. The short straight capillary
brings an obvious gain of speed in transferring. Moreover, because of
this speed, and the fact that the pressure during transference is always
from the outside inward, the danger of loss by leakage is considerably less
than it is with Hempel's apparatus. It is well known that in a rubber
tube an internal pressure may cause leakage, while an external pressure
tends to stop small outlets by causing the rubber tube to be pressed more
closely together.
On the other hand, the calculation is less obvious, because the volume
taken is not just a hundred cubic centimeters ; and somewhat more care
must be used to prevent the access of air into the pipette from below
while shaking. A little practice enables one to shake thoroughly the
liquid in the bulb without much agitation in the bottle if the movement is
hinged about the point D ; hence the danger is slight. Another slight
difficulty is the possible leakage of the absorbent around the stopper of
the pipette bottle, — an unpleasant occurrence which has no effect upon
the accuracy of the method.
In presenting for general use any new instrument one must record its
practical working in the laboratory. Everybody knows that plausible
Analysis of known Mixtures of Air and Carbon Dioxide.
Volume C02
taken.
Volume Air
taken.
Volume Air
found.
Error.
c.c.
c. c.
c. c.
c. e.
10.95
32.02
32.01
-0.01
18.45
32.21
32.12
-0.09
12.20
42.20
42.20
±0.00
20.00
32.00
32.10
+0.10
14.90
37.60
37 .GO
±0.00
13.00
34.50
34.48
-0.02
16.50
36.50
36.55
+0.05
Excess
of positive ovt
r negative err
ors, 0 03.
RICHARDS. — MODIFICATIONS OF HEMPEL'S GAS-APPARATUS. 277
inventions do not always stand the test of indiscriminate use. Accordingly
a large class in gas analysis has been asked to use the ne*v devices, with
favorable outcome.
The pipette and burette were tested as follows. A definite amount of air
was run into the burette, and the volume measured with the usual care.
Pure carbon dioxide was then run in from a generator, and the gain in
volume was noted. This known mixture of air and carbon dioxide was
run over into the new pipette, and after suitable shaking the residual air
was returned to the burette and measured.
These figures, taken at random from among the results of the class,
agree with one another as well as could be expected ; and since the posi-
tive deviation balances the negative, there is no constant error. No
trouble was experienced as to manipulation.
I am much indebted to Mr. Bisbee, the assistant, and to the gentlemen
of the class in gas analysis, for their kindness in carrving out the practical
trial of the apparatus.
Cambridge, May 3, 1901.
Proceedings of the American Academy of Arts and Sciences.
Vol. XXXVII. No. 11. — January, 1902.
THE PARAMETRIC REPRESENTA TION OF THE NEIGH-
BORHOOD OF A SINGULAR POINT OF
AN ANALYTIC SURFACE.
By C. W. M. Black.
THE PARAMETRIC REPRESENTATION OF THE
NEIGHBORHOOD OF A SINGULAR POINT
OF AN ANALYTIC SURFACE.
By C. W. M. Black.
Presented by W. F. Osgood. Received September 9, 1901.
INTRODUCTION.
A. — Outline of Kobe's Treatment of the Problem.
The problem of the representation, by a finite number of parametric
formulae in two variables, of the neighborhood of a singular point of
an algebraic surface is considered and alleged to be solved in an article
" Sur la theorie des functions algebriques de deux variables," * by Gus-
tav Kobb. A brief outline of Kobb's method follows : —
1. Treatment of the Original Singular Point. 1) Let the equation
of the surface be written in the form
F(x,y,z) = 0,
where F is a function of the three independent variables x, y, z analytic
in the point x = a, y = b, x = c. The function F is transformed by
means of a change of axes to the form
* (6 V, 0 = (6 V, Om + (6 V, Om+l + = 0 (a)
where the expression (£, 17, 'Qn is a homogeneous polynomial of degree
n, the resulting surface (a) having the singular point considered at the
origin, while the function (£, 77, £),„ is of a form convenient for later
treatment.
2) By the quadratic transformation
£ = t£ , 7] = a'C,
$ (£ rj, 0 = tT [(r, a, 1)„, + t (r, <r, 1),)1+1 + ] )
= Cni<f>(T,o-) + ZX(T, (r)+ ] (b)
* Journal de mathe'matiques pures et applique'es, 4th Series, Vol. VIII. (1892),
p. 385.
282 PROCEEDINGS OF THE AMERICAN ACADEMY.
and the neighborhood of the original point is represented by the neigh-
borhood of the curve
0(t,o-)=O, f=0, (c)
on the surface
* (r, cr, 0 = 0.
3) The neighborhood of the curve (c) is included in the domains of
a finite number of points which are
a. regular points of the curve (c), the domain of each being repre-
sented by a single power series
t = V (er, 0 I (d)
b. critical points of the curve (c), the domain of each being repre-
sented by an equation of the form
t" + ^(tr, 0 tm_1 + + /V-iO, 0 r + ?m 0, 0=0; (e)
c. points at an infinite distance on the curve (c), the domain of each
being represented by an equation of form (d) or (e) in the variables
Tj, cti, 7], where
- = Tj , - = crx , £<r = t; .
cr o-
4) The selection of the points in 3) depends upon the character of
the curve
0 (t, a) = 0 .
a. If c£ is irreducible, all points of class 3) b are first taken, then all
points of class 3) c, these being regular; finally a finite number of
points of class 3) a. Here, all the points selected, if singular, are of
order less than m.
h. If <f> is reducible, but contains no multiple factors, the same selec-
tion of points holds as in a, but there may occur a singular point of
order m.
c. If <f> contains multiple factors, all critical points of the curves cor-
responding to any factor, together with all points of intersection of two
different factors, are first taken, then all points of class 3) c, these being
possibly singular ; finally, a finite number of regular points of the several
curves corresponding to the different factors of <£, these last points being
possibly singular points of the surface. In this case, there may occur
a number of singular points of order m.
2. Treatment of Points Determined in 1. The same treatment as in
1 is applied to each of these points and to each of the corresponding
BLACK. — THE NEIGHBORHOOD OF A SINGULAR POINT. 283
resulting points in turn, so long as they are singular. If after a finite
number of such processes, all the resulting points are regular, then by
combining the results it is assumed that the neighborhood of the origi-
nal point is represented by the domains of a finite number of regular
points, and so by a finite number of parametric formulae as desired.
3. Proof that a Finite Number of the Processes of 1 will be Sufficient
to make all Points in 2 Regular. Starting with the surface
f(u, v, w)=0, (f )
in which the singular point considered is at the origin, the transfor-
mations in 1, 1) and 2) are combined in the form
u = (out + fro- + yOn
v = (a2T + /?2o-+72)£>- (g)
W= (a3r + fi3o- + y3)0
We can assume that
y-2 + 0 , y8 4= °
by making, if necessary, upon / (it, r, w) a suitable homogeneous
linear transformation. Then the next set of transformations, in 2, can
be expressed in the form
r=(a1'r1 + /Vo-! + y/Ki )
<r= (a2'Tl + A/o-! + y2') & V (h)
C=(o,'t1 + /V^ + y/Kx J
in which y3' -^ 0,* and the later sets of transformations are of the same
type with the corresponding y3's :
y3"^0, y3"'t0, etc.
So we consider a succession of transformations of type (g), which give
a succession of surfaces with multiple points each of order m. These
transformations will combine in the form
«=[yiy3'y3" ys(r) + (*„ °v, £■)]£• = [A + (rr, <rr,£r)] {,A
V = [y2y3'y3" ya"1 + (r„ <r,, £) ] tr = [T\ + (r„ cr,, £.)] lr \ (i)
«> = [y3 y3' y3" y3M + (r,, <rr, £.)] C = [r, + (r„ <rr, £.)] C )
where the symbol (t,., <rr, £r) represents in the expression in which it
occurs all of the variable terms, and r2 =}= 0, T3 4= 0.
* To secure this, Kobb makes unwarranted use of a quadratic transformation,
which, however, might be replaced by a homogeneous linear transformation. He
also overlooks one class of transformations which will arise (see 4).
284 PROCEEDINGS OP THE AMERICAN ACADEMY.
Next, as f (u, v, w) can be supposed to be irreducible, we have a
relation of the form
9
L (u, v, w)f{u, v, w) + M(u, v, w) «-[/(«, v, w)~\ — x (v, w)
C/U
= (v, w)K + (v, w)K+i + + (v, w)n =j= 0. (j)
Now it is shown that the first member of equation ( j ) becomes divisible
by £r(m-1) (r+1) after the substitutions (i), and the establishment of an
upper limit for the power of £r which can then be taken out as a factor
of the function resulting from ^ (v, w), will secure a corresponding limit
for r, as is needed to finish the proof.
B. — Critiqde of Kobb's Analysis.
We now show in what respects Kobb's method and proof are at fault.
Some of these errors are noted in a memoir " Sulla riduzione delle siuso-
larita puntuali delle superficie algebriche dello spazio ordinario per tras-
formazioni quadratiche," by Beppo Levi.*
4. Kobb overlooks in his succession of transformations of type (g)
the occurrence of transformations which arise from 1, 3), c. These are
equivalent to
£ = t\ v
v =
and here the number corresponding to y3' of (h) is zero; so that the
proof, even if correct in other respects, would fail to cover all the cases
involved, f
5. Without specific discussion of several unwarranted assumptions
of Kobb.J we show by an example the failure of his proof for the
upper limit of the exponent of the power of £,. to be taken out as a
factor of x (v-> w) m (j) under the substitution (i). Let the given sur-
face be
f =: u2 — 2uw — v2 + 2vw + uvw — vw2 — uw2 + wz = 0. (k)
Here,
X (v, w) = (4 + w2) (w — v)2.
The curve
</> (u, v) = u2 — 2u — v* + -2v = 0
* Annali di matematica, Series 2, Vol. XXVI. (1897), p. 219.
t Cf. Levi, 1. c, p. 224. \ Cf. Levi, 1. c, pp. 225-G.
BLACK. — THE NEIGHBORHOOD OP A SINGULAR POINT. 285
has a singular point at
u = 1, V = 1.
So the first transformation is
i; = (o- + 1) £ V (1)
which, applied to (k), gives
£2 (r2 - o-2 + to-0 = 0 (m)
and
x(t.,«,)=£2o-2(£2+4). (n)
Now the set of transformations to which Kobb is naturally led in this
case is the following : — *
T = Ti & O" = 0^ & £ = £j
*"l = T2 £2 0"l = 0"2 £2 £l — £2
whence
T = TV C, O- = OY £/> £ = £r-
But this substitution in (11) gives
x (v, w) = Vr+2 <r* (C2 + 4)
in which the exponent of £r increases indefinitely with r.
6. In the case in which the curve
c£ (r, «x) = 0
has multiple factors, the regular points of such factors taken in 1, 4) c
are possibly singular points of the surface, whose domains are repre-
sented by equations of form (e). When a further quadratic transfor-
mation is applied to such a point, we are not warranted in assuming
that the resulting developments will represent the whole of the domain
of the point considered. f Kobb makes this assumption in proposing to
* This set, combined with the transformation (1), possesses all the properties
required by Kobb in (g), (h), and (i) ; its appearance here invalidates his proof.
It can easily be shown, moreover, that the most general set of transformations
which he could use in this case would produce the same condition as shown here.
t The development about the point first considered, to begin with, is a relation
im Kleinen ; it becomes, however, on passing to the later transformations, a relation
286 PROCEEDINGS OP THE AMERICAN ACADEMY.
use in 2 only the set of points determined in 1. We are not warranted,
either, in assuming that, when a reduction of singularity arises from the
appearance of a term of lower degree in a different'variable from that
with reference to which the first development is derived, the resulting
development will hold throughout the same region as the first develop-
ment. As an example consider the surface
r2 + cr£ - £ = 0.
Regarded as a development for t, its coefficients converge for all finite
values of o- and £ ; but when we develop for £,
*> — , 5
1 — O"
and the resulting series converges only when
| o- 1 < 1.
7. From geometrical considerations we should not expect the quad-
ratic transformation used to resolve the singularity in all cases. In
ordinary space the transformation
£ = t£, rj — cr£,
will transform in a one-to-one manner, without change of the £ coordinate,
all points except those in the £ = 0 plane. Now in the surface from (m),
t2 - a' + t(t£ = 0,
all points in the £-axis are singular, and whatever the reduction that
may be secured for the origin, there will be within the neighborhood of
the origin points whose singularity is not reduced. The same consider-
ations would be seen to apply if we had any space curve as a singular
line.
Levi, in the article previously mentioned, does not attempt a proof
of the entire proposition, but directs his work toward establishing by
geometrical considerations the reduction of the singularity, making ex-
ception, however, of certain cases,* which are closely related to the one
considered in 7.
Having thus considered the failure of Kobb to establish the proposi-
tion even for the general case of an algebraic surface, we shall, in the
im Grossen, the limit to the number of points taken being determined by finding
the extent of tbe domain of each ; while the developments about the later points
giye relations im Kleinen, as far as the first point is concerned.
* Cf. Levi, 1. c. p. 227. Cf. also a second paper by Levi, Atti R. Ace. Sci. Torino,
Vol. XXXIIL, 5 Dec, 1897.
BLACK. THE NEIGHBORHOOD OP A SINGULAR POINT. 287
present article, supply the deficiency, and treat at once the more general
case of an analytic surface, i. e., the case that the function F (x, y, z) is
not merely a polynomial, but is any analytic function which vanishes
at the point (a, b, c.)
§ 1
A. — The Fundamental Theorem.
1. The theorem, the proof of which forms the subject of this article,
is the following.
Theorem: Let F (x, y, z) be a function such that
1) F (x, //, z) is analytic in the three independent variables in the
neighborhood of the point x = a, y = b, z = c ;
2) F(a, b, c) = 0;
3) (— \ =(9~) =( — ) =0-
\dzj[a.b,c) \5y/(a.6,c) \dzj[a,b,c)
then we can represent all values of (x, y, z) satisfying the equation
F(x,y, *)=0
and lying in the neighborhood of the point (a, b, c) :
\x — a | < S, \y — b\<8, \z — c\<$>
by a finite number of parametric formulae of the following type :
x = <f>p (u, v) 1
y = <AP(M> «0 y p = 1, 2, p, (A)
z = Xp(?/' v) J
where t/>p, if/p, \p are analytic in the arguments (u, v) throughout a cer-
tain region ; further for each set of values of (x, y, z), the values (0, 0, 0)
excepted, there corresponds for at least one value of p a pair of values
(u, v) lying within the region in which the functions <f)p, \pp, xP are con-
sidered, and for any value of p for which this is the case, there corresponds
no second pair of values. To the set of values (0, 0, 0) corresponds at
least one, and in general an infinite number of pairs of values (u, v) for
every value of p.
2. Explanation of Symbols. The symbol (x, y, z, )„ indicates,
in the expression in which it appears, the total collection of terms
of degree n in the arguments taken together, which belong to that
expression.
288 PROCEEDINGS OF THE AMERICAN ACADEMY.
A functional sign expressed by means of a letter will always represent
an analytic function.
The symbol E (x,y, z, ) will always represent a function which
is analytic at the point (0, 0, 0 ) and for which E (0, 0, 0 )
4= 0. If written with a subscript, as Er (x, y, z, ) it represents a
particular function of the class; if without a subscript, it represents a
general function of the class ; so that two functions E (z, y, z, )
both expressed by the same symbol, need not be equal to each other.
B. — The Transformations.
3. The equation
F(x,y, z) = '0
can be transformed to the form
<*> (£ V, 0 = (£ r), 0™ + (6 V, Om+i + - o
where
1) m > 2,
2) the polynomial
(£, v, i)m = *(£, v)
contains the term £m,
8) the points in which the curves corresponding to the irreducible
factors of <£ (£, r/) cut the line at infinity shall be distinct from each
other and from the point in which the line $ = 0 cuts that line.
To do this, we first make the transformation
x = u + a, = v + b , z = w + c ,
thus obtaining
F(x, y, z ) =f(u, v, w) = (u, v, w)m + (u, v, w)m+l +
Here, m >; 2, the singularity now being at the origin. Next we make
a linear homogeneous transformation with non-vanishing determinant,
U = Ox | + /?! 7} + yi £ J
v = a,£ + (32V + y,C> (1)
w = a3 £ + & rj + y3 £ )
with the result :
/(U, V, W) = $ ($, Tj, 0 = (6 ">?, Dm + (£ ??> Qm+1 + = 0 .
For this equation, conditions 2) and 3) can be secured, as is readily seen
by a proper choice of the coefficients in transformation (1).
BLACK. THE NEIGHBORHOOD OP A SINGULAR POINT. 289
The surface $ = 0 corresponds in the neighborhood considered, point
for point, to the surface F = 0, and thus it is only necessary to prove
the theorem for <t> = 0.
We may assume that of the irreducible factors* of 4> there are none
of degree lower than m vanishing at the point (0, 0, 0), for otherwise
each of such factors could be treated separately by the methods here
used, and the results combined. This provision excludes the case in
which one of the variables has equal roots for all values of the other
two in the neighborhood of the point (0, 0, 0).
4. The quadratic transformation
*=?: v = v (2)
reduces <i> (ft r;, £) to the form
<Kft^0 = ^W>(ft^) + £x(fti0]
= £m<b(lv,Q (3)
where, au arbitrarily large positive number r having been chosen at
pleasure, 8 can be so determined that the function <i> will be analytic
when
|?|<r, \v\<t, |C|<«.
Equation (3) follows at once from the intermediate form
4> a, v, o = c id v, i)<» + c(#, t. iu + £2 (i, v, i)»+2 + ]•
We now proceed to the proof that the function 0 (£, 77, £) is analytic
within the above limits.
Let <P (ft 17, 0 = 2 J .x. £ rf £* , t + / + * > m ,
and suppose it to be convergent when
|f I < h, \v\ < /,, |C| < h h> o\.
Then, for the general term, we have
\Aijk\^+k<M,
M being a positive constant.
By transformation (2)
<*> (ft V, 0 = 2 j* ? 7 ri+*
* For the definition and the fundamental properties of the irreducihle factors
of an analytic function of several variables, which vanishes in a point, cf. Encyclo-
piidie der mathematischen Wissenschaften, II. B. 1, Nr. 45.
vol. xxxvil. — 19
290 PROCEEDINGS OP THE AMERICAN ACADEMY,
and
*ffi* 0 = 34* ???***-
Now choose 8 so that r 8 < ox .
Then, when
|?] = rx, |^| = r1} K| = 8, rx>i,
the absolute value of the general term of series <fr becomes
< | AiJk | . iy+->' . &+j+*-"
< | Aijk | . 8»J . S*-
JAljk\.W+j+k
*> gm
< gn,
3 4* ??{*»**-
Accordingly, the series
is convergent when
\l\<Tt |7l<Ti |C|<8,*
and it represents an analytic function for these values of the arguments.
5. The family of lines tangent to the surface <J> (f, ??, £) = 0 at the
point (0, 0, 0) forms a cone that cuts the plane £ = 1 in the curve
$ (£, 77) = 0. If the line -q/t, = /?, £/£ = a, (a and /? being finite) is
one of this family, then the point £ = a, -q = ft, £ = 0 of the surface
<1> (£, 77, £) = 0, (3) is at most a singular point of order m of that sur-
face, and its neighborhood corresponds to a portion of the neighborhood
of the singular point of the original surface <I> ($, rj, £) = 0. In fact,
cut the surface
* (6 * 0 = 0
by the plane
»7-/3£=0.
Then the curve of intersection C will have a multiple point at (0, 0, 0)
and the equations of the tangents to C at (0, 0, 0) will be
v-j3£=0)
> cr = 1, 2, s < m.
* Cf. Stolz, Allgemeine Arithmetik, Vol. I. p. 293.
BLACK. — THE NEIGHBORHOOD OF A SINGULAR POINT. 291
Now, the transformation (2) being made, the points of the region
T: |*| < 8, h|< 8, |C|<8,
which lie in the neighborhoods of the lines
> cr = 1, 2, 5,
can, with the exception of the point (0, 0, 0), be transformed in a one-
to-one manner on the neighborhoods of the points (0, 0, 0) of a set of
surfaces
9« (£r> VU 0 = ° . Or = 1, 2, S ,
the coordinates being connected by the relation
r (4)
*=£foi + /?> S
By the neighborhood of the above line is here meant the set of points
(£, 7/, £) which satisfy the condition
|*-«**|<«|C|, h-£C|:S«|C|, ICK8-
To deal with the points for which a, /? would be infinite, cut the
surface
4> (£ r/, 0 = 0
by the plane
C = o.
The equations of the tangents to the curve of intersection at (0, 0, 0)
are
f- t=1, 2, «<m.
By means of a transformation corresponding to (2),
the points of T which lie in the neighborhoods of the lines
£ - «T 77 = 0 )
[ T= 1, 2, < < TO,
£ = oj
can, with the exception of the point (0, 0, 0), be transformed in a one-
to-one manner on the neighborhoods of the points (0, 0, 0) of the set
of surfaces
SV(lT,^£) = 0, t= 1, 2, *<m,
292 PROCEEDINGS OF THE AMERICAN ACADEMY,
the coordinates being connected by the relations
( = vi I
By the neighborhood of the line
£-aTr, = 0l
is here meant the set of points (£, 77, £) which satisfy the condition
l^-u^l^hl, |fl<«|*|, \v\<8.
The singularities of the surfaces
9A^ Vi, O = o,
ffT it* v, 0 = 0
at the points (0, 0, 0) are at most of order m. Their further proper-
ties will be considered later.
Let G be an arbitrarily chosen (large) positive quantity, 8 a second
suitably chosen positive quantity : then any point of T, for which
I*i<g|ci, \v\<e\t\, o<m<s,
is carried by the transformation (4) into one of the neighborhoods above
considered on the surfaces ga = 0. If £ = 0, but £, 77 do not both van-
ish, then the point (f, 71, £) is carried by (5) into one of the neighbor-
hoods considered on the surfaces gT = 0.
In (3), the function <j> ($, rj) contains the term $ m by 3, 2). Apply the
transformation
V-P= *7i, (6)
whence (3) takes the form
* (6 v, 0 = C" Oi (I vi) + t Xi (?» ft> 0].
In (j>x (£, tij), take out all terms not containing rju so that
_ « _ ^a _
01 (£ *h) = n (£ — a„) + 77 1 i^ (£, ??!), (U! + + ^ = m.
<r = l
Then make the transformation
* ~ «„ = C (60
and we have
* (6 ,, 0 = r tc n' & + aa - v)'v + 71 * (*a, in) + :x (k %. 0]
<r1=: 1
= Vg9 (*„ % 0 = 0 (7)
BLACK. — THE NEIGHBORHOOD OF A SINGULAR POINT. 293
where ga has a term in ^ free from Vl aud £, since aa — aa, £ 0. So
there are near the point (0, 0, 0) ^ values of £a satisfying the equation
ga — 0 for every pair of values of ^ aud £ in the neighborhood of the
point r\x = 0, £ = 0. Now, for any such set of values of c , rju £,
different from the set (0, 0, 0), satisfying the equation gv = 0, there is
a corresponding set of values of £, rj, £ satisfying the equation $ (f, rj, £)
= 0, their coordinates being connected by the relations (2), (6), and (6'),
which are equivalent to the required relation (4). Also by considering
s
the other factors of IT (£ — a^0", we get (s — 1) other equations of form
(7), the corresponding coordinates being connected by relations of
form (4).
No two points (£ v, £), (£f, v>, £') of T (distinct from (0, 0, 0)), de-
rived from points (£ffl rjv Q (^„ %, £2) lying respectively in the neigh-
borhoods of the singularities which are given by two distinct equations
9, = °, <J°' = 0,
can be the same. For suppose
*=& = It (4 + a,) = £2 Ua, + a,,)
£ = £' = Ci = £2
Then we must have
4 + a<r = £r' + <V'
4 - £
'cr'
and, by taking the neighborhoods of the singularities in question suffi-
ciently small, we can insure that the difference £v — £a, is less in abso-
lute value than the difference a , — a . In a similar manner it is shown
that, if the equation g = 0, regarded as an equation in £ , has equal
roots for all values of ij1} £ in the neighborhood of the point -qx = 0,
£ = 0, the equation <S> = 0 must also have equal roots at the corre-
sponding points, and this case has been excluded. So as each equation
g = 0 has near the point (0, 0, 0) p values of £ , in general distinct,
t
for each pair of values of rji and £, aud as 2 /j. = m, the collection of
equations
ga = 0 , o- = 1 , 2, 8 ,
has within sufficiently small limits as many different roots as the equa-
294 PROCEEDINGS OF THE AMERICAN ACADEMY.
tion 4> = 0, and thus represents the latter equation within the corre-
sponding limits, i. e., when
|£|<s, M<*> U<c>
or
|*-a,{|<e|C|f h-i»C|<«|t|. |f|<«.
Next we consider points for which £ = 0, but f, -q are not both zero.
For these we use the transformation
t = €v, t = Zy- (8)
Then, by the same method of treatment as above, putting £ for rj and
7) for £, and taking (3 = 0, we derive a set of surfaces
9v(£fV>l) = 0, t= 1, 2, <<m,
on which are mapped all points of the original neighborhood for which
£
M < 8i » i — < €i »
I v
and so all points for which
Here, we have a function corresponding to <£ (J, 77) :
<M?,f) = (|, i,1)m
Now, for the infinite roots of
*(£})r=0,
we put the equation into the form
(f-,.,4)=o.
So the equation
<M?,f) = o
is such that its roots for £ = 0 are the same as the ratios of the infinite
roots of the equation
$(lv) =o,
and by 3, 3) these ratios are all finite.
BLACK. — THE NEIGHBORHOOD OF A SINGULAR POINT. 295
C. — The Number of the Neighborhoods, tu U, t,
REQUIRED TO REPRESENT T IS FlNITE.
6. In the foregoing paragraph it has been shown that the neighbor-
hood of each tangent line to the surface 4> = 0, at the singular point
can be mapped on the neighborhood of a (regular or singular) point
of the surface g = 0. We now proceed to show that the whole
neighborhood
'b'
T: |*| <*, hl<S, \£\<&
can be covered by the neighborhoods of a finite number of such lines.
We distinguish two cases : —
Case I. — The polynomial </> (£, 77) has no multiple factors.
Case II. — This polynomial has multiple factors.
Theorem: The neighborhood T can be completely covered by a finite
number of regions Tu T.2, Tv, which overlap each other and which
are mapped respectively on the following regions tx, f2, tv:
In Case I: 1) the region t{, i = 1, 2, k, consists of the neigh-
borhood of a singular point of the surface gw = 0 ;
2) the extent of each of the neighborhoods tx, t.2, tK having been
arbitrarily determined^ the regions tfi j — k + 1, v, then consist
of regular regions of surfaces g<J> = 0.
In Case II : 1) the region tit i = 1, 2, k, consists of the neigh-
borhood of a singular point of the surface g{i) = 0 ;
2) the extent of each of the neighborhoods tx, t.2, tK having been
arbitrarily determined, the regions fj,j = K + 1, v, then consist
of regions of surfaces g'j) = 0 defined as follows ■' omitting the index j
throughout, we write
9 (£., Vv 0 = [£ + ft (Vv 0 C + + pr(Vv Ol^d,, Vv 0,
where pe (r^, £) is analytic throughout a region
M<h, \£\<8-
Here r,for a given value ofj, is a positive integer satisfying the relation
1 5; r < m.
Case I. — The polynomial </> (f, 77) contains no multiple factors.
Here, the equation
296 PROCEEDINGS OP THE AMERICAN ACADEMY.
can have multiple values of $ only for a finite number of values of 77,
these being the values for which the equations
* = 0, ^ = 0
have common roots, and by the condition 3, 3) none of these values of
r) become infinite.
Now we consider all such values of -q
V = cr, r = 1, 2, /,
for which the equation, considered as an equation in J,,
*(?,}) = <>
has multiple roots. Deal with each of these as in 5, cr taking the place
of /3 in (6) ; then, in equation (7), some of the // 's will, in general, be
greater than unity, i. e. some of the equations g ■=. 0 will have for the
lowest terms in £ alone exponents greater than 1. For such as have
their /x = 1, there are regular points. The others will afford singular
points unless they have terms of the first degree in either ^ or £.
Surround these points by neighborhoods
141 < 8, \m\<*, |CI<*»
i. e.
|?-aj<&, \V-Cr\ < J, \t\< 8,
which are to be considered later.
Now let t] = b be any value for which the equation
<£ (?, V) = o
has not equal roots. Then the equations g = 0 of (7) each have a term
in £ to the first degree, free from -qx and £, and thus the points of the
surface g = 0 lying in the neighborhood of the point $a = 0, rjx = 0,
£ = 0, can be represented by a power series
So, in this case, we have m developments
$,=£rO&i©i <r=l, 2, m,
and, by using the relations (4), we have
£=p9(r), Q, <r=l,2, m.
It is readily seen that the function
BLACK. — THE NEIGHBORHOOD OF A SINGULAR POINT. 297
is analytic within the region
\-m\<h-et |C| < Sx4=03
where h is the distance to the nearest value of ^ for which the equation
corresponding to
has a critical point, e is a positive number which can be taken arbi-
trarily small and, having been chosen, determines an upper limit, not
zero, for o\. In fact, f is a continuous function of the two independ-
ent variables rju £ within this region; furthermore, for any fixed value
of £ such that |£| < 61; £a is an analytic function of r]1 throughout the
region | qx \ < A — e ; and, similarly, for any fixed value of r/x such that
| >7i | < h ~ e' £ is an analytic function of £ throughout the region
Also consider the surfaces
in 5. Here also we have m regular points of surfaces, and as a result
m functions of the form
These, by the same method of proof as above, are seen to be analytic
when
III < *i-*, \v\ < **,
where A is the nearest point in the 4-plane for which the equation
has multiple roots for £, i. e. the smallest value of £ for which the
equation
(?, 1, ?)m = 0
has equal roots for $. But this is the smallest value of - for which the
V
equation
a 1, i)
= 0
* Cf. Briot et Bouquet's The'orie des fonctions elliptiques, § 28. The proof of
continuity there given for polynomials in two variables will apply with very
slight mollifications to analytic functions of any number of variables. Cf. further
Jordan's Cours d'analyse, I. § 206, § 258.
298 PROCEEDINGS OF THE AMERICAN ACADEMY.
regarded as an equation in £/r], has equal roots. Thus — is the largest
value of t) for which the equation
has a critical point. So the functions are analytic and give all points
of the original neighborhood for which
I-
< hi — «n \v\ < 82>
or for which
/ > jt^— = t + rrr1 — \ = ** + «*» f*> = r)»
thus securing the limits
\v\ < Sai Ul < S3, U| > (^ + e2)|4l,
where A2 is the distance to the furthest point in the r/-plane for which the
equation
has a critical point, and if e2 is first chosen arbitrarily small, 83 can be
determined not zero.
Now consider the neighborhoods of the critical points of the curve
*(?, v) = 0.
In these, however small we take the 8, all the remainder of a circle in
the 77-plane including all the values for which the curve cf> = 0 has
critical points can be covered with circles such as were determined for
the domains of the regular points above, these circles overlapping the
circles about the singular points and not reaching out to these points in
any case. Let the radius of the large circle be G where
G > 1 , G > h, + e2 .
Then, if we take for 84 the smallest value of any ^ or S", the develop-
ments within these circles together with the neighborhoods of the set
of new singular poiuts will represent all points of the original neigh-
borhood for which
Finally, taking for 8 the smallest of the three quantities $2, 83, o4, the
BLACK. — THE NEIGHBORHOOD OF A SINGULAR POINT. 299
whole set of functions thus determined will represent all points of the
original neighborhood for which
h| < 8, |C|< 5.
The new set of singular points may or may not be all of degrees lower
than ?n, but if they are we have simplified the problem ; we have reduc-
tion, as we shall say, borrowing a term frequently used in the theory
of algebraic invariants of a linear transformation ; and if not, the further
treatment will be considered later.
D. — An Example.
Before taking up Case II, however, we consider an example in which
the degree is reduced by one quadratic transformation, and the para-
metric representation (A) is at once secured.
Let the surface be
The transformation
secures for the equation corresponding to (3)
*(6^0 = P + ?-l-?C = O.
Here
0 (£$ = ? + ?-l
and the critical points are
1=0, 5=1,
?=0, , = -l.
Let
and we have
Hence
Also let
and we have
d = €> Vi = V ~ l t
^2 + ^2+2t7i-^C=0.
m = -i + Vti(t-&) + i- (a)
£2 = l> f]i = V + ! >
In (a) and (b), only that branch of the radical is taken which becomes
+ 1 for zero values of the arguments.
300
PROCEEDINGS OF THE AMERICAN ACADEMY.
Again, we make the transformation
and derive the surface
Here
and for the value £ = 0 we have the roots
? = * j I = — **•
Let
$3=1 — i,
and we have the surface
L2 + 2*& - e - ?V& - i?V = 0,
1 + h ^/?t?2+4|=2-4.
whence
£3 =
2
In a similar way, from the other root,
(c)
(d)
In (c) and (d), for the radical is taken only that branch which becomes
+ 2 i for zero values of the arguments, and the function is seen to be
analytic for sufficiently small values of q when
CI
'/
< i - « i ;
and similarly when
V
\v\ =
> 1 + e.
Thus, in the ^-plane, we have
by the formulas (a), (b), (c), (d)
covered two, small circles about
the points 1 and — 1 corre-
sponding to developments (a)
and (b), and all of the region
outside of a circle of radius
(1 + e), corresponding to devel-
opments (c) and (d). We must
now obtain further formulas
so as to till up the remaining unshaded region.
BLACK. — THE NEIGHBORHOOD OP A SINGULAR POINT. 301
Consider the point
Let £ = £5 — 1 and we have
&2- 2 & + ?-&£+ £=0,
whence
^ = ^-2-i^-^+4.
(e)
In the same way, about the point
£=1, ^ = 0,
we liave the function
£
6= — + W£2-4?+4 (f)
In (e) and (f), for the radical we take only that branch which becomes
-f 2 for zero values of the argument, and for sufficiently small values
of f the functions are analytic when
| rj | < 1 — e2 .
Agaiu, consider the point
Let
1 = & + 2 Vl - i , ^ = -77 + 1 + 2*,
and we have
^72 + 4 yi^^7 4-7 + Vl2 + 2 (1 + 2 1) 777 - £7£ - 2 vT^?£ = 0,
whence
j^-4^1-*-^ 1^16-16^+^-4^-8 (l + 2^7. (g)
For the corresponding point
4r=-2A/l -i, ^ = l + 2»,
we have the formula
4 Vl — * + £
& = 2 ^ - £ Vl6 - 16* + ? - 4 V - 8(1 + 2t)%. (h)
In (g) and (h), for the radical we take only the branch which becomes
+ 4 V4 — i for zero values of the arguments, the same value of the
radical \/l — i being taken in all cases. These functions are analytic
for sufficiently small values of £ when
I *77 | = 1 17s | < 2 — e7 •
Also, considering the corresponding points of
302
PROCEEDINGS OF THE AMERICAN ACADEMY.
for which
^ = -1 + 2*,
V= 1-2*,
V= -1-2/,
we have evidently similar re-
gions for each. Then, by taking
the e's all small enough, we
cover the whole unshaded re-
mainder of the ^-plane by five
circles within each of which there
is a development as required.
The sets of parametric form-
ulae, derived by using the inter-
mediate transformations, are
£ = UV, 7] — v \/u (v — u) + 1 ,
£ = uv , r) = — v y/u (y — u) + 1 ,
$ = -(u2v + a/mV-F 4w2 — 4),
v
$ = ~(u2v — V«*4»a + 4w2— 4),
7] = V,
( = uv
from
u
U
^z=^(u-V"2-4t;2+4),
^ = -(«+V"2-4r2 + 4),
rj — uv, £ = a
f] = uv, t, = u
00
(b)
(c)
(<*)
(e)
(0
u
£= -( u + Vl6 — 16/ + u2-4v2-8(L + 2i)v ),
v = u (v + 1 + 2 1) ,
$
M
)#=!(
M _ Vl6 - 16t + w2 — 4u2- 8(1 + 2%)v ),
(g)
00
with three more sets similar to (g) and (h).
Case II. — The polynomial <£(£, rj) contains multiple factors.
Here, any points which are common to two different irreducible
factors of <£(£, rj), or are critical points of a single irreducible factor,
will be critical points of the curve
*(£v) = o,
BLACK. — THE NEIGHBORHOOD OP A SINGULAR POINT. 303
and all such points, a finite number in all, will be treated like the
critical points of the previous case. But also any point on a multiple
factor is a critical point of the curve, and further treatment is needed
for such points.
Suppose I = a, 7] = P is a regular point of a factor fa (£, rj) of mul-
tiplicity r, i. e. of the irreducible factor whose rth power is equal to
</>i(£> v) an(* not a P°int of any different factor of <£(£, rj). Then, in
the corresponding equation of form (7), g will contain a term £r as the
lowest term in ifa free from ^ and £, and by Weierstrass's Theorem *
we can develop the function about the point in the form
PC + pi fa OC + + Pr (*» 0 1 E(^ Hi 0 = o. (9)
These functions
Pk(vi, 0' X = l, 2, r,
are shown by a method similar to that used for the functions in Case I
to be analytic within a region
hi|<A-«, KKSn
where h is the distance to the nearest value of r/i which gives a point
of intersection of two different irreducible curves corresponding to factors
of <£(£, if), or to a critical point of one of the irreducible curves.
Now none of the excepted points can be at infinity, on account of the
provision in 3, 3). So the points on the surfaces g = 0 in 5 will also
afford developments of order (9), and by the method of Case I, we
have a similar region for tbe convergence of the coefficients of the
different powers of £r in the polynomial, i. e. the exterior of a circle
including all of the excepted points.
Accordingly, in this case also, we represent the neighborhood of the
original singular point by a finite number of neighborhoods of new
singular points together with a finite number of functions, some of which
are now not analytic for the values of the arguments considered, but
satisfy equations of the form
£ + Pl(Vl, OC + + Pr (*» 0 = 0- C11)
For the further treatment of these functions, we shall establish an
auxiliary theorem in § 2.
* See Picard's Traite d'analyse, Vol. II. p. 241.
304 PROCEEDINGS OP THE AMERICAN ACADEMY.
Any point in T'can be carried by a suitable transformation into a
point on one of the surfaces g — 0 or gr = 0. Let G be an arbitrarily
chosen (large) positive quantity; then any point of T for which
\i\< G\t\, \-n\<G\Z\, \C\<8,
is carried by the transformation (4) into one of the neighborhoods con-
sidered on the surfaces g = 0.
If '(, — 0, but £3 77 do not both vanish, then the point (£, 77, s) is car-
ried by (5) into one of the neighborhoods considered on the surfaces
9T = Q-
§ 2.
A. — A Lemma.
1. The treatment of the multiple curves of Case II depends on the
following
Lemma. — Given an analytic surface
*(*» y, z) = £(*> y) + »*(*i y> z) — o, (a)
<£(*, y) = 0
is a multiple curve ; let <f>(x, y) have the form in the neighborhood of the
point x = 0, y = 0,
<f>(x,y) = [x+p(y)]'»JE(x,y), (/?)
where p (y) is analytic at the point y = 0, and p (0) — 0. The function
ty (x, y, z) shall be analytic at the point (0, 0, 0), but shall not be divisi-
ble by x + p{y) at that point. Consider a region for which \y\ < h,
and let h be chosen
a) less than the radius of convergence of the Taylor's series which
represents the function p (y) developed about the point y = 0, and
b) sufficiently small, so that the points (x=p(y),y) will lie in the
region in which E(x,y) is analytic and different from zero. Then the
part of the neighborhood of the curve
x + p(y)--=0, z = 0,
which lies on the surface
&(x,tf, z) = 0
can be transformed, by means of quadratic transformations of the type
x =■ xz,
BLACK. — THE NEIGHBORHOOD OP A SINGULAR POINT. 305
on a finite number of regions ru t2, t , which fall into two
categories : —
1) the region rt(i = 1, 2, k) is the neighborhood of a singular
point of order < m ;
2) each of the neighborhoods of 1) having been determined arbitrarily
small, the region ts (i = k + 1 , v) is then a regular piece of an
analytic surface, represented in its whole extent by a single set of para-
metric formulae of the type {A).
By the neighborhood of the curve
x+p(y) = 0, s = 0,
is meant the set of points (cc, y, z) satisfying the relation
\y\<h, |*| < 8, \x + p(y)\<e.
B. — Proof of the Lemma.
2. To prove the lemma we begin by expressing equation (a) by means
of (J3) in the form
* (*, y,z) = [x+p (y)y» E(x, y) + z*(x, y, z) = 0, (y)
and then making the transformation
x + p (y) = xx , (S)
thus obtaining the equation
$0, y, z) = 4>j (a?!, y, z) = x1mE(xu y) + zipx(xu y, z) = 0. (y')
Here, the function E (xu y) is analytic and different from zero in the
neighborhood of any point xx = 0, y = y0, (\y0 | < h), which corresponds
to the neighborhood of the point x0 = p (y0), y0, and lience E (xx, y) is
analytic throughout a region including in its interior the region
l*i I < e> \y\ < h>
if the positive quantity € is suitably chosen. A similar remark ap-
plies to the analytic character of the function \px (xu y, z), and hence
<!>! (xu y, z) is an analytic function of its three arguments throughout
a region including in its interior the region
l^i I < e> |y| < A» 1*1 < s-
Now express equation (y') in the form
*i(*n y? z) = 2p,..(y)^ir2s + F(x1} y, z) = 0, (e)
where
0 < r + s = mi < m,
vol. xxxvii. — 20
806
PROCEEDINGS OP THE AMERICAN ACADEMY.
ml being the lowest degree of any term in xt and z together, and
F(xuy, z) including all terms of degree higher than m^ in the two
variables xu z. Each coefficient pr3 (y) may be divisible by a power
of y, yl. In that case, however, nti must be less than m, for the term
in x™ is present in $a (a^, y, z).
By means of a transformation with non-vanishing determinant,
xx = ax x2 -f /?! z2 )
Z = a2 X2 + Pi Z2 )
4>j can be thrown into the form :
*i (*i> V, z) = $2 fa, y, z2) =
9o(y)^mt + qi(y)x2'n-1z, + + qmi(y)z2"h + F,(x2, y, z2) = 0 (,)
where q0 (y) =j= 0.
Consider first the points of the circle \y\ < h at which q0 (y) = 0, if
such exist. Each one of these points y{, (i = 1, 2, «) is a singu-
lar point of <J>2 = 0 of order not greater than /«, and its neighborhood
|*i|<«i |y-y*|<«, M<s
may be chosen arbitrarily small.
Surround each of these points in the
circle \y\ = h by a circle of arbitrar-
ily small radius e'. We now proceed
to consider the region about an arbi-
trary point a of the circle \y\ < h not
lying in any of the regions just cut
out. Let
#2 = y — «
and let <J>.2 then be written in the form
$2 (*2, y, *2) = *2 (*2> Vi, *2) =
<A>02)*2mi + q~i{ydx™l~l z* + + qMj (y-i)z,n\ -f F2(x2, y,, z2)
= [*."•« + nbtixt-i-1* + + rmJy2)l.2'"qF(y2)+F2(x2,y2,z2)
= 0. (6)
3. Apply to the function <I>2 the quadratic transformation
X2 =^ x$ z2.
* Here, for the first time, a quadratic transformation of the type that trans-
forms but a single variable is employed. Such transformations do not occur in
Ivobb's analysis. They appear to be indispensable.
BLACK. — THE NEIGHBORHOOD OF A SINGULAR POINT. 307
Let the result be written as follows : —
<£2(x2, y2, 22) = z2'"x<P8(x3, y2, z2) =
z2mi{[x3">l + rl(i/2)xzmi-1 + + rm{y2)]E(y2) + z2F&(xz,y2,z2)} =0.(k)
From this last equation we deduce the following theorem : —
All points of the surface <!> = 0 in the neighborhood of the curve
<f>(x,y) = 0, 2i = 0,
are mapped upon a finite number of new neighborhoods which are
1) neighborhoods of singular points of degree < m, which neighbor-
hoods may be taken arbitrarily small ;
2) neighborhoods of new multiple curves on surfaces constituted like
the surface <I> (a:, y, z) = 0 of the lemma, the values of in thus arising
never exceeding the original m of the lemma.
By the same kind of reasoning as in § 1, 5, we show namely that for
any one of the above values of a, the corresponding value of y2 being
in or on the circle of convergence of the Taylor's development about
the point z2 = 0 of the function
rx(V2)> A=l, 2,
r/h
i\y2j> k — i, ±, /«!,
all points of the surface <£2 = 0 in the neighborhood of the curve
<f>(x,y) = 0, sz = 0,
are represented by points in the neighborhoods of points of the curve
*3m' + rx (yjx^-1 + + r,% (y2) = 0 , z2 = 0,
on the surface 4>3 = 0, i. e. if such a value of y is b, so that the corre-
sponding value of y» is (b — a), and if the roots of the equation
a^K + n (b - a) x3m~l + + rmi (b - a) = 0 (p)
are ux, a2, a,„ then points of the surface 4>2 — 0 for which
|*«| < 8, K| < 8, y — b,
are connected with the points of the surface (k) by the relation
x2 = z, (xo + av) , y, — b — a, a = 1, 2, mx.
Further, if we limit y.2 to a circle not reaching out to the nearest point
for which qo(y2) vanishes, we have an upper limit for a„ as a root of
the equation (u), and thus by taking z2 and xa small enough we can make
x2 as small as we please. Then the transformations (8) and (£) still
308 PROCEEDINGS OF THE AMERICAN ACADEMY.
secure a limit for the values of x and 2, and thus we have represented
a neighborhood of the curve
<f>(x, 20 = 0, « = 0,
on the surface
$ (a:, y, z) = 0
as required.
Now, however small the neighborhood we shut off about the points
in the region \y\ < h for which q0(y) vanishes, since the results estab-
lished above would hold also in a circle of radius hx > h, but still less
than the radius of convergence of the series for p (y) in (/3), we can fill
up the remainder of the circle of radius h with circles within which
g0 (y) does not vanish, these circles overlapping at all points the bounda-
ries of the excepted neighborhoods and not reaching up to the excepted
points. Within each of these circles we have a development of type
(k). Consider one of these new circles. We want to consider the
neighborhood of the curve
& (*» ft) = *3mi + rx (y2) xzm -1 + + rmi(y2) = 0. (v)
If this is a multiple curve of the mx-th. order and mx < m, we have
reduction. Moreover, if mx = m, but
«."» + rx(y2)xzm^ + + n„,(y2) 4= [>a + />3(y2)]"\,
we also have reduction. We need consider, therefore, only the case
that
*3m' + rx (j^W^1 + + rmi(ya) = [x, + PsCya)]"1!, > , ,.
mx = m, >
and show that this case can repeat itself at most but a finite number of
times.
4. Suppose the function <£3(x3, y2) has the form (v'). Apply to the
surface <J>3 (xs, y2, z2) = 0, (k), the transformation
xs + p3(yz) = xi>
and reduce the result to the form
^O^ y» z*) = x^Efa) + 22-^4(^4) yt, 22) = (0). (o)
If any term in z2Fi(xi, y2, z2) is of degree in xi and z2 together less
than mu it appears at once that we have a line of lower order. So we
assume there are no such terms. Also, as the coefficient of a;4mi does
not vanish identically in y2 (in fact, not at all) no transformation of
BLACK. — THE NEIGHBORHOOD OF A SINGULAR POINT. 809
type (£) is needed, and after collecting all terms of the mrth order we
make at once the substitution
and proceed in the same manner as before if the degree is not reduced.
For convenience, we suppose the succession of multiple curves of the
same order to begin with that on the surface 4> = 0, and use a nota-
tion independent of that hitherto employed.
Our successive transformations are of the type
x —pi (y) = *i
(»■)
xv-x-pv(y) = x
whence
x - px (y) +p*(y)z + pz(y)z'x+ + pv(y)zv~1 + x/. Q>)
Develop the function <J> in (y) by Weierstrass's Theorem :
<P(x, y, z) = [xm + qx (y, z)xm~1 + + qm(y, z)-]E(x, y, z)
= F(x,y, z)E(x,y,z).
From (p) we derive the relation :
9F _9F9xv __ 1 9F
9x
*l
=
xxzy
X<i
x2z
■
X
V
=
X z
v J
9xv9x
zv9xv
(-)
The succession of transformations (jr) so long as it does not reduce the
degree in x and z, takes out of the F factor at each step the factor zv,
since, on account of the constant term in the E factor, no power of z
could come out of it. So, after the v transformations (ir), we have
F(x,y,z) = zVmF(xv,y,z) =
*"'"[<" + q»(2f, z)K"-1 + + 9mvbt, *)]. to
and by (o-)
9F , 9F„
Qx 9xv
Now we may consider i^as having no multiple factors vanishing at the
point (0, 0, 0). So we have the relation
L(x,y, z)F+ M(x,y, *)^= Rfa z)=z*Rl(y, z) (?)
310 PROCEEDINGS OF THE AMERICAN ACADEMY.
where
fi(y,z)±0, -fiifo, 0)£0.
9F
Substitute in equation (y) for x from (p), using for F and 7=— their
values as derived above, and we have
9F
z™ Lv (xv, y, z) Fv + z«™-"Mv (xv, y, z) ^— = z* R1 (y, z).
dx„
The left side of this equation is divisible by zvim~1} and so the right side
must be also.
v(m — 1) ^ A,
and we have an upper limit for v, the number of transformations which
leave the order of the multiple line unchanged.
The securing of the regions of class 2) in 1, follows from the reduc-
tion just proved. If for all multiple curves of order n or less the lemma
is assumed to hold, this reduction establishes it for all curves of order
n + 1, since by it the neighborhoods are represented by those of lower
order. But we know it to be true for curves of the first order, and so
by mathematical induction we establish it for curves of all orders.
5. Hie neighborhoods of singular points in 3, if they are of the m-th
order can be taken along the curve
<f>(x,y) = 0, z = 0,
on the surface
®(x,y, z) = 0.
In fact, the first lot of points excepted, those for which in equation
(77) q0 (y) vanishes, are along the line
x2 = 0 , 22 = 0 ,
which is connected with the original curve by the one-to-one transfor-
mations (8) and (0- Also so long as the multiple curve does not break
up into simpler curves, the neighborhoods correspond, and when this
reduction takes place we can cut out the neighborhoods of the points
common to all of the resulting curves uy cutting out neighborhoods
along the original curve for the same values of y.
C. — The Reduction of the Original Singularity.
The transformations hitherto considered, when applied to the original
surface 3> (f, rj, £) = 0, make it possible to map the neighborhood of
the point (0, 0, 0) of that surface on a finite number of regions which
are of two classes : —
BLACK. THE NEIGHBORHOOD OP A SINGULAR POINT. 311
1) neighborhoods of singular points of transformed surfaces ;
2) regular pieces of transformed surfaces.
The pieces of class 2) lead at once to representation by means of para-
metric formulae of type (A). The singular points of class 1) are all
of lower order than the original singularity except in one case, and it
is this case that it remains to consider in §§ 3, 4. The case can pre-
sent itself at the outset only if the polynomial (£, rj, Qm is the product
of m linear factors in £, rj, £, all vanishing for a single set of values of
the arguments $, rj, £ not all zero. Geometrically, the tangent cone,
($, rj, £)„, = 0, of the surface <J> (£, rj, £) = 0 at the point (0, 0, 0) con-
sists of m planes having a common line of intersection. It is found
necessary to distinguish two sub-cases according to whether the planes
themselves are not all coincident, or are all coincident.
To sum up, then, we already have reduction in all cases except when
we are led to singular points in class 1) of the particular type just
described.
§3.
A. — The Singular Points of Special Ttpe.
1. In the special case in which the function (£, rj, £)m is composed of m
linear factors, each vanishing for all points on a common line, it is possi-
ble to reduce the singularity by means of a finite succession of quadratic
transformations together with certain additional transformations.
We consider two cases : —
Case A. — The m linear factors of (|, rj, £)m are not all equal.
Case B. — The m linear factors of (£, rj, £)m are all equal.
2. Case A. — (£, rj, £)m is composed of m linear factors not all equal.
The surface can be expressed in the form
*(6 rj, 0 = (ft rj)m + (ft rj, Qm+1 + = 0 (13)
where (£, 77),,, contains terms in both $"1 and r/"1.
If the surface were in a form
f(u, v, w) — (u, v, io)m -I- (u, v, w)m+1 + = 0
with the condition that the m linear factors of {u, v, w)m all vanish for
the line
u = aw, v = (iw,
we could make the transformation
^ — u — aW, rj — V — /?«>, £ = W,
312
PROCEEDINGS OP THE AMERICAN ACADEMY.
and all the resulting linear factors would have to vanish when
£ = 0, 77 = 0,
and so not contain £.
Also by a linear homogeneous transformation in £ and rj we can se-
cure the presence of terms in £"* and rf1, and in such case every linear
factor of <£ (f, rj), which here is (£, rj)m itself, will contain $ and thus
secure condition 3) of § 1, 3.
B. — Quadratic Transformations.
3. The succession of surfaces and corresponding quadratic transfor-
mations which are applied to the new singular points as found, so long
as they do not reduce the degree, can be written in the form
^ (14)
Apply to the surface (13) the transformation
f = £i£i 7 = 7i£>
and we have
*(£, r;, o = r"[(^ >?om + £&, ti, i)m+i + ]
= r[&, 7i)»K«A(^,7i» 0] as)
= r*i(ii,7i, 0-
As we assume the transformation does not reduce the degree of the
singular point, there can be no term of degree less than m in the part
^(iu 7u £) and as all terms of this contain £, when we put the expres-
sion in the form
*, Hi, VI, 0 = (*1. 7l, Om + (*„ 71, 0-+1 + (16)
we will secure reduction by another quadratic transformation unless
($v 7i» Om is tne product of w linear factors with a common line of
intersection. In this case the factors cannot be all equal," for then
(£i> Vi> 0)m would have its linear factors all equal, but these are the
factors of (£1} rji)m. Also the common point of intersection of the lines
BLACK. — THE NEIGHBORHOOD OP A SINGULAR POINT. 313
in which the plane £ = 1 cuts the planes corresponding to these factors
is at a finite distance. We have now the conditions 2) and 3) of § 1, 3,
and are ready to apply the transformations
giving
*i (&, *, 0 = C" [(& vi, 1). + C(fi. vu i)m+i + ] = 0. (17)
Now if f] = y2, r;x = S2, is the common point for which the m factors of
(li> t)u l)m vanish, then the substitution
& = fi — y2> % = vi ~ ^2>
gives a group of with degree terms in £2 and 770 exactly corresponding to
the terms of (£, rj)m. So in the successive collection of terms of the
wth degree, the terms of (£, rf)m are always carried over with merely
a change of subscript, and thus we never introduce the condition of m
equal linear factors. Accordingly so long as the degree of the singular
point is not reduced, the intermediate transformations are of the type
vh = s ~~ vi-i ' vr ~ \ — <V+i *
thus securing the succession of transformations (14).
4. The succession of transformations in 3 will lead to the relation
e-Z (&, * 0 <*>, + M(U Vv,£) tf-*» 9^ = B(V,£)$0 (18)
where
**(£,, >to 0 = &*(£», Vv, l)E(Jsv, yv, 0-
Combining transformations (14) we have the relations
£ = yi£ + y2£2 + + y,P + P&\
v = s1z + 82f+ + 8vz» + e>Vv]
*(6 v, 0 = C"**(t» n» 0
As <I> contains both £m and rjm terms, we can develop by Weierstrass's
Theorem.
*(*, * 0 = [£" + j»i(* OF''1 + +Pm(v,Q]Ei(e, v, 0
*(6 * 0 = Df + ?i(& 0vm~l + + ?„(*, 0]^(£, v, 0
= * (^ 17, 0 ^2 (6 V, 0- '
As the function i£, (£, 17, £) contains a constant term, when the first trans-
formation of (14yi is made, the factor £"• must come out of the <i>, and a
(20)
314 PROCEEDINGS OF THE AMERICAN ACADEMY.
similar result is true for all of the succeeding transformations. So in the
first part of (14) we could write <l> for <£, ^ for 3>M, (^ = 1, 2, v)
where the <i>'s are derived successively in the same way as the 3>'s. At
each stage the $ factor must contain all the terms of lowest degree in
the corresponding <P (except for a constant multiple), and no lower
terms ; for, otherwise, either there would be lower terms in the product
by the corresponding E factor on account of its constant term, or the
required terms would not be present.
Now, by (19),
5* _5$ 9£y_ J_5<5>
Also
(22)
<i> =
£,mv®v;
and,
combining
with
(21)
, we
have
9®
_ £(m
-l)v
9<5>v
9£v
(23)
But as <f> has no multiple factors vanishing at (0, 0, 0) (see § 1,3), we
have the relation
L($, v, 0* + M& V) 0 || = R(v, 0 + 0. (24)
Then, substituting for £ and 77 from (19) on the left side of equation (24)
and using the relations (22) and (23), we have the required relation (18).
5. If v is taken large enough the transformations (14) will lead to the
relations
A(fe v„ 0** + mv($v, Vv, 0 %r = ?l O* + <»i(QT*fi(v» 0, (25)
PAiv, v» Q*v + Qv&, vv, 0p- = M£ + ^(m^{U 0, (26)
vrjv
where
<M&, v^ 0 = *v(£v, vv, 0^i (&, v^ 0 = **(& vv, 0&(€v, vv, £)■ (27)
We consider the effect of the transformations (14) on R in (18). Ex-
press it in the form
R(v, 0 = n(v, On + (* 0n+i + 3 = ?S(v, 9,
where
S(v, 0) * o.
If (17, £)n contains no term in 77, the first transformation of (14) will al-
low the factor £" to be taken out of S, leaving behind a constant term,
and thus securing the form (25) at once with
BLACK. THE NEIGHBORHOOD OF A SINGULAR POINT. 315
qx =p + n, rt = 0.
Next, suppose (77, £)„ does contain terms in 77, but no term in 77", i. e. we
can express it in the form
where (77, £)„_,._, contains terms in both ^"_r_5 and £"-r-* and s > 0.
Then if any transformation
is applied, there can be divided out of (77, £)n the factor £" leaving behind
as the term of highest degree one in rf*~*. This cannot be cancelled
with any term from another part (77, £)„+i, for any term from this would
have as a factor tf after the £" has been divided out. As long, then, as
the ?7 variable does not enter to the highest degree in the expression
corresponding to (77, £)„ if n > 0, the degree of the S factor is decreased
with each transformation, while the expouent of £ outside may be in-
creased. Accordingly, by a finite number of transformations, we re-
duce the S factor either to an E function or to an expression in which
the 7; variable enters to the highest degree in the collection of terms
of lowest order. In the former case we have the form required. In
the latter case, suppose for convenience that this condition holds for the
function £(77, £). By Weierstrass's Theorem we develop in the form
S(?h 0 = It + niOv"-1 + + rn(0]£(v, 0
= T(v,0E(V)0- . (28)
Consider the n factors of T(rj, £),
2?(^0 = n[, + fx(0]. (29)
A=l
If the factors are not all equal, pair them off, so that in each pair there
will be two different factors, leaving a number of equal factors :
fr! + «ta(0] [*+**«)]} {Lv+sth(.Q]tv+suA(01}bi+s»(Qy- (so)
Now, for each pair,
^=[? + ^(0]D» + **(o:i,
we have the relation
Nk+Pk(V,i:)9~k = Lktt)$0, (31)
at]
since the two. factors are unequal. Then, by the same reasoning as used
316 PROCEEDINGS OF THE AMERICAN ACADEMY.
in 4, the succession of transformations (14) which leaves the degree of
T unchanged will secure for equation (31) a form
The left side of the equation is divisible by £v, and so the right side
must be,
v = ^>
and we have an upper limit for v, the number of transformations which
leave the factor Nk of the second degree, and as a result leave the func-
tion T of the rath degree. So, unless the function T(rj, £) in (28) is
composed of n equal factors of form
bi + s (0?i (32)
the transformation of (14) will finally reduce its degree. Then, by ap-
plying the same reasoning to the resulting function, we see that finally
the function corresponding to S(r], 'Q either becomes an E function or
has besides the E factor a factor of form (32), thus securing the form
(25) if we divide out the factor £<"»-i)»\
The condition (26) is secured by using on the second equation in
(20) the same kind of reasoning as applied in 4 and 5. Then we take
for v the larger of the two values required to secure conditions (25)
and (26).
C. — Further Transformations.
6. A transformation
& = £-<»2(0j (33)
i)v — y]v — oja (£) )
applied to the surface
iu 5 will secure a form in which the singularity will be reduced by
either
1) a further succession of transformations as in 3,
2) the method of the Lemma, § 2.
Let us consider here the case in which either rx or r2 in (25) and (26)
is zero. Then iu one of the equations a further succession of trans-
formations of type (14) will not change the power of £ as a factor on
the right ; and if there are /x such further transformations, the reasoning
BLACK. — THE NEIGHBORHOOD OP A SINGULAR POINT. 317
of 4 shows that the left side becomes divisible by £(m-1)M. So we have
either
(m—l)/x<ql or (m — 1)^ < y2
and thus an upper limit for /x, the number of transformations which
leave the order of the singular point unchanged.
Now, to consider the transformation (33), we see that it is a one-
to-one transformation by which the surface remains analytic near the
origin. (Dx (£) and w2 (0 contain no constant term, for otherwise the
factor
rjv + wj (£) or £, + w2 (£)
could be combined with the E factor. Then the transformation (33)
leaves the E factors still E factors, and the factors vanishing at the
origin still vanishing there. Also, it is easily seen that this transfor-
mation leaves the terms of type (£, rf)m still in the part (£„, tjv, £)m.
Further, if the function «!>„(£„, -qv, £) goes over into X(£v, rjv, £), we have
9®v _9X _9X9lv _9X
9 £ v 9i„ 9 £„ 9£v 9 $v
and similar conditions hold for the partial derivative with reference to
7/v. Accordingly, if by the transformation (33) <&„(£„, Vv, £) goes over
into £2(£„, rjv, £) we replace equations (25), (26), and (27) by
1 v
Lv(iV} £, t)X(l, Vv, 0 + MvQvi yv, 0— - = frvSiEfa 0, (34)
9tv
Pv(l, vv> QBQ„ £,, £) + &<&, Vv, 0-J?= ^~^E($V, 0, (35)
9rjv
Q(|*» Vv> 0 = XQv* Vi"> CAlC?** V"> 0 — &(€vj t]v, O-^aClfj Vv, 0- (36)
Now, in a further succession of transformations of type (14) on the
surface f2 (£„, Vi>> £) — 0, if there enters either a y or a 8 not 0, then on
the right side of equation (34) or (35) the only factor remaining outside
of the E factor is a power of £, and we must finally have a reduction as
shown above. So it is only in the case in which all the y'a and S's of
the later transformations are 0 that we are not already sure of reducing
the singularity. Now if in £2 (f„, r),,, £) there is any term of degree less
than m in £„ and -qv combined, such a succession of transformations must
reduce this term to a degree less than m and thus reduce the singularity.
318 PROCEEDINGS OP THE AMERICAN ACADEMY.
For suppose such a term to be aljrjjt,h, where /+ g < m. Then, by
a succession of p transformations such as defined, we have
L = £,p$v+p, V" = £pyv+pj
(derived from form of (19) when all y's and S's are 0). Substituting
this in the expression above we get
a?v+PV,,+p£
But we must divide out of this £mp, so that we have left the term
n t} J yh+piZ-hg-m)
"^v+pVv+p^
This term could not combine with any other derived in a similar way,
for if we had another term b$* rjg £\ we should get
7 >/ 9 yk+p{f+g—m)
o?v+pvv+P£
and this would not combine with the other unless k = h. Now, if the
degree of the singular point is not reduced, we must have for the sum
of the exponents
f+g + h + p(f+g — nij^rn
or (p + 1) (m — /— g) ^ h,
and as m > f + g
h
+ 1^
»» — /— g
thus securing an upper limit for p, the number of transformations which
leave the term and the singular point of the mth order.
So it is only in the case in which all terms of Q (£„, r/v, Q are °f
degree not less than m in £" and rjv together that we do not have a re-
duction of singularity by the succession of transformations of type (14).
But, in this exceptional case, we have the conditions of the Lemma of
§ 2, where in equation (0) we take
lv = a?a, Vv = z-i, t = y-i,
the singular line being
^ = 0, |„ = 0.
There is in D, (£„, rjv, £) a term in £vm, and so the expression q0 (y2)
does not vanish when y2 = 0. Accordingly, within a neighborhood
about this point, we can break up the singularity by the methods of
BLACK. — THE NEIGHBORHOOD OP A SINGULAR POINT. 319
§ 2. Further, since the expression (f„, rjv),n is not composed of m equal
factors, the part
q0(0)xami + qx{0)x^-lz + + ?«h(0)si"i
from (6) which corresponds to (£„, nv) is not composed of m equal factors,
and the resulting curve in (k)
*3CTl + niy^x^-1 + + rmi(j/2) = 0
has not m equal roots when y2 = 0. So a single transformation of the
kind in § 2, 3, reduces the singularity in the neighborhood considered
here.
7. The neighborhood of the original singular point is mapped upon
a finite number of neighborhoods of simpler points.
At every stage the function (£M, rj^, *£),„ contains the terms of the
type (£, rj)n found iu the original equation (13). So there is but one
singular point of the m-th order in the finite region of the 77^-plane.
Further, the equation (^, 1, Qm = 0 for the value £ = 0 cannot have
m equal roots since (£, v)m is not a perfect m-th. power of a linear factor.
Accordingly, the transformation corresponding to (8) in § 1, 4, cannot
produce a singular point of the m-th order. So, at each step, the
neighborhood of the singular point is represented by a number of regions
as in § 2, C, in which but one of the points of class 1) is of the mth order.
Further, the extra transformations (33) carry the neighborhood of the
singular point over into that of the new point. So, by combining all
the representations, as the singularity is finally reduced, we have the
original neighborhood mapped upon a finite number of regions as in
§ 2, C, in which all points of class 1) are of order lower than m.
§ 4.
A. — The Singular Points of Special Type (continued).
1. Case B. — The m linear factors of (f, rj, £)m are all equal.
The surface can be expressed in the form
*(& v, 0 = [F + Pn(a, Of-2 + + Pm(r,, 0] #(6 v, 0
= X(£,v,0£&vU) = 0, (37)
where, in X, $'" is the only term of degree m.
If it were iu the form
f(u, v, w) = (ail + (3v + yw)m + (it, v, w)m+1 + = 0,
as one of the three numbers, a, (3, y, is not zero, suppose a = 0.
320 PROCEEDINGS OF THE AMERICAN ACADEMY.
Then by a linear homogeneous transformation
u = au + (3v + yW
v = v
w = w
we secure the form
f(u, v, w) =f(u, v, w)
— um + («, v, w)m+l +
By Weierstrass's Theorem we can express this in the form
f{u, v, w) = \um + p, (v, w) u"1-1 + + pm (v. w)-] E{u, v, w). (38)
Now, in the exjjression
pK(v, w), A = 1, 2, m
there is no term of degree less than A + 1, for otherwise on account of
the constant term in the i£ factor, there would have to be present in^a
term of degree < m containing v or w.
Make in (38) the transformation
u + r* Pi (v w)
v
w
As pi (v, w) contains no term of degree less than 2, by the considera-
tion above, f goes over into form (37).
B. The Quadratic Transformation.
2. The transformation
£ = i£> v — v&
applied to <E> (£, 77, £) secures the form
*(*, v, 0 = *"•*(£ v, 0 = £*[?" + £*(!, v, 01 (39)
Here the curve <f> Q, ij) = 0 becomes |m = 0, and so, applying the
Lemma of § 2 to a circle in the y^-plane however large, we have within
it but a finite number of singular points to treat further. But one such
circle is needed, for by taking it large enough we can deal with all of
the ^-plane outside of that circle by the transformation
So we need to consider for further treatment only a finite number of
points along the line $ = 0, and the point at infinity.
BLACK. THE NEIGHBORHOOD OF A SINGULAR POINT. 321
3. The quadratic transformations to be used are of two types
1) £p =s &+1&4 Vn = Ofo+1 + VrO &u (40)
2) in — in+iVnt Cm = (&+1 + ef.+i)Vn' (41)
In a succession of transformations of type (14) we see that yx = 0,
since the first set of points is taken on the line |" = 0. Further, sup-
pose after the substitution q — 8X = ^ in <I> of (39) the expression
(!, 171 Qm
contains terms besides the £m ; then it cannot be composed of m equal
linear factors, for that would require a term containing fm_1 ; but no
such term can arise from the factor X of (37), and, on the other hand,
it could not be the product of a term from X by a non-constant term of
the E factor, for then, on account of the constant term of the E factor,
there would have to be present in <f> a term of degree lower than m. So
as soon as the function corresponding to <f> of 4> contains more than the
mih power of the £ variable, the function corresponding to (£, 77, £)„, iS
no longer the product of m equal linear factors, and we have one of the
cases treated earlier.
The same considerations apply to the transformations corresponding to
type 2), since, when the transformation which deals with the infinite
region is introduced, the first one of that order is of form
Accordingly, the most general succession of transformations here is
one in which groups of types 1) and 2) alternate. We shall call them
the £ and q types respectively, and when a change is made from one type
to the other, we shall speak of it as a reversal of type.
We shall treat the subject in two cases, first supposing that there is
no reversal of type in the succession of transformations used, and later
supposing that reversals of type occur.
C. — Succession op Quadratic Transformations in avhich
THERE IS NO REVERSAL OF TYPE.
4. After a sufficient number of quadratic transformations the surface
can be reduced to the form
-,v + • • • + vv
VOL. XXXVII. 21
[(C + ~<2&E(n»> 0 C"2 +■■•■• + % ?vE(ji*, i)] m» i, 0> (42)
322 PROCEEDINGS OF THE AMERICAN ACADEMY.
while all later transformations can be taken of the type
£M = £y+lL rjy. = Vn+iC (43)
After v transformations of type (40), since there can be no interchange
of terms among the coefficients of the different powers of the £ variables
in the X factor of (37), the surface will take the form
[C + v» (v* 0 C2 + + P™ (Vv, 0] * (&, to 0 = 0. (44)
Now by the same reasoning as used for the function R in § 3, 5, if v is
taken large enough, the coefficients of the powers of £„ in Xv will all be
of the type
s = 2, 3, m.
For any one of the functions
there is a determinate succession of transformations of type
Vy = £(Vn+l + <V+i)
which will leave it of the same degree after the £ is divided out, all
others reducing the degree at once , i. e., if
Vy + v (£) = Vy + <*i £ + tt2 £2 + ,
we must take
Vy = UVy+1 — "i)»
rjy+1 = £(Vy+2 — a2),
etc.
So, unless the factors
V" + v, (Oj s = 2, 3, m
are all equal, we must have finally some coefficient of a power of £„ with
the rjv present only in the E factor, and by taking y large enough we
come to a point where all the factors
V' + v*(0> S = 2, 3, m,
are equal, some of them possibly having zero exponents.
Then we use the transformation
np + v.OO^n, (45)
BLACK. — THE NEIGHBORHOOD OF A SINGULAR POINT. 323
and arrive at the form (42) required. Now any further transformation
of type (40) in which the 8 is not zero will leave the -q variable present
only in the E factors, so that the general term (after the first) of the
function Xv is of type
pUfayQC-, s = 2,3, m.
Suppose, after this, there are p transformations of type (40). Then the
corresponding term after the factor £mp has been divided out is
9%+{ m—s)p—mp jg, on. gm— s
and if this is of degree not less than m, as it must be if we are not to
secure reduction, we have
m — s -f <7s — Ps = m
or p < — »
~ s
thus securing an upper limit for the number of transformations of type
(40) which do not give reduction of singularity. Accordingly, after the
form (42) is reached, it is only when all later S's are zero that we are
not sure of reduction.*
5. A sufficient number of transformations of type (43) applied to (42)
secures either
1) reduction of singularity, or
2) the condition that for some term (the rth) of the X factor
> s = 2, 3, m.
r ~~~ s )
If, for any term
a transformation of type (43), after the factor £'" has been divided out,
yields
„Pr yQr+Pr—r jfi / y\ j.m-r
decreasing the exponent of I by r — pr. This decrease takes place at
every such transformation, and thus the exponent of £ must finally be
* We do not need to consider the possibility of having all the coefficients of the
powers of £„ lower than the m-th vanish, for then the function Xv would have
m equal factors £„ and this case has been excluded.
324 PROCEEDINGS OF THE AMERICAN ACADEMY.
reduced to a value q'r less than r — pr, in which case the sum of the
exponents of the three variables,
pr + q'r + m — r,
is less than m and reduction ensues. So it is only in the case in which
for every term
ps> s, s = 2, 3, m,
that we are not sure of reduction. Suppose the number of transforma-
tions after this point to be n. Then we get for the new exponent of £
9s + n(Ps~ *)•
Now by taking n large enough we can make the quotient
n (P* - *) + 9s
7) ™— S
have the lowest value for the term in which — is lowest, while if
s
this is the same for two or more terms, we can make the fraction above
lowest for the one in which — is lowest. Accordingly, by a finite
number of transformations of type (43) we secure the condition that
V — T V . Q
— and so — is lowest in the same term in which — is lowest.
r r
6. A succession of transformations of type
& = |M+i£, (46)
followed by a succession of type
£1 = ^+117, (47)
secures the surface with condition 5, 2) in the form
J. (48)
where for some particular term in Xp, the rth,
Pr <r, qr<r. j
Consider the surface (42) with the condition 5, 2), the sth term being
and suppose we apply to the surface n transformations of type (46),
dividing out each time the factor £"'. The resulting term is
BLACK. — THE NEIGHBORHOOD OF A SINGULAR POINT. 325
If n is taken large enough, the exponent
is made less than s, so that we have
s > qs — ns > 0,
or Si— I <n<Sl.
s s
So the term for which — is least is among those first reached in which
s °
the new exponent of £ is lower than s.
In the same way we show that, by applying a succession of transfor-
V
mations of type (47), the term for which — is least is among the first
s
lot reached for which the new exponent of -q is less than s. But, by
condition 2) in 5, — and — were least in the same term. So we secure
' s s
the surface in form (48).
7. A further succession of quadratic transformations of type (43) as
applied to the surface in form (48) will reduce the singularity. This
follows at once by the reasoning in the first part of 5.
D. — Succession of Quadratic Transformations in which
THERE ARE REVERSALS OF TYPE.
8. A succession of transformations in which there is a sufficient num-
ber of reversals of type will secure a surface of type (42).
If there is but a finite number of reversals, after the last one we are in
the same positiou as at the start in 4, and the succession of trans-
formations which follows, not having any reversal of type, will enable us
to secure the condition derived by the method of 4. So we need here to
consider only the possibility of an indefinitely large number of reversals
of type.
In equation (37) consider any one of the coefficients
pr(V,0 = ?Pr(v,Q = tl(v,0nr + (v,Onr+l + ]
where pr(v-> °) ^ °-
A transformation of type (40) will give for pr a function from which we
326 PROCEEDINGS OF THE AMERICAN ACADEMY.
take out the factor C, the other factor being of degree less than nr unless
the part (7/, £)nr has nr equal linear factors. For, if
nr
(V> t)nr — n (aprj — jB pt)
pr=l
and not all the linear factors are equal (or linearly dependent), then the
substitution
V = C(vi + Si)
gives
fir
C II (apr/x + dp^ — /3p)
P = l
and leaves an absolute term in any factor for which
apSj 4= /3P,
thus securing in the product of the factors terms of degree less than nr.
Also the degree might be lowered on account of terms in some later part
as (77, £,)nr+k- But, if all the factors of (7/, £)«,. are equal (or linearly
dependent) and 8j is taken so as to satisfy the condition
aP^i = fip, p = 1» 2, «r,
then after the factor C is divided out, we have left but one term in rj1nr,
which cannot cancel with any term from another part of the function, as
all later terms have as a factor some power of £. Accordingly a suc-
cession of transformations of type (40), if it does not reduce the degree of
the part not divisible by £, must leave a term in rj Br, Now when the
reversal of type is first made, the e of (41) is zero, as is seen by con-
sidering the use of transformation (8) § 1, 5. Then we take out a
factor 7/ "'' and leave a constant term. So a succession of transformations
which contains reversals of type must reduce the degree of the function
pr (possibly to zero), except for factors taken out which are powers of
the r/ and £ variables. Accordingly, by a succession of transformations
containing a sufficiently large number of reversals of type, the coefficient
pr must be reduced to the type
9. All further transformations to be considered may be taken of the
types
in = t».+\yi, £m = C+1^7- (50)
BLACK. — THE NEIGHBORHOOD OF A SINGULAR POINT. 327
For if a transformation of type (40) or (41) in which the 8 or c is not
zero were used, we should have in all the coefficients of Xv in (42), out-
side of the E factor, only powers of one variable. Suppose it to be £ ;
then, by means of a succession of transformations of type (46), we can
reduce some term to a form in which the exponent of £ is less than r,
and thus secure a reduction of singularity.
10. A sufficiently long succession of transformations of types (49) and
(50), applied to surface of type (42), unless it first secures reduction
of singularity, will secure the condition that, for some term (the rth),
s = 2, 3, m.
<M
r s J
Consider the two terms
f&sh o r~s, vpt tqtE{-n, o r~*
Any transformation of type (49) leaves the pa and pt unchanged, and
increases the
qs by ps — s,
9t " Pt — t.
Any transformation of type (50) leaves the q„ and qt unchanged, but
increases the
p, by qs ~ s,
Pt " qt - 1.
Represent
q,. — r
r = 2, 3, m, (51)
So, for each transformation of type (49) the Kr is increased by the Ilr,
and for each transformation of type (50) the IIr is increased by the K,..
We shall show that finally we must have one of two conditions
«) ns > 17„ K, > Kt,
b) Us<Ut, Ks < Kt.
Suppose, at any stage, neither of these conditions holds, and we have,
for example,
ns > n„ K, < Kt. (52)
328 PROCEEDINGS OF THE AMERICAN ACADEMY.
Then, for a transformation of type (49), supposing the new K's to be
K,', K/, we have
K,' = K, + ITS,
K/ = K, + IT,,
and so
K/ — K/ = K, — Ks - (n, — nf) < K( - Ks.
Also, for a transformation of type (50), if the new El's are Uj IT/, we
have
UJ = n. + K„
uj = Ut + K„
and
IV - uj = us-ut- (k, - k.) < n3 - n,.
So when a condition of type (52) holds, any transformation applied will
reduce the difference of either the ITs or K's, if in fact it does not
change the sign of the difference. Further, the reduction is each time
by a value not infinitesimal, for it is at least 1 j st, as is seen by con-
sidering the values of Kr and IT,, in (51). So the succession of trans-
formations of whatever kind must finally reduce the difference of either
the II's or the K's to zero, or change its sign, and then we secure either
condition a) or b).
When one of these conditions has once been secured, any further
transformation will not change it; for, in condition a), a transformation
of type (49) will add at least as much to the Ks as to the K„ and so
retain the inequality of the same order, and similar conditions are seen
to hold in the other cases. Also, as one of the conditions «) or b) must
hold finally, whatever the pair of values s and t, we shall have some
value as r such that
n,. < ITS, K, < K„ s = 2, 3, m.
from which follows the required condition
Pr KPs
r ~~ z s
9r<91
2, 3 m.
11. The method of 6, applied to the surface resulting from the treat-
ment of 10, will secure the result of 6. It may be that already either
pr < r or qT < r, but in such a case the number of transformations of
BLACK. — THE NEIGHBORHOOD OP A SINGULAR POINT. 829
type (46) or (47) can be considered zero, while in the other case we
have exactly the initial conditions of 6, the result of which then can be
secured in any case whatever.
12. In tlie case of surface (48) any succession of transformations of
types (40) and (50) will finally reduce the degree of the singular point.
Consider the term
Any transformation of type (40) adds to the exponent of £, pr — r, and
as pr < r, the exponent of £ is reduced. In the same way we see that
any transformation of type (50) reduces the exponent of the 77 variable.
So in any case, by virtue of the reduction of degree, we must have finally
either
Pr <r — qr or qr < r — pr,
in either of which cases the sum of the exponents of the three variables
(m — r) + pr + qr
is less than m, and we have reduction of the singularity.
§ 5.
Parametric Representation of the Neighborhood of the
Original Singular Point.
We have shown that in all cases T, the neighborhood of a singular
point, can be mapped upon a fiuite number of regions tu t.2, tv as
defined in § 2, C. Apply a properly chosen transformation to each point
of class 1) and repeat the operation on each set of resulting points of the
same class as they are formed. We have proved also that after a finite
number of operations all the resulting points of class 1) are of order
lower than m. Then, by continuing the process, it follows that, after a
finite number of transformations, all points of class 1) must disappear,
and so we shall have left only regions of class 2). Each of these regions
admits of representation by means of a finite number of sets of para-
metric formulae of tj'pe (A).
Classify all the singular points which present themselves in groups as
follows : —
In the first group, place the original point; in the second, all singular
points derived from it by the first quadratic transformation, together witli
whatever auxiliary transformations accompany it ; these points corre-
spond to the singular points of the curves that represent the irreducible
330 PROCEEDINGS OF THE AMERICAN ACADEMY.
factors of <j> (£, rj), to the points of intersection of two such curves, and
to the points of class 1) in § 2, 1. In the third group place all singular
points derived in a similar way from those of the second group, etc.
Suppose n to be the number of the last group in which there are
singular points. From what we have proved, n must be finite.
The neighborhood of a point in the wth group is represented by the
neighborhoods of a finite number of regular points, together with a finite
number of regular regions, and so by a finite number of parametric
formulae of type (.4). The neighborhood of a point in the (ra — l)st
group is represented by the neighborhoods of a finite number of points of
the ?ith group, together with a finite number of regular regions, however
small the neighborhoods of the singular points are taken ; but as the
neighborhood of any point in the wth group is represented by a finite
number of parametric formulae of type (A), the same follows for any
point of the (n — l)st group, using the intermediate transformation to
get the parametric formulae.
This reasoning can be carried on until the original singular point is
reached, since the mapping of the neighborhood of the original point
upon a finite number of regions of classes 1) and 2) applies to each of the
later singular points also, and then furnishes the step by which we know
that we can always pass from the (y + l)st to the vth group.
Thus we have the coordinates £, rj, £ of the surface
expressed in parametric formulae of the desired type, the parameters
being in general coordinates of points of some simple surface. Then by
using the intermediate transformations connecting x, y, z with $, rj, £, we
represent the first set of coordinates in the desired form.
Proceedings of the American Academy of Arts and Sciences.
Vol. XXXVII. No. 12. — December, 1901.
CONTRIBUTIONS FROM THE CRYPTOGAMIC LABORATORY OF
HARVARD UNIVERSITY. — XLVIII.
A PRELIMINARY ENUMERATION OF THE
SOROPHOREJE.
By Edgar W. Olive.
♦
CONTRIBUTIONS FROM THE CRYPTOGAMIC LABORATORY OF
HARVARD UNIVERSITY. — XLVIII.
A PRELIMINARY ENUMERATION OF THE
SOROPHOREiE.
By Edgar W. Olive.
Presented by Roland Thaxter. Received November 9, 1901.
Owing to unavoidable delay iu the publication of a monograph of the
Acrasieae and their allies which the writer has in preparation and for
which figures have already been drawn, the following preliminary
synopsis, which includes all the known forms and which will be sup-
plemented as soon as possible by the more extended paper, has seemed
advisable. This investigation was undertaken some years since at the
suggestion of Professor Thaxter, and a majority of those species that I
have myself studied have been kept under observation in pure cultures
for a long period, so that the constancy of the characters distinguishing
them has been definitely determined. As far as I am aware only one
member of the group has been heretofore reported from America,
although certain of them are very abundant in laboratory cultures. Of
the European representatives several remain unknown except through
the original diagnoses, which are unfortunately, in a majority of cases,
meagre and unaccompanied by figures.
A comparison of the conditions presented by the individuals which
constitute the so-called fructifications of these organisms indicates that
the term spore cannot be properly applied to them in all cases. In the
genera Sappinia and Guttulinopsis the individuals, even in mature
fructifications, are merely slightly contracted and hardened, secreting no
definite wall. At germination such resting individuals, therefore, gradu-
ally assume the form of a vegetative amoeba without casting off a spore
wall of any kind. In order to distinguish these bodies from true spores,
such as occur in a majority of the genera, as well as from the transi-
tory resting conditions of isolated vegetating amoeba? which were first
characterized as " microcysts " by Cienkowsky, the term pseudospore is
334 PROCEEDINGS OF THE AMERICAN ACADEMY.
here employed, since it expresses with sufficient exactness the actual
conditions.
It will be noted further that in characterizing the Acrasieae as a
whole, emphasis has been laid on the fact, usually overlooked in accounts
of these organisms, that the vegetative stage ends before the pseudo-
plasmodium condition begins. The latter, therefore, is a phenomenon con-
nected not with vegetation but with fructification, and is by no means
homologous with the plasmodium of true Myxomycetes; nor is it com-
parable to the vegetative net-plasmodium of the Labyrinthuleae.
I have followed Zopf, moreover, in characterizing as a " net-plasmo-
dium " the peculiar form of association occurring in the Labyrinthuleoe,
although it appears to be doubtful whether, in all cases at least, the con-
dition thus distinguished represents a true fusion, or whether the relation
is merely one of contact.
SOROPHOREtE Zopf.
Amcebas of the usual irregular myxamceba form or more or less reg-
ular and spindle-shaped, never possessing a swarm spore stage, forming
either a pseudoplasmodium or a net-plasmodium ; resting bodies borne
in sessile or stalked sori, which are either naked or imbedded in a
gelatinous matrix.
ACRASIEiE Van Tieghem.
Saprophytic, usually coprophilous, organisms, having two definitely
recurring stages, — a vegetative period, in which independent myxamoebaa
crawl about by means of amoeboid movements and undergo multiplication
by division ; and a fructifying period, in which the myxainccbse typically
aggregate into colonies called pseudoplasmodia and form either spores
or pseudospores, held together by a mucus substance, and borne in
stalked or sessile naked masses, or sori.
SAPPINIACE^E.
Myxamcebas comparatively large, with lobose pseudopodia. The
resting sta^e consisting either of a single encysted individual or of
many individuals encysted in masses at the ends of projections of the
substratum.
This group is included here only provisionally, since the amoeba?
normally become encysted singly, thus forming microcysts, and do not
show the characteristic phenomenon of aggregation, or colony formation.
The aggregations which, it is true, often occur at the distal ends of
OLIVE. — PRELIMINARY ENUMERATION OP THE SOROPHORE.E. 335
small projections above the surface of the substratum, are not due to
any chemotactic stimulus such as must be assumed to cause the formation
of true pseudoplasmodia, but, although they may perhaps suggest the
possible beginnings of such conditions, are probably accidental, resulting
rather from a tendency of the arnoebaj to seek drier situations at the
period of fructification.
SAPPINIA Dangeard (1896).
Characters of the order.
Sappinia pedata Dangeard.
Le Botaniste, 5 Ser. p. 1-20. 5 Figs in text. 1896.
Amoeba? forming resting conditions of three kinds : " amibes pedicel-
Ices," in which they are transformed into a pear-shaped body without
definite wall raised above the substratum by a stalk of about equal
length ; " hjstes pedicelles" in which they are similarly modified but
which form a definite wall about the oval body; and '' spores," in which
groups of individuals become encysted at the ends of projections from
the substratum.
On dung of horse, cow, dog. France ; Russia; Massachusetts ; Indiana.
At least two species of this genus appear to be common on various
kinds of dung in this country, but owing to the fact that Dangeard gives
no measurements I have been uncertain which of them should be referred
to S. pedata. In both forms resting bodies comparable to the aggregated
"spores" occur, as well as u amibes pedicellees" although I have not as
yet observed the definitely walled "kystes" which Dangeard appears to
distinguish from them.
The larger and more frequent of the American species, which I have
assumed to beloDg to S. pedata, has the following measurements : stalk
of the "amibes pedicellces" 30^-125^, head 30^-60^ long; rounded
individuals (" spores ") of the aggregations 20^-50^ in diameter.
GUTTULINACEvE Zopf.
Myxamoebse either limax-shaped, without pseudopodia, or of the
ordinary form with rounded or lobose short pseudopodia. The sori,
irregular in shape or spherical, sessile or stalked, consisting of either
spores or pseudospores.
GUTTULINOPSIS nov. gen.
Myxamceba3 having lobose pseudopodia. Sori sessile or stalked, com-
posed of pseudospores, those of the stalk usually slightly elongated.
336 PROCEEDINGS OP THE AMERICAN ACADEMY.
Guttulinopsis vulgaris nov. sp.
Sori usually stalked, sometimes sessile, about 150^-500/* in height
X 150//.-4.CKV broad. Fructifications varying in color from whitish to
dirty yellowish according to the character of the substratum and the dry-
ness of the sorus. Pseudospores usually irregularly spherical, about 4/z-
8p in diameter.
On dung of horse, cow, pig, mouse, etc. Cambridge, Mass ; Alabama j
Indiana ; Maine ; Porto Rico.
This form, which has conspicuous fructifications so large that they
may be readily seen with the naked eye, lias been met with very fre-
quently on fresh cultures of various kinds of dung. Although Guttulina
aurea Van Tieghem may prove to be identical with the ahove species,
the fact that, according to the original description, it possesses resting
bodies which are characterized as " spores," having a golden yellow color,
renders it improbable that the two forms are the same.
Guttulinopsis stipitata nov. sp.
Sori yellowish white, long stalked, the stalk composed of individuals
similar to those of the head. Sorus about 1 mm. -1.2 mm. high; the
stalk about 800/a long, the head 250/* in diameter. Pseudospores spher-
ical, 3^-5^ in diameter.
On dung of dog. New Haven, Conn.
This species, the largest representative of the genus, has been met
with but once, and is founded on a mounted specimen and dried material
collected at New Haven some years ago by Dr. Thaxter.
Guttulinopsis clavata nov. sp.
Sori yellowish white when young, comparatively long-stalked, the stalk
composed of a column of slightly elongated individuals surrounded by
mucus. The stalk-cells held within the peripheral mucus adhere together
after the deliquescence of the pseudospores of the head, forming at the
apex a rounded or conical columella of elongated adherent cells. Sorus
about 400iu-800iu in height, the stalk about 170^-250//. long, the head
I00(u-400iu in diameter. Pseudospores of the head somewhat broadly
oval, 3//.-4/A X 6// - 7/a, or spherical, then 4^-5//. in diameter ; those of
the stalk about 3fi-Ofi X 7/j-10ix.
On dung of dog. Cambridge, Mass. ; Indiana.
This distinct species is frequently met with in fresh cultures of the
dung on which it has its habitat. The base of the stalk is often imbedded
OLIVE. — PKELIMINARY ENUMERATION OP THE SOROPHORE^E. 337
in an abundant mucus, which is especially noticeable when it swells after
being placed in water.
GUTTULINA Cienkowsky (1873).
Myxamcebre limax-shaped, without pseudopodia. Sori irregular in
shape or spherical, sessile or stalked, composed of spores which have a
definite protective cell-wall. The cells of the stalked forms somewhat
differentiated in shape.
Guttulina rosea Cienkowsky.
Trans. 4th Session of Russ. Nat. at Kazan, 1873.
' ' Sori short-stalked and rose-colored ; head IQQfx long, supported upon
a stalk of about equal length. Spores of the head spherical ; those of
the stalk closely laid and wedge-shaped."
On dead wood. Russia.
Known only from the original description above quoted.
Guttulina protea Fayod.
(Copromyxa protea Zopf.)
Bot. Zeit., 11, p. 167-177. 1 Plate. 1883.
Sori l-3mm. high, sessile or short-stalked, of somewhat irregular form,
yellowish white, with crystalline lustre. Spores 9/aX14u; hyaline,
colorless or slightly yellowish, more or less oblong or oval, bean-shaped,
or almost triangular in outline.
On dung of horse and cow. Germany.
This form, which is known only from Fayod's original description, is
retained under its original name, notwithstanding the fact that it has
been separated by Zopf under the name Copromyxa on the ground that
the " myxamcebae undergo no differentiation into stalk and head cells,
whereas in Cienkowsky's form, there is a slight differentiation." The
fact that certain species of Guttulinopsis show both stalked and sessile
forms in the same culture diminishes the importance of the stalk as a
character of generic value and justifies the resumption of the original
name given by Fayod.
Guttulina aurea Van Tieghem.
Bull, de la Soc. Bot. de France, XXVII. p. 317. 1880.
" Guttulina aurea has its fruit pedicelled and resembles closely G.
rosea, but differs in color. The spores spherical, Ap.-6fA, golden-yellow.
Upon dung of horse." France.
338 PROCEEDINGS OP THE AMERICAN ACADEMY.
Guttulina sessilis Van Tieghem.
Bull, de la Soc. Bat. de France, XXVII. p. 317. 1880.
" Fruit sessile ; a simple droplet of pure white, resting directly on the
substratum. Spores oval, colorless, aggregated in a sphere and cemented,
as in the preceding species, by a gelatinous substance ; 4/a X 8/t. On the
integument of beans in a state of decay." France.
Guttulina aurea and G. sessilis are known only from the original
descriptions above quoted.
DICTYOSTELIACEiE Rostafinski.
Myxamcebce possessing slender elongated pseudopodia. Sori consist-
ing of spherical masses of spores or of a chain of spores ; stalked, the
stulks composed of distinct parenchyma-like cells with cellulose walls.
ACRASIS Van Tieghem (1880).
Spores concatenate, terminating an erect simple filament, consisting of
a single row of superposed cells.
Acrasis granulata Van Tieghem.
Bull, de la Soc. Bot. de France, XXVII. p. 317. 1880.
Spores spherical, with a slightly roughened or granular wall, having
acuticularized external portion of deep violet color ; 10^-15^ in diam-
eter, often unequal in the same chain, the chain varying much in the
number of component spores and cells.
On a culture of beer yeast. France.
Known only from the original description.
DICTYOSTBLIUM Brefeld (1869).
Sori stalked ; the stalk simple or only occasionally bearing irregularly
disposed branches ; luxuriant fructifications frequently gregarious. Sori
spherical, or subglobose.
Dictyostelium mucoroides Brefeld.
(Ceratopodium elegans Sorokin.)
Abh. d. Senck. Nat. Ges., VII. p. 85-108. PI. I-III. 1869.
Sorus and stalk white, or when old, yellowish ; the fructifications
varying in height from 2-3 mm. to 1 cm. or more. Spores oval or
elongated ellipsoid, 2A/x-S^ X 4/x-6/x.
OLIVE. — PRELIMINARY ENUMERATION OP THE SOROPHORE.E. 339
On the dung of various animals, such as horse, rabbit, clog, guinea pig,
grouse, etc. Also found on cultures of yeast, paper, fleshy fungi, etc., in
a state of decomposition. Germany, Russia, common in America.
This very common species is extremely variable in the size of its spores
and fructifications. The limits of the spore measurements as given by
Brefeld in his original description have been therefore somewhat
increased.
Dictyostelium sphserocephalum (Oud.) Sacc. and March.
{Hyalostilbum sphcerocephalum Oudemans.)
Aanw. Myc. Nederl., IX.-X. p. 30. PL IV. 1885.
Sorus white; when old, yellowish or greenish-white. Stalk frequently
very long and luxuriant, varying from 2 mm. to 1.5 cm. Spores oval,
rarely spherical, or sub-inequilateral, 3^-5/x X 5/a-IO/a.
Dung of mouse, (common), rat, bird, toad, deer, turtle, muskrat, etc.
Belgium ; Cambridge and Boston, Mass. ; New Hampshire ; Florida ;
Pennsylvania ; Liberia.
In the above description the limits of the measurements of spores and
of the length of stalks are greater than those given by Marchal, by
whom the maximum length of the spore is stated as 8^ and that of the
stalk as 5mm. The measurements of the fructifications are certainly
more variable than indicated by Oudemans. This species was founded
by Marchal from the fact that the spores differed in size from those of
Dictyostelium mucoroides, which he states to be only about one-half as
large. As will be seen by the measurements given above, this difference
is by no means as great as indicated ; and, although the present arrange-
ment is retained for the present, it may prove desirable to unite these
two variable species.
Dictyostelium roseum Van Tieghem.
Bull, de la Soc. Bot. de France, XXVII. p. 317. 1880.
" Spore mass spherical, of a bright rose color. Spores elongated oval,
4/x X Sp.. On the dung of various animals ; especially on rabbit dung,
in company with Pllobolus micros'porus.'n France.
Dictyostelium lacteum Van Tieghem.
Bull, de la Soc. Bot. de France, XXVII. p. 317. 1880.
"The mass of spores forms a milk-white drop at the summit of a stalk
which I have always seen composed of a single row of cells. Spores
340 PKOCEEDINGS OF THE AMERICAN ACADEMY.
colorless, spherical, very small, 2[x-3fi in diameter. This form has
been met with several times on decaying agarics." France.
Neither of the two ]5receding forms have been found in American
cultures, hence the writer can add nothing to our knowledge concerning
them.
Dictyostelium brevicaule now sp.
Sorus white ; stalks 1-3 mm. high. Spores oval, 3/^-4/j. X 4//-7/Z
or rarely spherical and 3^-4//. in diameter.
Dung of sheep and goat. Cambridge, Mass.
A small, erect fructification, quite constant in the possession of a short
rather rigid stalk bearing a sorus of comparatively large size and very
different in aspect from the long, luxuriant, frequently flexuous, fructifi-
cations of D. mucoroides and D. sphcerocephahcm. Throughout the four
years that this species has been kept growing in laboratory cultures, it
has retained its original distinct characters.
Dictyostelium purpureum nov. sp.
Sorus and stalk purplish or violet ; when mature, almost black. Spores
oval, rarely somewhat inequilateral, 3/*.-5/x X 5/x-Sfx.
Dung of mouse, toad, cow, horse, sheep, muskrat. Cambridge, Mass.;
Indiana ; Florida.
This distinct species, well-marked by its color, was collected in Aug-
ust, 1897, in Crawfordsville, Indiana, on mouse dung cultures, and in
October of the same year by Dr. Thaxter in Eustis, Florida, on toad
dung. Both forms have been cultivated ever since in the laboratory,
with no particular precautions as to the dissemination of the spores, and
it is not impossible that the fructifications which appeared at Cambridge
on sub-strata other than the two just mentioned represent laboratory
escapes.
Dictyostelium aureum nov. sp.
Mature sori light to golden yellow, 1.5mm. -4mm. high. Spores oval,
or frequently inequilateral, 2.5^-3^ X Ofi—Sfi.
Mouse dung from Porto Rico.
This species, communicated by Dr. Thaxter, is quite well defined
through the color of its fructifications, but especially so by its myxamcebse
and its manner of growth. It matures very slowly on a horse dung de-
coction or on other media especially favorable for the rapid development
of the common species ; while the myxamoeboe, instead of possessing the
OLIVE. — PRELIMINARY ENUMERATION OF THE SOROPHORE^. 341
usual form with elongated, sharp pseudopodia, are in general irregularly
lobed and nodulated, even when growing under normal conditions. Such
irregular shapes are similar to those assumed by the rnyxamcebre of other
species when they are growing under such abnormal conditions as are
furnished by an insufficient water supply.
POLYSPHONDYLIUM Brefeld (1884).
Sori spherical, borne terminally on primary and secondary stalks, the
latter branching in whorls from the main axis ; the fructification occa-
sionally simple as in Dictyostelium. Whorls varying in number from
1-10, and the number of branches in each whorl from 1-6.
Polysphondylium violaceum Brefeld.
Schimmelpilze, VI. p. 1-34. PI. I, II. 1884.
Sori and stalks purplish or dark violet, varying in height from about
^cm.-2cm. ; sori about 50/x.-300^u in diameter. Spores elongated oval,
2.0/i.-5/x X 6ix-8fx.
On dung of horse, bird, sheep, toad, muskrat. Italy, Maine, New
Hampshire, Massachusetts, Florida.
The limits of spore measurements as given by Brefeld have been in-
creased here as in other instances. The form growing on bird dung,
brought by Prof. F. O. Grover from Center Ossipee, N. EL, and the
Massachusetts form on the dung of muskrat, seem to correspond very
closely to the type description. The spores of the Maine and Florida
forms are somewhat smaller, while the general aspect of the fructifica-
tions is different in that they are more delicate and less luxuriant and
the sori have a less diameter than those of the type. These differences,
however, seem hardly more than varietal.
Polysphondylium pallidum nov. sp.
Sori and stalks white, the sori about 50/^-80/x in diameter. Spores
oval, 2.5/x-3/x X 5^-6.5/^, or occasionally spherical, about 7fx-8fi in
diameter.
On duug of ass, rabbit, muskrat. Liberia, Africa ; Arlington and
Stony Brook, Mass.
This delicate species is well characterized by the small size of its sori.
In an interesting specimen, found by Mr. A. F. Blakeslee on muskrat
dung, luxuriant fructifications showed that some of the branches them-
selves bore several whorls of branchlets. That this doubly verticillate
342 PROCEEDINGS OF THE AMERICAN ACADEMY.
character was not constant, however, was proved by growing the form
on a sterilized nutrient medium, on which the fructifications showed
simply the normal method of branching.
Polysphondyliura album nov. sp.
Sori and stalks white, the sori 100^. to 200^ in diameter. Spores oval,
2.5^-3/x X 4^-5.6^.
On dung of toad from Eustis, Florida.
Although the two forms above described have some features in com-
mon, their gross characters are such as to justify their being placed in
separate species. The sori of P. album are not only larger but are
usually more numerous in a whorl, hence its fructifications are more
conspicuous ; moreover, the stalks of this species are rather constantly
weak at the base, so that the fructifications lie close to the substratum
in a characteristic fashion.
CCENONIA Van Tieghem (1884).
Sorus globular, borne at the summit of a stalk which is dilated into a
sort of cupule, in which the sorus is supported.
Ccenonia denticulata Van Tieghem.
Bull, de la Soc. Bot. de France, XXXI. p. 303-300. 1884.
Sorus yellowish; stalk colorless, 2-3 mm. high, having a dilated
base and expanding at the summit into a cupule which is finely toothed
at its edges ; each peripheral cell of the stalk bearing a tooth or papilla
on its exposed side. Spores Q^-S/j. in diameter, with yellowish cell
walls.
On decaying beans. France.
This remarkable form, so far as I am aware, has not been met with
since it was originally described by Van Tieghem.
LABYRINTHULEiE Cienkowsky.
Organisms having two definitely recurring stages, — a vegetative stage
in which spindle-shaped or rarely spherical amoebae, bearing usually
bipolar filiform pseudopodia singly or in tufts, may be either isolated or
combined by the union of the pseudopodia into colonies forming net-plas-
modia; and a fructifying stage, in which aggregations of individuals, com-
parable to pseudoplasmodia, form spores borne in stalked or sessile sori.
OLIVE. — PRELIMINARY ENUMERATION OP THE SOROPHORE^E. 343
Saprophytic or parasitic organisms living on dung, or on alga? in fresh
or salt water.
LABYRINTHULA Cienkowsky (1867).
Amoeba? spindle-shaped, colorless, or colored by means of yellow fat
bodies. Spores borne in formless masses, producing one to four amoeba?
at germination.
The species of this genus have thus far been observed only by the
authors cited.
Labyrinthula vitellina Cienkowsky.
Archiv. f. mikros. Anat., III. p. 274, Taf. 15-17. 1867.
Amoebae containing orange-red coloring matter, which turns blue with
iodine. Spores oval or spherical, 12^ in diameter, producing four amoeba?
at germination.
Living on sea-weeds growing on piles in Odessa harbor, Russia.
Labyrinthula macrocystis Cienk.
Archiv. f. mikros. Anat., III. p. 274, Taf. 15-17. 1867.
Colorless or feebly yellowish. Spores spindle-shaped, 18^-25^ long,
imbedded in a hyaline substance ; the contents producing four amoeba?
at germination.
Living on alga? growing on piles at a higher elevation than L. vittelina,
only submerged by the surf. Russia.
Labyrinthula Cienkowskii Zopf.
Beitriige zur Pliys. u. Morph. niederer Organismen, II. p. 36-48, Taf. IV, V. 1892.
Sori colorless, naked. Spores at germination producing only one or
at most two amoeba?.
Living in fresh water, parasitic on Vaucheria. Germany.
DIPLOPHRYS Barker (1868).
Amoeba? spindle-shaped or nearly spherical, with yellowish oil globules.
Fructification (in D. stercorea) a definite stalked or sessile sorus.
Diplophrys Archeri Barker.
Quart. Jour. Mic. ScL, VII. p. 123. 1868.
Individuals nearly spherical or broadly elliptical, 4^-5^ in diameter,
bearing at almost opposite poles a tuft of filiform pseudopodia ; the pro-
344 PROCEEDINGS OP THE AMERICAN ACADEMY.
toplasm containing an oil-like refractive globule of an orange or amber
color. Fructification unknown.
Living in fresh water. Ireland, Germany, Pennsylvania and New
Jersey (Leidy).
In this provisional arrangement, I have followed Cienkowsky in refer-
ring this species to the Labyrinthulese, although I regard it as improbable
whether Diplophrys Archeri and D. stercorea should be included in the
same genus. The aggregations of the vegetating amcebce of D. Archeri
seem to be an association of the young iu groups, the colonies being
formed by successive division of the individuals ; and there is nothing
definite known concerning a resting stage.
Diplophrys stercorea Cienkowsky.
Archiv. f. mikr. Anat, Bd. XII. p. 44. PI. VIII. 1876.
Individuals lens- or spindle-shaped, about 4^-6^ long, bearing at both
ends several pseudopodia, almost bilaterally symmetrical. In the interior
a nucleus, one or two contractile vacuoles and a yellow pigment body.
Both the isolated and united individuals of the net-plasmodium finally
becoming aggregated to form without change of shape pseudospores borne
in sori, which are usually stalked, sometimes sessile.
On dung of horse, cow and porcupine. Russia; Cambridge, Mass.;
Intervale, New Hampshire.
This species has been met with twice in American cultures, and so
far as I am aware, with the exception of D. Archeri, is the only repre-
sentative of the Labyrinthuleae which has been found in this country.
A form, which is probably the resting condition of Cldamydomyxa laby-
rinthuloides Archer, has been found growing in the cells of sphagnum,
at Kittery, Maine, by Professor Thaxter. As Archer and others have
pointed out, however, it is very doubtful whether this peculiar organism
should be included in the Labyrinthuleae.
Proceedings of the American Academy of Arts and Sciences.
Vol. XXXVII. No. 13. — January, 1902.
CONTRIBUTIONS FROM THE CHEMICAL LABORATORY
OF HARVARD COLLEGE.
THE DECOMPOSITION OF MERCUROUS CHLORIDE
BY DISSOLVED CHLORIDES: A CONTRIBUTION
TO THE STUDY OF CONCENTRATED SOLUTIONS.
By Theodore William Richards and Ebenezer Henry Archibald.
CONTRIBUTIONS FROM THE CHEMICAL LABORATORY OF
HARVARD COLLEGE.
THE DECOMPOSITION OF MERCUROUS CHLORIDE BY
DISSOLVED CHLORIDES: A CONTRIBUTION TO THE
STUDY OF CONCENTRATED SOLUTIONS.
By Theodore William Richards and Ebenezer Henry Archibald.
Received November 23, 1901. Presented December 11, 1901.
Introduction.
Long ago Miahle observed that a concentrated solution of common
salt acts upon calomel with the formation of small amounts of mercuric
chloride.* Many years afterwards, one of us,f without knowing of his
work, rediscovered this reaction, and found that the fluctuations in the
potential of the " normal calomel electrode " of Ostwald, are due to ita
disturbing influence. At that time it was shown that the reaction is
much diminished by dilution, and hence that a decinormal solution is far
better as an electrolyte than a normal solution. The "decinormal
electrode," thus recommended for the first time, has since come into
common use.
It was shown also that neither light nor oxygen are important causes
in effecting the decomposition, but that the reaction is much furthered by
increase of temperature. No attempt was made at the time to fathom
the matter, but a suggestion was made that the reaction might be due to
the catalytic action of the ionized chlorine of the dissolved chloride.
The investigation of the problem which was at that time promised has
now been continued, and the object of this paper is to show that while the
second condition of this suggestion seems probable, the first does not hold.
Another example is thus afforded of the frequently recurring circum-
stance of the removal of a reaction from its classification among catalytic
phenomena after better acquaintance with its nature.
* Miahle, J. Pharm., 26, 108; Ann. Cliim. et Phys. (3), 5, 177 (1842).
t Richards, These Proc, 33, 1 (1897) ; Z. phys. Ch., 24, 39.
348 PROCEEDINGS OF THE AMERICAN ACADEMY.
The method employed was to treat calomel with solutions of chlorides
of various concentrations for varying times, and to determine the extent
of the reaction by determining the amount of mercury dissolved.
Preparation of Materials.
Mercury already very pure was thoroughly freed from the possible
presence of substances with greater solution-tension by treatment with
sulphuric acid and potassic dichromate, and subsequent spraying through
ten per cent nitric acid. Calomel was resublimed at as low a temperature
as possible, and thoroughly washed with water and with the solution to
be used in each particular case. One of us had previously shown that
the source of the calomel is immaterial.* Sodic chloride was precipitated
by pure hydrochloric acid from a saturated solution of the so-called
" chemically pure " salt. It was then twice recrystallized from water,
and thoroughly dried to drive off any possible traces of acid. Pure
calcic nitrate was made by many recrystallizations ; this was converted
into carbonate, and the carbonate converted again into chloride. Several
recrystallizations freed this chloride from every trace of the nitrate or of
ionized hydrogen. Baric chloride was crystallized first from a solution
strongly acid with hydrochloric acid, and subsequently from aqueous
solutions by precipitation with pure alcohol. It also was wholly neutral
to methyl orange. Cadmic chloride was made by dissolving the pure
metal in pure acid and recrystallizing twice. The salt was dried
thoroughly in order to make certain of the absence of ionized hydrogen,
which is less easily detected in this case. Hydrochloric acid itself was
purified by redistillation, the purest acid of commerce serving as the
starting-point.
Apparatus and Method of Analysis.
It was necessary to digest the mixtures for long periods of time
at a constant temperature. For this purpose they were placed in large
test-tubes of sixty cubic centimeters capacity arranged to rotate tran-
sit-fashion in an Ostwald thermostat after the manner suggested by
Schroder. f In the case of the weaker solutions several of these tubefuls
were used for each analysis, but with the stronger solutions fifty cubic
centimeters sufficed. The tubes were corked with rubber stoppers
* Richards, loc. cit.
t Richards and Faber, Am. Ch. J., 21, 168 (1899). The thermometer used to
register the temperature was of course suitably verified.
RICHARDS AND ARCHIBALD. CONCENTRATED SOLUTIONS. 349
which had previously been boiled with dilute alkali and scrupulously
rubbed and washed. Into each tube was placed a large excess of
calomel, about a decigram of mercury, and fifty cubic centimeters of one
of the solutions of chlorides.
After a slight shaking, the settled precipitate was always covered
upon standing with a layer of gray partially reduced material, which
settled more slowly and hence gave more opportunity for reduction.
When the equilibrium was completed by prolonged shaking, this gray
material was mixed evenly throughout, and no longer appeared on the
surface of the precipitate. Thus the absence of a gray film on settling
was a rough guide to the completion of the reaction.
After five or six hours of agitation in the thermostat at 25.° ± 0.05°
one of the tubes was opened, its contents filtered, and the dissolved mer-
cury determined analytically. At intervals of an hour successive tubes
were similarly treated, and after seven or eight hours no change was
found in any case. Evidently a state of equilibrium is soon attained,
and the reaction cannot be called catalytic. The values given below are
of course the values corresponding to this maximum.
In this paper no evidence is given concerning the size of the grains of
calomel. Ostwald * has recently shown that this may be an important
factor in determining the concentration of a saturated solution, and
hence in fixing the basis of the present equilibrium. Concerning this
point it need only be said that while the absolute extent of solubility
may vary with the size of the grains, the relative results, upon which
alone the conclusions of this paper are founded, are not affected. This is
the case because the same preparation of calomel was used in every
instance. Moreover, since the calomel was sublimed and since it is
notoriously difficult to powder, the individual diameters could not have
been very small, hence a value approximating that corresponding to a
flat surface must have been obtained.
A number of experiments indicated that the mercury salt thus dis-
solved was in the mercuric rather than in the mercurous state. The
visible deposition of mercury during the reaction is alone almost enough
to prove this. Moreover, neither permanganate nor bichromate suffered
more than the faintest trace of reduction upon addition to a solution
which contained much dissolved mercury. The minute trace of decolor-
ization which was observed was no greater than that produced by a solu-
tion of mercurous chloride in pure water. On the other hand, small
* Zeitschr. phys. Chem., 34, 495 (1900).
350
PROCEEDINGS OP THE AMERICAN ACADEMY.
amounts of stannous chloride gave plentiful white precipitates of
calomel.
In all cases except that of cadmium, the mercuric salt in solution was
determined as sulphide. The black precipitate produced by hydrogen
sulphide was collected on a Gooch crucible, washed with alcohol, carbon
disulphide, and again with alcohol, and finally dried at 100°. Satis-
factory agreement between parallel analyses, which were almost always
made in duplicate, was obtained. In the tenth-normal solutions of sodic
chloride the amount of mercuric chloride was too small to be collected,
hence it was determined colorimetrically by comparison with known
solutions of similar dilution.
The following table explains itself. The last-column contains an arbi-
trary ratio which is an index of the changing relationship between the
amounts of mercuric chloride formed and the amounts of sodic chloride
present. The values in the third column were calculated from those in
the second ; and the values in the fifth column from those in the third
and fourth.
Mercuric Chloride found in Solutions of Sodic Chloride.
No. of
Exp.
( a
Sa
Wt. of
Solution
taken.
grm.
64.5
66.1
65.9
80.3
75.4
83.0
73.8
80.3
58.7
69.7
Vol.
of
Solution.
62.0
63.5
61.1
74.5
68.8
75.7
64.6
70.3
49.4
58.8
Wt. of
HgS
found.
m.g.
2.2
2.3
6.8
8.2
11.4
12.6
21.1
22.8
27.2
32.5
Wt. of
HgCI., in
1 Litre of
Solution.
grm.
0.0041
Mean Wt.
of HgClj
in
1 Litre.
grm.
0.0041
0.041
0.129
0.194
0.380
0.643
C
Cone, of
NaCl
Solution
in Equiv.
Grams.
equiv.
0.10
1.00
2.00
2.50
3.80
5.00
1000 -c
Milligrams
Hg<Jl2 for
every Mol.
NaCl.
41.0(?)
41.5
64.5
.7.6
100.0
128.6
RICHARDS AND ARCHIBALD. — CONCENTRATED SOLUTIONS. 351
These facts, together with similar facts concerning solutions of three
other chlorides, are represented in the accompanying diagram. Evidently
the first parts of the four curves are very similar in tendency, but as the
highest concentrations are reached, the curves develop individuality.
Mercuric Chloride foond in various Solutions.
The ordinates represent equivalent concentrations of the solvent chlorides, and
the abscissae represent grams of mercuric chloride per litre of solution. The data
for baric, calcic, and hydric chlorides are to be found on pages 352, 353, and 354.
Manifestly some particular property of the several solutions must be
responsible for the reaction ; and since the reaction results in raising the
quanti valence of the mercury, it may be concluded that the particular
property in question is the tendency of some molecular species already
in the solution to combine with mercuric chloride.
352
PROCEEDINGS OP THE AMERICAN ACADEMT.
This conclusion concerning the action of the substances on mercurous
chloride is reinforced by the facts concerning the extent to which mer-
curic chloride is dissolved by solutions of various chlorides. Solutions of
sodic chloride dissolve amounts of mercuric chloride which increase with
the amounts of common salt present, until the saturation point is reached,
while solutions of hydrochloric acid dissolve a maximum of mercuric
chloride at a concentration of acid of seven times normal, remaining
almost constant in action upon further concentration.*
The parallelism between the tendency of these soluble chlorides to dis-
solve mercuric chloride on the one hand, and their tendency to decompose
mercurous chloride on the other hand, is thus rather striking.
In addition to the four chlorides given iu the tables, cadmic chloride
was used iu a special series of experiments. The solution after digestion
with calomel was analyzed by immersing in it a roll of clean copper
gauze, which was dried and weighed, and then ignited in hydrogen and
weighed again. Preliminary experiments showed this to be a convenient
and sufficiently accurate method of determining mercury in the presence
of cadmium.
Although solutions of 2, 4, and 8 times normal were used, in no case
Mercuric Chloride found in Solutions of Baric Chloride.
No. of
Exp.
(a
2
(a
4
Wt. of
Solution
taken.
grm.
100.5
112.0
101.8
120.3
91.5
112.8
131.2
106.8
Vol.
of
Solution.
c. c.
97.8
103.0
89.8
10G.1
80.2
95.7
103.8
84.5
wt. of
HgS
found.
m. g.
3.6
3.9
6.7
8.0
7.3
8.8
20.5
16.7
wt. of
HgOl, in
1 Litre of
Solution.
grm.
0.043
Mean Wt.
of two Det.
of UgCl2 in
1 Litre
Solution.
gnu.
0.044
0.088
0.107
0.231
c
Cone, of
BaCl2
Solutions
iu Equiv.
Grams.
equiv.
1.00
1.50
2.00
3.00
1000 ^,
Milligrams
HgCI2 for
every J Mol
BaCl,.
44.0
58.G(?)
53.5
77.0
* Homeyer and Ritsert, Pharm. Ztg., 33, 738, quoted by Comey, Diet, of Solubili-
ties, 227 (1896).
Ditte, Ann. Chim. phys., (5) 22, 551 ; Engel., ibid. (6), 17, 362. See Comey, as
above.
RICHARDS AND ARCHIBALD. — CONCENTRATED SOLUTIONS. 358
could a trace of mercury be detected in the solution. Moreover, no gray
precipitate of reduced mercury was ever observed when the cadmium solu-
tion was shaken with calomel in the first place. One infers that there
is not in dissolved cadmic chloride any considerable concentration of a
molecular species capable of combining with mercuric chloride.
This conclusion is quite in accordance with the fact that the tempera-
ture-coefficient of the potential of the calomel electrode with solutions of
cadmic chloride exhibits none of the irregularities observed when other
chlorides are used.*
Mercuric Chloride found in Solutions of Calcic Chloride.
No of
Exp.
a
b
a
b
a
1 b
a
(a
7
h
h
Wt. of
Solution
taken.
grin.
80.2
75.6
75.4
78.4
59.4
61.5
92.2
99.4
57.4
67.0
48.7
76.4
50.0
47.5
Vol.
of
Solution.
Wt. of
HgS
found.
c. c.
m. g.
75.4
5.2
69.3
4.7
68.2
6.9
70.9
7.2
51.6
10.3
53.5
10.8
76.5
21.0
82.5
22.8
46.2
17.0
53.9
19.9
37.0
16.4
58.1
25.8
36.8
16.1
34.9
15.2
Wt. of
HgCl2 in
1 Litre of
Solution.
grm.
0.022
0.033
0.082 )
0.079 )
0.118)
0.118 S
0.232 )
0.230 )
0.320 )
0.323 )
0.429 )
0.431 )
0.518 )
0.519 )
0.511)
0.509 )
c
Mean Wt.
from two
Det.ofUgCl,
in 1 Litre
Solution.
grm.
0.022
0.081
0.118
0.231
0.322
0.430
0.518
0.510
C
Cone, of
CaOl, Solu-
tion in
Equiv.Grms.
Q CaCl2)
eqmv.
0.72
1.00
2.00
2.50
3.52
4.64
5.85
7.80
9.00
1000 j,
Milligrams
HgCl2 for
every h Mol.
CaCl„.
31.6
40.5
47.2
65.6
69.3
73.4
66.4
56.6
* llioliards, These Proceedings, 33, 1 (1897).
vol. xxxvii. — 23
354
PROCEEDINGS OF THE AMERICAN ACADEMY.
Interpretation of Results.
There are two possible interpretations of the phenomena under discus-
sion. According to one, the undissociated mercuric chloride may be
supposed to combine with the undissociated part of the electrolyte,
forming an undissociated double salt, while according to the other, the
undissociated mercuric chloride may be supposed to combine with the
chlorine ion to form a complex ion. The following considerations at-
tempt to decide which of these is more probable.
Mercuric Chloride found in Solutions of Hydrochloric Acid.
No. of
Exp.
3
lb
4
6
a
Wt. of
Solution
taken.
gnn.
132.0
179.0
74.5
87.8
85.2
75.8
85.4
90.4
82.6
95.6
70.0
95.8
115.0
123.0
Vol.
of
Solution.
126.7
171.8
69.7
82.0
78.1
69.5
76.8
81.3
73.8
85.5
61.8
84.6
99.6
106.5
Wt. of
HgS
found.
m. g.
22.4
30.6
23.9
28.0
36.6
32.6
42.9
45.5
42.7.
49.3
35.4
48.6
57.7
61.4
Wt. of
HgCU in
1 Litre of
Solution.
grm.
( 0.034
( 0.034 '
C 0.048 (
} 0.048 !
0.206 :
0.208 j
0.400 j
0.398 i
0.548 )
0.548 )
0.653 )
0.655 j
0.676 )
0.673 )
0.669
0.671
0.672
0.674
c C
Mean Wt. Cone, of
ofHgCl2 I HC1
in 1 Litre Solution
of i in Equiv.
Solution. Grams.
grm.
0.034
0.048
0.207
0.399
0.654
0.675
0.670
0.673
equiv.
0.83
1.00
2.50
4.15
7.00
7.30
8.31
10.00
0.548 5.48 100.0
1000-
Milligrams
HgCi, for
every Mol.
HC1.
41.0
48.0
83.0
96.1
92.8
92.3
80.6
67.3
RICHARDS AND ARCHIBALD. — CONCENTRATED SOLUTIONS. 355
The shape of the first section of the curves, where the concentration of
the mercury present increases at a greater rate than does the correspond-
ing amount of electrolyte, suggests at first that the undissociated part of
the latter is the portion concerned in the reaction ; but the curve repre-
senting a power of the concentration of the ionized chlorine has of course
a similar tendency.
Hence the general shape of the curve is an insufficient basis for de-
cision between the two hypotheses.
The fact that strong solutions of cadmic chloride have little or no
influence on mercurous chloride supports the latter of the two hypotheses,
since concentrated cadmic chloride solutions contain but a very small
concentration of ionized chlorine.
More direct light upon the question is obtained by the measurement
of electrolytic conductivity. According to the first hypothesis, which
demands the presence of an undissociated double salt, the conductivity of
salt solution should be considerably decreased by the addition of mercuric
chloride. As a matter of fact, we found that the dissolving of mercuric
chloride to saturation in a twice normal solution of common salt dimin-
ished but slightly the conductivity of the solution. The work of Le Blanc
and Noyes* furnishes similar results concerning hydrochloric acid; and
moreover these investigators showed by the catalysis of methyl acetate
that the concentration of the hydrogen ion was undiminished by the addi-
tion of mercuric chloride. Hence the new compound is to be considered
as highly ionized.
Yet further evidence is to be obtained by referring to the specific con-
ductivities of strong solutions of the chlorides studied. f Here we find
that while the conductivities of solutions of sodic and baric chlorides
increase with the concentration as far as they may be followed, those of
calcic and hydric chlorides exhibit maxima at a concentration about six
times normal. The agreement between these maxima and those ex-
hibited by our own curves at seven times normal is close enough to
suggest an essential relation between the cause of conductivity and the
cause of Miahle's reaction.
The evidence thus furnished is all consistent in indicating that the
nature of the reaction is the addition of HgCL to the chlorine ion, with
the formation of a complex ion. This conclusion agrees with that of Le
Blanc and Noyes, based upon other data.
* Le Blanc and Noyes, Zeitschr. phys. Chem., 6, 389, seq. (1890).
t See Kohlrauseh and Holborn (1898), Leitvermogen d . Eleetrol., pp. 145-154.
356 PROCEEDINGS OF THE AMERICAN ACADEMY.
It remains now to detect the mechanism of the reaction. The work
of Le Blanc and Noyes led them to believe that in dilute solutions con-
taining an excess of the soluble electrolyte the new ion is bivalent, being
formed by the reaction 2 CI' + HgCL = HgCl/'. It will be shown that
our own evidence supports this conclusion also.
The reaction with which we are concerned may perhajis be written
thus : —
xHCl ±; xH- + xCl'
+
Hg2Cl2 *; HgCl2 + Hg
•fl +1 ♦ I
1+ 1+ I *
Solid Hg2Cl2 HgCl,2 i x\ Liquid mercury
The ion HgCl(2+I) will of course be the bearer of x negative charges of
electricity. The above expression does not attempt completeness, but
strives merely to represent the most essential features of the reaction in
the simplest possible form.
The first conclusion to be noted is that the concentration of the un-
combined but dissolved mercuric chloride will be constant, since it is
formed by a reaction involving two precipitates. Hence the concentra-
tion of the ion HgC\i2+%] should vary as the concentration of the chlorine
ion raised to the x(h power.
It is immediately clear that x must be more than unity, for in the less
concentrated solutions the concentration of the mercury present increases
faster than that of the dissolving chloride, while the concentration of the
ionized chlorine is supposed to increase less rapidly than the latter.
By taking x = 2 we obtain much more satisfactory agreement. If we
assume that the concentration of the ions present is proportional to the
specific conductivity,* we find that for solutions as far as twice normal the
calculated curve agrees almost precisely with the actual amounts of mer-
cury found. The specific conductivity of a twice normal solution of
hydrochloric acid is 0.505, while that of a normal solution is 0.295.
The squares of these numbers are respectively 0.255 and 0.087, two
values which are very nearly proportional to the weights 148 and 48
milligrams of mercury per litre which were actually found to be dis-
solved from calomel by twice normal and by normal solutions of hydro-
chloric acid respectively.
With more concentrated solutions the results of this calculation agree
* The possible dangers of this assumption are well known. It is made here
simply in default of more certain knowledge.
RICHARDS AND ARCHIBALD. — CONCENTRATED SOLUTIONS. 357
less and less satisfactorily with the facts, the amount of mercury actually
found always exceeding the calculated amount. Evidently this disagree-
ment may be due to the fact that some of the new complex acid remains
in the uudissociated state; the calculation considers only the ion, while
the mercury weighed in analysis constituted the sum total. The exact
calculation of the amount undissociated is impossible for two reasons;
in the first place, the mode of dissociation of such a tri-ionic comjxmnd as
H2HgCl4 is uncertain ; and in the next place, we have no data for the
extent of the dissociation of the compound beyond the strength of a nor-
mal solution. •
In spite of this double uncertainty, it is possible to make an approxi-
mate calculation. This is sufficient to show that in a general way the
argument is sound. The approximate calculation is based upon the fact
that so far as the extent of dissociation of the complex acid is known, it
is equal to that of hydrochloric acid at the same concentration.* On mak-
ing the assumption that this relation holds in very strong as well as in
moderately strong solutions, and waiving entirely the uncertainty as to the
possible existence of the half-way ion HHgCl4', the proportion of the
Approximate Calculation of the Total Amount of Mercury.
Concentra-
tion of
Hydrochloric
Acid Solution
or Qrani-
Equiv. per
Litre.
K = specific
Conductivity of
Uydrochloric
Acid a\t
K2.
A„
a = •
Aoo
385 if-
a
Milligrams
Mercury
found in
1 Litre
Solution. %
1
0.295
0.087
0.79G
42
48
2
0.505
0.255
0.G72
148
148
3
0.645
0.417
0.5G8
282
2G3
4
0.727
0.530
0.48
427
383
5
0.7(50
0.580
0.40
500
495
G
0.702
0.582
—
—
—
7
0.745
0.554
028
765
654
10
0.G35
0.420
0.17
955
672
* Le Blanc and Noyes, loc. cit.
t These figures were obtained by graphic interpolation from the figures of
Kohlrausch and Holborn, Leitvermogen U. Eiectrol., p. 154 (1898).
\ By interpolation.
358 PROCEEDINGS OP THE AMERICAN ACADEMY.
undissociated complex may be calculated by simply multiplying the sup-
posed concentration C of the ionized part of the complex by , when
a
a is the degree of dissociation of the acid. The total concentration of the
-i ri
mercury present would then be C -f- C = -. But if the new
ion has the formula HgCl4", its concentration should be proportional to
the square of the specific conductivity, k, according to our previous
C k2
reasoning. That is to say, — =k — .* This equation is tested in the
a a
following table, by taking a value for the constant k which best satisfies
the early part of the curve — namely 385.
The bearing of these rather discrepant figures is best seen by plotting
the results. The curve which depicts the relation of the quantity
385 k2
to the concentration of the hydrochloric acid is indicated by a
dotted line in the diagram on page 351. While with great concentrations
it deviates considerably from the curve representing the amount of
mercuric chloride formed by hydrochloric acid, it is nevertheless of the
same general character. Considering the many uncertainties, including
the doubt concerning the equation a = — , which interfere with its exact
00
determination, the agreement is indeed as close as one has a right to
expect.
Corresponding curves, with about the same degree of agreement, may
be calculated for the other chlorides. It is perhaps worth while to call
attention to the fact that the amount of mercury found in the most dilute
solution studied, the tenth normal solution of sodic chloride, although very
small, is too great to correspond to the theoretical value. The excess of
about three milligrams per litre above the requirement of theory may
well be due to dissolved calomel, which possesses a slight but unknown
solubility of its own.f
All these arguments, reinforcing the conclusions which Le Blanc and
Noyes reached from a different series of facts, seem to indicate that as
*k — = kf-Tr because a = and k' = kAaa. Tlie more complex form is
o \ Ax
retained because its meaning is the more obvious.
t The work of Kohlrausch and Rose (Zeitschr. pliys. Cliem. 12, 241) is not con-
clusive concerning this solubility, since the behavior of calomel on solution is too
little known. Their results seemed to indicate that the solubility amounted to
three or four milligrams per litre.
RICHARDS AND ARCHIBALD. — CONCENTRATED SOLUTIONS. 359
nearly as the present means can determine, the reaction which we have
been studying is to be thus represented in its simplest form : —
Hg2Cl2 + 2C1' = Hg + HgCl4".
It is of interest to classify the equilibrium under consideration accord-
ing to the Phase Rule of Willard Gibbs. Looked at from this point of
view, we may speak of the system as consisting of four components, —
water, soluble salt, mercury, and mercuric chloride. It is clear, therefore,
that when we have together the four phases, — mercury, mercurous
chloride, solution, and vapor, — at a fixed temperature, a single condition
of freedom remains to be fixed in order to fix the system. The concen-
tration of the ionized chlorine seems to supply this sixth (n + 2d) con-
dition, determining the fixed points in the tables.
At the seven times normal point the concentration of the mercury dis-
solved seems to attain almost a constancy, being no longer increased by
further addition of soluble electrolyte. According to the Phase Rule,
such a phenomenon might be caused by the appearance of a new phase.
This new phase would of course be one which would remove hydro-
chloric acid from the solution -} hence its presence or absence is easily
discovered.
As a matter of fact, we found that after continued shaking with
calomel, hydrochloric acid having an original concentration of 9.22
normal was reduced only to 9.20 normal. This is quite too small a
difference to be due to the formation of a new phase ; it must be ascribed
either to adsorption by the calomel or to analytical error.
Hence the constancy of mercury dissolved is to be ascribed to con-
ditions within the solution, and not to the appearance of a new
phase.
Since the reaction seems to be effected primarily by the action of the
chloride ion, it might be used to determine the concentration of the
chloride ion, — or in the corresponding cases, that of the bromide or
iodide ion. Especially would the case be applicable to the ionized
chlorine because here the amount of mercury dissolved is too small to
affect seriously other equilibria existing in the solution. Of course, with
very dilute solutions the solubility of mercurous chloride itself would
have to be taken into account.
This tendency of mercuric chloride to add to the chloride ion is
a highly interesting circumstance. Other similar phenomena are being
more and more frequently reported.* The tendency of cadmium to form
* Cushman, Zeitschr. fur anal. Chem., 34, 3G8 (1895).
360 PROCEEDINGS OF THE AMERICAN ACADEMY.
a similar complex ion is well known ; it has even been used by Cushman
under Sanger's direction as a means of separating cadmium from other
metals. In this case the complex ion was formed simply by adding an
excess of sodic chloride, which prevents cadmium from being precipitated
by hydrogen sulphide. Upon dilution the sulphide of cadmium hegins to
be precipitated, owing to the splitting apart of the ion in dilute solutions
according to the law of " mass " action.
The same tendency has been used to explain the otherwise incom-
prehensible migration values of cadmium salts. Very recently Noyes has
shown that probably a similar ion, BaCl/',* exists in baric chloride so-
lutions ; and the migration values of concentrated calcic and magnesic
chloride solutions lead one to infer that in these cases yet a greater
concentration of CaC'l4" and MgCl/' may exist.
It is interesting to note that the decomposition of the mercurous
halide is carried to a much greater extent under similar conditions in the
case of the bromide than in that of the chloride,f and yet further in
the case of the iodide. This may be due simply to the greater solubilities
of mercurous bromide and iodide, but besides this cause there may exist
a greater affinity of the molecule for the ion. The study of the migra-
tion values of cadmium salts seems to show that the iodide has a much
greater tendency to add to ionized iodine than the chloride has to add to
ionized chlorine ; and it is probable that the same relation exists in the
case of mercury.
The facts recorded above show that an accurate quantitative analysis
of a mercurous salt by precipitation with a soluble chloride is not to be
expected, unless the chloride is added only in very slight excess, and
then the solubility of mercurous chloride itself must be considered.
When, however, a large excess of mercuric salt is present, as for example
in the recent work of Ogg,} it is obvious that the disturbing effect of the
side-reaction must be much hindered, according to the law of " mass "
action.
It is possible that the medicinal action of calomel is due to the small
but definite concentration of mercuric complex salt produced by common
salt or hydrochloric acid in the alimentary canal. In any case, one is
disposed to recommend cautious medicinal use of other chlorides in con-
nection with calomel.
Preliminary experiments with sulphates showed that with these salts
* A. A. Noyes, J. Am. Chem. Soc, 23, 37-57 (1901).
t Richards, loc. cit.
t Ogg, Zeitschr. phys. Chem., 27, 291 (1898).
RICHARDS AND ARCHIBALD. — CONCENTRATED SOLUTIONS. 361
the tendency to form complex compounds is much less than that
exhibited by chlorides ; hence the Latimer-Clarke and Weston cells are
not much affected by this type of side-reaction.
The results of the present paper may be stated briefly as follows : —
1. The action of dissolved chlorides upon calomel is not catalytic, but
results in the establishment of a definite equilibrium.
2. With equivalent solutions, less concentrated than five times nor-
mal, hydrochloric acid and sodic chloride have about equal tendencies to
effect the reaction ; baric chloride has less tendency, calcic chloride still
less, and cadmic chloride no appreciable tendency.
3. The extent of the reaction in solutions not too concentrated is
approximately a simple function of the square of the concentration of the
chloride ion. This relation, taken in connection with a number of other
considerations, points to the existence of a highly ionized complex
HgCl/' in the solution, and thus confirms the work of Le Blanc and
Noyes.
4. If approximate allowance is made for the probable concentration of
undissociated complex salt present, all the figures, even as far as ten
times normal solutions, seem to be explicable.
5. The suggestion is made that the reaction may be of use as a
means of determining the concentration of the chlorine ion.
6. The corresponding reactions are much less marked with sulphates,
but much more so with bromides and iodides.
7. Caution is needed when using mercurous chloride as a means of
determining mercury in quantitative analysis.
Cambridge, 1899-1901.
Proceedings of the American Academy of Arts and Sciences.
Vol. XXXVII. No. 14. — February, 1902.
CONTRIBUTIONS FROM THE CHEMICAL LABORATORY
OF HARVARD COLLEGE.
A NEW INVESTIGATION CONCERNING THE ATOMIC
WEIGHT OF URANIUM.
By Theodore William Richards and Benjamin Shores Merigold.
CONTRIBUTIONS FROM THE CHEMICAL LABORATORY OF
HARVARD COLLEGE.
A NEW INVESTIGATION CONCERNING THE ATOMIC
WEIGHT OF URANIUM.*
By Theodore William Richards and Benjamin Shores Merigold.
Presented December 11, 1901. Received December 19, 1901.
Introduction.
Our knowledge of uranium dates from the year 1789, when it was first
recognized as an element by Klaproth. It can by no means, therefore,
be classed with the new elements, nor is it of great rarity. Nevertheless,
comparatively few determinations of the atomic weight of this element
have been made, and of these, one only has been carried out with the
degree of accuracy necessary in work of this kind. During the fifty
years following the discovery of uranium a number of atomic weight
determinations were made by Berzelius, Arfvedson, Schonberg, Mar-
chand, and Rammelsberg. This early work is now of historical interest
only, for the results vary widely, and in some cases are of such a nature
as scarcely to be considered quantitative, in the modern sense of the
word. For example, Rammelsberg obtained results varying from 184
to 234, calculated upon the modern basis.
In 1841 Peligot discovered that the substance then known as uranium
was not an element, but an oxide. This discovery, while it did not
impair the value of the analytical work previously done, necessitated a
recalculation of the numerical value of the atomic weight. The new
value was 120, and this remained practically unchanged during the next
thirty years. When the periodic classification of the elements was first
suggested, uranium, with the atomic weight 120, was one of the elements
for which there was no place. From a study of the properties of
uranium and its compounds, Mendeleeff declared that the atomic weight
* The greater part of the work described in this paper was presented to the
Faculty of Arts and Sciences of Harvard University by B. S. Merigold, as a thesis
for the degree of Ph.D., in June, 1901.
366 PROCEEDINGS OF THE AMERICAN ACADEMY.
of uranium was probably 240 instead of 120.* The question was not
definitely settled until Zimmermann, in 1885, carried out the suggestions
of Mendel eeff, and by specific heat and vapor density determinations
confirmed the higher value.f
Owing to the wide variations in the published results, the atomic
weight of uranium has long been considered one of the least satisfactorily
determined of the atomic weight values. A glance at the results thus
far obtained is sufficient to show the need for further work in this line.
A complete resume of the older work upon the subject is to be found in
Clarke's recent work on the atomic weights. | The following table
summarizes those investigations which seem to possess even a little
quantitative value: —
Less Inaccurate Pkeviocs Work on the Atomic Weight of Uranium.
O = 16.000
1841 Peligot §— Analysis of Green Chloride 240. ±
1842 Ebelmen || — Combustion of Oxalate 238. ±
1843 Wertheim IT — Double Acetate of Sodium and Uranium 239. ±
1846 Peligot** — Combustion of Oxalate and Acetate . . 240. ±
1886 Zimmermann ft — Reduction of Oxide, U308 to U02 . 239.6
1886 Zimmermann $$ — Ignition of Double Acetate . . . 239.5
The work of Ebelmen, "Wertheim, and the early work of Peligot is neces-
sarily of little weight in assigning a probable value to the atomic weight
of uranium. In some cases the material used was impure, and in others
the methods of analysis were faulty. Consequently it is not surprising
to find differences of whole units in the individual determinations of
each series.
Peligot's later determinations from the oxalate is perhaps the best of
the early work. His material was carefully purified, and his method is
far preferable to the work of Ebelmen and Wertheim. By combustion
* Annalen der Cliemie u. Pharmacie, Supp. Vol. 8, 178 et. seq.
t Annalen der Chemie u. Pharmacie, 216, 1.
J A Recalculation of the Atomic Weights, by F. W. Clarke, Smithson. Misc.
Coll., Constants of Nature, Part V. (1897), 263.
§ Compt. Rend. 12, 735. Ann. Chim. Phys. (3) 5, 5 (1842).
|| J. prkt. Chem. 27, 385 (1842).
1 Ibid., 29, 209 (1843).
** Compt. Rend., 22, 487 (1846).
tt Ann. d. Chem., 232, 299 (1886).
U Ibid.
RICHARDS AND MERIGOLD. ATOMIC WEIGHT OF URANIUM. 367
analysis he determined the ratio between uranium oxide and carbon
dioxide. Thus he eliminated the error involved in weighing a crystal-
lized salt which would probably contain more or less included water.
The principal sources of error are the questionable use of combustion
analysis in atomic weight investigations, and the possibility of unoxidized
carbon remaining in the uranium oxide. His best results vary from
239.4 to 241.1.
The work of these chemists, though a great improvement over the
attempts of Rammelsberg and the other early workers, leaves much to
be desired, and does little more than give an approximate idea of the
probable value of the atomic weight of uranium.
Zimmermann's investigation of the ratio between the oxides UO.. and
U308 was much more carefully carried out, and is the only work thus far
published that is worthy of serious consideration. Using carefully purified
material, and giving attention to detail, Zimmermann oxidized the lower
oxide by means of a stream of oxygen, and observed the gain in
weight. His results for the atomic weight varied from 239.49 to
239.76, an extreme difference of 0.27, or 0.11 per cent. The average
was about 239. G. The chief probable cause of error in this method is
the difficulty which is always experienced in forming a more voluminous
solid from a less voluminous one. Uranous oxide has a specific gravity
of 10.2, while the " Uranoso-uranic " oxide has a specific gravity of
only 7.3. The great increase of volume which occurs when the higher
oxide is formed must tend to protect particles of the lower oxide from
the action of the oxygen. Hence the gain in weight will be too small,
and the apparent atomic weight of the metal too large.* It is clear
that a very small deficiency in the weight of the higher oxide must
cause a great increase in the apparent atomic weight.
Moreover, any incompleteness in the reduction by which the lower
oxide was prepared, or any retention or occlusion of gases within this
oxide, would also tend to raise the apparent atomic weight. Hence one
is inclined to believe, even without further evidence, that Zimmermann's
result for uranium must be too high.
A new determination of the atomic weight of uranium has recently
been made by J. Aloy.f The method employed differs materially from
any previously used in uranium work. The values obtained are derived
* Compare Richards and Baxter, These Proceedings 34, 351 (1898). Ztsch.
anorg. Chem. 21, 251 (1890).
t Comptes Rendus, 132, 551 (1901). This work is discussed rather fully here,
since it is too recent to have been included in Clarke's book.
368
PROCEEDINGS OP THE AMERICAN ACADEMY.
from the ratio between the weight of nitrogen and that of uranous oxide
contained in crystallized uranyl nitrate. Uranyl nitrate was purified by
repeated crystallization. A quantity of the pure nitrate, the weight of
which need not be known, was put iuto a boat, and the boat surrounded
by a section of platinum tube, to prevent loss of material. The whole
was placed in a combustion tube between spirals of reduced copper.
One end of the combustion tube was connected with a carbon dioxide
generator, and the other with an absorption apparatus containing a con-
centrated solution of potash.
After sweeping the air out of the apparatus with a current of carbon
dioxide, the nitrate was heated so long as evolution of nitrogen occurred,
the temperature being finally raised to red heat. The reduced copper
was kept at red heat throughout the operation. When it was certain
that no more nitrogen was evolved, the green oxide remaining in the
boat was reduced by hydrogen to uranous oxide and weighed. The
nitrogen was transferred to a measuring tube reading to tenths of a
cubic centimeter. From the ratio of the weight of this volume of
nitrogen to the weight of the oxide, the atomic weight is calculated.
The following are the results of the eight determinations given : —
Atomic Weight of Uranium.
N = 14.04
Volume of nitrogen, 15.25 cc.
Atomic wt. of uranium, 239.3
33.5
239.4
38.0
239.6
52.5
239.5
81.25
239.4
125.0
239.5
151.2
239.4
165.0
239.4
This method has the merit of simplicity, and does not involve the
weight of the crystallized salt. There are, however, several sources of
possible constant error that have not been taken into account. When
crystallized uranium nitrate is heated, it first melts in its water of crystal-
lization. As in all similar cases, it requires the very greatest care to
prevent spattering while the crystal water is being driven off. It was
undoubtedly as a precaution against loss of material in this way that
Aloy used his platinum tube. By the time the crystal water is expelled,
the fused mass has hardened into a solid cake, changing in color from
yellow to orange, and finally to the green of urano-uranic oxide, U308.
This method of preparing the green oxide from pure uranyl nitrate
RICHARDS AND MERIGOLD. — ATOMIC WEIGHT OP URANIUM. 369
was used in the work to be described in the following pages. It was
invariably found, however, that during the decomposition of the dried
nitrate, and the subsequent oxidation, the oxide first produced forms a
protecting crust, as it were. This prevents, or at least very materially
retards, the decomposition of the material within the interior, even when
the temperature is maintained for several hours at red heat. On the
outside, the material had the appearance of being completely converted
to oxide. On powdering the lumps, however, and again heating, there
was in every case a further evolution of nitric fumes. Moreover, nitrogen
itself is often retained by oxides prepared in this way.* It seems thus
extremely probable that the quantities of nitrogen measured by Aloy
were in every case too small. Obviously, until this point is definitely
settled, Aloy's results must be regarded with more or less suspicion.
It has been pointed out that reduction is usually much more complete
than oxidation. f During the reduction of an oxide, there is formed,
jierhaps, by the removal of a portion of the oxygen, a kind of skeleton
framework, giving to the remaining substance a porous structure which
enables the reducing gas to penetrate farther into the interior of the
mass, until reduction is complete. Owing to this action, it is probable
that when the green oxide of uranium is finally reduced by hydrogen,
all the nitrogen is expelled, and the final product is pure uranous oxide.
Consequently, the weight of uranous oxide used in the calculation is
probably nearly correct, the principal error being in the volume of
nitrogen.
Aside from this special objection to the use of this method in its
application to uranium, there is the general objection to the use of such
a method where great accuracy is desired. The exact measurement of
small quantities of gas offers considerable opportunity for error, especially,
when, as in this case, the gas is first to be transferred from the collect-
ing to the measuring apparatus. When the volume or weight of a gas
is involved in an atomic weight investigation, it is customary to work
with as large volumes as possible, thus reducing to a minimum the
effect of the errors inevitably connected with the measurement of the
gas. The exact measurement of a volume no larger than 165 cubic
centimeters, even, — the largest volume measured by Aloy, — is a
matter of considerable experimental difficulty, while with the smaller
volumes, 15, 33, and 38 cubic centimeters, errors of at least 0.1% are
* Richards and Rogers, These Proceedings, 28, 200 (1893) ; also Richards,
Ibid. 33, 399 (1898).
t Richards and Baxter, loc. cit.
vol. xxxvn. — 24
370 PROCEEDINGS OF THE AMERICAN ACADEMY.
not only possible, but extremely probable. A difference of one tenth of
one per cent in the volume of nitrogen makes a difference of 0.3 in the
value of the atomic weight. The errors of collection and transference
of the gas are more likely to result in reading too small rather than too
large volumes, giving too high values for the atomic weight.
From these considerations, it is evident that Aloy's results are at least
somewhat doubtful. Aloy gives notice of his intention to apply this
method to the determination of other atomic weights, but it is to be
hoped that before doing so he will clear up some of the doubtful points
in connection with the process. As carried out in this investigation, the
method certainly is not a valuable addition to the methods of atomic
weight determination.
From the earlier results Clarke computed the value 239.6, while the
German Committee recommend 239.5. Both figures are practically
identical with Zimmermann's figures.
The investigation herein described was undertaken with the hope that
by increasing the experimental basis of our knowledge of the subject, we
might be able to reduce to somewhat narrower limits our present uncer-
tainty in regard to the real value of this constant.
Preliminary Work upon the Preparation, Properties, and
Methods of Analysis of Some Uranium Compounds.
In view of the well known advantages of the halogen compounds for
accurate analysis, when these compounds can be prepared and weighed
iu a state of purity, — it seemed desirable to use a halogen compound as
the basis of a determination of the atomic weight of uranium.
Of the four chlorides of uranium known to exist, none can be pre-
pared in a state of purity that is beyond question. Green uranous
chloride, UC14, which results from passing dry chlorine over a mixture
of uranium oxide and carbon at red heat, is easily converted to the
pentachloride, UC15, by further action of chlorine at high temperatures.
There can be no positive evidence that the green chloride would not
contain some of the pentachloride, and if the attempt is made to prepare
the pentachloride from the green chloride, it is equally difficult to be sure
that the conversion is complete. The trichloride, UC13, is made by reduc-
ing the tetrachloride with hydrogen, and here again it is difficult to be
sure that the tetrachloride is completely reduced. Uranyl chloride,
UOoCL, cannot be prepared in the dry state.
It is extremely probable, then, that any of the chlorides will contain
larger or smaller quantities of a higher or lower chloride. It may be
RICHARDS AND MERIGOLD. — ATOMIC WEIGHT OP URANIUM. 371
observed, in this connection, that Zimmermann used the chlorides in his
vapor density determinations, and his analyses show good agreement.
This does not show conclusively, however, that his material was free
from small, but fairly constant quantities of higher or lower chlorides as
impurities.
On the other hand, bromine forms with uranium only three distinct
compounds : the tribromide, UBr3 ; uranous bromide, UBr4; and the
oxybromide, or uranyl compound, U02I>i\>. The tribromide can be
produced only from the tetrabrotnide by the action of reducing agents.
Uranyl bromide, U02Br2, has been certainly formed only in solution,
resulting in hydrated crystals. It has never been definitely obtained in
an-hydrous form. Zimmermann made many attempts to form the penta-
bromide, corresponding to the pentachloride, by passing bromine at
high temperatures over sublimed uranous bromide. Every attempt
gave negative results, showing that at temperatures up to the subliming
point of uranous bromide higher bromides cannot exist. Since higher
bromides are non-existant under the conditions prevailing in the forma-
tion of the tetrabromide, the objections to the use of the tetrachloride
are not applicable in the case of uranous bromide. The investigations
of Zimmermann* have shown that the tetrabromide can be formed in
an apparently definite state. It seemed probable, therefore, from the
literature on the subject, that in uranous bromide we had a conqjouud
well suited to the purposes of our investigation.
The method of preparation followed at first was essentially that
described by Zimmermann.* In an apparatus constructed wholly of
glass, a mixture of dry nitrogen and bromine vapor was passed over a
mixture of the green oxide of uranium, U308, and pure carbon. The
air was first thoroughly swept out of the apparatus by a current of
nitrogen, and the oxide was heated to a high temperature. When the
bromine vapor was passed in, uranous bromide formed, and sublimed in
brilliant crystalline plates of a brownish color. After cooling in a
current of nitrogen, the sublimate was transferred to a weighing bottle.
At this point, however, unexpected difficulties arose, owing to the rapid
oxidation of the bromide. Uranous bromide is extremely deliquescent,
and forms with water and oxygen the oxybromide, with liberation of
hydrobromic acid. Consequently, when exposed to the moist air of the
laboratory even for the short time required for removing the sublimate
from the combustion tube, the bromide loses its brilliant lustre, and
* Annalen der Chemie, 216,3.
372 PROCEEDINGS OF THE AMERICAN ACADEMY.
assumes a dull, greenish yellow appearance, due to formation of the oxy-
salt. If not protected from further action of moist air, the salt liquifies
completely in a surprisingly short space of time.
In an attempt to change the coating of oxybromide back to the
normal salt, recourse was had to the method which has been used suc-
cessfully in many atomic weight investigations carried on in this labora-
tory. The salt was transferred to a platinum boat and placed, with a
weighing bottle of suitable size, in a glass bottling apparatus* A
stream of dry hydrobromic acid gas was then passed over the bromide at
a temperature just below the subliming point of the salt. This treat-
ment, however, fails to restore the original brilliant appearance of the
freshly sublimed bromide. The yellow color of the oxybromide still
remains. Apparently the oxybromide, once formed, cannot, by this
method, be reduced to the normal uranous bromide.
In the previous investigations upon zinc, magnesium, nickel, and
cobalt, in which this method of converting oxy-salts to the normal com-
pounds has been used, the presence of even minute quantities of oxy-salt
was made known by the opalescence of the solutions on account of the
insolubility of these salts. With uranium, however, this method of
detecting the presence of uranyl bromide cannot be used, for the oxy-
bromide of uranium is even more soluble than uranous bromide.
The analysis of uranous bromide presents further difficulties. All
uranous salts reduce silver nitrate. When a solution of silver nitrate,
slightly in excess of the calculated amount, is added to a solution of
uranous bromide, the silver bromide first precipitated is probably mixed
with metallic silver; for if the silver bromide is filtered off, and the
filtrate set aside, finely divided metallic silver soon separates. If a
lar^e excess of silver nitrate is added to the uranous bromide, a brilliant
purple precipitate is obtained. It is possible that the precipitate
may be a mixture of finely divided metallic silver and argentic
bromide, or perhaps of normal argentic bromide and the long sought
sub-bromide. Although this is an interesting phenomenon, it was
not considered advisable to interrupt the research at this period for
the length of time necessary for an investigation. The addition of
nitric acid prevents the formation of this colored precipitate, but owing
to the danger of the loss of bromine, this is not an advisable expedient.
Of course it is possible to determine the bromine by first precipitating
the uranium and adding silver nitrate to the filtrate, but this introduces
* For a description of this apparatus, see These Proceedings, 32, 59.
RICHARDS AND MERIGOLD. — ATOMIC WEIGHT OF URANIUM. 373
a complexity of operations incompatible with the degree of accuracy
requisite in an atomic weight investigation.
On account of these formidable difficulties in the preparation and
analysis of pure uranous bromide, it was thought best to search for some
compound which offered fewer obstacles. Jt will be seen that this
search was vain, although it required many mouths.
In view of the great tendency of uranous bromide to oxidize, under
ordinary conditions, the use of uranyl bromide seemed to offer the
simplest solution of the problem. Anhydrous uranyl bromide has never
been prepared in a pure state. In the preparation of uranous bromide,
if the nitrogen used contains a little oxygen, or if traces of moisture are
present, there is formed, in addition to the uranous bromide, a yellow
powder, very different in appearance from the brown color of finely
divided uranous bromide. This powder has been assumed by various
investigators to be the oxybromide. Owing to the fact that it is always
mixed with uranous bromide, an analysis has never been obtained.
There seemed to be, however, some basis for belief that under suitable
conditions of temperature, moisture, and oxygen supply, it might be
possible to obtain anhydrous uranyl bromide entirely free from the
uranous compound. With this end in view, the green oxide, without any
admixture of carbon, was heated in a stream of bromine, also in a
current of hydrobromic acid. In each case there was apparently no action
whatever other than a partial and gradual reduction to the black oxide.
This slight reduciug action is probably not due to the gases used, in the
sense of being peculiar to them, for Zimmermann has shown that this
reduction takes place whenever the green oxide is heated in a current of
inactive gas such as nitrogen or carbon dioxide. *
Both moist and dry gases were used. Mixtures of these gases and air
were also tried, at different temperatures. The green oxide was then
reduced by hydrogen to uranous oxide, U02, and this was then treated
with various combinations of dry and moist bromine vapor, hydrobromic
acid, and air, at various temperatures. Again the results were negative.
Under these conditions the bromine did not combine to the slightest
extent with the uranium. Since combination fails to take place, even in
the presence of considerable quantities of oxygen, there is naturally
some cause to doubt that the light colored powder above mentioned is
really an oxybromide. Possibly it is, after all, uranous bromide in a
different state of aggregation.
* Loc. cit. See also Eichards, These Proceedings, 33, 423 (1898).
374 PROCEEDINGS OF THE AMERICAN ACADEMY.
The hydrated uranyl bromide is more easily obtained. The green
oxide was reduced by hydrogen to urauous oxide, suspended in water,
and heated with bromine on the steam bath. After driving off the
excess of bromine, uranyl bromide remains in solution. The solution
may be evaporated to the consistency of a thick syrup, and even under
the best conditions the yield of crystals is very small. Moreover, it is
almost impossible to wash the crystals free from the mother liquor,
since they are extremely soluble in water and alcohol, and ether decom-
poses the compound, setting free bromine. Hence uranyl bromide was
abandoned.
Of the iodine compounds of uranium, the iodate alone seemed promis-
ing. This compound has been prepared and described by A. Ditte,*
who assigns to it the anhydrous formula U02(I03)2. The iodate was
prepared by us as follows : —
To a solution of uranyl nitrate, containing much nitric acid, was added
a solution of iodic acid, prepared by warming finely powdered iodine
with nitric acid of specific gravity 1.50. Both solutions were heated to
boiling before mixing. Uranyl iodate is precipitated as a yellow, finely
crystalline salt, but slightly soluble in water at ordinary temperatures.
At 100°, however, if some nitric acid is added, it is possible to obtain
a solution containing ten grams of iodate to the litre. On cooling,
2.5 to 3.0 grams of iodate crystallize out. By recrystallizing a few
times, in sufficiently large vessels, it is possible to obtain a compound in
a high state of purity.
The method of preparation described above is that recommended by
Ditte. Although Ditte's course of procedure was carried out as ex-
actly as possible, the compound obtained differed from that which he
describes. Instead of being anhydrous, it contained one molecule of
water. Inasmuch as Ditte's statement of the amount of nitric acid
which he used is extremely vague, different concentrations were tried,
from a solution slightly acid up to one containing twenty-five per cent of
strong nitric acid. In every case the hydrated compound was obtained.
Ditte did not recrystallize his compound, but our recrystallized product
was identical with that which was only once precipitated. The analysis
given is the average of ten concordant analyses of material prepared
from both hot and cold solutions. Both recrystallized iodate and that
precipitated only once are represented. The method of analysis is
described below.
* Annales de Chimie et de Physique, 6th Series, 21, 158 (1890).
RICHARDS AND MERIGOLD. ATOMIC WEIGHT OF URANIUM. 375
Analysis of Uranyl Iodate.
Found.
Caleul:itril for
U02(I03),1IJ>.
Uranous oxide
42.54%
42.34 %
Iodic acid
54.84
54.84
Water (by difference)
2.62
2.82
100.00% 100.00%
In determining the composition of the iodate, a weighed quantity of
the substance was used, and the percentage composition by weight cal-
culated in the usual manner. For an atomic weight determination,
however, any method which involves the original weight of a salt
crystallized from solution as a factor in the calculation must of course be
avoided on account of the ever present possibility of included mother
liquor. It was necessary, then, to determine directly the ratio of
iodine to uranium, or to uranium oxide. To determine the uranium,
advantage was taken of the behavior of the iodate on ignition. When
heated, the iodate is decomposed, water, oxygen, and iodine being given
off, leaving uranium oxide. The process was carried on in an ordinary
combustion tube of hard glass, a current of dry air being passed through
the tube. Since Zimmermann has shown that the green oxide under-
goes partial reduction at high temperature unless in an atmosphere of
oxygen, * a stream of oxygen was finally passed through the tube. The
oxide was then cooled in an atmosphere of oxygen. Treated in this
way, the decomposition of the iodate is not complete. Some iodine
always remained in the oxide, even when the heat was maintained for
three hours at a temperature just below the softening point of the com-
bustion tube. To correct for this amount of iodine, the oxide was
weighed, dissolved in dilute nitric acid, and the iodine precipitated as
argentic iodide. The amount of iodine found in this way varied from
0.1% to 1.0% of the total iodine, according to the duration of the period
of ignition.
Iodine was determined in another sample of material exactly similar
to that used for the uranium. The method was, briefly, reduction of
the iodate by sulphurous acid, and precipitation with silver nitrate.
Stas has shown that silver iodate can be converted completely and with-
out loss into silver iodide by the use of sulphurous acid,f and the same
* Annalen der Chemie u. Pharmacie, 232, 287 (1886).
t Untersuchungen iiber die Gesetze der chemischen Proportionen liber die
Atomgewichte u. ihre gegenseitigen Verhaltnisse, J. S. Stas. Aronstein's transla-
tion, p. 69.
376 PROCEEDINGS OF THE AMERICAN ACADEMY.
method applies equally well to uranium iodate. The iodate was sus-
pended in 200 c.c. of water acidified with 20 c.c. sulphuric acid, cooled in
ice to 0°, and pure sulphur dioxide was passed in until the solution
smelled strongly of this reagent. The flask was then removed from the
ice and shaken occasionally. From three to four hours is required
before complete reduction takes place and the last traces of iodate go
into solution. When completely reduced, silver nitrate is added, and
heated to 60° in order to cause the more coherent deposition of the
jjrecipitate.* Thus it was found possible to convert the" insoluble iodate
into soluble iodide without loss of iodine.
In this way the ratio of uranium oxide to iodine may be determined,
regardless of the presence of occluded water in the iodate used, provided
that the amount of water occluded be exactly the same in each of the
samples. It would obviously be more satisfactory to determine both
uranium and iodine in the same sample, provided a sufficiently simple
method could be found.
The following method was found to fulfil the required conditions
fairly well. A quantity of the iodate was placed in a boat in a com-
bustion tube, to one end of which was attached, by a ground glass joint,
a weighed U-shaped tube. The free end of this tube was drawn out and
fused to a smaller tube which dipped into a solution of sulphurous acid.
On heating the iodate in a stream of air and oxygen, the salt was decom-
posed and the iodine was carried over and condensed in the U-tube,
which was packed in ice. The small quantity of iodine vapor not con-
densed was collected in the sulphurous acid and precipitated as silver
iodide. The heating: was contiuued for an hour after no more iodine
could be seen coming off. The end of the U-tube was then sealed by
fusing off the small tube, and the other end was closed by a ground glass
stopper immediately after disconnecting from the combustion tube. In
this way about ninety-nine per cent of the total iodine was weighed
directly as free iodine. Of course the small amount of iodine remaining
in the oxide after ignition had to be determined separately, as already
described. By this method the amount of iodine found was practically
identical with that found by the sulphurous acid method.
In determining the iodine present in the oxide after ignition, it has
been assumed that the iodine is present as iodide. Although it is hard
* When silver iodide is precipitated in the presence of sulphurous acid, the
supernatant liquid does not become clear enough to filter even after several days,
unless heated to 60°.
Vide Stas, " Untersuchungen," p. 69.
RICHARDS AND MERIGOLD. — ATOMIC WEIGHT OP URANIUM. 377
to believe that at the temperature employed any of the iodine can exist
as iodic acid, it is impossible to prove the point experimentally. The
uncertainty in regard to this point renders the use of the method inadvis-
able where the greatest possible accuracy is desired. Hence none of
these analyses have any significance as a basis for computing the atomic
weight of uranium.
Besides the bright yellow, slightly soluble iodate, we prepared a paler
yellow, more soluble, and more highly hydrated salt, which suffers transi-
tion quickly into the earlier compound at a high temperature and more
slowly at a low temperature. Double iodates with sodium and potas-
sium were also prepared. Some of our observations were inconsistent
with the published record concerning the subject ; but in spite of our
desire to clear up the uncertainty and to study the rather interesting
transition phenomena, we abandoned the iodates because none of them
gave promise of a precise basis for the determination of the desired
atomic weight.
The next compound investigated was the oxalate, which has the com-
position UO2C2CV 3H20. Owing to the comparatively slight solubility
of this compound it can be obtained in a state of great purity by a few
crystallizations.
The best method of analysis is that of dry combustion, the carbon
dioxide being absorbed in potash in the usual manner. The uranium
is left in the combustion tube as the green oxide, U308, and consequently
can be compared directly with the weight of carbon dioxide obtained. This
obviates the necessity of using the weight of the oxalate as a factor in
the calculation of the atomic weight, and so eliminates the error due to
included water. As already mentioned, this method has been used by
Ebelrnen and Peligot in their determination of the atomic weight of ura-
nium. There is in this method a possible source of error, difficult of
detection and correction, but none the less dangerous, in the possibility
that the uranium oxide may after combustion still retain traces of carbon.
Moreover, it became evident, after a few analyses had been made, that
combustion analysis, as ordinarily conducted, is an exceedingly question-
able method where great accuracy is desired. The great difficulty in
obtaining absolute "blanks "is well known. Our experience amply
confirmed the observations of Mabery,* Auchy,t and others in regard to
* Inaccuracies in the Determinations of Carbon and Hydrogen of Combustion,
C. F. Maberyt Journal Am. Chera. Soc, 20, 510 (1898).
t George Auchy, Journal Am. Chem. Society, 20, 243 (1898).
/
378 PROCEEDLNGS OF THE AMERICAN ACADEMY.
the loss of water and possibly of carbon dioxide from the ordinary form
of potash bulbs. We also found a single sulphuric acid tube entirely
insufficient to absorb all the water. Clearly, then, if we were to use this
method, an elaborate investigation of the form of apparatus, method of
procedure, and limits of error, was absolutely imperative. The use of
the oxalate, however, did not seem sufficiently promising to warrant the
necessary expenditure of time.
After thus investigating the uranium compounds which seemed likely
to furnish a suitable basis for an atomic weight determination, anhydrous
uranous bromide, in spite of its disadvantages, seemed most likely to fulfil
the necessary requirements. As already mentioned, this confound oxi-
dizes with the greatest ease on exposure to moist air. It was necessary,
therefore, to devise apparatus which should preclude any possibility of
bringing the sublimed bromide in contact with the air of the laboratory
until it had been collected and weighed. After much experimenting
with different forms of apparatus, the following method was adopted.
Preparation and Collection of Puke Uranous Bromide.
The mixture of urano-uranic oxide and carbon was placed in a porce-
lain boat within the larger of two " telescoping " porcelain tubes. The
portion of the tube containing the oxide was heated in a Fletcher furnace,
and after thoroughly sweeping out the apparatus with dry nitrogen, a
mixture of dry nitrogen and bromine vapor passed over the oxide.
The sublimed bromide collected near the inner end of the smaller porce-
lain tube. The very efficient and elaborate desiccating apparatus which
served so well in the work on the atomic weights of cobalt and nickel,
was very kindly given by Dr. Baxter for use in this investigation.*
This apparatus , with slight modifications, was used for drying the nitro-
gen and bromide, and was connected by a ground glass joint with the
porcelain combustion tube.
With this apparatus traces of air diffused through the annular joint
between the porcelain tubes, forming a coating of oxide on the inner
tube.f In the case of uranium, the oxide is found to be copiously mixed
with the sublimate also. This diffusion of air takes place even when the
outer end of the inner porcelain tube is nearly closed, thus making a
considerable outward current within the tubes.
* For a full description of this apparatus see There Proceedings, 33, 124
(1897).
+ In the case of cobalt and nickel this oxide was easily removed by subsequent
treatment, but in the present case removal was impossible.
RICHARDS AND MERIGOLD.
ATOMIC WEIGHT OF URANIUM.
879
In order to obviate the difficulty and exclude air a glass jacket was
slipped over the joint between the tubes. The construction and use of
this jacket will be made clear by reference to the accompanying drawing.
Section of Subliming and Bottling Apparatus.
A, outer porcelain tube fitted with ground glass joint B; C, inner porcelain tube
with ground-glass stopper D ; E, boat containing oxide and carhon ; F, furnace ;
G, glass jacket; H, H, H, H, packing of asbestos wool; I, weighing bottle; L,
tube for admitting nitrogen, sliding within tube M through rubber connection N,
and carrying at its end stopper 0 of weighing bottle; P, sublimate; R, rod for
removing sublimate.
The jacket was drawn down at the ends, so as to fit the porcelain
tubes A and C as well as possible, and the spaces between the tubes and
the jacket were packed tightly with asbestos wool. This packing makes
a joint sufficiently tight to withstand a pressure equal to that of eight or
ten centimeters of water. The jacket was provided with a long tube, M,
within which slid a second tube, L, connection being made by 'means of
the short piece of rubber tubing, N. To the end of the inner tube was
attached, by platinum wires, the stopper, O, of the weighing bottle. The
outside diameter of L was very little less than the inside diameter of
M, thus leaving very little space between the walls of the two tubes.
For this reason, and also on account of the length of the tube M, — about
fifteen centimeters, — there was little danger of bromine diffusing up in
sufficient quantities to attack the rubber connection, N. Even if this
were the case there could be no possibility of contamination of the sub-
380 PROCEEDINGS OF THE AMERICAN ACADEMY.
limate thereby, since there was always a constant outward pressure of
bromine during the sublimation. The outer end of L was connected
with the nitrogen supply of the desiccating apparatus. All glass joints
and stop-cocks were lubricated with syrupy phosphoric acid.
The method of procedure was as follows : In the porcelain boat, E,
was placed an intimate mixture of urano-uranic oxide and pure carbon,
the carbon being about twenty per cent of the weight of the mixture,
thus insuring a large excess of carbon. The apparatus was then thor-
oughly swept out by nitrogen, which enters at B and L simultaneously.
After the air was completely expelled, the combustion tube was grad-
ually raised to a high temperature by the blast lamp. Heating in a
current of nitrogen was then continued for three hours at least, some-
times longer, in order to insure complete removal of all traces of air and
moisture. During this and subsequent operations, the outlet of the
stopper D of the inner tube was nearly closed by asbestos wool, thus
maintaining a constant and considerable pressure within the apparatus,
and hindering the diffusion of air. After this preliminary heating in
nitrogen, bromine vapor was passed in through B. During the first trials
of the apparatus it was our practice to keep a slow current of nitrogen
passing in at L during the sublimation. This kept the jacket entirely
free of bromine, a very slow current of nitrogen being sufficient to keep
any bromine from passing between the walls of the porcelain tubes. It
was found, however, that traces of air diffused through the permeable
asbestos packing, and were of course carried into the combustion tube by
the current of nitrogen, forming on the inner tube a coating of oxide,
and contaminating the sublimate. In order to avoid this, the nitrogen
was shut off from L sometime before turning on the bromine. After
turning on the bromine, the jacket slowly filled with dilute bromine
vapor. While the greater part of the sublimate collected within the
inner tube, a little collected between the walls of the two tubes, almost
sealing the annular space. This sublimate, which collected on the outside
of the inner tube, is a valuable indicator of the condition of the subli-
mate within. In the presence of mere traces of oxygen the lustrous
brown color of the uranous bromide gives place to a dull yellow color
easily distinguishable. Comparatively small quantities of oxygen form a
coating of black oxide. When the sublimation is conducted according to
the method described, the outside of the inner tube is free from any traces
of the supposed oxybromide or of oxide, thus showing that no appreciable
quantity of moist air could have reached the innermost portions of the
sublimate. The best proof of the purity of the sublimate is of course
RICHARDS AND MERIGOLD. — ATOMIC WEIGHT OP URANIUM. 381
found in the agreement of analyses of substance formed under various
conditions of bromine supply.
After the bromine had been run for about one and a half hours, the
sublimate was cooled for three hours in a current of nitrogen. When
the tubes were thoroughly cold, nitrogen was finally passed into the
jacket through L, in order to sweep out any traces of bromine that
might still remain. The inner tube, containing the sublimate, was then
carefully drawn out until the inner end reached a position over the
mouth of the weighing bottle, indicated in the diagram by the dotted
line. This can be done without seriously disturbing the asbestos pack-
ing, a rapid current of perfectly dry nitrogen being admitted meanwhile
through L. By means of the glass rod, R, the sublimate was pushed
out of the tube and dropped into the weighing bottle, I. The tube
L, carrying the stopper, was then pushed down and the stopper in-
serted. The stopper was held by the platinum wires so lightly that
after pushing it into place the tube L could be withdrawn, leaving the
stopper inserted in the bottle.
Thus uranous bromide was sublimed, collected, and bottled up in an
atmosphere of dry nitrogen ready for weighing, without once coming
in contact with the air of the laboratory. That the apparatus is effective
for the purpose intended, and capable of producing material of constant
composition, was shown by the first rough analyses of uranous bromide,
which yielded 57.41, 57.41, and 57.42 per cent bromine respectively.
These analyses were made with material that had not been purified, but
served to show the constancy of composition of the sublimate ; for not only
was the length of time occupied in the sublimation varied, but in one case
the sublimate was cooled in bromine instead of in nitrogen. Of course if
an appreciable amount of an oxygen compound were formed, by diffusion
of air or moisture, there would almost certainly be discrepancies in the
results, since it is hardly conceivable that under the varying conditions
exactly the same quantities of oxy-salt should be formed each time.
Because the specific gravity of uranous bromide was unknown, the fol-
lowing determinations were made : 2.0328 grams of the salt displaced on
one occasion 0.3332 gram of kerosene at 21°, and at another trial 0.3322
gram. The kerosene had been redistilled, and only the high boiling
portion was used. The density of the kerosene at 21°, referred to
water at 4°, was 0.7919. Hence the specific gravity of the uranous
bromide was (1) 4.830 and (2) 4.846, giving as the mean 4.838.
This value was used in reducing the observed weights of bromide to
the vacuum standard.
382 PROCEEDINGS OF THE AMERICAN ACADEMY.
During the weighing in the final analyses, the bromide of uranium
was still surrounded by an atmosphere of pure dry nitrogen in the
tightly stoppered weighing bottle. Since this bottle had been full of
dry air when it was first weighed, a small correction had to be applied
on this account. The difference in weight between 6.70 cubic centi-
meters (the interior volume of the weighing bottle) of air and the same
volume of nitrogen at 20° C. is 0. 0002(35 gram. Of this nitrogen a
gram of urauous bromide displaced - - = 0.206 cubic centimeters, or
4.84
0.24 milligram, while the brass weights used in weighing the bromide
displaced 0.145 milligram of air. Hence in vacuum a gram of uranous
bromide would weigh 0.265 + 0.24 — 0.145 = 0.36 milligram more
than Jthe observed weight, while two grams would weigh 0.265 +
2(0.24 — 0.145) = 0.46 more than the observed weight. All the weights
given in the tables are corrected in this way to the vacuum standard.
Methods of Analysis.
By the use of these devices we were able to prepare and weigh pure
uranous bromide in a definite state. There still remained, however, the
problem of devising a suitable method of analysis. As previously men-
tioned, all uranous compounds reduce silver nitrate, making impossible
the usual method of procedure in halogen determinations.
The method of precipitating the uranium and determining bromine in
the filtrate involves too much danger of loss of material in the multiplic-
ity of operations. The most satisfactory solution of the problem seemed
to be to oxidize the compound to the uranyl salt, provided this could be
done without loss of bromine. Nitric acid is of course effective as an
oxidizing agent, but the oxidation is accompanied by loss of bromine.
After much experimenting, hydrogen dioxide was found to be the most
suitable oxidizer. From neutral solutions of uranium compounds, hydro-
gen dioxide precipitates a hydrated peroxide of uranium. If the solution
is slightly acid, this precipitation is prevented and the uranous compound
completely oxidized to the uranyl state. The weighed sample of uranous
bromide was dissolved in considerable water — at least 400 cubic centi-
meters of water to each gram of bromide. The bottle containing the
bromide was opened by means of a suitable glass fork, either below the
water or just above the surface, so that it could be instantly submerged,
and thus avoid loss of hydrobromic acid by the action of moist air. The
calculated volume of a standard solution of pure hydrogen dioxide was
then diluted to about 100 c.c, one cubic centimeter of pure dilute sul-
EICHARDS AND MERIGOLD. — ATOMIC WEIGHT OF URANIUM. 883
pluiric acid was added, and the mixture was slowly run into the solution
of uranous bromide. The screen color of the uranous salt soon changes to
the yellow color characteristic of uranyl compounds. On adding the
first few cubic centimeters of the dilute hydrogen dioxide solution, a
greenish white precipitate came down. Addition of more of the acid
dioxide solution redissolved it, and the resulting solution was perfectly
clear. This peculiar hydrolytic action is due to the acid, and not to the
hvdric dioxide, for the same reaction occurs if dilute sulphuric acid alone
is added to the solution.
The explanation of this interesting phenomenon, which is just the
opposite of what might have been expected, is, undoubtedly, that the
bromide is already hydrolyzed to a great extent by merely dissolving in
water. The hydrate is probably in solution in the colloidal state. Evi-
dence of this is found in the fact that if the clear aqueous solution of
uranous bromide is allowed to stand exposed to the air, a hydrate gradu-
ally separates, giving to the solution a cloudy, murky appearance. After
two or three days this precipitate disappears, giving place to a clear
yellow solution of oxybromide and hydrobromic acid. The addition of
sulphuric acid coagulates the colloid before it can all be converted into
uranyl salt.
In order to be sure that no bromine or hydrobromic acid is lost by
this method of oxidation, the following experiment was made. 0.5 gram
of bromide was dissolved in 250 c.c. of water, 50 c.c. of dilute sulphuric
acid (1 :10) was added, and the hydrogen dioxide solution was run in.
This was done in a closed flask, similar in construction to a gas washing
bottle. A current of air was drawn through the bottle and then through
starch solution containing potassium iodide to see if bromine is liberated.
Not the slightest trace of blue color appeared in the starch solution, even
after adding a large excess of hydropen peroxide and allowing it to stand
over night. A test for hydrobromic acid was sought in a similar way,
by drawing the air through a solution of silver nitrate, again with nega-
tive results, as was to have been expected. These experiments show
conclusively that uranous bromide can be oxidized completely by hydro-
gen dioxide, without loss of bromine.
Silver nitrate, in moderately concentrated solutions, is not acted upon
by a three per cent solution of hydrogen peroxide. Consequently a con-
siderable excess of the latter reagent could do no harm. Nevertheless
care was taken never to add more than the calculated amount of hydro-
gen dioxide. Moreover, the solution of hydrogen dioxide used contained
only one per cent of this reagent, and this was diluted ten times before
384 PROCEEDINGS OF THE AMERICAN ACADEMY.
adding to the bromide solution, thus reducing to a minimum the possi-
bility of too vigorous oxidation, with consequent liberation of bromine.
After the oxidation, bromine was precipitated by pure silver nitrate in
the usual manner. This precipitation was conducted in an Erlenmeyer
flask fitted with a ground glass stopper. The silver bromide was col-
lected on a Gooch crucible, and dried in an electrically heated drying
oven. Of course the asbestos shreds carried away in washing the silver
bromide were collected by passing the filtrate and wash water through a
fine filter, and their weight was added to that of the silver bromide.
The bromine determination was carried on in orange colored light.
It was found in the work upon cobalt and nickel that the porcelain
tube is attacked by bromine vapor at the high temperature employed
during the sublimation, with the result that sodium bromide was always
present in the sublimate. In these investigations this impurity was de-
termined by the reduction of the bromide to the spongy metallic state by
means of hydrogen, and extraction by water.* A somewhat similar
method was tried with uranium. Since hydrogen reduces uranous bro-
mide only to the tri-bromide, the bromide was ignited in a current of air
and the resulting oxide leached with water. It was found to be impos-
sible to oxidize the bromide completely. A little uranous bromide
invariably remained and was washed out with the alkali. Both dry and
moist air was tried, also ignition in steam, but in every case uranium was
washed out in considerable quantity.
Precipitation of the uranium by hydrogen dioxide was next tried, but
it was found impossible to precipitate the uranium completely. The
rather unsatisfactory method of determining the sodium in the filtrate
from the bromine precipitation, or in a new sample of uranous bromide
as nearly similar as possible, after removing the uranium with ammo-
nium sulphide, appeared to be the only available method. The filtrate
and wash waters from the bromine precipitation were evaporated in
platinum to small bulk, and the uranium and excess of silver precipitated
by pure colorless ammonium sulphide. This reagent precipitates uranium
completely. The filtrate was then evaporated to dryness, the ammonium
salts expelled by ignition, and the residual sodic nitrate converted to the
sulphate and weighed as such. Of course these operations were all con-
ducted in platinum vessels. This method of work is not wholly satisfac-
tory, on account of the complexity of operations involved, but it seems to
be the only practical method.
* These Proceedings, 34, 329, 359 (1899).
RICHARDS AND MERIGOLD. ATOMIC WEIGHT OF URANIUM. 385
Purification of Materials.
As the source of uranium, commercial " chemically pure " uranium
acetate was used.* This was first converted to the chloride on account of
the greater solubility of this compound, — by precipitation as ammonium
uranate and redissolving in dilute hydrochloric acid. To the hot and
slightly acid solution, pure sulphuretted hydrogen was added to satura-
tion. The free acid was then neutralized with amnionic hydroxide, a
slight excess of the alkali was added, and more sulphuretted hydrogen
was run in. In this way some uranyl sulphide was precipitated, in order
to sweep down with it any colloidal sulphides of the higher groups which
might otherwise escape removal. The excess of sulphuretted hydrogen
was boiled off, and after standing over night the supernatant liquid was
decanted through a washed filter.
The next step depended upon the fact that uranium remains iu a
solution of the double carbonate of ammonium and uranium, in the
presence of an excess of ammonium sulphide, while all the other members
of the aluminum and iron groups are thrown down by this reagent.
Consequently amnionic hydrate and ammonium carbonate in slight excess
were added to the filtrate, forming the double carbonate. If the solu-
tions are concentrated, the double carbonate is precipitated when more
than a slight excess of amnionic carbonate is used. This happened in
some cases, when it was necessary to redissolve the precipitate in dilute
hydrochloric acid and again add ammonic carbonate in more dilute
solution. About fifty grams of carbonate per litre was found to give the
best results. Ammonic hydroxide was then added to the hot solution,
and sulphuretted hydrogen in excess. After stauding over night the
solution was filtered. In several of the more concentrated solutions, a
considerable quantity of the salt crystallized out. These crystals were
worked up separately, as they were probably purer than the solution.
On boiling the solution to decompose the excess of ammonium sulphide,
some of the ammonic carbonate was decomposed, causing the precipita-
tion of some uranium sulphide. This precipitate was discarded, as it
might have contained iron, or other analogous metals which had previ-
ously escaped precipitation. Dilute hydrochloric acid in slight excess
was added, and the carbon dioxide was expelled by boiling. The free
acid was then almost neutralized with pure ammonic hydroxide, and
* This method of uranium purification, with some modifications and additions,
is similar to that employed by Zimmermann. Annalen der Cliemie u. Pharmacie,
232, 299.
vol. xxxvn. — 25
38G PROCEEDINGS OF THE AMERICAN ACADEMY.
pure amnionic sulphhydrate added in excess. The color of the result-
ing precipitate of uranium sulphide varies greatly with the temperature.
In warm solution it was at first reddish brown, while that precipitated in
the cold varied from bright red to brownish yellow. On washing, all
turn black, the sulphide being decomposed into uranous oxide and sul-
phur. After thorough washing the resulting mixture of oxide and
sulphur was ignited in a porcelain dish, the green urano-uranic oxide
being the product.
The oxide was then dissolved in a platinum dish in redistilled nitric
acid, evaporated, and recrystallized from nitric acid solution. Uranyl
nitrate does not crystallize well from aqueous solution, but it was found
that if a little nitric acid is added, it crystallizes readily in fairly large
monoclinic prisms. This recrystallization was repeated ten times from
acid solution, and finally twice from aqueous solution. Finally the pure
nitrate was converted to the oxide by ignition in platinum. A second
sample, used in the preliminary series, was prepared by repeated
fractionation of the mother liquors of the first sample.
Since this work was carried out, Sir William Crookes * has published
the account of several methods by which he was able to prepare specimens
of uranyl nitrate which were not radio-active. The radio-activity of
uranium has hitherto been supposed to be characteristic of this element.
Crookes has shown, however, that this is not the case, but that the
active element can be separated by treatment with ether, by fractional
crystallization, or by treatment with excess of ammonium carbonate.
Unfortunately none of the pure oxide prepared for this investigation
remained, hence it is impossible to test directly its radio-activity. Since
two of Crookes's methods were used in purifying our material, viz. the
ammonium carbonate treatment and fractional crystallization, it is highly
improbable that our oxide was radio-active. In repeating Crookes's
work with nitrate made from some of the same material used in pre-
paring our best nitrate, it was found that a sample of the fifth crystalliza-
tion gave no trace of action on twenty-four hours exposure to a quick
photographic plate. The material used in this experiment had not been
submitted to the ammonium carbonate treatment. When it is con-
sidered that the material used for our atomic weight determinations was
first put through the carbonate process, — in itself sufficient to remove the
radio-active element, — and then was recrystallized twelve times as
nitrate, it would seem that our pure oxide must have been free from
all radio-active material.
* Proceed. Lond. Royal Soc, 66, 409 (1900).
RICHARDS AND MERIGOLD. — ATOMIC WEIGHT OF URANIUM. 387
There is another phase of this subject that deserves to be considered,
namely, the possible effect of radio-active matter, even if present, upon
the atomic weight value. The purest specimen of radium or "polonium"
yet obtained has consisted of a mixture containing probably little more
than fifty per cent of the active element, as nearly as could be estimated.
This highly impure material, however, possesses 8,000 times the radio-
activity of uranium. The radio-active power of the pure material is
undoubtedly very much greater than that of the impure mixture. Con-
sequently the quantity of ratio-active substance necessary to give to
uranium the comparatively slight degree of activity that it possesses must
be exceedingly minute. Giesel has recently shown * that a quantity of
radium so small that it cannot be detected by sulphuric acid is sufficient
to affect a photographic plate. Crookes also says on this point, " Con-
sidering my most active UrX does not contain sufficient of the real
material to show in the spectrograph, yet is powerful enough to give a
good impression on a photographic plate in five minutes, what must be
its dilution in compounds which require an hour, a day, or a week to
give an action ? " f Even in the ordinary active uranium compounds it
is most unlikely that the active element — if indeed it is an element —
could possibly be present in quautity sufficient to exert any influence
whatever upon the atomic weight of uranium.
Pure carbon was obtained by ignition of sugar. Large, clear crystals
of the best " rock candy " of commerce were ground up in a porcelain
mortar and ignited at low heat in a platinum dish as long as organic
gases were given off. The resulting charcoal was then powdered in an
agate mortar and ignited in a hard glass combustion tube ; first in a
stream of pure, dry nitrogen, and finally in a stream of bromine vapor.
In this way the carbon was freed from any impurities which might, if
present, be acted upon during the sublimation and contaminate the
sublimate. Owing to the presence of undecomposed carbohydrates, or
possibly of water, most of the bromine was converted into hydrobromic
acid. Heating in bromine was continued until acid fumes ceased to be
given off. Finally, the carbon was again heated in a current of dry
nitrogen. Five grams of carbon, thus prepared, left no visible or weigh-
able residue after combustion in oxygen.
The method of bromine purification was essentially identical with that
used in many other atomic weight investigations in this laboratory, and has
* Berichte der deutschen chemischen Gesellschaft, 33, 3569 (1900).
t Proceed. Lond. Royal Soc, 66, 422 (1900).
388 PROCEEDINGS OF THE AMERICAN ACADEMY.
been proved by long experience to be the most efficient and satisfactory.
Commercial, "pure" bromine was partially freed from chlorine by
shaking with a fifteen per cent solution of potassic bromide. One fourth
of the bromine was then converted to calcic bromide by running it
slowly into milk of lime in the presence of a large excess of ammonia.
The calcic bromide solution was filtered and concentrated by evapora-
tion, and the rest of the bromine was added to it. A little zinc oxide
was then added, and after standing over night the bromine was distilled,
nearly free from chlorine. Most of the iodine is removed as zinc
iodate. After redistilling the bromine, in order to remove any calcium
bromide that may have spattered over in the first distillation, it was con-
verted into hydrobromic acid by slowly dropping it into a mixture of
red phosphorus and hydrobromic acid. The red phosphorus was at first
washed free from chlorides. The hydrobromic acid, containing some
free bromiue, was distilled. The free bromine liberates any iodine
which may have escaped the zinc oxide. The first portion of the distil-
late, containing free bromine and iodine, and organic matter, was rejected,
and so was the last portion, which may have contained traces of arsenic.
The hydrobromic acid was then converted into bromine by distilling over
pure manganese dioxide previously treated with sulphuric acid and
washed. One half the bromine is obtained by the manganese dioxide
alone. As soon as no more bromine comes off, a little redistilled sul-
phuric acid is added, and the rest of the bromine was obtained. It was
then redistilled several times, rejecting the first and last portions, and
finally dried over pure phosphorous pentoxide.
The silver precipitation also presents no new features, except, perhaps,
its somewhat unusual thoroughness. Partially purified silver was dis-
solved in nitric acid, diluted, and precipitated with pure hydrochloric
acid. After thorough washing the chloride was reduced by invert sugar
and sodic hydrate which had been purified by electrolysis. The metallic
silver was thoroughly washed, dissolved in nitric acid, and again precipi-
tated as chloride and reduced. It was then dried and fused on charcoal ;
the lumps of silver were cleaned with sand, dissolved in pure nitric acid,
diluted to a volume of two litres, and again precipitated with pure hydro-
chloric acid. The resulting chloride was then digested on the steam
bath with aqua regia, washed, and once more reduced by invert sugar
and sodic hydrate. After drying, it was fused on pure sugar char-
coal. The buttons of silver were cleaned with sand, and then puri-
fied electrolytically, a small portion being dissolved in nitric acid to
serve as the electrolyte, and the rest serving as anode material. The
EICHARDS AND MERIGOLD. — ATOMIC WEIGHT OF URANIUM. 389
crystals of electrolytic silver were then dried over potash and fused
in vacuo on a boat of pure lime. The buttons of silver thus obtained
were treated with nitric acid to remove the surface, dried, and kept over
potash. A second sample was obtained by fusing in vacuo electrolytic
silver which had been prepared from the silver bromide obtained in Dr.
Baxter's work upon cobalt, which was known to be very pure.
Ilydric dioxide was purified as follows : To a solution of the ordinary
commercial peroxide prepared for medicinal use, was added a solution of
baric hydroxide, which had been purified by recrystallization. The pre-
cipitated baric dioxide was washed until a nitric acid solution of the
same showed no trace of halogen. It was then added to pure dilute sul-
phuric acid, and the resulting solution of hydric dioxide was filtered and
distilled in a partial vacuum. The solution thus obtained showed no trace
of halogen, and left no visible residue on evaporation in platinum.
Ammonium sulphide was made from pure ammonia, which had been
redistilled in platinum, and pure sulphuretted hydrogen. It left no visible
residue on evaporation in platinum.
Hydrochloric and nitric acids were redistilled in a platinum still, and
throughout the work platinum vessels were used wherever possible.
Water was twice redistilled, once over alkaline potassic permanganate,
and again over acid potassic sulphate from a Jena glass flask, a block-tin
condenser and Jena glass receiver being used.
The Results of the Analyses of Uranous Bromide.
The method of analysis has been already fully described.
The analyses recorded in the first series were made by adding an
excess of silver nitrate to the solution of uranyl bromide. From the
ratio of the observed weights of uranous bromide to argentic bromide,
the molecular weight of uranous bromide was calculated, that of argentic
bromide being assumed to be 187.885. From the results obtained from
this preliminary series the weight of silver necessary to precipitate the
bromine in one gram of uranous bromide was calculated. In the subse-
quent determinations the exact weight of silver required was weighed
out, as nearly as possible, and dissolved in pure nitric acid with suitable
precautions to avoid loss. The exact end point was reached by standard
hundredth normal solutions of argentic nitrate and hydrobromic acid, by
means of the nephelometer.* After determining the end point a slight
excess of argentic nitrate was always added, and the weight of the total
* Richards, These Proceedings, 30, 385 (1894). Z. anorg. Cliem., 8, 269 (1895).
390
PROCEEDINGS OF THE AMERICAN ACADEMY.
argentic bromide determined. Thus from each of these analvses two
distinct ratios were obtained as a basis for the calculation of the molecular
weight of uranous bromide, — the ratio of uranous bromide to argentic
bromide, and that of uranous bromide to silver.
As would naturally be expected from the complexity of operations
involved, determinations of the sodium in the filtrates from the argentic
bromide gave unsatisfactory results. The large quantity of filtrate and
wash waters had to be evaporated to small bulk, the uranium precipi-
tated, and the sodium determined in the residue. It seemed advisable to
make a series of separate analyses for sodium only, and use the average
percentage of sodium found as a constant correction. This method was
used in the work upon cobalt and nickel.*
Accordingly three alkali determinations were made, wholly in platinum,
the material not coming in contact with glass at any time except during
the original collection and weighing of the sublimed bromide. The sub-
limate was dissolved in pure water, in a platinum dish, and the uranium
was precipitated with pure ammonium sulphide. The ammonium sul-
phide was freshly prepared for each analysis, wholly in platinum. It left
no residue on evaporation in platinum. The precipitated sulphide was
digested on the water bath to expel most of the excess of ammonium
sulphide, filtered through a platinum funnel, and the filtrate and wash
water evaporated to small bulk in a platinum dish. The sodium bro-
mide was then converted to sodium sulphate and weighed. The follow-
ing table contains the data and result : —
No.
Weight of
Uranous
Bromide.
Weight Sodic
Sulphate
obtained.
Equivalent
Weight of
Sodic Bromide.
Per cent
Sodic
Bromide.
grams.
gram.
gram.
1
1.656
0.00092
0.00133
0.081
2
2.629
0.00143
0.00207
0.079
3
1.407
0.00121
0.00175
0.124
0 095
The average of these three determinations, 0.095, per cent, is practically
identical with the amount of sodic bromide found in the cobalt and nickel
work, which was 0.10 per cent. The porcelain tubes used in this inves-
* These Prcoeedings, 34, 339, 365 (1899).
RICHARDS AND MERIGOLD. — ATOMIC WEIGHT OF URANIUM. 391
tigation were of the same manufacture as those used in the nickel and
cohalt work, and since the method of preparation of the three bromides
was practically the same, probably the quantity of sodium extracted from
the tubes by the action of the hot bromine vapor was the same, — on the
average, — in all three cases, and not far from 0.10 per cent. Conse-
quently, in calculating the following results, this value was used as a
constant correction. The effect of applying the correction is to raise the
calculated atomic weight about two tenths of a unit. Of course by this
method the quantity of sodic bromide calculated will vary somewhat from
the exact quantity present, in individual determinations. The average
result, however, will undoubtedly vary but little from the result obtained
if the alkali could be determined in each sample. It certainly is very
much nearer the truth than the results to be obtained by the cumber-
some method of determining the alkali in the filtrate from each precipita-
tion of argentic bromide.
Analysis No. 2 was rejected on account of contamination of the
uranous bromide by shreds of asbestos from the packing of the jacket, and
No. 4 was not used because the combustion tube cracked during sublima-
tion, rendering probable the formation of some oxybromide. The silver
required in analysis No. 6 was determined for practice preparatory to
the final series, being 0.9087 gram when all corrections were applied. It
is not included in the table, since its nature was essentially preliminary.
As usual, all weighings were reduced to the vacuum standard. While all
THE ATOMIC WEIGHT OF URANIUM.
O = 16.000 ; Ag = 107.93 ; Br = 79.955.
First Series (preliminary). UBr4 : 4AgBr.
No. of
Analysis.
Total Weight
of Uranous
Bromide + So-
dium Bromide
iu vacuo.
Weight of
Uranous
Bromide
corrected
for NaBr.
Total Weight
of Silver
Bromide
in vacuo.
Weight of
Silver
Bromide
corrected
for NaBr.
Parts of Ura-
nousBromide
equiv. to 100
parts Argen-
tic Bromide.
Atomic
Weight of
Uranium.
1
3
5
6
grams.
2.20795
1.44321
1.40639
1.17607
grams.
2.2058
1.4418
1.4050
1.1749
grams.
2.97391
1.94272
1.89355
1.58396
grams.
2.9699
1.9401
1.8910
1.5818
grams.
74.272
74.316
74.299
74.276
238.36
238.69
238.56
238.39
Average 74.289
238.50
392
PROCEEDINGS OF THE AMERICAN ACADEMY.
Second Series. UBr4 : 4AgBr.
No. of
Analysis.
Weight of
Uranous Bro-
mide + Sodic
Bromide
in vacuo.
Wt. of Ura-
nous Bromide
corrected
for Sodic
Bromide.
Total Weight
of Silver
Bromide
in vacuo.
Weight of
Silver
Bromide
corrected
for NaBr.
Parts of Ura-
nous Bromide
equiv. to 100
parts Argen-
tic Bromide.
grams.
74.296
74.290
74.302
Atomic
Weight of
Uranium.
7
8
9
grams.
1.80174
1.06723
1*85698
grams.
1.7999
1.0662
1.8551
grams.
2.42588
1.4:3713
2.50009
grams.
2.4226
1.4352
2.4967
238.54
238.50
238.59
Average .
....
. 74.296
238.54
Third Series. UBr4 : 4Ag.
No. of
Analysis.
10(7)
11 (8)
12(9)
Weight of
Uranous
Bromide
with all
Corrections.
1.7999
1.0662
1.8551
Weight of Sil-
ver in vacuo
(not corrected
for Sodic
Bromidf).
grams.
1.39365
0.82559
1.43817
Weight of
Silver
with all
Corrections.
grams.
1.3918
0.8245
1.4342
Wt. of Uranous
Bromide corre-
sponding to
100 grams
Silver.
grams.
129.322
129.315
129.347
Atomic
Weight of
Uranium.
238.49
238.46
338.60
Average 238.52
Average of all determinations . .
Average of six final determinations
238.52
238.53
the weighings were actually made to the hundreths of a milligram the
final corrected data are rounded off to the nearest tenth of a milligram,
since the deviations of the results show that the hundredths could have
had no significance.
The extreme difference between the highest and the lowest values in
the preliminary series is 0.33 unit, in the second series 0.09 unit, and in
the third series 0.14 unit. At first sight these variations seem large, but
their relative magnitude appears smaller when the great molecular weight
of uranous bromide, 558.34, is taken into consideration. Thus the
extreme percentage error of the preliminary series is 0.06, while those
of the last two series are only 0.016 and 0.024 per cent respectively.
RICHARDS AND MERIGOLD. ATOMIC WEIGHT OF URANIUM. 393
The so-called " probable error " of the average atomic weight computed
from the six analyses numbered 7 to 12 inclusive, if each is given the
same weight, is 0.015. That is, according to the theory of least squares,
the atomic weisht of uranium should be between 238.515 and 238.545.
The magnitude of the maximum deviations in these two final series is,
moreover, about as large as would have been expected from known ana-
lytical uncertainty. The observed variation in the amount of sodic
bromide, for which a constant correction had to be applied, would account
for three quarters of it, and the rest, corresponding to less than the
tenth of a milligram in the weighings, might easily be due to unavoidable
errors of weighing or manipulation.
Further evidence of the trustworthiness of the figures is to be found in
the comparison of the amounts of silver used in analyses 10, 11, and 12,
with the corresponding amounts of argentic bromide, found in analyses
7, 8, and 9. This comparison is given in the following table, which
gives the weights of silver corresponding to 100.000 parts of argentic
bromide.
Weight of
AgBr
in vacuo.
Weight of Ag
iu vacuo.
Quotient x 100 =
per cent of Silver in
Argentic Bromide.
grams.
2.42588
1.43713
2.50009
grams.
1.39365
0.82259
1.43617
57.449
57.447
57.445
The result not only verifies the mechanical work, but affords evidence
that the precipitate must have been pure argentic bromide. Clearly,
then, the analysis is as accurate as need be. Further repetition of the
process might reduce the so-called " probable error," but could not
change the average by a significant amount. In the present state of the
question, the method seems to have been carried as far as expediency
demands.
It is worth while to inquire whether or not the method may conceal
some source of constant error beyond the reach of the experimental
precautions detailed above. Such an error could hardly have occurred
n
9-4 PROCEEDINGS OF THE AMERICAN ACADEMY.
during the analysis ; for every step of this procedure was verified by
confirmatory evidence. If a flaw existed, it must have been in the
purity of the original substance. Since the observed atomic weight is
lower than the former results, it is important to examine into only
those possible irregularities which could have had the effect of lowering
the apparent value.
The probable impurities tending to lower the atomic weight are, first,
sodic bromide; second, hydrobromic acid; third, free bromine; fourth,
uranic pentabromide ; and fifth, an unknown metal with a lesser equiva-
lent. The first impurity was found to be present, its amount was deter-
mined, and a suitable correction was applied. The second could not have
been formed during the sublimation of the uranous bromide, because com-
pounds of hydrogen were scrupulously excluded. If formed by the action
of water after the sublimation, the atomic weight would have appeared
too high — for moist uranous bromide emits hydrobromic acid instead of
absorbing it. The third impurity, free bromine, could hardly have been
imprisoned or absorbed by the sharply crystalline salt to any appreciable
extent, since the concentration of the bromine vapor in the issuing gases
was but small.
The evidence in regard to the absence of pentabromide is fairly conclu-
sive, although somewhat indirect. All attempts by many iuvestigators
to form this compound have failed, in spite of the recognized existence of
the corresponding chlorine compound. It seemed possible, however,
that while this compound is not formed at high temperatures, lower
temperatures might permit the addition of the extra bromine. Accord-
ingly the preparations used in Analyses 7, 8, 10, and 11, were cooled
in a current of dilute bromine vapor, instead of in pure nitrogen. The
presence of a comparatively small amount of pentabromide would make
a very decided difference in the quantity of bromine found. Hence the
essential agreement of the average result of these analyses, 238.50, with
the average result of all the others, 238.52, is good evidence of the
absence of uranium pentabromide.
With regard to the fifth possible impurity nothing can be said except
to point out the many operations involved in the purifications. These
seem to point toward probable purity ; but it is nevertheless to be re-
gretted that lack of time prevented the analysis of many different fractions
of material, prepared in varying ways.
The presence of oxybromide would of course cause low bromine anal-
yses, and too high an apparent atomic weight. Therefore this possible
cause of error need not be considered, even if the oxybromide had ever
RICHARDS AXD MERIGOLD. — ATOMIC WEIGHT OF URANIUM. 395
been made in the absence of water. In the light of all these consid-
erations, there would seem to be no good reason to question the purity
of our bromide.
On comparing the result of this investigation, 238.53, with that of
Zimmermann's, 239.59 (the only previous work worthy of serious consid-
eration), the difference of over a unit seems at first to be one of great
magnitude. The percentage difference (0.45%) is however smaller than
many a difference which often has been passed by unheeded in small atomic
weights, such as those of magnesium or aluminum. This point illustrates
the difficulty of obtaining results with high atomic weights which can
satisfy the cursory reader.
Nevertheless, such a difference is far too great to pass unchallenged.
It seems highly probable that the greater part of it is due to the
previously discussed sources of inaccuracy in Zimmermann's method, —
especially to the difficulty of wholly re-oxidizing the lower oxide.
The failure to oxidize half a per cent of the uranous oxide, involving an
error in the weight of only 0.017 per cent of the total weight of the
substance, would account for the discrepancy.
Hence it seems not unlikely that the atomic weight of uranium is
really as low as 238.53. Nevertheless, the question cannot be looked
upon as conclusively settled. Certainty can be obtained only by the
application of a new method, radically different from the two just com-
pared. Our experience of nearly four years of varied work seems to
indicate that the search for such method will not be an easy one. The
many degrees of quantivalence of uranium and the unsuitable properties
of its compounds combine to render the problem one of unusual difficulty.
When face to face with a problem of this kind one cannot but admire
Stas's wisdom in selecting chiefly univalent elements with powerful
affinities in order to prove the constancy of the atomic weights.
The result of our analyses of uranous bromide may be summed up in
the following words: If oxygen is taken as 16.000, and bromine as
79.955, the atomic weight of uranium appears to be not far from
238.53.
Cambridge, Mass., U. S. A. 1897-1901.
Proceedings of the American Academy of Arts and Sciences.
Vol. XXXVII. No. 15. — February, 1902.
CONTRIBUTIONS FROM THE CHEMICAL LABORATORY
OF HARVARD COLLEGE.
THE SIGNIFICANCE OF CHANGING ATOMIC VOLUME.
II. — THE PROBABLE SOURCE OF THE HEAT OF CHEMICAL
COMBINATION, AND A NEW ATOMIC HYPOTHESIS.
By Theodore William Richards.
Investigations on Light and Heat made and published whollt or in part with Appropriations
prom the rcmford fund.
CONTRIBUTIONS FROM THE CHEMICAL LABORATORY OF
HARVARD COLLEGE.
THE SIGNIFICANCE OF CHANGING ATOMIC VOLUME.
II. — THE PROBABLE SOURCE OF THE HEAT OF CHEMICAL
COMBINATION, AND A NEW ATOMIC HYPOTHESIS.
By Theodore William Richards.
Presented January 9, 1901. Received January 14, 1901.
I. Presentation of the Facts.
In a paper first presented to the American Academy of Arts and
Sciences in May, 1900, then revised and printed in the Proceedings a
year later,* certain interesting facts concerning the significance of chang-
ing atomic volume were pointed out and emphasized. It was shown
that the contractions and expansions occurring in liquids and solids during
chemical reaction are related to the affinities concerned, as nearly as we
can estimate those affinities. A greater affinity seems to produce a
greater contraction, if the compressibilities concerned are equal. It
seemed possible that this idea might have very fundamental and far
reaching applications as to matters of fact, and might lead moreover to a
somewhat new conception of the atomic h}rpothesis.
Many such applications have already been tested with plausible results.
The complete detailing of the ramifications of this idea would need the
compass of a book ; in the present paper the attempt will be made
merely to sketch the relations of a single side of the question.
In the paper already referred to the suggestion was made that the
heat of chemical reaction might be traceable to the work done by chemi-
cal affinity in compressing the substances concerned. The discussion
below will show the close relationship which exists between these facts.
The most serious difficulty in the way of determining the relationship
is the extreme scarcity of data concerning compressibility. Obviously
* These Proceedings, 37, 1 (June, 1901).
400 PROCEEDINGS OF THE AMERICAN ACADEMY.
the compressibility of a compound contains too many possible variables
to form at once the certain basis of exact reasoning ; and among elements
only mercury, lead, copper, and iron in the uncertain form of steel, seem
to have been even crudely studied.* The problem is moreover compli-
cated by the fact that the coefficient of compressibility diminishes as the
pressure increases.
The work which is needed in order to compress a given substance to a
given extent can only be computed accurately when the varying com-
pressibility through the whole range is known ; and since the pressures
involved in the present question are clearly many thousands of atmos-
pheres, the precise solution of the problem seems to be a distant matter,
although by no means impossible.
By a process of approximation some light may be obtained, however.
If one selects a single series of compounds, such as the chlorides, it is
obvious that a large part of the compressibility throughout the series
should correspond to the compressibility of the chlorine. In those cases
where the compressibility of the metal is smallest, the change of volume
would be due almost solely to the compression of the non-metal.
In view of these considerations, the first approximation should be
obtained by comparing the actual contractions taking place during the
formation of amounts of substance containing the same weight of chlorine
with the heat evolved in each case. The starting point in each case is
liquid chlorine, having a molecular volume of about 50 (or an atomic
volume of about 25) at 20°. The heat of formation of the chloride is
usually given in tables of data as starting from chlorine gas, under
atmospheric pressure ; hence the latent heat of evaporation and expan-
sion of tbe chlorine should be subtracted from the usual values in order
to institute a precise comparison. f However, these quantities cannot be
large in proportion to the heat of combination with the metal, and they
* Landolt and Bornstein, Phys. Cliem. Tab., pp. 268, 278 (1894). Unless
otherwise stated, all data used in this paper were taken from this admirable book
of tables.
t The latent heat might be approximately calculated from the data of Knietsch
(Landolt and Bornstein, p. 80 (1894)) as follows : —
_ RT*dP 8.32 X (293.5)2 X 0.19 .
Q = PdT ~ 6.62 X 1 = Joules, or 20.5
kilojoules, between 20° and 21° C, for the evaporation of one gram-molecule. The
wide deviations from the gas-law exhibited by chlorine render the calculation
very uncertain. It is enough, however, to show that the value is relatively small.
The heat absorbed on expansion must also be in doubt on account of the same
deviations.
RICHARDS. SOURCE OF CHEMICAL HEAT.
401
would apply equally in each case ; hence in the first approximation the
usual values for the heats of combination may be given without affecting
the argument.
The table of data herewith collected compares the contraction which
takes place when two gram-atoms of chlorine combine with some other
substance, and the heat evolved during the operation.
Comparison of Contraction with Heat of Formation involved in
the Synthesis of Chlorides.
Metal.
Atomic
Volume
of
Metal.
Atomic Vol.
Metal -f
11 times
Atomic Vol.
Chlorine.
Molecular
Volume
of
Chloride.
Difference
or
Contraction.
Contrac-
tion corre-
sponding
to 2 Atoms
Chlorine.
Heat of
Formation
correspond-
ing to 2
Atoms
Chlorine.
(Kilojoules.)
Lithium
11.9
36.9
20.9
1G.0
32.0
784
[CarbonIV] .
3.4
103.4
96.5
6.9
3.5
99
Sodium . .
23.7
48.7
27.2
21.5
43.0
816
Magnesium
13.3
63.3
43.9
19.4
19.4
632
Potassium .
45.5
70.5
37.8
32.7
65.4
872
Calcium
25.3
TO
too
50.0
2-3.3
25.3
760
Iron11 . .
7.1
57.1
42.6
14.5
14.5
343
Nickel . .
6.7
56.7
50.4 (?)
6.3
6.3
312
Cobalt . .
6.7
56.7
44.2
12.5
12.5
320
Copper . .
7.1
57.1
44.1
13.0
13.0
216
Zinc . . .
9.5
59.5
49.6
9.9
9.9
407
Strontium .
34.5
84.5
51.9
32.6
32.6
772
Silver . .
10.3
35.3
26.5
8.8
17.6
123
Cadmium .
13.0
63.0
46.5 (?)
16.5
16.5
390
Barium . .
37.0
87.0
53.9
33.1
33.1
815
Mercury11 .
14.7
64.7
50.0
14.7
14.7
223
Thallium .
17.2
42.2
34.1
8.1
16.2
406
Lead . . .
18.2
68.2
48.1
20.1
20.1
346
The parallelism of the heat of reaction and the contraction which
results from it, is obvious from the table and the accompanying diagram,
vol. xxx vii. — 26
402
PROCEEDINGS OP THE AMERICAN ACADEMY.
100 200 300 400 500 600 700 800 900 kj.
10 20 30 40 50 60 70 cubic centimeters.
Li
C
Na
Mg
K
Ca
Jbe
Mi
\
Co
Cu
,
/
Zn
Sr
Ag
C'd
Ea
Hg
Tl
Pb
RICHARDS. — SOURCE OF CHEMICAL HEAT. 403
which represents graphically the results recorded in the table. The ele-
ments are arranged in the order of their atomic weights, and both sets of
data are drawn as abscissae, because this method of treatment will facili-
tate later comparison, and because it obviates certain irregularities due to
periodicity. Each division stands for ten cubic centimeters of contraction
on the left hand curve, and a hundred kilojoules of heat-energy on the
right hand curve.
The correspondence is obviously too close to be the result of chance.
One is forced to believe that a fundamental relationship exists between
the two phenomena.
In these curves the compressibility is ascribed wholly to chlorine, and
that of the other substance is neglected ; but when the latter is large, it
also must enter into the problem. Unfortunately our data concerning
compressibility are unusually limited ; but approximate calculations,
based upon such as are known or may be guessed, show that at least
some of the irregularities in the parallelism may be ascribed to this
source.
We may thus formulate the following law : The work needed for the
compression involved in the formation of one solid or liquid by the combi-
nation of two others is approximately proportional to the heat evolved.
"While the general tendency of the law is manifest, and a correction
for individual compressibilities would undoubtedly make it more so, there
are nevertheless several exceptions to be explained. These may arise
from several causes ; in the first place, many specific gravities of solids
are known only approximately ; * in the next place, it is important that
the same modifications of each substance should enter into each calcu-
lation. A plausible explanation has been found even for the excep-
tionally wide deviation exhibited by argentic chloride ; but this point
will not be dwelt upon now, since it is being submitted to the test of
experiment.
The relation may be further illustrated by a table giving the data for
a few bromides, and of course many other data might also be given. In
order to eliminate as much as possible the contraction of the metal, it is
well to choose for comparison a common non-metal possessing a compara-
tively large coefficient of compressibility, hence both chlorine and
bromine serve well.
As a final example, the case of a single metal combining with several
* See Richards, These Proceedings, 31, 1G3 (1895); also Ostwald, Zeitschr.
phys. Chem. 3, 143 (1889).
404
PROCEEDINGS OF THE AMERICAN ACADEMY.
non-metals may be cited. Potassium is chosen in this last case because
it is probably among the most compressible of metals.
Comparison of Contraction with Heat of Formation involved in
the Synthesis of the Bromides.
Metal.
Atomic
Volume of
Metal.
Atomic Vol.
Metal +
n times
Atomic Vol.
Bromine.
Molecular
Volume of
Bromide.
Difference
or
Contraction.
Contrac-
tion corre-
sponding
to 2 Atoms
Bromine.
Heat of
Formation
corresp'd'g
to 2 Atoms
Bromine.
Sodium
23.7
49.2
34.2
15.0
30.0
718
Potassium
45.5
71.0
44.2
26.8
53.6
796
Calcium .
25.3
76.3
60.1
16.2
16.2
648
Zinc . . .
9.5
60.5
53.4*
7.1
7.1
318
Strontium.
34.5
85.5
58.4*
27.1
27.1
659
Cadmium .
13.0
64.0
56.9
7.1
7.1
315
Barium
37.0
88.0
62.2*
25.8
25.8
711
Comparison of Contraction with Heat of Formation involved in
the Synthesis of Potassic Halides.
Halogen.
Atomic
Volume of
Halogen.
Sum of At.
Vols, of Metal
and Halogen.
Molecular
Volume
of Salt.
Difference or
Contraction.
Heat of
Formation
of2Mols.
Chlorine .
Bromine .
Iodine . .
25.0
25.5
25.7
70.5
71.0
71.2
37.8
44.2
53.8
32.7
26.8
17.4
850-J-t
796
670
When the more obvious experimental errors have been considered,
two important questions at once suggest themselves : Does this propor-
tionality signify equality, or is some of the energy of compression stored
as potential energy and not manifested as heat? Again, if this equality
exists, is it always exact, or is it modified by subordinate secondary
effects ?
* These values are calculated from very accurate determinations of specific
gravity made recently in this Laboratory. See These Proceedings, 31, 163
(1895).
t Approximately corrected for heat of evaporation and expansion.
RICHARDS. — SOURCE OF CHEMICAL HEAT.
405
These questions cannot be answered at present. The total amount of
work done in any case cannot be computed without a knowledge of the
compressibility of the substances involved throughout the total range of
volume, as has already been said. Unfortunately no suitable data exist
10
20
300 400 500 600 700 800 kilojoules.
30 40 50 00 cubic centimeters.
2NaBr
2KBr
CaBr2
ZnBr2
SrBr,
CdBr2
BaBr.,
2C1K
2BrK
2IK
***«.
\
\
\
t
\
%
■
.
\
>
\
capable of satisfying the conditions of the problem. Before long I hope
to present such data, and to formulate answers to both questions ; for
the present the following unsatisfactory approximation is suggested as
being better than nothing.
From the study of many allied data I have been able to form an ap-
proximate evaluation of the compressibilities of sodium and chlorine.
406 PROCEEDINGS OP THE AMERICAN ACADEMY.
If one accepts these guesses, and imagines that the compressibilities
decrease with decreasing volume according to the usual approximate law,
one arrives at the conclusion that an amount of work equivalent to the
heat of combination of sodium and chlorine would correspond to a
change of volume in the system not far from the observed change
of volume. The outcome is complicated by the fact that even in ele-
ments, but especially in compounds, there may be superposed several
grades of compressibility. This can be explained hypothetically as fol-
lows : When the molecule is composed of two atoms, the highly com-
pressed portion of each atom at the point of chemical union should have
a much smaller coefficient of compressibility than the slightly compressed
remainder of the molecule. If the molecule is polymerized, there will
probably be yet other grades of compressibility in the various parts. The
only object of a calculation so uncertain as this is to show that the heats
of formation are of the same order of magnitude as the work involved in
the compression.
In spite of the inevitable difficulties in the way of interpretation —
difficulties which seem to be inherent in the problem — the presumption
is strong that the chief source of the heat of chemical combination is the
work performed in compressing the material. Since the heat of reaction
is known to represent only approximately the free energy of the reaction,
while the compression may really represent the affinities at work, one
would hardly expect the relation to be exact. The generalization is a
question of fact ; it does not necessarily involve any atomic hypothesis,
and can be regarded as uncertain only on account of the uncertainty
of the data at present accessible. It is my intention to carry out
the experimentation necessary to place the law on a more stable
basis.
In the same way any other manifestation of attraction or affinity, such
as cohesion or adhesion, should have a compressing effect and therefore
evolve heat. The superficial and limited nature of these phenomena
would ordinarily prevent any appreciable rise in temperature. In some
cases, however, as in the adsorption of liquids and gases by porous ma-
terial exposing a large surface, such a heating effect has been actually
observed. Thus the essential difference between water of crystallization
and adsorbed water is that the former penetrates the mass, while the
latter is merely superficial.
It is obvious, moreover, that the same considerations apply to solidifi-
cation and change of allotropic form. For example, liquid phosphorus,
yellow phosphorus, and red phosphorus have at 44° the atomic volumes
RICHARDS. SOURCE OF CHEMICAL HEAT. 407
17.66, 17.1, and about 14.1 respectively. The first small contraction is
attended with an evolution of 0.65 kilojoules, and the second larger one
with the evolution of 114 kilojoules of heat energy. In those cases
where there is a transition from a more compressible union to a stabler,
less compressible one, involving more work of compression, solidification
would involve increase of volume, as in the case of water.
II. A Plausible Interpretation.
It becomes now an interesting question to determine, if possible, the
mechanism by which this work is converted into heat. One is reminded
at once of the compression of a gas, where the work of compression re-
appears quantitatively as heat energy. But the compression under con-
sideration differs from the other in detail, because in the present case the
attraction of the two substances for one another seems to be the cause of
their mutual compression ; and this mutual compression takes place not
from the outside, but throughout the whole substance.
Those who shun the atomic hypothesis and consider substance only in
the mass, will rest contented without further attempt at interpretation ;
but those who hold that the hypothesis is a useful tool, to be thrown aside
when newer invention has devised a better one, will be tempted to go
further.
The case, considered hypothetically, seems to be this : "When two dif-
ferent atoms possessing mutual affinity approach one another, they are
drawn closer than they can be to their respective fellows, and in the
process evolve heat. The " repulsion " which is often supposed to sur-
round an atom, and prevent it from touching any other, seems to be par-
tially overcome by the potential energy of affinity. But of what nature
is this " repulsion" ? Ordinarily it is assumed to be due to the frequent
impacts of a hard atom in the centre of the space; but no evidence is
afforded of the existence of a free space. Indeed, it seems inconceivable
that solids should retain their structure, or should be capable of retaining
gases or liquids, if they are so loosely built up. A pile of sand would
be stable compared to such a fabric.
The present research points to quite a different interpretation of the
facts. The space occupied by a solid seems to have a chemical signifi-
cance as well as a physical one; it seems, indeed, to be as essential a
property of the material as any other property. Since the significance of
the total volume is a chemical one, the "free space" around each indi-
vidual atom must also have a chemical as well as a physical significance.
408 PROCEEDINGS OF THE AMERICAN ACADEMY.
In other words, we have no right to imagine that the space is " free " or
that there is a hard particle in the centre ; the shell is as essential an
attribute of the atom as the centre. But how are we to account for heat
vibration, if the atom is supposed to fill the whole space ? This question
is important; but before answering we must consider some of the con-
sequences of this form of compression.
Let us imagine two highly elastic spheres ; for example, two very thin-
walled india-rubber balls filled with gas. Imagine these to be drawn
together by a powerful attraction resideut throughout themselves. When
they come in contact, each will compress the other and evolve heat in
the process. They will remain bound together and distorted, unless some
force separates them. If the shell of an atom is elastic and compressible,
it is only reasonable to suppose that the interior is also. In that case
the whole substance of both of two combining atoms will suffer distortion
from the mutual attraction of every part of their substance ; and the con-
centration of those constituents in each atom which cause the affinity will
thus be increased in the half nearest the other atom. The supposition that
the affinity comes from within will cause here an essential divergence from
the actual conditions in two balls filled with gas, in which the gas is distrib-
uted equally throughout. As a consequence, the opposite half which is
not combined will lose some of it attractive constituents, aud should then
have less tendency to unite with the new substances than it had before
its union with the first atom. This plausible influence agrees with the
well-known facts of " false equilibrium " and the nascent state ; in fact,
it would account in general for the permanence of slightly stable
compounds.
By the process of hypothetical reasoning given above, one concludes
that the whole substance of the atom may be elastic. In that case heat
vibration might consist simply in alternate condensation and rarefaction
of the medium within the shell, started by the momentum of impact. This
would continue indefinitely, unless the vibration were imparted to other
substances possessing less. Such internal rarefaction and condensation
might well tend to distend the atom if any portion of the atom were held
by another.
Thus, it is evident that there is no difficultv in imagining internal
vibration in an atom which is packed on all sides closely with other
atoms, or in explaining the mechanism of the thermal expansion of solids
and liquids upon that basis. The chief reason for imagining a small
hard particle with a large free space around it is therefore removed.
Two other reasons for retaining the conception of the old atom may be
RICHARDS. — SOURCE OF CHEMICAL HEAT. 409
larked ; one, the continuity of the liquid and gaseous state, and the other,
the porosity of solids.
In answer to the first, attention may be called to the fact that the con-
tinuity of the liquid and gaseous condition exists actually only at the
critical pressure ; below that point they are, as a matter of fact, discon-
tinuous and very different. Perhaps the critical pressure is simply the
point where the gas molecules at the critical temperature are pressed
into actual contact. The compressibilities of very compressed gases are,
in fact, of the same order of magnitude as those of liquids.
Porosity is usually only manifest under very great pressure, which
might be enough to compress the atoms into smaller space, and thus
open orifices which previously did not exist.
From these considerations it seems to me that the new kinetic concep-
tion of the solid and liquid state has no disadvantages which the old
conception does not possess, while it has many advantages which the old
theory has not.
But it is not the intention of the present paper to enter into the detail
of so large a question. I hope that in the next few years I may be
permitted to study and report upon the possible consequences of the
significance of changing atomic volume.
In the preceding paper and the present one, the following phenomena
have been suggested as capable of a new and plausible interpretation if
atoms are considered as capable of altering their volume through a wide
range ; namely, the heat of chemical reaction, adsorption, adhesion,
and cohesion ; ordinary solution ; electrolytic solution ; electrolytic dis-
sociation ; the passage of electricity through solids, liquids and gases ;
the nature of cathode rays (and probably also X rays and radium) ; the
laws of Faraday and Dulong and Petit ; false and true equilibrium ;
heat capacity and thermal expansion ; quantivalence ; stereo-chemistry
and crystal form ; and the critical phenomena.
Following papers will be devoted to a development, quantitative
where possible, of these applications, as well as of many others. Unless
further study reveals discrepancies, which have hitherto been concealed,
I expect to be able to show : —
1. That the conception is not inconsistent with the two laws of energy.
2. That it conflicts with none of the quantitative conclusions of the
atomic hypothesis, nor with the kinetic theory of gases, if heat be assumed
to be due to mechanical energy operating upon atomic inertia.
3. That it is able to interpret the actual deviations of gases from the
gas law better than any other theory, retaining the essential import of
410 PROCEEDINGS OF THE AMERICAN ACADEMY.
the equation of van der Waals, and modifying this equation only as
regards the changeability of a and b.
4. That it is consistent with the varying specific heats of substances
in the solid, liquid, and gaseous states.
5. That with the help of this theory such physical properties as ten-
acity, ductility, malleability, and coefficient of expansion assume for the
first time a conceivable consistency.
6. That upon it may be based a definition of the essential influences
of chemical change and equilibrium.
7. That the variable compressibility of atoms furnishes a plausible
explanation for many of the phenomena of quantivalence, including even
the feeble affinities holding water of crystallization and other so-called
molecular combinations.
8. That it explains all the tridimensional relations of material, such as
stereochemistry and crystal form, at least as well as any other theory.
9. That with the proviso that electrical energy is a rhythmic mani-
festation of energy, — tending to repel itself and therefore to keep upon
the surface of material which is susceptible to it, and hence to expand
a free atom, — many of the electrical and magnetic phenomena of matter
become more conceivable.
10. That the effect of light in hastening the attainment of chemical
equilibrium, and the possibility of storing and emitting light energy
possessed by material, may be interpreted in a similar way.
11. That the careful consideration of all these and other facts leads
to a somewhat new conception of the relation between gravitation and
chemical affinity, as well as between matter and luminiferous ether.
This conception involves simply an antithesis of contracting and expand-
ing tendencies, and is thus founded entirely upon an energetic basis.
12. That the idea is capable of throwing light upon the periodic sys-
tem, and the genesis and permanence of the elements.
13. That it may be applied even to such astrophysical problems as
the cause of the sun's heat.
This is a large program ; some of it is already in manuscript, and more
must await further exact experiment. The program is given here only to
call attention to the wide possibilities of the consistent introduction of the
conception of atomic compressibility into chemistry and molecular physics.
The present paper is only one step in the direction indicated. It is
nevertheless an important step, for it adds approximate quantitative
evidence to the previously given qualitative evidence concerning the
significance of changing atomic volume.
RICHARDS. — SOURCE OF CHEMICAL HEAT. 411
III. Summary.
The contents of the paper may be divided into two parts : In the first
part is set forth an approximate generalization which rests upon facts
alone. This part of the paper can be overthrown only by the proof that
the facts upon which it rests are erroneous. In the second part of the
paper a plausible hypothetical interpretation of the facts is given. This
part of the paper stands ready to share the fate of all hypotheses, — •
namely, to retire into oblivion if it is not capable of aiding the discovery
of truth.
In brief, the chief points touched upon may be summed up as follows : — ■
I. (a) It has been shown that the contraction exhibited during
chemical combination is in many cases approximately proportional to the
heat evolved.
(b) Upon correcting the results for known differences of compressibility,
the approximation becomes closer.
(c) An approximate calculation of the work which would probably be
involved by the compression of a gram-atom each of sodium and chlorine
into the space occupied by a gram-molecule of salt showed this work to
be of the same order of magnitude as the actual heat of formation.
(d) From these facts and calculations the inference is drawn that the
heat of chemical reaction is chiefly due to the energy required for the
compression which takes place in the reaction.
(e) Possible corrections are pointed out.
(/) An explanation is given upon the same basis of the mechanism of
the heat of adsorption, adhesion, and change of allotropic form.
II. (a) While the evidence is not exact, it affords a strong presump-
tion in favor of the hypothesis of compressible atoms. The possibly far-
reaching effect of this simple and plausible hypothesis upon chemical
theory is pointed out.
(b) There is given a list of the especially prominent aspects of the
question which will form the subjects of immediate experimental and
theoretical study in this Laboratory.
Cambridge, Mass., U. S. A.
Proceedings of the American Academy of Arts and Sciences.
Vol. XXXVII. No. 16. — April, 1902.
CONTRIBUTIONS FROM THE CHEMICAL LABORATORY
OF HARVARD COLLEGE.
ON THE ACCURACY OF THE IMPROVED
VOLTAMETER.
By Theodore W. Richards and George W. Heimrod.
CONTRIBUTIONS FROM THE CHEMICAL LABORATORY OF
HARVARD COLLEGE.
ON THE ACCURACY OF THE IMPROVED VOLTAMETER.
By Theodore William Richards and George William Heimrod.
Presented February 12, 1902. Received January 29, 1902.
Introduction.
In a recent preliminary paper * it was shown that the disturbing in-
fluences in the common silver " voltameter " (or better, coulometer f) are
due to the concentrated liquid which falls from the anode. In order to
avoid the inaccuracy thus caused, it was suggested that the anode be
surrounded by a fine-grained porous cup, which is capable of preventing
this heavy liquid from reaching the kathode.
The weight of silver deposited by a given current in such a voltameter
was found to correspond very closely to the amount of copper deposited
at the same time in a copper voltameter shielded as much as possible
from all discoverable sources of error ; hence it seemed probable that the
new voltameter gives the true value of the electrochemical equivalent of
silver.
In a matter so important as this, however, it seemed advisable to ob-
tain much more information concerning the constancy and trustworthiness
of the new instrument, as well as to discover if possible the mechanism
of the phenomena which rendered the older form untrustworthy. The
investigation described below was undertaken with these objects.
I. The Constancy of the Porous Cup Voltameter.
The first problem was to determine if two instruments in series would
always give identical results; in other words, to find if the new voltam-
eter is always consistent with itself.
* Richards, Collins, and Heimrod, These Proceedings, 35, 123 (1899).
f The word " voltameter " was devised before electrical dimensions were
understood. It is moreover too much like the universally used and suitable word
" voltmeter." Now that the former instrument is placed upon a firm basis of
accuracy, it may appropriately receive also an accurate name ; and it is hoped that
the new word "coulometer" may replace wholly the anachronism.
416
PROCEEDINGS OP THE AMERICAN ACADEMY.
Nine such duplicate experiments were made. The first of these was
a crude trial, and need not be recorded ; the eight others are given in
the following table.
The apparatus employed was precisely like that described in the pre-
vious paper. For the sake of easy reference, the description is repeated
below.
Small cylinders of Pukal's porous ware (Berlin), suitable for osmotic
pressure experiments, were used to enclose the anode in order to prevent
the heavy anode-solution from reaching the kathode. These vessels
were 50 millimeters high and
—J A * 20 in diameter ; their walls
were not much over one milli-
meter in thickness. Their
impurities were removed by
boiling with nitric acid and
thorough washing with water.
Before being used they should
be carefully searched and
tested for cracks or imperfec-
tions. They were suspended
in the solution by means of a
platinum wire hung upon a
glass hook, which insulated
the wire from the electric
connections. By means of a
siphon, or a small pipette
with a rubber top, the liquid
within the cup was always
kept at a lower level than
that without, so as to prevent
outward filtration.
The kathodes consisted of
large crucibles weighing only
GO grams, although they were
capable of holding 120 cubic
X^
Figure 1. — Porous Cup Voltameter
(§ actual size).
A, glass hook for supporting anode. B, glass
ring for supporting porous cup. C, silver anode, centimeters; they were pro-
D, porous cup. E, platinum kathode. vided with lips. A crucible
exposes a smaller surface of
liquid to the impurities of the atmosphere, and gave in our experiments
a more evenly distributed deposit than a bowl.
RICHARDS AND HEIMROD. — THE IMPROVED VOLTAMETER. 417
The anodes were bars 5xlXl centimeters of the purest silver, sup-
ported by silver wires and not enclosed in filter paper ; and the electro-
lyte usually contained ten grams of pure, freshly prepared argentic
nitrate in a hundred cubic centimeters of solution.
The manipulation was simple. The platinum crucibles were cleaned,
dried at 160°, and weighed after three or four hours' cooling in a large
desiccator kept in the balance-room. In order to prevent leakage during
the electrolysis, the several stands were insulated by separate glass plates,
and all the connections were air lines. The apparatus was protected, as
in the earlier experiments with copper, by a miniature house with walls
of fine cotton cloth, which helped to exclude dust. When the current
was broken, the electrolyte was removed, the silver was rinsed twice
with water, a third filling with water was allowed to stand in the cru-
cible for two or three hours, and a fourth one remained in it over niffht.
The wash-waters were collected and filtered if the silver showed any
tendency to break off. In such cases a Gooch crucible was employed to
collect the particles ; and a very small filter, afterwards burned, served
to catch the minute flakes of asbestos detached from the mat. On the
next morning the crucibles were washed once more, rinsed twice with
pure alcohol, and finally dried and weighed as before. This method of
treatment gave opportunity for the diffusion of mother liquor from the
intricate recesses of the crystallized mass, while it did not run the risk of
dissolving silver which may attend the use of boiling water for washing.
As has been said, the crucibles were dried at 100°. It was subse-
quently shown, in agreement with the results of Lord Rayleigh and Mrs.
Sidgwick, that a red heat is needed to drive off all the included liquid
from the silver crystals; but since the amount included is fairly constant,
this fact does not interfere with the availability of the uncorrected data
for the present purpose of comparing one weight of silver with another.
Weighings were made upon the balance which served for the weigh-
ings in the earlier work upon copper, — one which has served also for
many determinations of atomic weights. Its results with small objects
may he depended upon to within ^ milligram. All weighings were made
by double substitutions, a similar vessel being used as a tare, and the
weights were of course carefully standardized. Since the question con-
cerned merely the comparison of silver with silver, the results were not
at first corrected to the vacuum standard.
The results show that the average difference between the weights of
the silver deposited in two crucibles placed in series was less than the
tenth of a milligram, or only about four parts in one hundred thousand.
vol xxxvii. — 27
418
PROCEEDINGS OF THE AMERICAN ACADEMY.
Considering the size of the platinum vessels weighed, this average agree-
ment is all that could be expected ; hence the test of the constancy of the
apparatus seems to have been satisfactory.
TABLE I.
Test of the Constancy of the Porous Cup Voltameter.
No. of
Experiment.
Voltameter I.
Weight of
Silver.
Voltameter II.
Weight of
Silver.
Difference.
Percentage
Difference.
2
Q
O
4
5
6
7
8
9
grams.
2.43744
2.69691
2.36193
2.14900
1.65485
2.31480
2.22258
2.67264
grams.
2.43749
2.69713
2.36196
2.14913
1.65490
2.31500
2.22260
2.67268
milligram.
0.05
0.22
0.03
0.13
0.05
0.20
0.02
0.04
per cent.
0.002
0.008
0.001
0.006
0.003
0.009
0.001
0.002
0.004
There is of course nothing in this table to show whether the figures
represent the weight of silver which ought to have been deposited by the
quantities of electricity employed. It may be that the error of the old
voltameter was merely reduced, and that a small constant error still re-
mained. The most probable cause of such a remaining error seemed to
be the possible diffusion or migration of the heavy anode-liquid through
the bottom of the porous cup, in spite of the fact that it was continually
removed by means of a pipette or siphon. In order to prevent this, the
bottom and a few millimeters of the sides of a porous cup were filled
with melted paraffin, which effectually sealed the pores. The upper part
of the sides only served to allow the passage of the electricity. A tenth
comparison showed that a current which deposited 1.83370 grams of
silver in this cup deposited 1.83375 grams in the ordinary porous cup
coulometer. This difference is no greater than a possible experimental
error; hence we may conclude that the effect of the diffusion is impercep-
tible. It will be shown later that the substance which causes the chief
RICHARDS AND HEIMROD. — THE IMPROVED VOLTAMETER. 419
irregularity of Lord Rayleigh's voltameter is probably a heavy complex
ion ; hence it is not surprising that both the migration-rate and the
diffusion-rate of the impurity is small. On the other hand, when the
porous cup is too coarse-grained or too large, or when the anode solution
is allowed to rise too high and thus filter through, the effect of the diffu-
sion begins to be manifest. The same error begins to show itself when
the viscosity of the solution is diminished by increasing temperature, as
we showed in the preceding paper.
If now the formation of ionized silver at the anode is attended by such
disturbing side reactions, it is reasonable to assume that a remedy may
be found in the use of an anode of some other metal. For this purpose
zinc seemed to offer peculiar advantages ; it possesses only one degree of
quantivalence, and has so great a solution-tension as to avoid the possi-
bility of contaminating the deposit of silver at the kathode.
A zinc rod (so-called " C. P.") served as the anode in the following
two experiments, and it was surrounded by a ten per cent solution of
zincic nitrate prepared from the same material by solution in nitric acid
(standing for a week over zinc), filtration, and crystallization. The
kathode solution consisted of a ten per cent solution of argentic nitrate,
as usual.
TABLE II.
The Effect of a Zinc Anode.
No. of
Experiment.
Wt. of Silver
in Ordinary
Porous Cup
Voltameter.
Wt. of Silver
in Voltameter
with
Zinc Anode.
Difference.
Percentage
Difference.
11
12
grams.
2.69702
2.36195
grams.
2.69688
2.36209
milligram.
-0.14
+0.15
per cent.
-0.005
+0.006
0.001
A peculiar reaction was observed during this electrolysis. The zinc
rod was covered with a copious white flaky precipitate, and a marked
test for nitrite was observed in the supernatant solution.* Thus the
ionization of the zinc is attended with the formation of basic salt and
* See also Senderens, Comp. Rend., 104, 504 ; also Ber. d. d. oh. Ges., 20, 197 R
(1887).
420 PROCEEDINGS OP THE AMERICAN ACADEMY.
zinc nitrite. The N03' ion must have been decomposed into NO./ and
oxygen. This same reaction takes place when silver serves as an anode
in its nitrate solution, although to a much smaller extent.
In spite of the irregularities just described, the deposition on the
kathode proceeded in a perfectly regular manner, and the figures show
that as much silver was deposited in one cell as in the other.
Still another means of testing the porous cup voltameter was found in
its comparison with a device which eliminates the porous cup wholly,
but which nevertheless keeps the anode solution quite away from the
cathode. This device consists in placing the anode at the bottom of a
tall beaker filled with a concentrated solution of argentic nitrate (200
grams of the salt in a litre of solution), and arranging the kathode in
the upper part of the vessel.* The anode solution becomes heavier
and remains around the anode, while the kathode solution becomes
lighter and rises to the surface. In order to prevent this dilution
around the kathode from diminishing too much the concentration of the
contiguous liquid, it is well to sink the kathode at least two centimeters
below the surface. A circular disk of platinum wire gauze, f six centi-
meters in diameter, was used as the kathode, since many holes in gauze
permitted the ready escape upward of the impoverished electrolyte.
The gauze was bent around a stout circular platinum wire, and the disk
was stiffened by four radial wires, and was hung rigidly from the centre.
The vertical distance between this kathode and the anode was about
seven centimeters. The anode consisted of a plate of pure silver, and its
platinum connecting wire was protected from the solution by an enclos-
ing glass tube.
The chief trouble encountered in manipulating the voltameter thus
constructed is the danger of losing fine crystals of silver from the flexi-
ble gauze. In the two experiments described below every precaution
was taken to avoid this source of error, and it is believed that no appre-
ciable weight was lost. Another disadvantage of the gauze is the fact
that metals deposited upon it are very apt to include minute quantities of
electrolyte because of the interstices arising from its woven structure.
Even silver deposited in a crucible contains some included mother
liquor, and that deposited on the gauze contains much more. In the
two experiments given below, the first deposit on the gauze lost 0.42
milligram on gentle ignition in a large porcelain crucible, and the
* Merrill, Phys. Rev., X, 169 (1000).
t Paweck, Zeitsch. fur Berg. u. Huttenwesen, 46, 570 (1898) ; Winkler, Ber. d.
d. ch. Ges., 32, 2192 (1899).
RICHARDS AND HEIMROD. THE IMPROVED VOLTAMETER.
421
second lost 0.72 milligram, while the two crucible deposits lost respec-
tively 0.20 and 0.24 milligram. These losses, accompanied by audible
decrepitation, must have been due to retained electrolyte.
In the table the weights of the iguited precipitates are given.
TABLE III.
Comparison of Porous Cup Voltameter with Wire Gauze Voltameter.
No. of
Experiment.
Weight of
Silver in
Porous Cup
Voltameter.
Weight of
Silver
deposited on
Gauze.
Difference.
Percen tage
Difference.
13
14
grams.
2.10326
2.31237
grams.
2.10344
2.31234
milligram.
+0.18
-0.03
per cent.
+0.00!)
-0.001
Average €
rror . . .
. +0.08
+0.004
The gauze kathode thus showed an average surplus of less than a
tenth of a milligram. But even this slight error is explicable, for it is
clear that the argentic nitrate held by the electrolyte must have left silver
nitrite or silver behind on heating. If we assume that the temperature
of ignition was enough wholly to decompose the electrolyte, the average
loss of 0.57 milligram would correspond to a residue of about 0.1 milli-
gram, while the corresponding residue from the weaker solution used in
the porous cup voltameter could not have exceeded 0.02 milligram. The
difference between these two figures is exactly equal to the observed
difference between the gauze voltameter and the porous cup voltameter,
so that the two may be said to give precisely identical results.
An important point connected with this experiment is the fact that
the kathode surface available for deposition on the gauze had an area of
less than half that on the inside of the large crucible. Hence the current
density in the gauze voltameter must have been over twice that in the
standard.
There has thus been accumulated a convincing array of evidence indi-
cating that the porous cup voltameter affords a means of depositing the
amount of silver which really corresponds to the quantity of electricity
sent through it. The numerical averages may be summed up in a brief
table as follows : —
422 PROCEEDINGS OP THE AMERICAN ACADEMY.
Average deviation of two porous cup voltameters in series = ± j^-j*^
Difference caused by sealing bottom of cup = — looooo
Difference caused by use of zinc anode = ± lofnjoo
Difference (corrected) between gauze voltameter and cup voltameter ± 0
The agreement of these results is as close as could be expected, since
the discrepancies do not exceed the possible experimental error. With
Lord Rayleigh's method, when two precisely similar voltameters are
compared, Kahle * and Rodger and Watson f have shown that an ac-
curacy of 6 or 7 parts in 100,000 can be obtained. On the other hand,
the least variation of size of kathode or anode, or of any other condition,
causes large deviations which may amount to ten times as large an error.
In our experiments given above, the most radical changes of method were
introduced, without affecting the results.
Among the efficient forms of apparatus described above, the porous
cup voltameter with a silver anode is the most convenient. Hence for
the further purposes of this paper it will be chosen as the standard
method.
II. The Separate Effect of each Anode Irregularity.
It is obvious from the study of earlier work that more than one irreg-
ularity exists at the anode in a silver cell ; and the separation and iden-
tification of the individual effect of each irregularity became a matter of
considerable interest. The outcome was instructive as an example of
the multitude of hidden minor influences which so often modify the ob-
vious outcome of chemical experiment.
Qualitative testing revealed not only acid, but also nitrite, in the anode
liquid ; and in those cases where the anode is very small, some experi-
menters have indicated the formation of highly oxidized compounds of
silver. Moreover, the singular crystalline silver dust which forms
around the anode demands an explanation. In order to solve the prob-
lem, of course an obvious available method was to introduce artificially
each impurity in turn into the pure liquid around the kathode in the
porous cup voltameter, and study its effect on the gain in weight of the
kathode.
The first impurity to be investigated was the nitrite. In order to pre-
* Wied. Ann. N. F., 67, 22 (1899).
t Phil. Trans., 186 A, 633 (1895).
RICHARDS AND HEIMROD. THE IMPROVED VOLTAMETER. 423
pare the nitrite, we had recourse at first to a method used by Proust.*
lie has found that on boiling an argentic nitrate solution with finely di-
vided silver, the nitrite is produced in quantity. In repeating this ex-
periment, powdered silver reduced from purest silver chloride by the
Stas method was boiled in a ten per ceut argentic nitrate solution.
Nitrite was indeed formed, but a very fine film of crystallized metallic
silver was formed on the surface ; a complication which seemed to point
towards the existence of a reaction similar to the solution of copper in
cupric sulphate. But it was found that pure silver nitrite in neutral
silver nitrate solution likewise deposits a fine silver mirror on exposure
to the light; hence the silver in both cases must be supposed to result
simply from the decomposition of the nitrite. The solution boiled with
silver was filtered through a Gooch crucible, and after cooling was em-
ployed iu a voltameter with a porous cup. The solution containing the
nitrite deposited 2.27945 grams of silver, while pure argentic nitrate in
another standard voltameter deposited 2.27944 grams, a difference of
only 0.01 milligram. (Exp. 15.)
Evidently the nitrite present had no effect at the kathode ; and the
liquid in an ordinary voltameter could hardly contain more nitrite than
this solution which had been boiled with metallic silver. In order to
pursue the matter further, however, we prepared silver nitrite from pure
potassium nitrite and silver nitrate.f Pure potassic hydrate was neutral-
ized with nitric acid ; the nitrate was re-crystallized and fused in a silver
crucible, and the resulting mixture of nitrate and nitrite was extracted
TABLE IV.
Standard vs. Voltameter with Solution Saturated with AgN02.
No. of
Experi-
ment.
Type of Voltameter
containing Nitrite.
Wei prh t of
Silver
in Standard.
Weight of
Silver iu Vol-
tameter con-
taining AgN02.
Difference.
Percentage.
Difference.
16
17
Standard.
Filter paper volt.
grams.
2.27944
2.30276
grams.
2.28011
2.30539
milligrams.
0.67
2.G3
per cent.
0 030
0.114
* Journ. de Physique, March, 1806, 211 ; also Nicholson's Journal, 15 : 378.
This reference has evidently been lost, since no text-book, including Dam-
mer, gives it, although all mention Proust's observation. After a long search
through the journals published in Proust's days, the reference was rediscovered.
t Victor Meyer, Liebig's Ann., 171, 23 (1874).
424 PROCEEDINGS OF THE AMERICAN ACADEMY.
with boiling water. The great bulk of nitrate may then he removed by
one crystallization. If to the mother liquor is added a solution of ar-
gentic nitrate, the argentic nitrite will precipitate at once as a thick
yellow paste. This is washed and re-crystallized from hut water, until
the color has changed to white. The pure nitrite was dissolved in a
nitrate solution to saturation, and this was employed, first, with a jjorous
cup (16), and second, with a paper-wrapped anode (17).
The results show that a saturated solution of nitrite really has the
effect of increasing the kathode deposit.
Since the increase due to a paper-wrapped anode over the weight
found with a porous cup would have been from 0.04 to 0.08 per cent, the
nitrite caused an increase of about the same amount in each case. But
this' increase happens only when the solution is saturated with nitrite ;
hence it is interesting chiefly as a limiting effect, and can hardly bo im-
portant in solutions of nitrite as dilute as those formed spontaneously
around the anode. The formation of nitrite is evidently the result of
the breaking up of the N03- ion into the nitrite ion N02~ and ox3rgen,
and the latter is probably taken up by the silver in forming one of the
oxidized compounds to be discussed later.
It is not at all surprising that this side reaction should take place to a
small extent. The current is normally carried from the anode to the
solution by the formation of the silver ion from the metal ; but a slight
tardiness in this reaction (which might be named " physico-chemical in-
ertia") would result in assistance from the anions in the neighborhood.
They would seek to adjust the potential by discharging their negative
electricity on the anode. Of course the most plentiful anion in the vicin-
itv is the nitrate ion ; its deionization would make possible the form-
ation of the nitrite ion anil oxygen, which might at once oxidize the
silver plentifully present.* The reaction might be written thus: —
N08 + 3Ag = Ag + + N02- + Ag20.
Thus the electrolysis of a strong solution of argentic nitrate might be
predicted to result, in the neutralization of a previously acid solution —
a prediction which agrees with the fact discovered by Rodger and
Watson f with thirty per cent solutions of argentic nitrate. It is pos-
sible that a higher oxide also would be found if the anode were small.
* The probable presence of silver in supersaturated solution around the anode
will be shown later.
1 Rodger and Watson, Phil. Trans., 186 A, 031 (1895).
RICHARDS AND HEIMROD. — THE IMPROVED VOLTAMETER. 425
But Kahle * found that in weaker solutions acid is produced instead
of being removed, and we have verified his results. Clearly this must be
due to yet another irregularity. When the solution is dilute and neutral,
oxygen and hydroxy], ions are both present in appreciable amount, ac-
cording to modern electrochemical interpretation. Their greater ease of
deionizatian would compensate for their relatively small concentration,
and traces of negative electricity might be carried out of the solution
through their agency with the formation again of argentic oxide, or even
oxygen gas. The reaction would, however, leave an excess of ionized
hydrogen (acid) in solution, a state of affairs not paralleled in the case of
the nitrite. This would explain the phenomena in question.
But would not the argentic oxide at once dissolve in the simultaneously
formed acid, and thus form argentic nitrate again? Or, in other words,
does argentic oxide form with silver an oxide-complex of any degree of
stability ? Hellvvig f in a recent paper has shown that the weak silver
ion in the presence of the strong N03~ ion tends to strengthen itself by
taking up a molecule of some other undissociated substance, as AgCl,
A"I, A"Br, or AgCN. He has proved also that the solution actually
contains ions like Ag2I+, since on electrolysis the iodine accumulates at
the kathode, and disappears from the anode.
In order to find if argentic oxide could in a similar way associate itself
with the silver ion, we boiled very pure argentic oxide with a concen-
trated solution of argentic nitrate, and filtered the solution hot. Upon
being diluted with cold water this solution yielded a white precipitate,
which turned gray upon standing. The precipitate was soluble in dilute
nitric acid, hence it could not have been an argentic halide ; besides,
every precaution had been taken to exclude the halogens. The com-
pound precipitated on dilution must, therefore, be silver hydroxide or a
basic salt; and a basic complex must have existed in solution.
It is by no means inconceivable that this complex, although finally de-
composed by acid, should not yield at once to its action. In the meantime
the acid, diffusing at a far more rapid rate than the heavy complex, would
have partly left the immediate neighborhood of the anode, and hence the
heavy solution around the latter would fail with its basic load to the
bottom of the kathode vessel. There the complex ion (possibly Ag3Of)
would be capable of transferring electricity as well as any other ion, and
upon deionization would deposit over three times the weight of material
* Kalile, Wied. Ann., 67, I (1899).
t Zeitschr. anorg. Cliem., 25, 157 (1900).
426
PROCEEDINGS OF THE AMERICAN ACADEMY.
contained in the silver ion carrying the same quantity of electricity.
Part of this material would be in the form of oxide, and would therefore
cause dark spots on the surface of the kathode, — spots which have
actually been noticed by other experimenters.
This interpretation serves to explain also the very high results ob-
tained by Lord Rayleigh in the presence of argentic acetate. The
possibility of forming slightly dissociated acetic acid would prevent any
considerably accumulation of ionized hydrogen, and the oxide-complex
would grow in concentration without hindrance. This explanation
seems more plausible than the provisional one suggested by Lord Ray-
leigh, — namely, that the acetate itself might be carried down with the
silver.
In order to submit these interpretations to the test of experiment,
electrolyses were conducted with solutions saturated with argentic oxide.
Kahle, Patterson and Guthe, and others, have likewise carried out such
electrolyses, showing that the deposit is as a matter of fact too great ; but
our trial is easier to interpret, because by means of the porous cup all
anode complications were excluded, and the result of experiment gives
the effect of argentic oxide alone.
Three trials were made, in which a given current of 0.25 ampere as
usual was run first through a standard porous cup voltameter, and then
through a cell precisely similar except that the kathode solution in the
latter was saturated with the argentic oxide,
tains the results : —
TABLE V.
The following table con-
Standaed vs. Standard saturated with Ag20.
No. of
Experiment.
Weisht of
Silver
in Standard.
Weight of
Ag Standard
with Ag20.
Difference.
Percentage
Difference.
18
19
20
grams.
2.30276
2.34799
2.21379
grams.
2.30449
2.34887
2.21489
milligrams.
1.73
0.88
1.10
per cent.
0075
0.037
0.050
Mean
, 0 055
The solution after boiling with silver oxide thus really contains, there-
fore, some ion heavier than Ag+. Since this has been formed directly
RICHARDS AMD HEIMROD. — THE IMPROVED VOLTAMETER.
427
from the oxide, it probably contains Ag20, and may be assumed to have
the formula already given, Ag30+. Thus the preceding interpretation
is confirmed.
The next question which arises concerns the permanence of this com-
plex in the presence of acid. In order to test this, a solution of argentic
nitrate was saturated with argentic oxide, and then treated with a slight
excess of nitric acid. After a short time, perhaps an hour, electrolyses
were made with this solution in series with the standard, as usual.
TABLE VI.
Standard vs. Standard saturated with Ag20, but afterwards acidified.
No. of
Experiment.
Weight
of Ag
in Standard.
Weight Ag
from Sol. with
Ag20+HN03.
Difference.
Percentage
Difference.
21
22
grams.
2.34799
2.21379
grams.
2.34836
2.21361
milligrams.
+0.37
-0.18
per cent.
+0.016
-0.008
The results are somewhat less regular than usual, but clearly most if
not all of the oxide-complex had been removed by the acid. Thus, while
the complex is capable of existence in a neutral solution, the speed of its
reaction with acid results in its decomposition in a short time, as would
be expected.
It is possible that this oxide-complex is not the only one capable of
being formed at the anode. Kahle, Sulc,* Mulder and Heringaf and
others, present evidence showing that with a small anode, where both
silver and nitrate ions would be less available for transferring electricity,
a highly oxidized compound having some such formula as Ag7NOn may
be formed. This compound is capable of dissolving in acids, forming a
brown solution ; and it may be responsible for the colored rings which
Kahle has noticed from old acid solutions. The fact that after boiling
with metallic silver such solutions cease to yield colored rings is evidence
that the foreign compound is a highly oxidized substance.
In spite of the fact that the nitrite, the oxide-complex, and the per-
* Sulc, Z. anorg. Cliem., 12, 89, 180 (1896) ; 24, 305 (1900).
t Mulder and Heringa, Ber d. d. ch. Ges., 29<, 583 (189G).
428
PROCEEDINGS OF THE AMERICAN ACADEMY.
oxide-complex, may explain many of the irregularities observed during
the electrolysis, they cannot explain them all. The chief questions re-
maining to be answered concern the cause of the high results which are
still to be obtained when all the preceding causes of irregularity have
been eliminated, as well as the mechanism of the formation of the plentiful
" anode dust."
A number of facts point to the conclusion that some other complex
compound exists in the electrolyzed liquid which is capable of deposit-
ing metallic silver upon a silver surface. Among others is the well
known fact that a pure silver kathode receives a larger deposit with a
given current than a platinum kathode in the old Lord Rayleigh vol-
tameter. It seemed to be worth while to test once more this relation, in
order to confirm the results of Lord Rayleigh, Kahle, and others, and
also to discover if a pure argentic nitrate solution in the porous cup
voltameter would give like results. The following tables record the
results of our experiments. In the first place we repeated Kahle's ex-
periments, using an anode protected only by filter paper.
TABLE VII.
Filter Paper Voltameter on Platinum and on Silver.
No. of
Experiment.
Weight of
Deposit
on Platinum.
Weight of
Deposit
on Silver.
Difference.
Percentage
Difference.
Weight of
Anode.
23
24
25
26
grams.
2.26680
2.17215
2.18071
2.11134
grams.
2.26672
2.17250
2.18100
2.11162
milligram.
-0.08
4-0.35
4-0.29
4-0.28
per cent.
-0.003
4-0.016
4-0.013
40.013
grams.
2
4.5
6.7
8.8
Mphyi
... . 4-0.010
There is an undeniable surplus when the deposit is made on silver.
The main question now arises, — Is this effect due to the anode solution, or
is it an irregularity which would come equally from pure argentic nitrate ?
The answer to the question is easily determined by means of our porous
cup ; a comparison of deposits made iu a standard voltameter on a silver
and a platinum kathode .gave the following results: —
RICHARDS AND HEIMROD.
THE IMPROVED VOLTAMETER.
429
TABLE VIII.
Standard Method on Platinum and on Silver.
No. of
Experiment.
Weight of
Deposit
on Platinum.
Weight of
Deposit
on Silver.
Difference.
Percentage
Difference.
27
28
grams.
2.69700
2.25769
grams.
2.69674
2.25770
milligram.
0.26
0.01
per cent.
-0.009
+0.000
The only difference is now in the opposite direction ; and this was due
to known experimental error. In experiment 27 a small loss of silver
particles in the wash-water from the silver cell produced the difference of
0.009 per cent. It is highly probable that but for this accident, the deposit
on silver would have been equal to that on platinum, as it is in No. 28.
These results permit us to draw two conclusions. First, it is not the greater
inclusion of silver salt in the crystals which increases the total weight
when the kathode is silver. Otherwise 27 and 28 should have grown
heavier in the same ratio. Secondly, it is the anode solution again
which is responsible.
The increase in the deposit on a silver surface indicates the existence of
silver in the solution in a supersaturated state ; and this existence shows
that there must be present some complex gradually dissociating, with
metallic silver as one of its products. If this is the case, we should ex-
pect to find that an oxidizing environment would be capable of removing
this cause of inaccuracy, while substituting another easily removed by
nitric acid. As a matter of fact, Schuster and Crossly * have shown
that deposits made in vacuo are heavier than when made in air; again
those made in an atmosphere of air are heavier than when made in oxy-
gen. Of course it is understood that in all three cases the anode was
only wrapped in filter paper. The solution usually contained fifteen
per cent of silver nitrate, but sometimes as much as thirty per cent.
They used the solution over and over again, thereby accumulating the
irregular compounds. Under reduced pressure (about " 1 J inch"), the
deposits exceeded those made in air by about 0.04 per cent, while the lat-
ter exceeded those in oxygen by 0.04 per cent more. Myers, f who re-
peated these experiments, found the difference between deposits in air
and in vacuo to be as much as 0.10 per cent for 20-40 percent solutions.
* Proc. Roy. Soc, 50, 350 (1802).
t Wied Ann., 55, 291 ff. (1895).
430
PROCEEDINGS OF THE AMERICAN ACADEMY.
In an atmosphere of nitrogen an excess of .05 per cent in the deposit
was observed. Our own experiments in the same direction verify the
results of these experiments, and need not be recorded here.
Putting aside for the moment the question concerning the nature of
the irregular compound which can thus be partly oxidized out of exist-
ence, it seemed worth while to discover if an oxidizing a<jent in the
solution could remove this compound to such an extent as to cause the
filter paper voltameter to yield accurate results. The only practical
oxidizer for this purpose is hydrogen peroxide. A fairly strong solution
was prepared from pure crystalline barium peroxide and dilute sulphuric
acid. The excess of acid was removed with barium hydroxide, and the
solution was filtered. In this solution the usual amount of silver nitrate
was dissolved, and this was used in the large bowl as well as in the lipped
crucible, both anodes being wrapped in filter paper. In the large bowl
black crystals of argentic peroxide, or Ag7NOn, were soon formed
which bridged across to the kathode. While the result in the bowl thus
became useless, the crucible showed no such disturbance, but yielded
nevertheless a deficit of .14 per cent on comparison with a standard.
This must have been due to a side reaction, especially since the kathode
was found covered with small gas bubbles, which were probably oxygen.
It is possible that negative electricity was carried from the kathode to
the solution by the ionizing of a trace of oxygen. Better results were
obtained after the hydrogen peroxide had been diluted to one-tenth its
former strength ; these are recorded below: —
TABLE IX.
Standard vs. Filter Paper Voltameter containing H.,09.
No. of
Experiment.
Standard.
Filter paper
Voltameter
+ II.,02.
Difference.
Percentage
Difference.
30
31
32
grams.
1.78593
1.78593
1.83375
grams.
1.78648
1.78G42
1.83406
milligram.
0.55
0.49
0.31
per cent.
0.031
0.027
0.017
Mean .
+0.025
The usual difference of from .04 to .08 per cent is thus reduced to
.025 per cent ; therefore hydrogen peroxide seems to eliminate a part
RICHARDS AND HEIMROD. — THE IMPROVED VOLTAMETER. 431
of the usual disturbance. But in view of the fact that even a deficit of
0.14 per cent can be obtained, not much importance can be attached to
these results, since it is impossible to say how much is due to the oxidiz-
ing action, how much to the disturbing influence capable of causing an
actual deficiency.
These indirect methods of determining the presence of a complex yield-
ing metallic silver being somewhat unsatisfactory, recourse was had to a
more direct method. It seemed highly probable that the anode solution
ought to be able to deposit silver without the help of the galvanic current.
In order to show this, a porous cup voltameter was set up in the usual
manner, except that the anode was closely wrapped in filter paper to
retain the fine crystal powder which always separates from it. A current
of 0.25 ampere was sent through the voltameter, and every ten minutes
a portion of the clear anode solution was taken from the bottom of the
porous cup by means of a small pipette, and quickly transferred to a
small weighed platinum crucible.
The crucible had been previously coated with silver in order to estab-
lish equilibrium more quickly in case a compound existed in the solution
which tended to deposit silver.
After one hour's standing, the liquid was removed and the crucible was
washed and dried, as a deposit from electrolysis would have been. The
increase in weight of the crucible must represent the deposit from the
anode solution.
TABLE X.
Gain in Weight of Silver in Contact with Anode Solution.
No. Increase in Weight.
Milligram
33 0.35
31 0.08
35 0.25
3G 0.63
Mean . . 0.33
The weight of the same crucible did not change perceptibly when
allowed to remain in contact with a solution of silver nitrate of like con-
centration, through which no current had previously been passed. The
above increase in weight shows beyond a doubt, therefore, that the anode
solution is capable of depositing on a silver surface either silver or
some compound of this metal which must have been formed at the anode.
432 PROCEEDINGS OF THE AMERICAN ACADEMY.
The most striking evidence that a compound exists around the anode
which is capable of depositing pure silver is the existence of the " anode
dust." This consists of a fine powder, more or less closely adhering to
the anode. Examination with the microscope indicates that this powder
consists of minute crystals, which have every appearance of being metallic
silver. Rodger and Watson * analyzed the air-dried powder, and found
as a matter of fact that the metal is essentially pure. The contrary con-
clusions of Myers f and others may have been based upon results obtained
with small anodes, where argentic peroxide may have been formed.
In our experience the weight of this dust is approximately propor-
tional to the area of the silver anode, with a given current. It seems
highly probable, then, that the silver at first tends to separate from the
anode as a polymerized ion, perhaps Ag3+, according to the common
principle that an unstable compound often forms the bridge between two
stable conditions. $ The greater portion of this complex ion would be
expected to break up at once into the normal argentic ion and metallic
silver (Ag3+ = Ag+ + 2Ag), the latter forming the " anode dust." The
last traces of the complex might, however, persist for some time, and
give rise to all the phenomena seeming to be due to the existence of
supersaturated silver in the solution.
The argument has been so protracted that it is perhaps worth while
to recapitulate the way in which this interpretation would explain the
irregularities not to be attributed to the nitrite and oxycomplexes.
This complex ion of polymerized silver undoubtedly unloads silver at a
lower potential (*. e. more easily) than the simple silver ion. Hence the
larger the kathode surface exposed, the greater part will the complexes
take in the carrying of the current, and the larger will be the deposit of
silver. This consequence of the theory agrees with the experience of
all experimenters. Moreover, since the complexes are unstable, and
continually tending to decompose, there must be always in solution a
trace of molecular unionized silver, which, being supersaturated, will
deposit on contact with solid silver. If the platinum bowl has been
previously lined with silver, this extra deposition will begin almost
immediately ; while if it has not been thus lined, an appreciable silver
surface will have to be formed before the relieving of the supersaturation
will begin to take place. This reasoning explains the invariable excess
of the deposit upon a silver kathode over and above the amount deposited
* Phil. Trans., 186 A, 632 (1895). t Wied. Ann., 55, 295 (1895).
\ Ostwald, Z. phys. Chera., 22, 307 (1897).
RICHARDS AND HEIMROD. — THE IMPROVED VOLTAMETER. 433
on one of platinum by the same current when only filter paper is used
to protect the kathode. The results of Kahle and others seem to indi-
cate that the presence of acid, which prevents the formation of the simple
oxycomplex, is favorable to the formation of the ion Ag3 + . This is
not surprising, since the oxycomplex is probably formed at the expense
of some of the silver which would otherwise remain in the polymerized
condition. The fact that the kathode deposit in the common voltameter
consists of comparatively few large crystals, while the porous cup voltam-
eter yields a host of evenly distributed small crystals, is also explained
by this interpretation. Solutions having a tendency to supersaturation
always tend to deposit large crystals, for obvious reasons. When
the absence of acid increases the number of available hydroxyl ions,
the formation of the silver-complex is less considerable ; but the oxide-
complexes then begin to affect the result. In concentrated solutions of
the nitrate, this ion also enters into the irregularities. Thus the various
irregularities are not necessarily coexistent ; circumstances determine
which one shall play the most importaut part.
There seems, then, to be concordant evidence of conflicting tendencies
at work, some oxidizing and some reducing ; some tending to cause the
dissolving of too much silver at the anode, and some to cause the dissolv-
ing of too little. It seemed worth while to test the complicated conclu-
sion by determining accurately the loss of weight of silver at the anode,
in order to obtain a last ray of light upon the cjuestion. The disintegration
of the anode renders the determination of the loss somewhat difficult ;
but by carefully collecting all the silver powder left in the porous cup
(when no filter paper is used) on a Gooch crucible, and adding this
weight to the weight of the coherent part of the anode, fairly good
results may be obtained. The following table records a series of such
determinations. In each case the current strength amounted to about
0.25 ampere. The experiments are arranged below in the order of cur-
rent density.
In some cases the anode loses more than the ideal amount, in other
cases less. Such results can only be explained by the assumption of
several causes of inaccuracy, and the four which we have discussed sjeem
capable of explaining all the changes. But it is not worth while to
trace out every possible variation ; enough has been said to emphasize
the great complexity of the side reactions which interpenetrate a
process apparently so simple, and at the same time to permit those
readers who are especially interested to work out the combinations for
themselves.
voi.. xxxvii. — 28
434
PROCEEDINGS OF THE AMERICAN ACADEMY.
TABLE XI.
Loss at Anode compared with Gain at Kathode.
No. of
Determ.
Weight of
Anode.
Loss of Anode,
corrected for
Silver Powder.
Deposit
on
Kathode.
Difference
in
Weight.
Percentage
Difference.
37
38
39
40
41
42
43
grams.
6
9
12
13
28
31
oo
OO
grams.
2.43854
2.60603
3.05185
1.76332
2.44485
2.43613
2.60399
grams.
2.43744
2.60420
3.04996
1.76283
2.44599
2.43744
2.60420
milligrams.
+1.10
+1.83
+1.89
+0.49
-1.14
-1.31
-0.21
per cent.
+0.045
+0.070
+0.062
+0.028
-0.047
-0.054
-0.008
In the porous cup voltameter all the anode reactions which constitute
the most serious causes of inaccuracy are safely eliminated by keeping
the contaminated liquid within the porous cup. It is ohvious that this
device, or some other accomplishing the same end, should always be used
when accuracy is desired.
III. The Purity of the Silver Deposit.
An important question remains to be answered, namely, is the deposit
thus obtained perfectly pure silver, or does it contain traces of included
mother liquor?
That impurities in the solution, such as copper, or any of the common
metals occurring with silver, do not affect silver deposit to any great
extent has been shown by Lord Rajleigh. Even if the solution actually
turns green from the copper dissolved at the anode, not a trace of copper
can be detected in the deposit. We used on one occasion commercial
sihier nitrate with an anode of sterling silver wrapped in paper, and
found that the difference between this and the standard was about .024
per cent, or only about .02 per cent smaller than a similar deposit with
the purest silver. Metals of greater solution tension than silver have
therefore no important effect on the weight of silver, although they may
change the structure of the silver deposit. Of course they had always
been excluded in this work.
RICHARDS AND HEIMROD.
THE IMPROVED VOLTAMETER.
435
On the other hand, the deposit, in common with most crystals, may-
retain small quantities of solution or wash-water. Lord Rayleigh seems
to be the only one who has taken this possible source of error into ac-
count. He heated the crucibles to incipient redness, after they had been
dried at 130° to 160°, and weighed. A loss of about .014 per cent
was thus found. Richards and Collins, in looking for an explanation
of the cause of discrepancies in the atomic weight of copper, had
found by analysis the silver deposit to contain about 0.01 per cent of
impurity.
For our purpose the direct method of Lord Rayleigh seemed better
than the indirect analytical one. The deposits, which had been dried
thoroughly at 100° and weighed, were heated over an alcohol lamp to
constant weight. Care was taken to heat the whole crucible evenly, and
to use as high a temperature as possible without the formation of an
TABLE XII.
Loss of Weight of Silver Deposits on heating.
No. of
Experiment.
At 150°.
At Incipient
Redness.
Difference
—0.10 Big.
Percentage
Loss.
grams.
grams.
milligram.
per cent.
44
1.97875
1.97859
0.06
0.003
45
1.97946
1.97907
0.29
0.015
4G
1.98032
1.97998
0.24
0012
47
1.69330
1.69284
0.36
0.021
48
1.G9351
1.69307
0.34
0.020
49
1.69471
1.69411
0.50
0.030
50
2.10356
2.10326
0.20
0.010
51
2.06825
2.06764
0.51
0.025
52
2.31268
2.31234
0.24
0.010
53
2.06714
2.06663
0.41
0.020
54
1.64322
1.64266
0.46
0.028
55
1.64212
1.64166
0.36
0.022
Mean
0018
436 PROCEEDINGS OF THE AMERICAN ACADEMY.
alloy, — although several times this could not he prevented. For heat-
ing the deposits on platinum gauze (see Tahle IX), a small oven was
constructed from a large porcelain crucible, covered by a platinum fun-
nel. The platinum disc was supported by a wire reaching through the
tube of the funnel. In this case, the silver in the platinum crucibles
with which that on the gauze was to be compared, was heated in the
oven also, in order to expose both to the same temperature. Since the
figures of this comparison are given in Table IX, it is necessary only to
tabulate here the loss observed in crucibles when heated directly. Of
course ^allowance has been made for the very slight hygroscopic loss
(0.10 milligram) which a platinum crucible without silver deposit would
have undergone. The silver films were usually those remaining from
some of the preceding determinations.
This percentage loss is slightly higher than that given by Lord Rny-
leigh, and still larger than that determined indirectly by Richards and
Collins. It is evident that the amount of included mother liquor varies
according to the rate and mode of deposition, and it is quite possible that
different average amounts were really included in the several investiga-
tions. The inclusion is probably chiefly in recesses in the platinum
kathode. The differences in included liquid given in the above table are
of the same order as the differences in the uncorrected weights of silver
given at first ; * hence we may ascribe at least a part Of the differences
in the early table to inclusion of mother liquor.
All this evidence unites in indicating that even under the best condi-
tions the silver does not exceed a purity of 99.99 per cent ; and in apply-
ing a correction, one should obviously use the value found in the particular
investigation under review.
IV. The Atomic Weight of Copper.
Having thus clear light upon the various errors of the silver voltam-
eter, it became a matter of great interest to recur to the original ques-
tion which started the whole investigation, namely, the quantitative
accuracy of Faraday's law.
Accordingly, a voltameter like that used by Richards and Collins f —
a modified form of Lord Rayleigh's instrument — was compared with
a standard porous cup voltameter, neither precipitate being ignited. The
* See page 418.
t These Proceedings, 35, 133 (1899).
RICHARDS AND HEIMROD.
THE IMPROVED VOLTAMETER.
437
eighteen results, including three given in the last paper, are recorded
helow : —
TABLE XIII.
Comparison of Porous Cup with modified Lord Rayleigh Voltameter.
No. of
Experiment.
Current
Strength.
Weight Ag
in Standard
(Porous Cup).
Weight Ag in
Filter Paper
Voltameter.
Difference.
Percentage
Difference.
amperes.
grams.
grams.
milligrams.
per cent.
A. 37
1.94124
1.94267
1.43
+0.074
A. 38
1.76283
1.76425
1.42
+0.080
A. 39
3.04996
3.05270
2.74
+0.090
56
0.25
2.26624
2.26680
0.56
+0.024
57
0.25
2.17289
2.17215
0.26
+0.012
58
0.25
2.17896
2.18071
1.75
+0.080
59
0.25
2.11095
2.11134
0.39
+0.019
GO
0.25
2.14906
2.14974
0.68
+0.032
61
0.25
2.09580
2.09648
0.68
+0.033
62
0.25
2.09580
2.09650
0.70
+0.033
63
0 25
1.65487
1.65520
0.33
+0.020
64
025
2.09756
2.09840
0.84
+0.040
65
0.25
2.09756
2.09834
0.78
+0.037
66
0.25
2.02063
2.02100
0.37
+0.018
67
1.25
2.02063
2.02144
0.81
+0.040
68
0.45
2.31490
2.31568
0.78
+0.034
69
0.12
2.22259
2.22343
0.84
+0.038
70
1.00
2.67266
2.67364
0.98
+0.037
Mean .
+0.041
The comparison of the deposits thus shows that when the anode is
wrapped in paper, the deposit is on the average greater by 0.041 per cent.
This average difference is smaller than that given in the previous paper,
but it is probably more accurate, because it comprehends so many deter-
438 PROCEEDINGS OP THE AMERICAN ACADEMY.
minations. The wide deviations between the individual determinations
illustrate the uncertainty of a voltameter in which the anode is merely-
wrapped in filter paper.
When to this difference is added the amount (0.018 per cent) caused
by the included mother liquor, it is obvious that the weight of silver
observed in the experiments upon Faraday's law made by Richards
and Collins must have been 0.059 per cent too heavy. This would
cause the observed electro-chemical atomic weight of copper (63.563 *) to
be too small by the same percentage. Correcting for this error, the
atomic weight of copper calculated from the results of the experiments
upon Faraday's law becomes 63.601, while the most probable value
found in purely chemical ways is 63.604. f
The agreement is as close as the probable accuracy of the electrolytic
determinations. Thus good experimental evidence is furnished, showing
that Faraday's law holds rigorously true in aqueous solution at ordinary
temperatures. Apparent deviations are simply due to the disturbing
effect of side reactions.
V. The Electrochemical Equivalent of Silver.
It becomes now an important matter to determine, if possible, a cor-
rection which might be applied to the methods of earlier physical ex-
periments upon the electrochemical equivalent of the ampere. Such
correction must at best be an unsatisfactory expedient ; the ouly really
satisfactory method of proceeding would be to repeat the work wholly,
using: the new voltameter as a chemical measure of the current. But
such a proceeding involves an expenditure of time not now at our dis-
posal ; hence it seems not wholly fruitless to attempt the correction of
the older results.
The series of comparisons of the standard with the filter paper voltam-
eter just given (p. 422) will hardly serve for the purpose, since the
latter voltameter changes in its indications with every change of form ;
and the two comparisons with Lord Rayleigh's form, given in the
previous paper, form too small a basis upon which to make so serious a
correction. Hence another series of these experiments was made, in
which the porous cup voltameter was compared directly with a voltameter
* This result was obtained by extrapolation for a copper kathode of zero area.
It harl a " probable error " of 0.004, and possibly contained a source of error tending
to make it slightly too large.
I Richards, These Proceedings, 26, 293 (1891).
RICHARDS AND HEIMROD. — THE IMPROVED VOLTAMETER. 439
made exactly according to Lord Rayleigh's directions. These are given
below, together with the two determinations given in the last paper.
TABLE XIV.
Comparison of Porous Cup with Original Rayleioh Voltameter.
No. of
Experiment
Weight of
Silver in
Standard.
Weight of
Silver in
Lord Rayleigh's
Form.
Difference.
Percentage
Difference.
grams.
grams.
milligrams.
per cent.
A. 40
3.09629
3.09918
2.89
+0.093
A. 41
2.53256
2.53439
1.83
+0.072
71
2.16429
2.1G538
1.09
+0.050
72
2.09580
2.09653
0.73
+0.035
73
1.G5487
1.G5549
0.G2
+0.038
Mean
. +0.058
This is 0.017 per cent more than the average of the preceding series.
Probably a mean of the average of the two series, or +0.050 per cent,
represents as nearly as possible the correction to be applied to Lord
Rayleigh's voltameter. This value is not only an average of averages,
involving twenty-three determinations, but is also very nearly the mean
between the two extreme results 0.012 and 0.003. It may probably be
relied upon to within 0.01 per cent of the total weight of the silver.
It finds support in some results given in Kahle's* paper. He made a
comparison between an ordinary voltameter and one in which the anode
solution was constantly siphoned off and thus prevented, more or less
perfectly, from reaching the kathode. The solution in botli voltameters
was strongly acid, but equally so. The siphon voltameter deposited, in
good agreement with the above results, 0.0.3 per cent less silver than
the ordinary voltameter.
The fact, however, that the extremes vary from .012 per cent to .093
per cent indicates that unless great care is taken in the way in which
the anode is wrapped, in the strength of the current and in the size of
the anode, the depositions in the ordinary voltameter according to Lord
Rayleigh are untrustworthy.
* Wied. Ann.N. F., 67, 30 (1899).
440
PROCEEDINGS OF THE AMERICAN ACADEMY.
In order to correct Patterson and Guthe's results, it became necessary
to repeat comparisons of the standard with the voltameter containing
old solution saturated with oxide, as used by them.
TABLE XV.
Standard vs. Patterson and Guthe's Method.
No. of
Experiment.
Date.
Amp.
Weight of
Silver in
Standard.
Weight of
Silver in
P. <&G.
Differ-
ence.
Percentage
Difference.
grams.
grams.
milligrams.
per cent.
A. 43
6-11-99
1.89800
1.90238
4.38
0.230
A. 44
6-18-99
2.55012
2.55460
4.48
0.176
74
3- 6-01
0.25
2.08330
2.08492
1.62
0.078
75
3-14-01
0.25
2.09756
2.09951
1.95
0.094
76
3-27-01
0.25
2.02063
2 02217
1.54
0.077
77
4- 1-01
0.45
2.31490
2.31734 •
2.44
0.106
78
4- 4-01
0.12
2.22259
2.22344
0.85
0.039
79
5- 8-01
1.00
2.67266
2.67527
2.61
0.098
Mean
. 0112
This result is perplexing, and much lower than the average computed
from the first two determinations, which was given in the preceding paper.
It indicates that the Patterson and Guthe method gives results 0.0G per
cent higher than those given by Lord Ravleigh's method, while Patterson
and Guthe's own comparisons give a difference of 0.1 1 per cent.* Evi-
dently the saturated-oxide method is more variable in different hands
even than Lord Rayleigh's. Perhaps the safest number to use in the
correction is the average of both, 0.085 per cent above the Lord Ray-
leigh method, or 0.135 per cent above the porous cup method.
We are now in a position to make an approximate correction for the
effect of the contaminating anode liquid in each of the more important
investigations which bear upon the electro-chemical equivalent of silver.
Of these, those of Lord Rayleigh, Fr. and W. Kohlrausch, K. Kahle,
* Pliys. Peview, 7, 280. Kahle (Wieel. Ann. 67, 32, also Brit. Ass't. A. Sc.
1892, 148), found 0.05 per cent, but his solutions were probably fresher.
RICHARDS AND HEIMROD. — THE IMPROVED VOLTAMETER. 441
and Patterson and Guthe have attracted most attention. Since the first
three investigations used a voltameter of the original Lord Rayleigh
type, a correction of — 0.05 per cent should be applied to each. More-
over, Kohlrausch and Kahle did not heat their deposits to redness ;
hence an additional reduction of about 0.016 per cent* is necessary.
Finally, Kohlrausch deposited the silver on a silver kathode, while
Lord Rayleigh and Kahle made their determinations with platinum
kathodes — a correction which leads to a further reduction of .01 per
cent for Kohlrausch's value, or 0.076 in all. Patterson and Guthe, on
the other hand, deposited the silver on platinum, but used old solutions
saturated with silver oxide. Such solutions may have yielded about
0.135 more silver than the standard. When the correction for heating
is added to this the total reduction becomes 0.15 per cent. Thus we are
led to the following table : —
TABLE XVI.
The Corrected Electrochemical Equivalent of Silver.
(1) Lord Rayleigh and Mrs. Sidgwick,f 0.0011179 —0.050% 0.0011173
(2) Fr. & W. Kohlrausch,* 0.0011183—0.076 0.0011175
(3) Kahle,§ 0.0011183 —0.066 0.0011176
(4) Patterson & Guthe, || 0.0011192-0.150 0.0011175
Average ..... 0.0011175
The greatest deviation from this average is 0.02 per cent, a remark-
able agreement considering the variety of physical method used by the
experimenters. Lord Rayleigh and Kahle used an electro-dynamometer
and Kohlrausch an accurate tangent galvanometer for the calculation of
the current, while Patterson and Guthe made themselves entirely free
from the acceleration of gravity or the strength of the magnetic field by
means of an absolute electro-dynamometer. Hence for the present the
great bulk of evidence seems to favor the value 0.0011175, the mean of
four entirely independent determinations, as the true electrochemical
equivalent of silver. Our data also give the electrochemical equivalent
of copper in the cupric condition as 0.00032929 gram per ampere per
second.
The number of coulombs attached to one gram equivalent of any
electrolyte is therefore 96,580.
* The average of Lord Rayleigh's results and ours.
t Phil. Trans., 175, 411 (1884). } Wied. Ann. N. F., 27, p. 1 (1886).
§ Wied. Ann. N. F., 67, 1 (1899). || Fhys. Review, 7, 257 (1898).
442 PROCEEDINGS OF THE AMERICAN ACADEMY.
A few more points may be touched upon here, which follow directly
from the new value of the equivalent. A great number of physical
instruments have been standardized on the basis of a somewhat higher
electrochemical equivalent of silver, 0.001118. "Will they be affected
by the lowering of this number ? Evidently not, since if the value cor-
responding to a given mode of deposition is applied throughout, when-
ever this method is used, no constant error can result. Thus our low
value cannot be employed when the anode is unprotected, and the de-
posit not heated to redness.
Therefore, as was shown in our last paper, the discovery of a constant
error in the silver voltameter cannot help the discrepancy which exists
between the electrical and mechanical methods of determining Joule's
equivalent.
It is to be hoped that in the future, however, all experimenters will
use some method, such as ours, in which the anode complications are ex-
cluded. Obviously even the present condition of electrical science de-
mands a more precise electrochemical definition of the ampere than that
now prescribed.
The present research seems to define the practical unit of current
strength no less accurately than the practical unit of electro-motive force
has been defined. Thus in a laboratory provided with pure chemicals,
each of these units may be established without outside help, and with
their assistance a standard ohm may be produced without comparison
with any other standard ohm.
VI. Summary.
The results of the prolonged investigation may be summed up as
follows : —
1. The electrochemical equivalent of silver as determined by the
Lord Rayleigh voltameter is too high by at least 0.05 per cent.
2. The true rate of deionization of silver can be determined by the
use of a porous cup which prevents the solution at the anode from reach-
ing the kathode. Results of great consistency and accuracy are then
obtainable.
3. The porous cup does not introduce any new source of error, for
without it the same low results may be obtained when the anode is placed
below the kathode.
4. At higher temperature the complications grow larger.
5. The main disturbing factor is a complex silver ion formed at the
anode and carried over to the kathode, where it decomposes, thereby
RICHARDS AND HEIMROD. — THE IMPROVED VOLTAMETER. 443
increasing the deposit of silver. Most of this potymerized material
decomposes at once, however, forming the silver dust at the anode.
6. The hydroxy! ion discharges at the anode, forming silver oxide
and probably so-called peroxide. Ionized hydrogen is thus developed.
7. Dissolved gases affect the deposit whenever they react with the
complex ions. '
8. Nitrite is formed at the anode, but has probably not much effect
on the weight of the deposit.
9. The deposited silver always contains included solution, varying in
amount from 0.01 per cent to 0.04 per cent according to circumstances.
10. A new name, coulometer, is proposed, to replace the old and
unsuitable designation voltameter.
11. The true electrochemical equivalent of silver is probably
0.0011175 milligram per coulomb.
12. Therefore, 96580 coulombs are associated with one gram equiv-
alent of any electrolyte.
13. The electrochemical equivalent of cupric copper is 0.00032929;
therefore the electrochemical atomic weight of copper (G3.G01) is in
close agreement with the chemical value (G3.604).
14. Faraday's law is thus verified for two kathions more exactly than
ever before.
Cambridge, Mass., U.S.A.
Proceedings of the American Academy of Arts and Sciences.
Vol. XXXVII. No. 17. — March, 1902.
CONTRIBUTIONS FROM THE GRAY HERBARIUM OF
HARVARD UNIVERSITY.
New Series. — No. XXII.
By M. L. Fernald.
I. The Northeastern Carices of the Section Hyparrhenae.
II. The Variation of some Boreal Carices.
With Five Plates.
Copyright, 1902,
By the President and Fellows
of Harvard College.
CONTRIBUTIONS FROM THE GRAY HERBARIUM OF
HARVARD UNIVERSITY.
New Series. — No. XXII.
By M. L. Fernald.
Presented May 8, 1901. Received January 31, 1902.
I. — THE NORTHEASTERN CARICES OF THE SECTION
HYPARRHENAE.
The Carices of Koch's subgenus Vigneae, with its sections Acroar-
rhenae and Hi/parrhenae of Fries, have always perplexed the systematist,
and by the general student they have as a rule been ignored or vaguely
referred to such characteristic species as Carex straminea or C.
echinata. Recently, however, the generally widening interest in sys-
tematic botany has brought together in Carex, as in other groups, a
large mass of material ; and an attempt to identify these specimens has
made it necessary to study in great detail the minuter but tolerably con-
stant characteristics of the fruiting plants.
In general, the classification of Carices has always been based upon
characters in the inflorescence ; and although the detailed study of the
perigynia (or utriculi) has been the final resort of the specialist, an
attempt has been made in our manuals to separate species as much as
possible upon the more obvious characters of the inflorescence. Thus
Carex scoparia is described in the two current manuals as having the
spikelets (spikes) " all contiguous or bunched " or " usually aggre-
gated; " while in oidy one of these works is Boott's var. minor
given recognition, and there as a mere dwarf variety. Yet in plants
which are undoubtedly C. scoparia the spikelets are often scattered,
forming a loose moniliform spike ; and the northern plant described by
Boott as var. minor has a distinct range and unique habitat, while its
minute thick-bodied perigynia distinguish it at a glance from the more
southern species with which it has been associated.
The case of Carex scoparia is only one of many in which the attempt
to rely upon superficial characteristics has led us to confuse plants
448 PROCEEDINGS OF THE AMERICAN ACADEMY.
which are genetically very distinct. Consequently, as stated, an attempt
has been made to get at a more satisfactory basis for classification by
studying the characteristics of the perigynia, which, naturally, are sub-
ject to less variation than is the superficial aspect of the inflorescence
as a whole. But since variations in texture and nerving, which are per-
fectly evident upon comparison of specimens, are extremely difficult to
render clear iu descriptions, it has been found advisable to employ as
the primary basis of division, at least in the groups here discussed, the
actual or proportional measurements of the perigynia or the achenes.
Even this method of careful measurement may sometimes prove mislead-
ing, but in most species the perigynia vary within certain clearly defined
limits, and it is only the very exceptional individual which will not fit
the system here proposed. And, although in rare cases a species thus
presents perplexing forms in which the perigynia are not characteristic,
many attempts to classify the members of this group have convinced
the writer that by actual measurement alone can we safely identify
plants of such strong outward resemblance as Carex straminea, C
scoparia and C. tenera, or C. alata and C. albolutescens.
As a result of these studies it has been found desirable to treat many
plants in a manner somewhat different from that in any current synopses
of the genus, and in some cases a study of the original descriptions and
specimens has brought the writer to conclusions very different from
those generally accepted by American caricologists. Some of these
points are of slight significance, others of fundamental importance ; and,
since it is inadvisable to complicate the synoptic treatment of the species
with detailed discussions as to the identity and synonymy of different
forms, the more important questions may be here discussed.
Carex scoparia, Schkuhr, presents little difficulty, as the original
figure is unmistakable. The species has, however, been made to harbor
plants of very different aspect ; and a study of the fruiting characters
shows these to fall into three groups with marked and constant char-
acteristics. C. scoparia, itself, has the perigynium very thin and scale-
like, with the wings so strongly developed as to minimize the apparent
thickness of the body. This plant in its different forms is of broad
range south and west of the Gulf of St. Lawrence.
The other two species which have been included with Carex scoparia
have the narrower subulate or elongate-lanceolate perigynia so little
winged as quite to lack the scale-like character seen in that species.
The best known of these two plants is the form described by Francis
Boott as C. scoparia, var. minor. The material from which Boott's
FERNALD. — CARICES OF SECTION HYPARRHENAE. 449
plate was drawn was collected by Tuckerman at the base of the White
Mountains; and since it is necessary to distinguish the plant by a new
specific name {minor having been used too often as a varietal name to
be eligible) and since there is already a Carex Tuckermani, it is a
pleasure to commemorate the explorations and generous services of the
Crawford family, familiar to a long generation of visitors to the White
Mountains. This plant with which their name now becomes associated
is common in northern New England and about the Great Lakes, thence
extending far northward.
The other plant with narrow thick perigynia is more puzzling. In
the dark brown color of its broad scales it is unlike the other forms
which have been referred to Carex scoparia. In fact, by different
students it has been referred with doubt to C. tribuloides, C. lepornia,
and C. foenea as well. Yet in its perigvnium it resembles only Boott's
C. scoparia, var. minor. This tall dark-spiked plant, which is common
in the region of Orono, Maine, has been collected by Professor Lamson-
Scribner and by the writer, but it seems to be unknown from other
regions. This fact immediately suggests that it may be an introduced
form, but a careful search through Old World material and descriptions
fails to show anything to which it cau be referred. It is, therefore,
here treated as a local species, taking the name of the town from which
all our material has been collected.
One other form of the scoparia group should be specially mentioned
since, by an unfortuuate misinterpretation, it has already caused needless
confusion. This is Carex scoparia, var. moniliformis, Tuckerman. A
specimen in the Gray Herbarium from Tuckerman himself, is without
question a slender-spiked form of C. scoparia. The variety was so
treated by Francis Boott, in whose table 3G8 it is well represented.
Yet in his Preliminary Synopsis of the genus Professor Bailey treated it
without question as identical with his own C. tribuloides, var. reducla ;
and Professor Britton, following las lead, has since made the new com-
bination, (7. tribuloides, var. moniliformis (Tuckerman) Britton, for a
plant very different from that to which the varietal name was originally
applied.
Carex tribidoides, Wahl., has been clearly treated by Professor Bailey.1
C. Bebbii, Olney, however, which by him is reduced to a variety of that
species, seems to be as well marked as other members of the subgenus,
and it is here given equal rank with them. In its shorter, broader, and
i Mem. Torr. CI., I. 54.
vol. xxxvu. — 29
450 PROCEEDINGS OP THE AMERICAN ACADEMY.
thicker perigynia it is more nearly related to C. straminea and its
allies. So, likewise, C. cristata, Schwein., is reinstated as a species,
since its tolerably constant habit and its shorter, firmer perigynia place
it as near C. straminea as to C. tribuloides.
The diverse plants which have been treated by various authors, now
as distinct species, now as forms of Carex straminea, fall into groups
which are, in the main, fairly free from complexity. The attempt to
separate these forms by color-characters has naturally led to much con-
fusion, for plants which in bright sunlight have a strongly marked
ferrugineous tendency, in shade are often quite green. The shape, size,
nerving, and texture of the perigynia, however, show that almost with-
out exception the species proposed by Willdenow, Schkuhr, Torrey,
Schweinitz, Dewey, and other early students of the group were based on
permanent characters. To treat all these well marked and constant
forms as varieties of one species is adding confusion rather than clearness
to our interpretation of the genus, especially when several of them are
as closely related to other well recognized species.
The identity of Willdenow's Carex straminea was settled by Professor
Bailey1 in 1889, and a recent examination of Willdenow's material by
Dr. J. M. Greenman has verified Professor Bailey's conclusions. C.
albolutescens, Schweinitz, is now well understood, as are likewise C.
mirabilis, Dewey, C. tenera, Dewey, C. Bichiellii, Brittou (C. straminea,
var. Crawei, Boott), and C. alata, Torrey. But C.festucacea, Schkuhr,
C. straminea, var. brevior, Dewey, and C. foenea, var. /3, Boott, seem
to have been less clearly understood.
Schkuhr's Carex festucacea, according to the original description, was
a plant with about eight spikelets subapproximate or in a loosely
cyliudric spike, and the species is so represented in Schkuhr's figure. It
is likewise well represented by Dr. Boott, who apparently had a clear
conception of the species, in his table 386. Schkuhr's C. straminea,
which we now know to be different from Willdenow's plant of that name,
was an extreme form of C. festucacea with fewer spikelets, and until
recently it passed as the type of the species ; i. e., C. straminea (typica)
of Boott and others. This plant, however, was called by Dewey C.
straminea, var. brevior, and under that name it has been treated by
Professor Bailey. He includes with it, though, the C. festucacea of
Schkuhr, a plant which, though closely related, is of rather marked
appearance and of more limited range. More recently Dr. Britton, in
i Mem. Torr. CI.. I. 21.
FERNALD. CARICES OF SECTION HYPARRHENAE. 451
restoring to specific rank G festucacea, has included in it Dewey's G.
straw inea, var. brevior, and in the Illustrated Flora he figures the
latter plant under the former name. But the late Dr. Eliot C. Howe,
in his admirahle treatment of the New York Species of Carex, has
recognized both plants, thus following the general treatment of Francis
Boott and other earlier writers and at the same time clearing the names
festucacea and brevior from the confusion which has recently surrounded
them.
Carex foenea, var. /? of Boott has had a peculiarly unsettled history.
When Francis Boott described and figured the plant as a variety of C.
foenea, the latter name applied to G albolutescens, Schweinitz, not to
the true G. foenea of Willdenow. It was Boott's opinion, then, that
the slender brown-spiked plant of the interior was a phase of what we
now know without much doubt to be G. albolutescens. In the fifth
edition of the Manual Dr. Gray took up G. foenea, var. ft as G. foenea,
var. ( ?) ferruginea ; and later the plant was distributed by Oluey as a
variety of Dewey's G tenera (G. straminea, var. aperta, Boott). In his
Preliminary Synopsis in 1886, Professor Bailey reduced it to synonymy
under G. straminea, Schkuhr (not Willd.), aud later in his Critical
Studies of Types he treated this plant along with C. festucacea, Schkuhr,
and C. straminea, var. Grawei, Boott (C Bicknellii, Britton) as iden-
tical with C. straminea, var. brevior, Dewey (C. straminea, Schkuhr,
not Willd.). Subsequently, however, he has taken out of his C. stra-
minea, var. brevior, two plants, which he treats as parallel varieties,
var. Crawei, Boott, and var. ferruginea (C. foenea, var. /?, Boott); and at
the same time he has discussed as a species C. albolutescens, Schweinitz
(C. foenea of authors, not Willd.). This course has greatly cleared
the group from its former confusion ; but it is unfortunate that while
separating C. albolutescens specifically Professor Bailey should have
attached C. foenea, var. fi to the slender usually flexuous-spiked C.
straminea, whose identity he had already so carefully worked out. C.
foenea, var. fi in its stiff habit, its strongly appressed broad-ovate peri-
gynia, and the texture of its leaf-sheaths, is quite unlike that species,
but is very close to C. albolutescens with which it had been placed by
Francis Boott. In these characters, likewise, it is equally close to C.
alata, Torr., while its perigynia and the occasional awn-tips of the scales
are so like those of the latter species as to place it nearer to that than
to the former plant.
The two species, Carex foenea, Willd., and C. adusta, Boott, have
already been discussed and very clearly settled by Professor Bai-
452 PROCEEDINGS OF THE AMERICAN ACADEMY.
ley. 1 But his own C. foenea, var. perplexa has proved very puzzlino- to
students of the groujj. In the original description of this varietv at
least two distinct species are referred to, while the words " head erect or
nearly so " have proved misleading for u plant with more rlexuous spikes
(heads) than ordinarily occur in the type of the species.
Dr. J. M. Greenman has kindly compared with Willdenow's orio-inal
material various plants passing in America as Carex foenea, and he has
furnished the writer with detailed camera-drawings from Willdenow's
material. From these comparisons there seems no doubt that the origi-
nal C. foenea was, as Professor Bailey has already stated, the smallest
form of the species, with 4 to 9 spikelets in a suberect linear-cylindric
spike. This is the plant subsequently described by Tuckerman as
C. argyrantha and figured by Boott in his table 382, fig. 2.
Professor Bailey's Carex foenea, var. perplexa was based on Boott's
table 380 and, a portion of table 382 (presumably fig. 1), upon Olney's
C. albolutescens (Exsicc. fasc. 1, no. 8), as well as his C. albolutescens,
var. sparsiflora (fasc. V. no. 11). Now, the perigynia of good Carex
foenea are strongly and conspicuously nerved on both faces, and the
spikelets are pale green or silvery brown. The first part of var. per-
plexa (Boott's table 380) shows a perigynium quite nerveless or only
faintly short-nerved on the inner face ; the second component (table
382, fig. 1) is the characteristic large form of C. foenea with crowded
spikes of large spikelets; the third (C. albolutescens of Oluey) is, as
represented by two sheets in the Gray Herbarium, a form betweeu the
large state and the small typical C. foenea ; while the fourth component
(C. albolutescens, var. sparsiflora, Oluey — at least the New Brunswick
plant) in habit as well as in the nerveless inner face of the perigynium
closely matches the first cited plate (Boott's table 380). From the fact,
that vox. perplexa was proposed as a variety of C. foenea it is probable
that its author had in mind the coarse form represented by Boott's table
382, fig. 1, and in the present treatment of the group it has seemed
advisable to retain that name for the large plant.
Olney's Carex albolutescens, var. sparsiflora is represented in the
Oluey Herbarium by two different plants. One of these, from Oregon,
is the dark-spiked form of C. praticola which has been described as C.
pratensis, var. furva, Bailey. The other, from Kent Co., New Bruns-
wick, the northeastern plant which is identified with Boott's table 380, is
much more closely related to C. adusta, Boott, than to C. foenea, Willd.
i Mem. Torr. CI., I. 24
FERNALD. CARICES OP SECTION HYPARRHENAE. 453
From the former species it differs constantly in its more slender habit
and flexuous elongated spikes of clavate-based spikelets, as well as iu
smaller achenes. It is a plant of broad range from Labrador to British
Columbia, creeping south to the coast of New England and the mountains
of New England and New York. Since its varietal name, sparsijiora,
is preoccupied in the genus, another specific name is here proposed in
reference to the characteristic color of the mature inflorescence.
The other large group of the Jlyparrhenae which has been treated
by recent authors as the subsection Elongatae contains plants of two
markedly different tendencies. One group is characterized by strongly
divergent thin-edged perigynia which are spongy at base. The other
group has ascending plump or plano-convex perigynia which are rarely
thin-edged and are without conspicuously spongy bases. Mr. Theodor
Holm, who has recently studied some of the members of the first group,
includes with them Carex gynocrates and C. exilis, which by most other
authors have been placed in the Dioicae. The texture and aspect of
the perigynia seem to justify the treatment proposed by Mr. Holm and
formerly for C. exilis by Francis Boott;1 and for the group thus con-
stituted Mr. Holm suggests the name Astrostachyae.2 The other group,
with ascending blunt-edged perigynia, may well retain the subsectional
name Elongatae, since the characteristic species, C. elongata, C brunne-
scens (C. Gebhardii), C canescens (C curtd), etc., were originally
included in it by Kunth.
Mr. Holm, in the paper cited, takes exception 3 to Professor Bailey's
recent treatment4 of Carex echinata, C. sterilis, and C. scirpoides, on
the ground that that author had been more controlled by the original
specimens of Willdenow and of Schkuhr than by the original diagnoses.
That Willdenow's original descriptions do not accord well with Pro-
fessor Bailey's conclusions there can be no doubt ; and when we are
told by Professor Bailey that C. sterilis and 0. scirpoides are identical,
and when he says "the figures of both G. sterilis (fig. 146) and C. scir-
poides (fig. 180) in Schkuhr's ' Riedgraser ' are unequivocal,"5 we find
it indeed difficult to understand his observations. An examination of
Schkuhr's figures shows his C. sterilis (fig. 146) to be a coarse plant
with sharp-pointed ovate scales and broad-ovate cordate perigynia with
distinct beak shorter than the body. Schkuhr's O. scirpoides (fig. 180),
on the other hand, is represented with broad-obloug or elliptical blunt
1 Boott, 111., I. 17. - Holm, Theo., Am. Jour. Sci., Ser. 4, XI. 205-223.
3 Holm, 1. c, 212. 4 Bailey, Bull. Torr. CI., XX. 422.
5 Bailey, 1. c, 424.
454 PROCEEDINGS OP THE AMERICAN ACADEMY.
scales and deltoid-ovate obscurely short-beaked perigynia. These figures
of Schkuhr's agree very well with his descriptions. Furthermore, they
agree equally well with Willdenow's diagnoses, for these latter were
essentially the same as Schkuhr's. Professor Bailey further states that
C. sterilis and C. sc/'rpoides are identical with the common American
plant which he had formerly treated as C. echinata, var. microstachi/s,
a plant with lanceolate or narrowly ovate slender-beaked perigynia ;
and for this aggregate he takes up the name C. sterilis. After thus
bunching three very different species as C. sterilis, lie separates from
"our so-called Carex echinata" two plants, C. atlantica and C. interior,
with '; ample specific characters."
Through the kindness of Dr. J. M. Greenman the writer has been
able to examine camera-drawings of Willdenow's original material ;
while from Professor Carl Mez he has received fragments from the
original material of Schkuhr. The drawings of the Willdenow mate-
rial of both Carex sterilis and C. scirpoides, and the Schkuhr specimens
of C. scirpoides agree with the original diagnoses. Dr. Greenman has,
further, compared critically specimens sent him of the different Ameri-
can forms with Willdenow's plants and with authentic specimens of
C. stellulata, Gooden. (C. echinata, Murray). The identification thus
made of these forms, leads to a conclusion very different from that
published by Professor Bailey. These results may best be stated by
discussing separately the three clearly cut species which have been so
unfortunately confused.
Carex echinata, Murray (C stellulata, Gooden.). This species was
long considered a boreal plant of broad range, and it was so treated
by Torrey, Tuckerman, Dewey, Carey, and other early students of
American Carices. Francis Boott distinctly implied that the European
species occurs in British America, saying: "I have not seen specimens
which I can satisfactorily refer to the European C. stellulata, south of
the British provinces of North America." 1 Yet Professor Bailey has
interpreted this to mean that " Francis Boott questioned if the Ameri-
can plant is the same as the European C. stellulata (or C. echinata) ; "
and in "eliminating the European species from our flora," he says:
" Definite specific characters of separation are obscure, and yet I am
convinced that they exist. The American plant is habitually taller
than the European, the scales are sharper and usually longer, the
perigynia are more strongly nerved and more attenuated or conical,
i Boott, 111., I. 56.
FERNALD. — CARICES OF SECTION HYPARRHENAE. 455
and above all, it is far more variable. . . . There are probably no
species common to both countries, except those which are hyperboreal
and occur through the Arctic regions of both hemispheres, being found
in Greenland." *
Then Professor Bailey defines his conception of the "habitually
taller" American plant with "sharper" scales, etc., etc., including in it
forms varying from the low slender Carex stellulata, var. angustata,
Carey, with " narrowly-lanceolate perigynia tapering into a long . . .
beak,"'2 to the tall (often nearly 1 m. high) coarse C. sterilis, Willd.,
with broad-ovate perigynia, and the slender C. scirpoides, Schkuhr, with
thick scarcely beaked often nerveless deltoid-ovate perigynia and elliptic
blunt scales. The two latter constituents of this aggregate apparently
do not occur outside North America and if they are included with the
other American representative of C. echinata as one species, it is of
course easily said that the American plant is taller or shorter, coarser or
more slender than the European ; and certainly a species so constituted
is " far more variable."
When, however, we eliminate from the complex Carex sterilis of Pro-
fessor Bailey's treatment the true C. sterilis and C. scirpoides, there is left
a plant characterized by slender culms and leaves, the perigynia barely
half as broad as long, and tapering to a slender conspicuous beak which
is often nearly as long as the body. This is the C. echinata or C. stellu-
lata of American authors and it includes as formal variations the very
slender var. angustata, Carey (C. echinata, var. tnicrostachys, Boeckeler),
and the tall C. sterilis, var. excelsior, Bailey, while a very coarse varia-
tion with rather better defined characteristics is C. echinata, var. cep/ia-
lantha, Bailey.
This American species with the narrow perigynia has been compared
many times by the writer with European C. echinata in a vain attempt
to find some point of distinction. Specimens collected by Godet at
Lignieres on the River Cher in central France are inseparable from
Mertens' material from Sitka, and, again, Japanese specimens collected
by Chas. Wright and by Maries are identical in their slender perigynia
with Newfoundland plants. In order, however, to test still further the
specific value of the American plant a portion of Allen's Labrador mate-
rial was forwarded to Dr. Greenman at Berlin, and he was asked to
compare it, along with other American forms, with Willdenow's types
1 Bailey, Bull. Torr. CI., XX. 423.
- Carey in Gray, Man. 544.
456 PROCEEDINGS OF THE AMERICAN ACADEMY.
and with other authentic European specimens of the group. In reply
Dr. Greenman writes of this specimen :
" No. 4. Differs from the original C. sterilis, Willd., in the following
characters : (a) narrower, more gradually acuminate and longer beaked
perigyuium ; {b) more oblong achene, which is less narrowed at the
base. To me, however, your No. 4 is a perfect match for Carex stellu-
lata in herb. Willdenow, and for European C. echinata, Murr. I am
quite unable to make any distinction between them. The perigynial
characters are exactly the same."
Extreme difficulty is experienced, then, in attempting to distinguish
the American Carex echinata from Old World material. The range of
the American plant, too, from Labrador to Alaska, and southward in the
mountains, immediately places the species in the hyperboreal flora from
which Professor Bailey, at least by inference, would exclude it. In view
of these two facts there seems, then, as Mr. Holm has already indicated,
good reason to consider both the American and the European plant C.
echinata, Murr.
Carex sterilis, Willd. This plant has already been sufficiently defined
in the discussion of Willdenow's original description and of Schkuhr's
figure. The writer has, however, examined with much care camera-
drawings of Willdenow's material made by Dr. Greenman and fragments
of Schkuhr's material generously sent by Professor Carl Mez. The
Willdenow plant, which alone is of final importance, proves to be iden-
tical with the large species of the Atlantic seaboard recently described
as C. atlantica. The fragment sent by Professor Mez from the Schkuhr
herbarium is, however, from cultivated material, and is only a form of
C. echinata with narrow perigynia quite unlike those shown in Schkuhr's
figure and in the Willdenow plant as further shown by Dr. Greenman's
report of his critical comparisons in the Willdenow herbarium.
Besides No. 4, the Labrador Carex echinata, two other forms were
sent to Dr. Greenman for comparison with C. sterilis. No. 1 is C.
echinata, var. cephalantha, Bailey, collected by Dr. C. B. Graves at
Waterford, Connecticut, May 27, 1896. No. 2 is characteristic C. at-
lantica, Bailey, collected by Dr. G. G. Kennedy at Ponkapog, Canton,
Massachusetts, July 12, 1899. Of these two plants Dr. Greenman
writes :
"No. 1. This differs from C. sterilis, Willd., in the following charac-
ters: (a) longer inflorescence, more remote and slightly longer spikelets;
(b) longer and more prominently beaked perigynium ; (c) achene less
narrowed at the base.
FERNALD. — CARICES OP SECTION HYPARRHENAE. 457
"No. 2. I am quite unable to distinguish this plant from the original
of C. sterilis, Willd. It has the same broad-ovate, short-acuminate or
short-beaked perigynium, and tbe same achenial cliaracters, that is, the
achene is rather conspicuously narrowed below. The characters of the
inflorescence are the same, except as to color. The Willdenow plant is
more brownish : this, however, may be due, at least to a certain extent,
to age."
From Willdenow's original description, from Schkuhr's description
and figure, and from Dr. Greenman's examination and drawings of the
Willdenow plant, there seems no question, then, that Carex atlantica,
Bailey, is the true C. sterilis, Willd.
Carex scirpoides, Schkuhr. The characters of this species, likewise,
are sufficiently stated in the discussion of Schkuhr's and Willdenow's
characterizations. Material from the Schkuhr herbarium received through
Professor Mez is identical with camera-drawings made by Dr. Green-
man from Willdenow's plant. These accurately agree, also, with
Schkuhr's fig. 180. This species, was, furthermore, correctly inter-
preted by Sartwell, Carey, and Boott, and it is well represented as 0.
stellalata, var. scirpoides in Boott's Illustrations, t. 146.** Sartwell's
No. 36 and Boott's plate are the only exact citations given by Professor
Bailey for his C. interior, and his description of the so-called new species
accords well with those of Willdenow and of Schkuhr. In distinguishing
C. interior from C. scirpoides, Bailey says that the former has " greenish-
tawny spikes," while the latter is "fulvous;" and he furthermore de-
scribes Schkuhr's C. scirpoides, " as the plate plainly shows," with
"long-beaked broad-winged perigynia." How such a statement and
such conclusions could have been made is very puzzling. There can
be no question, however, that the figure of Schkuhr's C. scirpoides as
interpreted by Dewey, Schweinitz, Torrey, Sartwell, Carey, Francis
Boott, Holm, and other students of the genus, is the same as Boott's
table 146** upon which, ii part, C. interior was founded.
The name Carex scirpoides, Schkuhr, so long attached to this plant,
was published in 1805, but it cannot, unfortunately, be retained for the
species, since in 1808 Michaux published C. scirpoidea, the well known
dioecious plant of extreme boreal and alpine regions. The next clearly
defined name for the plant seems to be C. interior, although, as originally
intended by its author, that name was supposed to apply to a species
very distinct from C. scirpoides. Tuckerman, it is true, published in his
Enumeratio Methodica the name C. stelhdata, var. scirpina, citing C.
scirpoides, Schkuhr, as a synonym. On a preceding page, however,
458 PROCEEDINGS OF THE AMERICAN ACADEMY.
in an unfortunate endeavor to latinize one of Michaux's names, he had
substituted C. scirpina for C. scirpoidea, Michx., not C. scirpoides,
Schkuhr. This unfortunate citation of WC. scirpina" as a pure synonym
of Michaux's C. scirpoidea attaches to that name a decided element of
indefiniteuess. It is, therefore, wiser to take for the plant of Schkuhr
and of Willdenow the more clearly defined name, C. interior.
One other plant of the Astrostachyae has been the source of much con-
fusion in the treatment of New England species of this group. Unlike
Carex echinata, C. sterilis, and C. interior, the perigynia of this plant
are broadest at the middle, thence tapering to a narrow base. In aspect
the plant is strikingly like the largest form of C. canescens, but its thin-
edged strongly recurved perigynia place it clearly in the Astrostachyae.
The species is not uncommon from eastern Massachusetts to Delaware
and central New York, and in New England herbaria it has recently
passed variously as C. atlantica, C. interior, C. canescens, var. vulgaris,
C sterilis, var. excelsior, &c. From notes left by the late William
Boott it is apparent that he recognized in some of Chas. Wright's
Connecticut material an undescribed form, but evidently he never
described the plant. A portion of the original material of the late
Dr. Eliot C. Howe's Carex seorsa, generously furnished the writer by
Professor C. H. Peck, agrees in every regard with the perplexing New
England plant, and under that name the species should now be known.
The members of the Elongatae, as here interpreted, offer less difficulties
than the other species of the Hyparrhenae, and special discussion is
needed only of the forms which have been at various times associated
with Carex canescens. These plants present two marked forms in their
perigynia : in one plant, C. arcta, the perigynium is broadest at the
rounded or subcordate base; while in C. canescens and C. brunnescens
( C. vitilis, Fries) the perigynium is nearly elliptic in outline, being
broadest near the middle.
Carex arcta of Francis Boott was originally published by him as C.
canesceyis, var. polystachya, but in his latest treatment of the plant he
considered it a distinct species. As stated, its perigynial character is
very constant. Furthermore, its rather limited strictly American range
and unique habit quickly separate it from most forms of C. canescens. C.
canescens, var. oregana, Bailey, said to differ from var. polystachya in
having the " bead larger and more dense . . . becoming brownish,"
has identical perigynia with that plant, and the spikes (heads) are green
or brownish, as are those of the eastern plant, a character dependent on
age and exposure to light.
FERNALD. CARICES OF SECTION HYPARRHENAE. 459
Car ex canescens, L., is characterized by its glaucous color and strongly
appressed-ascending elliptic pointed perigynia tapering very gradually
to, the short beak. Another plant, C. brunnescens, Poir. (C. canescens,
var. alpicola, Wahl., C. canescens, var. vulgaris, Bailey), is usually
bright green, and the few loosely spreading-ascending perigynia are
rather abruptly contracted to a definite serrulate-based beak. This plant
is common in dry soils throughout the boreal sections of America and
Europe ; while the glaucous G. canescens is a species of very wet
situations. Under various names, G vitilis, Fries, C. Gebhardii, Hoppe,
etc., C. brunnescens has been treated as a species, and as often agaiu as a
variety of C. canescens. An examination of much material shows its
characters to be essentially constant, and, though the plant superficially
resembles small forms of C. canescens, its claim to specific rank rests
upon a number of definite characters.
When Carex arcta aud O. brunnescens are removed from C. canescens,
there remains a species characterized by its glaucous foliage and ap-
pressed scarcely beaked perigynia. This species presents in America
three noteworthy variations. The true C. canescens, L., of northern
Europe has the spikes 2.5 to 5 cm. long, of 4 to 7 oblong-cylindric to
narrowly obovoid spikelets 0.6 to 1 cm. long. This plant occurs in
Arctic America coming south to northern New England and New York,
the Rocky Mts., and Vancouver. Rare in the eastern United States
and Canada, the typical form of G canescens has been misinterpreted
by recent American students, although the species was very clearly
discussed by Francis Boott. The American plant which has passed
as true G. canescens is, however, strikingly different in aspect, and
consequently the typical plant has more than once been published as
a local American variety — var. dubia, Bailey, and var. robustina,
Macoun.
Another form of Carex canescens common to northern Europe and
America is var. subloliacea. Laestadius. In this plant the spike is
usually rather shorter than in typical C. canescens, the less approximate
globose or short-oblong few-flowered spikelets are only 4 to 7 mm. long,
and the smaller perigynium is nearly or quite smooth. In its smooth
perigynium this plant approaches C heleonastes, which, however, has
larger spikelets and perigynia and quite lacks the distinctive glaucous
aspect of C. canescens. The var. subloliacea, which is commoner in
northern New Eugland than is the true C. canescens, also simulates
G. brunnescens ; but it is very canescent and the perigynia otherwise as
in true G. canescens are essentially smooth, while in the greener C.
460 PROCEEDINGS OF THE AMERICAN ACADEMY.
brunnescens they are distinctly beaked, of more membranous texture, and
usually with serrate margins.
The commonest form of Corex canescens in North America is the
plant mentioned without name by Francis Boott and figured by him
in his Illustrations, IV. table 496. This unique American form, which in
essential characters is like true C. canescens, differs in its elongated in-
florescence, 5 to 15 dm. long, at least the lower spikelets very remote.
The plant seems to have been generally treated by American authors as
typical C. canescens, and no published name is available for it.
The following synopsis presents the characters and ranges of the
northeastern Hyparrhenae as now understood by the writer. In its
preparation he has studied the material in the Gray Herbarium and the
herbarium of the New England Botanical Club ; as well as the hundreds
of sheets in the herbarium of the Geological Survey Department of
Canada, kindly placed at his disposal by Mr. James M. Macoun ; those of
the Olney Herbarium of Brown University, made accessible to him by Mr.
J. Franklin Collins; and a series from the Fairbanks Museum at St. Johns-
bury, Vermont, rich in forms of the scoparia group, specially accumulated
by the director, Dr. T. E. Ilazen, for detailed study, and then generously
forwarded to the writer. He has also been greatly assisted by the use
of material from the private herbaria of the Honorable J. R. Churchill ;
President Ezra Brainerd ; Doctors C. B. Graves, J. V. Ilaberer, G. G.
Kennedy, and C. W. Swan ; and Messrs. Luman Andrews, C. H. Bissell,
Walter Deane, E. L. Rand, W. P. Rich, and E. F. Williams. The
identification of dubious species of Willdenow and of Schkuhr has been
facilitated by the cooperation of Dr. J. M. Greenman while at the Royal
Botanical Museum in Berlin, and by Prof. Carl Mez of the University
of Halle ; and authentic material of the late Dr. E. C. Howe's Car ex
seorsa has been generously furnished by Prof. C. H. Peck.
HYPARRHENAE, Fries. Staminate flowers scattered or at the
base of the uniform spikelets (only in exceptional individuals and in the
often dioecious C. gynocrates and C. exilis the entire spikelet staminate).
Key to Species.1
* Perigynia with thin or winged margins.
•4- Perigynia ascending, the tips only sometimes wide-spreading or recurved,
not spongy at base, the margins winged at least toward the beak.
1 The perigynial characters are here based on study of mature plants. In gen-
eral the perigynia at the tip of the spikelet are less characteristic than those nearer
the middle ; and, if possible, the latter alone should be used in critical comparisons.
FERNALD. — CARICES OF SECTION HYPARRHENAE. 461
- Bracts wanting or setaceous, if broad at most twice as long as the spike.
= Plant strongly stoloniferous ; culms rising from an elongated root-
stock : perigynium firm, 5 to (3 mm. long (4) C. siccata.
= Plant not strongly stoloniferous ; culms solitary or in stools.
a. Perigynia less than 2 mm. broad.
1. Perigynia 5 mm. or more long.
O Perigynia 7 to 10 mm. long: spikelets oblong-cylindric, pointed,
1.5 to 2.5 cm. long (1) C. muskingumensis.
O O Perigynia shorter (or, when exceptionally 7 mm. long, in
shorter spikelets).
+ Perigynia half as broad as long, plump, nerveless or obscurely
short-nerved on the inner face (21) C.aenea.
+ + Perigynia one-third as broad as long.
X Perigynia thin and scale-like, scarcely distended over the
achenes, distinctly nerved on the inner face, and promi-
nently exceeding the subtending scales.
§ Leaves at most 3 mm. wide : spikelets 8 to 9, glossy
brown or straw-colored, pointed.
Spike oblong-ovoid or subcylindric, with ascending
approximate spikelets (2) C. scoparia.
Spike moniliform . . (2) C. scoparia, var. moniliformis.
Spike short-globose or broad-ovoid, the spikelets
crowded and divergent .
(2) C. scoparia, var. condensa.
§ § Leaves more than 3 mm. wide: spikelets 8 to 14, green
or dull brown, blunt (3) C. tribuloides.
(For vars. see below.)
X X Perigynia firm, obviously distended over the achenes,
nervele s or obscurely nerved on the inner faces,
equalled by the subtending scales .... (7) C. praticola.
2. Perigynia less than 5 mm. long.
O Perigynia thin and scale-like, scarcely distended over the
achenes : leaves 3 to 8 mm. broad.
-f Perigynia with appressed tips.
Spike oblong, the spikelets approximate . (3) C. tribuloides.
Spike moniliform, the 6pikelets scattered
(3) C. tribuloides, var. turbata.
+ + Perigynia with spreading tips : spike flexuous
(3) C. tribuloides, var. reducta.
O O Perigynia firm, obviously distended over the achenes.
-f- Perigynia elongate-lanceolate or subulate, less than one-third
as broad as long, at most 1.4 mm. broad.
X Tips of perigynia conspicuously exceeding the lance-
subulate dull scales.
Culms 1 to 4 dm. high : leaves 1 to 2.5 mm. wide :
spikelets 3 to 7 mm. long (5) C. Craw/ordii.
462 PROCEEDINGS OP THE AMERICAN ACADEMY.
Culms taller: leaves broader: spikelets 8 to 11 mm. long
(5) C. Crawfordii, var. vigens.
X X Tips of perigynia equalled by the ovate bluntish glossy
dark scales (6) C. oronensis.
+ + Perigynia broader, nearly or quite half as broad as long.
X Tips of perigynia distinctly exceeding the subtending
scales.
§ Leaves 2.5 mm. or more wide.
□ Spikelets compactly flowered, the mature perigynia
with recurved or spreading tips concealing the
scales (8) C. cristata.
n □ Spikelets with ascending or slightly spreading peri-
gynia ; scales apparent.
A Mature perigynia greenish or pale straw-colored, in
loose spikelets : spikes more than 2.2 cm. long
(if shorter, with dark chestnut scales).
Spikelets approximate in ovoid or oblong spikes.
Scales pale, not strongly contrasting with the
perigynia (10) C. mirabilis.
Scales dark chestnut, strongly contrasting with
the perigynia . . (10) C. mirabilis, var. tincta.
Spikelets scattered in a moniliform spike
(10) C. mirabilis, var. perlonga.
A A Mature perigynia brown, in dense spikelets : spikes
at most 2.2 cm. long : scales pale brown
(17) C. Bebbii.
§ § Leaves narrower.
Spike stiff, with crowded closely flowered spikelets
(17) C. Bebbii.
Spike flexuous and moniliform, or at least with the
loosely flowered spikelets scattered . (11) C. straminea.
X X Tips of perigynia equalled by the subtending scales.
§ Spike stiff and erect, or at least with the spikelets ap-
proximate.
Spike brown or ferrugineous .... (19) C. leporina.
Spike brownish white (20) C. xerantica.
§ § Spike flexuous, or at least with the lower spikelets
remote.
□ Perigynia nerveless or minutely short-nerved on the
inner face.
Mature perigynia straw-colored or pale brown, one-
third as broad as long (7) C. praticola.
Mature perigynia olive-green or bronze, one-half as
broad as long (21) C. aenea.
□ □ Perigynia with strong ribs the length of the inner face :
spike silvery green (18) C.foenea.
b. Perigynia 2 mm. or more broad.
1. Tips of the perigynia distinctly exceeding the subtending scales.
FERNALD. — CARICES OF SECTION HYPARRHENAE. 463
O Perigynia thin and scale-like, barely distended over the achenes,
one-fourth to one-third as broad as long.
Perigynia 7 to 10 mm. long (1) C. muskingumensis.
Perigynia shorter (2) C. scoparia.
(For vars. see above.)
O O Perigynia firmer, obviously distended over the achenes, nearly
or quite half as broad as long.
+ Perigynia lance-ovate, about half as broad as long.
X Leaves 2.5 mm. broad, or broader .... (10) C. mirabilis.
(For vars. see above.)
X X Leaves narrower.
§ Perigynia distinctly about 10-nerved on the inner faces,
4 to G mm. long.
Spikelets 8 to 12 mm. long : perigynia 4.8 to 6 mm.
long (12) C. tenera.
Spikelets 5 to 8 mm. long : perigynia 4 to 5 mm. long
(12) C. tenera, var. invisa.
§ § Perigynia 3- to 5-nerved on the inner faces, mostly less
than 4 mm. long.
Perigynia with ascending inconspicuous tips
(11) C. straminea.
Perigynia with divergent conspicuous tips
(11) C. straminea, var. echinodes.
+ + Perigynia with broad-ovate to orbicular bodies.
X Spike moniliform and flexuous, with mostly clavate-based
spikelets.
Spikelets brownish-white ; of close-appressed obscurely
beaked firm perigynia (14) C. silicea.
Spikelets ferrugineous ; the abrupt slender beaks of the
perigynia with conspicuous loosely ascending or spread-
ing tips (12) C. tenera, var. Richii.
X X Spike stiff (or, if flexuous, with brown or ferrugineous
spikelets).
§ Perigynia 5.6 to 7.7 mm. long, very thin, scale-like, al-
most transparent : scales blunt . . . (13) C. Bicknellii.
§ § Perigynia less than 5.6 mm. long, firm and opaque
(when exceptionally longer in C. alata, with aristate
scales).
□ Scales long-acuminate or aristate : perigynia 4 to 5.5
mm. long : achenes oblong.
A Spike green, or finally dull brown: scales lance-
subulate : perigynia obovate, 2.8 to 3.7 mm. broad,
abruptly narrowed at base .... (15) C. alata.
A A Spike dark brown or ferrugineous : perigynia 2.3 to
2.8 mm. broad.
Spikelets closely approximate: scales ovate-lance-
olate : perigynia ovate, tapering gradually to
the beak . . . . (15) C. alata, var. ferruginea.
464 PROCEEDINGS OF THE AMERICAN ACADEMY.
Spikelets scattered in a flexuous spike : scales
lanceolate : perigynia orbicular, abruptly slen-
der-beaked (12) C. tenera, var. Richii.
□ □ Scales blunt or at most acutish.
Spikelets gray-green or finally dull brown, with
strongly appressed-ascending very firm perigynia
3.5 to 4 (very rarely 4.5) mm. long
(9) C. alboluteseens.
Spikelets straw-colored or ferrugineous, with spread-
ing-ascending perigynia 4 to 5.5 mm. long.
Spike of 5 to 10 mostly distinct spikelets
(16) C.festucacea.
Spike of 3 to 6 approximate spikelets
(16) C.festucacea, var. brevior.
2. Tips of perigynia equalled by the subtending scales.
O Spike stiff and erect, or at least with approximate spikelets.
+ Spike whitish or gray-green.
X Perigynia lance-ovate, 4 to 4.8 mm. long, nerveless on the
inner faces, golden-yellow at base . . (20) C. xerantica.
X X Perigynia broad-ovate to suborbicular.
Perigynia strongly ribbed the length of the inner faces,
2 mm. broad (18) C.foenea.
Perigynia nerveless or faintly nerved on the inner faces,
broader (9) C. alboluteseens.
+ + Spike bronze or ferrugineous.
Perigynia distinctly concave on the usually nerved inner
faces: achene 1 mm. broad (19) C. leporina.
Perigynia flat or convex on the usually nerveless inner
faces, very plump: achene 2 mm. broad . (22) C. adusta.
O O Spike flexuous, at least the lowest spikelets remote.
+ Perigynia nerveless or only faintly short-nerved on the inner
faces.
Perigynia ovate-lanceolate, one-third as broad as long :
achene 1 mm. broad (7) C.praticola.
Perigynia ovate, half as broad as long : achene 1.5 mm.
broad (21) C. aenea.
+ + Perigynia distinctly nerved on the inner faces.
X Perigynia 2.8 to 4.4 mm. long, at most 2.4 mm. broad, 7- to
13-ribbed on the inner faces, abruptly beaked.
Spike of 4 to 9 spikelets 6 to 10 mm. long : perigynia 2.8
to 4 mm. long (18) C.foenea.
Spike of 6 to 15 spikelets 10 to 17 mm. long: perigynia
3.5 to 4.4 mm. long . . . (18) C.foenea, var. perplexa.
X X Perigynia 4 to 5.3 mm. long, 2.5 to 3 mm. broad, 3- to 5-
nerved on the inner faces, obscurely broad-beaked
(14) C. silicea.
** ++ Bracts leaf-like and much prolonged, the lowest 1 to 2 dm. long :
spikelets crowded : perigynia subulate .... (23) C. sychnocephala.
FERNALD. CARTCES OF SECTION HYPARRHENAE. 465
+- h- Perigynia horizontally spreading or reflexed when mature, spongy at
base, with thin but scarcely winged margins.
•w Spikelets solitary and terminal, pistillate or staminate, or with the
flowers variously scattered.
Stoloniferous ; the filiform culms at most 3 dm. high, from filiform
rootstocks . . . . (24) C. gynocrates.
Not stoloniferous ; the wiry culms 2 to 7 dm. high, in caespitose stools
(25) C. exilis.
++ -w Spikelets 2 to several.
= Perigynia broadest at base : beak rough or serrulate.
a. Perigynia at most half as broad as long, finally yellowish, with
slender beak nearly equalling the body : scales pointed.
1. Perigynia ovate, 3 or 4 mm. long.
O Spikelets at most 12-flovvered.
Spike 1 to 3 cm. long, the 2 to 6 spikelets subapproximate
(26) C. echinata.
Spike 2 to 6 cm. long, the 2 to 4 spikelets very remote, the
terminal with a clavate base 0.5 to 1 cm. long
(26) C. echinata, var. ormantha.
O O Spikelets with more flowers.
Leaves 1 to 2.5 mm. broad : spikelets scattered, 12- to 20-
f owered : perigynia less than half as broad as long
(26) C. echinata, var. excelsior.
Leaves 2 to 4 mm. broad : spikelets mostly approximate, 15-
to 40-flowered ; perigynia half as broad as long
(26) C. echinata, var. cephalantha.
2. Perigynia lanceolate or ovate-lanceolate, 2.5 to 3 mm. long : spike
of 2 to 6 approximate spikelets (26) C. echinata, var. angustata.
b. Perigynia more than half as broad as long, firm, brownish or dark
green, the beak one-fourth to one-half as long as the body.
1. Scales sharp-pointed : leaves 2.5 to 4.5 mm. broad : spike 1.5 to 3.5
cm. long ; spikelets 15- to 50-flowered : coarse plant (27) C. stcrilis.
2. Scales blunt : leaves narrower : spike 1 to 2 cm. long ; spikelets
5- to 15-flowered : slender plants.
Leaves 1 to 2 mm. broad : perigynia faintly nerved or nerve-
less on the inner faces (28) C. interior.
Leaves narrower : perigynia strongly nerved
(28) C. interior, var. capillacea.
= = Perigynia broadest near the middle, less than 2 mm. broad, very
thin and conspicuously nerved, with short smooth beak : spikelets
remote (29) C. seorsa.
* * Perigynia not thin-winged, ascending from the first, plano-convex.
t- Perigynia 4 mm. or more long, long-heaked.
Spikelets lanceolate, in a loosely linear-cylindric spike : perigynia 1 to
1.3 mm. broad, strongly nerved : scales oblong : leaves 1 to 2.5 mm.
broad (33) C. bromoides.
Spikelets ovate, in flexuous spikes, the lowest very remote : perigynia
1.6 to 1.9 mm. broad, faintly nerved or nerveless : scales ovate : leaves
2 to 5 mm. broad (34) C. Deweyana.
vol. xxxvii. — 30
466 PROCEEDINGS OF THE AMERICAN ACADEMY.
+- *r Perigynia less than 4 mm. long.
++ Perigynia 2 mm. or more long.
= Perigynia with serrulate beaks or margins.
a. Spike elongate, from linear-cylindric to oblong.
1. Perigynia ovate, broadest at base : spikelets mostly or all ap-
proximate in an oblong-cylindrie spike . . . (30) C. arcta.
2. Perigynia broadest near the middle.
O Plant glaucous : leaves 2 to 4 mm. broad : spikelets with many
appressed-ascending glaucous obscurely beaked perigynia.
Spikelets 6 to 10 mm. long, approximate, or the lowest
rarely 1.5 cm. apart : perigynia 2.3 to 3 mm. long
(31) C. canescens.
Spikelets 4 to 7 mm. long, subapproximate or remote : peri-
gynia about 2 mm. long (31) C. canescens, var. subloliacea.
Spikelets 6 to 12 mm. long, remote, the lowest 2 to 4 cm.
apart (31) C. canescens, var. disjuncta.
O O Plant green, not glaucous : leaves 1 to 2.5 mm. broad : spike-
lets with few loosely spreading dark green or brown dis-
tinctly beaked perigynia (32) C. hrunnescens.
b. Spike subglobose, of 2 to 4 closely approximate subglobose
loosely flowered silvery spikelets : perigynia oblong, beakless,
nerved, 3 to 3.4 mm. long (35) C. tenuiflora.
= = Perigynia smooth throughout.
a. Spike whitish, silvery-green or pale brown, not ferrugineous nor
dark brown.
1. Spike elongate, at least the lower spikelets scattered.
Uppermost spikelet divaricate-pedunculate, the lowermost
subtended by a long leaf-like bract : perigynia more than
J! mm. long (36) C. trisperma.
Spikelets continuous in a linear-cylindric loose spike, bract-
less or only short-bracted : perigynia 2 to 3 mm. long
(31) C. canescens.
(For vars. see above.)
2. Spike subglobose, of 2 to 4 closely approximate subglobose
loosely flowered spikelets : perigynia beakless, 3 mm. or more
long .... (35) C. tenuiflora.
b. Spike ferrugineous or dark brown.
1. Terminal spikelet with conspicuous clavate base : perigynia ab-
ruptly beaked : culms smooth (or harsh only at tips).
O Spikelets distinct ; the lowest 4 or 5 mm. thick ; the terminal
1 to 1.8 cm. long: perigynia pale, about equalled by the
yellowish-brown blunt scales (38) C. norvegica.
O O Spikelets approximate ; the lowest less than 4 mm. thick.
Plant weak and lax : leaves involute, 0.5 to 1.5 mm. broad :
perigynia pale, equalled by the ferrugineous acutish scales
(39) C. (jlareosa.
Plant stiff and upright : leaves flat, 1 to 3 mm. broad : peri-
gynia brown or reddish, exceeding the fuscous obtuse
scales (40) C. lagopina.
FERNALD. CARICES OF SECTION HYPARRHENAE. 467
2. Terminal spikelet without conspicuous clavate base : perigynia
obscurely beaked, brown-tinged, exceeding the blunt scales :
culms sharply angled, harsh and stiff : leaves flat, erect
(41) C. heleonastes.
Perigynia at most 1.5 mm. long, oblong-cylindric, plump, nerveless,
beakless or with a very short broad truncate beak :. culms wiry :
spike linear-cylindric, dull brown (37) C. elachijcarpa.
SYNOPSIS OF SPECIES.
Ovales, Kunth. Perigynia ascending or slightly spreading (when
horizontally spreading, always with winged margins), with thin or winged
margins, mostly with concave inner faces when mature.
§ Ovales proper. Bracts, when present, setaceous, or, if broader,
only once to twice longer than the spike.
* Mature perigynia one-fourth to one-third (.24 to .36) as broad as long.
-<- Perigynia extremely thin and scale-like, barely distended over the achenes.
++ Perigynia 7 to 10 (average 8.3) mm. long.
1. C. muskingumensis, Schweinitz. — Figs. 1, 2. — Culms 1 m. or
less tall, very leafy : the loose flat leaves subcordate at their junction
with the loose green sheaths ; those of the sterile shoots crowded and
almost distichous : spike oblong, of 5 to 12 appressed-ascending oblong-
cylindric pointed spikelets 1.5 to 2.5 cm. long. — Ann. Lye. N. Y. i. 66;
Dewey, Am. Jour. Sci. x. 281 ; Bailey in Gray, Man. ed. 6, 620; Britton
in Britton & Brown, 111. Fl. i. 355, fig. 861. C. arida, Schweiii. and
Torr. Ann. Lye. N. Y. i. 312, t. xxiv. fig. 2; Carey in Gray, Man.
545; Boott, 111. i. 20, t. 54; Boeckeler, Linnaea, xxxix. 112; Bailey,
Proc. Am. Acad. xxii. 147 ; Macoun, Cat. Can. PL ii. 129. C. scoparia,
Torr. Ann. Lye. N. Y. iii. 394, in part, not Schkuhr. C. scoparia, var.
muskingumensis, Tuck. Enum. Meth. 8, 17. — Meadows, swamps, and
wet woods, Ohio to Manitoba and Missouri. July, August.
*+ ++ Perigynia at most 6.5 (very rarely 7) mm. long.
= Perigynia 5 to 6.5 (average 5.7) mm. long.
2. C. scoparia, Schkuhr. — Figs. 3, 4. — Culms 0.2 to 1 m. high,
mostly slender and erect : leaves narrow (at most 3 mm. wide), shorter
than the culm: spike oblong-ovoid to subcylindric, of 3 to 9 straw-
colored or brownish mostly shining and ascending ovoid pointed spikelets
0.5 to 1.5 cm. long. — Schkuhr in Willd. Sp. iv. 230, & Riedgr.
468 PROCEEDINGS OF THE AMERICAN ACADEMY.
Nachtr. 20, t. Xxx. fig. 175; Dewey, 1. c. viii. 94; Schwein. & Torr.
1. c. 313 ; Torr. 1. c. ; Carey, 1. c. ; Boott, 1. c. iii. 116, t. 368, in part;
Bailey, 1. c. 148, & in Gray, 1. c. ; Macouu, 1. c. 131 ; Britton, 1. c. 356,
fig. 863 ; Howe, 48 Rep. N. Y. Mus. Nat. Hist. 42. G. leporina,
Mich. Fl. ii. 170, not L. C. lagopodioides, var. scoparia, Boeckeler, 1. c.
114. — Low grounds or even dry open woods, Newfoundland to
Saskatchewan and Oregon, and southward. May- August.
Var. moniliformis, Tuck. Spikelets scattered in a slender monili-
form spike, the lowest usually remote. — Enum. Meth. 8, 17 ; Boott, 111.
1. c. t. 368, in part. G. tribuloides, var. reducta, Bailey, Proc. Am.
Acad. xxii. 147, as to syn., in part. G. tribuloides, var. moniliformis,
Britton, 1. c. as to syn., in part. — Range of species, but infrequent.
Var. condensa. — Fig. 5. — Spikelets spreading, crowded in a short
globose or broad-ovoid head. — New Hampshire, Randolph, July 23,
1897 (E. F. Williams) : Vermont, Westmore, July 26, 1894 (E. F.
Williams); Rutland, July 14, 1899 ( W. W. Eggleston) : Massachu-
setts, Tewksbury, July 21, 1858, Medford, July 26, 1865, Mystic
Pond, Aug. 9, 1868, and July 20, 1873 (Wm. Boott): Rhode Island,
Providence, July 19, 1871 (S. T. Ohiey) : Connecticutt, Griswold,
June 16, 1899 (C. B. Graves, no. 150) : Neav York, Jefferson Co.
(Craive) ; Fulton Chain Lakes, August, 1895 (J. V. Haberer): Ontario,
Courtland, June 26, 1901 (John Macoun, Herb. Geol. Surv. Can., no.
26,631).
= = Perigynia 3.7 to barely 5 (average 4.5) mm. long.
3. C. tribuloides, Wahlenb. — Figs. 6, 7. — Culms loose and usually
tall, 0.3 to 1 m. high, sharply trigonous : leaves soft a?id loose, 3 to 8 mm.
broad, numerous ; the upper often nearly or quite overtopping the culm ;
those of the sterile shoots crowded and somewhat distichous : spike oblong,
of 8 to llf. obovoid ascending more or less crowded gray-green or dull
brown spikelets 7 to 12 mm. long: perigynia with oppressed tips. —
Kbngl. Acad. Handl. xxiv. 145, and Fl. Lapp. 250; Bailey, Proc. Am.
Acad. 1. c, in Gray, 1. c, & Mem. Torr. CI- i. 54 ; Macoun, 1. c. 130 ;
Britton, 1. c. fig. 862 ; Howe, 1. c. 41. C. lagopodioides, Schkuhr in
Willd. 1. c, & Riedgr. Nachtr. 20, t. Yyy, fig." 177 ; Dewey, 1. c. 95 ;
Schwein. & Torr. 1. c. ; Carey, 1. c. ; Boott, 111. 1. c. t. 370; Boecke-
ler, 1. c. 113. G. scoparia var. lagopodioides, Torr. Ann. Lye. N. Y.
iii. 394; Tuck. 11. cc. — Swales and rich open woods, particularly in
alluvial soil, New Brunswick to Saskatchewan, and southward.
June-Sept.
FERNALD. — CARICES OF SECTION HYPARRHENAE. 469
Var. turbata, Bailey. Spikelets remote, forming a moniliform spike.
— Mem. Torr. CI. i. 55, & in Gray, Man, 1. c. — C. lagopodioides, var.
Boott, 1. c. 117, t. 371, fig. 1. — Range of species.
Var. reducta, Bailey. — Fig. 8. — Spike usually flexuous, at least
the lowest spikelets scattered: perigynia with loosely spreading or recurred
tips. — Proc. Am. Acad. 1. c, Mem. Torr. Cl. i. 5G, & in Gray, 1. c. ;
Macoun, 1. c. ; Howe, 1. c. 42. C. cristata, Kunze, Car. t. 44, fig. g;
Boott, 1. c. 117, in part, t. 373; not Schvvein. C. lagopodioides, var.
moniliformis, Olney, Exsicc. fasc. ii. no. 8 ; Bailey, Bot. Gaz. x. 380.
0. tribuloides, var. moniliformis, Britton, 1. c, not C. scoparia, var.
moniliformis, Tuck. — Gulf of St. Lawrence to Nova Scotia, New
England, New York, Iowa, and western Ontario ; ascending in
the White Mts. to 1,385 m. altitude.
-i- -t- Perigynia firm, not scale-like, obviously distended over the achenes.
++ Plant strongly stoloniferous ; culms rising from an elongated rootstock.
4. C. siccata, Dewey. — Figs. 9 to 11. — Culms slender, 1 to 6 dm.
high ; leaves stiff, 1 to 3 mm. wide : spike of 3 to 7 approximate or scat-
tered, glossy broivn spikelets, the staminate and pistillate flowers variously
mixed or in distinct spikelets: perigynia 5 or 6 mm. long, 2 mm. broad,
usually with distinct serrulate wings. — Am. Jour. Sci. x. 278, t. F. fig.
18; Hook. Fl. Bor.-Am. ii. 212; Torr. 1. c. 391; Carey, 1. c. 539;
Boott, 111. i. 19, t. 52; Boeckeler, 1. c. 134; Bailey, Proc. Am. Acad.
I.e. 147, & in Gray, 1. c. 619; Macoun, 1. c. 114; Britton, 1. c. 355,
fig. 860; Howe, 1. c. 47; Meinsh. Acta Hort. Petrop. xviii. 319. C.
pallida, C. A. Meyer, Mem. Acad. St. Petersb. i. 215, t. 8. C. Liddoni,
Carey, 1. c. 545, not Boott. — Dry or sandy soil, Vermont to British
Columbia and Alaska, south to Massachusetts, Connecticut, New
Yd*RK, Ohio, Michigan and westward. May-July.
++ +*■ Plant not strongly stoloniferous, culms solitary or in dense stools.
= Perigynia at most 1.4 mm. wide, elongate-lanceolate or subulate, 3.5 to 4
(rarely 4.5) mm. long.
a. Tips of perigynia conspicuously exceeding the lance-subulate scales : plant
comparatively low, in dense stools.
5. C. Crawfordii. — Figs. 12, 13. — Very slender, 1 to 3 dm. high ;
the narrow (1 to 2.5 mm. wide) leaves ascending, often equalling or
exceeding the culms : spike dull brown, oblong or ovoid, often subtended
by an elongate-filiform bract; the 3 to 12 oblong or narrowly ovoid
470 PROCEEDINGS OP THE AMERICAN ACADEMY.
ascending spikelets 3 to 7 mm. long, approximate : the linear-lanceolate
perigynia plump at base, about 1 mm. wide. — C. scoparia, var. minor,
Boott, 111. iii. 116, t. 369; Gray, Man. ed. 5, 579; Bailey in Gray,
Man. ed. 6, 621 ; Howe, 1. c. 43. — Dry or rocky soil, or open woods.
Newfoundland, Whitbourne, Aug. 15, 1894 (Robinson § Schrenk, no.
94) : Prince Edward Island, Tignish, July 20, 1888 (J. Macoun, Herb.
Geol. Surv. Can. no. 30, 382) : New Brunswick, Nepisiquit Lakes, July,
1884 (J. Brittain, Herb. Geol. Surv. Canada, no. 30,377) : Quebec,
Riviere du Loup, Aug. 2, 1896, Lake Edward, Aug. 21, 1896, Tadou-
sac, Aug. 26, 1896 (Ezra Brainerd) ; Roberval, July 27, 1892 ( G. G.
Kennedy) : Manitoba, Lake Winnipeg, July 29, 1884 (John Macoun,
Herb. Geol. .Surv. Can., no. 30,307, in part) : Assiniboia, Cypress
Hills, June 25, 1894 (J. Macoun, Herb. Geol. Surv. Can., no. 7,461)
Saskatchewan, Carleton House and Bear Lake (Sir John Richardson)
Athabasca (Sir John Richardson, Herb. Geol. Surv. Can. no. 30, 396)
Maine, Van Buren, July 25, 1893 (M. L. Fernald, no. 163); St. Fran-
cis, Aug. 7, 1893, Farmington, July 8, 1896 (31. L. Fernald) ; Beech
Mt., Mount Desert Island, Aug. 20, 1890, Somesville, July 5, 1891,
Southwest Harbor, Aug. 1, 1892, Little Cranberry Isle, July 10, 1894,
Seal Harbor, July 5, 1897 (E. L. Band) ; Gilead, Aug., 1897 (Kate
Furbish) : New Hampshire, Randolph, July 23, 1897 (E. F. Wil-
liams); near Crawfords, July 6, 1878, Mt. Washington, July 29, 1887,
Franconia, July 6, 1878 (E. fy C. E. Faxon); Crawford Notch,
Aug. 24, 1891, Aug. 13, 1897, and Lebanon, July 22, 1890 ( G. G.
Kennedy): Vermont, Mt. Mansfield, July 24, 18$4 (C. W. Swan),
Sept. 9, 1897 (E. Brainerd); Willoughby, July 21, 1896 (G. G. Ken-
nedy); Middlebury, July 11, 1896, Ripton, July 19, 1898 (E. Brain-
erd); Rutland, July 1, 1899 (W. W. Eggleston) : Massachusetts,
Maiden and Revere, June 21, 1879 (H. A. Young) ; Chelsea, July 19,
1891 (W. F. Rich): Michigan, Houghton, Sept. 15, 1871 (H. Gill-
man) ; Keweenaw Co., Sept., 1888 (O. A. Fanvell).
Var. vigens. — Fig. 14. — Stouter throughout: culms 3 to 6 dm.
high : leaves 2.5 to 3 mm. broad : spikelets mostly greener, 8 to 11 mm.
long, densely crowded in a broad-ovoid to globose head. — Thickets and
damp gravelly soil. New Brunswick, Cam pbellton, July 20, 1880 (R.
Chalmers, Herb. Geol. Surv. Can. no. 30,363) : Quebec, Gaspe, Aug.
1, 1882 (John Macoun) ; Riviere du Loup, July 20 and Aug. 4, 1896,
Lake Edward, Aug. 21, 1896 (Ezra Brainerd) : Ontario, Eastmans
Springs, Sept. 16, 1892 (/. Macoun, Herb. Geol. Surv. Can. no. 30,
386); Cache Lake, July 11, 1900 (John Macoun): Saskatchewan,
FERNALD. — CARICES OF SECTION HYPARRHENAE. 471
plains, Aug. 1, 1872 (J. Macoun) : British Columbia, Nelson, Koote-
nay Lake, July 3, 1890 (/. Macoun, Herb. Geol. Surv. Can., no. 30,
393) : Maine, St. Francis, Aug. 9, 1893, Sherman, Aug. 23, 1897
(M. L. Fernald) : New Hampshire, Randolph, Aug. 2, 1897 (E. F.
Williams); Mt. Washington, July 28, 18G1 (Wm. Boott); Mt. Pleas-
ant House, July 31, 1897 ( W. Deane) : Vermont, Burlington, July
13, 1896 (JB. Brainerd): Michigan, Keweenaw Co., Aug., 1890 {0.
A. Fa?- well).
b. Tips of perigynia mostly equalled by the ovate blunt or acutish scales : plant
tall, forming loose stools.
6. C. oronensis. — Figs. 15, 16. — Culms tall and erect, 0.5 to 1 m.
high, sharply angled and harsh above: leaves smooth, 2.5 to 4 mm.
broad, much shorter than the culms : spike oblong-cylindric, erect, of 3 to
9 ascending dark brown rhomboid-ovoid pointed spikelets 0.5 to 1 cm.
long: scales mostly glossy brown, with pale scarious margins: perigynia
appressed, about Jf. mm. long, 1.3 mm. broad, very narrowly winged above.
— Dry fields, thickets, open woods, and gravelly banks. Maine, Orono,
about 1870 (F. Lamson-Scribner), June 28, 1890, June 30, 1891, July
3, 1897 (M. L. Fernald). •
= = Perigynia 1.5 to to 2 mm. broad, ovate-lanceolate, 4.5 to 6.5
(average 5) mm. long.
7. C. praticola, Rydberg. — Figs. 17, 18. — Culms smooth and
slender, 3 to 6 dm. high, overtopping the smoothish flat (2 to 3.5 mm.
broad) leaves ; spike slender, flexuous, moniliform, the 3 to 7 silvery
brown mostly remote pointed spikelets few-jiowered, 7 to 1.7 mm. long,
mostly long-clavate at base ; perigynia nerveless or minutely short-nerved
on the inner face, equalling the ovate-lanceolate acutish or blunt scales.
— Mem. N. Y. Bot. Card. i. 84; Bvitton, Man. 226. G. pratensis,
Drejer, Rev. Crit. Car. Bor. 24; Fl. Dan. xiv. 8, t. 2368; Bailey,
Proc. Am. Acad. xxii. 147 ; Britton, in Britt. & Brown, 1. c. 354, fig.
858; not Hose. C. adusta, var. minor, Boott in Hook. Fl. Bor. -Am. ii.
215, & 111. iii. 119, t. 383. C. Liddoni, in part, of authors, not Boott.
— Open woods, clearings, and prairies, Labrador to Saskatchewan
and British Columbia, south to Nova Scotia, Aroostook County,
Maine, Lake Superior, and North Dakota ; also in Greenland.
June-Aug.
472 PROCEEDINGS OF THE AMERICAN ACADEMY.
* * Mature perigynia distinctly more than one-third (.44 to .75) as broad
as long.
•*- Perigynia one-fifth to one-third (.19 to .34) as thick as broad (rarely
thicker in C. mirabilis).
++ Mature perigynia 3 to 4 mm. long (very rarely longer in C. mirabilis and
C. albolutescens).
— Mature perigynia with roseate-spreading tips.
8. C. CRISTATA, Schweinitz. — Figs. 19 to 21. — Culms 1 m. or less
high, harsh above : leaves soft and flat, 3 to 7 mm. broad, often equalling
the culms, sheaths loose : spike usually dense, linear-cylindric or oblong,
of 6 to 15 globose closely flowered greenish or dull-brown spikelets 0.5 to
1 cm. long. — Ann. Lye. N. Y. i. 66 ; Schwein. & Torr. Ann. Lye.
N. Y. i. 315, t. 24, fig. 1 ; Dewey, 1. c. 44 ; Boott, 1. c. 117, in part ;
Gray, Man. ed. 5, 579; Boeckeler, 1. c. 115; Howe, 1. c. 41. C.
lagopodioides, var. cristata, Carey, 1. c. 545. C straminea, var. cristata,
Tuck. 1. c. 9, 18. C tribuloides, var. cristata, Bailey, Proc. Am. Acad,
xxii. 148, in Gray, Man. ed. 6, 620, & Mem. Torr. CI. i. 55 ; Macoun,
1. c. 130. C. cristatelbi, Britton, 1. c. 357, fig. 865. — Swales and wet
woods, western New England to Pennsylvania, " Virginia/' Mis-
souri, Saskatchewan, and British Columbia. June-Aug.
= = Mature perigynia with ascending tips.
a. Plant stout and stiff: spikes stiff and upright ; the gray-green mostly approx-
imate spikelets with appressed firm perigynia.
9. C. albolutescens, Schweinitz. — Figs. 22 to 24. — Culms 2 to 8
dm. high : leaves erect, long-pointed, pale green, 2 to 5 mm. wide,
shorter than the culms : spike linear-cylindric to subglobose, with or
without elongated bracts, of 3 to 30 (sometimes compound) conic-ovoid
to subglobose spikelets 0.6 to 1 cm. long : perigynia 2 to 3 mm. broad,
rhombic-ovate to suborbicular, with a short deltoid firm greenish tip. —
Ann. Lye. N. Y. i. 66; Bailey, Bull. Torr. CI. xx. 422 (incl. var.
cumulata) ; Britton, 1. c. 359, fig. 873; Howe, 1. c. 43. C. foenea,
Ell. Sk. ii. 533 ; Schwein. & Torr. 1. c. 315 ; Carey, 1. c. 546; Boott,
1. c. 118 (excl. vars.), t. 375; not Willd. C. straminea, var. foenea,
Torr. Ann. Lye. N. Y. iii. 395 ; Bailey, Proc. Am. Acad. xxii. 150,
& in Gray, Man. ed. 6, 622 ; Macoun, 1. c. 132. C. straminea, var.
intermedia, Gay, Ann. Sci. Nat, ser. 2, x. 364. C. leporina, var.
bracteata, Liebmami, Mex. Halv. 76. C. straminea, var. chlorostachys,
Boeckeler, 1. c. 118. 0. straminea, var. cumulata, Bailey, Mem. Torr.
FEBNALD. CARICES OP SECTION HYPARRHENAE. 473
CI. i. 23, & in Gray, 1. c. — Damp or even very dry soil, principally on
the coastal plain, New Brunswick to Florida, Texas, Mexico, and
Central America; rarely inland to Bear Mt., Livermore, Maine
(Kate Furbish) ; Mt. Monadnock, alt. 925 in., New Hampshire (R.
M. Harper) ; Taghkanick Range, Columbia Co., New York (L. H.
Hoysradt) ; also from Lake Huron to Manitoba. July-Sept.
b. Plant not very stiff : the bright green or brownish spikelets with spreading
or ascending (not appressed) perigynia.
1. Leaves 2.5 to G mm. wide : culms 0.3 to 1.5 m. high.
10. C. mirabilis, Dewey. — Figs. 25, 26. — Culms very loose and
smooth; leaves soft and thin, the sheaths rather loose : spikelets 4 to 12,
greenish, subglobose or ovoid, 5 to 9 mm. long, mostly approximate in an
oblong spike ; perigynia with divergent tips. — Am. Jour. Sci. xxx. 63,
t. Bb, fig, 92; Boott, 1. c. 117 (under C. cristata), t. 374; Howe, 1. c.
46. C. straminea, var. mirabilis, Tuck. 1. c. 9, 18; Bailey, Proc. Am.
Acad. xxii. 150, & in Gray, Man. ed. 6, 621 ; Britton, 1. c. 358. C.
festucacea, var. mirabilis, Carey, 1. c. 545. C. cristata, Kunze, Car.
t. 44, figs. a, e, and f (colored), not Schwein. C. cristata, var. mirabilis,
Gray, Man. ed. 5, 580. C. lagopodioides, var. mirabilis, Olney, Exsicc.
fasc. ii, no. 9. C. tribuloides, var. cristata, Macoun, 1. c. 130, in part,
not Bailey. — Dry banks, open woods, or even moist copses, central
Maine to Manitoba, south to North Carolina and Missouri.
June. July.
Var. perlonga. — Fig. 27. — Spikelets scattered in a moniliform spike.
— New Hampshire, dry thicket, Barrett Mt., New Ipswich, June 5, 1896
(M. L. Fernald): Vermont, Little Notch, July 9, 1901 (E. Brainerd) :
Massachusetts, Stoueham, June 5, 1887 (F. S. Collins); Oak Island,
Revere, July 5, 1891 (W. P. Rich); Beaver Brook Reservation, July 6,
1894 (C. W. Swan) ; Sharon, June 17, 1896 (W. P. Rich) : Connecti-
cut, dry open woods, Southington, June 17, 1900 (C. H. Bissell) :
New York, Binghamton, June 29, 1871 ( Wm. Boott); Sacondago
River (J. V. Haberer) : Michigan, Grosse Isle, June 30, 1867 (Wm.
Boott) ; open swales, Lansing, June 8, 1886 (L. H. Bailey, no. 283,
in part) : Illinois, Marion Co. (M. S. Bebb).
Var. tincta. Spike of 8 to 7 ovoid approximate broion-tinged spike-
lets : scale brown with a pale margin. — New Brunswick, banks of
St. John River, July 4, 1899 (/. Macoun, Herb. Geol. Surv. Can. no.
22) :. Maine, Fort Kent, June 16, 1898 (no. 2158), Masardis, June 6,
1898 (no. 2159), Ashland, June 13, 1898 (no. 2160), Fort Fairfield,
474 PEOCEEDINGS OF THE AMERICAN ACADEMY.
July 12, 1893 (no. 165), Foxcroft, June 25, 1894, Dover, June 28,
1894, Orono, July 6, 1891,— all coll. M. L. Fernald ; Sangerville,
July 17, 1896 (67. B. Fernald, no. 176): New Hampshire, between
Marshfield and Fabyans, July 6, 1878, Bethlehem, June 20, 1887 {E. $
C. E. Faxon); Wbitefield, July 3, 1896 (W. Deane) : Vermont, St.
Johnsbury, June 21, 1901 ( T. E. Hazen, no. 206). Resembling north-
western forms of the polymorphous /estiva group, but not satisfactorily
referable to any of them.
2. Leaves 0.5 to 2 mm. wide: culms 3 to 7 dm. high : spikelets remote or at
least distinct in a moniliform or linear-cylindric spike.
11. C. straminea, Willd. — Figs. 28, 29. — Culms very slender,
smooth except at summit : spikelets 3 to 8, yellow-brown, or rarely green,
ovoid or subglobose, 4 to 8 mm. long, usually forming ftexuons spikes :
perigynia with ascending inconspicuous tips ; the inner faces S- to 5-nerved
or nerveless. — Willd. in Schkuhr, Riedgr. 49, t. G, fig. 34; Bailey,
Mem. Torr. CI. i. 21, & in Gray, Man. ed. 6, 621 ; Britton, 1. c. fig.
868 ; Howe, I. c. 44. C. straminea, var. minor, Dewey, Am. Jour.
Sci. xi. 318, t. N, fig. 45 ; Torr. 1. c. 395. C. festucacea, var. tenera,
Carey, 1. c. 545. C. straminea, var. tenera, Boott, 1. c. 120, t. 384
(except perigynia from Olney) ; Gray, Man. ed. 5, 580 ; Macoun, 1. c.
132. — Meadows, or occasionally on dry banks or in open woods, New
England to British Columbia, Kentucky and Arkansas. June-
All£f.
Var. echinodes. — Fig. 30. — Tips of the slightly longer perigynia
divergent and conspicuous. — Ontario, Wyoming, June 24, 1901 (J.
Macoun, Herb. Geol. Surv. Can., no. 26,624) : Michigan, Detroit,
July 20, 1867 (H. P. Sartwell), June 26, 1870, and June 22, 1873
(Wm. Boott): Iowa, Ames, 1872, Spirit Lake, June 21, 1881 (J. C.
Arthur). Superficially resembling C. tribuloides, var. reducta.
++ ++ Mature perigynia more than 4 mm. long (very rarely shorter in exceptional
individuals of C. tenera, var. invisu, and C. festucacea, var. breviov).
= Perigynia elongate-ovate, about half as broad as long (suborbicular in
var. Richii).
12. C. tenera, Dewey. — Figs. 31, 32. — Culms slender and flexuous,
sharply angled, smooth except at summit, 3 to 9 dm. high: leaves
shorter than or rarely exceeding the culms, very ascending, 1 to 2.5 mm.
broad: spike slender, moniliform (or on late culms more or less con-
gested), of 3 to 9 broadly ovoid broionish spikelets 8 to 12 mm. long, with
FERNALD. — CARICES OP SECTION HYPARRHENAE. 475
or without subtending elongated bracts: perigynia ascending or rarely
spreading, distinctly about 10-nerved on either face, J/..8 to 6 (average 5.2s)
nun. long : scales lance-attenuate or aristate. — Am. Jour. Sci. viii. 97, &
ix. t. C, fig. 9 ; Britton, 1. c. fig. 870. G. straminea, var. aperta, Boott,
1. c. 120, t. 385; Gray, Man. ed. 5, 580 ; Bailey, Proc. Am. Acad. xxii.
152, & in Gray, Man. ed. 6, 622 ; Macoun, 1. c. 133 ; Howe, I. c. 15.
G. tenera, var. major, Olney, 1. c. no. 15. G. straminea, var. tenera,
Bailey, Bot. Gaz. x. 381, & Mem. Torr. CI. v. 94. — Brackish or
fresh marshes, mostly near the coast, Gulf op St. Lawrence to
Delaware and Iowa ; also in British Columbia, Yellow Head Pass
(Spreadborough, Herb. Geol. Surv. Can. no. 20,871). June- Aug.
Var. invisa, Britton. — Figs. 35, 36. — Lower; with spikelets 5 to 8
mm. long, and perigynia 4 to 5 (average 4.5) mm. long. — Britton,
1. c. 358. C. straminea, var. invisa, W. Boott, Bot. Gaz. ix. 86 ; Bailey,
Proc. Am. Acad. xxii. 152, & in Gray, Man. ed. 6, 622 ; Howe, 1. c. —
Range of the species and too often iutergradiug with it ; mostly in dry
soil or even in pure sand.
Var. Richii. — Figs. 33, 34. — Perigynia 4 to 5 mm. long, with
suborbicular bodies abruptly contracted to slender conspicuous loosely
ascending or spreading beaks. — Massachusetts, Reading, June 14,
1883 ( G. E. Perkins) ; Fresh Pond, Cambridge, June 8, 1887 ( W.
Deane) ; near Spot Pond, and north end of Doleful Pond, Stonebam,
May 30, 1894, near Bear Hill, Stoneham, June 5, 1894 ( Wm. P. Rich) ;
Amherst (E. Tuckerman): Connecticut, Newington, May, 1879 (Ghas.
Wright). In its elongate loose brown spikes and subulate- or awn-
tipped narrow scales clearly an extreme form of G. tenera, although the
perigynia when well developed suggest those of G. festucacea.
= = Perigynia with broadly ovate to suborbicular bodies, more than half as
broad as long.
a. Perigynia 5.7 to 7.7 mm. long.
13. C. Bicknellii, Britton. — Figs. 37 to 40. — Culms comparatively
stout, 4 to 9 dm. high, smooth except at summit : leaves ascending,
rather short and firm, 2 to 4.5 mm. broad: spike of S to 7 silvery brown
or greenish ovoid obovoid or subglobose approximate or slightly remote
spikelets 8 to 14 mm. long: perigynia ascending, the tips becoming con-
spicuous, broadly wing-margined, when mature almost translucent and with
about 10 nerves on either face. — Britton, 1. c. 360, fig. 874. G. stra-
minea, var. Grawei, Boott, 1. c. 121, t. 388 ; Bailey, Bull. Torr. CI. xx.
422 ; Howe, 1. c. G. straminea, var. Meadei, Boott, 1. c. t. 389 ; Gray,
476 PROCEEDINGS OF THE AMERICAN ACADEMY.
Man. ed. 5, 581. C. straminea, var. brevior, Bailey, Mem. Torr. CI. i.
22, in part, not Dewey. — ■ Dry or rocky soil, eastern Massachusetts
to Manitoba, New Jersey, Ohio, and Arkansas. May-July.
b. Perigj'nia at most 5.5 mm. long.
1. Spikelets whitish or silvery -brown, mostly scattered in a flexuous
moniliform spike.
14. C. silicea, Olney. — Figs. 41, 42. — Culms slender, stiff,
smooth except at summit, 3 to 8 dm. high : leaves erectish, shorter than
or equalling the culms, usually glaucous, 2 to 4.5 mm. wide, often be-
coming involute : spike of 3 to 12 usually remote conic-ovoid usually
clavate spikelets 1 to 1.5 cm. long : perigynia strongly oppressed, firm
and opaque, 4 to 5 mm. long, 2.2 to 3 mm. broad, short-beaked, broad-
winged, the body distinctly 3- to 5-nerved on. the inner, 6- to 12-nerved on
the outer face. — Proc. Am. Acad. vii. 393 ; Bailey, Mem. Torr. CI. i.
24, & in Gray, Man. ed. 6, 621 ; Britton, 1. c. 358, fig. 869 ; Howe, 1. c.
44. G. straminea, var. moniliformis, Tuck. 1. c. 9, 17 ; Bailey, Proc.
Am. Acad. xxii. 151 ; Macoun, 1. c. 133. C. adusta, Carey in Gray,
Man. ed. 2, 516, not Boott. C foenea, var. y, Boott, 1. c. 118, t. 377.
C. foenea, var. (?) subulonum, Gray, Man. ed. 5, 580. C. straminea,
var. silicea, Bailey, Carex Cat. 4. — Saud and rocks near the sea,
Prince Edward Island to Newt Jersey. June-Aug.
*o-
2. Spikelets green or brownish, approximate or only slightly remote in a mostly
upright spike (C. tenera, var. Bicl/ii, with moniliform flexuous spikes might be
looked for here).
O Sheath of the leaf green and strongly nerved nearly or quite to the narrow
subchartaceous auricle : perigynia appressed-ascending : achenes mostly
oblong.
15. C. alata, Torr. — Figs. 43, 44. — Culms rather stout, smooth
except at summit, 0.5 to 1 m. high : leaves mostly short and harsh, 2.5 to
4.5 mm. wide: spike oblong or ovoid, of 3 to 8 compact green or finally
dull-brown conic-ovoid to oblong spikelets 8 to 15 mm. long : perigynia
firm and opaque, orbicular or obovate, 4.3 to 5.5 mm. long, 2.8 to 3.7 mm.
broad, broad-winged, very faintly nerved or nerveless, much broader than
the lance-subulate usually rough-awned scales. — Ann. Lye. N. Y. iii. 396 ;
Boott, 1. c. 118, t. 378; Gray, Man. ed. 5, 581 ; Britton, 1. c. 359, fig.
872 ; Howe, 1. c. 45. C. straminea, var. alata, Bailey, Carex Cat. 4,
Proc. Am. Acad. xxii. 150 & in Gray, Man. ed. 6, 622. — Marshes
and wet woods, New Hampshire to Michigan and Florida, mostly
near the coast. June, July.
FERNALD. — CARICES OP SECTION HYPARRHENAE. 477
Var. ferruginea. — Figs. 45, 46. — Slender : the 3 to 5 irregularly
clustered spikelets tawny or ferrugineous from the first : perigynia ovate, 4
to 5 mm. long, 2.3 to 2.8 mm. broad : scales lance-ovate, mostly awnless. —
C. foenea, var. (3, Boott, I. c. 118, t. 376. O.foenea, var.? ferruginea,
Gray, Man. ed. 5, 580. G. tenera, var. suberecta, Olney, Exsicc. fasc. ii.
no. 16. C. straminea, var. ferruginea, Bailey, Bull. Torr. CI. xx. 421. —
Ohio to Michigan, Illinois, and Iowa.
0 O Sheath with a thin barely nerved or nerveless pale band extending down
from the membranaceous auricle : perigynia spreading-ascending : achenes
suborbicular.
16. C. festdcacea, Schkuhr. — Figs. 47, 48. — Culms stiff, 0.5 to
1 m. high : leaves stiff', erect, shorter than the culms, 2 to 4 mm. wide :
spike narrowly oblong, rarely ovoid, of 5 to 10 distinct or rarely approx-
imate subglobose or broadly ovoid-conic yellow-brown or green-brown as-
cending spikelets 7 to 12 mm. long: perigynia broad-ovate to suborbicular,
4 to 5.5 mm. long, 2.7 to 3.5 mm. broad, strongly 7- to 15-nerved on the
outer, nerveless or faintly nerved on the inner face : scales blunt. —
Schkuhr in Willd. Sp. iv. 242, & Riedgr. Nachtr. 23, t. Www. fig. 173 ;
Dewey, Am. Jour. Sci. viii. 96 ; Schwein. & Torr. 1. c. 316 ; Torr. 1. c.
394; Carey, 1. c. 545 ; Britton, 1. c. 359, in part. G. straminea, var.
festucacea, Tuck. 1. c. 9, 18 ; Boott, 1. c. 120, t. 386 ; Macoun, 1. c. 132;
Bailey, Mem. Torr. CI. v. 94, in part ; Howe, 1. c. G. straminea, Bailey,
Proc. Am. Acad. xxii. 149, in part, not Willd. C. straminea, var.
brevior, Bailey, Mem. Torr. CI. i. 22, in part, not Dewey. — Dry or
rocky soil, Maine to Manitoba and Pennsylvania. June-Aug.
Var. brevior. — Figs. 49 to 51. — Lower (rarely more than 0.6 m.
high), and more slender : spikelets 3 to 6, approximate or subapproxi-
mate. — G. straminea, Schkuhr, Riedg. Nachtr. 23, t. Xxx, fig. 174;
Schwein. & Torr. 1. c. 314; Carey, I. c. 546; Torr. 1. c. 395; Boott,
1. c. 121, t. 387 ; Bailey, Proc. Am. Acad, xxii, 149, in part ; not Willd.
in Schkuhr, Riedgr. 49, t. G. fig. 34, & in herb. G. straminea, var.
brevior, Dewey, Am. Jour. Sci. xi. 158 ; Bailey, Mem. Torr. CI. i. 22,
in part, & in Gray, Man. ed. 6, 622 ; Howe, 1. c. G. straminea, var.
Schkuhrii, Gay, Ann. Sci. Nat. ser. 2, x. 363^ Tuck. 1. c. 8, 17. G.
straminea, var. typica, Gray, Man. ed. 5, 580; Macoun, 1. c. 131. G.
festucacea, Britton, 1. c. 359, in part (including fig. 871), not Schkuhr. —
Commoner than the species, extending to British Columbia, Arkan-
sas, &c. May-July.
478 PROCEEDINGS OF THE AMERICAN ACADEMY.
*- -t- Perigynia two-fifths to one-half (.40 to .50) as thick as broad.
++ Tips of the perigynia distinctly exceeding the scales : spikes short, compact,
ovoid or short-oblong, brown : perigynia 3 to 3.5 mm. long.
17. C. Bebbii, Olney. — Figs. 52, 53. — Culms rather slender, 2 to
6 din. high, smooth except at tip : leaves mostly shorter, ascending but
not stiff, 1.7 '5 to 4.5 mm. wide : sjnkes 1 to 2 cm. long, of 3 to 12 glohose
or ovoid-oblong ascending spikelets 5 to 8 mm. long : perigynia narrowly
ovate, mostly dull broivn and loosely ascending, faintly few-nerved or
nerveless, 1.5 to 2 mm. broad : scale oblong, bluntly acuminate. —
Exsicc. fasc. ii, no. 12, as nomen nudum. C tribuloides, var. Bebbii,
Bailey, Mem. Torr. CI. i, 55 & in Gray, Man. ed. 6, 620 ; Britton,
1. c. 356; Howe, 1. c. 42; Cratty, Bull. Lab. Nat. Hist. Univ. la., iv.
359, t. 8. — Low ground, Newfoundland to western Massachu-
setts, central New York, Illinois, the Rocky Mts., British
Columbia, and northward. June-Aug.
++ ++ Tips of the perigynia nearly or quite equalled by the scales : perigynia more
than 3.5 mm. long (sometimes shorter in the slender-spiked silvery green C.
foenea).
= Perigynia with strong nerves the entire length of the inner face (very rarely
nerveless).
a Spike loose and elongated, green or silvery-brown.
18. C. foenea, Willd. — Figs. 54, 55. — Culms slender and lax,
smooth except at tip, 3 to 9 dm. high : leaves soft and loose, pale green
or glaucous, mostly shorter, 2 to 4 mm. broad : spike linear-cylindric or
moniliform, erect or flexuous, of 4 to 9 globose or ovoid clavate-narrowed
appressed-ascending spikelets 6 to 10 mm. long : perigynia ovate, 3 to If.
mm. long, 1.8 to 2.2 mm. broad, appressed-ascending, finally a little
spreading. — Enum. 957; Bailey, Mem. Torr. CI. i. 25, & in Gray,
Man. ed. 6, 621 ; Macoun, 1. c. 377 ; Britton 1. c. 357, fig. 867 ; Howe,
1. c. 43. C. argyrantha, Tuck, in Herb, distr. (1859). C. adusta, Boott,
1. c. 119, in part, t. 382, fig. 2, not Boott in Hook. Fl. Bor.-Am. ii.
215. C. albolutescens, var. argyrantha, Olney, Exsicc. fasc. i. no. 9.
C. adusta, var. argyrantha, Bailey, Carex Cat. 2. — Dry woods and
rocky banks, Maine to British Columbia and Maryland. July.
Var. perplexa, Bailey. — Figs. 56, 57. — Coarser, and often taller:
spikes heavier, mostly nodding, the 6 to 15 spikelets larger, 1 to 1.7 cm.
long, the terminal ones often crowded : perigynia 3.5 to If.Jf mm. long. —
Mem. Torr. CI. i. 27, in part, & in Gray, Man. Ed. 6, 621 ; Britton,
FERNALD. — CARICES OP SECTION HYPARRHENAE. g 479
I. c. ; Howe, 1. c. 44. C. adusta, Boott, III. iii. 119, in part, t. 381,
382, fig. 1 ; Gray, Man. ed. 5, 580; Macoun, 1. c. 129, in part (excl.
syn.) — Commoner than the species. Newfoundland to Manitoba
and Virginia. June- Aug.
b. Spike with approximate or subapproximate brown or ferrugineous spikelets.
19. C. leporina, L. — Figs. 58 to 60. — Culms stiff and ascending,
2 to 8 dm. high : leaves mostly short and rather firm, 1.5 to 4 mm.
broad : spike from subglobose to cylindric, of 3 to 6 obovoid to oblong-
ovoid ascending spikelets 8 to 1.4 mm. long: perigynia 3.8 to 4.5 mm.
long, 1.8 to 2.3 mm. broad, ascending. — Sp. 973, & Fl. Suec. ed. 2,
326 (excl. cit. Fl. Lapp.); Wahl. Fl. Lapp. 228; Reich. Ic. Fl.
Germ. viii. t. 211; Anders. Cyp. Scaud. 63, t. 4, fig. 26; Boott, 1. c.
iv. 190; Bailey, Proc. Am. Acad. xxii. 152, & in Gray, Man. ed. 6,
622; Britton, 1. c. 356, fig. 864; Meinsh. Acta Hort. Petrop. xviii.
324. C. oralis, Good. Trans. Linn. Soc. ii. 148; Eng. Bot. t. 306; Vahl.
Fl. Dan. vii. t. 1115; Host, Gram. i. 39, t. 51; Willd. 1. c. 955;
Schkuhr, 1. c. 20, t. B, fig. 8. — Europe and Asia: Newfoundland,
shores of Quiddy Viddy Lake, Aug. 2, 1894 {Robinson § Schrenk) :
Nova Scotia, Yarmouth, July 22, 1896 (E. Brainerd) : Maine, low,
rocky pasture, South Berwick, June 23, 1898 (J. C. Parlin, no. 959);
hillside pastures, East Parsonsfield, July 4, 1900 (/. F. Collins fy M.
L. Fernald): New Hampshire, dry hillsides, Alstead, July 9, 1901
(31. L. Fernald) ; Gap Mt., Troy, June 13, 1898 (E. L. Rand $ B. L.
Robinson, no. 508) : Massachusetts, Essex Co., Aug. 23, 1881 ( W.
P. Conant) ; Long Island, Boston Harbor, July 6, 1871, July 1, 1873
(Wm. Boott); Nobscot Hill, Framiugham, June 14, 1901 (3f. L.
Fernald) ; Purgatory Swamp, Dedham, June 23, 1878 (E. $ C. E.
Faxon) : New York, slopes of Bald Mt., north of Fulton Chain,
Herkimer & Hamilton Cos., Aug. 12, 1895 (J. V. Baberer, no. 1103)
New Jersey, ballast ground, Camden, 1878 (Isaac Burlc). Doubtless
introduced at the latter station, but perhaps indigenous northward.
= = Inner face of perigynia nerveless or only slightly nerved at base (excep-
tional individuals of C. leporina might be sought here).
a. Ellipsoidal spikelets brownish-white : the appressed perigynia golden-yellow
at base.
20. C. xerantica, Bailey. — Figs. 61, 62. — Culms stiff", scabrous
above, 3 to 6 dm. high : leaves short, mostly near the base, 2 or 3 mm.
broad : spike linear-cylindric, of 3 to 6 distinct ascending sjrikelets 8 to
480 g PROCEEDINGS OP THE AMERICAN ACADEMY.
13 mm. long: perigynia 4 to 4.8 mm. long, 2 to 2.3 mm. broad. — Bot.
Gaz. xvii. 151 ; Britton, 1. c. 355, fig. 859. — Open prairies, western
Manitoba and adjacent Assiniboia. July.
b. Obovoid spikelets brownish or ferrugineous : the loosely ascending perigynia
dark green or brown when mature.
1. Spike loose and flexuous ; spikelets mostly long-clavate at base, the lowest
remote : achene 1.5 (1.3 to 1.7) mm. broad.
21. C. aenea. — Figs. 63 to 66. — Culms smooth and wiry, but more
or less flexuous at tip, 0.25 to 1.2 m. high : leaves much shorter, rather
soft and flat, 2 to 4 mm. broad : spike loosely cylindric or moniliform,
of 3 to 12 spikelets 0.8 to 2.5 cm. long (in luxuriant plants often
peduncled or compound) : perigynium 4 to 5 mm. long, 1.9 to 2.7 mm.
broad. — C. adusta, Boott, 1. c. iii. 119, in part, t. 380, not Boott in
Hook. Fl. Bor.-Am. ii. 215. G. albolutescens, var. sparsiflora, Olney,
fasc. v. no. 11, in part (as nomen nudum), not G. sparsiflora Fries. G.
adusta, var. sparsiflora, Bailey, Carex Cat. 2 (as nomen nudum) ? 0.
foenea, var. perplexa, Bailey, Mem. Torr. CI. i. 27, as to syn. , in part.
G. foenea, var. sparsiflora, Howe, 1. c. 44. — Open woods, dry banks,
or rarely in low ground. Labrador, without station, Aug. 23, 1896
(Spreadborough, Herb. Geol. Surv. Can. no. 13,354) : Ungava, East
Main R., 1892 (A. H. 1). Ross, Herb. Geol. Surv. Can. no. 30,582) :
Newfoundland, Grand Lake, Bay of Islands, Aug. 6, 1897 (A. C.
Waghorne): Quebec, Riviere du Loup, July 23, 1861 ( Wm. Boott),
Aug. 2, 1896 (E. Brainerd): Calumet, June, 1891 (/. M. Macoun,
Hb. Geol. Surv. Can. no. 16,535) : New Brunswick, Kent Co.
(J. Fowler, in Olney, Exsicc. fasc. v. no. 11, in part): Maine, Fort
Fairfield, 1881 (Kate Furbish); Milford, June 30, 1864 (/. Blake);
Orono, July 7, 1892, July 3, 1897, June 8, 1901 (M. L. Fernald) ;
Mt. Desert Island, numerous stations (Rand, Faxon, Williams et al.) :
New Hampshire, Franconia, June 23, 1888 (E. fy G. E. Faxon) ;
Crawford Notch, July 16, 1895 ( G. G. Kennedy): Vermont, East
Mt., Middlebury, June 23, 1882, Moosalamoo Mt., Salisbury, July 5,
1901 (E. Brainerd) ; Massachusetts, Mt. Wachusett, June 27, 1878
(Wm. Boott) : New York, base of Stony Creek Mt., June 29, 1899
(Rowlee, Wiegand fy Hastings) : Ontario, near Michipicoten, July 26,
1869, Cache Lake, July 12, 14, 1900 (J. Macoun); Lake Victoria,
Sept. 12, 1901 (E. Brainerd): Michigan, Isle Royale (U. Gillman) :
Athabasca, Methy Portage (Sir John Richardson, fide Boott, 111. t.
380) : Alberta, Banff, Rocky Mts., July 10, 1891 (</". Macoun, Herb.
FERNALD. — CARICES OP SECTION HYPARRHENAE. 481
Geol. Surv. Can. no. 16, 536) : British Columbia, Beaver Creek,
Selkirk Mts., July 13, 1885 (no. 10,797) ; Kicking Horse Lake, Aug.
11, 1890 (no. 30,603); Revelstoke, May 19, 1890 (no. 30,604)—/.
Macoun, Herb. Geol. Surv. Can.
2. Spike dense and stiff, erect ; spikelets full and rounded at base, mostly
approximate : achene 2 (1.8 to 2 1) mm. broad.
22. C. adusta, Boott. — Figs. 67 to 69. — Culms smooth, stiffly
erect, 2 to 8 dm. high : leaves usually shorter, 2 to 5 mm. broad : spike
ovoid to cylindric, usually subtended by a stiff rather prominent bract, of
3 to 15 simple or compound spikelets 6 to 12 mm. long: perigynia 4 to
5 mm. long, 2 to 3 mm. broad. — Boott in Hook. Fl. Bor.-Am. ii. 215,
6 111. iii. 119, in part, t. 379 ; Bailey Mem. Torr. CI. i. 24, & in Gray,
Man. ed. 6, 621 ; Britton, 1. c. 357, fig. 866. C. albolutescens, var.
glomerata, Oluey, Exsicc. fasc. v. no. 10. O. adusta, var. glomerata,
Bailey, Carex Cat. 2, Bot. Gaz. ix. 139, & Proc. Am. Acad. xxii. 149.
C. pinguis, Bailey, Bull. iii. Geol. and Nat. Hist. Surv. Minn. 22 ;
Macoun, 1. c. 129. — Dry woods, rocky banks and recent clearings,
Newfoundland to Mount Desert Island, Maine, west to Minnesota,
Assiniboia, Saskatchewan, and Keewatin. June-Sept.
§§ Cyperoideae. Bracts leaf-like and much prolonged, forming a
conspicuous involucre.
23. C. sychnocepiiala, Carey. — Figs. 70, 71. — Culms smooth, 2
to 6 dm. high : leaves soft, ascending, 2 to 4 mm. wide ; bracts unequal,
the lowest longest, 1 to 2 dm. long : spikelets 4 to 10, oblong, 8 to 15 mm.
long, forming a dense ovoid or oblong spike : perigynia lance-subulate,
5 mm. long, barely 1 mm. wide, firm, slightly nerved or nerveless. —
Am. Jour. Sci. Ser. 2, iv. 24, & in Gray, Man. 545 ; Boott, 111. i. 46,
t. 118 ; Bailey, Proc. Am. Acad. xxii. 153; Macoun, 1. c. 121 ; Britton,
1. c. 360, fig. 875 ; Howe, 1. c. 46 ; Cratty, Bull. Lab. Nat. Hist.
Univ. la., iv. 363, t. 9. C. cyperoides, Dewey, Am. Jour. Sci. Ser. 2,
iii. 171, not L. — Meadows, ditches, and wet sandy soil, locally from
central New York to the Ottawa River (Canada), Iowa, Saskatch-
ewan, and British Columbia. July, Aug.
Astrostachyae, Holm. Monoecious or dioecious, the spikelets
often purely stamiuate or purely pistillate, or with the flowers variously
mixed. Bract not sheathing, if present short and filiform. Perigynia
horizontally spreading or reflexed at maturity, spongy at base, glabrous,
nervose, distinctly pointed or beaked, with thin margins and bidentate
apex.
VOL. XXXVII. — 31
482 PROCEEDINGS OP THE AMERICAN ACADEMY.
* Spikelets terminal and solitary (rarely one or two secondary ones below) :
plants usually dioecious.
-i- Culms filiform or setaceous, solitary or few from filiform creeping
stoloniferous rootstocks.
24. C. gynocrates, Wormskiold. — Figs. 72 to 77. — Culms 0.6 to
3 dm. high, mostly exceeding the setaceous leaves: spikelets 0.5 to 2 cm.
long, some stamiuate and linear or linear-lanceolate, with oblong mostly
blunt-pointed scales; others stamiuate above, with 1 or more pistillate
flowers below; others oblong, strictly pistillate, with 6 to 12 rather
jilump subterele, but thin-edged strongly nerved conic-beaked perigynia. —
Wormsk. in Drejer, Rev. 16; Fries, Mant. iii, 134, & Sum. 222.
Anders. Cyp. Scand. 71, t. 3, fig. 8; Kunze, Car. 123, t. 31, fig. 1 ;
Carey, in Gray, Man. ed. 2, 509; Boott, 111. iv. 143, t. 459, 460;
Bailey, Proc. Am. Acad. xxii. 142, & in Gray, Man. ed. 6, 617;
Macoun, 1. c. 109; Howe, 1. c. 49 (incl. var. monosperma, Peck);
Holm, 1. c. 209. C. Redowskiana, Bailey, Mem. Torr. CI. v. 89 ;
Britton, 1. c. 340, fig. 815 ; not C. A. Meyer, according to Meiushausen,
Acta Hort. Petrop. xviii. 305. C. dioica, Schwein. & Torr. 1. c. 293 ;
Dewey, 1. c. Ser. 1, x. 283; Carey, in Gray, Man. 537; not L.
C. monosperma, Macoun, in Bailey, Carex Cat. 3, nomen nudum.
C. alascana, Boeckeler, Engler's Bot. Jahrb. vii. 277, ace. to Bailey.
— Swamps and bogs, Labrador to Alaska, south mostly in Thuya
swamps to Restigouche Co., New Brunswick ; Aroostook and
Piscataquis Cos., Maine; Herkimer, Yates and Genessee Cos., New
York ; Alleghany Co., Pennsylvania ; and Alcona and Oscoda Cos.,
Michigan ; in the Rocky Mts. to Colorado : also in northern Europe
and Asia. June, July.
t- +- Culms stouter, rigid, forming strongly caespitose stools without stolons.
25. C. exilis, Dewey. — Figs. 78 to 83. — Culms iviry, 2 to 7 dm.
high, usually much exceeding the filiform stiff leaves: spikelets mostly
solitary, 1 to 3 cm. long, staminate, or pistillate, or with the flowers
variously situated : perigynia ovate-lanceolate, with serrulate thin mar-
gins, strongly convex on the outer, flattish and few-nerved or nerveless
on the inner face. — Am. Jour. Sci. xiv. 351, t. Q, fig. 53 ; Carey, 1. c.
538; Boott, 111. i. 17, t. 47; Bailey, Proc. Am. Acad. xxii. 142, & in
Gray, Man. ed. 6, 617; Macoun, 1. c. Ill ; Britton, 1. c, 340, fig. 816;
Howe, 1. c. 38 ; Holm, 1. c. 207. C. exilis, var. squamacea, Dewey,
1. c. fig. 54. C. exilis, var. androgyna, Dewey, in Wood, Class-book, ed.
FERNALD. CARICES OF SECTION HYPARRHENAE. 483
1861, 750— Bogs and meadows near the coast, or on the coastal
plain, locally from Labrador and Newfoundland, to New Jersey :
also summit of Smoky Mt., Cape Breton, Nova Scotia; Crystal,
Maine; Bristol and Peacham, Vermont; Essex and Onondaga Cos.,
New York; Mer Bleue, Ontario ; Calumet, Michigan ; and reported
from Hennepin and Crow Wing Cos., Minnesota. May-Aug.
* * Spikelets 2 to several, the staminate flowers mostly at their bases ; plants
very rarely dioecious.
t- Perigynia broadest at the rounded or subcordate base ; the beak rough
or serrulate.
*+ Perigynia .40 to .50 as broad as long, the slender beak conspicuous, often
nearly as long as the body : scales pointed.
26. C. echinata, Murray. — Figs. 84 to 88. — Culms rather wiry,
1 to 4 dm. high : leaves shorter than or equalling the culms, 1 to 2.5
mm. wide: spike linear-cylindric, 1 to 3 cm. long, of 2 to 6 subapproximate
or slightly remote subglobose or oblong 3- to 12- flowered spikelets .-
perigynia finally yellowish, narrowly ovate, early ascending, later wide-
spreading, faintly nerved or nerveless on the inner face, 3 to 4 mm.
long, one- third or one-half exceeding the ovate pointed brownish scale.
— Prodr. 76; Boeckeler, Liunaea, xxxix. 124; Bailey, Proc. Am.
Acad. xxii. 142; Mem. Torr. CI. i. 57, & Bull. Torr. CI. xx. 424;
Macoun, 1. c. 126; Richter, PI. Eur. i. 150; Holm, 1. c. 212. C.
muricata, Huds. Fl. Aug. 406 (1778): Leers, Fl. Herb. 200, t. 14.
fig. 8; not L. C. Leersii, Willd. Prodr. 28. C. stellulata, Gooden.
Trans. Linn. Soc. ii. 144; Schkuhr, Riedgr. 45, t. C, fig. 14; Host,
Gram. i. 41, t. 53; Schwein. & Torr. 1. c. 317; Reich. Ic. Fl. Germ,
viii. 9, t. 214, fig. 560; Carey in Gray, Man 544; Boott, III. i. 55.
Vignea stellulata, Reich. Fl. Exc. 57. C. sterilis, Gray, Man. ed. 5,
578 ; Bailey, Bull. Torr. CI. xx. 424 ; Britton, 1. c. 350, fig. 844 ;
Howe, 1. c. 38; not Willd. — Open low ground, Labrador and
Ungava to Alaska, south to Garrett Co., Maryland, Ohio, Michi-
gan, Saskatchewan, and Humboldt Co., California : also in
Europe and Asia. June-Aug. Extremely variable, passing by num-
erous transitions to the following more marked extremes.
Var. ormantha. — Fig. 89. — Spikes 2 to 6 cm. long, of 2 to 4-
very remote 3- to 9-flowered spikelets, the terminal one with a clavate
base 0.5 to 1 cm. long : perigynia as in the species, spreading or slightly
ascending, mostly twice as long as the scales. — C. echinata, W. Boott,
in Wats. Bot. Cal. ii. 237, in part. — Rhode Island, Providence, 1846
484 PROCEEDINGS OP THE AMERICAN ACADEMY.
(Geo.Thurber)-, Connecticut, without locality (Ghas. Wright); South-
ington, June 5, 1898 (0. H. Bissell) ; Waterford, May 29, 1889 (G. B.
Graves): Oregon, without locality, 1871 (E. Hall, no. 582) : Cali-
fornia, bogs along Strawberry Creek, El Dorado Co., alt. 1,815 m.,
July 18, 1897 (E. Brainerd, no. 160 [type]) ; Big Trees, Calaveras
Co. (Bolander, no. 2324) ; Santa Eosa (J. M. Bigelow) ; Bluff Lake,
San Bernardino Mts., alt. 2,280 m., June, 1895 (S. B. Parish, no.
3702).
Var. excelsior. — Fig. 90, 91. — Tall and slender, 0.3 to 1 m.
high : spike 3 to 5.5 cm. long ; spikelets 3 to 9, distinct, only the lower-
most remote, 12- to 20-flowered, at first oblong-cylindric, with the
perigynia ascending, later subglobose, with strongly reflexed perigynia
one-third longer than the scales. — G. sterilis (3, Boott, 111. i. 56, t.
146.* G. sterilis, var. excelsior, Bailey, Bull. Torr. CI. xx. 424; Howe,
1. c. — Newfoundland to Michigan and North Carolina.
Var. cephalantha, Bailey. — Figs. 92 to 94. — The coarsest form,
3 to 7 dm. high: leaves 2 to 4 mm" broad: spike cylindric or slightly
moniliform, 3 to 7.5 cm. long : the J/, to 8 broad-oblong spikelets approxi-
mate or slightly remote (rarely 1 cm. apart), 15- to IfJ-flowered :
perigynia ovate, one-half as broad as long, wide-spreading or reflexed. —
Mem. Torr. CI. i. 58, & in Gray, Man. ed. 6, 618. C. sterilis, Boott,
111. i. 55, t. 146. G. sterilis, var. cephalantha, Bailey, Bull. Torr. CI.
xx. 425 ; Britton, 1. c. ; Howe, 1. c. 39. G. sterilis, var. aequidistans,
Peck in Howe, 1. c. — Newfoundland to NoRTn Carolina, Michi-
gan, and British Columbia.
Var. angustata, Bailey. — Figs. 95 to 97. — Extremely slender or
almost setaceous, 1 or 2 dm. high (in shade often taller) : leaves 0.5 to
1.5 mm. wide : spike 0.75 to 2.5 cm. long ; the 6 or fewer 3- to 15-flow-
ered spikelets approximate (or slightly remote in shade) : the divaricate
perigynia lance-ovate or lanceolate, 2.5 to 3 mm. long, twice exceed-
ing the scales. — Mem. Torr. CI. i. 59, & in Gray, Man. ed. 6, 618. C.
stellulata, var. angustata, Carey in Gray, Man. 544. G. sterilis, var.
angustata, Bailey, Bull. Torr. CI. xx. 425 j Howe, 1. c. — Nova Scotia
to Connecticut, Lake St. John, Quebec, Illinois, and Michigan.
++ ++ Perigynia about .70 as broad as long, the beak short, one-fourth to
one-half as long as the body.
= Tall: leaves 2.5 to 4.5 mm. broad : perigynia 2 to 3 mm. broad : scales
sharp-pointed.
27. C. sterilis, "Willd. — Figs. 98 to 100. — Goarse, 1 m. or less
high •. leaves flat, shorter than or equalling the culms: spike 1.5 to 3.5
FERNALD. — CARICES OF SECTION HYPARRHENAE. 485
cm. long ; the 3 to 6 subglobose or oblong-cylindric densely 15- to 50-
flowered olive-green spikelets crowded or distinct: the thick strongly many-
nerved perigynia broad-ovate, 3 to 3.5 mm. long, squarrose or with
recurved tips. — Sp. iv. 208 ; Schkuhr, Riedgr. Nacht. 3, t. Mmm, fig.
146. G. stellulata, var. sterilis, Carey in Gray, Man. 544. G. stellulata,
var. conferia, Chapman, Fl. 534. G. echinata, var. conferta, Bailey,
Carex Cat. 2, Proc. Am. Acad. xxii. 143, Mem. Torr. CI. i. 58, & in
Gray, Man. ed. 6, G18 ; Macoun, 1. c. 126. G. atlantica, Bailey, Bull.
Torr. CI. xx. 425 ; Britton, 1. c. 350. — Bogs and clamp pine-barrens,
near the coast from Newfoundland to Florida, rarely inland on
cold bogs, at Lake St. John, Quebec {G. G. Kennedy)-, Squapau,
Aroostook Co., and northern flank (near Bell Camp) of Mt. Katahdin,
Maine (Fernald) ; Adirondack Mts., Essex Co., New York (Knies-
kern) ; and Mt. Sorrow, Valley Forge, Pennsylvania (C. E. Smith).
June, July.
= = Low : leaves 0.5 to 2 (very rarely 2.5) mm. broad: scales blunt.
28. C. interior, Bailey. — Figs. 101 to 105. — Slender, 1.5 to 5
dm. high ; the leaves 1 to 2 (rarely 2.5) mm. broad, shorter than or
exceeding the rather stiff culms : spike 1 or 2 cm. long ; the 2 to 5 spike-
lets all fertile, all sterile, or variously mixed, usually subglobose, J+ or 5
mm. in diameter, the terminal long-clavate at base, 5- to lo-flowered:
perigynia firm, plump, olive-green or -brown, more or less nerved or
almost nerveless, broadly deltoid-ovate, obscurely short-beaked and with
slightly thickened margin, 2.3 to 3.2 mm. long, 1.5 to 2 mm. broad,
fiually wide-spreading or recurved, much exceeding the oblong or ovate
blunt scales. — Bull. Torr. CI. xx. 426 ; Britton, 1. c. fig. 846 ; Howe, 1. c.
39. C. scirpoides, Schkuhr, Riedgr. Nacht. 19, t. Zzz, fig. 180 ; Willd.
Sp. iv. 237; Schwein. & Torr. 1. c. 317; Dewey, Am. Jour. Sci. viii.
96 ; not G. scirpoidea, Michx. C. stelhdata y, Torr. 1. c. 392. C.
stellulata, var. scirpina, Tuck. Enurn. Meth., 9, not G. scirpina, Tuck.
1. c. 8. C. stellulata, var. scirpoides, Carey in Gray, Man. 544 ; Boott,
111. i. 56, t. 146.** C. echinata, Boeckeler, Linnaea, xxxix. 124, in part,
not Murray. G. norvegica, E. P. Sheldon, Bull. Torr. CI. xx. 284, &
Minn. Bot. Studies, i. 224, not Wahl. In damp or wet soil, New Bruns-
wick to Rupert Land and Vancouver Island, south to Florida
and Arizona. Commonest northward and in the interior. May-July.
Var. capillacea, Bailey. Stiff, culms almost setaceous ; leaves about
0.5 mm. broad, often involute : perigynia strongly nerved. — Bull. Torr.
CI. xx. 426; Howe, 1. c. ; Britton, 1. c. 351. — New Hampshire to
New York, New Jersey, and Pennsylvania.
486 PROCEEDINGS OP THE AMERICAN ACADEMY.
-»- ■*- Perigynia broadest near the middle, tapering to a narrow base and a
smooth beak.
29. C. seorsa, E. C. Howe. — Figs. 106 to 109. — Culms soft, in
loose stools, 3.5 to 6.5 dm. high : leaves shorter, soft, pale, 2 to 4 mm.
broad : spikes 2.5 to 7 cm. long, of 2 to 6 mostly remote subglobose or
oblong 6- to 20-flowered green spikelets 3.5 to 7 mm. long, the ter-
minal one usually with a long-clavate base, the lower often subtended
by a setiform bract : perigynia very thin and conspicuously nerved, ellip-
tic-ovate, with a very short smooth beak and a narrow substipitate base,
2.7 mm. long, 1.9 mm. broad, wide-spreading or recurved, much exceed-
ing the acutish scales. — 48 Rep. N. Y. Mus. Nat. Hist. 40. C. canes-
cens, var. vidgaris, Deane, Met. Park Fl. 95, not Bailey. — Wet woods
and swamps, from Middlesex Co., Massachusetts to Suffolk and
Oneida Cos., New York, south to Delaware. May, June.
Elongatae, Kunth. Spikelets remote or approximate in a simple
elongated or short inflorescence. Staminate flowers at the base of the
spikelets. Perigynia ascending when mature, glabrous, ovate to oblong or
lanceolate, plano-convex, beaked or beakless, not thin-winged.
* Perigynia more or less roughened or serrulate on the upper edges (sometimes
smooth in exceptional forms of C. canescens ; and by exception obscurely toothed
in rare individuals of C. tenuiflora).
■*- Perigynia broadest at the rounded or subcordate base.
30. C. arcta, Boott. — ■ Figs. 110 to 113. — Pale green or somewhat
glaucous : culms eery soft, in loose stools, 1.5 to 6 dm. high, often over-
topped by the soft flat leaves 2.5 to Jf. mm. broad: spike oblong-cylindric,
of 5 to 13 ovoid or oblong closely approximate or slightly remote spikelets
6 to 11 mm. long: perigynia ovate, with a rather definite beak, strongly
nerved on the outer, faintly on the inner face, 2 to 3 mm. long, 1.2 to
1.5 mm. broad, somewhat exceeding the acute, often brown-tinged,
scales. — 111. iv. 155, t. 497; Macoun, 1. c. 124; Britton, 1. c. 352, fig.
850. C. canescens, var. polystachya, Boott in Richards. Arct. Exped. ii.
344; Bailey, Proc. Am. Acad. xxii. 144, Mem. Torr. CI. i. 75, & in
Gray, Man. ed. 6, 619. C. Kunzei, Olney, Proc. Am. Acad. viii. 406
(excl. syn.). C. canescens, var. oregana, Bailey, Mem. Torr. CI. i. 75.
— Wet woods, alluvial thickets and swales, from the larger river-valleys
of Maine and Quebec, Lake Champlain, Vermont, and the Adirondack
Mts., New York to Lake Nipigon, Ontario, and British Columbia,
south to Michigan, Minnesota, and the coast and mountains of
Washington and Oregon. June-Aug.
FERNALD. CARICES OP SECTION HYPARRHENAE. 487
-t- -*- Perigynia broadest near the middle.
++ Perigynia 2 to 3 mm. long, fully half as broad.
= Plant glaucous: spikelets oblong-cylindric to ovoid; the strongly appressed-
ascending pale perigynia slightly roughened or smooth above, tapering gradu-
ally to the short obscure beak.
31. C. canescens, L. — Figs. 114, 115. — Culms soft, in loose stools,
1.5 to 6 dm. high: leaves soft and flat, shorter than or exceeding the
culms, 2 to 4 mm- broad: spike 2.5 to 5 cm. long, of 4 to 7 oblong-
cylindric to narrowly obovoid appressed-ascending approximate or slightly
remote spikelets 0.6 to 1 cm. long, the lowermost rarely 1.5 cm. apart:
perigynia glaucous, ovoid-oblong, usually serrulate toward the short-
pointed tip, 2.3 to 3 mm. long, 1.3 to 1.7 mm. broad, more or less nerved
on both faces, somewhat exceeding the ovate pointed scale. Sp. ii.
974 ; Oeder, Fl. Dan. ii. 8, t. 285 ; Lightf. Fl. Scot. ii. 550 ; Reichb.
Ic. Fl. Germ. viii. 7, t. 206, fig. 546; Anders. Cyp. Scand. 57, t. 4,
fig. 39 ; Boott, 111. iv. 154, in part; W. Boott ex Rothrock in Wheeler,
Rep. 277 ; Ett. & Pok. Phys. PI. Aust. vi. t. 515 ; Richter, PI. Eu.
i. 151. C. brizoides, Huds. Fl. Aug. 349, not L. C. elongata, Leers,
Fl. Herb. 197, t. 14, fig. 7; Olney ex Wats. Bot. King Rep. 365;
Bailey in Coulter, Man. Rocky Mt. Reg. 394, in part ; not L. C. cinerea,
Pollich, PI. Palat. ii. 571. C. Richardi, Thuill. Fl. Par. (1799) 482.
C. curta, Good. Trans. Linn. Soc. ii. 145; Host, Gram. i. 37, t. 48;
Schkuhr, Haudb. iii. 347, t. 287C, fig. 13; Eng. Bot. xx. t. 1386;
Kunth, Enum. ii. 403. C. lagopina, Olney ex Wats. Bot. King Rep.
365, in part, not Wahl. C. canescens, var. dubia, Bailey, Bot. Gaz.
ix. 119 & Proc. Am. Acad. xxii. 143. C canescens, var. robustinn,
Macoun, 1. c. 376. — Northern Europe. In wet places, seen from the
following American stations — Labrador, (Spreadborough hb. Geol.
Surv. Can. no. 13,372) : Rupert Land, Lake Mistassini (J. M. Macoun,
hb. Geol. Surv. Can. no. 30,511) : Maine, Fort Kent, Island Falls,
and Foxcroft (M L. Fernald, nos. 2143, 2144, 2145): New Hamp-
shire, Mt. Washington and Mt. Lafayette (E. § C. E. Faxon) ;
Crawfords (E. F. Williams) : Vermont, Ripton (Ezra Brainerd) : On-
tario, Belleville & Lake Nipigon (J. Macoun, hb. Geol. Surv. Can.
nos. 30,513, & 30,512) : Michigan, Alma (C. A. Davis): Colorado,
Twin Lakes (/. Wolf, no. 1017); Bob Creek, alt. 3,230 m. (Faker,
Earle fy Tracy, no. 693) : Montana, Grasshopper Valley (S. Watson,
no. 435): Wyoming, without station (Parry, no. 278); Centennial
Hills (A. Nelson, no. 1730) ; Beaver Lake (A. § E. Nelson, no. 6130) :
488 PROCEEDINGS OP THE AMERICAN ACADEMY.
Utah, Bear River Canon, alt. 3,080 m. (S. Watson, nos. 1231a & 1233).
Alta, Wahsatch Mts., alt. 2,460 m. (M. E. Jones, no. 1273) : Alaska,
Ounalaska (J. M. Macoun, hb. Geol. Surv. Can., no. 30,514) ; Sitka
(Mertens) : Alberta, Lake Louise (E. Brainerd) : British Colum-
bia, Revelstoke (nos. 19 & 30,526), Comox (no. 371), Port Henly
(no. 20,500), Mt. Mark, Vancouver Id. (no. 30,515), Beaver Creek,
Selkirk Mts. (no. 30,519), Dead Man River (no. 30,522), —John
Macoun, hb. Geol. Surv. Can. ; Ilgacho Brook (Dawson, bb. Geol.
Surv. Can. no. 30.518) ; Lulu Island, Fraser River Delta (R. B. Dixon) :
Washington, upper valley of tbe Nesqually (O. D. Allen, no. 163).
May-Aug.
Var. subloliacea, Laestad. — Figs. 116, 117. — Smaller, the short-
oblong or subglobose spikelets 4 to 7 mm. long : perigynia smaller, hardy
2 mm. long, smooth throughout. — Nov. Act. Soc. Sci. Ups. xi. 282 ;
Andersson, Cyp. Scand. 57 ; Boott, 1. c. ; Bailey, Mem. Torr. CI. i. 66 ;
Richter, 1. c. 152. C. lapponicdt, Lange, Linnaea, xxiv. 539. C.
canescens in part, of Am. authors. — Lapland. In America specimens
examined from Ungava, Ungava Bay (L. M. Turner} : Hudson Bat
{Sir John Richardson): New Brunswick, South Tobique Lakes (G.
U. Hay, no. 55) ; Petitcodiac (J. Brittain, hb. Geol. Surv. Can. no.
30,510) : Nova Scotia, Halifax {J. Macoun) : Maine, Orono and
Southport (M. L. Fernald) : New Hampshire, Mt. Washington (Asa
Gray, et al.) ; Mt. Monadnock — ledges toward summit ( W. P. Rich) :
Vermont, Willoughby Lake (W. Boott, G. G. Kennedy); summit of
Mt. Mansfield (E. Brainerd) ; bog, Wallingford, alt. 675 m. (E.
Brainerd): Massachusetts, Sharon (W. P. Rich); "Washington,
Berkshire Co. ( W. Boott) : New York, Fairfield (A. Gray) ; Pen
Yan (Sartwell, no. 32) ; Oriskany Swamp (Kniesken) ; tamarack
swamps, Herkimer Co. (J. V. Haberer) : Ontario, Ottawa (J. Fletcher,
hb. Geol. Surv. Can., no. 7408) ; Hastings Co. (J. Macoun) : Michi-
gan, Flint (Z>. Clark) ; Lansing (L. H. Bailey, no. 262) ; Alma
(C. A. Davis): British Columbia, Mts. east of Adams Lake
(Dawson, hb. Geol. Surv. Can., no. 30,520) : Washington, Seattle
(C. V. Piper, no. 1106).
Var. disjuncta. — Figs. 118 to 120. —Tall and lax, 3 to 8 dm.
high: spike elongated, flexiioas, 0.5 to 1.5 dm. long ; the 5 to 8 oblong-
ovoid to cylindric spikelets 6 to 12 mm. long, all hit the terminal remote,
the lowermost 2 to 4 cm- apart: perigynia as in the species, serrulate
above. — C. canescens of most Am. authors. C. canescens, form, Boott,
111. iv. 154, t. 496. The common form in eastern America found in
FERNALD. — CARICES OP SECTION HYPARRHENAE. 489
most swamps or on wet shores from Newfoundland to Michigan,
Ohio and Pennsylvania. The following uumbered specimens belong
here — Prince Edward Island, Brackley Point (J. Macoun, hb.
Geol. Surv. Can. no. 30,509) : New Brunswick, Serpentine River
{Hay, no. 84) ; Chipman ( Wetmore, hb. Geol. Surv. Can. no. 30,507) :
Nova Scotia, Boylston (C. A. Hamilton, hb. Geol. Surv. Can., no.
25,443); Baddeck (no. 20,805), Sable Island (nos. 22,076 & 23,071),
Truro (no. 30,506) — J. Macoun, hb. Geol. Surv. Can. : Massachu-
setts : Framiugham {E. G. Smith, no. 628) : Connecticut, South-
incton (L. Andrews, no. 590) : Ontario, Cache Lake (J. Macoun, hb.
Geol. Surv. Can., no. 22,036).
= = Green, not glaucous : spikelets subglobose to short-oblong, few-flowered : the
loosely spreading dark green or brown perigynia serrulate at the base of
the distinct beak.
32. C. brunnescens, Poir. — Figs. 121 to 124. — Very slender and
lax: culms 1.5 to 7 dm. high: leaves soft, flat, 1 to 2.5 mm. ivide,
shorter than or equalling the culms : spike 1 to 6 cm. long, of 3 to 6
more or less remote or approximate spikelets S to 7 mm. long : perigynia
2 to 2.7 mm. long, 1 to 1.5 mm. broad, with distinct slender beaks,
loosely spreading when mature. — Suppl. iii. 286; Britton, 1. c. 351,
fig. 848. G. curta, var. brunnescens, Pers. Syn. ii. 539. G. canescens,
var. alpicola, Wahlenb. Fl. Lapp. 232 ; Bailey, Proc. Am. Acad. xxii.
143, & in Gray, Man. ed. 6, 618; Macoun, 1. c. 124; Howe, 1. c. 37.
G. Gebhardii, Hoppe Car. Germ. 30. Vignea Gebhardi, Reichb. Fl.
Exc. 58. G. canescens, j3, Torr. Ann. Lye. N. Y. iii. 393. C. Per-
soonii, Lange, Flora, xxv. (1842), 748 ; Reichb. Ic. Fl. Germ. viii. 7,
t. 206, fig. 547. G. canescens, var. sphaerostachya, Tuck. Enum.
Meth. 10, 19 ; Carey in Gray, Man. 544. C. vitilis, Fries, Mant. iii.
137 ; Anders. Cyp. Scand. 58, t. 4, fig. 38 ; Boott, 111. iv. 219 ; Fl. Dan.
xvii. t. 2973. C. Buckleyi, Dewey, Am. Jour. Sci. xlviii. 143, t. Dd,
fig. 104. G. sphaerostachya, Dewey, 1. c. xlix. 44, t. Ee, fig. 110.
G. canescens, var. vitilis, Carey in Gray, Man. ed. 2, 514. G. canescens,
var. brunnescens, Boott, 1. c. 220 (nomen nudum) ; Bailey. Mem. Torr.
CI. v. 74. C. canescens, var. vulgaris, Bailey, Bot. Gaz. xiii. 86,
Mem. Torr. CI. i. 66, v. 74, & in Gray, Man. ed. 6, 618 ; Macoun, 1. c.
123 ; Howe, 1. c. 37. G. brunnescens, var. gracilior, Britton, 1. c.
350. — Open woods and dry, rocky banks, Newfoundland and Labra-
dor to British Columbia, south to Idaho, Michigan, and mostly in
the mountains to North Carolina. Also in Greenland and northern
490 PROCEEDINGS OF THE AMERICAN ACADEMY.
Europe. June-Aug. On alpine summits becoming more rigid and
browner than in sheltered situations.
++ -H- Perigynia 4 to 5.5 mm. long, distinctly less than half as broad.
= Leaves very narrow (1 to 2.5 mm. broad) : spikelets lanceolate : perigynia
1 to 1.3 mm. wide.
33. C. bromoides, Schkuhr. — Figs. 125, 126. — Very slender and
lax, green, scarcely glaucous, the culms 3 to 8 dm. long, mostly exceed-
ing the soft flat leaves : spike loosely subcylindric, 2 to 5.5 cm. long, of
2 to 6 approximate or slightly scattered spiikelets 0.5 to 2 cm. long : beak
of the perigynium one-half to two-thirds as long as the strongly nerved
body, slightly exceeding the oblong pointed scale. — Riedgr. Nachtrag.
8, t. Xxx, fig. 17G; Willd. Sp. iv. 258; Schwein. & Torr. Ann. Lye.
N. Y. i. 300 ; Torr. 1. c. 391 ; Carey in Gray, Man. 539 ; Chapm. PL
533; Boott, 1. c. ii. 82, t. 227; Bailey, Proc. Am. Acad. xxii. 146;
Macoun, 1. c. 114 ; Britton, 1. c. 354, fig. 857 ; Howe, I. c. 47. — Rich
low woods and swamps, Nova Scotia, southern New Brunswick and
central Maine to western Ontario and Michigan, south to Florida
and Louisiana.1 May-July.
= = Leaves broader (2 to 5 mm. broad) : spikelets ovoid : perigynia 1.6 to
1.9 mm. wide.
34. C. Dewetana, Schweinitz. — Figs. 127, 128. — Very lax, glau-
cous, the culms 2 to 12 dm. long, much exceeding the soft, flat leaves :
spike jlexuous, 2 to 6 cm. long, of '2 to 5 (in very luxuriant individuals
rarely G or 7) 3- to 12-flowered spikelets 5 to 12 mm. long, the upper sub-
approximate or scattered, the lowest very remote, usually subtended by an
elongate slender bract : beak about one-half as long as the obscurely nerved
or nerveless body of the perigynium, somewhat exceeding the ovate acumi-
nate or short-cuspidate pale scale. — Ann. Lye. N. Y. i. 65 ; Dewey, Am.
Jour. Sci. ix. 62, t. 3, fig. 11 ; Schwein. & Torr. 1. c. 310; Torr. 1. c.
392 ; Carey, 1. c. 544 ; Boott, 1. c. i. 27, t. 70 ; W. Boott in Wats. Bot.
Calif, ii. 236 ; Bailey in Coulter, Man. Rocky Mt. Reg. 394, & Proc.
Am. Acad. xxii. 146; Macoun, 1. c. 124; Britton, 1. c. fig. 856; Howe,
1. c. 36. C. remota, Richards, in Frankl. 1st Journ. ed. 2, App. 35, ace.
to Boott, not L. — Rich open woods and banks, Nova Scotia and
1 Californian and other northwestern specimens referred here seem much better
placed with the 6touter broader-leaved C. Bolanderi, Olney.
FERNALD. — CARICES OF SECTION HYPARRHENAE. 491
Quebec to Athabasca and British Columbia, south to Pennsyl-
vania, Michigan, New Mexico, and Washington.1 May-Aug.
* * Perigynia entirely smooth at the tip (exceptional forms of C. canescens might
be looked for here ; and very rare individuals of C tenuiflora might be sought
in the preceding section).
-t- Perigynia oblong or ovate-oblong.
++ Perigynia 3 to 4 mm. long, uerved : culms weak, almost capillary :
spikelets 2 to 4, loose, silvery-green or silvery brown.
= Spikelets closely approximate in a small usually bractless terminal
cluster : perigynia beakless.
35. C. tenuiflora, Wahlenb. — Figs. 129, 130. — Lax, the culms
2 to 6 dm. loug, mostly exceeding the very narrow (0.7 to 2 mm. broad)
pale green leaves : spikelets subglobose, 3- to 10-flowered : perigynia 3 to
3.4 mm. long, 1.5 to 1.7 mm. broad, with the bluntish scarcely beaked
tip smooth or rarely with one or two teeth, about equalled by the ovate
or ovate-oblong white scale. — Kougl. Vet. Acad. Handl. xxiv. 147,
& Fl. Lapp. 232 ; Schkuhr, Riedgr. Nachtr. 17, t. Eeee, fig. 187 ;
Anders. Cyp. Scand. 59, t. 4, fig. 36; Hook. Fl. Bor.-Am. ii. 214;
Torr. 1. c. 392, 443 ; Carey, 1. c. 543 ; Boott, 111. iv. 144, t. 463 ; Fl.
Dan. Suppl. 13, t. 167; Bailey, Proc. Am. Acad. xxii. 145; Macouu,
1. c. 122 ; Britton, 1. c. 352, fig. 851 (as to habital drawing) ; Howe,
1. c. — Cold bogs among the mountains, Scandinavia. Bogs and wet
mossy woods, local, from eastern Ungava to western Keewatin and
Manitoba ; south to Westmoreland and Victoria Cos., New Bruns-
wick; southern Aroostook, Penobscot and Oxford Cos., Maine; Hamp-
shire Co., Massachusetts ; Oneida Co., New York ; Ingham Co.,
Michigan ; Milwaukee Co., Wisconsin ; Chisago and Hennepin Cos.,
Minnesota : also on Elbow River, Alberta, and near Victoria,
British Columbia (31acoun, hb. Geol. Surv. Can. nos. 25,571 &
30,517).
1 The California material which has been referred here is C. Bolanderi, Olney,
differing in its less acutely angled culm, longer spikes of more approximate usually
more numerous lance-cylindric many-flowered spikelets, the lowest with or without
a short bract. The northwestern C. Bolanderi, var. sparsiflora, Olney (C. Deweyana,
var. sparsiflora, Bailey) is a distinct species, probably C. laeviculmis, Meinsliausen,
Acta Hort. Petrop. xviii. 326, in its small short-beaked strongly nerved finally
spreading thin-edged perigynia much nearer related to the eastern C. seorsa than
to the members of the Elomjatae.
492 PROCEEDINGS OP THE AMERICAN ACADEMY.
= = Spikclets remote, the uppermost strongly divaricate-pedunculate ; the lower-
most subtended by a long leaf-like bract : perigynia beaked.
36. C. trisperma, Dewey. — Figs. 131, 132. — Culms almost fili-
form, 2 to 7 dm. long, usually much overtopping the soft narrow (0.5 to
2 mm. wide) leaves : the 2 or 3 spikelets, 2- to 5-Jlowered : the finely
many-nerved perigynia 3.3 to 3.8 mm. long, 1.6 to 1.8 mm. broad,
slightly exceeding the ovate-oblong pale obtuse to mucronate-acumiuate
scale. — Am. Jour. Sci. ix. 63, t. 3, fig. 12 ; Hook. Fl. Bor.-Am. ii. 213 ;
Schwein. & Torr. 1. c. 311 ; Carey, 1. c. 543 ; Boott, 1. c. i. 29, t. 74;
Bailey, Proc. Am. Acad. xxii. 144; Macoun, 1. c. 122; Britton, 1. c.
353, fig. 855; Howe, 1. c. 35. — Mossy woods and bogs, Newfound-
land and Labrador to Saskatchewan, south to northern Pennsyl-
vania, Ohio, Michigan, and Nebraska (according to Webber), and in
the mountains to Garrett Co., Maryland. Ascending to 770 m. in
the New England mountains. June-Aug.
++ ++ Perigynia 1.2 to 1.5 mm. long, nerveless, with a very short broad truncate
beak, or beakless : culms wiry : spikelets 3 to 5, closely flowered, in a
greenish-brown or straw-colored linear spike.
37. C elachycarpa. — - Figs. 133, 134. —Tufted, the stif slender
culms 3 or 4 dm. high, strongly scabrous above, longer than the soft
narrow (1 to 2 mm. broad) green leaves : spike 0.5 to 1.5 cm. long ;
the appressed ascending narrowly ovoid approximate or slightly remote
spikelets 3 to 6 mm. long : perigynia oblong, plump, smooth and nerveless,
subtruncate at base, shorter than the oblong-ovate acuminate dull-brown,
green-ribbed scales. — Maine, wet sandy river bank, Fort Fairfield, June
29, 1899 (31. P. Cook, E. L. Shaw & M. L. Fernald). A unique
plant, in maturity strongly suggesting an immature slender form of C.
echinata, or the little-known C. helvola, Blytt, which, however, have
very different perigynia.
h- •*- Perigynia broadly elliptic to suborbicular : spikes mostly tinged with
brown.
++ Terminal spikelet with conspicuous clavate sterile base : perigynia rather
abruptly contracted to the slender beak.
= Spikelets mostly distinct, the lowest 4 or 5 mm. thick.
38. C. norvegica, Willd. — Figs. 135, 136. — Glaucous and/ree/y
stoloniferous ; culms smooth and soft, 1 to 4.5 dm. high, mostly over-
topping the soft flat rather narrow (1 to 2.5 mm. broad) leaves : spike
FERNALD. — CARrCES OP SECTION HYPARRHENAE. 493
1.5 to 5.5 cm. long, of 2 to G ovoid or broad-oblong spihelets ; the lower
5 to 12 mm. long, the terminal, including the clavate sterile base, 1 to
1.8 cm. long : perigynia pale, faintly nerved, 2.5 to 3.3 mm. long, 1.6 to
2 mm. broad, conic-rostrate, usually abruptly contracted to a substipitate
base, about equalled by the yellotvish brown orbicular to ovate blunt scales.
— Willd. ex. Schkuhr, Riedgr. 50, t. S, no. 6G, & Spec. iv. 227 ; Wahlenb.
Kougl. Vet. Acad. Handl. xxiv. 146, & Fl. Lapp. 233, t. 15, fig. 3;
Anders. Cyp. Scand. 61, t. 4, fig. 29 ; Goodale in Holmes, Prelim.
Rep. Nat. Hist. & Geol. Me. (1861), 128, & Proc. Portland Soc. Nat.
Hist. i. 135; Gray, Man. ed. 3, Addend, xcvii : Boott, 1. c. iv. 211;
Fl. Dan. Suppl. 13, t. 103; Bailey, Proc. Am. Acad. xxii. 115;
Macoun, 1. c. 125 ; Britton, 1. c. 351, fig. 849 (as to babital sketch). —
Brackish marshes, northern Scandinavia. Damp usually brackish
soil, coast of southern Labrador : Anticosti Island, and Kamouraska,
Saguenay, Rimouski, and Gaspc Cos., Quebec : locally southward along
the coast in New Brunswick at Shediac, Westmoreland Co., and
Back Bay, Charlotte Co. (J. Brittain, herb. Geol. Surv. Can. nos.
30,421 & 30,420); Whale Cove, Grand Manau and Fryes Island
{Hay) : Nova Scotia, Baddeck, Cape Breton and Truro (/. Macoun,
herb. Geol. Surv. Can. nos. 20,846 & 30,422) ; Boylston (C. A. Ham-
ilton, herb. Geol. Surv. Can. no. 25,521) : Maine, Little Cranberry
Isle (Redfield) ; Wells (Blake): reported from Alaska.1 June-Aug.
= = Spikelets approximate at the tip of the culm, the lowest 2.5 to 4 mm.
thick.
a. Plant weak and lax, with filiform or involute leaves.
39. C. glareosa, Wahlenb. — Figs. 137, 138. — Culms acutely
angled, mostly curved, scabrous at tip, 1 to 3 dm. high, once and a half
or twice exceeding the flaccid narrow (0.5 to 1.5 mm. broad) leaves :
spike oblong to obovoid, 0.7 to 2 cm. long, with 2 to 4 oppressed-
ascending obovoid spihelets; the lower If. to 9 mm. long, 3 or If. mm. thick, .
the terminal larger, including the slender sterile base, 6 to 11 mm. long:
perigynia pale, elliptic or ovate, acute at base, with narrowly conic beak,
faintly nerved or nerveless, 2.5 to 3 mm. long, 1.1 to 1.0 mm. broad,
nearly or quite equalled by the ferrugi neons ivJiite-edgcd ovate acutish
scales. — Kongl. Vet. Acad. Handl. xxiv. 146, & Fl. Lapp. 230; Willd.
1 Prof. Conway MacMillan has courteously forwarded me the Minnesota speci-
mens referred to C. norvegica by Mr. E. P. Sheldon (Bull. Torr. CI. xx. 284, & Minn.
Bot. Studies, i. 224), and they prove to be C. interior, Bailey.
494 PROCEEDINGS OF THE AMERICAN ACADEMY.
Spec. iv. 251; Schkuhr, Riedgr. Nachtr. 24, t. Aaa, fig. 97; Anders.
1. c. 62, t. 4, fig. 31 ; Torr. 1. c. 39G; Dewey, Am. Jour. Sci. Ser. 2,
iv. 344; Boott, 1. c. 153, t. 494; Fl. Dan. xiv. 8, t. 2430; Bailey,
Proc. Am. Acad. xxii. 146 ; Macoun, 1. c. 127; Britton, 1. c. 353, fig.
854; Meiushausen, Acta Hort. Petrop. xviii. 325. — Arctic regions of
both hemispheres, extending south in America along the coast of
Labrador to Quebec, Bonne Esperance {Allen), Watsheeshoo (St.
Cyr, hb. Geol. Surv. Can. no. 16,524), and Tadousac (Kennedy),
Saguenay Co. ; Pointe des Monts (Bell) and Grand Etang (Macoun, hb.
Geol. Surv. Can. no. 30,413), Gaspe Co.: also on the coast of Alaska.
June-Aug.
b. Plant stiff and upright, with flat leaves.
40. C. lagopina, Wahlenb. — Figs. 139, 140. — Culms obtusely
angled, mostly erect, smooth except at tip, 1 to 4 dm. high, more or less
exceeding the narrow (1 to 8 mm. wide) leaves : spike from cylindric to
globose, 1 to 2.5 cm. long, with 3 to 6 ascending spikelets mostly larger
than in the last : perigynia brown or reddish-brown, from elliptic-lanceolate
to broadly obovate, rather abruptly beaked, 2.5 to 3.8 mm. long, 1.5 to
1.9 mm. wide, exceeding the ovate obtuse white-margined fuscous scales.
— Kongl. Vet. Acad. Handl. xxiv. 145, & Fl. Lapp. 229 ; Gay, Ann.
Sci. Nat. Ser. 2, xi. 177; Drejer, Rev. 25 ; Anders. 1. c. 63, t. 4, fig.
28; Reichenb. 1. c. t. 204, fig. 543 ; Torr. 1. c. 393 ; Boott, 111. iv. 189 ;
W. Boott in Wats. Bot. Calif, ii. 233 ; Bailey in Coulter, Man. Rocky
Mt. Reg. 395, & Proc. Am. Acad. xxii. 145 ; Britton, 1. c. 353, (fig.
uncharacteristic) ; Meinsh. 1. c. C. leporina, L. Spec. 973, in part
(cit. Fl. Lapp.) ; Oeder, Fl. Dan. ii. 9, t. 294 ; Willd. Spec. iv. 229 ;
Schkuhr, Riedgr. Nachtr. 17, in part (excl. t. Fff, fig. 129) ; Host,
Gram, iv, 45, t. 80 ; Eng. Bot. Supp. iii. t. 2815. C. Lachenalii,
Schkuhr, Riedgr. 51, t. Y. fig. 79. C. approximata, Hoppe, ex DC. Fl.
Fr. vi. 290. C. parviflora, Gaud. Etr. Fl. 84, ace. to Boott. C. furva,
Webb, Iter Hisp. 5. — Arctic and alpine regions of Europe and Asia :
Greenland : Arctic America, rarely south to Mt. Albert, Gaspe Co.,
Quebec, the mountains of Colorado, and northern California.
June-Aue.
*&■
++ ++ Terminal spikelet ovoid or subglobose, not conspicuously clavate at base :
perigynia tapering gradually to the tip : culms sharply angled and harsh,
upright, the 2 to 5 spikelets crowded at the tip: leaves flat.
41. C. heleonastes, Ehrh. — Figs. 141, 142. — Culms 1.5 to 3.5
cm. high, stiff, usually overtopping the erect narrow (1 or 2 mm. tcide)
PERNALD. — VARIATIONS OF BOREAL CARICES. 495
leaves: the globose or ovoid spikelets 4 t° 8 mm. long : perigynia 2.5 to
3.5 mm. long, 1.2 to 1.7 mm. broad, brown tinged, mostly exceeding the
ovate blunt scales. — Ehrh. in L. f. Suppl. 414; Wahlenb. Kongl. Vet.
Acad. Handl. xxiv. 14G, & Fl. Lapp. 230; Schknhr, Riedgr. 51, t. Ii,
fig. 97; Hoppe & Sturm, Car. Germ. t. 6; Hook. Fl. Bor.-Am. ii. 214;
Reichenb. Ic. Fl. Germ. viii. t. 204, fig. 542 ; Anders. Cyp. Scand. 62,
t. 4, fig. 30; Boott, 111. iv. 152, t. 489; Fl. Dan. Suppl. t. 31 ; Bailey,
Proc. Am. Acad. xxii. 145; Macoun, 1. c. 127; Britton, 1. c. 352, fig.
852. C. leporina, Schkuhr, Riedgr. Nacht. t. FfF, fig. 129, not L. C.
Carltonia, Dewey, Am. Jour. Sci. xxvii. 238, t. U. fig. 64 ; Torr. 1. c.
393. C. marina, Dewey, 1. c. xxix. 247, t. X, fig. 74 ; Torr. 1. c. —
Bogs and mossy places, arctic and alpine Europe. Very locally in
America: examined from the following stations: — Keewatin, York
Factory (Sir John Richardson) : Saskatchewan, Norway House and
Carlton House (Richardson) : Alberta, Lake Louise (Ezra Brainerd,
no. 172): British Columbia, Glacier (Ezra Brainerd); Kicking
Horse Lake (J. Macoun, hb. Geol. Surv. Can. nos. 28; 49; 30,410;
30,411; 30,412). July, Aug.
II. — THE VARIATIONS OF SOME BOREAL CARICES.
Carex aquatilis.
C aquatilis, Wahlenb., Kongl. Acad. Handl. xxiv. 165. — Plants 3 to
9 dm. high ; leaves 4 to 7 mm. broad : spikelets a slender ; the pistillate 1.5
to 5.5 cm. long, 3 to 4.5 mm. thick, the lowermost often long-attenuated
and remotely flowered at base : scales dark, subacute, hardly equal-
ling or barely exceeding the perigynia. — Northern Europe, Green-
land. In North America from the Shickshock Mts., Gaspe, Quebec,
1 The inflorescences of Carex are simple or compound spikes, racemes, or pani-
cles ; and, since in other genera of Cyperaceae, as Ci/perns and Scirpus, the ultimate
spicate divisions of the inflorescence are called spikelets, that term is here adopted,
for the sake of uniformity and clearness, for these ultimate spicate divisions of
the inflorescence of Carex. The species in which there is a solitary simple in-
florescence (or true spike), as C. (jy hoc rates and C. exilis, are few in comparison
with those in which the inflorescence has more than one such division. From the
occurrence in those plants, however, of occasional secondary divisions of the in-
florescence, the term spilcelet seems not inappropriate to the normal inflorescence
of such species.
496 PROCEEDINGS OP THE AMERICAN ACADEMY.
to Bear Lake, Mackenzie & British Columbia, south to Maine,
Vermont, central and western New York, and Utah. The Scandi-
navian material examined lias been referred to the true C. aquatilis by
Andersson, Fries, Laestadius, and Wickstrom, and it agrees well with
Lauge's representation of the plant in Flora Danica, Supplement, t. 33.
This is the plant of broadest range in America. Many extreme varia-
tions have been described by European authors. The identity of these
is too often obscure, but some of the forms recognized by Mr. Arthur
Bennett in Great Britain (Jour. But. xxxv. 248) are found to occur
also in America. As extreme variations these plants may well be dis-
tinguished, though many transitional specimens occur which render
their ready separation difficult. The best marked forms are the
following:
Var. elatior, Bab. Man. Brit. Bot. 341 ; Bennett, 1. c. 249. — Ro-
bust, 0.9 to 1.5 m. high: leaves 5 to 8 mm. broad: pistillate spikelets
stout and heavy, 3.5 to 8 cm. long, 5 to 8 mm. thick : scales dark, blunt
or acuminate, about equalling or slightly exceeding the perigynia. —
Maine, Fort Fairfield and Orono (M. L. Fernald, nos. 136, in part,
395) : New York, Pen Yan & Junius (Sartwell) ; -Dexter (G. Vasey) ;
Jefferson Co. (Crawe)', Niagara Falls ( W. Boott): Ohio (Sullivant):
Michigan, Pecke Isle, Detroit River ( C. F. Wheeler) : Manitoba,
English River (Sir John Richardson).1 I have been unable to see
authentic specimens of Babington's plant, but from his description and
the note of Mr. Bennett, it seems probable that our large form should
be referred there. The material from Orono (where the once abundant
plant has been exterminated by the ''improvement" of the meadow)
has been described as a hybrid, C. aquatilis X stricta, Bailey, Bot. Gaz.
xvii. 153; but there was little besides the local occurrence of the plant
to suggest hybrid origin. The same very large form is shown in Crawe's
New York material, as well as in Richardson's English River plant, and
it is closely matched by Boott's plate 542, drawn from New York
specimens.
1 Richardson's plant probably came from the river rising in Lake Sal and
flowing into Lake Winnipeg from the southeast. The name English Hirer has
been applied to a district between the Saskatchewan and Athabasca Lake, and it
was long used for the upper portion of Churchill River (emptying into Hudson
Bay). This larger northern river, however, was consistently spoken of by Rich-
ardson in his Arctic Searching Expedition (1852), p. 62, &c, as Missinippi or
Churchill River, while to the more southern river flowing from Lake Sal he ap-
plied the name English River (p. 362).
PERNALD. VARIATIONS OP BOREAL CARICES. 497
Var. virescens, Anders. Cyp. Scand. 46; Bennett, 1. c. — Scales
pale and short, mostly hidden by the closely imbricated perigynia, thus
giving the spikelets a pale green color. — Northern Europe. The
only American specimens seen are from Michigan, without locality
{Michigan State Collection in herb. Gray); near Alma (C. A. Ban's).
Material from Pownal, Vermont, closely approaches this variety, but
has longer darker scales.
Var. cuspidata, Laest. ex Fries, Bot. Not. (1843) 104; Bennett,
1. c. — Spikelets slender. 3 or 4 mm. thick : scales cuspidate, distinctly
exceeding the perigynia. — Northern Europe. Quebec, Grand Etang,
Gaspe (J. Macoun): New Jersey, Camden (C. F. Parker). The
Gaspe plant is a perfect match for Lapland material from Nylander,
but the New Jersey specimen shows a nearer approach to typical C.
aqnatilis.
Var. epigejos, Laest. Kongl. Vet. Akad. Handl. (1822) 339; Bennett,
1. c. — Very slender : the leaves 2 to 3.5 mm. broad : spikelets at most
5 cm. long, 2 to 4.5 mm. thick; scales dark and bluut. — Northern
Europe, Greenland. Newfoundland {La Pylaie) ; Packs Harbor
{A. C. Wag/tome, no. 35): Labrador, L'Anse au Loup (J. A. Allen):
Quebec, Mont Louis, Cape Rosier, and Madaline River, Gaspe {J.
Macoun, nos. 23, 27, 31). The material examined matches well Scan-
dinavian material from Ahlberg. It is also identical with plants from
Lapiand distributed by Andersson as var. sphagnophila. The latter
variety, however, is said by Andersson to differ from var. epigejos in
its pale not dark scales.
Carex pilulifera and C. communis.
Carex pilulifera, L., a common species of Europe, presents three rather
marked tendencies. The original plant of Linnaeus was apparently the
common form with the pistillate spikelets subapproximate or slightly
remote at the tip of the somewhat curved culm. This form with the
lower spikelets sometimes 1 cm. apart, is represented in the Gray
Herbarium by specimens from many parts of northern and central
Europe. In this plant the perigynium is 2.5 to 3.5 mm. long, tipped by
a short bidentate beak less than 1 mm. in length. Another phase of
the plant, evidently rare in Europe, has larger more scattered spikelets,
the lower often subtended by a conspicuous leafy bract; and the larger
perigynia more ellipsoid or with the longer beak equalling the stipitate
spongy basal portion and thus giving the perigynia a symmetrical spiudle-
vol. xxxvi. — 32
498 PROCEEDINGS OF THE AMERICAN ACADEMY.
form. This larger plant was described by Lange as var. longibracteata
and later figured by him in Flora Danica, xvii. t. 3050 ; and again it
has been described by Ridley and figured in Jour. Bot. xix. 97, t. 218,
as var. Leesii. A third European form, var. pallida, Peterm., as shown
by Reichb. Ic. Fl. Germ. viii. 26, t. 240, has the densely flowered spike-
lets closely approximate in an ovoid or subglobose head.
In studying this European species in connection with the well known
American plant which has recently been called C. communis, Bailey, the
writer has been baffled in every attempt to find constant distinguishing
characters to separate the plants of the two continents. The form of
the plant most common perhaps in America is apparently rare in Europe
(var. longibracteata, Lange ; var. Leesii, Ridley), but it passes by abso-
lutely promiscuous variations into a small form which can be distin-
guished in none of its characters from the smaller tendency of the
European C. pihdifera.
By early caricologists the American plant was supposed to be Carex
varia, Muhl., and under that name it passed until in 1889 Professor
Bailey showed that Muhlenberg's plant was the more slender species
described by Dewey as G. Emmonsii. In place of the misapplied name,
C. varia, Professor Bailey proposed for the plant which had long borne
that name the new appellation G. communis, giving no suggestion that
the plant has close affinity to the common G. pihdifera of Europe. To
earlier students, however, the separation of the American and European
plants of this group had presented many perplexities. Drejer stated in
his Revisio that he could find no distinctions either in the descriptions or
specimens : " Forsitan nostra planta rectius cum G. varia Muhlenb.
conjungitur ; quo modo autem G. variam a C. pihdifera. distinguam,
neque ex descriptione neque ex speciminibus eruere possum." 1 Schlech-
tendahl discussing specimens in the Willdenow herbarium which he took
for C. varia was unable to point out any character to separate it from
C. pihdifera .- " Species haec vero simillima C. puhdiferae et uti nobis
fere videtur eadem." 2 Whether Drejer and Schlechtendahl had true
C. varia of Muhlenberg or the coarser plant which so long passed under
that name is not perfectly clear, although it is probable that Schlechten-
dahl at least had the true C. varia.3 This plant, the true C. varia (C.
Emmonsii, Dewey) is readily distinguished from C. pihdifera by its
much more slender habit, very narrow leaves and smaller-bodied longer-
beaked perigynia.
1 Drejer, Rev. Crit, 55. 2 Linnaea, X. 262.
3 See Bailey, Mem. Torr. Club., I. 40.
PERNALD. VARIATIONS OP BOREAL CARICES. 499
The coarse American plant, C. communis, Bailey, which until recently-
passed as C. varia, presents, however, less definite marks of specific dis-
tinctness. The most careful analysis of the characters which are sup-
posed to separate C. communis (C. varia of authors) from C. pilulifera
was published by Francis Boott, who inclined to regard the two species
as separable. In his discussion of C. pilulifera, Boott said: "A C. varia,
Muhl. [6V. communis, Bailey], differt spicis confertis, plurifloris, subinde
apice masculis, e viridi-purpureo variegatis ; perigyniis enerviis, rostello
semper recto breviore bidentato ; basi styli persistente abruptecompresso-
deflexa ; culmo incurvo, basi vagiuis foliorum pallide ferrugineis tecto ;
foliis viridibus."1 In discussing C. varia \_C. com munis, Bailey] he
said : " A C. pilulifera differt inflorescentia laxa ; spicis plus minus re-
motis, laxifloris, saepe paucifloris ; perigyniis subinde nervatis, rostro
nunc excurvato, bihdo ; basi styli persistente recta; vaginis foliorum
purpureis." ~
When we analyze these supposed differences in the light of old speci-
mens and the abundant modern ones which have accumulated since the
publication of Dr. Boott's work, certain traditional marks of separation
fail. The large form of the American plant figured by Boott (t. 288)
as C. varia, and treated by Bailey as C. communis and by Britton as C.
pedicellata, has the spikelets more remote than in the common European
form of C. pilulifera ; but a comparison of this plate with Lange's illus-
tration of his C. pilulifera, var. longibracteata (Fl. Dan. xvii. t. 3050)
and the figure of C. pilulifera, var. Leesii (Jour. Bot. xix. t. 218), shows
that the rarest form of the European plant is not to be distinguished by
the crowding of the spikelets from our larger form of C communis. If,
furthermore, we compare Boott's C. varia, var. minor (t. 289), a common
plant in America, with the smaller European specimens of C. pilulifera
with slightly remote spikelets, no constant difference can be found to sepa-
rate them. The plant in America passes by innumerable transitions to
the coarsest form (var. longibracteata) , as shown in the large middle speci-
men in Boott's t. 289, but in its extreme form, as shown by the smaller
specimens in that plate, the spikelets are often subapproximate. A
comparison of this plate as well as scores of American specimens such as
Egglestou's no. 434 from Middlebury, Vermont ; Brainerd's material
from Mt. Mosalamoo, Vermont ; no. 4897b of the Biltmore Exsiccatae
from Craggy Mt., North Carolina ; Bailey's material of June 13, 1888,
from West Harrisville, Michigan, and his no. 187 from Lansing;
1 111., II. 96. 2 Ibid. 98i
500 PROCEEDINGS OF THE AMERICAN A CAD EM Y.
Wheeler's specimens from Grand Ledge, Michigan ; Macoun's 1876
material from Quesnelle, British Columbia, with specimens of C. piluli-
fera from Berne, Switzerland (Seringe) ; Stockholm, Sweden (Andersson) ;
Finland (Simming) ; the Grosser Pfalzberg, Austria (Haldcsy,no. 1064),
and St. Petersburg, Russia ( Turczaninow) ; shows conclusively that the
remoteness of the spikelets is not to be relied upon in separating our
smaller American material from the European plant. In the accom-
panying tabulation of measurements from European specimens and the
smaller form of the American plant it will be seen that in the length of
the inflorescence and the number, length and remoteness of spikelets
essentially identical conditions are found, although the European mate-
rial shows a tendency to a reduction in the length of the rachis between
spikelets, thus passing to the short-headed var. pallida, while the Ameri-
can plant varying toward the elongated variety longibracteata shows a
natural lengthening of the rachis.
Dr. Boott laid stress upon the more abundantly flowered spikelets of
C. pilulifera, but an examination of the European material shows that
this character is maintained only in the extreme specimens with unusu-
ally full spikelets. In the others many spikelets are found bearing less
than ten flowers while not a few have only four or five. The presence
or absence, in the American or the European plant, of staminate flowers
at the tips of the pistillate spikelets is likewise a character upon which
little reliance can be placed. Both Goodenough 1 and Dr. Boott'2 noted
this tendency in European specimens and in a sheet of Austrian material
it is very conspicuous. In America likewise this tendency to androgy-
nous spikelets occurs, but it seems to be quite as unusual as in Europe.
The pale or castaneous scales of Carex communis were emphasized by
Dr. Boott as opposed to the purple scales of C. pilvlifera. Students of
American Carices, however, are all familiar with specimens of C. com-
munis from sunny or open situations in which the scales are quite as
purple (or rather maroon) as in C. pennsylvanica ; and many specimens
of European C. pilulifera show quite as little color in the scales as do
the commoner plants of America.
The basal nerves supposed to distinguish the perigynium of C. com-
munis from that of C. pilulifera are also quite as often wanting as
present ; and although Dr. Boott laid stress upon this character in his
comparative note, he described the perigynia of C. communis (his C.
variety as ''enerviis vel basi plus minus nervatis pallidis." The length,
i Trans. Linn. Soc, II. 191. 2 111., II. 96.
FERNALD.
VARIATIONS OF BOREAL CARICES.
501
Table of Measurements of European Carex pilulifera and the Smaller
Form of American C. communis.
European Specimen.
Collector.
Length of
Jnlloresceuee
in mm.
c ~ 3
■=> 3.3
■U.f. ^
°B a
a,
Number of
pistillate
Spikelets.
«M 3
o » 3
— iS.S
§.- »
a.
02
0
ggts t
M a
Length of
Perigynia
in mm.
Length of
Beak iu
mm.
Strombacka, Sweden . .
Lauren
12-18
6-8
2-:!
4.5-6
4.5-7
3.4
0.6
Simming
16-19
6-7
3-4
4
8
2.8
0.8
Stockholm, Sweden . .
Andersson
17-22
10-11
2-3
7
5-7
2.7
0.7
Halifax, England . .
Leyland
13-22
7-10
2-3
5.5
5-10
3.0
0.7
Dresden, Germany . . .
20
9-13
3
4-6
7.5
2.9
0.7
Halle, Germany ....
A. Schulz
18-23
8-9
4
4-8.5
9
3.0
0.8
Berne, Switzerland . .
Seringe, no. 1238
17-22
10
2-3
4.5-7
3.5-7
3.0
0.8
Upsala, Sweden ....
Angstrom
14-26
9-1 G
2-4
5-9
3-9
2.8
0.7
Kyffhauser (Mt.), Germ'ny
17-22
11
6-8
6
3.0
0.7
Grosser Pfalzberg, Austria
Ilalacsy, no. 1064
14-26
7-18
1-3
3-6
3.5-6 5
2.7
0.9
Salzburg, Austria . . .
Hoppe
26-32
11-13
4-5
6-11
6-9
3.0
0.7
St. Petersburg, Russia
Turczaninow
18-23
9-11
2
5-7
6-9
20
0.7
I'jis.ila, Sweden ....
Tuckerman
25
10
4
6-8
9
3.0
0.8
Snowdori, Wales . . .
J. Ball
18
6.5
3
6
6
2.9
0.8
Extremes in Europe . .
12-32
6-18
1-5
3-11
3-10
2.7-3.4
0.6-0.9
American Specimen.
Keweenaw Co., Mich. .
Farwell, no. 653
10-13
4
2-3
4
5-6
3.3
0.8
Alcona Co., Mich. . . .
Bailey
15-10
4-8
o
5-7
7-15
3.2
0.8
Jones & Eggleston
11-23
6-13
1-2
6-8.5
7-8
3.2
0.8
Quesnelle, Brit. Columbia
Macoun
15-23
9-10
2-3
5-6
5-10
3.0
0.7
Grand Ledge, Mich. . .
Wheeler
18-10
8
3
5-6
6-9
3.3
0.8
Mt. Mosalamoo, Vt. . .
Brainerd
17-23
8
3
4-0
7-12
2.4
0.8
EastMt., Middlebury, Vt.
Eggleston, no. 434
17-24
9-11
2-3
5-6.5
5-13
2.6
0.9
Willoughby Mt., Vt. . .
Faxon
13-26
6.5-10
1-2
4-6
8-12
3.0
0 7
Lake Memphremagog, Q'b.
Faxon
13-29
3.5-9.5
2-4
4-8.5
7-11
3.0
0.9
Craggy Mt., No. Carolina
Biltmore Herb.,
no. 4807''
21-31
9-16
2-3
4-8
7-11
2.8
0.7
Orono, Me
Fernald
23-36
6-13
3-4
4-9
11-12
3.1
1.0
Franconia, N. H. ...
Faxon
24-39
8-11
3-4
4-9
7-15
3.3
0.8
Milwaukee, Wis. . . .
Lapham
30-35
14
3
4-7
9
3.0
0.9
Lansing, Mich
Bailey, no. 187
25-39
13-18
2
4-8
11-14
3.2
0.8
Extremes in America . .
10-30
3.5-18
1-4
4-9
5-15
2.4-3.3
0.7-1.0
502 PROCEEDINGS OF THE AMERICAN ACADEMY.
bending, and orifice of the beak show likewise considerable variation in
Old World specimens, all of which can be matched by our plant, while
the curving of the base of the style is a tendency not infrequent in
American as well as European specimens. On the other hand, the
straight style supposed to characterize the American plant is clearly
represented by Lange in his plate of C. pihilifera, var. longibracteata.
The deeper purple coloring of the lower sheaths of the American
plant, a character much emphasized by authors, is not a satisfactory
distinction. The color in the American plant is usually conspicuous
and is pronounced by Mr. F. Schuyler Mathews a dilute maroon with
no true purple tendency, but rather fading in the older sheaths to
chestnut. Mr. Mathews, who has likewise examined the sheaths of
European specimens, finds the same red present in them. This color
of the sheaths generally fades with age, yet in specimens collected by
John Ball on Snowdon, by Andersson at Stockholm in 18G0, by Lauren
at Strombacka in 1855, and by Tuckerman at Upsala in 1841 or 1842,
show quite as conspicuous a red as the average American plant.
The bright green color of the leaves of C. pihilifera has likewise been
maintained as a character separating that plant from the American C.
communis. From dried specimens alone it is impossible to make this dis-
tinction apparent, although the fresh plant may sometimes show a brighter
color than is often seen in C. communis. Yet in the American plant the
leaves vary from a weak to a deep green, and in Bailey's var. Wheeleri,
which is certainly inseparable from European specimens of C. jrihilifera,
the leaves were originally described as '"bright green."
The length of the stamiuate spikelet and the breadth of the leaves,
two characters upon which stress is sometimes laid, were not emphasized
by Dr. Boott. An examination of the accompanying table of measure-
ments of the inflorescence will show that the length of the staminate
spikelets is thoroughly inconstant and not concomitant with other char-
acters. In fact, both short and long staminate spikelets are often found
on the same individual, as shown by Halacsy's no. 10G4 of the Austro-
Hungarian Exsiccatae (staminate spikelets from 7 to 18 mm. long), by
Fernald's no. 151 from Maine (spikelets G to 13 mm. long), and a
Faxon plant from Franconia, New Hampshire (spikelets from 8 to 14
mm. long). The variations in the breadth of the leaf, likewise, are
very great on both continents. The young leaves at the fruiting season
are naturally much narrower than the old and weather-beaten ones,
which, unfortunately, are too often torn away in the preparation of
attractive specimens. Measurement of the breadth of these older leaves
FERNALD. — VARIATIONS OP BOREAL CARICES. .503
where present shows in the American plant a variation from 2 to 5.5
mm. and in the European from 2 to 4.5 mm. These measurements,
however, include the largest American form, in which all the parts are
conspicuously more developed than in the smaller American and the
apparently identical European plant. *
The length of the lower bract, emphasized in the descriptions of
C. pilulifera, var. longibracteata and var. Leesii, seems to the writer
an unfortunate character to make prominent. In America, at least,
this elongation of the bract accompanies no other definable character.
It is a purely vegetative development which may occur either in the
large form (C. varia [typical] of Boott's 111. t. 288) or in the smaller
C. communis, var. Wheeleri with shorter inflorescence and more approxi-
mate spikelets.
This study of the European Carex pilulifera and the American C.
communis (C. varia of many authors) has led to the following con-
clusions. The form of C. pilulifera of Europe with the pistillate spike-
lets subapproximate or slightly remote, the lowest from 0.5 to 1 cm.
apart, is also common in America, where the plant has passed generally
as C. varia, var. minor, Boott ; C. communis, Bailey, and C. pedicellata,
Britton, in part ; or C. communis, var. Wheeleri, Bailey (C. pedicellata,
var. Wheeleri, Britton). Another European form, the large C. pihdi-
fera, var. longibracteata, Lange, is rare in Europe, but in America is
represented by the large extreme which has passed as C. varia and later
as C. communis and C. pedicellata. The American plants, then, should
be called
C. PiLULiFKRA, L. Cidms 1 to 5 dm. high, usually overtopping the
leaves: inflorescence 1 to 3.5 cm. long, the lowest spikelet subtended
by a short and narrow or sometimes elongated broad bract : staminate
spikelet from green to chestnut-brown or maroon, sessile or stalked,
3.5 to 20 mm. long; pistillate spikelets 1 to 5, loosely flowered, 4 to
11 mm. long, sessile or short-pedicelled, subapproximate or slightly
remote, the lowest rarely 1.5 cm. apart: perigynia hairy, obscurely
3-angled, 2.5 to 3.5 mm. long, the body plump, obovoid or subglobose,
with a more or less elongated spongy nerveless or slightly nerved
stipitate base ; the beak broad, bidentate, rarely 1 mm. long, nearly
or quite equalled by the green brown or reddish-brown ovate acuminate
scale. — Sp. 976; Gooden. Trans. Linn. Soc. ii. 190; Schk. Riedgr.
78, t. I, fig. 39; Andersson, Cyp. Scand. 30, t. 7, fig. 82; Reichb. Ic.
Fl. Germ. viii. t. 260 ; Boott, 111. ii. 96, t. 283. C. filiformis, Pol.
PI. Palat. ii. 581 ; Vahl, Fl. Dan. vi. t. 1048; not L. C. Bastardi-
504 PROCEEDINGS OF THE AMERICAN ACADEMY.
ana, DC. Fl. Fr. vi. 293. C. varia, Authors, incl. Boott, 111. I. c.
97, in part, not Mulil. C. varia, var. pedicellata, Dewey, Am. Jour.
Sci. xi. 163, in part. C. varia, var. minor, Boott, I.e. t. 289. C.
communis, in part, and var. Wheeler i, Bailey, Mem. To it. CI. i. 41.
C. pedicellata, in part, and var. Wheeleri, Britton, Mem. Torr. CI.
v. 87, 88. — In dry soil, New Brunswick to British Colombia,
North Carolina, Ohio and Wisconsin: common in Europe.
Passing gradually to
Var. longibracteata, Lange. Coarser ; the inflorescence often
5 to 8 cm. long, the usually fuller and longer pistillate spikelets remote,
the lowest 1.5 to 4 cm. apart: perigynia larger, more ellipsoid or
spindle-form, with longer beak. — Ilaandb. Dansk. Fl. G21, & Fl. Dan.
xvii. 12, t. 3050; Kneucker, Allgem. Bot. Zeitschr. (1898) 128. C.
varia, Authors, in part, incl. Boott, 1. c. t. 288, not Muhl. C. varia,
var. pedicellata, Dewey, 1. c, in part. C. saxumbra, F. A. Lees,
Jour. Bot. xix. 25. C. pilulifera, var. Leesii, Ridley, Jour. Bot. xix. 98,
t. 218. C. communis, Bailey, 1. c. in part. C. pedicellata, Britton,
1. c. in part. — New Brunswick to Iowa and Georgia: rare and
local in northern Europe.
( Iarex pennsylvanica.
Carex pennsylvanica, Lam., is one of the widest-distributed of the
North American Carices, and as one of the earliest-flowering it is per-
haps better known to the general botanist than any of the other species.
In the length aud breadth of its leaves, the comparative height of its
culm, etc., the plant shows considerable variation, and many formal
varieties have been based upon these characters. But since they are
all of a purely vegetative nature, often produced in a colony of the
species by changes of ecological conditions, none of these variations
seem to the writer of sufficient constancy to merit recognition as more
than trivial forms. The color of the spikelets, also, a character too
commonly relied upon to separate C. pennsylvanica from the closely
related C. pilulifera, L. (C. communis, Bailey), is not to be accepted
as final, since C. pennsylvanica, ordinarily characterized by dark reddish
brown scales, may often have them pale or even straw-colored when
growing in deep shade. Furthermore, C. pilulifera in northern Europe
as well as in America is frequently found with dark red scales, especially
when growing in very sunny or exposed situations. The simplest means
of distinguishing C. pennsylvanica from its nearest common ally is in
its stoloniferous character ; for when well developed the plant produces
PERNALD. — VARIATIONS OF BOREAL CARICES. 505
conspicuous elongated stolons, while C. pilulifera (C. communis) is
caespitose, with short assurgent basal shoots. As may be implied,
varieties of C. pennsylvanica based upon color of the spikelets are
quite as inconstant as are those based upon the length or breadth of
the leaf, or other purely vegetative tendencies. In the character of its
perigynia, however, C. pennsylvanica presents three marked variations
which, from the material examined, seem to belong to well marked
geographic areas. These forms of the plant are :
C. pennsylvanica, Lam. Diet. iii. 388. Strongly stoloniferous ;
the slightly caespitose small stools with reddish bases : leaves soft, com-
paratively narrow, 1.5 to 3.5 mm. broad, 0.5 to 5 dm. long, shorter
than, equalling, or often exceeding the slender culms : pistillate spike-
lets 1 to 4, globose or ovoid, loosely flowered, approximate or more or
less remote, the lowest rarely peduncled, often subtended by a narrow
leafy bract: scales usually maroon or red-tinged, rarely pale: perigynia
from subglobose to obovoid, puberulent, the short bifid beak one-fourth
to one-fifth as long as the body : staminate spikelet clavate, 1 to 2 cm.
long, sessile or short-stalked, usually reddish, rarely straw-colored. — In
dry or sandy soil from Cumberland Co., Maine, to Alberta, south to
Georgia and New Mexico. It is impossible to say from the original
description whether this or the following variety was intended by
Lamarck, but the commonest form of the species has been accepted
as typical since it was so considered by Boott, Kunze, and other classic
writers on the genus. The varieties and forms described by Peck
(46 Rep. N. Y. Mus. Nat. Hist. 51 ; 48 Rep. 76) appear to be vegeta-
tive states due largely to different degrees of light and exposure.
Var. lucorum. Perigynium puberulent or glabrate, with a con-
spicuous slender beak nearly or quite as long as the body. — C. lucorum,
Willd. Enum. PL Berol. Suppl. 63; Kunze, Car. 153, t. 39; Boott,
111. ii. 98, t. 291, in part. — Maine to Michigan and "Arctic
America," and in the mountains to North Carolina. Maine,
Orono, May 31, 1890, June 4, 1898 (no. 2006) — M. L. Fernald;
Cambridge (F. S. Bunker); Glassface Mt., Rumford, July 13, 1890
(/. C. Parlin) : New Hampshire, Barrett Mt., New Ipswich, June 5,
1896 (M. L. Fernald) : Vermont, Chipman Hill, Middlebury, May 30,
1897, Burlington, June 16, 1898 {E. Brainerd) ; Pownal, May 29, 1898
{J. R. Churchill) : Massachusetts, Spot Pond, Stoneham, May 29,
1855, Maiden, June 11, 1861, Medford, May 21, 1865, Blue Hills, Milton,
June 3, 1870 (Wm. Boott); Purgatory Swamp, Dedham, May 26, 1878
{E. $ C. E. Faxon); Wilmington, May 14, 1899 (E. F. Williams):
506 PROCEEDINGS OF THE AMERICAN ACADEMY.
Rhode Island, Cumberland (S. T. Olney) : Connecticut, Southington,
June 4, 1899 (C. H. Bissell) ■ Fairfield, June 23, 1901 (E. H. Eames,
no. 168) : Michigan, Detroit, May 22, 1864, June, 1860, May 9, 1858
(Wm.Boott): Virginia, Harper's Ferry, May 7, 1881 (John Donnell
Smith): North Carolina, Broad River, May. 1841 (Rugel according
to Kunze, 1. a). The long slender beak of the perigynium and its
essentially northern and montane range suggest that further knowledge
of the plant may show it to be well distinguished from C. pennsylvanica.
No other character has yet been found by which it can be recognized, and
occasional individuals show transitions in the elongation of the beak.
Var. vespertina, Bailey, Mem. Torr. CI. i. 74. Rather coarser than
the species : the usually very dark staminate spikelet peduncled : peri-
gynia more coarsely hairy, almost hirsute. — The northwestern form,
from the Cascade Mts. of British Columbia to Oregon and Van-
couver Island.
Carex umbellata.
Like C. pihtlifera and C pennsylvanica, C. umbellata, Schkuhr, pre-
sents considerable variation in the length and breadth of its leases and
in the length of its culms and peduncles. As in those species, likewise,
these purely vegetative characteristics in C. umbellata seem to accompany
no fixed characteristic of the perigynia, nor any special geographic areas ;
and too often the loug-peduncled spikelets of the so-called var. vicina
may be found on portions of a clump which is otherwise good C. um-
bellata. As in the related species just discussed, however, C. umbellata
presents at least two geographic tendencies seemingly characterized by
constant differences in the perigynia. A third form, of which we as
yet know too little, has the perigynia glabrous, thus breaking through
one of the distinguishing marks of the Montanae.
Carex umbellata is related on the one hand to G. nigro-marginata, and
on the other to C. deflexa. From these two it is usually distinguished
without difficulty, but occasional specimens occur which are perplexing.
The writer has found that in such cases the best means of distinction
between C. umbellata and C. nigro-marginata is offered by the thickness
of the perigynia. In C. nigro-marginata the mature perigynia vary
from 1.3 to 1.6 mm. in thickness, while in mature C. umbellata they
are from 1.7 to 2.4 mm. thick. From doubtful forms of C. deflexa, C.
umbellata may best be distinguished by an examination of the scales.
In 0. umbellata the scales are nearly or quite as long as the subtended
perigynia, while in C. deflexa they are distinctly shorter.
FERNALD. — VARIATIONS OF BOREAL CARICES. 507
The most marked tendencies of C. umbeUata are
C. umbellata, Schkuhr, Riedgr. Nachtr. 75, t. "Www, fig. 171 (C.
umbeUata, var. vicina, Dewey, Am. Jour. Sci. xi. 317 & x. t. D, fig. 13).
Low and conspicuously caespitose, forming dense mats : leaves rather stiff,
0.5 to 4.5 dm. long, 1 to 4.5 mm. wide : culms mostly very short and
crowded at the base of the leaves, or some elongated, rarely even to 2 dm.,
and bearing both staminate and pistillate, or staminate spikelets alone:
pistillate spikelets 1 to 4, ovoid or oblong, 0.5 to 1 cm. long, sessile or
on short or occasionally elongate-capillary peduncles: perigynia plump,
stipitate or substipitate, puberulent, 3.2 to 4.7 mm. long ; the slender
beak nearly or quite as long as the ellipsoid-ovoid to subglobose or pyri-
form body, and about equalled by the ovate acuminate green or purple-
tinged scale: staminate spikelets subsessile or peduncled, 6 to 12 mm.
long. — Dry sandy or rocky places, Prince Edward Island to
central Maine, west to Saskatchewan and British Columbia,
and south to New Jersey, District of Columbia, and Indian
Territory.
Var. tonsa. Similar, but with the perigynia glabrous or merely
puberulent on the angles of the long beak. — Maine, Streaked Mt.,
Hebron, June 2, 1897 (J. A. Allen) : Connecticut, rocky wooded
slope of Lantern Hill, North Stonington, May 30, 1901 (C. B. Graves).
A plant with identical glabrous perigynia is figured in Boott, 111. ii.
t. 293, from specimens collected at Methy Portage, Athabasca, by Sir
John Richardson. This and the New England plant represent a tend-
ency unusual in the Montanae.
Var. brevirostris, Boott, 111. ii. 99, t. 294. Periirynia rather
smaller, the broad beak short, about one-third as long as the plump short-
hairy body. — The commonest form from Saskatchewan to Vancou-
ver Island, south in the mountains to California and New Mexico :
also Maine, Fort Kent, Ashland, Masardis, Island Falls and Foxcroft
(M. L. Fernald, nos. 2111, 2112, 2113, 2114, 2115); summit of Sargent
Mt., Mount Desert Island (E. fy C. E. Faxon) : New Hampshire,
Mt. Willard, and Bald Mt., Franconia (E. 3? C. E. Faxon).
Carex vaginata and C. saltuensis.
C. vaginata, Tausch, Flora (1821) 557 (C. vaginata, var. alto-caulis,
Dewey, Am. Jour. Sci., Ser. 2, xli. 227. C. saltuensis, Bailey, Mem.
Torr. CI. i. 7. C. altocaulis, Britton, in Britton & Brown, 111. Fl. i. 326,
fig. 773). The American plant was long considered by Francis Boott
508 PROCEEDINGS OF THE AMERICAN ACADEMY.
and other caricologists identical with the European ; but in 1866 the
New York plant was distinguished by Dewey, on account of its tall
slender culm, narrow leaves and loose spikelets as var. alto-caulis. In
1889, however, Professor Bailey raised the American plant to specific
rank as C saltuensis, separating it from the European C. vaginata " by
its much more slender and less caespitose habit, narrower leaves and
less conspicuous sheaths, its alternately-flowered spikes, and its much
smaller, less inflated, and conspicuously nerved perigynium." And Dr.
Britton, following Professor Bailey's lead in treating the plant as
strictly American, has taken up for it Dewey's varietal name as
altocaulis (not alto-caulis).
That American specimens from the deep swamps of western New
York, Ontario and Michigan are more slender than some European
specimens there can be no doubt; but in northeastern Maine, where the
plant is a common species of arbor-vitae swamps, it varies greatly in
these characters. Individuals growing in excessive shade are naturally
taller and more slender than those in bright light ; and the spikelets
vary indiscriminately from the slender alternate-flowered tendency sup-
posed to characterize the American plant to the dense-cylindric form
said to distinguish the European.
The height of the European plant, too, is often as great as that of the
American, while our own plant sometimes fruits when scarcely 2 dm.
high (Mt. Albert, Quebec — Allen ; Blaine, Maine — Fernald). A speci-
men from Christiania collected by Blytt is 5 dm. high, while the extreme
height given by Dr. Britton for his C. altocaulis is 2 feet (6 dm.).
The breadth of the leaf, likewise, is as variable on one continent as on
the other. Both Dewey and Bailey have maintained that the European
plant is broader-leaved ; yet a specimen from Fries collected in Jemtland
(Sweden) has leaves from 1.5 to 1.75 mm. wide, while the broadest
leaves seen on the European plant are those of a Lapland specimen
(5 mm. wide) from N. J. Andersson. In the American plant the leaves
vary from 1.5 mm. wide (Blaine, Maine) to 5 mm. (Montreal).
The variation in the density of the spikelet in the American plant has
been already mentioned. In Europe the same variation occurs, speci-
mens from Jemtland (A/dberg), Lapland (Andersson) and Finland
(Lehmann) having the spikelets as loosely flowered as in the most
extreme American form.
Nor are the differences assigned by Professor Bailey to the perigynia
maintained in mature specimens. Young individuals of the American
as well as the European plant have the nerves poorly developed, but in
FERNALD. VARIATIONS OP BOREAL CARICES. 509
mature fruit no difference is apparent between plants from Christiauia,
Norway, and Aroostook Co., Maine.
The sheath, said by Professor Bailey to be " less conspicuous " in the
American plant, is 4 cm. long, by 2.7 mm. wide in one of Macrae's
Montreal specimens, fully as conspicuous as in the best developed
European material. There is, then, no reason why the American Carex
saltuensis, Bailey (C. altocaulis, Britton) with no constant vegetative or
morphological character and witli a broad range from northern Labrador
to the Mackenzie River, northern New England, New York, the Great
Lakes and the upper Rocky Mts., should be treated as distinct from C.
vaginata of Greenland, northern- Europe and Asia.
Carex capillaris.
C. capillaris, L. Sp. 977. The Linnaean plant was the low plant
of the Scandinavian mountains, described as a span high. This plant,
well represented in the Gray Herbarium by European specimens from
Andersson, Holmgren, Hoppe, Lehmann, Tuckerman, and others, varies
in height from 3 to 25 cm., the spikelets being subapproximate or
scarcely remote, the lower at most 2 cm. apart. This dwarf plant
occurs likewise in Greenland and northeastern Asia. It has been ex-
amined from the following regions in America — Labrador, Dead
Islands (J. A. Allen) : Newfoundland, without locality (La Pylaie) ;
Middle Arm, Bay of Islands (A. C. Waghome) : Quebec, dry stony
ground, near summit — 1,150 in. — Mt. Albert (J. A. Allen): Maine,
Mt. Kineo (T. C. Porter et al) : New Hampshire, Mt. Washington
(Wm. Oakes et at): Colorado, Rocky Mts., alt. 8,385 m. (E. L.
Greene in Exsicc. Olney) ; South Park (J. Wolfe, no. 1059) ; Clear
Creek, Georgetown, alt. 2,615 m. (H. N. Patterson, no. 144, in part):
Utah (S. Watson, no. 1261) : Wyoming, La Plata Mines (E. Nelson,
no. 5260).
Var. elongata, Olney, in herb. & in Rothr. Prelim. Rep. Wheeler
PI. 53 (as nomen nudum). Tall, 2 to 6 dm. high, forming loose stools :
pistillate spikelets remote, often 6 or 8 cm. apart. — Mossy woods and
sphagnum-swamps. Rupert Land, Lake Mistassini (J. M. Macoun) :
Newfoundland, Coal River, Bay of Islands (A. C. Waghome, no.
24) : Quebec, Ste. Anne des Monts and Little Metis (J. A. Allen) :
New Brunswick, Drury's Cove, St. John (Wm. Boott) : Maine,
Fort Fail-field (nos. 140, 2029), Blaine (no. 2028), Mars Hill — M. L.
Fernald : New York, Otter Creek, near Cortland (S. N. Cowles) :
510
PROCEEDINGS OP THE AMERICAN ACADEMY.
Ontario, Bruce Co. (J. Macoun) : Michigan, Point de Tour ( Wm.
Boott) ; Port Huron (C. K. Dodge): Saskatchewan (Bourgeau) :
Assiniboia, Assiniboine River (J. Macoun) : Albekta, Bow River
(J. Macoun) : Colorado, Rocky Mts., alt. 2460 m. (E. L. Greene in
Exsicc. Olney) ; Twin Lakes (/. Wolfe, no. 1060 [type]) ; Clear Creek
(Parry, no. 386, Patterson, no. 144, in part) : Utah, Aquarius Plateau
(L. F. Ward, no. 484) : Idaho, Lake Pend d'Oreille (tSandberg, Mac-
Dougal S? Heller, no. 751). A plant confined in the East to arbor-
vitae swamps at low altitudes, and in its tall lax habit and very distant
spikelets hardly suggesting the dwarf alpine G. capillaris with approxi-
mate spikelets. Somewhat similar specimens in the Gray Herbarium
from Salzburg, Austria, suggest that the same form may be present in
Europe.
INDEX TO SPECIES.
Carex
adusta, 451, 452, 464, 476, 478,
480,
" var. argyrantha, 478.
" " glomerate, 481.
" minor, 471.
" sparsiflora, 480.
aenea, 461, 462, 464, 480.
alascana, 482.
alata, 448, 450, 451, 463, 476.
" var. ferruginea, 463, 477.
albolutescens, 448, 450, 451, 452,
var. argyrantha, 47
" " cumulate, 472.
" glomerate, 481.
" sparsiflora, 452,
altocaulis, 507, 508, 509.
approximate, 494.
aquatilis, 495, 496, 497.
X stricta, 496.
" var. cuspidate, 497.
" elatior, 496.
" epigejos, 497.
" sphagnophila, 497.
" " virescens, 497.
arcta, 458, 459, 466, 486.
argyrantha, 452, 478.
arida, 167.
479,
481.
464,
472.
453,
480.
Carex
atlantica, 454, 456, 457, 458, 485.
Bastardiana, 503.
Bebbii, 449, 462, 478.
Bicknellii, 450, 451, 463, 475.
Bolanderi, 490, 491.
var. sparsiflora, 491.
brizoides, 487.
bromoides, 465, 490.
brunnescens, 453, 458, 459, 460, 466,
489.
var. gracilior, 489.
Buckleyi, 489.
canescens, 453, 458, 459, 460, 466, 486,
487, 488, 491.
0, 489.
var. alpicola, 459, 489.
" brunnescens, 489.
" disjuncta, 466, 488.
" dubia, 459, 487.
" oregana, 458,486.
" polystachya, 458, 486.
" robustina, 459, 487.
" sphaerostachya, 489.
" subloliacea, 459, 466,
488.
" vitilis, 489.
" vulgaris, 458, 459, 486,
489.
capillaris, 509, 510.
FERNALD. — CARICES OP SECTION HYPARRHENAE.
511
Carex
capillaris, var. elongata, 509.
Carltonia, 495.
cinerea, 487.
communis, 497, 498, 499, 500, 501, 502,
503, 504, 505.
var. Wheeled, 502, 503,
504.
Crawfordii, 461, 469.
var. vigens, 462, 470.
cristata, 450, 462, 469, 472, 473.
" var. mirabilis, 473.
cristatella, 472.
curta, 453, 487.
" var. brunnescens, 489.
cj'peroides, 481.
deflexa, 506.
Deweyana, 465, 490.
var. sparsiflora, 491.
dioica, 482.
echinata, 447, 453, 454, 455, 456, 458,
465, 483, 485, 492.
var. angustata, 465, 484.
" cephalantha, 455, 456,
465, 484.
" conferta, 485.
" excelsior, 465, 484.
" microstachys, 454. 455.
" ormantha, 465, 483.
elachycarpa, 467, 492.
elongata, 453, 487.
Emmonsii, 498.
exilis, 453, 460, 465, 482, 495.
" var. androgyna, 482.
" " squamacea, 482.
festiva, 474.
festucacea, 450, 451, 404, 475, 477.
var. brevior, 464, 474, 477.
" mirabilis, 473.
" tenera, 474.
filiformis, 503.
foenea, 449, 451, 452, 462, 464, 472, 478.
var. ft 450, 451, 477.
" y, 476.
" (?) ferruginea, 451, 477.
" perplexa, 452, 464, 478,
480.
" sparsiflora, 480.
" (?) subulonum, 476.
furva, 494.
Gebhardii, 453, 459, 489.
glareosa, 4(50, 493.
Carex
gynocrates, 453, 460, 465, 482, 495.
var. monosperma, 482.
lieleouastes, 459, 467, 494.
helvola, 492.
interior, 454, 457, 458, 465, 485, 493.
var. capillacea, 465, 485.
Kunzei, 486.
Lachenalii, 494.
laeviculmis, 491.
lagopina, 406, 487, 494.
lagopodioides, 408, 469.
var. cristata, 472.
" mirabilis, 473.
" moniliformis, 469.
'• scoparia, 468.
lapponica, 488.
Leersii, 483.
leporina, 449, 462, 464, 468, 479, 494,
495.
var. bracteata, 472.
Liddoni, 469, 471.
lucorum, 505.
marina, 495.
mirabilis, 450, 462, 403, 472, 473.
var. perlonga, 462, 473.
" tincta, 462, 473.
monosperma, 482.
muricata, 483.
muskingumensis, 461, 463, 467.
nigro-marginata, 506.
norvegica, 466, 485, 492, 493.
oronensis, 462, 471.
ovalis, 479.
pallida, 469.
parviflora, 494.
pedicellata, 499, 503, 504.
var. Wlieeleri, 503, 504.
pennsylvanica, 500, 504, 505, 506.
var. lucorum, 505.
" vespertina, 506.
Persoonii, 489.
pilulifera, 497, 498, 499, 500, 501, 502,
503, 504, 505, 506.
var. Leesii, 498, 499, 503,
504.
" longibracteata,498,499,
500, 502, 503, 504.
" pallida, 498, 500.
pinguis, 481.
pratensis, 471.
" var. furva, 452.
512
PROCEEDINGS OF TIIE AMERICAN ACADEMY.
Carex
praticola, 452, 401, 462, 404, 471.
Redowskiana, 482.
remota, 490.
Richardi, 487.
saltuensis, 507, 508, 509.
sax umbra, 504.
scirpina, 458, 485.
scirpoidea, 457,458, 185
seirpoides, 453, 454, 455, 157, 458,485.
scoparia, 447, 448, 449, 400, 461, 463,
467.
" var. condensa, 401, 4G8.
" lagopodioides, 468.
" minor, 447,448,449, 470.
" moniliformis, 449, 461,
4G8, 169.
" muskingumcnsis, 467.
seorsa, 458, 460, 465, 486, 491.
siccata, 401, 469.
silicea, 463, 404, 476.
gparsiflora, 453, 480.
sphaerostachya, 489.
stellulata, 454, 455, 156, 483.
7, 485.
" var. angustata, 455, 484.
" conferta, 485.
" scirpina, 457, 485.
" seirpoides, 457, 485.
" sterilis, 485.
sterilis, 453, 454, 455, 456, 457,
405, 483, 484.
0, 484.
var. aequidistans, 484.
" angustata, 484.
" cephalantha, 484.
" excelsior, 455, 458, 484.
straminea, 447,41s, 450, 451, 462, 403,
171, 477.
" var. alata, 476.
" " aperta, 451, 475.
" brevior, 450, 451, 476,
477.
" " chlorostacliys, 472.
" Crawei, 450, 451, 175.
" cristata, 472.
" " cumulata, 472.
Carex
straminea, var. echinodes, 463, 474.
" ferruginea, 451, 477.
" festucacea, 477.
" foenea, 472.
" intermedia, 472.
" invisa, 475.
" Meadei, 475.
" minor, 474.
" mirabilis, 473.
" moniliformis, 476.
" Sclikubrii, 477.
" silicea, 470.
" tenera, 474, 475.
" typica, 477.
syclinocephala, 464, 481.
tenera, 1 18, 450, 451, 403, 474, 475.
" var. invisa, 403, 474, 475.
" " major, 175.
" Richii, 463, 464, 474, 475,
476.
" " suberecta, 477.
tenuiflora, 460, 480, 491.
tribuloides, 449, 450, 461, 468.
var. Bebbii, 478.
" cristata, 472, 473.
" moniliformis, 419,468,
169.
" reducta, 449,461, 168,
469, 474.
" " turbata, 461, 469.
trisperma, 466, I
Tuckormani, 449.
umbel lata, 506, 507.
var. brevirostris, 507.
" tonsa, 507.
" vicina, 560, 507.
vaginata, 507, 508, 509.
" var. alto-caulis, 507, 508.
varia, 498, 499, 500, 503, V 1
" var. minor, 499, 503, 504.
" " pedicellata, 504.
vitilis, 458, 459, 189
xerantica, 462, 464, 479.
Vignea
Gebbardi, 489.
stellulata, 483.
FERNALD. — CARICES OP SECTION HYPARRHENAE. 513
EXPLANATION OF PLATES.1
Plate I.
Carex muskingumensis : Fig. 1, spike; Fig. 2, perigynium.
C. sc.oparia: Fig. 3, spike; Fig. 4, perigynium.
C. scoparia, var. condensa : Fig. 5, spike.
C. tribuloides : Fig. 6, spike ; Fig. 7, perigynium.
C. tribuloides, var. reducta : ¥\g. 8, spike.
C. siccata : Figs. 9, 10, spikes ; Fig. 11, perigynium.
C. Craivfordii : Fig. 12, spike ; Fig. 13, perigynium.
C. Crawfordii, var. vigens: Fig. 14, spike.
C. oronensis : Fig. 15, spike ; Fig. 16, perigynium.
C. praticola : Fig. 17, spike; Fig. 18, perigynium.
C. cristata : Fig. 19, spike ; Figs. 20, 21, perigynia.
C. albolutescens : Figs. 22, 23, spikes; Fig. 24, perigynium.
Plate II.
C. mirabilis : Fig. 25, spike ; Fig. 26, perigynium.
C. mirabilis, var. perlonga : Fig. 27, spike.
C. straminea : Fig. 28, spike ; Fig. 29, perigynium.
C. straminea, var. echinodes : Fig. 30, spike.
C. tenera: Fig. 31, spike ; Fig. 32, perigynium.
C. tenera, var. Richii : Fig. 33, terminal spikelet ; Fig. 34, perigynium.
C. tenera, var. invisa : Figs. 35, 36, spikes.
C. Bicknel/ii : Figs. 37, 38, spikes ; Figs. 39, 40, perigynia.
C. slllcca: Fig. 41, spike; Fig. 42, perigynium.
C. alata : Fig. 43, spike ; Fig. 44, perigynium.
C. alata, \&v.ferruginea : Fig. 45, spike ; Fig. 46, perigynium.
Plate III.
C.festucacea : Fig. 47, spike ; Fig. 48, perigynium.
C.festucacea, var. brevior : Figs. 49, 50, spikes ; Fig. 51, perigynium.
C. Bebbii : Fig. 52, spike ; Fig. 53, perigynium.
C.focnea : Fig. 54, spike ; Fig. 55, perigynium.
C.foenea, var. pcrplexa : Fig. 56, spike ; Fig. 57, perigynium.
1 The plates illustrating this synopsis were prepared by Mr. F. Schuyler
Mathews from characteristic specimens. The figures of the spikes represent
life-sized individuals, while those showing the inner faces of the perigynia are
four times as large as in nature,
vor,. xxxvu. — 33
514 PROCEEDINGS OP THE AMERICAN ACADEMY.
C. leporina : Figs 58, 59, spikes ; Fig. 60, perigynium.
C. xerantica : Fig. 61, spike ; Fig. 62, perigynium.
C. aenea : Figs. 63, 64, spikes ; Figs. 65, 66, perigynia.
C. adusta : Fig. 67, spike ; Figs. 68, 69, perigynia.
C. sychnocephala : Fig. 70. spike ; Fig. 71, perigynium.
Plate IV.
C. gynocrates : Figs. 72, 73, 74, 75, spikes ; Figs. 76, 77, perigynia.
C. exilis : Figs. 78, 79, 80, 81, 82, spikes ; Fig. 83, perigynium.
C. echinata : Figs. 84, 85, 86, 87, spikes ; Fig. 88, perigynium.
C. echinata, var. ormantha : Fig. 89, spike.
C. echinata, var. excelsior : Figs. 90, 91, spikes.
C. echinata, var. cephalantha : Figs. 92, 93, spikes ; Fig. 94, perigynium.
C. echinata, var. angustata : Figs. 95, 96, spikes ; Fig. 97, perigynium.
C. sterilis : Figs. 98, 99, spikes ; Fig. 100, perigynium.
C. interior : Figs. 101, 102, 103, spikes ; Figs. 104, 105, perigynia.
C. seorsa : Figs. 106, 107, spikes ; Figs. 108, 109, perigynia.
Plate V.
C. arcta. Figs. 110, 111, 112, spikes ; Fig. 113, perigynium.
C. canescens : Fig. 114, spike; Fig. 115, perigynium.
C. canescens, var. subloliacea : Fig. 116, spike ; Fig. 117, perigynium.
C. canescens, var. disjuncta : Figs. 118, 119, spikes ; Fig. 120, perigynium.
('. brunnescens : Figs. 121, 122, spikes; Fig. 123, 124, perigynia.
C. bromoides : Fig. 125, spike ; Fig. 126, perigynium.
C. Deweyana : Fig. 127, spike ; Fig. 128, perigynium.
C. tenuijiora : Fig. 129, spike; Fig. 130, perigynium.
C. trisperma: Fig. 131, spike ; Fig. 132, perigynium.
C. elachycarpa : Fig. 133, spike ; Fig. 134, perigynium.
C. norvegica : Fig. 135, spike ; Fig. 136, perigynium.
C. glareosa: Fig. 137, spike; Fig. 138, perigynium.
C. lagopina: Fig, 139, spike; Fig. 140, perigynium.
C. heleonastes: Fig. 141, spike; Fig. 142, perigynium.
Fernald — Carex § Hyparrhen
yparrhenae.
Plate
Fernald — Carex g Hyparrhenae.
Plate II.
Fernald — Carex § Hyparrhenae.
Plate ill.
Fernald — Carex § Hyparrhenae
Plate IV.
Fernaid — Care* § Hyparrhenae
V A
Plate V.
1 1-1 Yf 11-2
.
Proceedings of the American Academy of Arts and Sciences.
Vol. XXXVII. No. 18. — March, 1902.
CONTRIBUTIONS FROM THE HARVARD MINERALOGICAL
MUSEUM. — X.
APATITE FROM MINOT, MAINE.
By John E. Wolff and Charles Palache.
With a Plate.
CONTRIBUTIONS FROM THE HARVARD MINERALOGICAL
MUSEUM.— X.
APATITE FROM MINOT, MAINE.
By John E. Wolff and Charles Palaciie.
Presented December 11, 1901. Received February 7, 1902.
In the summer of 1901, while prospecting for tourmaline or other
gem minerals on the farm of Mr. P. P. Pulsifer in Minot, Maine, a
pocket was opened in the granite containing the material here described.
It was first brought to our notice by Mr. C. L. Whittle, formerly of this
Department, and the whole was subsequently acquired by the Harvard
Mineralosrical Museum.
This find is noteworthy for the unusually rich purple color of the
crystals, and the purity, crystalline perfection, and abundance of the
material, which comprises about two thousand loose crystals or frag-
ments of crystals with a total weight of over a kilogramme, and about
a dozen large groups of crystals on the matrix. Of the loose crystals
about three hundred show at least one perfect termination, five hundred
are slightly less perfect, and the rest imperfect or fragmentary.
Paragenesis.
The apatite was found in a single cavity in pegmatitic granite, the
walls of which appear to have been lined with crystals of quartz, ortho-
clase, and lepidolite, with which in smaller amounts were albite, musco-
vite, and cookeite.
The quartz crystals range from small dimensions up to a height and
thickness of 15 cm. They show the common quartz forms only, the
positive and negative unit rhombohedrons and the prism, and are nota-
ble chiefly as presenting in a very striking manner the evidence of two
periods of growth. Wherever broken and whether large or small, the
crystals show a core of glassy, light to dark smoky quartz ; surrounding
this is a surface layer of white opaque quartz from 1 to 3 mm. in
thickness, crystallographically continuous with the smoky quartz, but on
many of the face*, especially those of the rhombohedrons, composed of
518 PROCEEDINGS OF THE AMERICAN ACADEMY.
a multitude of small parallel crystals which give the surface a pitted
appearance.
A thin section cut across this boundary showed under the microscope
that the outer opaque layer was in crystallographic continuity with the
inner part, but the line between them was sharp, the opaque layer con-
taining very abundant liquid and obscure solid inclusions and showing
faintly a division into libres or columns perpendicular to the surface.
The appearance pointed to a second period of quartz deposition rather
than to an alteration of quartz previously formed. The evidence of
the secondary deposition of the white quartz was rendered stronger by
the occurrence in several places between the two layers of a thin de-
posit, not more than 1 mm. thick, of tiny muscovite crystals, or of a
double layer of muscovite and cookeite. The apatite crystals are often
deeply embedded in the white quartz and seem to have developed in
part pari passu with this material ; but at no place does the apatite
appear to penetrate the smoky quartz.
The lepidolite is in part in confused lamellar aggregates, in part in
quite definite hexagonal prismatic crystals with somewhat rounded basal
terminations. The interior of these crystals is of the characteristic
pale lilac color of lepidolite, but their surfaces are everywhere covered
by a uniform layer of pale greenish-white muscovite about 1 mm. in
thickness. The cleavage of the lepidolite and of the bordering musco-
vite is absolutely continuous, but the boundary between them is sharp
and plane, showing that the muscovite represents, not an alteration of
lepidolite, but a later parallel growth of the new and isomorphic mineral,
a sort of secondary enlargement. Sharply bounded lepidolite crystals
without the muscovite border are sometimes enclosed in the smoky
quartz, showing that these two minerals were of contemporaneous
growth.
The orthoclase, a pale flesh-colored variety, and the albite, colorless,
in thin plates showing albite twinning, are small in amount, and their
relations to the smoky quartz show that they belonged to the same
period of growth with it.
Cookeite occurs quite abundantly on some of the specimens as crusts
or clumps of scales or platy crystals of a greenish-white color. It is
similar in appearance to the muscovite, but is slightly darker in color,
less pearly in lustre, and readily distinguished by its reactions before the
blowpipe. The cookeite appears to have been formed at several periods
of mineral growth in the cavity. It is seen occasionally as above stated
in thin layers between the outer white quartz layer a»d the coating of
WOLFF AND PALACHE. APATITE FROM MINOT, ME. 519
muscovite ; more frequently it forms an irregular layer on the lepidolite-
muscovite crystals, showing, however, no parallelism with them ; and it
is rarely included in, and in small amount deposited upon, the apatite
crystals. In no case does the cookeite appear to have heen formed at
the expense of any of the minerals previously formed in the cavity,
which are perfectly fresh and free from alteration.
The apatite is implanted upon the quartz crystals and upon the lepido-
lite-muscovite crystals or the cookeite which covers them. As stated
above the apatite is embedded at times in the white quartz layer in
which it leaves sharp moulds when broken out, it having maintained its
crystal form despite the interference of the quartz.
Finally a third generation of quartz in minute crystals is found as-
sociated with the cookeite, and rarely implanted upon the apatite
crystals.
To briefly recapitulate the facts relating to the paragenesis of this
deposit we may say that we find :
First, the crystallization of the smoky quartz, lepidolite, orthoclase,
and albite, the normal constituents of the granite, to form the walls of
the cavity.
Second, the crystallization of muscovite, coating smoky quartz crystals
in part and the lepidolite crystals wholly.
Third, the crystallization of cookeite, coating muscovite, wholly or in
part.
Fourth, the simultaneous crystallization of apatite and white quartz,
the latter confined to enlargement of smoky quartz crystals.
Fifth, a second period of cookeite formation, accompanied by a final
deposition of quartz.
Crystallography.*
The apatite crystals are in general of pronounced prismatic habit,
the average size being about 1 cm. in height and 0.5 cm. in diameter.
Crystals larger than this are, however, common, the largest measuring
nearly 3 cm. in height and diameter. Crystals smaller than the average,
which are also numerous, tend to assume a more or less rounded habit
by nearly equal development of prismatic and terminal planes.
The crystals are geuerally so implanted upon a terminal face that
one end has developed freely, and the fact that over three hundred
loose crystals with complete single termination and prism zone were
* By C. Palache.
520
PROCEEDINGS OF THE AMERICAN ACADEMY.
obtained from the collection shows how prevailing is this habit of
growth. Occasionally the attachment to the matrix is by a prism plane*
and then both terminations are developed.
The forms observed were as follows, the letters used being those of
Dana:
c (0001), m (10T0)), a (1120), h (2130), z (3031), y (2021), *(10Tl),
r (1012), w (7073), s (1121), ii (2131), ^ (3121).
Four crystals were carefully measured on the two-circle goniometer
and the same forms found on all. The results of measurement of the
better developed forms agreed so well among themselves that it seemed
worth while to calculate the axial ratio from the better readings, and this
was done, using the forms y, x, r, and s. The following table shows the
average angle to the base from each of these, the ratio calculated for
each crystal, and the average ratio obtained :
Angle from
No. of
d.*
Angle from
No. of
d.*
0001 to 2021.
Faces.
0001 to 1012.
Faces.
Cryst.
1 .
. 59° 29'
5
3'
Cryst
1
. 23° 00'
6
1'
tt
2 .
. 59° 29f
5
2'
tt
2
' 23° 00'
5
5'
U
Q
'J
. 59° 30i'
6
3'
tt
3
. 23° 00'
3
0'
it
4 .
. 59° 28J'
Angle from
0001 to loll.
5
3'
tt
4
. 22° 59f
Angle from
0001 to 1121.
4
Cryst.
1 .
. 40° 18'
6
3'
Cryst
1
. 55° 45'
6
1'
it
2 .
. 40° 19'
5
5'
ti
2
. 55° 46'
6
3'
it
O
. 40° 19'
5
6'
tt
O
. 55° 46'
4
it
4 .
. 40° 18'
5
2'
it
4
. 55° 45'
0
4'
Crystal 1, from 23 measurements, p0 = 0.848307
Crystal 2, from 21 measurements, p0 = 0.848739
Crystal 3, from 18 measurements, p0 = 0.848753
Crystal 4, from 20 measurements, p0 = 0.848148
Average from 82 measurements, p() = 0.848476 or a : c = 1 : 0.734800
Angle calculated from p0 = 0.848476, 0001 to 2021 59° 29' 22"
0001 to 10T1 40 18 50
0001 to 10T2 22 59 19
0001 to 1121 55 45 59
Two types of combinations may be distinguished among these crystals.
One of these is represented in figure 1, and consists essentially of the
* d is the difference in minutes between largest and smallest readings for faces
of any form.
WOLFF AND PALACHB. APATITE FROM MI NOT, ME. 521
prism of the first order and the base, the edges modified by narrow
plaues of the forms a, s, r, x, and y. Crystals of this type are not
uncommon and often show double terminations. They merge, however,
by slight gradations into the second type, more characteristic for the
locality, shown in figures 2 and 3. Here the pyramidal planes become
more prominent and the most notable feature is the simultaneous occur-
rence of the right and left third order pyramids, giving the appearance
of the normal dihexagonal pyramid.
The different forms may be characterized as follows :
c (0001) always present, generally large, brilliant, and plane giving
perfect reflections.
m (10T0) always present, generally dominant, brilliant, and generally
plane but sometimes faintly striated vertically.
a (1120) generally present but narrow and commonly dull from deep
striatiou, the striae vertical and bounded by faces of adjoining plaues
of m. Occasionally the striations stop abruptly in the centre or near
the boundaries of a face as shown in figure 3, or they may be wholly
lacking, in which case the face is brilliant and "fives <rood reflections.
h (2130) rarely developed and then narrow as shown in figure 4.
Surface plane, not involved in striations on a.
r (10T2), x (10T1), and y (2021) all nearly always present with all
their faces, in varying proportions and often large, faces always brilliant
and free from striations, giving perfect reflections.
w (7073) observed but once as a line face in the zone between y
and m.
z (3031) generally present only as a deeply striated face, sometimes
very large as in figure 4, giving no reflection but determined by its
zonal relation to /x and fi-y. The striae bounded by faces parallel to
adjoining planes of m and y. Narrow faces of z giving faint reflections
sometimes present on the edges of the striae nearest to m.
s (1121) always present with brilliant faces, often large.
p. (2131) and /xt (3T21) are both present on many crystals, but vary
widely in size, quality, and regularity of development. Generally the
faces of both are dull and the forms are then indistinguishable. On
some crystals their faces are brilliant and reflecting but grooved or
pitted, and a constant difference in the character of these markings was
found by which, when they were not too far developed, the two forms
could be distinguished. On fx the markings ordinarily take the form of
sharp grooves parallel to the intersection of m and /x as shown in figures
2 and 3. The grooves seem to be in a way continuations of the striae
522 PROCEEDINGS OF THE AMERICAN ACADEMY.
on the faces of z, for they never extend beyond the intersection of /x with
that face, and are absent if z is not developed. The grooves are bounded
by faces parallel to adjacent planes of s and of m. Very often they
stop short in the middle of the face as shown in figure 3.
On fxi the markings are in the form of irregular pits or curving
grooves, sometimes showing approximate parallelism to the intersection of
m and ^ but with an irregularity giving them a character wholly dif-
ferent from the lines on /x. No constant difference could be observed
in the brilliancy of the reflecting portions of faces of the two forms, nor
in their relative size. Both are irregular in their occurrence on individ-
ual crystals, lacking nearly always some of their faces. As shown in
the figures, both may present on the same crystal faces of very unequal
size which in some cases are so large as to dominate the termination of
the crystal.
The occurrence of third order pyramids in apparently holohedral
combination has been observed on apatite from various localities, notably
Knappenwand, Tyrol,* Ala, Piedraout,f and Elba.J But in none of the
crystals described does there appear to have been any observable dif-
ference between the faces of the right and left forms by which they
could be distinguished.
Reference has been made in the preceding pages to striations which
appear quite constantly on certain faces of the apatite. They are a
striking feature of the crystals and the attempt has been made to repro-
duce them in the drawings. Their most pronounced development was
on the largest crystal of the collection, which is reproduced in figure 4 ;
the striations on the faces of z and of a were almost equally strong and
gave the crystal a curiously tetragonal aspect when inspected casually.
On both of these forms the striations are doubtless growth forms, the
result of oscillatory combination, on a of adjacent faces of m, and on z
of planes of m and y. The markings on the faces of /x and /xx seem to
have a different character, however. The irregularity of their develop-
ment, appearing on some faces as mere grooves or pits, on others
invading the whole face and reducing it to a dull surface, indicates that
they are rather the result of etching by some agent which has attacked
the crystals after they were formed.
* C. Klein, Neues Jahrb. Miner., 1871, 485 ; 1872, 121.
t G. Struever, Att. Ace. Torino, 3, 125, 1867; 6, 363, 1871; Rendic. R. Ace.
Lincei, Roma, 1899, 8 (1), 427-434.
.t E. Artini, Rendic. R. Ace. Lincei, Roma, 1895, 4 (2), 259.
WOLFF AND PALACHE. — APATITE FROM MINOT, ME.
523
Chemical Composition. *
The material for analysis was taken from the deep purple clear
crystals, which were broken free from any adhering gangue and care-
fully examined with the lens ; while the microscope confirmed the
purity of the mineral. The method followed was essentially that used
A.
B.
Ratios.
J.
P,05 ....
41.30
41.58
0.2928 0.2928
39.84
(FeAl)203
0.71
0.71
0.0044 ,
(AL.O32.O2
iFet) 0.62
MnO . .
0.85
0.86
0.0121
0.22
CaO . .
MgO . .
53.43
0.70
53.79
0.70
0.9G05
0.0173
.1.0029
53.36
0.25
K20 . .
0.27
0.27
0.0028
0.52
Na20 . .
0.36
0.36
0.0058 t
0.42
ILO . .
0.29
0.29
t0.0323\
0.48
CI . . .
abs.
. . . > 0.1586
1.82
F . . .
2.38
2.40
0.1263)
1.03
Loss at 320°
0.04
0.04
Less 0 = F .
100.33
1.00
101.00
1.00
100.58
0.90
99.33
100.00
99.68
Sp. gr., 3.159 at 2
0°C.
A. Apatite from Minot, Maine.
B. Calculated to 100.
J. Apatite from Ceylon, Jannasch and Locke, loc. cit.
, p205
RO
F-OH,
1
3.42
0.57
1.5
5.13
0.85
or, CasP8[F.OH]012.
* By J. E. Wolff.
t Calculated as OH = 0.55 per cent OH.
524 PROCEEDINGS OF THE AMERICAN ACADEMY.
by Jannasch and Locke, * namely solution in nitric acid with addition of
mercuric oxide, precipitation with ammonia and determination of phos-
phoric acid, most of the lime and the other bases in the precipitate,
while the rest of the lime and the alkalies were determined in the first
filtrate. Water was determined directly by fusion with plumbic oxide
mixed with potassium di-chromate.
Fluorine was determined by the method of Fresenius, that is by
heating the finely powdered mineral, mixed with previously ignited
quartz, in a flask with strong sulphuric acid and absorbing the SiF4
in weighed tubes with the prescribed precautions. From the total
weight obtained there was subtracted a correction for the general gain
in weight of the absorption tubes due to the action of the air current
on the rubber connections; etc., which had been previously determined
by experiment. The process was continued for five hours or to a con-
stant weight. Chlorine was absent.
The mineral was soluble without residue in nitric acid. At about
320° C, the purple color disappears and the mineral becomes colorless
or faintly yellow ; this change is accompanied by some decrepitation,
by phosphorence, and the production of a vapor (in part water?) which
is deposited in drops on the walls of the tube ; there is also a petroleum-
like odor. The loss of weight accompanying this change was deter-
mined by gently heating three grammes of the mineral in a bulb tube
in a current of dry air, weighing, and heating again cautiously iu the
current of air to complete decolorization, and determining the loss of
weight.
Optical Properties. f
.-
For the determination of the indices of refraction one of the best clear
crystals was used, having a deep purple color and a brilliant basal plane.
The determination was made with the Abbe crystal refractometer by the
differential method J and for this purpose a glass prism was selected
having the index reNa r= 1.6326, for which the boundary of total reflec-
tion was carefully determined and the telescope clamped. The apatite
crystal was then placed with its base on the glass hemisphere of the
apparatus and the angular difference in the boundaries for w and c
determined by the millimeter screw reading to six seconds. The boun-
* Zeit. anorg. Chemie, 7, p. 154; also Jannasch, Praktischer Leitfaden d.
Gewichts Analyse, p. 259.
t By J. E. Wolff.
t C. Viola, Zeit. Krystall., 30, p. 438, and 32, p. 311.
WOLFF AND PALACHE. — APATITE FROM MINOT, ME. 525
dary lines were sharp and the readings generally good. From the
average of a large number of readings the following values were
obtaiued :
WNa = 1.63353 wLi= 1.63067
0,-6 = 0.00191 w — e = 0.0020
cNa= 1.63162 €Li= 1.62865
The crystal was then heated to 320° C. or until decolorized and the
indices again determined as follows :
a>Na == 1.63346 eNa =1.63165 w — c = 0.00181
The change in the bi-refringence and in both indices is within the limits
of error.
The pleochroism is strong and the ray vibrating parallel to c («) red-
dish purple, perpendicular to e (to) deep violet blue. In converging
light the thick clear crystals show on the basal plane a marked bi-axial
character with the vertical axis the acute (negative) bisectrix and a
division of the base into six sectors, in each of whicli the axial plane
is parallel to a prism of the second order (or perpendicular to a lateral
axis). These sectors come out clearly with the sensitive tint of the
gypsum plate ; while some are almost perfect, others merge together
and overlap at the centre of the crystal. The angle of the optic axes
in one of these sectors was measured in the optic angle apparatus :
2ENa = 20°,
but it appears to vary in different sectors of the same crystal. These
phenomena of apparent orthorhombic symmetry were described and fig-
ured by Mallard* for the violet apatite from Schlaggenwald, but appear
to be even more distinct in the Maine apatite. While driving off the
coloring matter destroys the pleochroism the anomalous bi-axial characters
are not affected.
Conclusion.
The Minot apatite is a pure fluor-apatite with a fluorine content lower
than that necessary for the formula Ca5F(P04)3 and indicating Groth's
formula Ca5P3(F.OH)01.2 as also deduced by Jannasch from the analysis
quoted above. Rammelsberg t explained the low content of fluorine
(and chlorine) in certain apatites as due to removal of these elements
* Annales des Mines, VII. 10, 1870, p. 147.
t N. J. M., 1897, 2, p. 38.
526 PROCEEDINGS OF THE AMERICAN ACADEMY.
by a process of alteration, and therefore, according to him, all such
apatites are altered. The freshness of the Minot material makes such
a supposition inapplicable here.
The axial ratio of the Minot apatite is the largest and the birefrin-
gence the lowest recorded for the species. It was interesting to see
what data existed for a comparison between fluorine or chlorine content
and the axial ratio, specific gravity, and birefringence.
The normal angle c to x and also the specific gravity of apatite have
been held by numerous observers to diminish with increasing chlorine
content.
G. Rose (Ref. 3 below), the first to discover the fluorine and chlorine
in apatite, stated as the result of his studies that the angles and specific
gravity were alike in all apatites of like composition, but that the reverse
of this statement was not proved.
Von Koksckarow (Ref. 2) extended this statement, holding that the
normal angle c to x of all chlorine-containing apatite was somewhat
less than that of pure fluor-apatite.
The analyses of Pusyrewsky (Ref. 18) seemed to confirm this view,
and he further maintained that the sj^ecific gravity regularly decreased
with increasing chlorine.
Von Kokscharow (loc. cit.) incorporated the results of the last writer
with his measurements and published a table showing the relations of
the three values, but without comment.
Baumhauer (Ref. 4) was the next to investigate the subject, and his
measurements, analyses, and specific gravity determinations seemed to
support the supposed relations. His table has been republished by
several authors with slight modifications (Dana, Syst., 1892, 7G4-, and
Weibull, Ref. 20 below).*
In order more fully to test the matter a table has been prepared and
is given below, arranged according to increasing values of the angle
c to x or of the axial ratio, and showing for all occurrences for which
accurate crystallographic data existed, the specific gravity, birefringence,
and chlorine and fluorine content so far as such data could be found.
* In Baumhauer's table and in all later tables of the same kind the locality
Schlaggenwald is given with c to x 40° 20', the largest value for this angle ob-
served on apatite. Reference to the description of this occurrence by Schrauf
(Ref. 8 below) showed that the measured crystals were poorly adapted to measure-
ment, having curved faces ; and the average axial ratio calculated from all the
measurements gave a value much lower, about 40° 17'. This locality was there-
fore omitted from the table below.
WOLFF AND PALACHE. — APATITE FROM MINOT, ME.
527
Table of Physical and Chemical Characters of Apatite.
Locality
1 Comba di Compare )
Robert, Piedmont )
2 Achmatowsk . . .
3 Laacher See . . .
4 Rothenkopf, Tirol .
_ ( Zillerthal, Tirol
6 Tirol ....
7 Ala, Piedmont
8 Kirjabinsk . .
'Jumilla, Spain
tt tt
9 i
Angle 0001
('
to 1011
O / //
40 4
0.7284
40 G 21
0.7294
40 G 21
0.7294
40 10 46
0.7313
40 10 40 0.7313
40 13 30 0.7325
40 11 48 0.7318
40 13 37 0.7326
10
\ Knappenwand, Tirol 40 1
11 Tirol (tale schist)
12 Sulzbachthal, Tirol .
13 Berg Blagodat . .
14 Nordmarken . . .
, r S St. Gotthard . .
15 <
16 Tavetsch ....
17 Floitenthal . . .
18 Schwarzenstein . .
19 Vestana (Mn. apatite)
20 Hiddenite Mine, N. C.
21 Turkistan ....
22 Tokowaja, Urals . .
Elirenfriedersdorf
5 26
40 16 10 0.7337
•1
40 16 10
40 17
40 17
40 17
40 17
40 17
40 17 20
40 17 45
40 18 10
40 18 22
40 18 22
24 Pisek 40 18 25
25 Elba 40 18 48
26 Minot, Me 40 18 50
27 Zwiesel (Mn. apatite) . . .
28 Ilmen Mts
29 Sudjanka River . . ...
0.7337
0.7340
0.7340
0.7340
0.7340
0.7340
0.7341
0.7343
0.7345
0.7346
0.7346
0.7346
0.7348
0.7348
Sp. Or. w-t
CI
3.120
0.51 . . .
3.202
3.1495
.00435
.0044
0 085
absent 1.54
3.126
trace . . .
3.235
.00448
.0042
0.557 . . .
3.153
( 3.132
) 3.200
.0026
3.197
3.2154
3.225
0042
3.199
3.201
3.212
3.211
3.094
0.24
0.47
0.028
0.03
0.20
0.21
trace
trace
trace
0.01
absent
absent
trace
1.98
3.54
3.G3
3.58
0.028
3.74
3.64
lief.
2&18
Q
o
4
5
6
7
4
2
8
2
9
19
5
10
4
10
10
7
11
2&3
4
12
12
4
20
13
14
3.159 .0020 absent
4.20 2 & 18
o
... o
2.27 5
3.56 15
... 16
2.38
3.169
3.216
3.178
absent 2.15
trace 3.97
0.109 4.02
17
18
18
1 G. Boeris, Atti. della R. Ace. Sc. di Torino, 34, 609, 1899.
2 Kokscharow, Mat. zu Min. Russ., V. 86, 1866.
528 PROCEEDINGS OF THE AMERICAN ACADEMY.
3 G. Rose, Pogg. Ann., IX. 206, 1827.
4 H. Baumhauer, Zeit. f. Kryst, 18, 31, 1890.
5 Hoskyns-Abrahall (Inaug. Diss. 1889), Abs. Zeit. f. Kryst., 21, 389.
6 Heusser, Pogg. Ann., 87, 468, 1854.
7 K. Zimanyi, Zeit. f. Kryst., 22, 331, 1893.
8 Schrauf, Ber. Acad. Wien, 62 (2), 745, 1870.
9 " " " " 42, 111, 1862.
10 Carnot, Bull. Soc Franc. Mineral., 19, 135, 1896.
11 Flink, Bihang t. K. Sv. Vet. Akad. H. Stockholm, 12 (2) No. 2, 42, 1886.
12 Schmidt, Zeit. f. Kryst., 7, 551, 1883.
13 Hidden & Washington, Zeit. f. Kryst., 14, 299, 1888.
14 Jeremejew & Nikolajew, Zeit. f. Kryst., 11, 389, 1886.
15 Vrba, Zeit. f. Kryst., 15, 464, 1889.
16 Artini, Rendie. R. Ace. Lincei, Roma, 4 (2), 259, 1895.
17 Sandberger (Hilger),.N. J. Min. 1885, 1, 171. 0
18 Pusyrewsky, Verb. k. k. Mineral. Gesell. St. Petersburg, 1859-1860 (cited
by Baumhauer, No. 4 above).
19 Latterman, Rosenbusch, Mik. Pliys., I. 409, 1892.
Weibull, Geol. For. Forh., Stockholm, 20, 63, 1898.
20
8, 492, 1886.
One point brought out by the preparation of this table is the lack of
studies of apatite in which on the same material all these characters have
been determined. It is also to be noted that no crystallographic data
whatever appear to have been secured on what could fairly be called a
chlor-apatite, the highest chlorine content in the table being about 0.5
per cent only. Without such data it does not seem that the theory of
Pusyrewsky and Baumhauer that axial ratio decreases with chlorine
content can be considered as established. Moreover exceptions to that
rule may be noted in the table, notably Nos. 5, Zillerthal, and 9,
Jumilla. On the other hand it seems fairly safe to accept the statement
that an apatite with large angle c to x (40° 17' or more) will be
practically free from chlorine.
The table shows that absolutely no definite relation exists between
the specific gravity and the chlorine content. Nos. 2 and 9, from
Achmatowsk and Jumilla, having about 0.5 per cent cblorine, have
specific gravity respectively 3.12 and 3.235; while the chlorine-free
varieties have specific gravities from 3.09 to 3.22, or practically the
same range. Observations on the birefringence are few, but so far as
they go do not point to a definite relation to the chlorine content.
Harvard Mineralogical Laboratory,
December, 1901.
Wolff and Palache Apatite.
Proceedings of the American Academy of Arts and Sciences.
Vol. XXXVII. No. 19. — March, 1902.
CONTRIBUTIONS FROM THE HARVARD MINERALOGICAL
MUSEUM. — XI.
A DESCRIPTION OF EP1DOTE CRYSTALS FRO 31
ALASKA.
By Charles Palache.
With a Plate.
CONTRIBUTIONS FROM THE HARVARD MINERALOGICAL
MUSEUM.— XI.
A DESCRIPTION OF EPIDOTE CRYSTALS FROM
ALASKA.
By Charles Palache.
Presented by John E. Wolff, January 8, 1902. Received February 7, 1902.
The ejtidote crystals described in this paper were sent to the Harvard
Mineralogical Laboratory for crystallographic study by Mr. W. C. Plart
of Manitou, Colorado, to whom we wish to express our thanks for the
generous supply of material placed at our disposal.
This material is from a new locality for the mineral and is remarkable
for the size and unusual habit of the crystals ; it therefore seemed well
worthy of description.
According to Mr. Hart the epidote is found at Sulzer, Prince of Wales
Island, Alaska. It is in the close vicinity of a body of copper ore and is
further associated with garnet, albite, magnetite, and quartz. The coun-
try rock of the region is limestone, which is cut by numerous igneous
dykes, and it seems probable that the deposit is the result of contact
metamorphism of the limestone by the dyke rocks, resembling closely in
this respect the epidote occurrence with copper ore in the ,Seven Devils
Mts. in Idaho.*
The specimens at hand consist of several loose crystals and a mag-
nificent cluster of large crystals implanted on massive epidote. The only
associated mineral is quartz in small clear crystals of later formation
than the epidote.
The epidote is very dark green to greenish black in color, but oil-
green and translucent in thin crystals or where bruised or cracked. The
larger crystals are in the form of nearly square tables, which measure as
much as 5.5 cm. each way and 3 cm. in thickness. In the smaller crystals
the tabular habit is less pronounced and the mineral sometimes assumes
the ordinary prismatic habit parallel to the b axis. The crystals are not
* Compare Am. J. Science, VIII, 1899, 299.
532 PROCEEDINGS OF THE AMERICAN ACADEMY.
infrequently doubly terminated. In the large group to which reference
was made about twenty of the tabular crystals are found on a surface
measuring about 15 by 20 cm., several of the crystals over 3 cm. on an
edge, and attached by an edge in such fashion as to present an appear-
ance altogether foreign to epidote. The crystals are frequently twinned
according to the ordinary law for epidote, twinning plane the orthopin-
acoid.
Measurement of numerous crystals proved the presence of some
tweuty-six forms as shown in the following list. The smaller crystals
were measured on the two-circle goniometer and most of the faces gave
excellent reflections. For the large crystals contact measurements were
used, and these, with a study of zonal relations made determinations of
forms fairly certain. A few forms were thus found that were not
observed on the smaller crystals. Two forms new for epidote are
marked with an asterisk.
c(001), b (010), a (100), u (210), z (110), o (011), e (101),
i (T02), N (304), r (T01), 1 (201), n (Til), a (212), F (154),
Z (232), <S» (353), <f> (121), 8 (T41), E (T51), q (221), O (544),*
j (755),* X (322), y(2ll), R (111), * (113).
Of these forms c, a, b, u, r, and n are nearly always present and
define the habit of most crystals, z, e, o, and q are also found on many
crystals ; the remaining forms are rare and subordinate in development.
The forms may be characterized as follows :
c (001) always present, bright and unstriated, often broad.
b (010) always present, always dull and striated parallel to intersec-
tion with n ; generally has narrow faces.
a (100) always present ; the largest face on tabular crystals ; bright
but often striated faintly horizontally.
u (210) always present, generally with large bright faces.
z (110) generally quite subordinate to u but frequently present as a
narrow face and always pitted and dull.
o (011) bright face, generally small.
e (101), i (T02), N (304), 1 (201) are infrequent forms in orthodome
zone, generally narrow, bright and unstriated when they do occur. This
zone is remarkably poor in forms and free from striation as compared
with most crystals of epidote.
r (T01) always present, broad, generally striated lightly and less
brilliant than c with which it is easily confused on the crystals.
PALACHE. — EPIDOTE CRYSTALS FROM ALASKA. 533
n (Til) always present, often large, brilliant, and striated. The only
form found in the re-entrant angles rarely found on twin crystals.
a (212) present on one crystal only (figure 7) as a large, fairly
bright face.
F (554), Z (232), <I> (353), c/> (T21), 8 (T41), and E (T51) are pyra-
mids of the zone [Til to 010]. Unimportant forms but several of them
sometimes present on single crystals as shown in the drawings. F (454),
a rare form for epidote, has been reported heretofore only from Pers-
berg, Sweden* by Flink ; he determined it hy a single bright face in two
zones, no angles being given. It was found with a single face on each
of two crystals and was measured as follows :
Measured. Quality. Calculated.
<p P 0 P
354 -160° 40' 67° 21' fair -1 60° 43' 67° 18' (010 as pole)
128° 01' 29° 33' fair 128° 18' 29° 27' (normal position)
<t> and 8 were determined solely by contact measurements ; Z and <£
by contact measurements and zonal relations.
q (221) often present, sometimes large, always dull.
O (o44), j (755), X (322), y (211), and R (411) are pyramids of
the zone [Til to 100]. Of these forms y alone is common; O and j are
new to epidote and X and R are rare.
O was measured on three crystals (two of them twins) with six faces
as follows :
Measured. Quality. Calculated (010 as pole).
544
Crystal No. 4,
" 5,
-42° 04'
42 57
p
38° 30'
39 11
poor
fair
42° 07'
42 07
p
39° 33'
39 33
137 06
38 58
fair
137 53
39 33
" " 6,
—42 13
-137 37
39 20
39 19
good
good
-42 07
-137 53
39 33
39 33
136 48
39 18
fair
137 53
39 33
Average -<t>'-±<t> I _42° 07' 39° 33' -42° 37' 39° 06'
or 180 — c/> )
The agreement of measured and calculated angles is not very close,
but the form seems assured.
J was measured on two twin crystals with three faces as follows :
* Biliang t. K. Sv. Vet. Akad. H. Stockholm, 12, No. 2, 1886.
534 PROCEEDINGS OP THE AMERICAN ACADEMY.
755
Measured.
<p p
37041' 42° 17/
Quality.
fair
Calculated.
<P p
37° 40' 42° 11'
142 07
41 44
poor
142 20 42 11
143 16
42 42
bad
142 07 42 11
Average <p or 180° -<£ = 37° 26' 42° 14' 37° 40' 42° 11'
The agreement between measured and calculated angles is here fairly
satisfactory and the form seems assured.
X (322) has been reported only once on epidote from Elba by A.
Artini * who measured a single bright face agreeing well with its cal-
culated angle.
It was found here on a single crystal with one measurable face, but
was noted frequently as a dull face in the zone [221 to T01].
Measured
Calculated (010 as pole)
<£ P
<f> p
142° 00' 66° 08'
141° 47' 66° 20'
322
y (211) and R (411) were the commonest forms of this series and
were well determined by measurem ;nt on several crystals.
* (513) present only on one crystal (figure 7) as a small face.
Several of the above forms are lacking in the Winkeltabellen of
Goldschmidt, and as the various values there given have been calculated
for each of them they are given in the following table, which also
includes two forms for which certain values were found to be incorrectly
stated in the Tabellen :
No Letter
Symb.
<P
P
Co
Vo
1
V
x'
y
d'
O 1
o /
O '
O 1
o •
O 1
154
*
353
67 34
. . .
• • >
> . .
f79
¥
413
63 34
53 31
50 27
3102
46 04
20 58
T.2113
0.6019
1.3525
83
F
454
19 17
67 18
38 18
66 06
T7 44
60 33
0.7897
2.2570
2.3914
84
O
544
3129
64 43
47 53
6101
28 11
50 27
1. 1060
1.8057
2.1176
85
J
755
35 39
65 46
52 20
6101
32 07
47 49
12955
1.8057
2.2224
86 X 322 38 13 66 29 54 53 6101 34 34 46 05 1.4220 1.8057 2.2983
The drawings show the extremely variable habit of the crystals.
Figure 1 represents perhaps the commonest type, a tabular twin
crystal, the two individuals entirely symmetrical to the twinning plane
* Mem. Acad. Lincei. 4, 380, 1887.
t Correction, Winkeltabellen, p. 130, line 32 from above, col. 10.
\ Correction, Winkeltabellen, p. 131, line 12 from above, wbole line.
PALACHE. EPIDOTE CRYSTALS FROM ALASKA. 535
and so developed as to present no re-entrant angles. Here as in all
the twin crystals the reversal of direction of the striations on 010 in
the twinned crystal is the easiest means of recognizing the composite
nature of the group.
Figures 2 and 2a are orthographic projections of the same crystal on
the orthopinacoid and the clinopinacoid respectively. They represent
the largest crystal studied in natural size, and show how irregularly the
two twinned crystals are sometimes united — in this case an imperfect
penetration having taken place. The upper surface of this crystal is
bounded by cleavage planes parallel to c where the crystal was broken
from its matrix.
The remaining figures (3 to 7) are orthographic projections on the
clinopinacoid.
Figure 3 is another tabular crystal in which the larger portion of
the crystal is a single individual. Rarely such tabular crystals are
untwinned.
Figures 4 and 5 are two very symmetrical twin crystals, both pris-
matic parallel to the axis b and doubly terminated. They show many
of the less common forms and the re-entrant angle between two faces of
n which is not common on these crystals.
Figure 6 is a type of the untwinned crystal, prismatic parallel to
axis b, the usual epidote habit. It is a left-hand termination. Many of
the smaller crystals are of this habit with varying development of the
planes of n and u.
Figure 7 is a small crystal of prismatic habit but quite unlike any
other found in its terminal planes.
In conclusion it may be said that this Alaska epidote ranks among the
finest occurrences of American crystallized minerals, and is only sur-
passed in the size, beauty, and complexity 6f its crystals by the epidote
from the Knappenwand in the Tyrol.
MlNERALOGICAL LABORATORY, HARVARD UNIVERSITY,
January, 1902.
Palache. — Epidote Crystals.
5>-b
u
a
2 a
Proceedings of the American Academy of Arts and Sciences.
Vol. XXXVII. No. 20. — March, 1902.
CONTRIBUTIONS FROM THE CHEMICAL LABORATORY OF
CASE SCHOOL OF APPLIED SCIENCE. — XL.
ON THE SPECIFIC HEAT AND HEAT OF VAPORIZATION
OF THE PARAFFINE AND METHYLENE
HYDROCARBONS.
By Charles F. Mabery and Albert H. Goldstein.
CONTRIBUTIONS FROM THE CHEMICAL LABORATORY OF
CASE SCHOOL OF APPLIED SCIENCE. — NO. XL.
ON THE SPECIFIC HEATS AND HEAT OF VAPORI-
ZATION OF THE PARAFFINE AND METHYLENE
HYDROCARBONS.
By Charles F. Mabeky and Albert II. Coldstein.
Received February 10, 1902. Presented February 12, 1902.
Since 1819, when Dulong and Petit, on the basis of their work on
thirteen of the chemical elements, announced the law that atoms of all
elementary bodies possess the same capacity for heat, or that the specific
heats of the elements vary inversely as their atomic weights, the specific
heats of the elements have been important physical constants. With
some exceptions, the constant 6.54 represents the product of the atomic
weight into the specific heat. Later work showed that this law could be
extended to compounds. In 1831, Neumann discovered that compounds,
with analogous composition have the same specific heat. Or in a series
of compounds with analogous composition the specific heat varies inversely
with the molecular weight. These laws apply to approximately forty ele-
ments and to solids only at temperatures much below their melting points.
The specific heats of many organic compounds have since been deter-
mined, and although no law has been stated, it is evident that, in certain
homologous series of organic compounds, a condition exists in some of
these series analogous to the law of Neumann. For instance, deter-
minations have been made on a few of the alcohols with the following
results *
Ethyl alcohol 0.680
Iso-propyl alcohol 0.5286
Iso-butyl alcohol 0.5078
Iso-amyl alcohol 0.49,'] 2
That the variations on certain homologous series so far as they have
been observed do not conform to a general law, is shown by the follow-
ing series, in which the specific heats increase with increase in molecu-
lar weights :
540 PROCEEDINGS OF THE AMERICAN ACADEMY.
Methyldichloracetate 0.3202
Ethyldichloracetate 0.33S4
Propyldicbloracetate 0.3506
In general, the data on specific heats of organic compounds are meagre
and not concordant. For the same substance the results of different
observers seldom agree in the third decimal place ; they often do not
agree in the second, and even in the first place (see tables of Landolt
and Bornstein). These variations are probably due to the fact that spe-
cific heat is materially affected by impurities in the substance, and the
temperatures at which it is taken. Then, furthermore, the details of the
determinations demand very careful attention to insure concordant results.
In the determinations of the hydrocarbons to be described in this paper,
it was found that impurities depressed the specific heats very considerably.
Although the paraffiue series of hydrocarbons offers the best field for
study of an homologous series, very little has been done in the direction
of ascertaining the specific heats of these bodies. In a study of distillates
separated from Pennsylvania petroleum, by Bartoli and Stracciati,* the
specific heats of the following hydrocarbons were determined :
Hexane
C,,IIU
.5042
16°-37°
Heptane
C7H16
.4869
16°-37°
Octane .
C8H1S
.5111
12-19°
Decane
V. io ' l-L'
.5057
14°-18°
Tetradecane
^ 1 1 1*30
.4995
Hexadecaue
^H.l'oi
.4963
l.V -22°
The inference derived from these results was that the specific heats of
these hydrocarbons were remarkably constant.
No data could be found relating to the specific heats of the methylene
hydrocarbons CnIL„, nor those of the series still poorer in hydrogen. With
the greatly extended uses of crude petroleum and refined distillates for
fuel, in gasoline and oil engines, accurate information concerning specific
heat and heat of vaporization is greatly desired.
Having in hand a great variety of hydrocarbons of the various series,
which have been prepared in as pure form as possible, and numerous
inquiries having been received for more complete information concerning
these physical properties, it seemed advisable to make some determin-
ations of these constants.
The hydrocarbons of the series CnH2n+2, were obtained from Pennsyl-
vania petroleum, those of the other series from California petroleum.
*Gazz. Cliim., 1885, 417-445.
MABERY AND GOLDSTEIN. — SPECIFIC HEATS OP HYDROCARBONS. 541
Each hydrocarbon had been separated by a long process of distillation,
and purified, by treatment with sulphuric acid, sodic hydrate, and drying
over sodium.
The determinations were made in a Bunsen ice calorimeter, to which
was attached a capillary side tube 70 centimeters long, and the bore of
such size that 1 centimeter contained 0.0579 grams of mercury. To
maintain the temperature at 0°, the calorimeter was placed in a jar ot
ice-water with an excess of ice, and this jar was placed in another jar
and the space between filled with cotton. The calorimeter was filled
with air-free water and dry mercury, and the inside film of ice, 2 to 3
millimeters thick, was formed by evaporation of ether by an air blast
within the inner tube. Approximately 2 grams of the hydrocarbon was
placed in a small glass stoppered tube of thin glass, whose heat equiva-
lent was determined. The tube and hydrocarbon were heated to 50°,
in a larger tube placed in a beaker of water, kept at this temperature
for at least 15 minutes, then transferred by a thread to the calorimeter,
^ith care this could be done without loss of heat by radiation. The
contraction of the mercury column was from 15 to 25 centimeters.
This method can be used for the paraffine hydrocarbons from C6H14 to
C16H34, the limit at which the hydrocarbons remain wholly liquid at 0°.
After obtaining the water constant of the apparatus, three to six de-
terminations of each hydrocarbon were made at the temperatures 0° and
50°, with results given in the following table :
Boiling Points.
Specific Heat
C6H14
68
.5272
C7Hli;
91
.5005
CrH1G
98
.5074
Cs"18
125
.5052
(- ".("20
151 '
.5034
^10 "22
162
.4951
^10^22
172
.5021
^llH24
195
.5013
V12"26
214
.4997
C13H2S
226
.4986
^uHso
242
.4973
^15 "82
260
.4966
^16"34
275
.4957
Commercial Gasoline
.5135
Crude Ohio Petroleum
.4951
542 PROCEEDINGS OF THE AMERICAN ACADEMY.
The following table gives the specific heats obtained from the series of
methylene hydrocarbons :
Boiling Points,
o
Specific Heat.
V-/6tli2
68
.5062
C7H14
98
.4879
^sH16
119
.4863
t^Hxs
135
.4851
^10 H2o
160
.4692
QuH22
190
.4819
C12H24
212
.4570
Ci3H2(;
232
.4573
^14^28
244
.4531
^15^30
263
.4708
It appears from these results that there is a uniform decrease in specific
heat with increase in molecular weight. Furthermore the normal hydro-
carbons, such as heptane, C7H16, B. P. 98°, and decaue, C10H22, B. P.
172°, have higher specific heats than their isomers, such for example as
isoheptane, C7H1G, B. P. 91°, and isodecaue, C10II22 B. P. 162°.
The same variation also appears in the methylene series, with high
values for certain members that probably indicate different structural
relations.
It is further interesting to observe the materially lower values given
by the methylene hydrocarbons as compared with the values for the
parafnne hydrocarbons. Whether this be due to greater compactness
in the methylene molecule or to some quality of its ring structure, it
would be interesting to ascertain.
Perhaps the falling off in specific heat with increasing molecular
weight will appear to better advantage when arranged as ordinates on
a curve with the molecular weights as abscissae. Only those compounds
are given on the curve that are known to be normal, although, of course,
this is not known with reference to the higher members. The different
values of the isomers heptane and decane is shown on the shorter curve.
This uniform decrease in specific heat with increasing molecular
weight in the series CnH2n+.2, suggest a constant relation analogous to
the law of Neumann.
If the constant K be expressed in terms of the specific heat multiplied
by the molecular weight and the product divided by the number of atoms
in the molecule, the specific heats found for the hydrocarbons of this series
give the following values for the constant :
MABERY AND GOLDSTEIN. — SPECIFIC HEATS OF HYDROCARBONS. 543
»
K.
2.26
2.21
2.21
2.22
2.23
2.23
2.23
2.24
2.23
2.24
2.23
A similar curve drawn for the specific heats of the methylene hydro-
carbons, so far as they were determined, show also a regular variation.
The constant K, for the methylene hydrocarbons calculated from the
determinations, shows a somewhat higher mean value than that of the
paraffine hydrocarbons :
Hydrocarbon.
Mol. Wt
CeH14
86
C7H16
100
C8H18
114
LgM.j,)
128
^10 ^22
142
^11 H24
156
^12^-26
170
^13^28
184
C14H30
196
C15H32
210
C16H34
224
The constant,
therefore,
CnHn2_|_2» 1S «•«««
Sp. Heat.
No. Atoms
.5272
20
.5074
23
.5052
26
.5034
29
.5021
32
.5013
35
.4997
38
.4986
41
.4973
44
.4966
47
.4957
50
fdrocarbon.
Mol. Wt.
Sp Ileat.
No. Atoms.
K.
M5U12
84
.5062
18
2.26
C7H14
98
.4879
21
2.28
CsH16
112
.4863
24
2.37
C0H18
126
.4851
27
2.27
C„H22
154
.4819
33
2.25
Ci5H30
210
.4708
45
2.20
The values for the specific heats of both hexane and hexamethylene
are higher than should be expected from the results on the other members
of the series. These hydrocarbons were well purified, except it seems
probable that the distillates contaiued certain proportions of both.
Determinations were also made of the specific heats of a series of
hydrocarbons separated from the high boiling portions of Pennsylvania
petroleum. This series is under examination to establish its composition
and relations to series, separated from heavy petroleums from other
fields. These hydrocarbons were cooled to — 10°, and filtered to remove
so far as possible the solid hydrocarbons with which they are associated
in Pennsylvania petroleum. They have been shown to be members of
the series CnH2n. A more detailed description of these bodies will be
presented in a subsequent paper, which is now in preparation.
544 PROCEEDINGS OF THE AMERICAN ACADEMY.
The following values were obtained for the specific heats of these
hydrocarbons :
B. P. Sp. Heat.
CigH32
173
.4723
Cl8 "36
202
.4723
^20 "40
223
.4706
C23"46
260
.4612
C»4"48
272
.4586
From data obtained with the paraffine hydrocarbons, there is no
opportunity to compare the specific heats, although the sudden drop
from the last member examined of the series CnH2n+2, C16H34, specific
heat .4957, to the first member of the last series above in which the
solid hydrocarbon C16H32 had been removed by cooling and filtration,
specific heat .4723, shows a marked difference in structure. This rela-
tion appears in the longer curve in the table.
Comparing the last member of the series CnH2n from California oil
C15H30, specific heat .4708, with the hydrocarbon C16H82, specific heat
.4746, it appears that the series CnH.2a from Pennsylvania petroleum is
a continuation of the same series from California petroleum. Unfortu-
nately the higher members of the series from California petroleum were
not available for comparison. But results already obtained as to the com-
position, specific gravity, refractive index, &c, are in accord with the
specific heats. The specific heat was also determined in several hydro-
carbons of the series CnH2n_2, and the series CnH2n_4, which had been
separated from Texas petroleum with the following results :
Series CnH2l,
— 2-
B. P. 50 mm.
Sp. Heat.
K.
^14"26
127
.4447
2.15
CisHog
142
.4439
2.15
CicH3t)
162
Series CnH2D
B. P. 50 mm.
.4426
-4-
Sp. Heat
2.14
C21H38
218°
.4560
C25"46
273°
.4650
The latter results cannot be accepted as reliable, for the quantities of
the hydrocarbons were very small, and the oils began to crystallize at 0°.
There is no doubt that the specific heats of these hydrocarbons are smaller
than those of the preceding series.
MABERY AND GOLDSTEIN. — SPECIFIC HEATS OF HYDROCARBONS. 545
To convey a clear idea of the variation in hydrocarbons in the same
series, and also to show the differences between the different series, the
results are brought together on the following coordinate table :
.520
8
6
4
2
.*SIO
8
1
In
/y
?n
^
6
£•«
Hi.
1 f
k£7
Hh
4
XC
sl\
,8
2
^Q
0
i f
.500
///.
(h
Oj
-*<
i, h
'24
8
SV
^U
-- Hi
6
•iss
6
(14
Hi
4
*%C
<>H
22 1
IS a
J
-xCi
//'
JJ
?.
.490
8
6
£7
Hi,
4
X^
•J/
'IS
2
480
^
C i '
Ui
8
\
"X
6
\
>s.
s.
CV
</7
zn
(>
o£
iVAj
A)
4
S
>s _
~-
f"'
//j.
2
V
^■C '
IH
)i
.470
*1
C/i
H J
>(?)
KC2
c H
4-0
8
\
6
\
\
4
\
\
2
\
.460
C 2
irt
46
\
8
c
2-t
JU
N
6
4
?,
.450
8
6
C,
?/
zr,
-2
(1
ItX
Ail
4
V
k"'
Vic
?
^c
J 6
! /■
\a
440
ft
80 100 120 140 160 180 200 220 240 260 280 300. 320 340
Mo/ ecu far Weight
VOL. XXXVII. — OO
546 PROCEEDINGS OF THE AMERICAN ACADEMY.
The regular variation in members of the series CnH2n+2, appears in its
curve, and the differences in what are known to be isomeric forms in the
same series. It is further interesting to observe the continuation of the
curve representing the members of the series CnH2n from the curve con-
taining the members of the series CnH2n from California petroleum. The
lower values in the series CnH2n_2 from Texas petroleum form a char-
acteristic curve near the base of the table.
The specific heat was determined in the following crude oils from
various fields :
Specific Gravity.
Specific lleat
Pennsylvania
0.8095
.5000
Berea Grit
0.7939
.4690
Japanese
0.8622
.4532
Texas (Lucas
well)
0.9200
.4315
Russian
0.9079
.4355
Wyoming
0.8816
.4323
California
0.9600
.3980
Texas
0.9466
.4009
Ohio
.4951
Commercial Gasoline
.5135
These values show that the specific heat of the crude oils is an im-
portant property from a practical point of view. It also appears that
there is no close agreement between specific heat and specific gravity.
Pennsylvania oil stands at the head, and Berea Grit with a much
larger proportion of volatile constituents is next. Of the heavier oils
it appears in general that the specific heats are much lower, but with
no definite relation.
It would be interesting to ascertain the specific heats of the less
volatile constituents of petroleum from different fields, including the
solid hydrocarbons. This would require observations at different tem-
peratures, and it would add to the interest of the data if all determina-
tions could be made within a wide range of temperatures.
Heats of Vaporization of Hydrocarbons of the Paraffine
and Methylene Series.
Since it had been found that a boiling point constant can be calculated
from the absolute boiling point, and latent heat of evaporation, which
may be used as a basis of a method for the determination of molecular
weights, more complete knowledge of the latent heat of evaporation or
MABERY AND GOLDSTEIN. —SPECIFIC HEATS OF HYDROCARBONS, 547
heat of vaporization of liquids at their boiling points has become of great
importance. FYorn a practical point of view, the greatly extended use
of crude petroleum and its constituents can only be economically con-
tinued with the aid of further information concerning the heats of
vaporization. Numerous inquiries from persons interested in these
directions attest an appreciation of further knowledge on this subject.
In 1885 the following law was
proposed by Dudley, on the heats
of vaporization of members of a
homologous series.*
" In any homologous series the
heat of vaporization in a unit of
volume of the vapor, under the
same conditions of temperature
and pressure, is proportional to
the density and also to the abso-
lute boiling point." This gen-
eralization was based on data
selected from determinations of
the heats of vaporization of the
formiates, acetates, propionates,
butyrates, isobutyrates, alcohols,
and aromatic hydrocarbons.
With numerous members of the
different series of hydrocarbons
at hand, it was our intention to
determine the latent heat of the
Series ^n"^'2n4-2^ ^n 2n' ^n 2n 1*
But the only apparatus available
was constructed of glass, which E~
would not withstand the high tem-
peratures necessary in determina-
tions of thehydrocarbons with high
boiling points, and the time was too
limited to permit of the construc-
tion of a metallic apparatus.
For the apparatus used, we are indebted to the kindness of Professor
Kahlenberg of the University of Wisconsin, who allowed us to use the
* Journ. Am. Chem. Soc , Vol. XVII., No. 12.
548 PROCEEDINGS OF THE AMERICAN ACADEMY.
form devised by him, before he had published his description which
appeared in the Journal of Physical Chemistry, April, 1901.
This apparatus is an ingenious modification of Berthelot's method, in
which the suhstance is heated and volatilized by means of an electric cur-
rent within the body of the liquid, thus avoiding errors due to external
heating. Through the kindness of Professor Kahleuberg and Profes-
sor Trevor we are able to show in this connection the form of this
apparatus.
In the publication referred to, the apparatus is described as follows :
" The retort consists of a tube 17 centimeters long and 5.5 centimeters in
diameter, into the bottom of which is fused a tube which fits into a con-
denser with a ground glass joint. At the other end of the inner tube
are two large lateral openings. Glass tubes pass through the cork at
the top, and into these are fused the ends of the spiral of platinum wire.
This spiral consists of about 40 centimeters of fairly stout platinum wire,
to the ends of which are welded short heavy jjieces of platinum rod, and
these rods are in turn fused into the glass tubes. Long, rather heavy
copper wires pass down into the glass tubes, at the bottom of which
they are connected with the ends of the platinum rods by means of a few
drops of mercury. The calorimeter is covered with a heavy piece of
asbestos board and the retort is enclosed in asbestos and cotton batting."
A current from eight to ten amperes, regulated by a rheostat, gave suf-
ficient heat to vaporize from 20 to 30 grams of the oil in from 5 to 6
minutes. The calorimeter, about 2500 cubic centimeters capacity, was
made of thin nickel-plated sheet copper. It was elliptical in form, to
conform to the shape of the condenser, and was provided with a cop-
per stirrer. The capacity of the calorimeter was reduced, as shown
in the figure, by bending closer together the glass tubes leading from
the body of the condenser. Temperatures were taken on a Beckman
thermometer.
The water equivalent of the calorimeter, condenser, stirrer, and ther-
mometer were found to be 185 grams, practically the same value as the
equivalent calculated from the weights and specific heats of the parts of
the apparatus.
As mentioned above, this form of the apparatus is limited in this work
by the fact that when oils of boiling points higher than 125° are volatil-
ized, the sudden change in temperature at the water line of the condenser
is so great that glass will not stand it.
The following results were obtained with a few members of the
series CnH2n+2, as the mean of several observations :
4
MABERY AND GOLDSTEIN. — SPECIFIC HEATS OF HYDROCARBONS. 549
Boiling Point. Heat of Vaporization in Calories.
o
Hexane, C6H14 68 79.4
Heptane, C7H1(J 98 74.
Octane, C8H18 125 71.1
Determinations were also made on the methylene hydrocarbons that
could be volatilized in this form of apparatus :
Hexamethylene, C6H12
Dimethylpentamethylene, C7HU
Methylhexamethy lene, C7 H14
Dimethylhexamethylene, C8'H16
These results indicate a rapid falling off in latent heat, with increase
in molecular weight. It is to be regretted that we had not the metallic
condenser, which would have enabled us to carry these observations up
to include the less volatile hydrocarbons of both series. Advantage will
be taken of the earliest opportunity to continue this work.
The hydrocarbons used in the work described in this paper were pre-
pared with assistance granted by the Academy from the C. M. Warren
Fund for Chemical Research.
Boiling Point.
Heat in Calories
68-70
87.3
90-92
81.
98
75-7
118-119
71.7
Proceedings of the American Academy of Arts and Sciences.
Vol. XXXVII. No. 21. — April, 1902.
CONTRIBUTIONS FROM THE ZOOLOGICAL LABORATORY OF THE
MUSEUM OF COMPARATIVE ZOOLOGY AT HARVARD COLLEGE,
UNDER THE DIRECTION OF E. L. MARK.— No. 129.
CERTAIN SENSE ORGANS OF THE PROBOSCIS OF THE
POLTCHAETOUS ANNELID RHYNCHOBOLUS
D1BRANCH1ATUS.
By Adele Oppeniieimer.
With Six Plates.
CONTRIBUTIONS FROM THE ZOOLOGICAL LABORATORY OF THE
MUSEUM OF COMPARATIVE ZOOLOGY AT HARVARD COLLEGE,
UNDER THE DIRECTION OF E. L. MARK. — No. 129.
CERTAIN SENSE ORGANS OF THE PROBOSCIS OF
THE POLYCHAETOUS ANNELID RHYNCHOBOLUS
DIBRANCHIATUS.
By Adele Oppenheimer.
Presented by E. L. Mark, April 13, 1898. Received February 15, 1902.
The proboscis of Rhynchobolus dibranchiatus was described by Elders
('64-68, p. 670) as "short, thick, club-shaped, with small egg-shaped
papillae (compare Plate 1, Fig. 1), and was divided by him (p. 678)
into two parts, the " Russelrohre," or sheath of the proboscis, and the
" Kiefertriiger," or bearer of the jaws. Before eversion the " Russel-
rohre " is anterior to the " Kiefertriiger," but when the proboscis is
everted (Fig. 1) the latter is anterior. The " Keifertriiger " may be
subdivided, as Ehlers suggested, into three regions, which in the non-
everted state are respectively anterior, middle, and posterior: (1) the
anterior has none of the small egg-shaped papillae ; (2) the middle
region is that supporting the four jaws; and (3) the posterior is, as
a rule, not everted, it is the region of the four glands (gl.) of the
jaws and the remainder of the proboscis following the glands. The
boundary between " Kiefertriiger " and "Russelrohre" is marked, ac-
cording to Ehlers, by the place of attachment to the proboscis of four
partial diaphragms, called by him " Lappen " (Fig. 1, hnn.).
When cross sections of the -everted proboscis are made in the region
of the four partial diaphragms (Fig. 2), one encounters in succession in
passing from the surface toward the centre (1) a cuticula (eta.) ; (2) an
epithelial layer ie'th.); (3) a connective-tissue layer (tis. co'nt.), in which
are embedded eighteen longitudinal nerves (n. lg.), and a nerve plexus;
(4) a region composed of eighteen longitudinal muscles (mu. lg.) ; (5) a
sheet of circular muscles (mu. crc.) ; (6) a fascia or peritoneum (pi'tn.)
554 PROCEEDINGS OF THE AMERICAN ACADEMY.
lining the body-cavity ; then in the body-cavity the four partial dia-
phragms ; and finally that part of the proboscis which has not been everted.
This consists of nearly the same kinds of layers arranged in the reverse
order, namely a peritoneum, circular muscles, longitudinal muscles, nerves,
connective tissue, and cuticula.
The epithelial layer directly beneath the cuticula is not mentioned as
such by Ehlers. Since it apparently undergoes an interesting metamor-
phosis, it is worthy of further study.
From the underlying connective-tissue layer eighteen projections of
connective tissue pass radially inward between the eighteen longitudinal
muscles to the region of the circular muscles. Where the radial projec-
tions are continuous with the outer circular portion of the connective
tissue the eighteen longitudinal nerves (n. Ig.) are seen cut crosswise.
(Compare PI. 2, Fig. 10.)
Concerning the structure of these longitudinal nerves I have nothing
to add to what Ehlers ('64-68, p. 696) has already pointed out. They
are evidently surrounded by a protecting connective tissue, within which
lie what are apparently nerve fibres. In preparations fixed in vom
Rath's picric-osmic-platinic chloride-acetic mixture, the nervous plasm
is flocculent and has shrunken away from the nerve sheath.
From these longitudinal nerves, fibres pass out (PI. 2, Fig. 10) to
form the peripheral nerve plexus, which is embedded in the connec-
tive tissue occupying the space between the longitudinal muscles and
the cuticula. Other nerve fibres (n. r.) starting from the plexus pass
radially inward, skirting the longitudinal muscle (Fig. 10); yet appar-
ently they do not innervate the muscles, for I have seen no nerve fibre
pass through the sheath enclosing the muscle. Still other radial nerve
fibres (n. ?'.') can be followed from the longitudinal nerves passing through
the middle of the radial connective-tissue projections toward the centre
of the sections as far as to the membrane immediately superficial to the
circular muscles (PI. 1, Fig. 2 ; PI. 2, Fig. 10). In the anterior region,
where the four partial diaphragms, the " Lappen " of Ehlers, are at-
tached to the wall of the proboscis, radial nerve fibres occupying the
same relative position as those marked in other regions n. r! can be
traced into these four pendent structures. Ehlers says concerning these
" Lappen " (p. 686) : " By means of a fold it [the fascia wdiich invests
the surface of all these parts] forms the four ' Lappen,' which are
attached at the boundary between ' Riisselrohre ' and ' Kiefertrager ; '
these ' Lappen ' therefore possess the fine tense membrane on both sur-
faces ; between lies a fibrous tissue, which is apparently identical with
OPPENIIEIMER. RHYNCHOBOLUS DIBRANCHIATUS. 555
the subcuticular tissue of the sheath of the proboscis, with which, more-
over, it is evidently continuous. This tissue . . . consists of a fibrous
network, in the meshes of which lie ganglion cells." Further on (p. 696)
he says : " The ganglion cells between the leaves of these ' Hautlappen '
lie in a single layer and are surrounded by strands of fibres, so that they
lie as it were in the meshes of such a net made up of bundles of fibres ;
however, it seems to me very doubtful whether these strands of fibres
which make the meshes are all of nervous nature ; on the contrary I
believe that the greater mass of this fibrous tissue is identical with that
which lies under the chitinous cuticula of the ' Russelrohre ' and forms
the sheath of the longitudinal nerves."
If I understand Ehlers correctly (he has no figures showing these
histological conditions), I do not entirely agree with him concerning the
structure of the " Lappen." Within the peritoneum I find connective
tissue, ganglion cells, and also cells not mentioned by Ehlers (PI. 2,
Figs. 7, 8). These last have an epithelial character; they form, indeed,
the main bulk of the lobe, as appears both in material prepared in the
vom Rath mixture and in two haematoxylin preparations made from
material fixed respectively in corrosive sublimate and in sublimate-
acetic. The " Fasergewebe " of Ehlers I consider nervous in large
part. Almost all of the fibres (Fig. 8) surround, not the ganglion cell,
as one might infer from his description, but its nucleus, and pass out at
one pole of the cell body to the longitudinal nerves of the proboscis.
Finally, nerve fibres from the longitudinal nerves and from the pe-
ripheral nerve plexus can be traced out peripherally into the small papil-
lae which are thickly distributed over the surface of the " Russelrohre."
Through the kindness of Mrs. Margaret Lewis Nickerson, who sug-
gested to me the subject of the present paper, I was able to begin my
study of the distribution of the sensory papillae of the proboscis on a
preparation of the cuticula already made by her. The cuticula had been
prepared by a method which was first employed by Mrs. Nickerson.
All my subsequent preparations of the cuticula of other individuals were
secured by the same method, which was as follows: The worm, after
being narcotized in a mixture of sea-water and alcohol, was placed in a
ten per cent solution of common salt until it was evident that its skin
was loosened from the body. A cut was then made through the cuticula
along a longitudinal line of the body, and the animal placed in tap-
water. After the salt had been thoroughly washed out, the worm was
cut transversely into pieces short enough for the cuticula to be mounted
conveniently on a slide. The cuticula was next peeled off with needles
556 PROCEEDINGS OP THE AMERICAN ACADEMY.
and floated upon glass slides. These preparations were ready for study
as soon as they were dry.
The whole surface of the proboscis, except the part which is most
anterior in the usual state of eversion (Fig. 1), is covered with conical or
thirnble-shaped papillae, which are arranged on the summit of transverse
folds (PI. 5, Figs. 32, 33). In general the axes of the papillae are per-
pendicular to the surface of the proboscis, or are directed outward and
either slightly backward or slightly forward. The rows of papillae are
as a rule separated from each other by regular intervals, but sometimes
there is an anastomosis (Fig. 32) of the folds from which these organs
project. The folds follow one another closely, and there are one or two
rows of papillae to each fold. At the posterior part of the everted
proboscis the transverse rows are divided into eighteen longitudinal
groups (Fig. 33); the interspaces correspond to the position, of the
eighteen longitudinal nerves. Otherwise the arrangement and frequency
of these organs is the same from the anterior to the posterior end of the
jiroboscis, and there is no other evidence of special grouping in any part.
The papillae are more or less ovoid or conical. On a proboscis about
o^- mm. in diameter at the anterior end, they were found to be about
80 [jl in height and about 35 /x in diameter at the thickest part.
The cuticula of the proboscis passes over each papilla, but is here re-
duced to about two-thirds the thickness it has elsewhere. The cuticula
of the posterior face of each papilla is coarsely corrugated. The
ridges are most clearly seen in preparations of removed cuticula (PI. 6,
Fig. 34), or in sections stained in Kleinenberg's haematoxylin (PI. 1,
Fig. 6 ; PI. 3, Fig. 13). Though varying in number in different
papillae, the ridges show considerable regularity of form and arrange-
ment, for the outlines produced by them are always rather sharply bent
in a region corresponding with the middle of the posterior face of the
papillae, so that the surface view of that face shows a series of V-shaped
outlines, like the longitudinal section of a nest of funnels, the apices of the
V's being directed toward the base of the papilla. Sometimes, however,
there is an anastomosis of the folds (PI. 3, Fig. 13). Elders (p. 679)
says of this species of Rhynchobolus that the cuticula of the papillae has
" fine folds, which, like those of the gills, occur in spiral lines, surround-
ing the papilla, or more rarely, standing out as sharply projecting
ridges." Concerning the gills he says (p. 676) : " The chitinous cov-
ering possesses at fairly regular intervals furrows which pass around
the circumference spirally ; their significance probably consists in their
laying the gill into definite folds when it collapses and withdraws into
OPPENIIEIMER. — RIIYNCHOBOLUS DIBRANCHIATUS. 557
the parapodial pouch." Whatever may be the condition in the case of
the gills, the furrows of the papillae do not encircle those organs, for I
have found that they exist on the posterior face of the papilla only.
That the function of the furrows of the papillae is similar to that sug-
gested by Ehlers for those of the gills, namely to determine the place of
folding when the organs are retracted, may well be questioned, for there
is no evidence that the papillae are ever retracted ; there are no muscles
to effect contraction, nor have I ever found the organs in a retracted
condition.
The papillae have been studied in sections fixed in a mixture of
corrosive sublimate and acetic acid and subsequently stained in Klein-
enberg's haematoxylin ; in sections fixed in corrosive sublimate and
stained iu iron haematoxylin ; in preparations fixed in vom Rath's
('95, p. 282) picric-osmic-platinic chloride-acetic mixture (to which tap-
water was sometimes added) ; and in methylen-blue preparations. The
sections stained in iron haematoxylin I prepared, through the kindness
of Professor Lloyd, in the laboratory of the Teachers College, Columbia
University.
The living substance of the papillae appears to consist of either four
or five cells, which are, to judge from the nuclei, of two kinds. Two of
the nuclei (PI. 1, Fig. 3 ; PI. 3, Fig. 16, nl. ba.) found in the papillae are
basal in position and larger than the others ; the remaining two or three
(ill. ax.) are nearer the apex of the papilla and also usually more nearly
axial in position (PL 1, P'igs. 3, 4 ; PI. 2, Figs. 9a, 9b, 1 1 ; PI. 3,
Figs. 1G, 17 ; PI. 4, Figs. 2G, 28, 30). The boundaries of the two cells
to which the two basal nuclei belong cannot be made out by any process
that I have employed.
In preparations made with vom Rath's mixture, the protoplasmic con-
tents of the papilla are distinctly vacuolated. The vacuoles are also seen
with nearly equal distinctness in the methylen-blue preparations, but not
quite so clearly in sections stained with iron haematoxylin or with Kleinen-
berg's haematoxylin. The vacuoles are merely clearer, usually roundish,
regions, which stand out distinctly, in contrast to the deeply stained granu-
lar or fibrous surrounding substance, and are quite variable in size, as is
to be seen in PI. 3, Figs. 18, 20; PI. 4, Figs. 22, 25, 29. I believe
that some of the more elongated vacuoles and the clusters of the
more rounded ones in the region of the central nuclei (Figs. 22, 29),
and perhaps a lighter coloring of the axial region of the papilla (PI. 1,
Fig. 4 ; PI. 2, Fig. 11), gave rise to the following opinion expressed by
Ehlers (p. 679) : " There lies under the chitinous covering a thin sheet
558 PROCEEDINGS OP THE AMERICAN ACADEMY.
of finely granular substance, which in the papilla appears to surround a
narrow cavity, and there is connected with this sheet a thick layer of
fibrous tissue."
Connective-tissue fibres pass from the connective tissue of the pro-
boscis into the papillae (PL 1, Fig. 4; PL 2, Fig. 11 ; PL 3, Figs. 12,
19, 20 ; PL 4, Fig. 27) ; as a rule, these could not be traced more than
half-way to the apex of the papilla, but sometimes the contents of the
papilla, in great part or entirely, looked fibrous (PL 1, Fig. 4 ; PL 3,
Figs. 12, 15, 19). These fibres of the papilla are, as Ehlers says, in
close connection with a finely granular substance. There is a particu-
larly dense and deeply stained layer of this finely granular substance
immediately under the cuticula (PL 1, Figs. 3, 4; PL 2, Fig. 11 ; PL 3,
Fig. 16; PL 4, Fig. 30) ; it surrounds not a cavity, but a central re-
gion in which there is a little granular substance and in which there
are many vacuoles. At one point of the base of the papilla, where the
connective tissue enters (PL 1, Fig. 4; PL 2, Fig. 11), and again at one
point near the apex, apparently in the region of the sensory termination
of the papilla (PL 4, Fig. 30c), there is a break in the dense layer of
finely granular substance.
Of the two basal nuclei (nl. ba.) one is near the anterior, the other
near the posterior face of the papilla (PL 2, Fig. 96). They are sphe-
roidal or ellipsoidal, and contain small irregularly scattered chromatin
granules in large numbers ; but in preparations stained in haematoxylin
(PL 1, Fig. 3; PL 2, Figs. 9/>, 11 ; PL 3, Figs. 16, 17) they appear less
deeply colored than the remaining nuclei.
The more distal nuclei (nl. ax.) are more elongated, being ellipsoidal
or spindle-shaped. They present an elliptical outline whether seen in
sections perpendicular to the axis of the proboscis (PL 1, Pigs. 3, 4 ;
PL 2, Fig. 11 ; PL 4, Fig. 30c), in longitudinal sections of the pro-
boscis passing through the axis of the papilla (Fig. 28), or in sections
perpendicular to the axis of the papilla (PL 2, Fig. 9a; PL 3, Figs. 16,
'17). The outline may be more or less pointed at one end, and is more
nearly circular in the sections perpendicular to the axis of the papilla
than in those parallel to the axis. The deeply staining granulations of
the distal, or axial, nuclei are larger and not less numerous than those of
the basal nuclei ; and it is perhaps for this reason that the first-named
nuclei appear more deeply stained than the basal ones. The gran-
ulations of the axial nuclei are also more evenly distributed. Both
kinds of nuclei have a clearly defined nuclear membrane. In the prep-
arations fixed in sublimate-acetic and stained in Kleinenberg's haema-
OPPENHEIMER. — RHYNCHOBOLUS DIBRANCHIATUS. 559
toxylin, I have seen a nucleolus in the basal nucleus only, and here
only occasionally (PI. 3, Fig. 16; PI. 4, Fig. 24). Sometimes,
though rarely, there are in a basal nucleus two larger granulations
(PI. 2, Fig. 11 ; PI. 4, Fig. 30c), which may perhaps be entitled to
rank as nucleoli. In preparations stained in iron haematoxylin and
in those fixed in vom Rath's mixture the nucleolus is regularly seen
with great distinctness near the ceutre of the basal nucleus (PI. 2,
Fig. 9b ; PI. 4, Fig. 26-28). The nucleolus is not infrequently sur-
rounded by a light area.
From the different effects produced on the two kinds of nuclei by
haematoxylin and by methylen blue, it is fair to conclude that the
cells to which the basal nuclei belong are very different from those
of the apical nuclei, and that they have nothing to do directly with
the nervous system. They are evidently indifferent subcuticular cells,
which probably have the same functions as the cover cells of more com-
plicated sensory organs.
The central elongated nuclei found in haematoxylin preparations,
judging from their position, evidently correspond to the two or three
spindle-shaped cell bodies which appear in methylen-blue preparations.
" I have not succeeded," says Pollers (p. 690), " in finding proof posi-
tive that there are nerves in the fibrous tissue which enters the papilla
from the common subcuticular layer." What Ehlers was unable to
find, I have, by the use of improved histological methods, succeeded
in demonstrating with entirely satisfactory clearness. The spindle-
shaped cells are evidently nerve cells of sensory function. For, on
the one hand, the basal end is connected with one of the eighteen longi-
tudinal nerves of the proboscis by a nerve fibre passing to that nerve,
either directly or, through the intervention of the peripheral nerve plexus,
indirectly; and on the other hand the peripheral end tapers toward
the apex of the papilla, where it terminates in a sensory structure, the
precise nature of which it is difficult to make out.
Each of the sensory cells of the papilla has the form of an elongated
spindle tapering at its free end to a delicate fibre-like structure, and
continuous at its basal end with a fibre traceable to a nerve trunk.
This spindle-shaped enlargement, or cell body, lies in the axis of the
papilla and about midway between its base and apex. An exception
to this rule regarding the position of the cell body is seen in Figure 20
(PI. 3), where the cell seems to have a basal position. I am, how-
ever, in doubt as to whether the sensory cells in this case are actually
basal in position, or whether the appearance may not be due to an
560 PROCEEDINGS OF THE AMERICAN ACADEMY.
accidental staining of parts adjacent to the nerve fibres, — a sort
of extravasation, — accompanied by a failure to stain on the part of
the real cell body and the more distal portions of the sensory cell.
The spindle-shaped enlargement is sometimes stained uniformly, but
more often the staining is irregular and blotchy ; in some cases a
nucleus is to be distinguished near the middle of the cell body in
the widest part of the spindle, which it almost completely fills. In
one case (PI. 3, Fig. 14) the nucleus was sharply differentiated from
the cell body, which was not at all blotchy, but distinctly fibrous and
sparsely granular.
From the distal end of the spindle-shaped cell body there passes off a
fibre that, I believe, breaks up into a number of fibrils, each of which
seems to me to end iu a disc (PI. l, Fig. 5 ; PL 3, Fig. 14). In Fig-
ure 31 (PI. 4), the fibrils are quite clearly recognizable ; in Figures 25
and 29 (PI. 4), though distinguishable, they are not so evident. The
terminal discs (PI. 3, Fig. 18; PI. 4, Figs. 25, 29) may, it is true,
be artefacts ; but the frequency of their occurrence and the similarity of
their appearance seem to me to be arguments against that supposition.
Sometimes the blue is deposited in great amount around this bunch of
fibrils (PI. 3, Figs. 12, 15, 18 ; PI. 4, Fig. 29), but in other cases it has
failed entirely to stain the portion of the sensory cell that is distal to the
spindle-shaped enlargement. On the other hand, there are cases in which
the peripheral part of the distal portion of the sense cell has been differ-
entiated by staining in haematoxylin (PI. 2, Fig. 11, not well brought out
in the figure). In the case in which I have seen fibrils with their terminal
discs most distinctly (PI. 3, Fig. 14), the discs at the ends of the fibrils
are at the surface of the papilla outside the cuticula ; in other prepara-
tions, the fibrils seem not to pass through the cuticula, but to end at its
deep surface. It is probable that in most cases the cuticula has been
artificially separated from the protoplasmic mass of the papilla, and that
normally the fibrils pass to the surface of the papilla.
The connection of the cell body with one of the eighteen longitudinal
nerves of the proboscis is often to be traced on a single thick section.
The process which the cell body sends centripetally either joins a longi-
tudinal nerve directly, or enters the peripheral nerve plexus, which in
turn joins the longitudinal nerve (PI. 2, Fig. 10; PI. 3, Fig. 19). The
basal end of each of the two or three cell bodies of the papilla seen in
methylen-blue preparations (PI. 3, Figs. 12, 14, 20; PI. 4, Figs. 23,
25, 29) is prolonged into a slender nerve fibre. While the fibre be-
longing to one of the cells of a papilla bends to the left when it joins
OPPENHEIMER. — RHYNCHOBOLUS DIBRANCHIATUS. 5G1
the nerve plexus, that belonging to another cell of the same papilla
may bend to the right, as is to be seen in Figures 10 (PI. 2), 12,
and 19 (PL 3). Occasionally the fibres twist around each other, and
there is sometimes to be found an appearance which suggests anas-
tomosis of these fibres, but focusing shows that in a great number of
such cases the fibres cross without touching each other ; in still other
cases (PL 3, Figs. 12, 19) the blue staining is not confined to the
fibres, and this makes the following out. of the fibres more difficult.
The condition shown in Figure 15 (PL 3), which seems to be an ex-
ception to the rule that the basal end of each spindle-shaped cell body
tapers into a nerve fibre, is probably the result of the well-known
capriciousness of methyleu-blue staining. In no case have I seen a
nerve fibre arise from an abruptly rounded basal end of one of these
sensory cells, but the cell body seems always to taper gradually into
the nerve fibre. There are, however, quite a number of cases in
which the inner end of the .cell body does not simply taper into a
single nerve fibre, but iu which it is prolonged into a few processes
which ultimately unite to form the fibre (PL 4, Figs. 23, 25).
These nerve fibres on their way to the longitudinal nerves often show
at intervals those characteristic swellings, or varicosities, which have been
so frequently figured in recent works on nerve fibres treated either by
the methylen-blue or the Golgi methods.
Summary.
The papillae of the proboscis of Rhynchobolus are sensory organs.
They are considered to be sensory on the following grounds: —
1. The papillae are well differentiated organs.
2. They are found over almost the entire surface of the everted
proboscis.
3. They are elevated above the surrounding surface.
4. The cuticula which passes over each papilla is reduced to about
two-thirds the thickness it has elsewhere on the proboscis.
It should be mentioned that the cuticula of the posterior face of each
papilla is coarsely corrugated, but the significance of this wrinkling is
unknown.
5. There are two or three spindle-shaped cells in a papilla, each of
which terminates — either below the cuticula or more probably at the very
apex of the papilla — in what is clearly a sensory structure, and each
of these cells tapers gradually at its base into a nerve fibre. These
VOL. XXX VI i. — oG
562 PROCEEDINGS OF THE AMERICAN ACADEMY.
nerve fibres are connected either directly or indirectly — through the in-
tervention of a peripheral nerve plexus — with the eighteen longitudinal
nerves of the proboscis.
G. There are two basal nuclei that belong to cells which probably
have the function of cover cells.
It remains to be said that there enter each papilla besides nerve fibres,
connective-tissue fibres. These latter are found in close connection with
a finely granular substance, of which there is a particularly dense and
deeply staining layer immediately under the cuticula. Standing out in
contrast to the deeply stained granular or fibrous surrounding substance
are the clear, generally rounded vacuoles.
If there is any differentiation in function between papillae, it is not
correlated with any pronounced difference in structure.
Bibliography.
Ehlers, E.
'64-68. Die Borstenwiirmer (Annelida chaetopoda) nach systemati-
schen und anatomischen Untersuchungen dargestellfc. Leipzig, xx + 748
pp., 24 Taf.
Rath, O. voni
'95. Zur Cunservirungstechnik. Anat. Anzeiger, Bd. 11, No. 9, pp. 280-
288.
EXPLANATION OF PLATES.
Abbreviations.
coel. Coelom, body-cavity.
eta. Cuticula.
cta. + e'th. Cuticula and epithelium.
gl. Gland.
gnu. Jaw.
linn. Lemniscus.
mu. crc. Circular muscle.
mu. Ig. Longitudinal muscle.
n. crc. Circular nerve.
nl. ax. Axial nucleus.
nl. ba. Basal nucleus.
n. Ig. Longitudinal nerve.
n. r. Radial nerve fibre skirting longi-
tudinal muscle.
11. rf Radial nerve fibre passing directly
to the membrane superficial to the
circular muscles.
pap. Papilla.
pi'tn. Peritoneum.
tis. co'nt. Connective tissue.
In many figures not only the papilla is shown, but also a portion of the under-
lying parts.
PLATE 1.
Fig. 1. Longitudinal section of the everted proboscis showing: (1) the sheath of
the proboscis; (2) the bearer of the jaws and its subdivision; and (3) the
lemniscus (Imn.), which marks the boundary between (1) and (2).
Narcotized in a mixture of sea-water and alcohol; fixed in Muller's fluid;
stained with Beale's ammonia carmine. X circa 11.
Fig. 2. Cross section of the partially everted proboscis in the region of the four
lemnisci (Imn.), showing, among other things, a diagrammatic representation
of the papillae and the connection of their sensory cells with the circular and
the longitudinal nerves, and also the nerve fibre (n. r.') passing to the membrane
which invests the circular muscles.
Chloroform, methylen blue, Bethe's ammonium molybdate for invertebrates.
X 14.5.
Fig. 3. Papilla from a cross section of the proboscis, showing two "basal" and
three " axial " cell nuclei.
Sea-water and alcohol, sublimate-acetic, Kleinenberg's haematoxylin. X 675.
Fig. 4. Longitudinal section of a papilla, from a cross section of the proboscis,
showing the two axial nuclei and one of the two basal nuclei, also fibrous struc-
tures entering the base of the papilla. Treatment the same as in Fig. 3.
X 585.
Fig. 5. Longitudinal section of a papilla, from a sagittal section of the proboscis,
showing two sensory axial cells with peripheral sensory termination and
prolongation of the basal end of each into a slender nerve fibre.
Chloroform, methylen blue, Bethe's ammonium molybdate for invertebrates.
X 650.
Fig. 6. Papilla from cross section of proboscis viewed from behind, showing the
corrugations of the cuticula on the posterior face of the papilla, and in optical
, section the two zones of living substance together with one of the basal nuclei.
Sea-water and alcohol, sublimate-acetic, Kleinenberg's haematoxylin. X 585.
Oppenheimer.- Sense Organs]
Pl.a
■
PLATE 2.
Fig. 7. Portion of cross section of proboscis, showing structure of lemniscus.
Sea-water and alcohol, vom Path's mixture. X 200.
Fig. 8. Part of Fig. 7 enlarged. X ca. 400.
Figs. 9a, 96. Sections of a papilla perpendicular to its axis. Figure 9a represents
the more distal of the two sections, and shows the form and position of the
three axial nuclei ; Figure 96 shows the two basal nuclei. The anterior face
of the papilla is directed toward the top of the plate in both cases.
Sea-water and alcohol, corrosive sublimate, iron haematoxylin.
Fig. 10. Portion of the cross section of an everted proboscis, showing one of the
eighteen longitudinal nerves (n. Ig.) cut crosswise, the peripheral nerve plexus,
the union of the centripetal processes from the sense cells with the longitudinal
nerve (in the case of the third papilla from the upper margin of the Figure,
one of the two nerve fibres bends to the left when it enters the nerve plexus, the
other to the right), a radial nerve (n. r.) following the surface of the longitu-
dinal muscle (this is sketched in from an adjacent section), and another radial
nerve (n. r.') passing directly to the membrane which is immediately superficial
to the circular muscles.
Chloroform, methylen blue, Bethe's ammonium molybdate for invertebrates.
X 145.
Fig. 11. Papilla from a cross section of proboscis showing one of the basal and
one of the axial nuclei ; there are two large granulations in the basal nucleus.
The differentiation of the distal portion of the sense-cell is not well shown.
Sea-water and alcohol, sublimate-acetic, Kleinenberg's haematoxylin. X 460.
Oppenheimer- Sense ., i :hobolus.
<«£?••.
■Ai
7
■
,
PLATE 3.
Figs. 12, 14, 15, IS, 19, 20. Prepnrations made by use of chloroform, methylen
blue, and Bethe's ammonium molybdate for invertebrates.
Figs. 13, 16, 17. Prepared by use of sea-water and alcohol, sublirr.ate-acetic,
Kleinen berg's haematoxylin.
Fig. 12. Papilla from cross section of proboscis, showing connective-tissue fibres
passing into the papilla; deep coloration of terminal fibrils; the nerve fibres
bending in opposite directions where they enter the nerve plexus. X 080.
Fig. 13. Papilla from cross section of proboscis, showing corrugations of
posterior face of papilla, and the outline of one of the basal nuclei. X 460.
Fig. 14. Papilla from sagittal section of proboscis; the two sensory (axial)
cells, their peripheral terminations, and their proximal nerve-fibre prolonga-
tions stained blue.
T lie nucleus of one of the sensory cells more deeply stained than the cell body.
Cuticula distended and detached from substance of the papdla by treatment.
X 710.
Fig. 15. Papilla from cross section of proboscis, showing deeply stained axial
body, from winch a single peripheral, deeply stained process extends to the apex
of papilla, where it terminates in a specialized and stained area ; the contents of
the papilla in great part fibrous. X 1020.
Fig. 1(5. Somewhat oblique cross sections of two papillae from a cross section of
the proboscis. In one papilla are two basal nuclei and a part of one of the
axial nuclei ; in the other the three axial nuclei cut crosswise. X 070.
Fig. 17. Cross sections of two papillae from a cross section of proboscis. In one
are seen two axial nuclei, each surrounded with a clear area; in the other a
basal nucleus and portions of two axial ( ' ) nuclei. X 070.
Fig. 18. Papilla from cross section of proboscis. The two sensory cells are
stained throughout ; their distal prolongations have a more or less spiral course
and terminate in a cluster of discs at the apex of the papilla. Vacuoles large.
X 715.
'Fig. 19. Papilla from cross section of proboscis, showing that where the cen-
tripetal fibres from two sensory cells meet the nerve plexus, one bends to the
right, the other to the left. X 725.
Fig. 20. Papilla from cross section of proboscis, showing the basal position of
the sensory cell body (?) ; the basal end of each sensory cell is prolonged into a
slender nerve fibre. X G82.5.
OppENHEiMERr Sense Organs Rhynchobolus.
k
/■j
M-
76
■
/;
\
J7
20
/
PLATE 4.
Figs. 21-23, 25, 27, 29, 30. Longitudinal sections of papillae from cross sections
of proboscis.
Figs. 21-23, 25, 29. Preparations made by use of chloroform, methylen blue,
Bethe's ammonium molybdate for invertebrates.
Figs. 24, 30. Preparations made by use of sea-water and alcohol, sublimate-
acetic, Kleinenberg's haematoxylin.
Fig. 21. Three sensory cells, two showing peripheral fibres and terminations.
X 715.
Fig. 22. Papilla showing a row of axial vacuoles.
Sea-water and alcohol, Miiller's fluid, Beale's ammonia carmine.
Fig. 23. The nuclei of the two sensory cells distinguishable from the cell body
by their deeper stain. Peripheral and proximal fibres stained. X 710.
Fig. 24. Basal nucleus of a papilla showing a large single nucleolus. X 070.
Fig. 25. Highly vacuolated papilla, fibrils and discs of the sensory termination
stained blue, the deep ends of each of the sensory cells prolonged into a few
processes, which unite to form the single nerve fibre. X 700.
Fig. 20. Cross section of a small papilla, showing a nucleolus in each basal
nucleus.
Sea-water and alcohol, vom Rath's mixture. X 680.
Fig. 27. Papilla showing one of the basal nuclei with large nucleolus, and the
passage of connective-tissue fibrils into the papilla.
Sea-water and alcohol, vom Rath's mixture.
Fig. 28. Papilla from sagittal section of proboscis, showing three axial nuclei
and two basal nuclei.
Sea-water and alcohol, sublimate, iron haematoxylin.
Fig. 29. Papilla from cross section of proboscis, showing numerous small
vacuoles, fibrils and discs of sensory termination. The basal end of each sen-
sory cell is prolonged into a slender nerve fibre. X 730.
" Figs. 30a-30<7. Four successive sections from a single papilla.
Fig. 306 shows one of the basal nuclei ; Fig. 30c, the other basal nucleus and
the two axial nuclei.
In the region of the apex of the papilla, there is an interruption in the cortical
layer of finely granular substance, not well shown, and the region is traversed
by fine fibres. X 585.
Fig. 31. Fibrils from the peripheral termination of a sensory cell.
Oppenheimer.- Sense Oj i
'
■
PLATE 5.
Fig. 32. From a photograph of the cuticula of the proboscis stripped by macera-
tion (consult text, p. 555) and mounted on glass slide. The part of the figure
nearest the top of the plate is toward the anterior end of the everted proboscis.
To show the arrangement of the papillae in transverse rows. X 22.5.
Fig. 33. From a photograph of a preparation similar to that of Fig. 32, showing
the appearance of the cuticula and attached papillae near the posterior end of
the everted proboscis. iSiine of the eighteen longitudinal columns of papillae
are shown. X 18 5.
Oppenheimer. -Sense Organs Rhynchobolus.
Plate 5.
■ >Vhi!
■•« tM <T
*^v >
*\ '1- -^ S? ->"N >>v .*, <&
r«»> #*v •*
*-*,* ^^>«»^«,f<?5*c,'*«i*e.^'*
32
33
PLATE 6.
Fig. 34. Highly magnified view of portions of four transverse rows of papillae, to
show the corrugations of the flattened and dried papillae, and the circular wall
and pit of the cuticula at the apex of the papilla, marking the position of the
termination of the sensory cells. X 110.
Oppenheimer.-Sense Organs Rhynchobolus.
Plate 6.
'$•>
^«R#
^
<*>5i«
34
Proceedings of the American Academy of Arts and Sciences.
Vol. XXXVII. No. 22.— May, 1902.
CONTRIBUTIONS FROM THE CHEMICAL LABORATORY OF
CASE SCHOOL OF APPLIED SCIENCE. — XLI.
THE COMPOSITION OF PETROLEUM.
By Charles F. Mabery.
ON THE HYDROCARBONS IN PENNSYLVANIA PETROLEUM
WITH BOILING POINTS ABOVE 216°.
Aid in the Work described in this Paper was given bt the Academy from the
C. M. Warren Fund for Chemical Research.
CONTRIBUTIONS FROM THE CHEMICAL LABORATORY OF
CASE SCHOOL OF APPLIED SCIENCE. — XLI.
THE COMPOSITION OF PETROLEUM.
By Charles F. Mabery.
ON THE HYDROCARBONS IN PENNSYLVANIA PETROLEUM
WITH BOILING POINTS ABOVE 210°.
Received March 24, 1902. Presented April 9, 1902.
In a former paper* the principal hydrocarbons in Pennsylvania,
Ohio, and Canadian petroleum below 216°, were shown to have the
composition represented by the general formula CnH2n + 2. Concern-
ing the constituents with higher boiling points very little is known.
Pelouze and Cahours t collected distillates to which they gave the fol-
lowing formulas : —
216°-218° 236°-240° 255°-2G0° 280°
C13H03 Cj4 H30 CiBrl82 Ci6H34
From paraffine the following hydrocarbons have been separated (Beil-
stein's Handbook) : —
212°-215° 230°-235° 252°-255° 273°-275°
Ci3H23 C14H30 (_/15H32 Ci6H34
So far as I am aware, these are the only allusions to the composition
of Pennsylvania petroleum in these portions. It appears that the dis-
tillations were made under ordinary atmospheric pressure in presence
of air with no attempts to avoid decomposition under these conditions.
Then, furthermore, as I have suggested in a former paper, the high
specific gravity of the distillates separated by Pelouze and Cahours
indicate that their distillates were obtained from Canadian petroleum.
It does not appear that any attempts have been made to ascertain the
molecular weights of the individual hydrocarbons. Indeed this has been
* These Proceedings, XXXII. 121.
t Ann. China. Phys. (4), 1, 5 (18G4).
566 PROCEEDINGS OF THE AMERICAN ACADEMY.
possible only within recent years since the freezing and boiling point
methods for the determination of molecular weights have been known.
Then it is not possible to determine the vapor densities of these hydro-
carbons, because, as I have recently ascertained, even in vacuo small
quantities of the hydrocarbons such as are used in vapor density deter-
minations, undergo serious decomposition; and this occurs even in oils
that have been distilled many times over in hulk in vacuo. In the ear-
lier work, it was evidently assumed that a few distillations under atmos-
pheric pressure were sufficient to collect the individual hydrocarbons
within the limits of their boiling points, sufficient at least to afford
reliable data as to their composition. A glance at the small differences
in percentage composition is sufficient to show that it is not possible by
analysis alone of products even well purified to distinguish between
homologous members of a series, although such analysis may define the
series.
But the chief difficulty is to obtain each hydrocarbon uncontaminated
by any admixture of its homologues or by products of decomposition.
This is well illustrated by the experience of MarkownikofF in separating
the hydrocarbons in the Russian oil, who found it impossible to collect
distillates closer than limits of five degrees on account of decomposi-
tion. That the same is true perhaps in a less degree in distillates from
Pennsylvania oil is evident whenever distillation is made of the higher
portions under atmospheric pressure. The rank odor is evidence of
cracking. Yet the constituents with higher boiling points are under the
influence of vapor tension as much as the constituents with lower boil-
ing points, and consequently require as prolonged distillation for com-
plete or approximately complete separation. In my experience it is
only possible to obtain even an approximate separation by exclusion of
air and depression of boiling points.
In this manner the higher hydrocarbons may be distilled any number
of times with no appreciable decomposition. The only limit is the
patience of the operator. But the stability of these hydrocarbons is
evidently dependent on the influence of mass. Since as mentioned
above, while distillation of any considerable quantity of the oil may be
carried on indefinitely, a limited quantity cannot be volatilized even in
vacuo without decomposition. Many attempts to determine the vapor
density of the hydrocarbons in Pennsylvania and California petroleum
by volatilization in vacuo according to the method of Lunge and Neu-
berg have failed on account of cracking, even so far as the separation
of sooty carbon from the members with high boiling points.
MABERY. — THE COMPOSITION OP PETROLEUM. 567
In September, 1896, I set out to ascertain the composition of the
principal hydrocarbons in Pennsylvania petroleum above 216° so far as
they can be separated by distillation on a laboratory scale. Through the
courtesy of the Standard Oil Company, I procured a barrel of crude oil
from Oil City and this material has been used to separate the hydro-
carbons that will be described in this paper. That this oil was an
approximately average specimen of Pennsylvania petroleum, appears
from its properties. A determination of the specific gravity of the crude
oil at 20° gave 0.8095. A combustion of the oil dried over sodium
gave the following percentages of carbon and hydrogen : Carbon, 85.80 ;
Hydrogen, 14.04. Eight hundred grams distilled in the ordinary way in
the following proportions : —
50°-150° 150° -200° 200°-250° 250° -300° +300°
166 88 83 100 337
Fifty-six kilos of the crude oil was distilled in quantities of 10 litres each
in a porcelain still, collecting under atmospheric pressure to 200°, and
within limits of 10° under a vacuum of 50 mm. to 300°, then within
limits of 5°, and finally within limits of 2°. After eight distillations the
following proportions collected: —
124°-126° 136°-138° 156°-158° 174°-176° 188°-199°
Grams, 125 145 240 205 240
199°-201° 210°-212° 226°-228° 242°-244°
225 335 150 130
Since the weights of these fractions represent all that came from the
original crude oil, it is possible to gain a very general idea of the pro-
portion of the hydrocarbons which are contained in the crude oil. But
such estimation must be only approximate from the fact that any dis-
tillation however thorough gives only an approximate separation, and a
considerable portion of any hydrocarbon must be contained in the in-
termediate distillates.
The percentages of the weights are as follows : —
Ci3H28 C14rl30 Ci5H32 C16H34 L17H3(5
124°-126° 136°-138° 156°-158° 174°-176° 188°-199°
0.22 0.26 0.43 0.37 0.43 per. cent.
Ci8H38 C19H40 C20H42 ^2i"44
199°-201° 210°-212° 230°-232° 242°-244°
0.40 0.60 0.27 0.23 per. cent
c
G8 PROCEEDINGS OF THE AMERICAN ACADEMY.
In the intervals between these fractions the weights were much
smaller.
After the eighth distillation each fraction was agitated at first with
common concentrated sulphuric acid until the acid was not much colored
and then several times with fuming sulphuric acid. That the distillates
consist almost entirely of the principal hydrocarbon is shown by the
slight change in specific gravity by the acid treatment : —
182°-184°
0.8100 Original distillate.
0.8093 After treatment with acid.
There was some loss in weight of the fraction by the acid treatment,
but it was doubtless due for the most part to solution of the principal
hydrocarbons in the acid. The weights of the fractions before and after
treatment were as follows : —
56°-158°
174°-176°
0.805
0.8064
0.7992
0.8031
156°-158°
174° -176°
182°-186°
240
215
205
195
190
155
This solvent action has been observed in other oils with high boiling
points in continuous treatment with fuming sulphuric acid, which caused
a gradual loss without changing materially the specific gravity. After
the purification with the acid, distillation was continued through a
Hempel column filled with glass beads or broken glass, under 50 mm.
within limits of one degree, until the hydrocarbons collected in consider-
able quantities. After the thirtieth distillation, the hydrocarbons came
together within the following limits : —
124°-126°, 142°-143°, 158°-159°, 173°-174°, 189°-190°, 198°-199°.
Even after nearly continuous distillation of sixteen months, these
products showed very little indication of decomposition. Leaks in the
■apparatus immediately cause decomposition, as shown by a disagreeable
odor, and the appearance of the distillates. So long as air is excluded
from the hot vapors there is no danger of decomposition. But as we
found in attempting to ascertain the boiling points under atmospheric pres-
sure, a single distillation in air causes a very rank odor of decomposition.*.
* The difference in stability of the constituents of different petroleums is
shown by their behavior when air comes in contact with the hot vapors. In acci-
dents that have occurred during distillation, letting in air on the hot vapors, in the
case of Pennsylvania petroleum the still becomes filled with dark vapors, but in a
MABERY. — THE COMPOSITION OP PETROLEUM. 569
In determining the boiling points of these hydrocarbons under at-
mospheric pressure, 70' grams of the fraction 124°-126° distilled as
follows, under 760 mm. and with the mercury column all within the
vapor : —
224° -225° 225°-226° 226°-227° 227°-228° 228°-229°
Grams, 4 28 20 3 3
Colored residue, 6
The portions between 225° and 227° collected almost entirely between
225°. 5 and 226°.5.
The fraction 142°-143° nearly all distilled at 237°-238° atmospheric
pressure, the fraction 158°-159° at 256°-257°, the fraction 173°-174° at
274°-275°, the fraction 188°-189° at 288°-289°, and the fraction 198°-
199° at 300o-301°. The hydrocarbon dodecane C12H26 was identified
in the fraction 214°-216°.*
Tridecane, C13H2S.
The next homologue, tridecane, was sought for in the series of distil-
lates that collected between 215° and 235°. After carrying these
fractions eight times through a Hempel bead column a larger portion,
200 grams, collected at 221°-222°. This portion was distilled twenty-
four times, when 70 grams collected, as shown above. The specific
gravity of the distillate before further treatment was 0.7866, and after
thorough agitation with fuming sulphuric acid, 0.7834. A combustion
gave the following values for carbon and hydrogen : —
0.1506 grm. of the oil gave 0.4690 grm. C02 and 0.2028 grm. H20.
Calculated for C13HM. Found.
C 84.78 84.94
H 15.22 14.96
The molecular weight of this oil as determined by the Beckman method
at the freezing point of benzol, in the hands of different workers, corre-
sponded to that of C13H28.
distillation of Russian petroleum, air accidently admitted caused such a violent
explosion that the thermometer was sent violently across the room and broken
against the wall.
* These Proceedings, XXXII. 138.
570 PROCEEDINGS OF THE AMERICAN ACADEMY.
I. 1.1209 grm. of the oil and 36.3043 grms. benzol gave a depression
of0°.82.
II. 1.2502 grm. of the oil and 33.3631 grms. benzol gave a depression
of r.oio.
III. 1.496 grm. of the oil and 32.9131 grms. benzol gave a depression
of 1°.205.
Calculated for Found.
Cl3H28. I. II. III.
184 184.5 181 184.9
In still further confirmation of the formula of tridecane, the index of
refraction was determined, and its molecular refraction calculated. The
index was found to be 1.4354 at 20°, and the molecular refraction as
follows : —
Calculated for CX3H28- Found.
61.94 61.44
JlJonochlortridecane, C13H27C1. — In the preparation of the chlorine de-
rivative of tridecane, chlorine was allowed to act on the hydrocarbon in
screened sunlight, over water. With care to avoid an excess of chlorine,
the product consisted for the most part of the mouochloride. It was
fractioned in vacuo under 12 mm. several times until considerable of the
oil collected at 135°-140°. This fraction gave as its specific gravity at
20°, 0.8973. A determination of chlorine gave a percentage required
for the mouochloride : —
0.1920 grm. of the oil gave 0.1273 grm. AgCl.
Required for Ci3H2-Cl. Found.
CI 16.23 16.39
The molecular weight as determined at the freezing point of benzol
corresponded to the same formula : —
0.4585 grm. of the oil and 18.35 grms. benzol gave a depression of 0°.568.
Calculated for C13U2jCl. Found.
218.5 216
A determination of the index of refraction confirmed the same formula;
the index as determined was 1.451, corresponding to the molecular
refraction : —
Calculated. Found.
65.71 66.67
MABERY. — THE COMPOSITION OF PETROLEUM. 571
Tetradecane, Ci4H30.
The fraction 142°-143°, collected after the twenty -fourth distillation,
gave as its specific gravity, after drying over sodium, 0.7848. Alter
agitating with concentrated sulphuric acid, washing, and drying over
sodium, it gave 0.7847. After treatment with fuming sulphuric acid it
gave 0.7814 ; this determination, like the others, was made at 20°.
A determination of the molecular weight of this fraction purified with
fuming sulphuric acid gave the following result: —
I. 1.1049 grm. of the oil and 36.8505 grms. benzol gave a depression
of 0°.735.
II. 1.052 grm. of the oil and 35.970 grms. benzol gave a depression
of0°.718.
Calculated for Found.
CmHjo. I. II.
198 199.9 199.5
A combustion gave the following percentages of carbon and hydrogen :
0.1502 grm. of the oil gave 0.4698 grm. C02 and 0.2024 grm. H20.
Calculated for C14II30. Found.
C 84.84 85.02
H 15.16 14.96
This specimen was purified with common concentrated acid ; another
portion purified with fuming sulphuric acid gave slightly different pro-
portions : —
0.1458 grm. of the oil gave 0.4532 grm. C02 and 0.1970 grm. H20.
Calculated for CUII30 Found.
C 84.84 84.76
H 15.16 15.02
The boiling point of this fraction under 760 mm. was 236°-238°. On
account of decomposition when the oil is distilled in air, it is difficult to
determine the boiling point with great precision.
A determination of the index of refraction of this hydrocarbon gave
1.4360, which corresponds to the following molecular refraction : —
Calculated or 0,41130. Found.
66.54 66.36
572 PROCEEDINGS OF THE AMERICAN ACADEMY.
Monochlortetradecane, C14Ho9Cl. — Since only small quantities of the
purified hydrocarbons were available for the study of the chlorides, great
care was necessary to avoid too high chlorination. Most of the hydro-
carbons gave only sufficient of the chlorine derivative to verify its formula
by the percentage of chlorine. The chlorine product obtained from
tetradecane was fractioned in vacuo until it collected in larger quantities
at 150°-153° under 20 mm. A determination of chlorine gave the
following result : —
0.1966 grm. of the oil gave 0.1245 grm. AgCl.
Calculated for C^IL^Cl. Found.
CI 15.25 15.65
Its specific gravity at 20° was found to be 0.9185. The quantity of
product was not enough for other determinations. Another portion of
the chlorine product collected at 175°-180°, 17 mm., which gave as its
specific gravity at 20°, 1.032. A determination of chlorine gave the value
required for the dichloride : —
0.1937 grm. of the oil gave 0.2125 grm. AgCl.
Calculated for CnH^Clj. Found.
CI 26.55 27.12
A determination of molecular weight at the freezing point of benzol
confirmed the dichloride : —
1.3407 grm. of the oil and 19.81 grms. benzol gave a depression of 1°. 255.
Calculated for C14H28C1S. Found.
267 264.3
Pentadecane, C15H32.
The specific gravity of the fraction 158°-159° (50 mm.) dried over
sodium was found to be 0.8U54 at 20°. After treatment with concen-
trated sulphuric acid it gave 0.7939, and after thorough treatment with
'fuming sulphuric acid it gave 0.7896.
The molecular weight was determined by the Beckman method : —
I. 1.050 grm. of the oil and 35.9775 grms. benzol gave a depression
of 0°.675.
II. 1.3946 grm. of the oil aud 23.2679 grms. benzol gave a depression
of 1°.37.
Calculated for Found.
C15H3l. I. II.
212 211 212
MABERY. — THE COMPOSITION OF PETROLEUM. 573
Combustion I. was made of the unpurified distillate dried over sodium ;
and combustion II., of the oil after treatment with fuming sulphuric
acid : —
I. 0.1440 grm. of the oil gave 0.4500 grm. C02 and 0.1919 grm. 11,0.
II. 0.1608 grm. of the purified oil gave 0.5002 grm. C03 and 0.2198 grm.
H20.
Calculated for Found.
C„H32. I. II.
C 84.92 85.21 84.87
H 15.08 14.80 15.20
In determining the boiling point of pentadecane under atmospheric
pressure, it distilled almost completely at 256°-257°.
A determination of the index of refraction gave 1.4413, from which
the molecular refraction was calculated : —
Calculated for C15H32. Found.
71.15 70.49
Dichlorpentadecane, C15H30C12. — With the small quantity of the hy-
drocarbon at hand, we did not succeed in limiting the action of chlorine
to the formation of the monochloride. Fractioned in vacuo under 13 mm.
the chlorinated product collected for the most part at 175°-180°. This
product gave as its specific gravity at 20°, 1.0045. A Carius determina-
tion for chlorine gave the following percentage : —
0.1411 grm. of the oil gave 0.1462 grm. AgCl.
Calculated for C^HjuCIj. Found.
CI 25.28 25.63
The molecular formula was established by a determination of its molec-
ular weight : —
1.4308 grm. of the oil and 18.53 grms. benzol gave a depression of 1.336.
Calculated for C10H30C12. Found.
281 283.2
Hexadecane, C16H34.
The heap that collected at 174°-175°, 50 mm., after the thirtieth
distillation gave as its specific gravity at 20°, 0.8000. After treatment
with concentrated sulphuric acid it gave 0.7964, and after treatment with
fuming sulphuric acid, 0.7911. It distilled almost completely at 275°—
574 PROCEEDINGS OF THE AMERICAN ACADEMY.
276° under 760 mm., barometric pressure. In determining the molecu-
lar weight of this fraction at the freezing point of benzol, it gave the
formula C16H34 : —
I. 1.1507 grm. of the oil and 35.27 grms. benzol gave a depression
of 0°71.
II. 1.1833 grm. of the oil and 35.63 grms. benzol gave a depression
of 0.715.
Calculated for Found.
C1(,H.34- I II.
226 225.2 227.6
Determinations of carbon and hydrogen were made in the unpurified
distillate (I.), in a portion purified with concentrated sulphuric acid (II.),
and in a third portion purified with fuming sulphuric acid (III.), with the
following results : —
I. 0.1477 grm. of the oil gave 0.4600 grm. C02 and 0.1973 grm. H20.
II. 0.1454 grm. of the oil gave 0.4522 grm. C02 and 0.1986 grm. H20.
III. 0.1454 grm. of the oil gave 0.4516 grm. C02 and 0.1971 grm. H20.
Calculated for
i.
Found.
II.
in.
c
84.96
84.94
84.80
84.60
H
15.04
14.84
15.18
15.06
The index of this hydrocarbon was found to be 1.4413, from which the
molecular refraction was calculated : —
Calculated for Cir,HM. Found.
75.750 75.555
Dichlorhexadecane, C16H33C12. — The chlorine product obtained from
hexadecane collected for the larger part at 205°-210°, under 16 mm.
Its specific gravity was 1.0314 at 20°. A determination of chlorine
gave a value required for the dichloride : —
0.1477 grm. of the oil gave 0.1525 grm. AgCl.
Calculated for C10H3,C12. Found.
CI 24.61 24.44
This formula was also confirmed by its molecular weight : —
0. 5019 grm. of the oil and 18.21 grms. benzol gave a depression of 0°.457.
Calculated for C16H3,Clj. Found.
295 295
MABERY. — THE COMPOSITION OP PETROLEUM. 575
A portion of the original distillate 174°-175° was cooled to —10°,
which caused the separation of a crystalline mass. It was filtered cold,
but the solid remaining formed but a small part of the original oil.
The specific gravity of the filtered oil 0.8005, was slightly higher than
the unfiltered distillate. The quantity of the solid was not sufficient for
analysis or further examination. No further examination was made of
the filtered oil, for it was evident that the small amount of solid hydro-
carbon could not change the composition, nOr other constants, especially
since, as shown above, the original distillate has the composition of the
series CnH2ll+2.
Heptadecane, Ci7H36.
The fraction which collected at 188°-190° after the 42d distilla-
tion gave as its specific gravity at 20° after drying over sodium, 0.8017.
After agitation with sulphuric acid it gave 0.8019, and after purification
with fuming sulphuric acid, 0.8000. Under 760 mm. pressure this oil
distilled almost entirely at 288°-289°, with very little residue above
289°. The small residue was badly colored from decomposition.
Evidently it would not be possible to distill this oil continuously under
atmospheric pressure in preseuce of air without serious decomposition.
The formula of this distillate was established by two determinations
of its molecular weight and by analysis.
I. 1.4294 grm. of the oil and 25.7086 grms. benzol gave a depression
of 1°.17.
II. 1.4382 grm. of the oil and 25.6785 grms. benzol gave a depression
of 1°.18.
Calculated for Found.
CJ7H36. I. II.
240 241.2 240.9
Analysis I. was made of the unpurified oil dried over sodium, and
Analysis II. after purification with fuming sulphuric acid.
I. 0.1534 grm. of the oil gave 0.4778 grm. C02 and 0.2044 grm. H20.
II. 0.1491 grm. of the oil gave 0.4641 grm. C02 and 0.2014 grm. H20.
Calculated for
^17^36.
Found.
I. II.
c
84.96
84.94 84.87
H
15.04
14.80 15.01
576 PROCEEDINGS OP THE AMERICAN ACADEMY.
Monochlorheptadecane, C17H35C1. — The chlorine product from hepta-
decane collected in considerable quantity at 175°-177°, 15 mm. Its
specific gravity at 20° was found to be 0.8962. The percentage of
chlorine corresponded to the monochloride : —
0.1510 grm. of the oil gave 0.0807 grin. AgCl.
Calculated for C^H^Cl. Found.
CI 12.92 13.21
On cooling a portion of the distillate 188°-189° to —10°, it formed a
pasty mass from which a small amount of a crystalline solid was ob-
tained by filtration. The solid after crystallization from ether and
alcohol melted at approximately 10°. The amount of solid was not
sufficient for purification or examination. The filtered oil gave as its
specific gravity at 20°, 0.8035, slightly higher than the distillate before
filtration. Since the original distillate showed the composition of the
series, CnH2n+2, it did not seem worth while to make any further exami-
nation of the filtered oil.
OCTODECANE, C18H38.
After the twenty-sixth distillation larger quantities of distillates col-
lected between 198° and 204°, mostly at 199°-200° (50 mm). The dis-
tillate l99°-200° distilled for the most part, although with considerable
colored residue and bad odor, at 300°-301°, under 760 mm. After dry-
ing over sodium its specific gravity was 0.8054, after agitation with
sulphuric acid, 0.8035, and after purification with fuming sulphuric acid,
0.8017, at 20°.
Its molecular weight was ascertained by the Beckman method at the
freezing point.
I. 0.9963 grm. of the oil and 36.4129 grms. benzol gave a depression
of0°.53.
II. 0. 9926 grm. of the oil and 23.2544 grms. benzol gave a depression
of 0°.84.
Calculated for Found.
CjgH^. I. IL
254 252.7 254.2
Combustion I. was made of the unpurified distillate dried over so-
dium ; combustion II., of the oil after purification with concentrated sul-
MABERY. — THE COMPOSITION OF PETROLEUM. 577
phuric acid; and combustion III., after treatment with fuming sulphuric
acid.
I. 0.1423 grm. of the oil gave 0.4435 grm. C02 and 0.1915 grm. H,0.
II. 0.1513 grm. of the oil gave 0.4702 grm. C02 and 0.2054 grm. H20.
III. 0.1524 grm. of the oil gave 0.4727 grm. C02 and 0.2064 grm. H20.
Calculated for
C 18^38-
i.
Found.
11.
in.
c
85.06
85.02
84.76
84.59
H
14.94
14.96
15.09
15.05
It is evident from the slight change in specific gravity after purifica-
tion, and the percentages of carbon and hydrogen, that the original
distillate consisted to a large extent of octodecane.
Monochloroctodecane, C18H37C1. — The product obtained by the action
of chlorine on octodecane, collected in greater part at 185°-190°, under
15 mm., and this fraction gave as its specific gravity at 20°, 0.9041.
The percentage of chlorine corresponded to the monochloride : —
0.1482 grm. of the oil gave 0.0782 grm. AgCl.
Calculated for C18H37C1. Found.
CI 12.35 13.05
The results given above were obtained with the hydrocarbon that was
liquid at ordinary temperatures. When it was found that crystals sepa-
rated from this distillate at 3°, and that it became pasty at 0°, it was
cooled to —10°, when it became so thick it filtered only slowly. The
solid after filtering was melted and again cooled and filtered, after which
it was perfectly white. It was then crystallized from ether and alcohol,
after which it melted at 20°. It was estimated that twenty per cent of
the original oil separated as the solid hydrocarbon on cooling. It was
difficult to separate the solid completely on account of the great solvent
action of the oil.
The filtered and pressed solid melted at 20°, and after crystallization
from ether and alcohol and from gasoline, the melting point could not be
raised. Kraff t * gave 28° as the melting point of octodecane, which he
obtained from stearic acid; but his octodecane boiled at 2 14°. 5 under
50 mm. pressure. The specific gravity of the solid hydrocarbon was
* Ber. deutsch. chera. Gesellsch., XV. 1703 (1882).
vol. xxxvu. — 37
578 PROCEEDINGS OF THE AMERICAN ACADEMY.
0.7830 at §£, and 0.7816 at %. Krafft gave 0.7768 as the specific grav-
ity of C18H38 at 28°. A determination of the molecular weight of the
purified hydrocarbon confirmed its formula : —
1.1003 grm. of the oil and 19.65 grms. benzol gave a depression of 0.941.
Calculated for C18H37C1. Found.
288.5 291.5
This molecular weight, showing that the hydrocarbon boiling at 300°
is octodecane, does not agree with Krafft's conclusion as to the formula
of the hydrocarbon obtained from stearic acid. In heating stearic acid
with hydriodic acid Krafft assumed that all the oxygen is removed,
leaving intact the carbon of the carboxyl, with the formation of octo-
decane. But when this work was done the only means of verifying the
formula was by analysis, which was sufficient to determine the series,
but not the individual members of the series. While the results of
Krafft's combustions gave almost exact values for the formula C18H38, the
size of the molecule could not be determined. Krafft looked upon the
hydrocarbon boiling at 303° as having the formula Ci7H36.
The specific gravity of the oil after cooling and filtration was some-
what higher than before, 0.8110 at 20°, and higher than the specific
gravity of the filtered solid octodecane, 0.7830. The molecular weight
of the filtered oil was the same as before filtration.
0.9904 grm. of the substance and 16.10 grms. benzol gave a depression
of 1°. 184.
Calculated for C]8H38. Found.
254 254.6
A combustion of the liquid hydrocarbon showed some change in the
proportions of carbon and hydrogen : —
0.1483 grm. of the substance gave 0.4636 grm. C02 and 0.1954 grm. FLO.
Calcul
^18^30-
ated for
^18^38-
Found.
c
85.70
85.06
85.25
H
14.30
14.94
14.64
While there is a narrow difference in calculated percentages between
the two formulae, the percentages found, together with the higher specific
gravity, indicate that the filtered oil was a mixture of the two series CnHn2
and Hna
•/2n+2*
MABERY. — THE COMPOSITION OF PETROLEUM. 579
A determination of the index of refraction, which was found to be
1.4435, and the molecular refraction, correspond more nearly to the
formula C18H36 : —
Calculated for Found
82.90 84.96 82.60
A combustion of the solid hydrocarbon gave proportions required for
the series CnH2n+2 : —
0.1564 grm. of the substance gave 0.4883 grm. C02 and 0.2083 grm. H20.
Calculated for Cl8H38. Found.
C 85.06 85.15
H 14.94 14.80
The position in the series was shown by its molecular weight : —
I. 1.9475 grm. of the solid and 25.21 grms. benzol gave a rise of
0°.7734.
II. 1.9475 grm. of the solid and 25.28 grms. benzol gave a rise of
0°.7830.
Calculated for Found.
^18^38- I- !*•
254 256 253.2
The formula of octodecane was further confirmed by its index of refrac-
tion. The index was found to be, at 20°, 1.440, which corresponds to
the molecular refraction : —
Calculated for Cl8H33. Found.
84.96 84.53
NONODECANE, C19TT
lo-
in the eighth distillation under 50 mm., 335 grams collected at 210°-
212° with much smaller weights on either side. After continuing the
distillation twenty-seven times, a portion of the fraction 210°-212° was
purified with fuming sulphuric acid ; before this treatment the oil gave
as its specific gravity at 20°, 0.8274, and afterward, 0.8122. In deter-
mining its molecular weight by the freezing point method the following
values were obtained : —
580 PROCEEDINGS OF THE AMERICAN ACADEMY.
I. 1.1039 grm. of the oil and 39.7462 grms. benzol gave a depression
of0°.575.
II. 1.1418 grm. of the oil and 36.2175 grms. benzol gave a depression
of 0°.505.
Calculated for Found.
C19H,0. I. II.
268 269.5 268
Determinations of carbon and hydrogen gave values for the series
T. 0.1530 grm. of the oil gave 0.4771 grm. C02 and 0.1994 grm. H20.
II. 0.1591 grm. of the oil gave 0.4976 grm. C02 and 0.2132 grm. H20.
Calculated for
Found.
I. II.
c
85.70 85.08
85.04 85.29
H
14.30 14.92
14.48 14.89
Analysis I. was made of the oil before purification, and Analysis II.
afterward.
A determination of the index of refraction gave 1.4522, which cor-
responds to the following molecular refraction : —
Calculated for C19H40. Found.
89.55 88.68
The results on the composition of the distillate 210°-212° were ob-
tained on the purified distillate without cooling to separate the solid
hydrocarbon. On cooling a portion of this distillate to —10°, filtering
cold and pressing the solid, 5 grams of the solid hydrocarbon, and 30
grams of the liquid hydrocarbon were obtained ; the solid hydrocarbon,
therefore, formed a small part of the original distillate. The specific
gravity of the filtered oil was 0.8208 at 20°. The specific gravity of the
distillate before cooling as shown above was 0.8122 at 20°.
'After crystallization from ether and alcohol, the specific gravity of
the solid hydrocarbon was 0.7725, !£, and 0.7781 at |£.
A determination of its molecular weight gave a value required for the
hydrocarbon Ci9H40.
1.4011 grm. of the solid and 26.66 grms. benzol gave a rise of 0°.496.
Calculated for C19H40. Found.
268 271.6
MABERY. — THE COMPOSITION OP PETROLEUM. 581
The melting point of the solid was found to be 33°-34° corresponding
to the melting point, 32°, that Krafft found for the solid hydrocarbon
distilling at, 226°. 5, 50 mm.
A combustion of the oil filtered from the solid hydrocarbon gave
percentages of carbon and hydrogen required for C19H3S.
0.1495 grm. of the oil gave 0.4715 grm. C02 and 0.1928 grm. H20.
Calculated for C^H^. Found.
85.70 86.00
14.30 14.33
A determination of the molecular weight confirmed the formula: —
2.5445 grins, of the oil and 24. G3 grms. benzol gave a rise of 0°.994.
Calculated for Ci3H38. Found.
266 267
The formula was further verified by its index of refraction.
It gave the index 1.4515, corresponding to the molecular refraction : —
Calculated for C^Hjg. Found.
87.46 87.51
With the distillate 212°-214°, 50 mm., the limit is reached of the
solid hydrocarbons whose molecular weight can be determined by the
freezing point method on account of the crystallization of the hydrocar-
bon before the benzol freezes. The molecular weights of solid higher
members were determined by the boiling point method.
The results described in this paper defining the physical properties and
formulae of the hydrocarbons separated from Pennsylvania petroleum dif-
fer in several essential particulars both from the hydrocarbons obtained
by Krafft by decomposition of the monobasic acids with high molecular
weights, and those formerly reported as among the constituents of Penn-
sylvania oil. It has been shown that the hydrocarbon at 196° is undecane,
CnH24, and not dodecane as found by Pelouze and Cahours. Likewise
the hydrocarbon at 216° proved to be dodecane and not tridecane.
Since there was no method for ascertaining the molecular weights of
these bodies at the time when they were separated by Pelouze and
Cahours, and elementary analysis could only determine the series, it was
only by analogy that the homologous members of the series could be
guessed at. Since 182° was accepted at the boiling point of undecane,
naturally dodecane and tridecane should fall into the heaps at 196° and
216°.
582 PROCEEDINGS OF THE AMERICAN ACADEMY.
The boiling point of tridecane has been variously stated at 219°, 216°
and 212°-2lo°. But neither of these temperatures can be accepted as
the boiling point of tridecane since its molecular weight is fouud to be
that of the hydrocarbon boiling at 225°-22G°.
The hydrocarbon tetradecane boils at 236°-238°, the same boiling
point as was assigned to the tridecane separated by Pelouze and
Cahours, but the specific gravity of tetradecane, 0.7812 at 20° is es-
sentially lower than that found by Pelouze and Cahours, 0.809.
Pentadecane, boiling point 156°-157°, is nearly the same in boiling
point as the hydrocarbon separated by Pelouze and Cahours, boiling
point 260°, although its specific gravity, 0.7896 at 20°, is much lower
than they found, — 0.825 at 19°.
The boiling point of hexadecane is not very different from that given
by Pelouze and Cahours, but its specific gravity is considerably lower.
It does not differ in boiling point materially from hexadecane which
Krafft obtained by heating palmitic acid, nor from that of hexadecane,
boiling point 278°, obtained by Zincke from normal octyl iodide.* Since,
however, the oils obtained by freezing out the solid hydrocarbons have
specific gravities considerably higher than those of the original distillates,
and apparently belong to another series, as shown by analysis and refrac-
tion indices, it is possible that the solid hydrocarbons held in solution in
the oils have their boiling points depressed in the fractional distillation
by which they were separated from the main body of the crude oil. Still,
the molecular weights of the solid hydrocarbons correspond to definite
formulas; for instance, from the distillate 300°-301°, atmospheric pres-
sure, octodecane was separated, in a practically pure form.
The less volatile portions of Pennsylvania petroleum consist of several
series of hydrocarbons. The series CnH2ll is liquid even at low tem-
peratures, of higher specific gravity, and another is composed of solid
hydrocarbons, of the series CnH2n+2.
In a former paper f it was shown that the high values assigned by
Pelouze and Cahours as the specific gravity of the distillates separated
'by them from petroleum, indicated that their hydrocarbons were sep-
arated from Canadian petroleum. The same inference is supported by
the high specific gravity of the hydrocarbons separated by Pelouze and
Cahours boiling above 216°, as compared with the specific gravity of
the hydrocarbons separated from Pennsylvania petroleum described in
this paper.
* Ann. Chem. u. Pharm. 152, 15.
t These Proceedings, XXXII. 171.
MABERY. — THE COMPOSITION OP PETROLEUM. 583
After establishing a homologous series by analysis, evidently the only
means available for Pelouze and Cahours to determine the molecular
size of the hydrocarbons was to assume that a hydrocarbon constituted
the chief portion of any distillates that collected in unusually large
amounts, and to compute the series in unbroken order from the lower
members.
Several attempts were made to ascertain the presence of the hydro-
carbon C2oH42 ; but the distillates between the limits 215° and 225°
were small, and in none of them did the molecular weight obtained
correspond to this formula.
Heneicosane, C2iH44, and Liquid Hydrocarbon, C2iH42.
From Distillate 230° -232°, 50 mm.
Larger quantities of distillates amounting to 200 grams collected at
230°-232°, for the most part at 230°-23 1° • The specific gravity of the
unpurified distillate was 0.8321 ; after purification it gave 0.8230. A
combustion of the purified oil gave the following percentages of carbon
and hydrogen : —
0.1540 grm. of the oil gave 0.4813 grm. CO., and 0.1968 grm. H20.
Calculated for
CnILn C,,HW.
Found.
C 85.70 85.14 85.23
H 14.30 14.86 14.32
There was evidently some loss in this analysis, but the percentages
are more satisfactory for the formula C21H42. It will be shown that this
distillate was a mixture of a solid hydrocarbon with an oil of higher
specific gravity. Its molecular weight was determined at the freezing
point of benzol.
I. 1.4807 grm. of the oil and 25.9125 grms. benzol gave a depression
of 0°.949.
II. 0.6845 grm. of the oil and 19.48 grms. benzol gave a depression
of 0°.579.
Calculated for Found.
C21II4;, C21H44. I. II.
294 296 295 297.4
The index of refraction of this hydrocarbon was found to be 1.4608,
corresponding to the molecular refraction : —
584 PROCEEDINGS OP THE AMERICAN ACADEMY.
Calculated for C2IH42. Found.
96.66 96.91
The molecular weight and molecular refraction show that this dis-
tillate is composed of a twenty-one carbon hydrocarbon, and the com-
bustion and high specific gravity point to the series CnH2n.
A portion of the oil was cooled to —10°, filtered cold, the solid well
pressed in filter paper, and crystallized from ether and alcohol. The
ready solubility of these solid hydrocarbons in ether and insolubility in
alcohol afford an easy means of purification. The melting point of the
purified solid was 40°-41°.
A combustion gave the following values for carbon and hydrogen : —
0.1353 grm. of the substance gave 0.4237 grm. C02 and 0.1778 grm. H20.
Calculated for 0^11^. Found.
C 85.13 85.39
H 14.87 14.72
The filtered oil gave as its specific gravity at 20°, 0.8424. The per-
centages of carbon and hydrogen were ascertained by a combustion : —
0.1498 grm. of the oil gave 0.4724 grm. C02 and 0.1898 grm. H20.
Calculated for C21H,2. Found.
C 85.70 85.98
H 14.30 14.08
Its molecular weight was determined at the freezing point of benzol.
0.9466 grm. of the oil and 21.01 grms. of benzol gave a depression
of 0°.737.
Calculated for C21H4J. Found.
294 299
docosane, c22h46, and llquid hydrocarbon, c22h44.
From Distillate 240°-242°, 50 mm.
After the thirtieth distillation, 150 grams collected at 240°-242°,
which gave as its specific gravity before purification 0.8341. After
purification with fuming sulphuric acid its specific gravity was 0.8262.
Combustions gave the following percentages of carbon and hydrogen : —
Calculated for
Cj2H44 C22II1(..
c
85.70 85.16
H
14.30 14.84
MABERY. THE COMPOSITION OP PETROLEUM. 585
I. 0.1538 grm. of the oil gave 0.4800 grin. C02 and 0.1992 grms.
H,0.
II. 0.1560 grm. of the oil gave 0.4874 grm. C02 and 0.2024 grm.
H20.
III. 0.1362 grm. of the oil gave 0.4257 grm. C02 and 0.1788 grm.
H20.
Found.
I. II. III.
85.09 85.21 85.25
14.40 14.42 14.59
The molecular weight was determined as follows : —
I. 0.8367 grm. of the oil and 20.38 grms. benzol gave a depression of
0°.642.
II. 2.5442 grms. of the oil and 21.91 grms. benzol gave a rise in boil-
ing point of 0°.9566.
Calculated for Found.
C22IIU. I. II.
308 313.4 311.3
The index of refraction was found to be 1.454 and the molecular
refraction : —
Calculated for CKH41. Found.
101.27 100.7
The distillates in the vicinity of 240°, 50 mm., deposited no solid on
standing at ordinary temperatures, but higher fractious all deposited
solids. When cooled to 0°, the fraction 242°-254° became nearly solid.
After further cooling to —10°, the solid was filtered in a funnel sur-
rounded with salt and ice, pressed in filter paper and crystallized from
ether and alcohol. The solid melted at 43°, and further purified from
gasoline, at 44°. Krafft gave 44°. 4 as the melting point of the hydro-
carbon C22H46. Its specific gravity at 60° was found to be 0.7796. A
combustion gave proportions of carbon and hydrogen required for the
series CnH2n+2.
0.1521 grm. of the solid gave 0.4721 grm. C02 and 0.2021 grm. H20.
Calculated for
Found.
c
85.70 85.16
85.13
H
14.30 14.84
14.86
586 PROCEEDINGS OF THE AMERICAN ACADEMY.
The quantity of the hydrocarbon was not sufficient for a determina-
tion of its molecular weight.
The filtered oil gave as its specific gravity at 20°, 0.8296, a value
somewhat higher than that obtained before filtration. A combustion
gave the following percentages of carbon and hydrogen : —
0.1505 grm. of the oil gave 0.4717 grm. C02 and 0.1937 grm. H20.
0.1411 grm. of the oil gave 0.4419 grm. C02 and 0.1819 grm. H20.
Calculated for C^H^. Found.
C 85.70 85.49 85.41
H 14.30 14.31 14.32
These proportions correspond to the formula C22H44, which is supported
by the high specific gravity.
The molecular weight of the filtered oil was also determined : —
1.0713 grm. of the oil and 19.60 grms. benzol gave a depression of 0°.858.
Calculated for C22Ha. Found.
308 312
The wide difference in specific gravity between the solid and liquid
hydrocarbons at 240°-242°, 50 mm., point to different series. While
the percentages of carbon and hydrogen given by analysis could not alone
be depended on to prove the different series, the results of combustion
with specific gravity are sufficient. The differences in theoretical com-
position of the two series are 0.5 of one per cent for carbon and for
hydrogen. In combustions conducted under the most favorable condi-
tions and with the greatest care, the different series may be shown in
well purified materials. But with so many determinations, and the ex-
treme care in details of the method, while the percentages obtained are
sufficiently close to indicate the series, the results are not in all cases as
close to the calculated percentages as should be reached in the greater
. precision of a few analyses.
Tricosane, C23H48, and Liquid Hydrocarbon, C23H46.
From Distillate 258°-260°, 50 mm.
After the nineteenth distillation, 175 grams collected at 258° -2 60°,
50 mm., for the most part at 260°-261°, which deposited a considerable
quantity of solid hydrocarbon on standing. The specific gravity of the
unpurified distillate decanted from the solid was as follows : —
MABERY. — THE COMPOSITION OF PETROLEUM. 587
60°, 0.8341 70°, 0.8320 80°, 0.8310
The oil was agitated several times with concentrated sulphuric acid
until the acid was not much colored, and washed with sodic hydrate and
water, and finally with salt brine. On account of the high specific
gravity of the oil some heavy solution such as brine or calcic chloride
was necessary to separate the water and oil. The oil was dried for
examination over calcic chloride and metallic sodium.
A combustion of the oil gave the following percentages of carbon and
hydrogen : —
0.1508 grm. of the oil gave 0.4711 grms. C02 and 0.1945 grm. H20.
Calculated for
Found.
c
85.70 85.18
85.21
H
14.30 14.82
14.33
A part of the carbonic dioxide was evidently lost, but the results point
to the series CnH2n, which represents the composition of the oil, much the
larger part of the distillate.
A portion of the distillate was cooled to —10°, and filtered cold to
separate the crystalline solid. The solubility of the solid hydrocarbon
seemed to diminish rapidly with lower temperatures, consequently a
small proportion of the solid remains in the oil below — 10°. After
pressing and crystallizing from ether and alcohol, the solid melted at 45°.
Krafft's hydrocarbon, C23H48, melted at 47°. 7. Two determinations of
its specific gravity at 60° gave (1) 0.7894, (2) 0.7900.
A combustion of the solid gave results for the series CnH2n+2 : —
0.1515 grm. of the substance gave 0.4710 grm. C02 and 0.1989 grm. H20.
Calculated for C^H^. Found.
C 85.20 85.06
H 14.80 14.64
»
A determination of its molecular weight at the boiling point of benzol
was made : —
1.1208 grm. of the substance and 23.08 grms. benzol gave a rise of
0°,412.
Calculated for C^H^. Found.
324 327
588 PROCEEDINGS OF THE AMERICAN ACADEMY.
The filtered oil gave as its specific gravity at 20°, 0.8569. It gave
percentages of carbon and hydrogen required for the series CnFI2n: —
0.1504 grm. of the oil gave 0.4711 grm. C02 and 0.1945 grm. H20.
Calculated for
Found.
c
85.70 85.18
85.41
H
14.30 14.82
14.36
The molecular weight was determined at the freezing point of benzol :
3.464 grms. of the oil and 26.06 grms. benzol gave a rise of 1°.0475.
Calculated for C^H^. Found.
322 325
The index of refraction was found to be 1.4714, from which was cal-
culated the molecular refraction : —
Calculated for C23II48. Found.
105.87 105.31
TETRACOSANE, Co4H50, AND LlQUID HYDROCARBON, C24H48.
From Distillate 272°-274°, 50 mm.
After the nineteenth distillation, 150 grams collected at 272°-274°,
50 mm., that became partly solid on standing. The decanted oil gave
as its specific gravity 0.8448 at 20°. A part of the distillate was then
cooled to — 10°, and the solid filtered cold under pressure.
The distillate was purified by treatment with successive portions of
fuming sulphuric acid, until the acid was nearly colorless, then washed
with sodic hydrate and a concentrated solution of calcic chloride, and
dried over fused calcic chloride and sodium. Nearly one third of the
volume was removed in purification. The purified oil then gave as its
specific gravity at 20°, 0.8598, and at higher temperatures: —
60°, 0.8375 70°, 0.8366 80°, 0.8354
A combustion of the purified oil gave percentages of carbon and
hydrogen required for the series CnH2n.
0.1539 grm. of the oil gave 0.4769 grm. C02 and 0.2000 grm. H20.
Found.
85.35
14.54
Calculated for
C24H,8 C^H^.
c
85.70 85.21
H
14.30 14.79
MABERY. — THE COMPOSITION OF PETROLEUM. 589
These percentages evidently support the formula C24H48.
A determination of the molecular weight of the liquid hydrocarbon
gave at the boiling point of benzol a result required for C24H48.
2.0681 grms. of the oil and 25.78 grms. benzol gave a rise of 0°.G096.
Calculated for C^H^. Found.
336 337.4
The index of refraction of the oil was found to be 1.4726, from which
the following molecular refraction was calculated : —
Calculated for Co4II18. Found.
110.47 109.75
Specific gravity of the oil at |§°, 0.8582.
The solid separated by filtration melted at 48°. Krafft's hydrocarbon,
C24H48, melted at 51°. It gave as its specific gravity the following
values : —
60°, 0.7902 70°, 0.7893 80°, 0.7875
With water at 4° these results reduce to 0.7742. The specific gravity
given by Krafft to tetracosane at 4° was 0.7784, the same as that of
the solid hydrocarbon which he separated from shale oil. The solid
products from Pennsylvania oil show only slight variations in specific
gravity. But the heavy oils show a decided increase in specific gravity
with increase in molecular weight.
A combustion gave percentages of carbon and hydrogen required for
the series CnH2n+2.
0.1433 grm. of the solid gave 0.4479 grm. C02 and 0.1895 grin. H20.
Found.
C 85.70 85.23 85.25
H 14.30 14.77 14.70
The molecular weight was determined at the boiling point of benzol.
Calculated for C^H^,. Found.
338 337
To ascertain whether the solid which separated at ordinary tempera-
tures was identical with what remains in solution, a portion of the oil
Calculated for
Cnli^n. ^24^50*
85.70
85.23
14.30
14.77
590 PROCEEDINGS OF THE AMERICAN ACADEMY.
was cooled to 0°, filtered at the same temperature, and the filtrate
cooled to — 10° and filtered under pressure at the same temperature.
The three solids were carefully purified by crystallization from ether
and alcohol and their melting points taken. The solid separated at
ordinary temperatures melted at 48°, that separated at 6° melted at
51°-52°, and that separated at —10° melted at 51°-52°.
It is therefore evident that this distillate consists chiefly of one solid
hydrocarbon, Co4H50i and that the oil remaining liquid at —10° belongs
to a different series.
Pentacosane, C25H52, and Liquid Hydrocarbon, C26H52.
From Distillate 280°-282°, 50 mm.
After the fifteenth distillation, 100 grams collected at 280°-282°,
50 mm., which deposited a larger quantity of solid hydrocarbon than the
lower distillates. This solid was separated from the oil and the latter
was then cooled to 0° and filtered at the same temperature.
The specific gravity of the filtered oil at 20° was 0.8580.
A combustion gave the following values : —
0.1593 grm. of the oil gave 0.4997 grm. C02 and 0.2107 grm. H20.
Calculated for C^Hjj. Found.
C 85.70 85.55
H 14.30 14.67
The formula was established by its molecular weight, determined at
the boiling point of benzol: —
3.9867 grms. of the oil and 30.19 grms. benzol gave a rise of 0°.936.
Calculated for C^H^. Found.
364 362
A determination of the index of refraction gave 1.4725, which cor-
responded to the molecular refraction : —
Calculated for C26H52. Found.
119.87 119.12
After crystallization from ether and alcohol, from which it separated
in crystalline plates, the solid hydrocarbon gave percentages of carbon
and hydrogen required for the series CnH2n+2.
MABERY. — THE COMPOSITION OF PETROLEUM. 591
0.1534 grm. of the substance gave 0.47S7 grin. CO., and 0.2006 grin.
ILO.
Calculated for C^IIjj.
Found.
c
85. 25
85.09
H
14.75
14.53
A determination of its molecular weight verified the formula : —
1.7583 grm. of the substance, and 24.39 grms. benzol gave by the
boiling point method a rise of 0°.5231.
Calculated for C25H52. Found.
352 353.4
Melting point of the solid hydrocarbon, 53° -5 4°.
Hexacosane, C26H54, and Liquid Hydrocarbon, C27HC2.
From Distillate 292°-294°, 50 mm.
After the fifteenth distillation, 100 grams collected at 292°-294°,
50 mm., which deposited a considerable quantity of solid crystalline
hydrocarbon. These crystals were filtered, pressed, and purified by
crystallization from ether and alcohol. Melting point, 58°. The
specific gravity of this hydrocarbon was determined as follows : —
60°, 0.7977 70°, 0.7956 80°, 0.7943
A combustion of the solid gave the following percentages of carbon
and hydrogen : —
0.1508 grm. of the substance gave 0.4709 grm. C02 and 0.2033 grm.
H20.
Calculated for C^H^. Found.
C 85.24 85.17
H 14.76 14.98
The molecular weight was ascertained at the boiling point of benzol.
1.2754 grm. of the substance and 24.2827 grms. benzol gave a rise of
0°.416.
Calculated for C2SHM. Found. t
366 364
592 PROCEEDINGS OF THE AMERICAN ACADEMY.
On cooling the original distillate to —10°, it formed a thick pasty
mass. It was filtered under pressure, keeping cold. The filtered crys-
tals were pressed, and crystallized from ether and alcohol. Melting
point, 58°. The solids pressed out from the fractions from 288° to
302°, 50 mm., showed very slight variations in melting points.
288°-290°, 56°. 800°-304°, 59°-G0°.
294° -296°, 58°. 302°-304°, 59°-60°.
The oil filtered under pressure was very thick and viscous. Its
specific gravity at 20° was 0.8G88. A combustion gave the following
percentages of carbon and hydrogen : —
0.1500 grin, of the oil gave 0.4750 grm. C02 and 0.1812 grm. II20.
Calculated for C27IIC2. Found.
C 80.17 86.36
II 13.83 13.43
Its molecular weight at the boiling point of benzol corresponded to
the formula C27IIC2.
3.650G grms. of the oil and 25.80 grins, benzol gave a rise of 0°.9G4.
Calculated for C2;II52. Found.
376 376.2
The index of refraction corresponded to the same formula.
The index was found to be 1.4722, and the molecular refraction: —
Calculated fcr Cj7HM. Found.
122 121.4
OCTOCOSANE, CagHss* AND LIQUID HYDROCARBON, C28IIC4.
From Distillate 310°-312°, 50 mm.
After the tenth distillation 75 grams collected at 310°-312°, from
which a considerable quantity of crystals collected above the oil on
standing. The oil separated from the crystals was then cooled to — 10°
and filtered cold under pressure. The solid was pressed and purified
by crystallization from ether and alcohol. Meltiug poiut 60°. Its
specific gravity was determined as follows : —
*
70°, 0.7945 80°, 0.7927 90°, 0.7911
MABERY. —THE COMPOSITION OF PETROLEUM. 593
A combustion gave the following percentages of carbon and hy-
drogen : —
0.1508 grm. of the substance gave 0.4703 grm. C02 and 0.2032 grra.
H20.
Calculated for C28U"38- Found.
C 85.28 85.07
H 14.72 14.97
The molecular weight at the boiling point of benzol corresponded
to the formula C2sIl58.
3.070 grms. of the solid hydrocarbon and 26.21 grms. benzol gave a
depression of 0°.7538.
Calculated for C^llsg. Found.
394 399
The very thick oil separated by filtration gave as its specific gravity
at 20, 0.8G94. A combustion gave percentages of carbon and hydrogen
required for the series, CnII2n_2.
0.1500 grm. of the oil gave 0.4729 grm. CO, and 0.1836 grm. H.,0.
Calculated for Found.
Casing C;eII-n Cjg(lr^.
C 85.28 85.70 86.02 85.96
H 14.72 14.30 13.98 13.60
The molecular weight was found at the boiling point of benzol.
I. 2.6792 grms. of the oil and 29.85 grm. benzol gave a rise of 0°.5826.
II. 1.9196 grms. of the oil and 27.98 grm. benzol gave a rise of 0°.4459.
Calculated for Found.
C28IIr4. I II.
392 396 394.4
The index of refraction was found to be 1.480, which corresponds to
the molecular refractions : —
Calculated for C^Hsg. Found.
127 126.78
It will be observed that the two liquid hydrocarbons last described
have been shown to belong to a series CDII2a_2. Results already ob-
vol. xxxvii. — 38
594 PROCEEDINGS OP THE AMERICAN ACADEMY.
tained but not yet published indicate that the same series of hydrocar-
bons constitute the less volatile portions of Canadian petroleum, and
probably also of Ohio petroleum. Results already published show that
the less volatile distillates from California and Texas petroleum are
composed of the same series and other series still poorer in hydrogen.
The unexpected appearance of the series CnH2n_2 in Pennsylvania
petroleum suggests a closer relationship between this petroleum and the
heavier oils from other fields, such as those in Texas and California,
than was suspected. To gain further information concerning the heav-
ier portions of Pennsylvania oil, we allowed three kilos of the sample
from which the hydrocarbons described in this paper were prepared, to
evaporate spontaneously in the air in a strong draught, but with no appli-
cation of heat. At the end of thirty days there remained one kilo that
gave as its specific gravity 0.8620, practically the same as that of C28H54,
0.8G94. A combustion gave percentages of carbon and hydrogen re-
quired for the series CnH2n_2. A distillation showed that 65 per cent of
the residual oil was composed of hydrocarbons above C15H30. The com-
position of these hydrocarbons will be ascertained iu connection with the
study of natural and commercial paraffine, which is now in progress.
This interesting relation, and others between the numerous petroleums
from different oil fields that have been examined in this laboratory will
be presented more at length in a later paper.
As a general summary of the results described in this paper, hydrocar-
bons have been identified as shown in table on opposite page.
It appears that the liquid hydrocarbon C23H54 iu fraction 310°-312°
has the same number of carbon atoms as the solid hydrocarbon octocosane
in the same fraction. In this respect the hydrocarbons in this fraction
differ from those in the two preceding fractions, in each of which the
liquid hydrocarbon is one carbon higher than the solid constituent. De-
terminations of the molecular weights of hydrocarbons with high carbon
content can only be made by the boiling-point method; and even with
the greatest care in manipulation, this method is somewhat uncertain for
high molecular weights of solid hydrocarbons, for the reason that the
rise in boiling points diminishes with the increase in molecular weight.
With oils there is less difficulty. For instance, the molecular weight,
370.2, of the liquid hydrocarbon C27ll52» given on page 592, is one of
five closely concordant determinations by different persons. As an illus-
tration of the care necessary in details, heating with a lamp supplied with
gas from the laboratory mains is so irregular on account of variation in
gas pressure that the gas must be supplied from a tank under water
MABERY.
THE COMPOSITION OF PETROLEUM.
595
Name.
Tridecane
Tetradecane
Pentadecane
Hexadecane
Heptadecane
Octodecane
Nonodecane
Heneicosaue
Hydrocarbon, liquid at —10°
Docosane
Hydrocarbon, liquid at —10°
Tricosane
Hj'drocarbon. liquid at —10°
Tetracosane
Hydrocarbon, liquid at —10°
Pentacosane
Hydrocarbon, liquid at —10°
Hexacosane
Hj-drocarbon, liquid at —10°
Octocosane
Symbol.
C15H
32
^16^34
Cl7HS6
^18^38
C19H40
C2iH44
C00H44
C22H46
C23H46
^-'23"48
^24"48
^24"50
C27Hg2
^20^54
^28^54
Boiling Point.
226°
236°-288°
256°-257°
274°-275°
288°-289°
300°-301°
210°-212°, 50 mm.
2.30°-231°,
240°-242°,
258°-260°, "
272°-274°, "
280°-2.-2°,
202°-294°,
310°-312°, "
Melting Point.
10°
20°
33°-34°
40°-41°
44°
45°
4S°
53°-54°
58°
G0°
pressure. Much attention has been given to these determinations, espe-
cially by Messrs. O. J. Sieplein and R. P. Cushing.
The preparation of the distillates described in this paper was begun
December 1, 1896, by Mr. A. S. Kittelberger, who distilled 56 kilos of
Pennsylvania crude oil. The distillations were later continued by
different assistants. The following gentlemen have also aided in the
purification, examination, and analysis of these hydrocarbons: Messrs.
Shaw, Latimer, R. P. Cushing, Dr. E. J. Hudson, and O. J. Sieplein.
To the latter especially is due the analysis and identification of the
chlorine derivatives of the hydrocarbons.
Proceedings of the American Academy of Arts and Sciences.
Vol. XXXVII. No. 23. —August, 1902.
RECORDS OF MEETINGS, 1901-1902.
A TABLE OF ATOMIC WEIGHTS. By Theodore William
Richards.
REPORT OF THE COUNCIL: BIOGRAPHICAL NOTICES.
Augustus Lowell. By Percival Lowell.
Truman Henry Safford. By Arthur Searle.
Horace Elisha Scudder. By Thomas Wentworth IIigginson.
Joseph Henry Thayer. By C. H. Toy.
John Fiske. By Andrew McFarland Davis.
James Bradley Thayer. By James Barr Ames.
OFFICERS AND COMMITTEES FOR 1901-1902.
LIST OF THE FELLOWS AND FOREIGN HONORARY
MEMBERS.
STATUTES AND STANDING VOTES.
RUM FORD PREMIUM.
INDEX.
(Title Page and Table of Contents.)
RECORDS OF MEETINGS.
Nine hundred and twenty-fifth Meeting.
May 8, 1901. — Annual Meeting.
Vice-President Thayer in the chair.
The Corresponding Secretary read letters from Frank S.
Collins, accepting Fellowship; from Franklin P. Mall, ac-
knowledging his election as Associate Fellow ; from VI. Mark-
ovnikoff, thanking the Academy for its message of congratulation ;
from the Johns Hopkins University, announcing the death of Pro-
fessor Henry A. Rowland ; from the Royal Lyncean Academy,
of Rome, announcing the death of its President, Professor
Angelo Messedaglia ; from the Royal Academy of Sciences of
Turin, announcing the death of Professor Giulio Bizzozero ;
from V. Pissaroff, Vice-President of the Ural Society of Natural
Sciences of Ekaterinburg, announcing the proposed establish-
ment of an ophthalmological hospital, and asking for gifts of
works or instruments ; from Arthur MacDonald, of Washington,
regarding the establishment of a Psycho-Physical Laboratory in
the Department of the Interior ; from S. C. Mastick, secretary
of the committee on the modification of the Federal legacy tax,
announcing that the desired changes have been incorporated in
the Statutes of the United States and that the committee has
adjourned sine die.
The Chair announced the death of William Stubbs,of Oxford,
Foreign Honorary Member in Class III., Section -\.
The Corresponding Secretary presented the Annual Report of
the Council.
The Treasurer presented his annual report, of which the
following is an abstract : — -
GOO PROCEEDINGS OF THE AMERICAN ACADEMY.
General 'Fund.
Receipts.
Balance from last y*ear $259.50
Investments $5,344.80
Assessments 915.00
Admission fees 20.00
Sale of publications 101.01 6,380.81
6,640.31
Expenditures.
General expenses $2,461.49
Publishing expenses 2,438.82
Library expenses 1,922.33
Expenses of moving 5.00
$6,827.64
Balance 187.33
$6,640.31
Rumford Fund.
Receipts.
Balance from last year $1,775.93
Investments $2,640.81
Sale of publications 35.00 2,675.81
$4,451.74
Expenditures.
Researches $916.00
Medals 327.00
Publishing 266.22
Library 374.44
Miscellaneous 11.25 1,894.91
Income invested during the year and transferred
to capital account 10.75
Balance ... 2,546.08
$4,451.74
RECORDS OP MEETINGS. 601
Warkkn Fund.
Receipts.
Balance from last year $994.57
Investments 1,332.97
$2,327.54
Expenditures.
Investigations $600.00
Income invested during the year and transferred
to capital account 451.25 $1,051.25
Balance ~ '. '. . 1,276.29
$2,327.54
Building Fund.
Receipts.
Balance from last year $539.52
Investments 783.02
$1,322.54
Expenditures.
Income invested during the year and transferred
to capital account $942.50
Balance 380.04
$1,322.54
The following reports were presented : —
Report of the Rumford Committee.
At the Annual Meeting of the Academy held May 9, 1900, the
amount of $1,000 was put at the disposal of the Rumford Committee for
the furtherance of research.
From this sum grants have been made as follows : —
Oct. 10, 1900: Two hundred dollars to Dr. Charles E. Mendenhall,
of Williams College, in aid of his investigations upon a hollow
bolometer.
Oct. 10, 1900: Five hundred dollars to Professor George E. Hale,
of the Yerkes Observatory, in aid of his researches in connection with
the application of the radiometer to a study of the infra-red spectrum of
the chromosphere.
602 PROCEEDINGS OF THE AMERICAN ACADEMY.
March 13, 1901 : Three hundred dollars to Professor Arthur A.
Noyes, of the Massachusetts Institute of Technology, in aid of his research
upon the effect of high temperature on the electrical conductivity of
aqueous .salt solutions.
It was furthermore voted by the Committee at its meeting of April
12, 1901, to recommend to the Academy the appropriation of the sum of
five hundred dollar, from the income of the Rumford Fund to Professor
Theodore W. Richards of Harvard University, in aid of his research
upon the Thomson-Joule Free Expansion Experiment, which recom-
mendation was favorably acted upon by the Academy.
The Rumford Committee has given much consideration to the question
introduced by Professor E. C. Pickering, of the feasibility of co-operation
among the various committees in this country having in charge the
administration of funds devoted to research. It was voted by the Com-
mittee that the Chairman be authorized to represent the Committee in
such consideration of the subject as might be brought about. Several
entirely informal conferences have taken place among representatives of
such committees, and it is hoped that some general understanding may
be reached which will be helpful to those engaged in research.
The following recommendations have been voted by the Committee,
and are now presented to the Academy for its consideration.
Oct. 10, 1900, it was voted that the Committee recommend to the
Academy the appropriation of one hundred dollars from the income of
the Rumford Fund to aid in the cataloguing of the books in the Academy
Library.
March 13, 1901, it was voted to recommend to the Academy that a
replica in bronze of each Rumford Medal hereafter awarded by the
Academy be struck off and preserved in the Hall of the Academy.
April 12, 1901, it was voted that the Committee recommend to the
Academy the appropriation of one hundred and fifty dollars from the
income of the Rumford Fund for the purchase and binding of the usual
periodicals for the current fiscal year.
At the same meeting it was voted that the Committee recommend to
the Academy the appropriation of the sum of one hundred and fifty
dollars from the income of the Rumford Fund for the purchase and
binding of books on light and heat, said works to be purchased upon the
recommendation of the Rumford Committee.
At the same meeting it was furthermore voted that the Chairman
of the Committee recommend to the Academy the appropriation from
the income of the Rumford Fund of one thousand dollars for the
immediate needs of the Committee in the furtherance of research.
RECOUDS OF MEETINGS. 603
A wish has frequently been expressed for a complete list of persons to
whom the Rumford Premium has been awarded, and to meet this desire
such a list is appended to the present report.
Papers embodying the results of researches conducted wholly or
in part by the aid of grants from the Rumford Fund as follows
have been printed during the past year in the Proceedings of the
Academy.
" On the Thermal Diffusivities of Different Kinds of Marble," by
B. O. Peirce and R. W. Willson.
" On the Thermal and Electrical Conductivity of Soft Iron," by
Edwin H. Hall.
" False Spectra from the Rowland Concave Grating," by Theodore
Lyman.
" A Study of Growing Crystals by Instantaneous Photomicrography,"
by Theodore W. Richards and Ebenezer H. Archibald.
In accordance with a vote of the Committee passed Nov. 10, 1897, all
persons receiving grants from the Rumford Fund are expected to
present an annual report of the progress of their work. In response
to the usual request such reports have been received from the following
persons, regarding their several researches as stated below : —
Mr. Arthur L. Clark, on the molecular properties of vapors in the
neighborhood of the critical point.
Professor Henry Crew with Mr. 0. H. Basquier, on electric arc
spectra.
Professor Edwin B. Frost, on the spectroscopic determination of the
radial velocities of stars.
Professor Edwin H. Hall, on the thermal properties of iron.
Professor George E. Hale, on the application of the radiometer to
the study of the infra-red spectrum.
Professor Frank A. Laws, on the thermal conductivity of metals.
Professor Edward L. Nichols, on the visible radiation from carbon,
accompanied by a paper for presentation to the Academy embodying the
result of his researches.
Mr. C. E. Mendenhall, on the hollow bolometer.
Professor Edward C. Pickering, on the determination of the light of
very faint stars.
Professor Theodore W. Richards, on (a) the photographic study of
growing crystals; (b) the transition temperatures of salts as fixed points
in thermometry ; (c) the experimental study of the Joule-Thomson
Effect.
604 PROCEEDINGS OP THE AMERICAN ACADEMY.
Professor Wallace C. Sabine with Mr. Theodore Lyman, on the study
of false spectra from the Rowland Concave Grating.
The Committee has devoted much time to the consideration of the
desirability of an award of the Rumford Premium. The claims of
several meritorious candidates have been investigated and discussed at
length. As a result of these deliberations the Committee voted unani-
mously on Feb. 13, 1901, for the first time, and on March 13, 1901, for
the second time, that the Academy be recommended to award the Rum-
ford Premium to Elihu Thomson for his inventions in electric welding
and lighting.
Chas. R. Cross, Chairman.
Awards of the Rumford Premium.
May 28, 1839. Robert Hare, of Philadelphia, for his invention of
the compound or oxyhydrogen blowpipe.
June 1, 1862. John Ericsson, of New York, for his improvements
in the management of heat, particularly as shown in his caloric engine
of 1855.
May 30, 1865. Daniel Tread well, of Cambridge, for improve-
ments in the management of heat, embodied in his investigations and
inventions relating to the construction of cannon of large calibre, and
of great strength and endurance. Presented November 14, 1865.
June 12, 1866. Alvan Clark, of Cambridge, for his improvements in
the manufacture of refracting telescopes as exhibited in his method
of local correction. Presented February 26, 1887.
May 25, 1869. George Henry Corliss, of Providence, for his im-
provements in the steam engine. Presented January 11, 1870.
June 6, 1871. Joseph Harrison, Jr., of Philadelphia, for his mode
of constructing steam-boilers, by which great safety has been secured.
Presented January 9, 1872.
May 27, 1873. Lewis Morris Rutherfurd, of New York, for his im-
* provements in the processes and jnethods of astronomical photog-
raphy. Presented March 10, 1874.
May 25, 1875. John William Draper, of New York, for his re-
searches on radiant energy. Presented March 8, 1876.
May 25, 1880. Josiah Willard Gibbs, of New Haven, for his re-
searches in thermodynamics. Presented January 12, 1881.
May 29, 1883. Henry Augustus Rowland, of Baltimore, for his
researches in light and heat. Presented February 14, 1884.
RECORDS OF MEETINGS. 605
May 25, 1886. Samuel Pierpont Langley-, of Allegheny, for his
researches in radiant energy. Presented May 11, 1888.
May 29, 1888. Albert Abraham Michelson, of Cleveland, for his
determination of the velocity of light, for his researches upon the
motion of the luminiferous ether, and for his work on the ahsolute de-
termination of the wave-lengths of light. Presented April 10, 1889.
May 26, 1891. Edward Charles Pickering, of Cambridge, for his
work on the photometry of the stars and upon stellar spectra. Pre-
sented January 13, 1892.
May 8, 189a. Thomas Alva Edison, of Oraage, N. J., for his
investigations in electric lighting. Presented May 13, 1896.
May 11, 1898. James Edward Keeler, of Allegheny, for his applica-
tion of the spectroscope to astronomical problems, and especially for
his investigations of the proper motions of the nebulae, and the physi-
cal constitution of the rings of the planet Saturn, by the use of that
instrument. Presented June 14, 1899.
May 10, 1899. Charles Francis Brush, of Cleveland, for the prac-
tical development of electric arc lighting. Presented March 14, 1900.
May 9, 1900. Carl Barus, of Providence, for his various researches
in heat.
Report of the C M. Warren Committee.
The C. M. Warren Committee recommends to the Academy the fol-
lowing appropriations from the income of the C. M. Warren Fund : —
To Professor C. F. Mabery, Case School of Applied Science, Cleve-
land, Ohio, four hundred dollars for use in his researches on petroleum.
To Professor A. A. Noyes, Massachusetts Institute of Technology,
three hundred dollars for use in his investigation of a systematic pro-
cedure for the qualitative analysis of the rare metals.
To Professor Charles H. Herty, Athens, Georgia, one hundred and
forty-five dollars for use in his research on platinum and allied metals.
C. L. Jackson, Chairman.
Report of the Committee of Publication.
The Publishing Committee begs leave to report that there have been
issued during the last academic year five numbers of Volume XXXV. of
the Proceedings and the first twenty-eight numbers of Volume XXXVI.,
aggregating 719 pages and 11 plates. Besides this a small edition of
Volume XXXIV. was reprinted, at a cost of $180, to replace losses by
606 PROCEEDINGS OF THE AMERICAN ACADEMY.
fire in the bindery. Four numbers of the current Proceedings (62 pages
and 4 plates) were printed at the cost of the Rumford Fund ($266.22).
The total expenditure for printing falling on the General Fund was
$2438.82. The appropriation was $2400, and the. return from sales
$101.01, leaving an unexpended balance of $62.19. The Committee
recommends for the coming year an appropriation of $2400, the same as
in the last.
For the Committee,
Samuel H. Scudder, Chairman.
Report of the Committee on the Library.
The two most important matters relating to the Library have been the
installation of a steel stack for folios by the Massachusetts Historical
Society, on the same terms as the other stacks were furnished, and the
commencement of a new card catalogue of subjects and authors, for which
$200 was appropriated last year. About 1300 cards, covering nearly
the whole of the works on mathematics and astronomy, have been type-
written at a total cost of $70.62.
The reappropriation of $100 and an appropriation of $100 from the
income of the Rumford Fund is requested to continue this work and to
purchase a catalogue case.
The accessions during the year have been as follows :
Vols. Parts of toIs.
By gift and exchange .... 473 2027
By purchase — General Fund . 28 717
By purchase — Rumford Fund . 36 340
Total 537 3084
Last year the total number of accessions was 3224.
28 volumes and 717 parts of volumes were bought with the appropria-
tion from the income of the General Fund at an expense of $339.52 ;
340 parts of volumes were bought with the appropriation from the income
of the Rumford Fund for $101.48; 36 volumes of the " Fortschritte der
Physik," needed to complete the set to date, for which a special appro-
priation was made from the income of the Rumford Fund, have been
purchased at an expense of $202.66; 698 volumes were bound at an
expense of $925.41, of which $861.11 was charged to the General Fund
and $64.30 to the Rumford Fund.
• ••••••••• ••
A. Lawrence Rotch,
Librarian and Chairman of the Committee on Library.
?ams.
296
Maps.
5
Total
2798
745
376
296
5
3919
RECORDS OF MEETINGS. 607
On the recommendation of the Rumford Committee, it was
Voted, To appropriate from the income of the Rumford
Fund —
One hundred dollars ($100) to aid in the cataloguing of the
books in the Academy Library.
One hundred and fifty dollars (8150) for the purchase and
binding of periodicals.
One hundred and fifty dollars ($150) for the purchase and
binding of books on light and heat, said works to be purchased
upon the recommendation of the Rumford Committee.
One thousand dollars ($1000) for the immediate needs of the
Committee in the furtherance of research.
Voted, That a replica in bronze of each Rumford Medal here-
after awarded be struck off and preserved in the Hall of the
Academy.
Voted, To award the Rumford Premium to Elihu Thomson for
his inventions in electric welding and lighting.
On the recommendation of the C. M. Warren Committee, it was
Voted, To appropriate from the income of the C. M. Warren
Fund —
Four hundred dollars ($400) to Professor C. F. Mabery, of
Cleveland, Ohio, for use in his researches on petroleum.
Three hundred dollars ($300) to Professor A. A. Noyes, of
Boston, for use in his investigation of a systematic procedure
for the qualitative analysis of the rare metals.
One hundred and forty-five dollars ($145) to Professor Charles
H. Herty, of Athens, Georgia, for use in his research on platinum
and allied metals.
On the recommendation of the Committee on Publication,
it was
Voted, To appropriate from the income of the General Fund
twenty-four hundred dollars ($2400) for publications.
On the recommendation of the Committee on the Library,
it was
Voted, To appropriate from the income of the General Fund
one hundred dollars ($100) to continue the catalogue of the
Library and to purchase a catalogue-case.
608 PROCEEDINGS OF THE AMERICAN ACADEMY.
On the recommendation of the Committee of Finance, it was
Voted, To appropriate from the income of the General Fund
two thousand, dollars ($2000) for general expenses.
Voted, That the assessment for the ensuing year be five dollars.
On the recommendation of the committee to whom certain
alterations of the Statutes were referred at the meeting of
December 12, 1900, it was
Voted, To amend the Statutes as follows : —
Ch. I., Sec. 1, first sentence. "The Academy consists of Resident
Fellows, Associate Fellows, and Foreign Honorary Members."
Ch. I., Sec. 2. " The number of Resident Fellows shall not exceed
two hundred. Only residents in the Commonwealth of Massachusetts
shall be eligible to election as Resident Fellows, but resident fellowship
may be retained after removal from the Commonwealth. Each Resident
Fellow shall pay an admission fee of ten dollars and such annual assess-
ment, not exceeding ten dollars, as shall be voted by the Academy at each
annual meeting. Resident Fellows only may vote at the meetings of the
Academy."
Ch. I., Sec. 3. " The number of Associate Fellows shall not exceed
one hundred, of whom there shall not be more than forty in either of the
three classes of the Academy. Associate Fellows shall be chosen from
persons residing outside of the Commonwealth of Massachusetts. They
shall not be liable to the payment of any fees or annual dues, but on re-
moving within the Commonwealth they may be transferred by the Coun-
cil to resident fellowship as vacancies there occur."
Ch. I., Sec. 4. Omit " And " at the beginning of last sentence.
Ch. II., Sec. 2, first sentence. " At the Annual Meeting of 1901, nine
Councillors shall be elected by ballot, one from each class of the Academy
to serve for one year, one from each elass for two years, and one from
each class for three years ; and at annual meetings thereafter three Coun-
cillors shall be elected in the same manner, one from each class, to serve
for three years ; but the same Fellow shall not be eligible for two succes-
sive terms."
Ch. II., Sec. 2, second sentence. Change " These " to " The." At
end of this sentence add : " Five members shall constitute a quorum."
Ch. V., Sec. 5. " The Committee of Publication, of three Fellows,
one from each Class, to whom all communications submitted to the
Academy for publication shall be referred, and to whom the printing of
the Memoirs and the Proceedings shall be intrusted."
RECORDS OF MEETINGS. 609
Ch. V., Sec. 6. "The Committee on the Library, of the Librarian
ex officio, and three other Fellows, one from each Class, who shall
examine the Library and make an annual report on its condition and
management.
Ch. VI., Sec. 1. Omit the second sentence.
Ch. VI., Sec. 2, third sentence. "He shall notify the meetings of
the Academy, apprise officers and committees of their election or appoint-
ment, and inform the Treasurer of appropriations of money voted by
the Academy.''
Ch. VI., Sec. 3. " The two 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 calculated
to promote its interests.'"'
Ch. VII., Sec. 2. Omit the words " by order of the President or
presiding officer."
Ch. VII., Sec. 3. "The Treasurer shall keep separate accounts of
the income and appropriation of the Kumford Fund and of other special
funds, and report the same annually."
Ch. VII., Sec. 4. Omit the words " on such securities as the Academy
shall direct."
Ch. VIII., Sec. 1. "It shall be the duty of the Librarian to take
charge of the books, to keep a catalogue of them, to provide for the
delivery of books from the Library, and to appoint such agents for these
purposes as he may think necessary. He shall make an annual report
on the condition of the Library."
Ch. VIII., Sec. 2. "The Librarian, in conjunction with the Com-
mittee on the Library, shall have authority to expend such sums as may
be appropriated, either from the General or Special Funds of the
Academy, for the purchase of books and for defraying other necessary
expenses connected with the Library."
Ch. VIII., Sec. 3. "To all books procured from the income of the
Kumford Fund, or other.special funds, the Librarian shall cause a stamp
or label to be affixed, expressing the fact that they were so procured."
Ch. VIII., Sec. 5. Omit " And " at beginning of second sentence.
Ch. VIII., Sec. 7. "The Librarian shall have custody of the Publi-
cations of the Academy and shall distribute copies among the Associate
Fellows and Foreign Honorary Members at their request. With the
advice and consent of the President, he may effect exchanges with other
associations."
Cli. X., Sec. 2, first sentence. " Candidates for election as Resident
voi.. xxxvn. — 39
610 PROCEEDINGS OF THE AMERICAN ACADEMY.
Fellows must be proposed by two Resident Fellows of the section to
which the proposal is made, in a recommendation signed by them, and
this recommendation shall be transmitted to the Corresponding Secretary,
and by him referred to the Council for nomination."
Ch. X., Sec. 2, second sentence. Change ''seven" to " five."
Ch. X., Sec. 3. Abbreviate first sentence, as follows : "The nomina-
tion and election of Associate Fellows may take place in the manner
prescribed in reference to Resident Fellows."
Ch. X., Sec. 6. Change first word (" each ") to " a majority of any."
Under Rumford Premium, change " a gold and silver medal " to " a
gold and a silver medal."
The annual election resulted in the choice of the following
officers and committees for the academic year 1901-02 : —
Alexander Agassiz, President.
John Trowbridge, Vice-President for Class I.
Alphetjs Hyatt, Vice-President for Class II.
James B. Thayer, Vice-President for Class III.
William M. Davis, Corresponding Secretary.
William Watson, Recording Secretary.
Francis Blake, Treasurer.
A. Lawrence Rotch, Librarian.
Councillors.
Harry M. Goodwin, for one year. ^|
Charles R. Sanger, for two years. V Class I.
George F. Swain, for three years. J
George H. Parker, for one year. \
Theobald Smith, for two years. ( V Class II.
Robert DeC. Ward, for three years. J
William Everett, for one year. ^
A. Lawrence Lowell, for two years. > Class HI.
Penman W. Ross, for three years. )
Member of Committee of Finance.
Eliot C. Clarke.
RECORDS OF MEETINGS. 611
Rum ford Committee.
Erasmus D. Leavitt, Amos E. Dolbear,
Edward C. Pickering, Arthur G. Webster,
Charles R. Cross, Theodore W. Richards,
Thomas C. Mendenhall.
C. M. Warren Committee.
Charles L. Jackson, Leonard P. Kinnicutt,
Samuel Cabot, Arthur M. Comey,
Henry B. Hill, Robert H. Richards,
Henry P. Talbot.
The Chair appointed the following standing committees : —
Committee of Publication.
Samuel H. Scudder, Seth C. Chandler,
Crawford H. Toy.
Committee on the Library.
Henry W. Haynes, Samuel Henshaw.
Theodore W. Richards.
Auditing Committee.
Henry G. Denny, Wjlliam L. Richardson.
The following gentlemen were elected members of the
Academy : —
George Frisbie Hoar, of Worcester, as Resident Fellow in
Class III., Section 1 (Philosophy and Jurisprudence).
John Fritz, of Bethlehem, Pennsylvania, as Associate Fellow
in Class I., Section 4 (Technology and Engineering).
Thomas Chrowder Chamberlin, of Chicago, as Associate
Fellow in Class II., Section 1 (Geology, Mineralogy, and Physics
of the Globe), in place of the late George Mercer Dawson.
Ferdinand Freiherr von Richthofen, of Berlin, as Foreign
Honorary Member in Class II., Section 1 (Geology, Mineralogy,
and Physics of the Globe).
Adolph Engler, of Berlin, as Foreign Honorary Member in
612 PROCEEDINGS OF THE AMERICAN ACADEMY.
Class II., Section 2 (Botany), in place of the late Jacob Georg
Agardh.
Angelo Celli, of Rome, as Foreign Honorary Member in
Class II., Section 4 (Medicine and Surgery).
Gaston Paris, of Paris, as Foreign Honorary Member in
Class III., Section 4, in place of the late Charles Jacques Victor
Albert, Due de Broglie.
The Treasurer proposed an amendment to Chapter V., Sec-
tion 2, of the Statutes. This proposition was referred to a
committee consisting of the Treasurer and James B. Ames.
James B. Thayer read an obituary notice of John E. Hudson.
Clarence J. Blake read an obituary notice of his father, John
H. Blake, and F. W. Putnam gave an account of the archaeo-
logical work of Mr. Blake.
The following papers were presented by title: —
" On Ruled Loci in w-Fold Space." By Halcott C. Moreno.
Presented by W. E. Story.
" The Possible Significance of Changing Atomic Volume."
By T. W. Richards.
" The Visible Radiation from Carbon." By Edward L.
Nichols.
Contributions from the Gray Herbarium of Harvard Uni-
versity. New Series. — No. XXII. I. " The Northeastern Car-
ices of the Section Hyparrhenae ; " II. "Notes on the Varia-
tions of Certain Boreal Carices." By M. L. Fernald.
Contributions from the Cryptogamic Laboratory of Harvard
University. — XLVII. "Preliminary Diagnoses of New Species
of Laboulbeniaceae." — IV. By Roland Thaxter.
. Nine hundred and twenty-sixth Meeting.
October 9, 1901. — Stated Meeting.
The Academy met at the house of the President, Cambridge.
The President in the chair.
The Corresponding Secretary read letters from Theodore
Lyman, accepting Resident Fellowship ; from George E. Hale,
W. W. Keen, E. H. Moore, C. O. Whitman, acknowledging
election as Associate Fellows ; and from Sir Lauder Brunton,
RECORDS OF MEETINGS. 613
A. V. Dicey, A. Engler, Henry Jackson, R. Koch, Miiller-
Breslau, Gaston Paris, Poincare, Fr. Richthofen, acknowledging
election as Foreign Honorary Members. He also read letters
from the President and Fellows of Yale University, inviting
the Academy to be represented at the celebration of the two
hundredth anniversary of the founding of Yale College ; from
the Natural History Society of Nuremberg, inviting attendance
at the celebration of its one hundredth anniversary; and from
a committee of the Anthropological Section of the American
Association for the Advancement of Science, announcing that
the thirteenth session of the International Congress of Ameri-
canists would be held at New York in 1902, and inviting the
Academy to appoint a representative to the General Committee
of the Congress.
On the motion of E. S. Morse, it was
Voted, To authorize the President to appoint delegates in
response to these invitations.
The Chair announced the following deaths: —
Truman Henry Safford, of Class I., Section 1, and John Fiske,
of Class III., Section 3, Resident Fellows.
Joseph LeConte, of Class II., Section 1, Associate Fellow.
Friherre Adolf Erik Nordenskiold, of Class II., Section 1,
Felix Joseph Henri de Lacaze-Duthiers, of Class II., Section 3,
and Friedrich Herman Grimm, of Class III., Section 3, Foreign
Honorary Members.
On the motion of the Recording Secretary, it was
Voted, To meet, on adjournment, on the second Wednesday
in November.
The following gentlemen were elected members of the
Academv: —
Henry Smith Pritchett, of Boston, to be a Resident Fellow
in Class I., Section 1 (Mathematics and Astronomy).
William Townsend Porter, of Boston, to be a Resident Fellow
in Class II., Section 3 (Zoology and Physiology).
George Wharton Pepper, of Philadelphia, to be an Associate
Fellow in Class III., Section 1 (Philosophy and Jurisprudence),
in place of the late William Mitchell.
614 PROCEEDINGS OF THE AMERICAN ACADEMY.
The President made a few remarks on the condition and
prospects of the Academy.
The Rumford Medals were presented to Carl Bar us and
Elihu Thomson.
The President gave an account of the Albatross Expedition
to the Tropical Pacific.
The following paper was read by title : —
" The Algae of Jamaica," by Frank S. Collins.
Nine hundred and twenty-seventh Meeting.
November 13, 1901. — Adjourned Stated Meeting.
The Academy met at the house of James Ford Rhodes.
Vice-President J. B. Thayer in the chair.
The Corresponding Secretary read a letter from Mrs. Cooke,
presenting to the Academy a bronze bas-relief of her husband,
the late Josiah Parsons Cooke, President of the Academy.
Voted, That the Academy gratefully accept this gift and that
the Corresponding Secretary be instructed to inform Mrs.
Cooke to that effect.
A letter from the National Society of Natural and Mathemat-
ical Sciences of Cherbourg, requesting sympathetic souvenirs on
the occasion of the fiftieth anniversary of its establishment, was
referred to the Council.
Letters were also read from W. T. Porter, accepting Resident
Fellowship ; from George Wharton Pepper, acknowledging
election as Associate Fellow ; from A. Mislawsky, of Ekaterin-
burg, acknowledging the congratulations of the Academy on
the occasion of the fiftieth anniversary of his -medical service;
from the Nobel Committee of the Royal Academy of Sciences
of Sweden, soliciting suggestions for the award of the Nobel
Prize in 1902.
Percival Lowell read a biographical notice of the late
Augustus Lowell.
William Everett read an essay entitled " The Malignity of
Dante."
A paper entitled " The Parametric Representation of the
Neighborhood of a Singular Point of an Analytic Surface,'' by
C. W. M. Black, was presented by title.
RECORDS OP MEETINGS. 615
Nine hundred and twenty-eighth Meeting.
December 11, 1901.
The Academy met at the Massachusetts Institute of Tech-
nology.
The Corresponding Secretary in the chair.
In the absence of the Recording Secretary, G. F. Swain was
elected Secretary pro tempore.
The Chair announced the death of Joseph Henry Thayer,
Resident Fellow in Class III., Section 2.
The following papers were read : —
" Some Results from the Last Opposition of Mars." By Pcr-
cival Lowell.
" The Atharva Veda and its Significance for the History of
Hindu Tradition and Hindu Medicine." By Charles R. Lanman.
The following papers were presented by title : —
" The Standard of Atomic Weights." By T. W. Richards.
" Modifications of Hempel's Gas-apparatus." By T. W.
Richards.
" A New Determination of the Atomic Weight of Uranium."
By T. W. Richards and B. S. Merigold.
" The Decomposition of Mercurous Chloride by Dissolved
Chlorides : a Contribution to the Study of Concentrated Solu-
tions." By T. W. Richards and E. H. Archibald.
" Apatite from Minot, Maine." By John E. Wolff and Charles
Palache.
Nine hundred and twenty-ninth Meeting.
January 8, 1902. — Stated Meeting.
The Corresponding Secretary in the chair.
A letter was read from A. Celli, acknowledging his election
as Foreign Honorary Member ; also, a circular inviting attend-
ance at the Thirteenth Session of the International Congress of
Americanists, in New York, in October, 1902.
The Chair announced the death of Aleksandr Onufrijevic
Kovalevsky, Foreign Honorary Member in Class II., Section 3.
The following gentlemen were elected members of the
Academy : —
G16 PROCEEDINGS OF THE AMERICAN ACADEMY.
Harry Ellsworth Clifford, of Newton, to be a Resident Fellow
in Class I., Section 2 (Physics).
Theodore Hough, of Boston, to be a Resident Fellow in Class
II., Section 3 (Zoology and Physiology).
Francis Henry Williams, of Boston, to be a Resident Fellow
in Class II., Section 4 (Medicine and Surgery).
Morris Hicky Morgan, of Cambridge, to be a Resident Fellow
in Class III., Section 2 (Philology and Archaeology).
Edmund Beecher Wilson, of New York, to be an Associate
Fellow in Class II., Section 3 (Zoology and Physiology), in
place of the late George Mercer Dawson.
Julius Hann, of Vienna, to be a Foreign Honorary Member
in Class II., Section 1 (Geology, Mineralogy, and Ph}rsics of the
Globe).
Edwin Ray Lankester, of London, to be a Foreign Honorary
Member in Class II., Section 3 (Zoology and Physiology), in
place of the late Felix Joseph Henri de Lacaze-Duthiers.
Victor Alexander Haden Horsley, of London, to be a Foreign
Honorary Member in Class II., Section 4 (Medicine and Surgery).
Friedrich Delitzsch, of Berlin, to be a Foreign Honorary
Member in Class III., Section 2 (Philology and Archaeology),
in place of the late Friedrich Herman Grimm.
Samuel Rawson Gardiner, of Sevenoaks, to be a Foreign
Honorary Member in Class III., Section 3 (Political Economy
and History), in place of the late William Stubbs.
The Corresponding Secretary announced that Thomas C.
Mendenhall had removed from the Commonwealth and that his
name had again been placed in the list of Associate Fellows.
Upon the recommendation of the Council, it was
• Voted, To transfer Percival Lowell, Resident Fellow, from
Class III., Section 4, to Class I., Section I.
Upon the recommendation of the committee on amending the
Statutes, it was
Voted, To amend the first sentence of Chapter V., Section 2,
of the Statutes to read as follows : —
" The Committee of Finance, to consist of the President,
Treasurer, and one Fellow chosen by ballot, who shall have full
RECORDS OF MEETINGS. 617
control and management of the funds and trusts of the Academy,
with the power of investing or changing the investment of the
same at their discretion."
A. Lawrence Lowell read a paper entitled, " Party Votes in
Parliament, Congress, and the State Legislatures."
The following papers were presented by title : —
Contributions from the Gray Herbarium of Harvard Univer-
sity. New Series. — No. XXIII. " A Revision of the Galapagos
Flora." By B. L. Robinson.
" The Probable Source of the Heat of Chemical Combina-
tions." By Theodore William Richards.
" A Description of Crystals of Epidote from Alaska." By
Charles Palache. Presented by John E. Wolff.
John E. Wolff exhibited a specimen of apatite from Mi not,
Maine.
Nine hundred and thirtieth Meeting.
February 12, 1902.
In the absence of the regular presiding officers, the chair was
taken by Charles R. Cross.
Letters were received from Theodore Hough and Morris II.
Morgan accepting Fellowship; from Edmund B. Wilson, ac-
knowledging his election as Associate Fellow ; and from the
National Society of Natural and Mathematical Sciences of Cher-
bourg, acknowledging congratulations on the occasion of its
fiftieth anniversary.
The Chair announced the following deaths : —
Alpheus Hyatt, Vice-President for Class II.
Clarence King, Associate Fellow in Class II., Section 1.
Karl Weinhold, Foreign Honorary Member in Class III., Sec-
lion 2.
In accordance with the Statutes, the following Councillors
were appointed a committee to nominate a candidate for the
office of Vice-President for Class II. : —
Harry M. Goodwin, of Class I.
George H. Parker, of Class II.
William Everett, of Class III.
618 PROCEEDINGS OF THE AMERICAN ACADEMY.
The following communications were presented : —
" Experiments on Forms of Least Resistance to Passage
through Air." By Samuel Cabot. Remarks on this subject
were made by Messrs. Davis, Atkinson, Webster, Clayton, and
the Recording Secretary.
" What Science has not yet Accomplished in the Art of War."
By Edward Atkinson.
The following paper was presented by title : — ■
" On the Specific Heat and Heat of Vaporisation of the Paraf-
fine and Methylene Hydrocarbons." By Charles F. Mabery and
Albert H. Goldstein.
Nine hundred and thirty-first Meeting.
March 12, 1902. — Stated Meeting.
Vice-President Trowbridge in the chair.
Letters were read from Friedrich Delitzsch, S. R. Gardiner,
Julius Hann, Victor Horsley, E. Ray Lankester, acknowledging
their election as Foreign Honorary members.
The Chair announced the following deaths : —
James Bradley Thayer, Vice-President for Class II.
Samuel Rawson Gardiner, Foreign Honorary member in
Class III., Section 3.
The vacancy occasioned by the death of Alpheus Hyatt was
filled by the election of
Henry P. Walcott, Vice-President for Class II.
The following gentlemen were elected members of the
Academy : —
Heinrich Oscar Hofman, of Boston, to be a Resident Fellow
in Class I., Section 4 (Technology and Engineering).
Thomas Augustus Jaggar," Jr., of Cambridge, to be a Resident
Fellow in Class II., Section 1 (Geology, Mineralogy, and Physics
of the Globe).
Edward Henry Strobel, of Cambridge, to be a Resident
Fellow in Class III., Section 1 (Philosophy and Jurisprudence).
Herbert Putnam, of Washington, to be an Associate Fellow
in Class III., Section 4 (Literature and the Fine Arts).
RECORDS OF MEETINGS. 619
The Chair appointed the following Councillors to serve as
Nominating Committee : —
*t>
William Everett, of Class III.
George H. Parker, of Class II.
Harry M. Goodwin, of Class I.
On the motion of the Recording Secretary, it was
Voted, To rescind Standing Vote 9, "The Annual Meeting
and the other stated meetings shall be holden at eight o'clock
P. M."
The following papers were read : —
" Biographical Notice of the late Horace E. Scudder." By-
Thomas W. Higginson.
" Biographical Notice of the late Joseph H. Thayer." By
Crawford IT. Toy.
" The Formation of River Terraces." By William M. Davis.
" The Spectra of Gases at High Temperatures." By John
Trowbridge.
The following papers were presented by title : —
" Experiments on the Effect of Freezing and other Low Tem-
peratures upon the Viability of the Bacillus of Typhoid Fever,
with Considerations regarding Ice as a Vehicle of Infectious
Disease." By William Thompson Sedgwick and Charles-
Edward A. Winslow.
" Statistical Studies on the Seasonal Prevalence of Typhoid
Fever in Various Countries and its Relation to Seasonal Tem-
perature." By William Thompson Sedgwick and Charles-
Edward A. Winslow.
Nine hundred and thirty-second Meeting.
April 9, 1902. — Stated Meeting.
The Academy met at the house of Robert Amory.
The Corresponding Secretary in the chair.
The following papers were read : —
" Account of the Ninth Jubilee Celebration of the University
of Glasgow." By William G. Farlow.
620 PROCEEDINGS OF THE AMERICAN ACADEMY.
" Biographical Notice of the late John Fiske." By A. McF.
Davis.
The following paper was presented by title : —
Contributions from the Case School of Applied Science. —
XLI. " On the Hydrocarbons in Pennsylvania Petroleum with
Boiling Points above 216 °." By Charles F. Mabery.
Nine hundred and thirty-third Meeting.
May 14,1902. — Annual Meeting.
Vice-President Trowbridge in the chair.
The Corresponding Secretary read letters from Henry P.
Walcott, accepting his election as Vice-President for Class II. ;
H. E. Clifford, H. O. Hofman, T. A. Jaggar, Jr., Edward H.
Strobel, accepting Resident Fellowship ; Herbert Putnam,
acknowledging election as Associate Fellow ; Madame Cornu,
announcing the death of her husband, Alfred Cornu; the
University of Oxford, inviting the Academy to send a repre-
sentative to the commemoration of the 300th anniversary of the
opening of the Bodleian Library, on October 8 and 9, 1902 ;
the Royal University of Christiania, announcing the celebra-
tion, in September next, of the 100th anniversary of the birth
of Nicolaus Henricus Abel and inviting the attendance of dele-
gates.
On the motion of the Recording Secretaiy, it was
Voted, To appoint Herbert Putnam, Associate Fellow, to
represent the Academy at the Bodleian Library commemora-
tion.
• The annual report of the Council was read by the Corre-
sponding Secretary.
The Treasurer presented his annual report, of which the fol-
lowing is an abstract : —
RECORDS OF MEETINGS. 621
General Fund.
Receipts.
Balance (Deficit), April 30, 1901 $187.33
Assessments $990.00
Admission fees 150.00
Sale of publications 138.78 $1,278.78
Income from investments 5,735.58 7,014.36
$0,827.03
Expenditures.
General expenses $2,780.94
Publishing $2,095.59
Library 1,570.08
Catalogue 95.40 3,707.07
Balance, April 30, 1902 '. ~ . 272.42
$0,827.03
Rumford Fund.
Receipts.
Balance, April 30, 1901 $2,540.08
Income from investments $2,514.17
Sale of publications 5.00 2,519.17
$5,005.25
Expenditures.
Researches $1,800.00
Medals 474.00
Publishing . 417.51
Library 183.12
Catalogue 70.00
Miscellaneous 23.66 $2,968.29
Income invested and transferred to capital acc't, 1,715.00
Balance, April 30, 1902 381.96
$5005.25
622 PROCEEDINGS OF THE AMERICAN ACADEMY.
Warren Fund.
Receipts.
Balance, April 30, 1901 $1,276.29
Income from investments 329.43
$1,605.72
Expenditures.
Investigations $845.00
Balance, April 30, 1902 760.72
$1,605.72
Building Fund.
Receipts.
Balance, April 30, 1901 $360.04
Income from investments 309.51
$689.55
The following reports were also presented : —
Report of the Librarian.
The card-catalogue, commenced in 1900, has been continued by the
Assistant Librarian, who has type-written during the past year 2770
cards, the total number of cards now being upwards of 4000. Most of
the works on general science, mathematics, astronomy, physics, optics,
heat and electricity are now catalogued. A catalogue-case was pur-
chased for $70. Of the $200 appropriated, the total amount expended
on account of the catalogue was $164.40, of which $95.40 was charged
to the General Fund and $70 to the Rumford Fund. The same appro-
priation that was made last year is requested for continuing this work,
namely: $100 from the income of the General Fund and $100 from the
income of the Rumford Fund.
The accessions during the year have been as follows : —
Parts of
Vols. Vols. Pams. Maps. Total.
By gift and exchange .... 496 2486 384 2 3368
By purchase — General Fund . 18 665 683
By purchase — Rumford Fund . 1 256 259
Total 515 3406 Ms 4 2 4310
RECORDS OF MEETINGS. G23
Last year the total number of accessions was 3919.
At the request of the Rumford Committee, 21 volumes on light and
heat, for the purchase and binding of which $150 was appropriated from
the income of the Rumford Fund, have been ordered but not paid for.
The expenses charged to the Library were as follows : — Miscellaneous,
which includes expenses in no way relating to the Library, $439.95 ;
Binding, $604.70; Subscriptions, $532.03, making a total of $1450.38.
The usual appropriation of $1500 from the income of the General Fund
is requested in addition to the customary appropriation from the income
of the Rumford Fund, namely $150.
A. Lawrence Rotch, Librarian.
Boston, May 14, 1902.
Report of the Rumford Committee.
At the Annual Meeting of the Academy held May 8, 1901, the sum
of $1000 was placed at the disposal of the Rumford Committee, to be
expended at its discretion iu aid of researches in light and heat.
The following grants have been voted : —
Nov. 13, 1901. One hundred dollars to Professor Henry Crew of
Northwestern University, in aid of his research on the order of appear-
ance of the different lines of the spark spectrum.
Nov. 13, 1901. Three hundred and fifty dollars to Professor R. W.
Wood of Johns Hopkins University, in aid of his researches on the
anomalous dispersion of sodium vapor.
Nov. 13, 1901. Sixty-five dollars to Professor A. G. Webster of
Clark University, in payment of the cost of fluorite plates purchased for
use in a research on the distribution of energy in various spectra.
Feb. 12, 1902. Three hundred dollars to Professor Ernest F.
Nichols of Dartmouth College, for the purchase of a spectrometer in
furtherance of his research on resonance in connection with heat
radiations.
April 9, 1902. Three hundred dollars as it is or may become avail-
able to Professor Arthur A. Noyes of the Massachusetts Institute of
Technology, in aid of his research upon the effect of high temperatures
upon the electrical conductivity of aqueous solutions.
At the meeting of February 12, 1902, it was voted to authorize the
Librarian to purchase certain books upon light and heat as specified iu
a list transmitted to him by the Committee.
624 PROCEEDINGS OF THE AMERICAN ACADEMY.
The following papers, embodying the results of researches aided by
appropriations from the Rumford Fund, have been printed in Volume
XXXVII. of the Proceedings of the Academy : —
" The Visible Radiation from Carbon," by Edward L. Nichols.
" The Arc Spectrum of Hydrogen," by O. H. Basquin.
" The Probable Source of the Heat of Chemical Combination and a
New Atomic Hypothesis," by Theodore William Richards.
Reports of the progress of unfinished researches which have been
aided by grants from the Rumford Fund have been received from the
following persons: Messrs. Arthur L. Clark, Henry Crew, Edwin B.
Frost, George E. Hale, Frank A. Laws, Charles E. Mendenhall, Ernest
F. Nichols, Arthur A. Noyes, Edward C. Pickering, Theodore W. Rich-
ards, Wallace C. Sabine, R. W. Wood.
The following recommendations have been voted by the Committee,
and are now presented to the Academy for its consideration.
On February 12, 1902, it was voted to ask the Academy to appropri-
ate the sum of seven hundred and fifty dollars from the income of the
Rumford Fund to be expended for the construction of a mercurial com-
pression pump designed by Professor Theodore W. Richards, and to be
used in his research on the Thomson-Joule Effect.
At the meeting of April 9, 1902, it was voted to request the Academy
to appropriate the sum of one thousand dollars from the income of the
Rumford Fund, for the immediate needs of the Committee in further-
ance of research, and also to appropriate the sum of one hundred and
fifty dollars from the same source for the purchase and binding of
periodicals.
At the meeting of May 14, 1902, it was voted to ask the Academy to
reappropriate from the income of the Rumford Fund the unexpended
balance of the amount granted at the last annual meeting, for the pur-
chase and binding of books on light and heat for the Library.
The Committee has considered at length the question of an award of
the Rumford Premium, and at the meeting of April 9 it was unani-
mously voted for the first time, and at the meeting of May 14 it was
unanimously voted for the second time, to recommend to the Academy
that such award be made to Professor George E. Hale, Director of the
Yerkes Observatory, for his investigations in Solar and Stellar Physics,
and in particular for the invention and perfection of the Spectro-
heliograph.
Chas. R. Cross, Chairman.
RECORDS OP MEETINGS. 625
Report of the C. M. Warren Committee.
The Committee in charge of the C. M. Warren Fund has the honor
to report that Professor Mabery and Professor A. A. Noyes have
reported satisfactory progress in the work supported by grants from the
Fund. Professor Herty, owing to an unforeseen change of occupation,
is unable to continue his work on platinum, and will return the money
granted him.
The Committee recommends the following grants from the C. M.
Warren Fund for this year : — •
C. F. Mabery, of Cleveland, $300.00 for the continuation of his
researches on Petroleum.
A. A. Noyes, of Boston, $300.00 for the continuation of his work on
the qualitative analysis of the rare elements.
H. O. Hofman, of Boston, $160.00 for a research on the decomposition
of sulphate of zinc.
C. L. Jackson, Chairman.
Report of the Committee of Publication.
The Publishing Committee begs leave to report that there have been
issued during the last academic year one number of Vol. XXXVI. and
twenty-one numbers of Vol. XXXVII. of the Proceedings, aggregating
648 pages and 15 plates.
Three numbers of the current volume (82 pp. and 2 pi.) were printed
at the cost of the Rumford Fund ($417.51). The expense of printing
falling on the General Fund was $2095.59 ; the appropriation was
$2400, and the returns from sales $138.59, leaving an unexpended
balance of $443. The Committee recommends for the ensuing year the
usual appropriation of $2400. An expensive memoir, closing Vol. XII.,
is in press.
For the Committee,
Samuel II. Scudder, Chairman.
Boston, May 14, 1902.
On the recommendation of the Committee of Finance, it was
Voted, To make the following appropriations from the in-
come of the General Fund for expenditures during the ensuing
year : —
VOL. XXXVII. — 40
626 PROCEEDINGS OP THE AMERICAN ACADEMY.
For general expenses, $2400
For the library, 1500
For cataloguing, 100
For publishing, 2400
On the recommendation of the Rumford Committee, it was
Voted, To make the following appropriations from the in-
come of the Rumford Fund: One thousand dollars ($1000)
for the immediate needs of the Committee in furtherance of
research ; seven hundred and fifty dollars ($750) to be ex-
pended for the construction of a mercurial compression pump
designed by Theodore W. Richards, and to be used in his re-
search on the Thomson-Joule Effect ; one hundred and fifty
dollars ($150) for the purchase and binding of periodicals.
Voted, To re-appropriate the unexpended balance of the
amount granted at the last annual meeting for the purchase
and binding of books on light and heat for the Library.
On the recommendation of the C. M. Warren Committee, it
was
Voted, To make the following grants from the income of the
C. M. Warren Fund: (1) To C. F. Mabery of Cleveland,
three hundred dollars ($300) for the continuation of his re-
searches on petroleum. (2) To A. A. Noyes of Boston, three
hundred dollars ($300) for the continuation of his work on the
qualitative analysis of the rare elements. (3) To H. O. Hof-
man of Boston, one hundred and sixty dollars ($160) for a re-
search on the decomposition of sulphate of zinc.
On the motion of the Corresponding Secretary, it was
Voted, That the assessment for the ensuing year be five
dollars ($5).
The annual election resulted in the choice of the following
officers and committees : — ■
Alexander Agassiz, President.
John Trowbridge, Vice-President for Class I.
Henry P. Walcott, Vice-President for Glass II.
John C. Gray, Vice-President for Class III.
William M. Davis, Corresponding Secretary.
&
RECORDS OF MEETINGS. G27
Willtam Watson, Recording Secretary.
Francis Blake, Treasurer.
A. Lawrence Rotch, Librarian.
Councillors for Three Years.
Arthur G. Webster, of Class I.
Edward L. Mark, of Class II.
Arlo Bates, of Class III.
Member of Committee of Finance.
Eliot C. Clarke.
Rumford Committee.
Erasmus D. Leavitt, Amos E. Dolbear,
Edward C. Pickering, Arthur G. Webster,
Charles R. Cross, Theo. W. Richards,
Elihu Thomson.
C. M. Warren Committee.
Charles L. Jackson, Samuel Cabot,
Henry B. Hill, Leonard P. Kinnicutt,
Arthur M. Comey, Robert H. Richards,
Henry P. Talbot.
The following standing committees were appointed by the
Chair : —
Committee of Publication.
Seth C. Chandler, of Class I., Edward L. Mark, of Class 11.,
Crawford H. Toy, of Class III.
Committee on the Library.
William F. Osgood, of Class I., Samuel Henshaw, of Class II.,
Henry W. Haynes, of Class III.
Auditing Committee.
Henry G. Denny, William L. Richardson.
628 PROCEEDINGS OF THE AMERICAN ACADEMY.
The following gentlemen were elected members of the Acad-
emy : —
Arthur James Balfour, of London, to be a Foreign Honorary
Member in Class III., Section 1 (Philosophy and Jurisprudence),
in place of the late Charles Russell, Baron Russell of Killowen.
William Edward Hartpole Lecky, of London, to be a Foreign
Honorary Member in Class III., Section 3 (Political Economy
and History), in place of the late Samuel Rawson Gardiner.
On the recommendation of the Rumford Committee, it was
Voted, To award the Rumford Premium to George Ellery
Hale, of the Yerkes Observatory.
James Barr Ames read a biographical notice of the late
James Bradley Thayer.
A biographical notice of the late Alpheus Hyatt, by Alpheus
S. Packard, was read by the Corresponding Secretary.
The following papers were presented by title : -*—
" The Influence of Atmospheres of Nitrogen and Hydrogen on
the Arc Spectra of Iron, Zinc, Magnesium and Tin, compared
with the Influence of an Atmosphere of Ammonia." By Royal
A. Porter. Presented by Charles R. Cross.
" On the Multiple Points of Twisted Curves." By John N.
Van der Vries. Presented by William E. Story.
" Regular Singular Points of a System of Homogeneous Linear
Differential Equations of the First Order." By Otto Dunkel.
Presented by Maxime BOcher.
Contributions from the Cryptogamic Laboratory of Harvard
University. — L. "Preliminary Diagnoses of New Species of
Laboulbeniaceae." — V. By Roland Thaxter.
Contributions from the Cryptogamic Laboratory of Harvard
University. — LI. "On Cauloglossum transversarium (Bosc)
Fries." By J. R. Johnston. Presented by Roland Thaxter.
" On the Ionization of Soils." Bv Anion Benton Plowman.
J
Presented by George Lincoln Good ale.
Contributions from the Gray Herbarium of Harvard Uni-
versity. New Series. — XXV. I. " Flora of Cocos Island of the
Pacific. " II. " Diagnoses and Synonymy of some Mexican
Spermatophytes." By B. L. Robinson.
REC0RD3 OP MEETINGS. 629
" On the Dibromdinitrobenzols derived from Paradibrom-
benzol." Second paper. By C. Loring Jackson and D. F. Cal-
hane.
" On the Colored Substances derived from Nitro-compounds."
Fourth paper. By C. Loring Jackson and R. B. Earle.
" On Certain Derivatives of Picric Acid." By C. Loring Jack-
son and R. B. Earle.
" On Symmetrical Dinitrobenzolsulphonic Acid." By C.
Loring Jackson and R. B. Earle.
" On Certain Derivatives of 1, 2, 3-tribrombenzol!" By C.
Loring Jackson and A. H. Fiske.
630
PROCEEDINGS OF THE AMERICAN ACADEMY.
A TABLE OF ATOMIC WEIGHTS
of Seventy-seven Elements.
Compiled in April, 1902, //om the most Recent Data.
By Theodore William Richards.
Name.
Symbol.
Atomic
Weight.
Name.
Symbol.
Atomic
Weight.
Aluminium . .
Al
27.1
Molybdenum . .
Mo
96.0
Antimony .
Sb
120.0
Neodymium
Nd
143.6
Argon .
A
39.92
Neon . .
Ne
19.94
Arsenic . .
As
75.0
Nickel . .
Ni
58.71
Barium . .
Ba
137.43
Niobium .
Nb = CI)
94.
Beryllium .
Be = Gl
9.1
Nitrogen .
N
14.04
Bismuth
Bi
208.
Osmium
Os
190.8
Boron . .
B
11.0
Oxygen (stanc
lar
a)
O
16.000
Bromine .
Br
79.955
Palladium .
Pd
106.5
Cadmium .
Cd
112.3
Phosphorus .
P
31.0
Caesium
Cs
132.88
Platinum .
Pt
195.2
Calcium
Ca
40.13
Potassium .
K
39.14
Carbon . .
C
12.001
Praseodymiur
n
Pr
140.5
Cerium . .
Ce
140.
Rhodium .
Rh
103.0
Chlorine .
CI
35.455
Rubidium .
Rb
85.44
Chromium
Cr
52.14
Ruthenium
Ru
101.7
Cobalt . .
Co
59.00
Samarium ?
Sm
150.
Columbium
Cb = Nb
94.
Scandium .
Sc
44.
Copper . .
Cu
63.60
Selenium .
Se
79.2
" Didymium '
Nd + Pr
142.±
Silicon . .
Si
28.4
Erbium . .
Er
166.
Silver . .
Ag
107.93
Fluorine
F
19.05
Sodium . .
Na
23.05
Gadolinium
Gd
156. ?
Strontium .
Sr
87.68
Gallium
Ga
70.0
Sulphur
S
32.065
Germanium
Ge
72.5
Tantalum .
Ta
183.
Glucinum .
Gl=Be
9.1
Tellurium .
Te
127.5 ?
Gold . . .
Au
197.3
Terbium ? .
Tb
160.
Helium .
He
3.96
Thallium .
Tl
204.15
Hydrogen .
H
1.0076
Thorium 1 .
Th
233. ?
Indium . .
In
114.
Thulium ? .
Tu
171. ?
Iodine . . .
I
126.85
Tin . . .
Sn
119.0
Iridium . .
Ir
193.0
Titanium .
Ti
48.17
Iron . . .
Fe
55.88
Tungsten .
W
184.
Krypton
Kr
81.7
Uranium .
U
238.5
Lanthanum
La
138.5
Vanadium .
V
51.4
Lead . .
Pb
206.92
Xenon . .
X
128.
Lithium
Li
7.03
Ytterbium .
Yb
173.
Magnesium
Mg
24.36
Yttrium
Yt
89.0
.Manganese
Mn
55.02
Zinc . . .
Zn
65.40
Mercury .
Hg
200.0
Zirconium .
Zr
90.6
RICHARDS. A TABLE OF ATOMIC WEIGHTS. 631
NOTE.
The accompanying table of atomic weights is but little changed since last year.
Caesium is made 132.88 instead of 132.9; calcium, 40.13 instead of 40.1 ; iron, 55.88
instead of 55.9; hydrogen, 1.0076 instead of 1.0075; and nickel, 58.71 instead of
56.70. The value for caesium is due to some work, as yet unpublished, of Richards
and Archibald, and that for calcium is increased in accuracy because the recent
investigation of Hinrichsen* supports the less recent Harvard value. t The other
very small changes are due simply to slight differences in the interpretation of
data already well known. The decimal might have been omitted from palladium,
because this element ma}' still be a whole unit in doubt ; but it has been retained
as a compromise.
The differences between the present table, that of the German Committee,! and
that of F. W. Clarke, § are diminishing year by year. Nevertheless to as many as
twenty-eight elements out of the seventy-seven are given values in these three
tables differing among themselves by over one tenth of a per cent; namely, the
atomic weights of antimony, bismuth, cerium, columbium, fluorine, gadolinium,
germanium, helium, hydrogen, lanthanum, magnesium, mercury, neon, osmium,
palladium, platinum, potassium, samarium, scandium, selenium, tantalum, tellurium,
thorium, thulium, tin, titanium, uranium, and zirconium. To this list of uncertain
elements should be added erbium, gallium, glucinum, indium, terbium, tungsten,
ytterbium, upon which the three tables agree only because of lack of data upon
which to base a disagreement. Thus nearly half of the elements are still in doubt
by at least one part in a thousand. This circumstance is not so much a reproof to
the many earnest workers upon the subject, as an evidence of the great difficulty
of some of the problems involved.
Three of the elements given in the list above should not properly be included
among the uncertain values, namely, hydrogen, magnesium, and potassium. The
first finds its way into the list because of the disregard of significant figures by the
German Committee, and the second chiefly because Clarke has included in his
calculation work upon magnesic oxide undoubtedly erroneous on account of the
presence of included gases. || The case of potassium is somewhat peculiar; for
in spite of the great wealth of data concerning this element, Clarke assigns to it
the value 39.11, while the German Committee chooses 39.15. The low value is
chiefly due to very unsatisfactory data concerning potassic iodide. To me it seems
that the most recent work of Stas is far more satisfactory than his earlier work or
than the work of any one else, hence the value 39.14 has been assigned to potassium
in the present table since its first publication. Careful analyses by E. H. Archi-
bald and myself confirm this conclusion.
* Hinrichsen, Zeitschr. phys. Chem., 39, 311 (1901).
t Richards, Journ. Am. Chem. Soc, 22, 72 (1900), also 24, 374 (1902):
J Landolt, Ostwald, and Seubert, Extra insertion in Berichte d. d. ch. Ges. 1902.
Heft 1.
§ F. W. Clarke, Journ. Am. Chem. Soc, 24, 201 (1902).
|| Richards and Rogers, These Proceedings, 28, 209 (1893).
AMERICAN ACADEMY OF ARTS AND SCIENCES.
Report op tiie Council. — Presented May 14, 1902.
BIOGRAPHICAL NOTICES.
Augustus Lowell Percival Lowell.
Truman Henry Safford
Horace Elisha Scudder
Joseph Henry Thayer .
John Fiske
James Bradley Thayer
Arthur Searle.
Thomas Wentworth Higginson.
C. H. Toy.
Andrew McFarland Davis.
James Barr Ames.
REPORT OF THE COUNCIL.
The Academy has lost sixteen members by death since the
annual meeting of May 8, 1901 : Six Resident Fellows, — John
Fiske, Alpheus Hyatt, Truman Henry Safford, Horace Elisha
Scudder, James Bradley Thayer, Joseph Henry Thayer ; two
Associate Fellows, — Clarence King, Joseph LeConte ; eight
Foreign Honorary Members, — Marie Alfred Cornu, Samuel
Rawson Gardiner, Friedrich Herman Grimm, William Edward
Hearn, Aleksandr Onufrijevic Kovalevsky, Felix Joseph Henri
de Lacaze-Duthiers, Friherre Adolf Erik Nordenskib'ld, Karl
Weinhold.
AUGUSTUS LOWELL.
Augustus Lowell was born in Boston, Jan. 15, 1830. His
father was John Ainory Lowell and his mother Elizabeth (Putnam)
Lowell, daughter of Hon. Samuel Putnam of Salem. Both the Lowell
and the Putnam families were early settlers in the new world, the former
landing in Newburyport in 1639, the latter in Salem in 1630. Mr.
Lowell thus came of Puritan stock on both sides. Otherwise the parts
of his inheritance differed, for the Lowells were Norman by descent — the
name, originally Lowle, dating from the conquest — while the Putnams,
originally Putteuham, were apparently Saxon. He inherited the quali-
ties of his name. Mentally he was the son of his father ; as a matter of
fancy as much as of fact, his mother's share in him being chiefly physical.
For while in feature he looked like her, in mind he not only resembled
his father but looked up to him with a very unusual amount of reverence
and esteem. The feeling doubtless was born of the fact and is note-
worthy because of the common belief that capable men have had capable
mothers. Yet not only in his case but in the case of his father, grand-
father, and great-grandfather before him, the capacity followed the name.
Indeed the family has proved a singular instance of prepotence in the
male line, while the temperament has been as strikingly a maternal gift.
GC6 AUGUSTUS LOWELL.
In Boston and in its immediate neighborhood his boyhood was spent.
Of the winter delights of town as seen through youthful eyes we are
given a glimpse in a letter written at the time to his friend, Mr. Augustus
Peabody. Chief among them it would seem was coasting on the Common,
and in the epistle we are informed of the existence of two coasts there:
" one the big boys' coast and the other the small boys' coast ; " " but,"
the writer adds to fire the ambition of his friend and so induce him to
come up for a visit, " the big boys do coast on the small boys' coast and
the small boys do coast on the big boys' coast." The rounded accuracy
of this statement, devoid of even the least suspicion of the elliptical,
testifies conclusively to the writer's time of life.
His father had inherited the family country place in Roxbury, which
then was country indeed, innocent of bricks and mortar, of city streets and
of course of railroads. Horses and carriages made sole means of outside
communication. Partly from necessity, therefore, partly for pleasure,
Mr. John Amory Lowell every day drove into town to his business and
with him he took his son to attend the Boston Latin School. This school,
so named from teaching " small latin and less greek," was then the popu-
lar school for boys of the place. To it in consequence went many well-
known men, among them his lifelong friends, Mr. George A. Gardner
and Mr. Thornton K. Lothrop. The " small latin " was, hardly such in
quantity, if one may judge by report of the approved Latin grammar of
the day. Indeed education would seem to have consisted of the learning
by heart — pathetically so called in such connection — of a mass of rules
and their elephantine exceptions, sufficient to stagger even a Roman into
speaking something else. At all events, of the sou's labors at that insti-
tution of learning the sole document extant is of the Incus a non kind : a
petition to his Honor the Mayor and Chairman of the School Committee
to allow the boys the first day of May as a holiday in which they might
" enjoy the beauties of nature and a recreation and relaxation from school
labors." Mr. Lowell appears heading the interesting document, which
was couched as convincingly as possible by a classmate.
By nature the place in Roxbury was beautiful, though one would never
divine it to-day. Shorn of its fine old trees, even pared of its hills, the
land is possessed now by a brewery and tenement houses. But in those
days it was otherwise, as fading photographs show, and its garden was
both a delight and a name. For Mr. John Amory Lowell had two pas-
times, algebra and botany. His spare moments were devoted to one or
the other of these pet pursuits. When he was not setting himself prob-
lems he was puttering over plants. And he did both to some effect.
AUGUSTUS LOWELL. Go7
His algebraic propensities won him local reputation as a mathematician,
and a manuscript volume upon the same, still in the family's possession,
is both curious and interesting reading. As a botanist he was known not
only at home but abroad, and was on terms of correspondence, not to say
criticism, with botanists of his day. His botanical care was not confined
to the living ; in his studies he collected a line herbarium which received
fully as much of his attention, and attracted attention from others. The
son inherited both paternal proclivities, but both rather as deep-seated
mental characteristics than as current mental traits. Mathematics he
neither cared for, nor was proficient in, but he derived from his father
that logical exactness of mind which is their basis. The botany bore
greater fruit. His tastes for plants, including both trees and flowers,
proved a very deep-seated passion. Doubtless fostered in part by his
father's familiarity with shrubs — though as a boy he showed no marked
symptoms of botanic zeal — the love of growing things later became his
most pronounced avocation.
In 1846 Mr. Lowell entered Harvard College where he spent the four
years enjoined for a degree and was duly graduated in 1850. It was not
then more than it is now the fashion to study, and he took his parchment
void of invidious distinction. Indeed his recollections do not seem to
have been specially academic, as one of the most vivid of them had to do
with a certain midnight ride for illicit purposes to the Watertowu arsenal.
His rank in his class, if I am right, was sixteenth, just below what was
at the time the <J>BK line. He was not therefore a member of that de-
servedly distinguished society of learning, but it is significant of his sub-
sequent standing in the community that on the fiftieth anniversary of his
graduation he was elected into it as an honorary member, an honor he
never lived to receive or even know of, as unknown to the election
committee he was on his deathbed at the time.
In college he was neither dissipated nor lazy. His course was much
like that of all his fellows, and is distinguished from the commonplace
only by a comical dream with which his ancestors saw fit to favor him
later on the subject. I say his ancestors advisedly as will shortly appear,
and I repeat the dream partly because of its touch of humor, of which he
was always fond, and partly because of its psychologic import. The gusto
with which he related it at the time proves the censure implied to have
been undeserved, but the atavism betrayed by it makes it worth recording.
It was the family tradition that at college its scions should be students,
a traditional devoir handed down from father to son, though I am not
aware that the fathers always followed it themselves as religiously as
638 AUGUSTUS LOWELL.
they inculcated it upon the sons. In consequence of his supposed neg-
lect of this precept, it was perhaps not unnatural that his ancestors should
disapprove and should show their disapproval. This they did in the only
way in their power — by means of a dream. For dreams are really
reversions to type and are in consequence very interesting things. When
we dream it is the atavic paths of which we are conscious. We think
again the thoughts of our progenitors.
The occasion of this visitation was the going up of his second son for
the entrance examinations, and the paternal mind was naturally full of
the subject. With the unimpeachable authority of dreams he was sud-
denly made aware one night that he had not done all he might in college.
Profoundly stirred by the thought, the singleness of which made it pass
for truth, he decided after due and weighty consideration — lasting at
least a tenth of a second — to enter the university once more and go
over the course again. The fact that he was middle-aged, married, and
had a large family only made the resolve seem, after the manner of
dreams, the more meritorious. On the strength of his already holding
a degree, the college faculty consented to admit him without examination.
He was thus enabled triumphantly to get in. His action caused some
comment, chiefly commendatory, such as follows an unusually pious deed.
He thus became, against his will, something of a cynosure. So the first
year glided by till with a speed peculiarly their own the annual examina-
tions were upon him and with them the eyes of the community. Then,
and somehow not till then, did he realize, to his consternation, that he had
done nothing and was quite unprepared to pass. The situation was
beyond words. At this awful moment he woke, — to the pleasing con-
sciousness that his son, not he, would have to pass them on the morrow.
Just before his graduation in 1850 his father, who was not very well,
decided to go abroad with his family, including his son Augustus, in the
event of needing his help. Mr. Lowell stayed with his father till the
spring of 1851. In Paris he was joined by his friend and classmate, Mr.
Lincoln Baylies, and there at the same time was John Felton, brother of
the* then president of the college, with whom the two young men fore-
gathered. John Felton was something of a character and a good deal of
a man, with fiery red hair on the outside of his head and much genial wit
and wisdom within it. Under his guidance, philosophy, and friendship
the two young men passed an interesting and not unprofitable winter,
frequenting the theatres to pick up French. Labiche was then in his
prime. In the spring the two classmates went off to travel in Germany
and Switzerland, and returned by themselves in the autumn to the
United States.
AUGUSTUS LOWELL. G39
On getting home he began his career in State Street, going into the
counting-room of Bui lard & Lee, East Indian merchants, to learn the
business. His quickuess of body as well as of mind here procured him
a questionable distinction. From his father he had inherited consider-
able athletic ability, and it was soon discovered in the office that he was
fleet of foot. In consequence he was promoted to the post of messenger,
with the duty of carrying the foreign business letters to the mail. Now
Mr. Lee was addicted to lengthy epistles, to extreme peculiarity in com-
pleting them, and to never finishing on time. As the mail was incon-
siderate of their importance, he eagerly embraced Lowell's pedestrian
possibilities. In consequence it soon became the regular thing for young
Lowell to be seen standing, watch in hand, waiting while Mr. Lee com-
pleted his last page, folded the foolscap down methodically with his
large thumb, and elaborately sealed it. Meanwhile the minutes slipped
by with the young man calculating if he still had time to catch the post.
It was midsummer and hot. Nevertheless the human Mercury was kept
standing within, regardless of how its metallic namesake stood without.
Finally when only running at his topmost speed would suffice to get the
letter in he would hint that there were but six minutes more before the
mail closed. " How many did you make it in last time, Augustus? " Mr.
Lee would ask. " Five and three-quarters, sir, but I had to get it in the
back way." " I think you can do it this time then." And he did.
This little episode occurred as regularly as mail day. After it had
been cheerfully going on for some months, Mr. Bullard, who had been
abroad, came home and one afternoon happened in on it. lie said
nothing at the time ; but when Lowell, hot and breathless, had returned
once more successful he called him into his private office. " Does what
I saw this afternoon occur often, Lowell ? " he said to him. '• Every
mail day, sir," the young man answered. "It shall not occur again," he
said. And it never did. With tact equal to his considerateness, Mr.
Bullard, on the ground — if I am right — of preferring to do it him-
self, from that day took the foreign correspondence into his own hands.
Perhaps — after Balzac's phrase — this episode may be put between
leads and given the air of a thought : the young man who goes quickly
will go far.
After two years spent with Bullard & Lee Mr. Lowell's father
thought it advisable the young man should learn another line of business,
— one in which the family was interested. Francis C. Lowell, the elder,
who was the founder of the cotton manufactures of New England and
after whom Lowell — their chief seat — was named, was the uncle of Mr.
G40 AUGUSTUS LOWELL.
Lowell's father. In consequence the father had come himself into con-
nection with them, and it seemed well that the son should do likewise.
He was therefore sent to Lowell to become practically acquainted with
the running of the mills. The house in which he boarded was kept
by a woman who was destined through her own exertions to no little
notoriety later on. She had a sister who had a beautiful voice. This
voice was one of the few alleviations of the place to the boarders, aud
the same voice, more ably than considerately exploited by the boarding-
house keeper, proved the family's making. For the boarding-house
keeper was so successful in her management that she soon became the
proprietress of the Revere House in Boston, and next emerged by the
help of the voice at her entertainments into one of the chief lights of
Newport and New York society. Such in a nutshell was the career of
Mrs. Paran Stevens.
After passing a year at the mills, Mr. Lowell in 1853 became engaged
to and in 1854 married Katharine Bigelnw Lawrence, the youngest
daughter of the Hon. Abbott Lawrence, then recently returned from his
post at the Court of St. James. Mr. Lawrence was as closely identified
with the then nascent cotton manufactures of New England as was Mr.
John Amory Lowell. Mr. Augustus Lowell thus found himself doubly
involved in them, first by birth and then by marriage. For the two
centres of the industry were the towns of Lowell and Lawrence, the one
named as I have said after his father's uncle, the other after his father-
in-law. On his engagement Mr. Lawrence put him in with J. M. Beebe,
Morgan & Co. Thus for the years preceding and following his marriage
he was busy learning the details of what was to make Massachusetts'
mercantile greatness, her manufacturing interests. With one exception,
from this period to the end of his life, he was always associated in one
way or another with the Lowell and Lawrence mills. He was succes-
sively treasurer, that is, the executive head, of more than one of them,
and president of many others.
The exception occurred some time after Mr. Lawrence's death, which
happened in 1855, when Mr. Lowell entered into business ventures of
his own, forming a partnership with Mr. Franklin H. Story for the pur-
pose of engaging in the East Indian trade. For some years this trade
was profitable, but the firm was brought to a close by the panic of 1857,
for though the firm did not suffer the East Indian trade did. The friend-
ship remained, and among the pleasantest incidents of the writer's boyhood
was the acquaintance of this genial gentleman. By a coincidence he
died only about a week before his former partner.
AUGUSTUS LOWELL. G41
In 1864 the health of his wife necessitated his taking her and his
family abroad. They sailed for England in May, and for the next two
years and a half lived in Europe; the summers spent in travelling, the
winters in Paris. To one so temperamentally prone to a busy life at
home, this existence was no sinecure. With a wife at the point of death
as it was thought and four young children, Mr. Lowell had his hands
full. For a long time Mrs. Lowell did not gain at all. Indeed it was
only during the second summer, under the treatment of a country doctor
fortuitously encountered in the Austrian Tyrol, that she began to mend.
It is instructive, if tardy, to perceive now, in view of the widespread
professional ignorance on the subject, that what Mrs. Lowell was suffer-
ing from was nervous exhaustion, — a disease, this, which it may be
noted incidentally, Faraday, Darwin, Huxley, and Parkman all suffered
from without knowing it.
Three little episodes may serve to mark these years of a search after
health. The first summer the wanderers happened to be at Bonchurch
in the Isle of Wight when the action between the " Kearsarge " and the
" Alabama" took place just across the channel off the coast of France. In
the second they were among the first to go to that nook in the Austrian
Salzkammergut, the village of Ischl, since become well known and popu-
lar. In the third and last they were lodged at Schwalbach near Wies-
baden, when that little watering place suddenly became one of the seats
of war, and thereupon was occupied alternately by the two opposing
forces, the invading Prussians and the native Hessians. Usually evacu-
ation considerately took place before occupation set in ; but once by acci-
dent the two interfered and a battle occurred between the rear guard of
the one army and the advance scouts of the other under the very windows
of the hotel. The Hessians, who had been quartered in the town, had
heard of the proposed Prussian advance and had at once started to
evacuate the place. But they were a little too Teutonically slow. The
invaders, although Prussians and landwehr at that, were, quite to their
own surprise, too quick for them; a belated squad of Hessians had got
only halfway up the hill on its way out when the Prussian cavalry was
heard cantering into the town. There was no time to go on unseen
when fortunately a friendly wood pile by the side of the road offered its
shelter.^ Instantly the squad deployed behind it and waited. Five min-
utes later three cavalrymen cantered past the hotel, their pistols pointed
at the windows as they went by, and started unsuspiciously up the hill.
The spectators in the secret stood waiting the surprise. Just as the
dragoons got abreast of the wood pile the squad deployed out and fired.
vol. xxxvn. — 41
642 AUGUSTUS LOWELL.
One dragoon fell on the spot, a second turned like a flash and leaped his
horse over an embankment twenty feet to a road below, while the third
wheeled in his tracks and came galloping wildly down the street again.
All which served to relieve the watering place dulness.
By the autumn of 1866 Mrs. Lowell was so far recovered that Mr.
Lowell was able to return with her to the United States. It was many
years before he left it again.
He now took an office next his father's, and became gradually con-
nected, on the one hand, with the manufacturing interests which his
father controlled, and on the other with the many trusts his father
managed. During Mr. John Amory Lowell's subsequent absences in
Europe the care of these things devolved upon his son, and with the
former's increasing years the care became more and more permanent.
In 1875 he was chosen treasurer of the Boott Cotton Mills. This office
he held for eleven years. About the same time he was elected to suc-
ceed his father on the board of the Massachusetts Hospital Life Insur-
ance Company, — familiarly known as the Life Office, State Street's oldest,
staidest, and most famous institution, whose real business has but a bowing
acquaintance with its name, — and later was put upon its executive com-
mittee. Of the corporation of the Provident Institution for Savings,
— another financial landmark, not so deceptively named to the uninitiated,
— he was likewise made a member, and eventually became its president,
succeeding the Mr. Lee of epistolary fame. At this date too he began
his long career upon the board of the Boston Gas Light Company, then
so ably managed by Mr. Greenough, a career which ended more than
twenty years later in the negotiations he conducted as its president when
it became necessary to sell the property, which he did for two and a
quarter times all it had ever cost. In addition to holding the offices above
mentioned he was treasurer of the Merrimack Manufacturing Company,
-Tune 20-October 29, 1877 ; president of the Massachusetts Cotton
Mills ; of the Massachusetts Mills in Georgia ; of the Pacific Mills ; of
the Merrimac Manufacturing Company, 1887-8, 1892 to death; of the
Boott 'Cotton Mills; of the Lowell Bleachery ; of the Lowell Machine
Shop ; of the Glendon Iron Company ; and a director of the Everett
Mills ; of the Middlesex Company ; of the Lawrence Mills ; of the
Lowell Manufacturing Company ; of the Suffolk National Bank ; of the
Cranberry Iron Company; of the Plymouth Cordage Company; besides
being a trustee of the Union Trust Company of New York. This long
list means even more than it usually would ; for Mr. Lowell was a director
who did direct. In every concern into which he entered he very soon took
AUGUSTUS LOWELL. 643
a leading part. Never seeking a place, his ability was such that he found
liimself forced into position after position of responsibility. Indomitable,
he was always selected to do what others agreed ought to be done but
were averse to doing. For Mr. Lowell knew no such thing as shirking:
in the discharge of duty. He disliked the disagreeable as much as any
one, but he was not weak. Of the financial position he held in the
down-town community it is enough commentary that seven bonds of
treasurers of great corporations were found in his tins at his death,
deposited with him as president.
Such were the business concerns with which he was connected. But
side by side with them he gave much time and thought to matters of
more public interest. For many years he was a trustee of the Boston
Eye and Ear Infirmary. Not simply one in name, for to him and to
Mr. Brown its management was for a long time chiefly due.
Ex-officio he was a trustee of the Boston Art Museum for twenty
years, and a trustee of the Lowell Textile School for the four years pre-
ceding his death. Of purely public functions he once performed one, that
of member of the Boston School Committee in 1857-58, and from the
echoes of this which have reached the writer it would seem that politics
played as objectionable a part in what should have been above them then
as now.
Before going abroad he had had a summer place at Beverly, but attrib-
uting the loss of a child there to unhealthiness of the shore he sold it.
On coming home he cast about for a country-place where he could live
the year round, as being alike beneficial for his wife and his children.
He found it in Brookline. His children were still young, and he took to
repeating the experience of his own boyhood, driving them and himself
into town every day to school and to business respectively. Out of it,
beyond business hours, his life was now quite bucolic. The place he had
bought possessed already a fine garden and two greenhouses. Iu them
he centred his affections, greenhouse and garden dividing the year
between them. Two hot-houses of grapes helped to shield the latter,
which lay in a hollow open to the south. Natural embankments enclosed
it on the east and west, and a raised roadway, shut off from view, made
artificial protection on the north. Clipped evergreens stood for sentinels
along a terraced path, ending in an arbor which fringed one side of it, and
a corresponding row faced them upon the slope opposite. In this shel-
tered spot he spent much of his time. Pruning his shrubs, tying up his
plants, and attending generally to the welfare of his flowers, he was
almost as much of an inhabitant of the place as they. It was a world iu
044 AUGUSTUS LOWELL.
which he found infinite satisfaction. His roses were his chief delight.
And fine they were — no finer than the feeling with which he showed
them off. But nothing vegetal was alien to him. He would point out
with almost as much zest, punctuated by a wink, a foreign thorn-tree,
which flanked the avenue, a platted mass of thorns a foot long, the
despair of squirrels and cats.
His botany was of the old-fashioned kind. He did not pursue it as a
science, but cultivated it as an art. His plants were rather pets than
subjects for vivisection. Philosophically he was not concerned with their
genealogy or relationship and disbelieved Darwinism to the day of his
death. But in his intercourse with them he knew the life and the merits
or demerits of each, and took pleasure in their thriving with something
like affectionate interest. He behaved like a distant relative, the while
stoutly denying that he was one. Indeed the relation did not seem so
very distant, for he was never tired of attending to them, and took a
paternal pride in their introduction to others. He would conduct you to
view some bush at the moment in flower, and point out in what lay its
peculiar praiseworthiness with the care of long acquaintance. Pretty
much every tree upon his place — and it included some rare ones — was
personally known to him. And if you strolled round with him he would
talk fine print about each with you. He was constantly importing new
plants and then watching them succeed. Though he made no parade of
knowledge or of success, he not infrequently had plants which knew no
rival in the neighborhood. A contrast this side of his life made with
that of his morning down-town, where he played so prominent a part in
the active affairs of men.
The long list of business offices held by him might lead one to infer
that his time in the city must have been fully occupied by them alone.
But he was much too busy a man for such to be the case. With all his
industrial and financial concerns he found time for an equal employment
in educational affairs. His ability was of the executive kind, which was
as vital to the one as to the other. It thus came about that side by side
with his business, and almost hand in hand with it, so practical was he
in his workings, went another employment — usually only on speaking
terms with the first, and then those of a beggar — the conduct of educa-
tional concerns. Busy as Mr. Lowell was with purely business affairs,
he was equally engaged in matters of mind. Partly the accident of
birth, partly the possession of ability, placed him in positions of authority
in two important educational institutions : the Lowell Institute in the
first place, and the Massachusetts Institute of Technology in the second.
AUGUSTUS LOWELL. Q-^
Of the first of these he became the trustee in 1881, on the death of his
father. Even before this, however, much of the work had fallen to him.
The Lowell Institute is too well known to need description, but one
phase of it will bear mention in connection with the man who for so long
was its trustee. Most institutions of learning live by begging. If they
happen to be possessed of presidents who are past masters in the art,
they thrive ; if not so blessed, they languish. That a president should
be an able intellectual director is unfortunately not so pressing a demand
as that he should be a persistent, importunate, and successful beggar. In
view of this fact deficits in college finances have lost their terror and
surpluses are unknown, a sympathetic public being with confidence relied
on to stand in the gap. Now the peculiarity of the Lowell Institute has
been not only that it is not dependent upon alms-giving hut that it has
thriven and grown without it. Although on the one hand it has paid
larger salaries than any college or kindred institution to the teacher, it
has asked no fee whatever of the taught. Yet despite this liberality on
both sides, its funds have more than quadrupled in amount. Part of this
increase has been due to the wise terms of the endowment, part to the
like wisdom of the two successive trustees. Kindred wisdom it has been
in both senses, for by a provision of the testator the trustee must be of
the testator's family if a fit person exist of the name. How fit Mr.
Lowell was for the post this able result of his administration of the
finances attests.
But besides being its financial head, Mr. Lowell was its intellectual
body and its executive arm as well. For the Institute is a one man
power, an absolute dictatorship. Mr. Lowell was president, corporation,
and treasurer all together. And the success he made of it shows again
the wisdom of such a rule, provided only the ruler be fit. Of his capacity
as financier the property speaks ; of his ability in general administration
the list of lecturers before the institution sufficiently betokens. At the
time the Institute was founded lectures were a popular form of instruc-
tion, and the object of the testator was to secure for the people of Boston
lectures by the most eminent men at home and abroad, and to give these
to the public free of charge. His wish has been well carried out. On
the roster of the books are to be found a, majority of the names which
are known the world over, and almost every one of those to whose pos-
sessors distance or age or language did not prove an impassable bar.
America, Europe, even Asia have contributed to the list. Some of these
men came more than once ; and many of them became well known per-
sonally to Americans. But the fact conuected with them which speaks
£4:6 AUGUSTUS LOWELL.
most for the institution and its trustee is that well-nigh without exception
each came originally at his instigation. Almost all the famous foreigners
in science, literature, or art who have been in this country have owed
their personal introduction to it to the trustee of the Lowell Institute.
Since from over seas these lecturers came, simply as a bond between
countries the Institute has played no unimportant part.
Mr. Lowell's tie to science was thus rather indirect than direct, but it
was none the less intimate if in a different way. By virtue of his office
he was brought personally in contact with the scientists of his day, and in
a most pleasant and withal domestic manner. For besides meeting them
at the lectures, of which he always attended the opening one and oftener
than not the whole course, he was in the habit of entertaining the lee-
turers during their stay in Boston at his house at dinner, sometimes more
than once. Many is the memorable evening he passed in consequence
with men who have made the world what it is. Such personal knowledge
of a man is as invaluable as it is invigorating. Even in an estimate of
the mind a side light of no mean value is shed on it by intercourse with
the personality. The man proves a footnote to his own writings. This
advantage of glosses on the text Mr. Lowell possessed ; and in various
aspects in as much as he was thrown with these men in diverse relations.
Intercourse of the sort he enjoyed more or less for nearly half a century.
For, as I have said, before he became trustee he had been acting for his
father, and even before that had met the lecturers at his father's house.
During the second half of the nineteenth century he had thus been
familiar, not only with the century's best thought, but with most of its
best thinkers. And he passed away just as the century itself was
drawing to a el'ose.
Coincident with holding this responsible post in educational matters of
a general character Mr. Lowell filled a second position of a more direct
kind and not less important. For quite as long :i term as he managed
the Lowell Institute was he associated with the government of the
Massachusetts Institute of Technology. Entering the corporation of
that institution in the early seventies, he very soon took a leading part
in its policy. From that time the conduct of its affairs had been inti-
mately connected with him, much more so than the public is cognizant
of. For Mr. Lowell never put himself forward, having an innate aver-
sion to unnecessary publicity. Even on the few occasions when it was
indispensable for him to appear, he only did so, as those in his confidence
are aware, after great reluctance.
Mr. Lowell was identified with this phenomenally successful institution
AUGUSTUS LOWELL. 047
almost from its start. The Massachusetts Institute of Technology was
fouuded in 1861, chiefly through the instrumentality of Prof. William B.
Rogers. To the same eminent mind it owed its early success. Measure
of the man's executive ability in the first place, its success was in the,
long run the sign of his forethought in founding it. A scfiool of technol-
ogy was exactly what the American genius had demanded for many years
in vain. It seems strange that no one should have heeded this unmis-
takable cry of nature before; but men are prone to being thus strangely
deaf, till an interpreter arises. For a century the American has been
noted for his innate inventiveness and general ingenuity, and has been
equally noted for the untrained character of his craft. In some things
this did well enough, but in the higher branches it left a good deal to be
desired. To supplement natural aptitude with proper training was thus
the one thing needful. To think of it was so simple a matter as to
require a master mind for the thought. It was a piece of educational
acumen of the highest order. And it has borne its inevitable result.
But though it was destined to great and permanent success it would be
contrary to common sense to suppose that the move was fully appre-
ciated, from the very start. On the contrary, had it not been for its
founder the institution would probably have gone under.
After Mr. Rogers' death much came to devolve upon Mr. Lowell ; and
since then, that is for the last quarter of a century, the policy of the
Institute has been intimately associated with him. Elected a member of
the corporation in 1873, he was chosen a member of the executive com-
mittee in 1883, and was kept upon it to the day of his death. During
his term of service were chosen four presidents, and I need only mention
the name of General F. A. Walker, who was the longest incumbent, to
suggest how wisely made these choices were. But the work of the
committee did not end with the selection of the executive ; as its name
implies, it was itself a part of that executive and its function was con-
tinual. As the senior member of the committee Mr. Lowell's force was
felt in every portion of the policy pursued. Not a measure was passed
which had not been influenced by his opinion. His judicious advice was
fully appreciated by General Walker. Indeed the two men were natural
complements to each other, General Walker with his brilliant, engaging
personality, and Mr. Lowell with his uncommon judgment and invincihle
determination.
The position taken by the Institute under this leadership is well known.
The institution has quadrupled in size, and what is far more important,
has more than quadrupled in prestige. It is recognized to-day not only
648 AUGUSTUS LOWELL.
as the first, but as easily the first, school of technical arts in this country.
To it now flock students from the farthest portions of these United
States: from Oregon aud Texas, from Illinois and Ohio, as well as
from New York and Massachusetts. And as graduates they go back
again to help develop the country. If any such institution may
fairly be called national the Massachusetts Institute of Technology is
the one.
Nor is this all. Not confined to the limits of this continent, its fame
has successfully invaded lands across the sea. It is not long since Sir
Robert Ball informed the writer that it was in advance of anything of
the kind iu Great Britain ; a belief which he had years before acted on
by sending his sou to it, who is now practising in England. The belief
would seem to be spreading; for in June, 1901, examinations for admis-
sion to it were held in London. Its rank would seem even to be recog-
nized at home, which means that it probably is of some importance, as
the American believes firmly in the ignota pro magnifico. The post-
graduate course, pursued by the ranking men of the U. S. Naval
Academy at foreign institutes heretofore, is in future to be taken at the
Institute. It has been the custom of the Academy since 1883 to send
the first few scholars of the highest grade, the construction department,
abroad to finish their education. At first it was Greenwich they went
to, till the British Government ludicrously enough became sensitive to
the cadets outstripping their own students and forbade them. Then the
Navy sent men to the University of Glasgow, and lastly to the Ecole
Poly technique in Paris, where the recent ones have all graduated. In
future it will be in Boston. Evidently the United States Government is
convinced of the primacy of the Institute.
What Mr. Lowell's share in this success was may best be gathered
from an episode which occurred about a twelvemonth before his death.
Feeling himself worn by a painful trouble which he had had for years,
he was minded in a moment of acute access of it to give up active work.
Accordingly he sent in his resignation to his colleagues of the corpora-
tion. They refused to accept it, and the committee did their best to
persuade him to reconsider his determination; but in vain. AVhereupon
a memorial was drawn up, signed by every member of the corporation
accessible at the time, protesting against his resignation, and begging him
not to withdraw his services from the institution. Such unanimous spon-
taneity of appreciation in a body of forty odd members is not common.
That he was profoundly touched by this mark of confidence and esteem
needs no saying.
AUGUSTUS LOWELL. G4U
Of the American Academy of Arts and Sciences he was made a mein-
her in 1886. He was first the treasurer and then the vice-president. On
the death of Professor Cooke, deeming it fitting that the post of presi-
dent should be filled by a man of science, he secured the election of
Agassiz. When the change into sections was made he became the vice-
president of his section, — jurisprudence and literature. He was also a
member of the American Association for the Advancement of Science from
1898; of the Massachusetts Historical Society in 1900; of the Colonial
Society of Massachusetts from 1898. He died on June 22, 1901.
Such, in brief, was what Mr. Lowell did. Quite as important is what
he was. For the man was always behind his measures, as the whole in-
cludes the part. His actions were but parcel of himself. Not always is
this the case. Some men become noteworthy for what they do, while
being notorious for what they are. But with him the act was outcome
of the man. He said what he meant and meant what he said. In this
unity lay one element of his force. To those with whom he came in con-
tact this oneness with one's self made itself felt. To the world at large,
which sees the works but not the workings, his hand in matters which he
had brought about often escaped notice. For a certain ingrained aver-
sion to publicity prevented him from putting himself forward. Nothing,
however, restrained him from pushing his measures. In consequence,
many as were the acts one can point to in his unusually active life, those
which actuated others without appearing themselves were more; in con-
sequence also, the world remained in ignorance of the motive cause. For
he acted for results ; and what is to take effect does not need to make it.
Effect indeed was the very opposite of what Mr. Lowell was in
thought or word or deed ; and very refreshing it is, like a cool breath of
pure air in the artificial heat and closeness of a crowded room, to consider
such a character in these days of blatant, forth-putting mediocrity.
When to seem is at a premium, and to be at a discount, it is invigorating
to turn to a life which owed nothing to adventitious or meritricious aid;
a life which not only was fine, but escaped the soiling consequent upon
too much mental fingering by the world at large. To be generally in
evidence means a loss of that delicacy of distinction, if it means nothing
more, which is for so much in beauty of character. But it means usually
very much more ; it leads inevitably to a substitution of superficiality for
solidity, of appearance for reality, of a sinking to a level of one's audience
instead of a rising superior to applause. To say that a man owed nothing
to effect is to say of him the best that can possibly be said. The natural
forces with which we daily come in contact owe nothing to such cause;
650 AUGUSTUS LOWELL.
on the contrary they stir us all the deeper, if we stop to think, for the
very fact that they do not stir us without such thought. We are im-
pressed the more by what seems superior to the impression it makes.
There is, too, another merit in the absence of effect — a gain in effec-
tiveness. It is the greatest compliment to a man's ability that he should
succeed without seeming to do so, because it shows that all his force has
been massed upon the one strategic point. We are all familiar with this
when it is done of intent aforethought.
As potent is the principle when the self-effacement is unconscious.
The one obliteration differs from the other only in being instinctive in-
stead of being thought out ; and the one is as telling as the other. How-
ever it be brought about, the fact that the self is effaced is proof that the
work has been done well. For it shows that the result has been brought
to pass with the least expenditure of force. Personality causes friction,
and evidence of self is therefore proof that force has been uselessly em-
ployed. The fact that a man has succeeded in having his idea prevail
without forcing himself along with it is sign of the best kind of work.
Now this was the case with Mr. Lowell. It was so because of an un-
usual combination of characteristics, a singular wedding of energy in deed
with dislike of its external trappings.
To an exceptional extent, therefore, Mr. Lowell's distinction lay in
character. Three qualities he possessed to an unusual degree, qualities
each rare enough as it is : will, ability, and integrity. He was, in the first
place, a combination of force and ability as simple and as uncommon as
success, which is its immediate consequence. The one is but the neces-
sary premiss to the other's conclusion. If a man be originally possessed
of the first he is sure eventually to possess the second. Schopenhauer's
definition of the world as all will and representation certainly holds of
one part of it, — the affairs of men. If the affairs consist rather in the
dealing with men than nature the representation takes the form of words,
and may be paraphrased as first the skill to put a thing convincingly
and then the will to put it through. Mr. Lowell combined the two
qualities.
Will he possessed to the full. He was noted for his determination.
To his lot, in consequence, fell many necessary and thankless tasks. He
likewise escaped many empty honors. For where he went he worked.
No one ever thought of preferring him to a post merely honoris causa.
For people knew that in getting him they eot not a figure-head, but a man
who was certain to make himself felt; not because he tried to do so, but
because it was in him to do it. He entered concerns not by the postern
AUGUSTUS LOWELL. 651
gate of popularity, but by the portal of inevitableness. He was chosen
because he was necessary. And he stayed for the same reason.
Now will is pure force, uucomplexioned, the mere dynamic outcome of
the idea. Its effectiveness to any particular end depends, therefore, upon
the character of the idea whose explosive force it is. With Mr. Lowell
the idea owed its carrying power to two characteristics : judiciousness in
itself and judiciousness in its presentation. In the first place he was apt
to be right, that is, to be wise. His judgment of things within his own
field was excellent. It was essentially sound. His was that uncommon
sense-possession, the possession of common sense. Instinctively his mind
worked correctly. It was the exact opposite of the mind of the crank,
which may often hit off a brilliant conception, but which is too unsafe to
be trusted. With him no one idea ever usurped the right of way to the
exclusion of others. Each had its due effect; which fundamental balance
makes the only safe foundation for superstructure.
In the next place he was as shrewd as he was sound. He had a keen-
ness for the essential point which almost assured success in advance. In-
sisting upon what was vital, he waved less important issues to the other
side. In this consists the consummation of the art of commerce with
one's kind. An instance of the combined breadth and shrewdness of his
business insight occurs to my mind. "When I lease a building," he once
said to me, " I ask a good price of the tenant and then do all the little
repairs he wants. The price makes its impression but once; the perqui-
sites repeatedly, and the latter impressions stand nearer to the falling due
of the lease."
Backing up his judgment was his excellence of exposition. His ideas
were the more telling for being well told. His words were few and to
the point. In a twinkling he would dissect a situation, and with equal
terseness suggest its remedy. With ability for audience this had imme-
diate effect; with mediocrity it was rather his tact that told. His logic
was too accurate for popular approval, which prefers the coloring of
emotion to the lines of thought. For very few men care for truth as
they care for their feelings. And Mr. Lowell's forte was not the silver
tongue of eloquence, but the more golden gift of statement, lie could
put a point so that it pierced perception instantly.
Lastly, there was about his advocacy of his measures an impersonality
as potently as it was subtly persuasive. It was not that the ideas them-
selves were what one would call impersonal, but that the idea appeared
by itself with so little of that aura of the personal, which in human affairs
the man unconsciously throws around it, as to appear to stand alone. For
652 AUGUSTUS LOWELL.
in Mr. Lowell's case it was as if he were but the mouthpiece of the idea,
so heartily did he identify himself with it, and yet so single was his intent.
It was the idea he thought of, not of himself. Such a condition tends in
a twofold way to conviction ; first, by the sincerity of the pleading, and
secondly, by the absence so far as is humanly possible, of the antagonism
roused by personality.
Recognition of his ability followed any knowledge of him ; it did not,
as with some men, precede it. Those qualities compounded of sociability
and forth-puttingness, however unintentional, which make for instant dis-
tinction among one's fellows, were not his by nature. His abilities were
solid, not showy. Nor was it his bent to go out of his way in the road
we all travel to make a new path. He neither courted position nor
shirked it. When it once fell to him he became as it were the office.
Nothing was ever done by him for his own sake, however incidentally.
He seemed simply to embody his trust. In intent he was singularly
single. Indeed, in describing his action I find it difficult to convey the
combination of self-obliteration and of self-sufficiency in its best sense,
which he was. For the character is uncommon. One often witnesses
self-abnegation. But it is usually wedded to weakness. Or, on the other
hand, one sees strength associated with self-seeking. Few men are essen-
tially impersonal enough to strive strenuously for the thing in itself, as if
it were a person. He did.
This was perhaps the stranger that his mental makeup was not of the
abstract but of the distinctly concrete kind. In practical, not in theoreti-
cal matters, he was great. Widely read as he was he never seemed to
care to theorize. He enjoyed highly the theories of others, when they
did not collide with the puritanism which, as I have said, he inherited
doubly distilled. Even this was perhaps as much due to the society in
which he had been brought up. He was educated before the modern
movement in thought took place, and Boston of sixty years ago was even
behind the rest of the world in this stirring of the waters of stagnation.
Not in knowledge nor in intellect ; it was in cast of mind he differed. His
preference W*as for action. Of this he never tired. To recreation he was
less {riven. Such as he took was of a serious kind. He was a member
of the Wednesday Evening Club, of the Thursday Evening Club, and of
a class dinner club ; but clubs which consist but of a local habitation and
a name he never cared to join. Loafing and he were strangers.
Will and the power of representation were, as I have said, two of his
attributes. But the second of these should, though it often does not,
include a quality which is itself fundamental to all character, and which
AUGUSTUS LOWELL. 653
Mr. Lowell possessed to the utmost — the quality of honesty. In these
days, when successful financial operations so often depend upon will and
misrepresentation, it is no small thing to say of a successful man of affairs
that lie was conspicuously honest. When to steal enough is to steal with
credit, it is cheering to see business triumph attendant on unimpeachable
integrity. And this was typically true of him. Honest he was by
essence. Verity was of the very fibre of his being.
Nor is it only of the grosser form of that attribute which has usurped
the generic name of honesty of which I would speak, but of that finer
sense of fair dealing which we include under the appellation of a just
man. His uprightness was perfectly well known. No adversary ever
questioned that. A tribute to the fact once came in an amusing manner
to Mr. Lowell's ears in one of the latter years of his life. He was pass-
ing through a railway station in Boston one afternoon when he chanced
to overhear two men unknown to him discussing his character. It was
his own name that caught his attention. " Augustus Lowell," said one,
" is a hard man, but he is absolutely honest." " Yes," said the other,
"he is emphatically that." It is not often that one overhears a bit of
one's own obituary during one's life, nor is made privy to concurrent
testimony on the subject from both sides of a discussion. As to the
hardness imputed to him, it had no foundation in fact, though it was often
attributed to him by people who knew him only from the outside. A
cast of countenance which looked stern when in repose, and which was
purely a matter of feature, was chiefly responsible for the reputation.
He was quite aware of the look himself, as well as of that to which it
was due. As a matter of fact he was very tender-hearted, singularly so
for a man of his determination. Few suspected him of the kindnesses he
was constantly doing, so unostentatiously were they performed, and
almost no one credited him with the affection he felt.
The complexion of his character — for will is an uncomplexioned
force — may be described in one word: exactness. Accuracy of state-
ment and honesty of purpose are both but facets of a crystallization of
thought. A man who sees clearly must be honest by instinct if he be
not dishonest by intent. There is with him no limbo of self-deception.
Much of the untruth current in the world is due to an initial haziness
of conception subsequently seized upon and distorted to its own ends by
passion, without disquiet to the perpetrator, because unrecognized as
distortion by him. Mr. Lowell was essentially exact. His nature
therefore imposed honesty. He saw much too correctly either to jumble
or to juggle with his thoughts.
654 TRUMAN HENRY SAFFORD.
Important as the qualities he possessed are to the making of a man,
they are no less so to the making of a community. And in any consti-
tutional country no small part of the value of a man lies in his value
as a citizen. Indirect as well as direct his influence may be, and with
universal suffrage the former is apt to be the case with the best men.
To be determined, discerning, and honest does not, unfortunately, in our
system of supposed political equality, lead to purely civic distinction.
For the choice of a popular suffrage cannot rise above its source. But
if the qualities do not lead to civic distinction for their possessor they do
something as enduring, — they tend to raise to his level the community
of which he forms a part. For without the first attribute, nothing is
possible; without the second, foolishness; without the third, knavery.
The apathy of most of us, the crankiness of a few, and the financial
trickery of others, are the several results of the absence of these qualities.
Too strong a personality to be generally popular, recognition of such
a character is slow. For we are all prone to praise what we like. Only
when distance does away with personal perspective do men, like hills,
reveal their height.
Posterity gives the final judgment. For posterity judges of a man's
worth unhaloed by the engaging lack of it, and sets the seal of its appre-
ciation upon those who have contributed to the world's advance and
incidentally to posterity's own existence. To make for this advance is
the best any man can do, and to this end to be determined, discerning,
and honest is one of the surest means. If a man possess these attributes
he will not have lived in vain.
Percival Lowell.
TRUMAN HENRY SAFFORD.
Truman Henry Safford was born January 6, 1836, at Royalton,
Vermont. The course of his life was determined by a phenomenal ca-
pacity for the mental solution of arithmetical problems, which began to
display itself when he was only six years old. This faculty, which might
under easily conceivable circumstances have been wasted in mere display
for the amusement of the curious, fortunately attracted the attention of
judicious and eminent men, and thus secured for him the advantages of
a thorough education. He graduated at Harvard College in the class
of 1854, which he joined at the beginning of its Junior year. As a boy
he had computed an almanac, and given other evidences of interest in
astronomy, and capacity for it ; and immediately after his graduation he
TRUMAN HENRY SAFFORD. <555
obtained employment at Harvard College Observatory, where he con-
tinued for nearly twelve years. He married Elizabeth M. Bradbury, of
Cambridge, in March, I860, ''on six hundred dollars a year," as he
once told the writer of this notice; for astronomy has never been a prom-
ising road to riches for young Americans insufficiently endowed with the
practical turn of mind generally regarded as characteristic of their coun-
trymen. He was elected Fellow of the Academy, Nov. 13, 1861.
Safford's position at Cambridge, if not pecuniarily advantageous,
offered him in some other respects greater advantages than, perhaps, he
could secure in later life; for lie had here comparatively few hindrances
to the undisturbed development of his scientific abilities. Accordingly,
the results of his work soon began to make him widely and favorably
known in astronomical circles. One of the most generally interesting of
these investigations related to the orbital movement of Sirius. Many
years before, the observed want of uniformity in the proper motion of
this star had led astronomers to the belief that it formed one of a system
of bodies revolving about a common centre of gravity ; its companion, or
companions, as the case might be, being too faint to he visible, at least
with the existing instrumental means. Still more recently, the character
of the supposed revolution of Sirius had been discussed by means of its
right ascensions, as observed at different times. Safford now undertook
a similar discussion of its observed declinations, and after combining the
result of this work with that previously found, on the supposition that
only one disturbing body occasioned the observed effects, was able to
indicate its direction from Sirius at the time, in excellent agreement with
the actual place of the companion discovered almost simultaneously by
the younger Alvau Clark.
A catalogue of the declinations of five hundred and thirty-two stars,
intended for use in the government survey of the lake region, was pre-
pared by Safford during his connection with Harvard College Observa-
tory, and probably marks the beginning of the geodetic work which
occupied a large part of his time iu later years.
In 18G3 he received the formal title of Assistant Observer; and two
years later, upon the death of Professor G. P. Bond, he was placed in
charge of the Observatory. At this time, he completed and prepared for
publication Professor Bond's researches on the nebula of Orion, which
appeared as Volume V. of the Observatory Annals. Volume IV. of the
same series is also the work of Safford. The first part, dealing with the
preparation of a list of fundamental stars for transit observations, was
published in 1863. By means of these fundamental stars, the right as-
65Q TRUMAN HENRY SAPFORD.
censions of five hundred and five stars were determined by observations
in the years 1862 to 1865 ; the second part of the volume, containing the
result of this work, appeared in 1878.
In 1866 Safford was appointed director of the Dearborn Observatory
at Chicago, which had recently been provided with the large refracting
telescope, by means of which, while still in its maker's hands, the com-
panion of Sirius had been discovered. This position, with which was
connected a professorship of astronomy in the University, seemed to offer
the fairest prospect of permanent and congenial employment to its occu-
pant ; but the disastrous fire which destroyed so large a part of Chicago
in 1871 deprived the Observatory of the financial support upon which its
activity depended. Professor Safford, accordingly, now found it neces-
sary to maintain his family by geodetic work connected with the govern-
ment surveys. He had undertaken the observation of one of the zones
of stars distributed among various observatories under the general system
arranged by the Astronomische Gesellschaft ; but this, and other pieces
of work begun at Chicago, were now necessarily laid aside.
In 1876, however, Professor Safford was restored to his favorite pur-
suits by appointment to the chair of astronomy at Williams College. In
this position, teaching required much of his time, and of course largely
impeded his attention to scientific investigation ; he also acted as libra-
rian of the College, and was at times engaged in other business con-
nected with its administration. It is not probable that he felt the work
of instruction to be a burden ; on the contrary, he took great interest
in the subject of pedagogy, which he studied theoretically as well as
practically. Notwithstanding all hindrances to the pursuit of strictly
astronomical research, he accomplished much in that direction during
the years spent at Williamstown, devoting himself largely, as before, to
the subject of accuracy in the determinations of the positions of fixed
stars. One of the principal results of this work was the publication
(in the Proceedings of this Academy, Volume XIX.) of a catalogue of
the mean riffht ascensions of one hundred and thirty-three stars near the
north pole ; but many other articles in scientific periodicals, particularly
the Monthly Notices of the Royal Astronomical Society, attest Professor
Satford's perseverance and success in scientific work during his later
years.
He died June 13, 1901, at Newark, New Jersey, where he was resid-
ing at the time with one of his sons. A stroke of paralysis, three years
previously, had put an end to his activity in science. His widow, with
four sons and a daughter, survives him.
Arthur Searle.
HORACE ELISHA SCUDDER. 657
HORACE ELISHA SCUDDER.
It is a merit of the American Academy of Arts and Sciences that it
does not limit itself to one form of intellectual pursuits, as do the merely
historical or scientific societies or even some which share the name of
Academy. It also has the merit that it is ready to recognize the various
subdivisions of each pursuit, and has a place of honor for every such
department. Intellectual self-respect is to be found only iu honoring
every form of work in its place. It has been generally felt, I think,
that no disrespect was shown to our late associate, John Fiske, when the
New York Nation headed its very discriminating sketch of him with the
title " John Fiske, Popularizer ;" and in speaking of another late associate
who has left us, I should feel that I showed no discourtesy, but on the
contrary, did him honor in describing him as Horace Elisha Scudder,
Literary Workman. I know of no other man in America, perhaps, who
so well deserved that honorable name ; no one, that is, who if he had a
difficult piece of literary work to do could be so absolutely relied upon to
do it carefully and well. Whatever it was, compiling, editing, arranging,
translating, indexing, — his work was uniformly well done. Whether
this is the highest form of literary distinction is not now the question.
What other distinction he might have won if he had shown less of
modesty or self-restraint, we can never know. It is certain that his few
thoroughly original volumes show something beyond what is described in
the limited term, workmanship. But that he brought simple workman-
ship up into the realm of art is as certain as that we may call the
cabinet-maker of the middle ages an artist.
Mr. Scudder was born in Boston on October 16, 1838, the son of
Charles and Sarah Lathrop (Coit) Scudder ; was a graduate of Williams
College and after graduation went to New York, where he remained for
three years engaged iu teaching. It was there that he wrote his first
stories for children, entitled " Seven Little People and Their Friends "
(New York, 1862). After his father's death he returned to Boston and
thenceforward devoted himself almost wholly to literary pursuits ; pre-
pared the " Life and Letters of David Coit Scudder" his brother, a mis-
sionary to India (New York, 1864) ; edited the " Riverside Magazine"
for young people during its four years' existence (from 1867 to 1870) ;
and published " Dream Children " and " Stories from My Attic."
Becoming associated with Houghton, Mifflin and Company he edited for
vol. xxxvn. — 42
658 HORACE ELISHA SCUDDER.
them the Atlantic Monthly Magazine from 1890 to 1898, preparing for it
also that invaluable index, so important to bibliographers ; he also edited
the "American Commonwealth" series, and two detached volumes,
"American Poems" (1879) and "American Prose'' (1880). Repub-
lished also the " Bodley Books " (8 vols. Boston, 1875 to 1887) ; " The
Dwellers in Five Sisters' Court" (1876); "Boston Town" (1881);
" Life of Noah Webster" (1882) ; "A History of the United States "
for schools (1884); "Men and Letters" (1887); "Life of George
Washington" (1889); " Literature in School" (1889); "Childhood in
Literature and Art" (1894), besides various books of which he was the
editor or compiler only. He was also for nearly six years (1877-82) a
member of the Cambridge School Committee ; for five years (1884-89) of
the State Board of Education ; for nine years (1889-98) of the Harvard
University visiting committee in English literature ; and was at the time
of his death a trustee of Williams College, Wellesley College, and St.
John's Theological School, these making altogether a quarter of a cen-
tury of almost uninterrupted and wholly unpaid public service in the
cause of education. Since May 28, 1889, he was a member of this
Academy, until January 11, 1902, when he died. This is the simple
record of a most useful and admirable life, filled more and more, as it went
on, with gratuitous public services and disinterested acts for others.
As a literary workman, his nicety of method and regularity of life
went beyond those of any man I have known. Working chiefly at
home, he assigned in advance a certain number of hours daily as due
tn the firm for which he labored; and he then kept carefully the record
of these In mis. and if he took out a half hour for his own private work,
made it up. He had special work assigned by himself for a certain
time before breakfast, an interval which he daily gave largely to the
Greek Testament and at some periods to Homer, Thucydides, Herodotus,
and Xenophon ; working always with the original at hand and writing out
translations or commentaries, always in the same exquisite handwriting
and at first contained in small thin note-books, afterwards bound in
substantial volumes, with morocco binding and proper lettering. All his
writings were thus handsomely treated, and the shelves devoted to his
own works, pamphlet or otherwise, were to the eye a very conservatory
and flower garden of literature ; or like a chamberful of children to whom
even a frugal parent may allow himself the luxury of pretty clothes. All
his literary arrangements were neat ami perfect, and represented that
other extreme from that celebrated collection of De Quincev in Dove
Cottage at Grasmere, where that author had five thousand books, by
HORACE ELISHA SCUDDER. 659
his own statement, in a little room ten or twelve feet square; and his old
housekeeper explained it to me as perfectly practicable " because he had
no bookcases," bnt simply piled them against the walls, leaving here and
there little gaps in which he put his money.
In the delicate and touching dedication of Scudder's chief work " Men
and Letters" to his friend Henry M. Alden, the well known New York
editor, he says : " In that former state of existence when we were poets,
you wrote verses which I knew by heart and I read dreamy tales to you
which you speculated over as if they were already classics. Then you
bound your manuscript verses in a full blue calf volume and put it on
the shelf, and I woke to find myself at the desk of a literary workman."
Later, he says of himself, " Fortunately, I have been able for the most
part to work out of the glare of publicity." Yet even to this modest
phrase he adds acutely : " But there is always that something in us which
whispers 7, and after a while the anonymous critic becomes a little tired
of listening to the whisper in his solitary cave, and is disposed to escape
from it by coming out into the light even at the risk of blinking a little,
and by suffering the ghostly voice to become articulate, though the sound
startle him. One craves company for his thought, and is not quite con-
tent always to sit in the dark with his guests."
The work in which he best achieves the purpose last stated is undoubt-
edly the collection of papers called by the inexpressive phrase " Men
and Letters ; " a book whose title was perhaps a weight upon it and
which yet contained some of the very best of American thought, and crit-
icism. It manifests eveu more than his " Life of Lowell " that faculty
of keen summing up and epigrammatic condensation which became so
marked in him that it was very visible, I am assured, even in the literary
councils of his publishers, two members of which have told nie that he
often, after a long discussion, so summed up the whole situation in a sen-
tence or two that he left them free to pass to something else. We see the
same quality for instance in his " Men and Letters,"' in his papers on Dr.
Mulford and Longfellow. The first is an analysis of the life and literary
service of a man too little known because of early death, but of the rarest
and most exquisite intellectual qualities, Dr. Elisha Mulford, author of
" The Nation" and then of " The Republic of Cod." In this, as every-
where in the book, Mr. Scudder shows that epigrammatic quality which
amounted, whether applied to books or men, to what may be best de-
scribed as a quiet brilliancy. This is seen, for instance, when in defending
'Mulford from the imputation of narrowness, his friend sums up the whole
character of the man and saves a page of more detailed discussion by say-
000 HORACE ELISHA SCUDDER.
ing, " He was narrow as a canon is narrow, when the depth apparently
contracts the sides" (page 17). So in his criticism called "Longfellow
and His Art," Scudder repeatedly expresses in a sentence what might
well have occupied a page, as where he says of Longfellow, " He was
first of all a composer, and he saw his suhjects in their relations rather
than in their essence" (page 44). He is equally penetrating where he
says that Longfellow " brought to his work in the college no special love
of teaching," but " a deep love of literature and that unacademic attitude
toward his work which was a liberalizing power"' (page 66). He touches
equally well that subtle quality of Longfellow's temperament, so difficult
to delineate, when he says of him : " He gave of himself freely to his in-
timate friends, but he dwelt, nevertheless, in a charmed circle, beyond
the lines of which men could not penetrate " (page 68). These admirable
statements sufficiently indicate the rare quality of Mr. Scudder's work.
So far as especial passages go, Mr. Scudder never surpassed the best
chapters of " Men and Letters," but his one adequate and complete work
as a whole is undoubtedly, apart from his biographies, the volume en-
titled "Childhood in Literature and Art" (1894). This book was
based on a course of Lowell lectures given by him in Boston, and is
probably that by which he himself would wish to be judged, at least up
to the time of his admirable " Biography of Lowell." He deals in suc-
cessive chapters with Greek, Roman, Hebrew, Mediaeval, English,
French, German, and American literary art with great symmetry and
unity throughout, culminating, of course, in Hawthorne and analyzing
the portraits of children drawn in his productions. In this book one may
justly say that he has added himself, in a degree, to the immediate circle
of those half dozen great American writers whom he commemorates so
noblv at the close of his essay on " Longfellow and his Art," in " Men
and Letters." " It is too early to make a full survey of the immense
importance to American letters of the work done by half a dozen great
men in the middle of this century. The body of prose and verse created
by them is constituting the solid foundation upon which other structures
are to rise; the humanity which it holds is entering into the life of the
country, and no material invention, or scientific discovery, or institutional
prosperity, or accumulation of wealth will so powerfully affect the spir-
itual well-being of the nation for generations to come" (p. 69).
If it now be asked what prevented Horace Scudder from showing
more fully this gift of higher literature and led to his acquiescing, through
life, in a comparatively secondary function, I can find but one explana-
tion, and that a most interesting one to us in New England as illustrating
JOSEPH HENRY THAYER. (J61
the effect of immediate surroundings. His father, so far as I can ascer-
tain, was one of those Congregationalists of the milder type who, while
strict in their opinions, are led by a sunny temperament to be genial with
their households and to allow them innocent amusements. The mother
was a Congregationalist, firm but not severe in her opinions ; but always
controlled by that indomitable New England conscience of the older time
which made her sacrifice herself to every call of charity and even to
refuse, as tradition says, to have window curtains in her house, inasmuch
as many around her could not even buy blankets. Add to this the fact
that Boston was then a great missionary centre, that several prominent
leaders in this cause were of the Scudder family and the house was a sort
of headquarters for them, and that Horace Scudder's own elder brother,
whose memoirs he wrote, went as a missionary to India, dying at his post.
Speaking of his father's family in this memoir, he says of it, " In the
conduct of the household, there was recognition of some more profound
meaning in life than could find expression in mere enjoyment of living ;
while the presence of a real religious sentiment banished that counterfeit
solemnity which would hang over innocent pleasure like a cloud" (Scud-
der's Life of David Coit Scudder, p. 4). By one bred in such an atmos-
phere of self-sacrifice, that quality may well be imbibed ; it may even
become a second nature, so that the instinctive demand for self-assertion
may become secondary until a man ends in simply finding contentment
in doing perfectly the appointed work of every day. If we hold as we
should that it is character, not mere talent, which ennobles life, we may
well feel that there is something not merely pardonable, but ennobling in
such a habit of mind. Viewed in this light, his simple devotion to
modest duty may well be to many of us rather a model than a thing to
be criticised.
Thomas Wentworth Higginson.
JOSEPH HENRY THAYER.
Joseph Henry Thayer was born in Boston, November 7, 1828.
He graduated from Harvard in 1850, spent one year (1854-55) in the
Harvard Divinity School, graduated from the Andover Theological
Seminary in 1857, and was minister of the Crombie Street Church in
Salem from 1859 to 1864 ; a part of this time, from September, 1862 to
May, 1863, he served as Chaplain of the Fortieth Infantry Regiment
of Massachusetts Volunteers. His career as teacher began in 1864,
662 JOSEPH HENRY THAYER.
when he became Professor in the Andover Theological Seminary. Re-
signing his chair in 1882, he came to Cambridge, was Lecturer in the
Harvard Divinity School for the year 1883-84, and in 1884, on the
death of Ezra Abbot, succeeded him as Bussey Professor of New Testa-
ment Criticism and Interpretation; this position he held up to 1901.
He was a member of the Harvard Corporation from 1877 to 1884. He
was elected a Fellow of the American Academy of Arts and Sciences
March 9, 1887, and, though not an active member, was always deeply
interested in the work and fortunes of the Academy. Other societies to
which he belonged are the Archaeological Institute of America, the
American Oriental Society, and the Society of Biblical Literature. He
received the degree of A.M. from Harvard, the degree of S.T.D. from
Yale, Harvard, and Princeton, and the degree of Litt.D. from Dublin.
Dr. Thayer chose as his field of study the grammar and lexicography
of the New Testament, and his distinguished services in this department
have been universally recognized in Europe and America. He brought
to his task wide learning, patience in investigation, minute accuracy in
details, and critical acumen. His " Greek-English Lexicon of the New
Testament" will long remain a manual for students and a monument of
erudition and industr}'. The statement on the title-page, that it is a
"revised and enlarged translation" of a German lexicon (Grimm's Wilke),
hardly conveys a correct impression of its character. In fact the increase
of the breadth and precision of definitions, the verification of references,
the addition of further references, and the construction of the New Testa-
ment text from the best manuscript authorities, entailed an amount of
labor almost equivalent to the production of an independent lexicon.
This breadth of research and exactitude of statement characterized all
his scientific work — his articles in the Bible Dictionaries of Smith and
Hastings, his translation of the New Testament Greek grammars of
Winer and Buttmann, and his work on the Revised Version of the New
Testament. To this last he gave many years of labor, as a member
of the American Committee collaborating with the English Committee,
ami as principal editor of the American Version (the English Version
with the changes introduced by the American Committee), which by
agreement with the English Committee was published last year. His
reading in his chosen field was wide and critical. He found time
amid pressing professional and editorial duties to keep up with the
enormous mass of New Testament literature that every year produced
in Europe and America, and to form well-defined opinions as to its
value.
JOSEPH HENRY THAYER. 6QS
He was not only singularly precise in details, he had a marked capacity
for organization. He conceived large plans, and worked them out with
patience and success. As early as 1864 he announced his purpose to
translate Grimm — he completed the translation in Cambridge in 1885.
It is mainly to him that we owe the establishment of the American
School of Oriental Research in Jerusalem. Year after year he set forth
the desirableness and the feasibility of such a school, and by unwearied
exertions secured the indorsement of the Society of Biblical Literature
and of the American Oriental Society, and the cooperation and financial
support of a number of colleges, and of the Archaeological Institute of
America. The school went into operation in the year 1900, and seems
certain to give an impulse to Oriental study in this country, and to
increase our knowledge of Oriental (especially Semitic) life, ancient
and modern.
Dr. Thayer was an enthusiastic teacher, ever ready to give sympathy
and time to his students. He was exacting in his demands, had small
patience with negligence, and refused to lower his standards on any per-
sonal grounds, such as lack of previous preparation, or sickness; but he
knew how to encourage and assist backward students, and to stimulate
all by his own sense of the requirements of scholarship. He held firmly
to the traditional New England standard of a minister's outfit, insisting
on the necessity of Hebrew and Greek for the preacher. This point was
the subject of debate in the Harvard Divinity Faculty for years, and the
final decision made it possible for a student to take the degree of Bach-
elor of Divinity without a knowledge of Hebrew or Greek, the Faculty
reserving the right, however, to pass on every individual case. In point
of fact, it is true, in the past thirty years at least, only one man without
Greek had received the degree, and he was a Japanese, from whom crit-
ical study of the Chinese classics was accepted in lieu of Greek. But
Dr. Thayer, seeing that the Hebrew requirement was practically given
up, believed there was danger that the Greek requirement would go
the same way. Against this disposition to dispense with the original
languages of the Bible he set his face steadfastly ; he lost no opportunity
to protest against what he regarded as a lamentable lowering of the
standard of ministerial learning. When the question was finally decided,
he, of course, accepted in good faith the action of the Faculty. Accept
it cordially he could not : he was not an easy-going man, willing to fall
in gracefully with the opinions of the majority ; on the contrary, he took
things very seriously, and, in matters that interested him, expressed him-
self pointedly. To the last he never spoke of the attitude of the Faculty
004 JOSEPH HENRY THAYER.
toward the Hebrew and Greek requirements without a word of emphatic
distrust and condemnation.
His thinking was notably clear-cut — he could not abide haziness. This
trait, which is prominent in his scholarly work, appears also in his theo-
logical views. He was not intolerant of other men's opinions ; he only
held tenaciously to his own opinions, and claimed the right to define
his position precisely. When he found, in 1882, that he could not sub-
scribe the Andover Creed as it was then interpreted by the governing
boards, he resigned his professorship in the Seminary — a sundering of
old ties that gave him great pain. His own creed was distinct, yet cath-
olic; he held firmly to certain principles and facts that he believed to be
fundamental, and among these he gave a prominent place to scientific
truth and personal experience.
Born and brought up in Boston, his traditions and training were those
of New England, modified, however, by travel in foreign countries, and
by a wide knowledge of men and things. He was a scholar and a man
of affairs, a Puritan aud a man of the world. In personal intercourse he
showed an engaging frankness and friendliness, and the same devotion
that appears in his scholarly undertakings manifested itself in his rela-
tions with his friends, for whom he was always ready to do the uttermost.
He was fortunate in retaining his physical soundness and vigor up to a
few months before his death. His erect carriage, alert step, and cheery
manner gave him, even in his last years, a remarkably youthful appear-
ance, and his bodily alertness was in keeping with his mental activity.
His literary career extended over forty years, apparently without dimi-
nution of interest. He had the great happiness of seeing his main under-
takings brought to a successful completion — the Greek lexicon, the
revision of the English New Testament, and the establishment of the
Jerusalem School.
At the close of the year 1900-01 he resigned his position in Harvard,
and was made Professor Emeritus. The following summer he spent in
Europe, and, returning to America, died in Cambridge after a short
illness, No'vember 26, having not long before passed his seventy-third
birthday.
C. H. Toy.
JOHN FISKE. 665
JOHN FISKE.
On the 4th of July, 1901, John Fiske, philosopher, lecturer, and
historian, died at Gloucester. On the morning of the fifth, hundreds of
obituary notices of this distinguished man. were read in the daily news-
papers from Maine to Texas, from the Atlantic to the Pacific, and even
across the water in the capital of Great Britain, by a public familiar,
through his ministrations on the platform, with his giant form and ruddy
countenance. These preliminary notices were followed at a later date
by biographical and critical articles treating of his career, more finished
in style and more analytical in character, in reviews and magazines ;
in weekly, monthly, and quarterly publications. Many of these were
characterized by a familiarity with the details of Mr. Fiske's early life,
unusual under such circumstances, but easily to be accounted for, since
his biography had been partially written during his lifetime by two
competent authors.
The first of these sketches, and in some respects the more complete
of the two, was published by Edwin D. Mead, in the " Christian Register,"
in a series of papers occasioned by an address by Mr. Fiske before the
Concord School of Philosophy in 1886. The second was by the late
Horace E. Scudder, and appeared in a sort of introduction to one of the
editions of " The War of Independence." The striking similarity of
these biographies extends even to the language used, and indicates a
common origin. It is certain that Mr. Fiske himself furnished the
material for Mr. Mead's sketch, and there can be but little doubt that
he did the same by Mr. Scudder. This will fully explain the points of
coincidence, and will also give to both the authoritative character, which
neither in words claims, of being practically autobiographical.
From these sketches we learn that on the 30th of March, 1842,
there was born in Hartford, Connecticut, to Edmund Brewster Green
and Mary Fiske Green, a son named by them Edmund Fiske Green,
the greater part of whose child life was spent in Middletown, Connecticut.
This Edmund Fiske Green was our John Fiske, his name having been
changed during boyhood to that borne by his maternal grandfather.
At an early age the wonderful precocity of the child foreshadowed the
marvellous attainments of his later years. His education was carried
on first in the lower schools at Middletown and later at Stamford.
Then he returned to Middletown and was placed in a private school,
after which he went to Cambridge. Meantime he seems to have browsed
<oGQ JOHN FISKE.
in a library in the family mansion, and to a great degree taught himself
much that is acquired with difficulty by persons of ordinary intellect
even when assisted by the best of masters.
In his '• Dutch and Quaker Colonies," Mr. Fiske says of James Logan :
'•'He was an infant prodigy; at the age of twelve his attainments in
Greek, Latin, and Hebrew had attracted much notice, and he afterward
obtained distinction in modern languages, mathematics, physics, and
natural history." The story of Logan's precocity is fairly eclipsed by
Fiske's own record, but what he says of Logan shows us what his
dispassionate judgment was as to his own childhood career. Fiske's
biographers recapitulate his progress from year to year. It is needless
to give in full detail the story of his prodigious acquisitions. Suffice it
to say, that when six years old he began the study of Latin, and at the
age of seven he amused himself by reading Cagsar, and found entertain-
ment in such authors as Rollins and Josephus, and in the perusal of
Goldsmith's Greece. The taste for history thus disclosed led him on to
the works of other authors, and before he was eleven years old he had
not only devoured many histories of divers peoples, but had from memory
filled a quarto blank-book of sixty pages with chronological tables of
events between 1000 B. C. and 1820 A. D. By the time he was thir-
teen he had read the greater part of the writings of about a dozen Latin
authors, the work thus accomplished being in fact more than would be
required in that line of a graduate at Harvard. Meantime, mathematics
had not been neglected. Beginning with algebra at the age of eight, he
had, by the time he was thirteen, gone through Euclid, plane and spher-
ical trigonometry, surveying and navigation, and analytical geometry,
and had made a good start in differential calculus.
Until he had mastered Latin sufficiently to make use of a Greek
lexicon in which the meanings were given in Latin, he could not take
up Greek, a lexicon of this description being the only one at his com-
mand. So trifling a discouragement as that did not long delay him.
As soon as he felt competent to make use of the means at hand, he
entered upon. the study of Greek, and even before he obtained a modern
lexicon he made considerable progress in his knowledge of the language.
With the facility for study gained through the acquisition of a suitable
key to the meanings of the words, he reached such proficiency, at the
age of fifteen, that he could read Plato and Herodotus at sight.
He began his philosophical studies at the age of eleven with Locke's
" Essay of the Understanding," and at fourteen himself wrote an essay
on the habitability of the planets, in which he made the point that
JOHN PISKE. 667
Jupiter and Saturn, owing to their great size and slow refrigeration, are
in a much earlier stage of development than Venus, Mars, and the
Earth.
His taste for philology led him to attack the modern languages at
the age of fifteen. He began with German ; took up Spanish, in which
he kept a diary ; conquered French; and then attacked Italian. At the
end of six months he had read the whole of Giuccardini, with parts of
Ariosto and Petrarch. He then turned his attention to Portuguese.
We have followed him as a hoy down to the time when he is about
to leave home to go to Cambridge. What had college to offer him in
the way of instruction ? It is true that in much of the work he had
performed he had been without a master, and of course there was much
that he might still learn, but clearly the regular curriculum would
practically be merely review work for him. Nevertheless, he looked
forward with yearning to the time he should spend at Harvard, knowing
that he could discover avenues in which the extraordinary mental activity
which had impelled him along this wonderful path of study could find
exercise.
We are told that until he was sixteen "he averaged twelve hours study
daily for twelve months in the year." With the qualifications which will
naturally suggest themselves this statement would seem probable, yet
this boy who could cope with problems which present difficulties to the
ordinary collegiate student, and whose learning at fifteen years of age far
exceeded in many directions the standard which we should set for a
cultivated man of maturity, found time for other occupations than delving
in books. He taught himself to play upon the piano; participated iu
out-of-door sports, and took pleasure in walking, riding, and boating upon
the Connecticut. He was much interested in church and oratorio music,
was a member of the church choir, and his fondness for choral music,
then developed, is said to have abided by him throughout life. We do
not find evidence that works of fiction had much attraction for him as a
boy. Later in life, we know that he was fond of novels, and that the
characters portrayed by the masters of fiction were as real to him as the
heroes with whom he met in history. His reading at this time must
have been controlled by his surroundings, and what the libraries at his
command furnished we can conjecture from the list of his acquirements.
He mves us a hint of what there was at hand for him to read, in addition
to what might he termed '"useful books," in the following: "I remem-
ber," he says in one of his essays, " that when I was about ten years old,
a favorite book with me was one entitled k Criminal Trials of all Coun-
liti.S JOHN FISKE.
tries by a Member of the Philadelphia Bar.' I read it and read it, until
forbidden to read such a grewsome work, and then I read it all the
more."
He also tells us that he had access to a few scientific books owned by
a strange character in Middletown, a sort of hermit ; a dabbler in biol-
ogy and geology, who led a solitary life ; immersed, apparently, in
studies and speculations concerning things far above his stage of culti-
vation. In the curious den — the library, workshop, and probably liv-
ing room also — of this friendly recluse, among stuffed birds, mounted
animals, strange creatures preserved in alcohol, specimens of fossil foot-
prints from the Connecticut sandstone, and a few books on the subjects
in which the owner was interested, the learned boy was admitted as a
privileged guest, and here he talked with his strange companion con-
cerning the surrounding objects, and from his host young Fiske bor-
rowed such of the books as he cared to read.
The future author of " Outlines of a Cosmic Philosophy" and "Through
Nature to God," was at this time a teacher in the Sunday-school and
was active at prayer-meetings. What it cost him to reach the frame of
mind which could put forth these works is substantially set forth in
his Cosmic Philosophy. "A person," he says, "is educated in an
environment of Presbyterian theology, accepting without question all
the doctrines of Calvinism. By and by his environment enlarges.
Facts in science or in history, methods of induction, canons of criticism
present themselves to his mind as things irreconcilable with his old
creed. Hence painful doubts, entailing efforts to escape by modifying
the creed to suit new mental exigencies. Hence eager study and fur-
ther enlargement of the environment, causing fresh disturbance of
equilibrium and renewed doubt, resulting in further adaptation. And
so the process continues, until, if the person in question be sufficiently
earnest and sufficiently fortunate, the environment enlarges so far as to
comprehend the most advanced science of the day, and the process
of adaptation goes on until an approximate equilibrium is attained
between the order of conception and the order of phenomena, and
scepticism, having discharged its function, exists no longer, save in
so far as it may be said to survive in the ingrained habit of weigh-
ing evidence and testing one's hypotheses." Elsewhere, and this time
speaking in the first person singular, he refers to his early religious
opinions as being based upon the fear of the " burning hell with which
my childish imagination had been unwisely terrified."
He entered the sophomore class at Harvard in 1860 at the age of
JOHN FISKE. 669
eighteen, and was graduated in 18G3. His study of the modern lan-
guages, which as we have seen already comprehended nearly all those in
use in Eastern Europe, was followed by an attack on the ancient
tongues, Hebrew and Sanskrit; the former before he entered college, the
latter after he reached Cambridge. While in college he is said to have
worked from twelve to fifteen hours each day, during vacations as well
as terms, his time being divided between comparative philology, ancient
and modern history, and modern literature. His philological studies at
this period comprehended the Icelandic, Gothic, Danish, Swedish, Dutch,
and Roumanian tongues, and an attack on the Russian.
" He was but a lad of seventeen," says one of his eulogists, " when
Darwin's great work appeared and aroused in him the zeal that deter-
mined his mental activity for more than a score of years." Mr. Mead, in
his sketch, gives a long list of the authors whose books were read in
prosecution of the study thus kindled, and adds that Fiske's training
was that of a literary character even when he studied science. It is per-
haps unnecessary to recapitulate the names of these writers. Every
page of the Cosmic Philosophy bears evidence of Fiske's extensive
researches at this time, and apart from the fact that he is avowedly
preaching the doctrines of Spencer, it is clear that the scientific work
upon which his reasoning is based does not claim to be original. He
had not prosecuted laboratory researches in chemistry or biology ; he had
not gained his knowledge of astronomy at the observatory ; he simply
made skilful use of that which was done by others, never claiming for
himself more than was his due.
While still an undergraduate he published two papers. The first,
in 1861, was entitled Mr. Buckle's Fallacies ; the second, in his senior
year, was an essay on the Evolution of Language. The latter is said
to have attracted the attention of Mr. Spencer, and thus laid the founda-
tion for the intimate friendship which afterwards existed between Fiske
aud himself.
After his graduation, Mr. Fiske entered the Harvard Law School,
and in 1865 took his degree of LL.B. In 1864, while a member of
the Law School, he was admitted to the Suffolk bar, and in September
of that year he married Abby Morgan Brooks of Petersham. After
receiving his degree from the Law School, he opened an office in
Boston and entered upon the practice of his profession. It is said that
his prospects at the bar were fairly good, but he found professional
work distasteful, and in about a year abandoned his office. In thus
closing the door to a possible success in the profession which he had
670 JOHN FISKE.
chosen, and taking upon himself the chance of supporting his family
through the precarious channels of literary contributions to newspapers
and magazines, there is a touch not only of the simple faith and opti-
mism of youth, but of the Bohemian indifference to money-matters
characteristic of the John Fiske whom we knew in later years. His
confidence in himself was apparently justified by the result, for by
some means or other, then and ever after, he was able to keep the wolf
away from the door, and in an easy and comfortable style of living to
support his family. It is evident, however, that at a later period he
realized the boldness of the step then taken. " Literature as a pro-
fession," he said to an interviewer a few years ago, '"looked as precari-
ous in that generation as it does to you in this, but by the time I was
four years out of college I managed by constant labor to earn enough by
my pen to keep house and support a small family. ... I wrote at first
for the magazines and newspapers . . . upon science and philosophy
and literature, and I sometimes wrote political leaders. ... I earned
more by my review work and historical and literary studies than I
thought was possible when I stood upon the brink ; but an intellectual
revolution will be necessary before my experiences and that of my
generation can be repeated by the young men who are looking towards
literature to-day."
In 1868, he published a little book called " Tobacco and Alcohol.
It does pay to Smoke — The Coming Man will Drink Wine." In this he
criticised the hasty and unscientific writings of James Parton on the
same subject, and as a reviewer states, " clearly developed " '• the funda-
mental principle that everything in diet and medication depends on the
dose."
He was appointed, in 1869, as Lecturer on Positive Philosophy at
Harvard, which place he filled for two years. During the second half
of 1869 he was also an Instructor of History, and from 1872 to 1879
he was Assistant Librarian. In 1885 he received the appointment as
Professor of American History at Washington University, St. Louis.
The duties of this position were fulfilled by the delivery there of occa-
sional courses of lectures. During 1895-96 he was Lecturer at Harvard
on the Campaigns of the Civil War west of the Alleghanies, and was also
during 1896-97 Lecturer on Colonial Virginia and other Southern Colo-
nies. He was elected an Overseer of Harvard in 1879, again in 1885,
and a third time in 1899. He took his A.M. at Harvard in course, and
in 1894 received the honorary degree of LL.D. The same year the
University of Pennyslvania gave him the degree of Litt.D. He was a
JOHN FISKE. 671
Fellow of the Academy and a Member of the Massachusetts Historical
Society.
The character of the thoughts which occupied his mind for nearly
twenty years after his graduation is shown by the publications which
rapidly followed. In 1872 we have " Myths and Myth Makers;" in
1874, " Outlines of Cosmic Philosophy ; " in 187 G, " The Unseen World
and Other Essays;" in 1879, "Darwinism and Other Essays ;" in 1884,
" Excursions of an Evolutionist and the Destiny of Man viewed in the
Light of his Origin ;" and in 1885, " The Idea of God as affected by
Modern Knowledge."
It will be noticed that during his career as an Instructor at Harvard
his time was divided between philosophy and history. It is generally
understood that a professorship there would have been grateful to him.
In that event, if he had found a place in the philosophical department,
we should probably never have had from his pen his contributions to
American History. Two reasons have been assigned for his failure to
secure this appointment, — each of which may have had weight. One
was the attack upon Harvard by the religious press after the publication
of his Cosmic Philosophy, and the other was his iconoclasm. Harvard
had its idols. Of these Agassiz was one, and him the aggressive young
evolutionist did not spare.
His position as Assistant Librarian was not worthy of him, nor was
the work congenial. He therefore resigned from the library corps. He
had previously, as we have seen, cut adrift from the law. In which of
the two fields of literary labor, philosophy or history, for which he
was specially fitted, was there the best chance for a young man with the
growing responsibilities of a family on his hands to find the means of
support? Such, to a person glancing at his career, would seem to have
been the problem which was submitted to him when he severed his con-
nection with Harvard. Yet, if we may accept his own statement, the
wonderful amount of learning displayed in the pages of his Cosmic
Philosophy was simply acquired as a formative process by way of prep-
aration for his future historical work. " The absorbing and overmastering
passion for the study of history," he says, "first led me to study evolu-
tion in order to obtain a correct method."
Professor Royce, whose analysis of Fiske's contributions to philo-
sophical and religious discussions is very thorough and far reaching,
gives him credit for being entirely in earnest in making this statement.
"Any critic," he says, "who lacks his [Fiske's] range of reading must
be easily tempted to regard his literary activities as too miscellaneous,
672 JOHN FISKE.
and so must in some measure fail to understand in what degree he had
his vast resources of imagination under control. Any judge whose humau
sympathies are narrower than his must find it a baffling task to look for
the unity of interest, of opinion, and of ideal which in his mind bound
together the many undertakings that marked his career, and the various
stages of development through which his thought passed." The critic
who had Fiske's range of reading is probably not to be found among
us, but if we accept the proposition that he had historical work in view
during all the time of this preliminary study in so many fields, still we
can safely state that the precise form in which he proposed to put forth
his labor was not determined until after he met John Richard Green in
London, and talked with him about the " Short History of the English
People" which Green was then planning. " I heard him," says Fiske,
" telling about his scheme, and I thought it would be a very nice thing
to do something of the same sort for American history."
This meeting with Green could not have taken place until 1879. It
is plain, therefore, that if he relied upon his own capacity to support his
family when he left the Harvard Library, it must have been through
literary labor. He had been invited in 1878, while still connected with
the Library, to deliver six lectures in the Old South Meeting House
Course. This service was performed in 1879, and in June of the same
year he was invited by Huxley to lecture before the University College
in London. The acceptance of this invitation was fraught with great
results. His lectures before the Harvard students were characterized
by President Eliot : the first set, as '• interesting and inspiring ; " the
later lectures, as "graphic and stimulating." The Old South lectures
demonstrated his power with the public. The London lectures, before
a radically different audience, corroborated this conclusion, and his visit
brought him in friendly contact with the great body of distinguished men
in England who were then busy investigating Darwin's " Theory of
Development" and Spencer's " Doctrine of Evolution." Here, too, he
met Green and had his mind turned definitely towards specific work in
t lie field of American history. Circumstances thus determined that it
was to be through lectures and writing American history that he was
to earn his living, a determination which necessarily involved serious
limitations as to the time which he could devote to research and which
materially influenced the quality of his work.
His success as a lecturer in London led to his being called there again
in 1880, when he delivered his three lectures on '" American Political
Ideas" at the Royal Institute. These he repeated at the Philosophical
JOHN FISKE. 073
Institute of Edinburgh and again in London. He was, indeed, invited
to deliver them at the Sorbonne, but the invitation came too late.
His historical publications appeared in the following chronological
order. The first was "American Political Ideas," in 18G5; he was one
of the editors of "Appleton's Cyclopaedia of American Biography, 1887-
1889" (his selection being in part due, undoubtedly, to his reputation as
an historical student) ; " The Critical Period of American History," m
1888 ; " Washington and His Country," a book for the young, in 1889 ;
'"The War of Independence," a book of the same character, in 1889 ;
" Beginnings of New England," in 1889 ; " Civil Government in the
United States," a school book, in 1890; "American Revolution," in
two volumes, in 1891 ; " Discovery of America," also in two volumes,
in 1892; "History of the United States," for schools, 1894; "Old Vir-
ginia and Her Neighbors," in two volumes, in 1897; "Dutch and
Quaker Colonies in America," in two volumes, in 1899.
Throwing out school books and volumes for the young, we have in
the above series ten volumes, written as monographs, and published
entirely without regard to their chronological succession, yet each intended
as a contribution towards a complete history. Concerning this method
of treatment he himself said ':" I found myself dwelling upon special
points, and insensibly without any volition on my part, it [the history]
has been rather taking the shape of separate monographs. But I hope
to go on that way until I cover the ground with these separate books."
It is not unlikely that Parkman's example may have influenced him in
this respect. His enthusiastic admiration for that great and popular
writer of history shines forth from every page of the charming essay
which he wrote on Parkman's life and works. The condensed form of
" Beginnings of New England," containing as it does only the essentials
for the development of the theme, suggests the process of digestion and
careful elimination which characterizes Parkman's works. Besides the
ten historical volumes mentioned, Fiske also published in 1900 a mono-
graph on the " Mississippi Valley in the Civil War," and it is stated
that a "History of the United States" will be issued in three volumes
posthumously.
Mr. Fiske's works naturally divide themselves into two classes, and
these divisions are practically chronological, thus representing the sub-
jects to which his mind turned at different periods of his life. The brief
period between the two, when he first took up lecturing and for a few
years published only essays and magazine articles, indicates, in all
probability, merely a time of study and preparation for future work.
vol. xxxvii. — 43
674 JOHN FISKE.
Mr. Scudder says that the impulse toward American history was given
by the preparation for the first course of Old South lectures, which were
concerned especially with the Colonial period. When Fiske settled
down deliberately to his life-work, he found that he could make the
lectures subservient to his publications. He describes his method of
doing this as follows: " I look it up or investigate it and then write an
essay or lecture on the subject. That serves as a preliminary statement
either of a large subject or of special points. It is a help to me to try
to state the case. I never publish anything after this first statement,
but generally keep it with me for, it may be, some years, and possibly
return to it several times." "While the general proposition is undoubtedly
true that the preparation of historical work in tentative form, and the
frequent recurrence to it under the stimulus of new studies and varying
conditions of mind are of great assistance to the historian, still it must
have been true that the great draft upon Mr. Fiske's time and strength
occasioned by his lecture tours seriously affected the character of his
work. " Fiske's lectures were a drag upon him," says Professor Hart,
"because they were so good. Even big men have a limited stock of
vitality, and he put into his lectures a power which ought to have gone
into investigation. For years together, he appeared as a lecturer, more
than a hundred times annually, besides numerous lectures abroad. So
far as this work was a needed support for a man with a rising family, it
was simply a misfortune; so far as it took the place of equally well
paid literary work it was a mistake."
If we turn to the prefaces of his several publications we can there see
how much of his time was occupied with these lectures, and we can also
learn from the same source how famdiar his form must have become to
the lecture-going people of the entire country. Yet while his time was
thus occupied, tbe old topics with which his name was associated earlier
in life asserted their control over him, and found vent in essays or
addresses upon occasions. In 1900 he published a volume entitled "A
Century of Science ; " following this came " Through Nature to God."
The last address which he delivered, " Life Everlasting," was issued by
his publishers after his death. This was made possible because Fiske
rarely changed a word after he had once put his thoughts on paper.
His great fondness for music was not only evident to those who knew
him well, but crops out in his books. He enjoyed the skilful perform-
ance of a symphony by an orchestra, and was also capable of interpreting
it. To him there was not only harmony aud rhythm and melody and
the perfection of mechanical execution in the rendering of the music,
JOHN FISKE. 675
but there was some underlying sentiment expressed by the composer
which was conveyed to his mind. " When I look upon Parkman's
noble life," he says, " I think of Mendelssohn's Chorus, ' He that shall
endure to the end,' with its chaste and severely beautiful melody, and
the calm, invincible faith which it expresses." Were it not that one
cannot conceive how he found time to do it, it would occasion no sur-
prise to learn that he composed a mass as well as several songs.
Mr. Fiske was a large man, and at the time of his death be was very
corpulent. He enjoyed good health, borrowed no troubles, and was
the type of a vigorous, happy human being, full of affection for his
family and of good-will towards his fellow-men. He was absolutely
independent and unconventional in his habits, both mentally and phys-
ically. The humorous description which he gave of his mode of life
thoroughly illustrates this. " I always sit in a draught when I find
one," he said, " wear the thinnest clothes I can find, winter and sum-
mer ; catch cold once in three or four years, but not severely ; and
prefer to work in a cold room 55 to 60 degrees. Work the larger
part of each twenty-four hours, and by day or night indifferently.
Scarcely ever change a word once written ; eat when hungry ; rarely
taste coffee or wine or smoke a cigar, but drink two or three quarts of
beer a day and smoke a pipe all the time when at work ; never experi-
enced the feeling of disinclination for work and therefore never had
to force work." The indifference which he expresses to night or day
he brings forth in his essay on Chauncey Wright. " At two o'clock
in the morning," he says, " he [Wright] would perhaps take his hat
and saunter homeward with me by way of finishing the subject ; but
on reaching my gate a new suggestion would turn us back, — and so
we would alternately escort each other home, perhaps a dozen times,
until tired Nature asserted her rights, and the newly opened vistas of
discussion were regretfully left unexplored." This quotation from
Fiske's own works brings him before us as a willing disputant. It
must, however, be taken with a grain of salt. If he discussed questions
orally with persons from whom he differed in opinion, he selected his
opponent. He could not under ordinary circumstances be dragged into
an oral discussion.
As a lecturer, his manner of delivery was described as " simple, direct,
sincere, and in a way appealing. He talked to his audience in a man-
ner to make them feel that he was talking with them. He had :i
certain eloquence, which was engaging rather than stirring."
His reviewers concur in saying that his Cosmic Philosophy was
676 JOHN FISKE.
more than a mere exposition of Spencer's doctrine. Fiske not only
made clear that which was confused, but he added new propositions.
Among these was his chapter on the prolongation of human infancy,
a doctrine of great significance and a contribution of importance to the
general argument. Its value was recognized by his fellow evolutionists,
and he himself repeatedly referred to it in his works, claiming with
evident pride it was his and his alone. Most of his biographers find
in his later works devoted to religious topics a softened tone which they
attribute to a change of views. He himself maintained that he was
consistent. Perhaps he was affected and made less aggressive by the
change of opinion then going on. There can be no doubt that the public
of to-day can read the vigorous attacks of the young evolutionist upon tra-
ditional faiths and ingrained prejudices with less feeling than was provoked
by them when they were first delivered. On the other hand Fiske may
have been unconsciously borne upon the wave of scholarship whose
" philosophical, idealistic trend," according to Professor Munsterberg, is
" only swelling to-day, but whose highest point may be ten or twenty years
hence." At any rate such a sentence as this — "I believe in the immor-
tality of the soul, not in the sense in which I accept the demonstrable
proofs of science, but as a supreme act of faith in the reasonableness
of God's work " — could not have found place in the pages of Cosmic
Philosophy. Fiske may not have changed his doctrines, but he cer-
tainly modified his manner of expressing them. He combined, accord-
ing to Professor Royce, " the child's love of the unseen and mysterious
with the modern sceptical student's scorn for superstition." These
characteristics pervade both his early and late works.
Fiske quotes from Humboldt, u Nous avons considere le style comme
expression de caractere, comme reflet de l'interieur de l'homme."
There can be no doubt that Fiske's publications reveal the personality
of the author to the reader. We can easily see, through the lines, the
image of the good-natured, straightforward, genial man, whose intel-
lectual honesty leads him to say what he thinks, and whose sense of
humor impels him to enliven with a jest even those pages which are
devoted to the most abstruse subjects. The weary student of philos-
ophy experiences relaxation from the strain upon his attention consequent
upon his effort to follow the argument, when he is told that " the
waves of motor energy which the human organism absorbs in whiffs of
tobacco smoke are but a series of pulsations of transformed sunlight."
The reader, perplexed by the abstruse speculations quoted from some
learned philosopher, finds relief in the assertion that the troublesome
JOHN FISKE. (577
paragraph is regarded by Mr. Fiske as " sheer nonsense," or that the
whole of a certain system of philosophy is " made up of tawdry rhet-
oric, quite innocent of observation or induction." It is a satisfaction
to learn that an objectionable Spaniard is a " green-eyed, pitiless, per-
fidious, old wretch." It is refreshing to have such positive opinions
occasionally expressed concerning books, as the following : " For per-
verse ingenuity in creating difficulties where none exist, this book is a
curiosity in the literature of psychology. From long staring at mare's
nests the author had acquired a chronic twist in his vision." The most
ardent protectionist could not fail to be amused at the vigorous attacks
on his favorite doctrine with which the several volumes on American
History are interspersed. Lovers of " Alice in Wonderland " will recog-
nize upon the pages of Fiske's books their old acquaintance, the Jabberwok,
and readers of the "Arabian Nights Entertainment" will find that several
familiar genii do service by way of illustration or to make some point.
Characters from Cervantes, Scott, Lowell, Dickens, and Charles Reade
intrude themselves upon the reader, generally with the claim that they al-
ready know him and therefore the form of an introduction may be dispensed
with. One thing is noticeable, and that is the absence of quotations from
our favorite poets. " Hudibras " and " The Biglow Papers " attract him ;
the quaint attempts at verse of some of our early American writers
evidently amuse him ; but poetry as such does not appeal to him. On
the other hand humor always does, and we find him gravely quoting
Diedrich Knickerbocker, with the warning of course that he is dealing
with fiction, but nevertheless accepting Irving's burlesque descriptions
as representative of his conception of the persons therein characterized.
The mention of large oysters in Virginia recalls to Fiske an anecdote
of Thackeray, with which his reader is assumed to be familiar. " We
remember Thackeray," he says, " when we encounter oysters so large
that Basil Ringrose has to cut them into quarters." The detection of an
error on the part of a famous writer leads to the following foot-note :
"Aliquando dormitat bonus Homerus." No reader of the Discovery of
America but will understand this. By such means, Fiske lures the
reader on, and entices him over passages in his books which might
otherwise prove dull. His simple, direct, and lucid style ; his obvious
purpose to deal honestly with facts ; his pronounced opinions upon
points not free from doubt in the minds of many students ; his dis-
crimination in sifting out the events which are significant ; his sagac-
ity in measuring the proportion of their relative importance ; even his
open advocacy of those whose career appealed to him no matter what
678 JOHN FISKE.
the opinion of others, all combined to secure the approval of a large
reading public, and thus earned for him the honorable title which has
been conferred upon him since his death, " Popularizer of useful knowl-
edge." — In its restricted application to the field of history, this
epithet was adopted by Colonel Higginson in some remarks before the
Massachusetts Historical Society in February, and was repeated by him
with emphatic recognition of the honor thereby intended to be conferred,
at the March meeting of the Academy.
Fiske's whole life was, in the words of Mead, " a noble illustration
of resolute intellectual integrity." " Only another John Fiske," says
Professor Royce, " if such a being were possible — a man as widely read as
he was, and with a soul as sweetly humane in sentiment, as clear in vision,
as free from pettiness, as childlike in faith in what it had once accepted,
and yet as keen in critical intelligence regarding what it rejected as was
his soul — only such a man could estimate adequately Fiske's beneficent
life-work and his manifold mental accomplishments."
In conclusion let me say, that in accepting the appointment to write
Mr. Fiske's memoir, I did so with the full consciousness of my unfitness
for the task, if knowledge of the subjects discussed in what the London
"Times" terms the bewildering variety of his publications, were to be
made the basis of one's qualifications. To find a memorialist up to this
standard might be difficult even in the Academy. It seemed to me,
therefore, that all that could be expected of any person would be to
throw upon the screen a composite picture, made up from contributions
by Fiske himself and by the various writers who have furnished biog-
raphies of his life and criticisms of his works. This is what I have
striven to do.
Andrew McFarland Davis.
JAMES BRADLEY THAYER. 079
JAMES BRADLEY THAYER.
A Massachusetts man by ancestry, birth, and training, James
Bradley Thayer, our late vice-president, represented by the simplicity of
his life, his scholarly tastes and achievements, his practical good sense,
his public spirit, and generous sympathies, the highest type of the New
Englander. He was born January 15, 1831, in Haverhill, where his
father exercised a wide and wholesome influence as a journalist. He
entered Harvard College at the age of seventeen, having fitted himself
for the examinations after his fourteenth year, like his brother before
him, without the aid of a teacher. He ranked high in his class and
was the class orator. After an interval spent in teaching he entered
the Harvard Law School in 1854. Here he gave proof of his literary
and legal ability by winning, in his second year, the class prize for an
essay on the " Law of Eminent Domain." It is interesting to note that
his first legal essay, which was printed at once in the leading law
periodical of the day, was upon a topic in Constitutional Law, one of
the two branches of law in which he afterward acquired his great
distinction.
An incident in his career at the Law School exhibited the character
of the man. The Harvard Corporation had appointed Judge E. G.
Loring to a professorship in the Law School. But the Board of
Overseers, on account of the Judge's decision, sending back to slavery
the fugitive slave Anthony Burns, refused to confirm this appointment.
The Southerners and their sympathizers in the Law School moved in
their parliament a vote of censure upon the Overseers. The motion
was opposed on various parliamentary grounds, but finally the majority
determined to put the vote through in disregard of orderly procedure,
and the Clerk was directed to call the roll of yeas and nays. Mr.
Thayer, who was Clerk, rose, and in a quiet but impressive manner
declined to be a party to this unparliamentary action, resigned his
office, and walked away from his desk. The motion was ultimately
carried, but Mr. Thayer's calm, dignified rebuke of their proceedings
robbed the victory of well-nigh all its glory even in the minds of the
victors.
For nearly twenty years Mr. Thayer was active in the practice of his
profession, residing during the greater part of this time in Milton, where
he was conspicuous for his public-spirited interest in all that affected the
welfare of the town.
680 JAMES BRADLEY THAYER.
In 1874 he was appointed a professor in the Harvard Law School.
He had previously declined the offer of a professorship in the English
Department of the College. Although his rare gift for thoughtful,
graceful, and effective writing could not have failed to make him highly
successful as a professor of English, his decision not to give up his
chosen profession was doubtless a wise one. Certainly it was a fortu-
nate one for the Law School and the law.
Wherever the Harvard Law School is known, he has been recognized
for many years as one of its chief ornaments. When, in 1900, the
Association of American Law Schools was formed, it was taken for
granted by all the delegates that Professor Thayer was to be its first
President. No one can measure his great influence upon the thousands
of his pupils. While at the School they had a profound respect for his
character and ability, and they realized that they were sitting at the
feet of a master of his subjects. In their after life his precept and
example have been, and will continue to be, a constant stimulus to
genuine, thorough and finished work, and a constant safeguard against
hasty generalization or dogmatic assertion. His quick sympathy, his
unfailing readiness to assist the learner, out of the class-room as well as
in it, and his attractive personality, gave him an exceptionally strong
hold upon the affections of the young men. Their attitude towards him
is well expressed in a letter from a recent graduate of the School, who
describes him as " one of the best known, best liked, and strongest of
the Law Professors."
During the early years of his service he lectured on a variety of
legal topics, but Evidence and Constitutional Law were especially con-
genial to him, and in the end he devoted himself exclusively to these
two subjects, in each of which he had prepared for the use of his
classes an excellent collection of cases. Evidence was an admirable
field for his powers of historical research and analytical judgment. He
recognized that our artificial rules of evidence were the natural out-
growth of trial by jury, and could only be explained by tracing carefully
the development of that institution in England. The results of his work
appeared in his " Preliminary7 Treatise on the Law of Evidence," a worthy
companion of the masterly "Origin of the Jury," by the distinguished
German, Professor Brunner. His book gave him an immediate repu-
tation, not only in this country, but in England, as a legal historian and
jurist of the first rank. An eminent English lawyer, in reviewing it,
described it as " a book which goes to the root of the subject more
thoroughly than any other text-book in existence."
JAMES BRADLEY THAYER. 681
Although he published no treatise upon Constitutional Law, he
achieved, by his essays, by his collection of Cases, and by his teaching,
a reputation in that subject hardly second to his rank in Evidence. To
the few who knew of it, President McKinley's wish to make Professor
Thayer a member of the present Philippines Commission seemed a
natural and most fitting recognition of his eminence as a constitutional
lawyer, and if he had deemed it wise to accept the position offered to
him, no one can doubt that the appointment would have commanded
universal approval.
It is greatly to be deplored that he was not permitted to give to
the world the additional contributions to legal literature, which the
vigor of his powers and his known purposes led us to expect from
him. That he did not realize these purposes earlier was due to his very
virtues. His wide range of interests, his constant service in helping
other writers in their work, and above all his passion for perfection in
his own work, explain why the message he might have given remains
incomplete. The pathetic interest of high hopes unfulfilled attaches to a
memorandum found among his papers, and written last September.
" Sept. 15
For next year.
Have a single plan to put through. Without that the small everyday
matters eat up all the time. They easily may, for they can be done either
well enough or perfectly.
That plan must be the 2nd volume of Evidence.
For the year following, a small Vol. on Const. Law.
For the time following that, the works, writings and life of Marshall —
and then an End."
The relations of the law professors are probably closer than those of
any other department of the University. No one who has not known,
as his colleagues have known, the charm of his daily presence and
conversation, and the delightful quality of his vacation letters, can
appreciate the deep and abiding sense of the irreparable loss they have
suffered in the death of Professor Thayer.
In our great grief we find our chief comfort in the thought of his
simple and beautiful life, greatly blessed in his home and family, rich
in choice friendships, crowned with the distinction that comes only to
the possessor of great natural gifts nobly used, full of happiness to
himself, and giving in abundant measure happiness and inspiration
to others.
James Barr Ames.
682 PROCEEDINGS OF THE AMERICAN ACADEMY.
There have been no resignations during the year. One Resi-
dent Fellow, formerly an Associate, having again made his resi-
dence outside of Massachusetts, has been restored to Associate
Fellowship.
New members elected are : Resident Fellows, 9 ; Associate
Fellows, 3 ; Foreign Honorary Members, 5.
The roll of the Academy therefore now includes 200 Resident
Fellows, 100 Associate Fellows, and 71 Foreign Honorary
Members.*
* By the death of a Resident Fellow, and by the election of new members at the
annual meeting of May 14, 1902, the roll stands at date of publication 199 Resident
Fellows, 100 Associate Fellows, and 73 Foreign Honorary Members.
American Academy of Arts and Sciences.
OFFICERS AND COMMITTEES FOR 1902-03.
president.
Alexander Agassiz.
Class I.
John Trowbridge,
Class I.
Charles R. Sanger,
George F. Swain,
Arthur G. Webster,
Alexander Agassiz,
VICE-PRESIDENT.
Class II.
Henry P. Walcott,
CORRESPONDING SECRETARY.
William M. Davis.
RECORDING SECRETARY.
William Watson.
TREASURER.
Francis Blake.
librarian.
A. Lawrence Rotch.
COUNCILLORS.
Class II.
Theobald Smith,
Terms expire 1903.
Robert De C. Ward,
Terms expire 1904.
Edward L. Mark,
Terms expire 1905.
committee of finance.
Francis Blake,
Class III.
John C. Gray.
Class III.
A. Lawrence Lowell,
Denman W. Ross,
Arlo Bates,
Eliot C. Clarke.
RUMFORD COMMITTEE.
Erasmus D. Leavitt, Edward C. Pickering, Charles R. Cross,
Amos E. Dolbear, Arthur G. Webster, Theodore W. Richards,
Elihu Thomson.
c. m. warren committee.
Charles L. Jackson, Samuel Cabot, Henry B. Hill,
Leonard P. Kinnicutt, Arthur M. Comey, Robert H. Richards,
Henry P. Talbot.
COMMITTEE OF PUBLICATION.
Seth C. Chandler, of Class I., Edward L. Mark, of Class II.,
Crawford H. Toy, of Class III.
COMMITTEE ON THE LIBRARY.
A. Lawrence Rotch,
William F. Osgood, of Class I., Samuel Henshaw, of Class II.,
Henry W. Haynes, of Class III.
AUDITING COMMITTEE.
Henry G. Denny,
William L. Richardson.
LIST
OF THE
FELLOWS AND FOREIGN HONORARY MEMBERS.
(Corrected to May 14, 1902.)
RESIDENT FELLOWS. — 199.
(Number limited to two hundred.)
Class I. — Mathematical and Physical Sciences. — 82.
Section I. — 20.
Mathematics and Astronomy.
Solon I. Bailey,
Maxime Bocher,
William E. Byerly,
Seth C Chandler,
Gustavus Hay,
Percival Lowell,
Henry Mitchell,
William F. Osgood,
James Mills Peirce,
Edward C. Pickering,
William H. Pickering,
Henry S. Pritchett,
John Ritchie, Jr.,
John D. Runkle,
Edwin F. Sawyer,
Arthur Searle,
William E. Story,
Henry Taber,
O. C. Wendell,
P. S. Yendell,
Cambridge.
Cambridge.
Cambridge.
Cambridge.
Boston.
Boston.
Nantucket.
Cambridge.
Cambridge.
Cambridge.
Cambridge.
Boston.
Roxbury.
Cambridge.
Brighton.
Cambridge.
Worcester.
Worcester.
Cambridge.
Dorchester.
Section II. —23.
Physics.
A. Graham Bell, Washington, D.C.
Clarence J. Blake, Boston.
Francis Blake, Weston.
Harry E. Clifford, Newton.
Charles R. Cross, Brookline.
Amos E. Dolbear, Somerville.
A. W. Duff, Worcester.
H. M. Goodwin, Roxbury.
Edwin H. Hall, Cambridge.
Hammond V. Hayes, Cambridge.
William L. Hooper, Somerville.
William W. Jacques, Newton.
Frank A. Laws, Boston.
Henry Lefavour, Williarnstown.
Theodore Lyman, Brookline.
Benjamin O. Peirce, Cambridge.
A. Lawrence Rotch, Boston.
Wallace C. Sabine, Boston.
John S. Stone, Boston.
Elihu Thomson, Swampscott.
G86
BESIDENT FELLOWS.
John Trowbridge,
A. G. Webster,
Robert W. Willson,
Cambridge.
Worcester.
Cambridge.
Section III. — 22.
Chemistry.
Samuel Cabot, Boston.
Arthur M. Comey, Cambridge.
James M. Crafts, Boston.
Charles W. Eliot, Cambridge.
Henry B. Hill, Cambridge.
Charles L. Jackson, Cambridge.
Walter L. Jennings, Worcester.
Leonard P. Kinnicutt, Worcester.
Charles F. Mabery, Cleveland, O.
Arthur Michael, Boston.
George D. Moore, Worcester.
Charles E. Munroe, Wash'gton,D.C.
John U. Nef, Chicago, 111.
Arthur A. Noyes, Boston.
Robert H. Richards, JamaicaPlain.
Theodore W. Richards, Cambridge.
Charles R. Sanger, Cambridge.
Stephen P. Sharpies, Cambridge.
Francis H. Storer,
Henry P. Talbot,
Charles H. Wing,
Edward S. Wood,
Boston.
Newton.
Ledger, N. C.
Boston.
Section IV. — 17.
Technology and Engineering.
Eliot C. Clarke, Boston.
Heinrich O.Hofman, Jamaica Plain.
Ira N. Hollis, Cambridge.
L. J. Johnson, Cambridge.
Gaetano Lanza, Boston.
E. D. Leavitt, Cambridge.
William R. Livermore, Boston.
Hiram F. Mills, Lowell.
Cecil H. Peabody, Brookline.
Alfred P. Rockwell, Manchester.
Andrew H. Russell, Manilla.
Peter Schwamb, Arlington.
H. L. Smyth, Cambridge.
Charles S. Storrow, Boston.
George F. Swain, Boston.
William Watson, Boston.
Morrill Wyman, Cambridge.
Class II. — Natural and Physiological Sciences. — 66
Section I. — 14.
Geology, Mineralogy, and Physics of
the Globe.
II. H. Clayton,
Algernon Coolidge,
William O. Crosby,
William M. Davis,
Benj. K. Emerson,
O. W. Huntington,
Robert T. Jackson,
T. A. Jaggar, Jr.,
William H. Niles,
John E. Pillsbury,
Nathaniel S. Shaler,
Robert DeC. Ward,
John E. Wolff,
J. B. Woodworth,
Milton.
Boston.
JamaicaPlain.
Cambridge.
Amherst.
Newport, R. I.
Cambridge.
Cambridge.
Cambridge.
Boston.
Cambridge.
Cambridge.
Cambridge.
Cambridge.
Section II. — 11.
Botany.
F. S. Collins,
Geo. E. Davenport,
William G. Farlow,
Charles E. Faxon,
Merritt L. Fernald,
George L. Goodale,
John G. Jack,
B. L. Robinson,
Charles S. Sargent,
Arthur B. Seymour,
Roland 'Thaxter,
Maiden.
Medford.
Cambridge.
Jamaica Plain.
Cambridge.
Cambridge.
JamaicaPlain.
Cambridge.
Brookline.
Cambridge.
Cambridge
Sectiox TIL — 25.
Zoology and Physiology.
Alexander Agassiz, Cambridge.
Robert Amory, Boston.
RESIDENT FELLOWS.
687
James M. Barnard, Milton.
Henry P. Bowditch, Jamaica Plain.
Cambridge.
Brookline.
Cambridge.
Williamstown.
Boston.
William Brewster,
Louis Cabot,
William E. Castle,
Samuel F. Clarke,
W. T. Councilman,
Charles B. Davenport, Chicago, 111.
Harold C. Ernst, Jamaica Plain
Edward G. Gardiner, Boston.
Samuel Henshaw, Cambridge.
Theodore Hough, Boston.
John S. Kingsley, Somerville.
Edward L. Mark, Cambridge.
Charles S. Minot, Milton.
Edward S. Morse, Salem.
George H. Parker, Cambridge.
William T. Porter, Boston.
James J. Putnam, Boston.
Samuel H. Scudder, Cambridge.
William T. Sedgwick, Boston.
James C. White, Boston.
William M. Woodworth, Cambridge.
Section IV. — 16.
Medicine and Surgery.
Samuel L. Abbot, Boston.
Edward H. Bradford, Boston.
Boston.
Boston.
Boston.
Boston.
Boston.
Boston.
Boston.
Boston.
Boston.
Jamaica Plain.
Boston.
Cambridge.
Boston.
Arthur T. Cabot,
David W. Cheever,
Frank W. Draper,
Thomas Dwight,
Reginald H. Fitz,
Charles F. Folsom,
Frederick I. Knight,
Samuel J. Mixter,
W. L. Richardson,
Theobald Smith,
O. F. Wadsworth,
Henry P. Walcott,
John C. Warren,
Francis H. Williams, Boston.
Class III. — Moral and Political Sciences. — 51.
Section I. — 9.
Philosophy and Jurisprudence.
James B. Ames,
Horace Gray,
John C. Gray,
G. Stanley Hall,
Geo. F. Hoar,
Francis C. Lowell,
Josiah Royce,
Jeremiah Smith,
Edward H. Strobel,
Section II.
Cambridge.
Boston.
Boston.
Worcester.
Worcester.
Boston.
Cambridge.
Cambridge.
Cambridge.
-21.
Philology and Archaeology.
William S. Appleton, Boston.
Charles P. Bowditch, Jamaica Plain.
Lucien Carr, Cambridge.
Franklin Carter, Williamstown.
Joseph T. Clarke, Boston.
Henry G. Denny, Roxbury.
William Everett, Quincy.
J. W. Fewkes, Washington, D.C.
William W. Goodwin, Cambridge.
Henry W. Haynes, Boston.
Charles R. Lanman,
David G. Lyon,
Morris H. Morgan,
Bennett H. Nash,
Frederick W. Putnam, Cambridge.
Edward Robinson, Boston.
F. B. Stephenson,
Crawford II. Toy,
John W. White,"
John H. Wright,
Edward J. Young,
Cambridge.
Cambridge.
Cambridge.
Boston.
Boston.
Cambridge.
Cambridge.
Cambridge.
Waltham.
Section III. — 10.
Politicdl Economy and History.
Charles F. Adams, Lincoln.
Edward Atkinson, Brookline.
Andrew McF. Davis, Cambridge.
Ephraim Emerton, Cambridge.
688
RESIDENT FELLOWS.
A. C. Goodell, Salem.
Henry C. Lodge, Nahant
A. Lawrence Lowell, Boston.
James F. Rhodes, Boston.
Charles C. Smith, Boston.
F. W. Taussig,
Cambridge.
Section IV. — 11.
Literature and the Fine Arts.
Francis Bartlett, Boston.
John Bartlett,
Arlo Bates,
George S. Boutwell,
J. Elliot Cabot,
T. W. Higginson,
George L. Kittredge,
Charles G. Loring,
Charles Eliot Norton,
Denman W. Ross,
Barrett Wendell,
Cambridge.
Boston.
Groton.
Brookline.
Cambridge.
Cambridge.
Boston.
Cambridge.
Cambridge.
Boston.
ASSOCIATE FELLOWS.
089
ASSOCIATE FELLOWS. — 100.
(Number limited to one hundred. Elected as, vacancies occur.)
Class I. — Mathematical and Physical Sciences. — 38.
Section I. — 14.
Mathematics and Astronomy.
Edward E. Barnard, Williams Bay,
S. W. Burnham, Chicago. [Wis.
George Davidson,
Fabian Franklin,
Asaph Hall,
George W. Hill,
E. S. Holden,
San Francisco.
Baltimore.
Goshen, Conn.
W. Nyack, N.Y.
New York.
Emory McClintock, Morristown,X.J.
E. H. Moore, Chicago.
Simon Newcomb,
Charles L. Poor,
George M. Searle,
J. N. Stockwell,
Chas. A. Young,
Washington.
New York.
Washington.
Cleveland, O.
Princeton, N. J.
Section II. — 8.
Physics.
Carl Barus, Providence, R.I.
J. Willard Gibbs, New Haven.
G. E. Hale, Williams Bay, Wis.
S. P. Langley, Washington.
T. C. Mendenhall,
A. A. Michelson, Chicago.
Ogden N. Rood, New York.
E. L. Nichols, Ithaca, N. Y.
Section III. — 8.
Chemistry.
T. M. Drown, So. Bethlehem, Pa.
Wolcott Gibbs, Newport, R.I.
Frank A. Gooch, New Haven.
S.W.Johnson, New Haven.
Charlottesville , Va.
Cleveland, O.
New Orleans.
Baltimore.
Section IV. — 8.
Technology and Engineering.
Henry L. Abbot, Cambridge.
Cyrus B. Comstock, New York.[Va.
W. P. Craighill, Charlestown, W.
John Fritz, Bethlehem, Pa.
F. R. Hutton, New York.
George S. Morison, New York.
William Sellers, Edge Moor, Del.
Robt. S. Woodward, New York.
J. W. Mallet,
E. W. Morley,
J. M. Ordway,
Ira llemsen,
Class II. — Natural and Physiological Sciences. — 33.
Section I. — 12.
Geology, Mineralogy, and Physics of
the Globe.
Cleveland Abbe, Washington.
George J. Brush, New Haven.
T. C Chamberlin, Chicago.
Edward S. Dana, New Haven.
Walter G. Davis,
G. K. Gilbert,
J. Peter Lesley,
S. L. Penfield,
J. W. Powell,
R. Pumpelly,
A. R. C. Selwyn,
Charles D. Walcott.
Cordova, Arg.
Washington.
Milton, Mass.
New Haven.
Washington.
Newport, R.I.
Vancouver.
Washington.
XXXVII.
44
690
ASSOCIATE FELLOWS.
L. H. Bailey,
D. H. Campbell,
J. M. Coulter,
C. G. Pringle,
John D. Smith,
W. Trelease,
Section II. — 6.
Botany.
Ithaca, N. Y.
Palo Alto, Cal.
Chicago.
Charlotte, Vt.
Baltimore.
St. Louis.
Section III. — 9.
Zoology and Physiology.
Joel A. Allen, New York.
W. K. Brooks, Lake Roland, Md.
F. P. Mall, Baltimore.
S. Weir Mitchell, Philadelphia.
II. F. Osborn,
A. S. Packard,
A. E. Verrill,
C. O. Whitman,
E. B. Wilson,
New York.
Providence, R.I.
New Haven.
Chicago.
New York.
Section IV. — 6.
Medicine and Surgery.
John S. Billings, New York.
W. S. Halsted, Baltimore.
W. W. Keen, Philadelphia.
William Osier, Baltimore.
Wm. H. Welch, Baltimore.
H. C. Wood, Philadelphia.
Class III. — Moral and Political Sciences. — 29.
Section I. — 7.
Philosophy and Jurisprudence.
James C Carter, New York.
Joseph H. Choate, New York.
Melville W. Fuller, Washington.
Williarn W. Howe, New Orleans.
Charles S. Peirce, Milford, Pa.
G. W. Pepper, Philadelphia.
T. R. Pynchon, Hartford, Conn.
Section II. — 7.
Philology and Archeology.
Timothy Dwight, New Haven.
B. L. Gildersleeve, Baltimore.
D. C. Gilman, Baltimore.
T. R. Lounsbury, New Haven.
Rufus B. Richardson, Athens.
Thomas D. Seymour, New Haven.
A. D. White, Ithaca, N.Y.
Section III. — 6.
Political Economy and History.
Henry Adams, Washington.
G. P. Fisher, New Haven.
H. E. von Hoist, Chicago.
Henry C. Lea, Philadelphia.
H. Morse Stephens, Ithaca.
W. G. Sumner, New Haven.
Section IV. — 9.
Literature and the Fine Arts.
James B. Angell, Ann Arbor, Mich.
L. P. di Cesnola, New York.
H. H. Furness, Wallingford, Pa.
R. S. Greenough, Florence.
Herbert Putnam, Washington.
Augustus St. Gaudens, Windsor, Vt.
John S. Sargent, London.
E. C. Stedraan, Bronxville, N. Y.
W. R. WTare, New York.
FOREIGN HONORARY MEMBERS.
091
FOREIGN HONORARY MEMBERS. — 73.
(Number limited to seventy-five. Elected as vacancies occur.)
Class I. — Mathematical and Physical Sciences. — 23.
Section I. — 7.
Mathematics and Astronomy.
Arthur Auwers, Berlin.
George H. Darwin, Cambridge.
H. A. E. A. Faye, Paris.
Sir William Muggins, London.
H. Poincare, Paris.
Otto Struve, Karlsruhe.
II. C. Vogel, Potsdam.
Section II. — 5.
Physics.
Ludwig Boltzmann, Vienna.
Oliver Heaviside, Newton Abbot.
F. Kohlrausch, Berlin.
Lord Rayleigh, Witham.
Sir G. G. Stokes, Bart., Cambridge.
Section III. — 6.
Chemistry.
Adolf Baeyer, Munich.
Marcellin Berthelot, Paris.
J. H. van't Hoff, Berlin.
D. Mendeleeff, St. Petersburg.
Sir H. E. Roscoe, London.
Julius Thomseu, Copenhagen.
Section IV. — 5.
Technology and Engineering.
Sir Benjamin Baker, London.
Lord Kelvin, Largs.
Maurice Levy, Paris.
H. Miiller-Breslau, Berlin.
W. Cawthorne Unwin, London.
Class II. — Natural and Physiological Sciences. — 27.
Section I. — 7.
Geology, Mineralogy, and Physics of
the Globe.
Sir Archibald Geikie, London.
-Julius Hann, Vienna.
Albert Heim, Zurich.
Sir John Murray, Edinburgh.
Freih. v. Richthofen, Berlin.
Henry C. Sorby, Sheffield.
Heinrich Wild, Zurich.
Section II. — 6.
Botany.
E. Bornet, Paris.
A. Engler, Berlin.
Sir Joseph D. Hooker, Sunningdale.
W. Pfeffer, Lcipsic.
II . Graf zu Solms-
Laubach, Strassburg.
Eduard Strasburger, Bonn.
692
FOREIGN HONORARY MEMBERS.
Section III. — 7.
Zoology and Physiology.
Sir Michael Foster, Cambridge.
Carl Gegenbaur,
Ludimar Hermann,
A. von Kolliker,
H. Kronecker,
E. Ray Lankester,
Elias Metschnikoff,
Heidelberg.
Konigsberg.
Wiirzburg.
Bern.
London.
Paris.
Section IV. — 7.
Medicine and Surgery.
Sir T. L. Brunton, London.
A. Celli, Borne.
V. A. H. Horsley, London.
R. Koch, Berlin.
Lord Lister, London.
F. v. Recklinghausen, Strassburg.
Rudolf Virchow, Berlin.
Class III. — Moral and Political Sciences. — 23.
Section I. — 5.
Philosophy and Jurisprudence.
A. J. Balfour, Prestonkirk.
Heinrich Brunner, Berlin.
A. V. Dicey, Oxford.
F. W. Maitland, Cambridge.
Sir Frederick Pollock,
Bart., London.
Section II. — 7.
Philology and Archaeology.
Ingram By water, Oxford.
F. Delitzsch, Berlin.
W. Dorpfeld, Athens.
Sir John Evans, Ilemel Hempstead.
H. Jackson, Cambridge.
J. W. A. Kirchhoff, Berlin.
G. C. C. Maspero, Paris.
Section III. — 4.
Political Economy and History.
James Bryce, London.
Theodor Mommsen, Berlin.
Sir G. O. Trevelyan,
Bart., London.
W. E. H. Lecky, London.
Section IV
.—7.
Literature and the
Fine Arts.
E. de Amicis,
Florence.
Georg Brandes,
Copenhagen
F. Brunetiere,
Paris.
Jean Leon Gerome,
Paris.
Rudyard Kipling,
Rottingdean
G. Paris,
Paris.
Leslie Stephen,
London.
STATUTES AND STANDING YOTES.
STATUTES.
Adopted May 30, 1854 : amended September 8, 1857, November 12, 1862, May
24, 1864, November 9, 1870, May 27, 1873, January 26, 1876, June 16,
1886, October 8, 1890, January 11 and May 10, 1893, May 9 and October
10, 1894, Afarc/t 13, April 10 and May 8, 1895, May 8, 1901, and January
8, 1902.
CHAPTER I.
Of Fellows and Foreign Honorary Members.
1. The Academy consists of Resident Fellows, Associate Fellows and
Foreign Honorary Members. They are arranged in three Classes,
according to the Arts and Sciences in which they are severally proficient,
viz.: Class I. The Mathematical and Physical Sciences; — Class II.
The Natural and Physiological Sciences ; — Class JII. The Moral and
Political Sciences. Each Class is divided into four Sections, viz. :
Class I., Section 1. Mathematics and Astronomy ; — - Section 2. Physics;
— Section 3. Chemistry; — Section 4. Technology and Engineering.
Class II., Section 1. Geology, Mineralogy, and Physics of the Globe ; —
Section 2. Botany ; — Section 3. Zoology and Physiology ; — Section 4.
Medicine and Surgery. Class III., Section 1. Philosophy and Juris-
prudence : — Section 2. Philology and Archaeology ; — Section 3.
Political Economy and History ; — Section 4. Literature and the Fine
Arts.
2. The number of Resident Fellows shall not exceed two hundred.
Only residents in the Commonwealth of Massachusetts shall be eligible
to election as Resident Fellows, but resident fellowship may be retained
after removal from the Commonwealth. Each Resident Fellow shall
pay an admission fee of ten dollars and such annual assessment, not ex-
ceeding ten dollars, as shall be voted by the Academy at each annual
694 STATUTES OP THE AMERICAN ACADEMY
meeting. Resident Fellows only may vote at the meetings of the
Academy.
3. The number of Associate Fellows shall not exceed one hundred,
of whom there shall not be more than forty in either of the three classes
of the Academy. Associate Fellows shall be chosen from persons resid-
ing outside of the Commonwealth of Massachusetts. They shall not be
liable to the payment of any fees or annual dues, but on removing within
the Commonwealth they may be transferred by the Council to resident
fellowship as vacancies there occur.
4. The number of Foreign Honorary Members shall not exceed
seventy-five ; and they shall be chosen from among persons most emineut
in foreign countries for their discoveries and attainments in either of the
three departments of knowledge above enumerated. There shall not be
more than thirty Foreign Members in either of these departments.
CHAPTER II.
Op Officers.
1. There shall be a President, three Vice-Presidents, one for each
Class, a Corresponding Secretary, a Recording Secretary, a Treasurer,
and a Librarian, which officers shall be annually elected, by ballot, at
the Annual Meeting, on the second Wednesday in May.
2. At the Annual Meeting of 1901, nine Councillors shall be elected
by ballot, one from each Class of the Academy to serve for one year,
one from each Class for two years, and one from each Class for three
years ; and at annual meetings thereafter three Councillors shall be
elected in the same manner, one from each Class, to serve for three
years ; but the same Fellow shall not be eligible for two successive terms.
The nine Councillors, with the President, the three Vice-Presidents,
the two Secretaries, the Treasurer, and the Librarian, shall constitute the
Council. Five members shall constitute a quorum. It shall be the
duty of this Council to exercise a discreet supervision over all nomina-
tions and elections. With the consent of the Fellow interested, they
shall have power to make transfers between the several Sections of the
same Class, reporting their action to the Academy.
3. If any office shall become vacant duriug the year, the vacancy
shall be filled by a new election, and at the next stated meeting, or at a
meeting called for this purpose.
OF ARTS AND SCIENCES. 695
CHAPTER III.
Of Nominations of Officers.
1. At the stated meeting in March, the President shall appoint from
the next retiring Councillors a Nominating Committee of three Fellows,
one for each class.
2. It shall be the duty of this Nominating Committee to prepare a
list of candidates for the offices of President, Vice-Presidents, Corre-
sponding Secretary, Recording Secretary, Treasurer, Librarian, Coun-
cillors, and the Standing Committees which are chosen by ballot ; and
to cause this list to be sent by mail to all the Resident Fellows of the
Academy not later than four weeks before the Annual Meeting.
3. Independent nominations for any office, signed by at least five
Resident Fellows and received by the Recording Secretary not less thau
ten days before the Annual Meeting, shall be inserted in the call for the
Annual Meeting, which shall then be issued not later than one week
before that meeting.
4. The Recording Secretary shall prepare for use, in voting at the
Annual Meeting, a ballot containing the names of all persons nominated
for office under the conditions given above.
5. When an office is to be filled at any other time than at the Annual
Meeting, the President shall appoint a Nominating Committee iu accord-
ance with the provisions of Section 1, which shall announce its nomina-
tion in the manner prescribed in Section 2 at least two weeks before
the time of election. Independent nominations, signed by at least five
Resident Fellows and received by the Recording Secretary not later
than one week before the meeting for election, shall be inserted iu the
call for that meeting.
o
CHAPTER IV.
Of the President.
1. It shall be the duty of the President, and, in his absence, of tin-
senior Vice-President present, or next officer in order as above enumer-
ated, to preside at the meetings of the Academy ; to summon extraor-
dinary meetings, upon any urgent occasion ; and to execute or see to
the execution of the Statutes of the Academy. Length of continuous
membership in the Academy shall determine the seniority of the Vice-
Presidents.
/
696 STATUTES OF THE AMERICAN ACADEMY
2. The President, or, in his absence, the next officer as above enumer-
ated, is empowered to draw upon the Treasurer for such sums of money
as the Academy shall direct. Bills presented on account of the Library,
or the Publications of the Academy, must be previously approved by the
respective committees on these departments.
3. The President, or, in his absence, the next officer as above enumer-
ated, shall nominate members to serve on the different committees of the
Academy which are not chosen by ballot.
4. Any deed or writing to which the common seal is to be affixed
shall be signed and sealed by the President, when thereto authorized
by the Academy.
CHAPTER V.
Of Standing Committees.
1. At the Annual Meeting there shall be chosen the following Stand-
ing Committees, to serve for the year ensuing, viz. : —
2. The Committee of Finance, to consist of the President, Treasurer,
and one Fellow chosen by ballot, who shall have full control and man-
agement of the funds and trusts of the Academy, with the power of
investing or changing the investment of the same at their discretion. The
general appropriations for the expenditures of the Academy shall be
moved by this Committee at the Annual Meeting, and all special appro-
priations from the general and publication funds shall be referred to or
proposed by this Committee.
3. The Rumford Committee, of seven Fellows, to be chosen by ballot,
who shall consider and report on all applications and claims for the
Rumford Premium, also on all appropriations from the income of the
Rumford Fund, and generally see to the due and proper execution of
this trust.
4. The C. M. "Warren Committee, of seven Fellows, to be chosen by
ballot, who shall consider and report on all applications for appropria-
tions from the income of the C. M. Warren Fund, and generally see to
the due and proper execution of this trust.
5. The Committee of Publication, of three Fellows, one from each ♦
Class, to whom all communications submitted to the Academy for publi-
cation shall be referred, and to whom the printing of the Memoirs and
the Proceedings shall be intrusted.
6. The Committee on the Library, of the Librarian ex officio and
three other Fellows, one from each class, who shall examine the Library,
and make an annual report on its condition and management.
OF ARTS AND SCIENCES. 697
7. An Auditing Committee of two Fellows, for auditing the accounts
of the Treasurer.
CHAPTER VI.
Of the Secretaries.
1. The Corresponding Secretary shall couduct the correspondence of
the Academy, recording or making an entry of all letters written in its
name, and preserving on file all letters which are received ; and at each
meeting he shall present the letters which have been addressed to the
Academy since the last meeting. Under the direction of the Council
for Nomination, he shall keep a list of the Resident Fellows, Associate
Fellows, and Foreign Honorary Members, arranged in their Classes and
in Sections in respect to the special sciences in which they are severally
proficient ; and he shall act as secretary to the Council.
2. The Recording Secretary shall have charge of the Charter and
Statute-book, journals, and all literary papers belonging to the Academy.
He shall record the proceedings of the Academy at its meetings ; and
after each meeting is duly opened, he shall read the record of the pre-
ceding meeting. He shall notify the meetings of the Academy, apprise
officers and committees of their election or appointment, and inform the
Treasurer of appropriations of money voted by the Academy. He shall
post up in the Hall a list of the persons nominated for election into the
Academy ; and when any individual is chosen, he shall insert in the
record the names of the Fellows by whom he was nominated.
3. The two 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 calculated to promote
its interests.
CHAPTER VII.
Of the Treasurer.
1. The Treasurer shall give such security for the trust reposed in
him as the Academy shall require.
2. He shall receive officially all moneys due or payable, and all
bequests or donations made to the Academy, and shall pay such sums
as the Academy may direct. He shall keep an account of all receipts
and expenditures ; shall submit his accounts to the Auditing Committee ;
and shall report the same at the expiration of his term of office.
698 STATUTES OF THE AMERICAN ACADEMY
3. The Treasurer shall keep separate accounts of the income and
appropriation of the Rumford Fund and of other special funds, and
report the same annually.
4. All moneys which there shall not be present occasion to expend
shall be invested by the Treasurer, under the direction of the Finance
Committee.
CHAPTER VIII.
Of the Librarian and Library.
1. It shall be the duty of the Librarian to take charge of the books,
to keep a correct catalogue of them, to provide for the delivery of books
from the Library, and to appoint such agents for these purposes as he
may think necessary. He shall make an annual report on the condition
of the Library.
2. The Librarian, in conjunction with the Committee on the Library,
shall have authority to expend such sums as may be appropriated, either
from the General, Rumford or other special Funds of the Academy, for
the purchase of books, and for defraying other necessary expenses con-
nected with the Library.
3. To all books in the Library procured from the income of the
Rumford Fund, or other special funds, the Librarian shall cause a stamp
or label to be affixed, expressing the fact that they were so procured.
4. Every person who takes a book from the Library shall give a
receipt for the same to the Librarian or his assistant.
5. Every book shall be returned in good order, regard being had to
the necessary wear of the book with good usage. If any book shall
be lost or injured, the person to whom it stands charged shall replace
it by a new volume or set, if it belongs to a set, or pay the current
price of the volume or set to the Librarian ; and thereupon the remain-
der of the set, if the volume belonged to a set, shall be delivered to the
person so paying for the same.
6. All books shall be returned to the Library for examination at
least one week before the Annual Meeting.
7. The Librarian shall have custody of the Publications of the
Academy and shall distribute copies among the Associate Fellows and
Foreign Honorary Members, at their request. With the advice and con-
sent of the President, he may effect exchanges with other associations.
OF ARTS AND SCIENCES. li'.l'.l
CHAPTER IX.
Of Meetings.
1. There shall be annually four stated meetings of the Academy;
namely, on the second Wednesday in May (the Annual Meeting), on
the second Wednesday in October, on the second Wednesday in January,
aud on the second Wednesday in March. At these meetings only, or at
meetings adjourned from these aud regularly notified, shall appropria-
tions of money be made, or alterations of the statutes or standing votes
of the Academy be effected.
2. Fifteen Fellows shall constitute a quorum for the transaction of
business at a stated meeting. Seven Fellows shall be sufficient to con-
stitute a meeting for scientific communications aud discussious.
3. The Recording Secretary shall notify the meetings of the Academy
to each Fellow residing in Boston and the vicinity ; and he may cause
the meetings to be advertised, whenever he deems such further notice
to be needful.
CHAPTER X.
Of the Election of Fellows and Honorary Members.
1. Elections shall be made by ballot, and only at stated meetings.
2. Candidates for election as Resident Fellows must be proposed by
two Resident Fellows of the section to which the proposal is made, in a
recommendation signed by them, and this recommendation shall be
transmitted to the Corresponding Secretary, and by him referred to
the Council for nomination. No person recommended shall be reported
by the Council as a candidate for election, unless he shall have received
a written approval, signed at a meeting of the Council by at least five
of its members. All nominations thus approved shall be read to the
Academy at a stated meeting, and shall then stand on the nomination
list during the interval between two stated meetings, and until the
balloting. No person shall be elected a Resident Fellow, unless he
shall have been resident in this Commonwealth one year next preceding
his election. If any person elected a Resident Fellow shall neglect for
one year to pay his admission fee, his election shall be void ; and
if any Resident Fellow shall neglect to pay his annual assessments
700 STATUTES OP THE AMERICAN ACADEMY
for two years, provided that his attention shall have been called to this
article, he shall be deemed to have abandoned his Fellowship ; but it
shall be in the power of the Treasurer, with the consent of the Council,
to dispense (sub silentio) with the payment both of the admission fee and
of the assessments, whenever in any special instance he shall think it
advisable so to do.
3. The nomination of Associate Fellows may take place in the manner
prescribed in reference to Resident Fellows. The Council may in like
manner originate nominations of Associate Fellows, which must be read
at a stated meeting previous to the election, and be exposed on the nom-
ination list during the interval.
4. Foreign Honorary Members shall be chosen only after a nomina-
tion made at a meeting of the Council, signed at the time by at least
seven of its members, and read at a stated meeting previous to that on
which the balloting takes place.
5. Three fourths of the ballots cast must be affirmative, and the
number of affirmative ballots must amount to eleven to effect an elec-
tion of Fellows or Foreign Honorary Members.
6. A majority of any section of the Academy is empowered to pre-
sent lists of persons deemed best qualified to fill vacancies occurring in
the number of Foreign Honorary Members or Associate Fellows allotted
to it ; and such lists, after being read at a stated meeting, shall be re-
ferred to the Council for Nomination.
7. If, in the opinion of a majority of the entire Council, any Fellow —
Resident or Associate — shall have rendered himself unworthy of a
place in the Academy, the Council shall recommend to the Academy
the termination of his Fellowship ; and provided that a majority of two
thirds of the Fellows at a stated meeting, consisting of not less than
fifty Fellows, shall adopt this recommendation, his name shall be stricken
off the roll of Fellows.
CHAPTER XI.
Of Amendments of the Statutes.
1. All proposed alterations of the Statutes or additions to them, shall
be referred to a committee, and, on their report at a subsequent meeting,
shall require for enactment a majority of two thirds of the members
present, and at least eighteen affirmative votes.
2. Standing votes may be passed, amended, or rescinded, at any
OF ARTS AND SCIENCES. 701
stated meeting, by a majority of two thirds of the members present.
They may be suspended by a unanimous vote.
CHAPTER XII.
Of Literary Performances.
1. The Academy will not express its judgment on literary or
scientific memoirs or performances submitted to it, or included in its
publications.
702 STATUTES OP THE AMERICAN ACADEMY
STANDING VOTES.
1. Communications of which notice had been given to the
Secretary shall take precedence of those not so notified.
2. Resident Fellows who have paid all fees and dues charge-
able to them are entitled to receive one copy of each volume or
article printed by the Academy, on application to the Librarian
personally or by written order, within two years from the date
of publication. And the current issues of the Proceedings shall
be supplied, when ready for publication, free of charge, to all the
Fellows and members of the Academy who desire to receive them.
3. The Committee of Publication shall fix from time to time
the price at which the publications of the Academy may be, sold.
But members may be supplied at half this price with volumes
which they are not entitled to receive free, and which are needed
to complete their sets.
4. Two hundred extra copies of each paper accepted for publi-
cation in the Memoirs or Proceedings of the Academy shall be
placed at the disposal of the author, free of charge.
5. Resident Fellows may borrow and have out from the
Library six volumes at any one time, and may retain the same
for three months, and no longer.
6. Upon special application, and for adequate reasons assigned,
the Librarian may permit a larger number of volumes, not exceed-
ing twelve, to be drawn from the Library for a limited period.
7. Works published in numbers, when unbound, shall not be
taken from the Hall of the Academy, except by special leave of
the Librarian.
8. Books, publications, or apparatus shall be procured from the
income of the Rumford Fund only on the certificate of the Rum-
ford Committee that they, in their opinion, will best facilitate
and encourage the making of discoveries and improvements which
may merit the Rumford Premium.
9. A meeting for receiving and discussing scientific commu-
nications may be held on the second Wednesday of each month
not appointed for stated meetings, excepting July, August, and
September.
OF ARTS AND SCIENCES. 703
RUMFORD PREMIUM.
In conformity with the terms of the gift of Benjamin, Count
Rum ford, granting a certain fund to the American Academy of
Arts and Sciences, and with a decree of the Supreme Judicial
Court for carrying into effect the general charitable intent and
purpose of Count Rumford, as expressed in his letter of gift, the
Academy is empowered to make from the income of said 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 in heat, which shall
have been made and published 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 being always given to
such discoveries as shall, in the opinion of the Academy, tend
most to promote the good of mankind ; and to add to such
medals, as a further premium for such discovery and improve-
ment, if the Academy see fit so to do, a sum of money not
exceeding three hundred dollars.
INDEX.
Note. For index to the species of Carex, see pp. 510-512.
Acanthophora Thierii, 256.
Acetabularia crenulata, 247.
Acetylene Flame, Temperature of
the, 88. .
Acompsomyces, 37.
Corticariae, 37.
Acrasieae, 334.
Acrasis, 338.
granulata, 338.
Agardhiella tenera, 253.
Agassiz, A., Albatross Expedition to
the Tropical Pacific, 614.
Alaska, Epidote Crystals from, 529-
535, 617.
Albatross Expedition, 614.
Algae of Jamaica, 229-270, 614.
Amansia multifida, 257.
Americanists, International Congress
of, 613, 615.
Ames, J. B., Biographical Notice of
James Bradley Thayer, 628,
679-681.
Amphiroa charoides, 260.
debilis, 261.
fragilissiina, 261.
Anadyoniene stellata, 247.
Antithamnion Butleriae, 258.
Apatite from Minot, Maine, 515-528,
615, 617.
Archibald, E. H. See Richards,
T. W., and Archibald, E. H.
Asparagopsis Delilei, 255.
Assessment, Amount of, 608, 626.
Atharva Veda. 615.
Atkinson, E., What Science has not
yet accomplished in the Art of
War. 618.
Atomic Hypothesis, A New, 307-41 1 .
Atomic Volume, The Possible Sig-
nificance of Changing, 1-17, 397-
411, 612.
Atomic Weight of Copper, 436.
vol. xxxvi i. — 45
Atomic Weightof Uranium, 363-395,
615.
Atomic Weights, Table of, 630;
The Standard of, 175-181, 615.
Avrainvillea longicaulis, 245.
nigricans, 245.
Balfour, A. J., elected Foreign
Honorary Member, 628.
Bams, C.,Rumford Medal presented
to, 614.
Basquin, O. H., The Arc Spectrum
of Hydrogen, 159-174.
Bizzozero, G., Death of, 599.
Black, C. W. M., The Parametric
Representation of the Neighbor-
hood of a Singular Pojnt of an
Analytic Surface, 279-330, 614.
Blake, C. J., Obituary Notice of J.
H. Blake, 612.
Blake, F., Report of Treasurer (1900-
01), 599, (1901-02), 620.
Blake, J. II., Obituary Notice of, 612.
Bostrychia Mazei, 257.
Moritziana var. intermedia, 257.
tenella, 257.
Botryophora occidentalis, 217.
Brunton, L., accepts Membership,
612.
Bryopsis Harveyana, 244.
pennata, 244.
Bryothamnion Seaforthii, 257.
triangular^, 257.
Building Fund, 601, 622.
Cabot, S., Experiments on Forms
of Least Resistance to Passage
Ih rough Air, 618.
Calhane, D. F. See .Jackson, C. I./.,
and Calhane, D. F.
Callithamnion byssoideum var. Ja-
maicensis, 258.
706
INDEX.
Callithamnion corymbosum, 258.
Caloglossa Leprieurii, 255.
Calothrix aeruginea, 241.
confervicola, 241.
Calothrix Contarenii, 241.
fusca, 241.
Juliana, 241.
pilosa, 242.
Carbon, The Visible Radiation from,
71-118, 612.
Carex. (For index of species, see
pp. 510-512.)
Carices of the Section Hyparrhenae,
445-495, 612.
Carices, Variations of some Boreal,
495-514, 612.
Case School of Applied Science. See
Chemical Laboratofy.
Catenella Opuntia var. pinnata, 253.
Caulerpa cupressoides var. ericifolia,
244.
cupressoides var. mamillosa, 244.
cupressoides var. Turned, 244.
cupressoides var. typica, 244.
pinnata forma Mexicana, 244.
plumaris forma brevipes, 245.
plumaris forma longiseta, 244.
prolifera, 245.
racemosa var. clavifera, 245.
racemosa var. clavifera forma
macrophysa, 245.
taxifolia, 245.
verticillata, 245.
verticillata forma charoides, 245.
Cauloglossum transversarium, 628.
Celli, A., elected Foreign Honorary
Member, 612 ; accepts Member-
ship, 615.
Ceramium byssoideum, 259.
clavulatum, 259.
fastigiatum, 259.
gracillimum, 259.
nitens, 259.
tenuissimum, 259.
tenuissiinum var. pygmaeum,
259.
Ceratomyces Braziliensis, 44.
curvatus, 43.
Mexicanus, 43.
procerus, 43.
spinigerus, 42.
Chaetomorpha aerea, 243.
brachygona, 243.
clavata, 243.
Linum, 243.
Chaetomorpha Linum var. brachyar-
thra, 243.
Melagonium, 243.
Chamaedoris annulata, 247.
Chamberlin, T. C, elected Associate
Fellow, 611.
Champia parvula, 255.
Chantransia Saviana, 251.
Chemical Combination, Probable
Source of the Heat of, 397.
Chemical Laboratory of 4Iarvard
College, Contributions from, 175,
271, 345, 363, 397, 413.
Chemical Laboratory of the Case
School of Applied Science, Con-
tributions from, 537, 563.
Cherbourg, National Soc. of Nat.
and Math. Sci., Fiftieth Anni-
versary, 614, 617.
Chitonomyces Bullardi, 31.
Hydropori, 32.
occultus, 30.
Orectogyri, 32.
psittacopsis, 30.
Chlamy domyxa labyrinthuloides, 344.
Chondria Baileyana, 256.
dasyphylla, 256.
tenuissima, 256.
Christiania, Royal University of, The
100th anniversary of birth of
N. H. Abel, 620.
Chroococcus turgidus, 239.
Chroothece Richteriana, 239.
Chrysymenia halymenioides, 255.
Cladophora crystallina, 243.
fascicularis, 243.
fuliginosa, 243.
Hutchinsiae, 243.
intertexta, 243.
trichocoma, 244.
Clifford, II. E., elected Resident
Fellow, 616 ; accepts Fellowship,
620.
Cocos Island, Flora of, 628.
Codium adhaerens, 246.
tomentosum, 246.
Ccenonia, 342.
denticulata, 342.
Collins, F. S., accepts Fellowship,
599 ; The Algae of Jamaica, 229-
270, 614.
Colpomeuia sinuosa, 248.
Committee, Nominating, 617, 619.
Committees elected, 610, 627; List
of, 683.
INDEX.
707
Concentrated Solutions, 345.
Cooke, J. P., Bronze Bas-relief of, 614.
Corallina capillacea, 261.
Cubensis, 261.
pumila, 261.
rubens, 261.
subulata, 261.
Cordylecladia irregularis, 254.
Peasiae, 255.
Corethromyces Latonae, 41.
Stilici, 42.
Cornu, A., Death of, 620.
Council, Report of, 620, 635.
Crew, EL, Grant from Income of
Rumford Fund to, 623.
Cross, C. R., President pro tern., 617 ;
Report of the Rumford Com-
mittee (1900-01), 601, (1901-
02), 623.
Crouania attenuata, 258.
Cruoriella Armorica, 260.
Cryptogamic Laboratory of Harvard
University, Contributions from,
19, 331, 612, 628.
Cryptonemia crenulata, 260.
Curves, Multiple Points of Twisted,
628.
Cutleria, 248.
Cylindrospermum musciola, 240.
Cymopolia barbata, 247.
Dante, The Malignity of, 614.
Dasya arbuscula, 257.
Gibbesii, 257.
niucronata, 257.
Dasycladus clavaeformis, 247.
Davis, A. McF., Biographical Notice
of John Fiske, 620, 665-678.
Davis, W. M., The Formation of
River Terraces, Iil9.
Delitzsch, F., elected Foreign Hon-
orary Member, 616 ; accepts
Membership, 618.
Dibromdinitrobenzols, 629.
Dicey, A. V., accepts Membership,
'613.
Dichomyces Australiensis, 28.
Belonuchi, 27.
bifidus, 26.
Homalotae, 29.
Mexican us, 28.
Dicothrix penicillata, 242.
Dictyerpa Jamaicensis, 1251.
Dictyopteris delicatula, 249.
Justii, 249.
Dictyopteris plagiogramma, 249.
Dictyosphaeria favulosa, 247.
Dictyosteliacepe, 338.
Dictyostelium, 338.
aureum, 340.
brevicaule, 340.
lacteum, 339.
nmcoroides, 338.
purpureum, 340.
roseum, 3;!!).
sphasrocephalum, 339.
Dictyota Bartayresiana, 250.
cervicornis, 250.
ciliata, 250.
dentata, 250.
dichotoma, 250.
divaricata, 250.
fasciola, 250.
Dictyurus occidentalis, 257.
Digenea simplex, 256.
Dilophus alternans, 250.
Guineensis, 250.
Dinitrobenzolsuli>honic Acid, Sym-
metrical, 629.
Dioicomyces, 33.
Anthici, 33.
onchophorus, 34.
spinigerus, 34.
Diplochaete solitaria, 242.
Diplophrys, 343.
Archeri, 343.
stercorea, 344.
Directive Stimuli, Reactions of Limax
maximus to, 183-227.
Dunkel, ()., Regular Singular Points
of a System of Floniogeneous
Linear Differential Fquations
of the First Order, 628.
Earle, R. B. See Jackson, C. L., and
Earle, R. B.
Ectocarpus Mitchellae, 248.
Engler, A., elected Foreign Honor-
ary Member, 611 ; accepts Mem-
bership, 613.
Enteromorpha erecta, 242.
nexuosa, 242.
intestinalis, 212.
prolifera, 242.
Epidote Crystals from Alaska, 529-
535, 617.
Eucheuma echinocarpum, 253.
Euhaplomyces, 25.
Ancyrophori, 25.
Xanthophaeae, 26.
708
INDEX.
Eumonoicomyces, 21.
Californicus, 22.
Papuanus, 22.
Everett, W., The Malignity of Dante,
614.
Farlow, W. G., Account of the Ninth
Jubilee Celebration of the Uni-
versity of Glasgow, 619.
Federal Legacy Tax, 599.
Fellows, Associate, deceased, —
King, C, 617.
LeConte, J., 613.
Rowland, H. A., 599.
Fellows, Associate, elected, —
Chamberlin, T. C, 611.
Fritz, J., 611.
Pepper, G. W., 613.
Putnam, H., 618.
Wilson, E. B., 616.
Fellows, Associate, List of, 689.
Fellows, Resident, deceased, —
Fiske, J., 613.
Hyatt, A., 617.
Safford, T. H., 613.
Thayer, J. B., 618.
Thayer, J. H., 615.
Fellows, Resident, elected, —
Clifford, H. E., 616.
Hoar, G. F., 611.
Hofman, H. O., 618.
Hough, T., 616.
Jaggar, T. A, Jr., 618.
Morgan, M. H., 616.
Porter, W. T., 613.
Pritchett, H. S., 613.
Strobel, E. H., 618.
Williams, F. II. , 616.
Fellows, Resident, List of, 685.
Fernald, M. L., The Northeastern
Carices of the Section Hypar-
rhenae, 445-495, 612; The Va-
riation of Some Boreal Carices,
495-514, 612.
Fiske, A. H. See Jackson, C. L.,
and Fiske, A. H.
Fiske, J., Death of, 613; Notice of,
620, 665-67S.
Foreign Honorary Members de-
ceased, —
Cornu, A., 620.
Gardiner, S. R., 618.
Grimm, F. H., 613.
Kovalevskv, A. O., 615.
Lacaze-Duthiers, F. J. H., 613.
Foreign Honorary Members de-
ceased, —
Nordenskiold,FriherreA.E.,613.
Stubbs, W., 599.
Weinhold, K., 617.
Foreign Honorary Members elected, —
Balfour, A. J., 628.
Celli, A., 612.
Delitzsch, F., 616.
Engler, A., 611.
Gardiner, S. R., 616.
Hann, J., 616.
Horsley, V. A. H., 616.
Lankester, E. R., 616.
Lecky, W. E. H., 628.
Paris, G., 612.
Richthofen, Freiherr F. von,
611.
Foreign Honorary Members, List of,
691.
Forms of Least Resistance to Pas-
sage through Air, 618.
Frandsen, P., Studies on the Reac-
tions of Limax maximus to
Directive Stimuli, 183-227.
Fritz, J., elected Associate Fellow,
611.
Fugacity, 54-69.
Galapagos Flora, Revision of, 617.
Galaxaura cylindrica, 252.
lapidescens, 252.
marginata, 252.
obtusata, 252.
rugosa, 252.
Gardiner, S. R., Death of, 618 ; elected
Foreign Honorary Member, 616 ;
accepts Membership, 618.
Gas- Apparatus, Hempel's, 271-277,
615.
Gases, Fugacity of Imperfect, 66 ; at
High Temperatures, Spectra of,
619.
Gelidium coerulescens, 252.
crinale, 253.
rigidum, 253.
supradecompositum, 253.
General Fund, 600, 621, 625.
Geotaxis, 190.
Glasgow, University of, Ninth Jubi-
lee Celebration, 619.
Gloeocapsa quaternata, 239.
Gloeotrichia natans, 242.
Goldstein, A. H. See Mabery, C.
F., and Goldstein, A. H.
INDEX.
709
Gomontia polyrhiza, 244. _
Goniotrichum Humphreyi, 251.
elegans, 251.
Gracilaria Blodgettii, 253.
caudata, 253.
cervicornis, 253.
compressa, 253.
confervoides, 253.
cornea, 253.
Curtissiae, 253.
damaecornis, 254.
divaricata, 254.
Domingensis, 254.
ferox, 254.
multipartita, 254.
Wrightii, 254.
Grants, from Income of C. M. War-
ren Fund, 605, 607, 625, 626;
from Income of Kumford Fund,
601, 623, 626.
Grateloupia filicina, 260.
dichotoma, 260.
prolongata, 260.
Gray Herbarium of Harvard Univer-
sity, Contributions from, 445,
612, 617, 628.
Grimm, F. H., Death of, 613.
Guttulina, 337.
aurea, 337.
protea, 337.
rosea, 337.
sessilis, 338.
Guttulinacese, 335.
Guttulinopsis, 335.
clavata, 336.
stipitata, 336.
vulgaris, 336.
Gymnosorus variegatus, 249.
Hale, G. E., accepts Fellowship,
612 ; Grant from Income of Rum-
ford Fund to, 601 ; Radiometer,
601; Rumford Premium awarded
to, 624, 628.
Halimeda Opuntia, 246.
tridens, 246.
Tuna, 246.
Halodictyon mirabile, 258.
Haloplegma Uuperryi, 258.
Halymenia Floresia, 260.
Hann, J., elected Foreign Honorary
Member, 616; accepts Member-
ship, 618.
Hapalosiphon fontinalis, 241.
Harvard College. See Chemical Lab-
oratory, Cryptogamic Labora-
tory, Gray Herbarium, and
Zoological Laboratory.
Harvard Mineralogical Museum, Con-
tributions from, 515, 529.
Heat of Chemical Combination, Prob-
able Source of, 397-111, 617.
Heat of Vaporization, 537-549, 618.
Heimrod, G. W. See Richards, T.
W., and Heimrod, G. W.
Hempel's Gas- Apparatus, Modifica-
tions of, 271.
Herty, C. H., Grant from C. M.
Warren Fund to, 605, 607.
Heterosiphonia Wurdemanni, 257.
Higginson, T. W., Biographical No-
tice of Horace Elisha Scudder,
619, 657-661.
Hildenbrantia prototypus, 260.
Hoar, G. F., elected Resident Fellow,
611.
Hofman, II. O., elected Resident
Fellow, 618 ; accepts Fellow-
ship, 620; Grant from Income
of C. M. Warren Fund to, 625,
626.
Hormothamnion enteromorphoides,
241.
Horsley, V. A. II., elected Foreign
Honorary Member, 616; accepts
Membership, 618.
Hough, T., elected Resident Fellow,
616; accepts Fellowship, 617.
Hudson, J. E., Obituary Notice of,
612.
Hyatt A., Death of, 617 ; Notice of,
628.
Hydrocarbons in Pennsylvania Pe-
troleum, 563-595, 620.
Hydrocarbons, Paraffiue and Methy-
lene, 537-549, 618.
Hydroclathrus cancellatus, 248.
Hydrogen, Arc Spectrum of, 159-174.
Hyparrhenae, Carices of the Section,
445-495.
Hypnea, divaricata, 254.
musciformis, 251.
Valentiae, 254:
Iron, Arc Spectrum of, 028.
Jackson, C. L., Report of the C. M.
Warren Committee (1900-01),
605, (1901-02), 625.
710
INDEX.
Jackson, C. L., and Calhane, D. F.,
On the Dibromdinitrobenzols
derived from Paradibromben-
zol, 629.
Jackson, C. L., and Earle, R. B., On
certain Derivatives of Picric Acid,
621); On Symmetrical Dinitro-
benzolsulphonic Acid, 629 ; On
the Colored Substances derived
from Nitro-compounds, 629.
Jackson, C. L., and Fiske, A. H.,
On certain Derivatives of 1, 2,
3-Tribrombenzol, 629.
Jackson, H., Foreign Honorary Mem-
ber, 613.
Jaggar, T. A., Jr., elected Resident
Fellow, 618 ; accepts Fellowship,
620.
Jamaica, Algae of, 229-270.
Johnston, J. R., On Cauloglossum
transversarium (Bosc) Fries, 628.
Kainomyces, 44.
Isomali, 45.
Keen, W. W., accepts Fellowship,
612.
King, C, Death of, 617.
Koch, R., accepts Membership, 613.
Kovalevsky, A. O., Death of, 615.
Laboulbeniaceae, Preliminary Diag-
noses of New Species of, 19-45,
612, 628.
Labyrinthula, 343.
Cienkowskii, 343.
macrocystis, 343.
vitellina, 343.
Labyrinthulesc, 342.
Lacaze-Duthiers, F. J. II. de, Death
of, 613.
Lankester, E. R., elected Foreign
Honorary Member, 616; accepts
Membership, 618.
Lanman, C. R., The Atharva Veda
and its Significance for the His-
tory of Hindu Tradition and
Hindu Medicine, 615.
Laurencia cervicornis, 255.
implicata, 255.
obtusa, 255.
papillosa, 255.
perforata, 256.
tuberculosa var. gemmifera, 256.
Lecky, W. E. H., elected Foreign
Honorary Member, 628.
LeConte, J., Death of, 613.
Legacy Tax, Federal, 599.
Lewis, G. N., The Law of Physico-
chemical Change, 47-69.
Liagora Cheyneana, 251.
decussata, 252.
elongata, 252.
pulverulenta, 252.
valida, 252.
Librarian, Report of, 606, 622.
Libraiy, Appropriations for, 607.
Library, Committee on the, Report
of, 606.
Limax maximus, Reactions of, 183-
227.
Lithothamnion incrustans, 260.
Lenormandi, 260.
Loci in n-Fold Space, On Ruled, 119—
157, 612.
Lophosiphonia obscura, 257.
Lowell, A., Notice of, 614, 635-654.
Lowell, A. L., Party Votes in Par-
liament, Congress, and the State
Legislatures, 617.
Lowell, P., Biographical Notice of
Augustus Lowell, 614, 635-654 ;
Some Results from the Last
Opposition of Mars, 615.
Lyman, T., accepts Fellowship, 612.
Lyngbya aestuarii, 240.
confervoides forma violacea, 240.
majuscula, 240.
putalis, 240.
versicolor, 240.
Mabery, C. F., Grant from Income
of C. M. Warren Fund to, 605,
607, 625, 626 ; On the Hydrocar-
bons in Pennsylvania Petroleum
with Boiling Points above 216°,
620, 563-595.
Mabery, C. F., and Goldstein, A. H.,
On the Specific Heats and Heat
of Vaporization of the Paraffine
and Methylene Hydrocarbons,
537-549, 618.
MacDonald, A., Psycho-Physicai Lab-
oratory, 599.
Magnesium, Arc Spectrum of, 628.
Mall, F. I'., accepts Fellowship, 599.
Manchioneal, 255.
Mark, E. L. See Zoological Labor-
atory etc., Contributions from.
Markovnikoff, V., 599.
Mars, Last Opposition of, 615.
INDEX.
711
Mastick, S. C, Federal Legacy Tax,
599.
Mastio-ocoleus testarum, 241.
Melobesia farinosa, 200.
Lejolisii, 260.
membranacea, 260.
pustulata, 260.
Mendenhall, C. E., Bolometer, 601 ;
Grant from Income of Rumford
Fund to, 601.
Mendenhall, T. C, Associate Fellow,
616.
Mercurous Chloride, The Decompo-
sition of, 345-361, 615.
Merigold, B. S. See Richards, T.
W., and Merigold, B. S.
Messedaglia, A., Death of, 599.
Microcoleus chthonoplastes, 240.
tenerrimus, 240.
vaginatus, 240.
Microdictyon umbilicatum, 247.
Minot, Maine, Apatite from, 515-
528, 615, 617.
Mislawsky, A., Fiftieth Anniversary,
614.
Monoicomyces, 23.
Aleocharae, 24.
Echidnoglossae, 23.
furciliatns, 24.
Moore, E. PL, accepts Fellowship,
612.
Moreno, H. C, On Ruled Loci in
rc-Fold Space, 119-157, 612.
Morgan, M. II., elected Resident
Fellow, 616, 617.
Miiller-Breslau, H., accepts Member-
ship, 613.
Murrayella periclados, 257.
Museum of Comparative Zoology.
See Zoological Laboratory.
Mycoidea parasitica, 243.
Neighborhood of a Singular Point,
279.
Neomeris dumetosa, 247.
Nichols, E. F., Grant from Income
of Rumford Fund to, 623.
Nichols, E. L., The Visible Radia-
tion from Carbon, 71-118, 612.
Nitro-compounds. Colored Sub-
stances derived from, 629.
Nobel Committee, Nobel Prize, 614.
Nordenskiold, Friherre A. E., Death
of, 613.
Nostoc commune, 240.
Nostoc microscopicum, 240.
verrucosum, 210.
Noyes, A. A., Electrical Conductivity,
602; Grant from Income of C.
M. Warren Fund to, 605, 607,
625, 626; Grant from Income of
Rumford Fund to, 602, 623.
Nuremberg, Natural History Society
of, One hundredth Anniversary,
613.
Officers elected, 610, 618,626; List
of, 683.
Olive, E. W., A Preliminary Enum-
eration of the Sorophorae, 331-
344.
Ophthalmological Hospital, 599.
Oppenheimer, A., Certain Sense
Organs of the Proboscis of the
Polychaetous Annelid Rhvncho-
bolus dibrancliiatus, 551-562.
Oscillatoria anguina, 239.
Corallinae, 239.
formosa, 239.
princeps, 239.
princeps forma purpurea, 239.
proboscidea, 239.
tenuis, 239.
Oxford, University of, 300th Anni-
versary Bodleian Library, 620.
Packard, A. S., Biographical Notice
of Alpheus Hyatt, 628.
Padina Durvillaei, 249.
Palache, C, A Description of Epi-
dote Crystals from Alaska, 529-
535, 617.
Palache, C. See Wolff, J. E., and
Palache, C.
Paraffine and Methylene Hydrocar-
bons, Specific Heat of, 537-549,
618. _
Parametric Representation of the
Neighborhood of a Singular
Point, 279-330, 614.
Paris, G., elected Foreign Honorary
Member, 612 ; accepts Member-
ship, 613.
Penicillus capitatus, 245.
dumetosus, 245.
Pennsylvania Petroleum, Hydrocar-
bons in, 5<!3.
Pepper, G. W. , elected Associate
Fellow, 613 ; accepts Fellowship,
614.
712
INDEX.
Petroleum, Composition of, 563-595,
620.
Peyritschiella Xanthopygi, 29.
Peysonnellia Dubyi, 260.
rubra, 260.
Phormidium Retzii, 239.
Phototaxis, 206.
Physico-chemical Change, The Law
of, 47-69.
Pickering, E. C, Co-operation in Ad-
ministering Research Funds,
602.
Picric Acid, Derivatives of, 629.
Pissaroff, V., Ophthalmological Hos-
pital, 599.
Plectonema Nostocorum, 240.
Wollei, 240.
Plowman, A. B., On the Ionization
of Soils, 628.
Poincare, H., accepts Membership,
613.
Points, Multiple, 628.
Points, Regular Singular, 628.
Polysiphonia cuspidata, 256.
ferulaea, 256.
Havanensis, 256.
Havanensis var. Rinneyi, 256.
Pecten-Veneris, 256.
secunda, 256.
subulata, 256.
Polysphondylium, 341.
album, 342.
pallidum, 341.
violaceum, 341.
Porter, R. A., The Influence of
Atmospheres of Nitrogen and
Hydrogen on the Arc Spectra
of Iron, Zinc, Magnesium and
Tin, compared witli the Influ-
ence of an Atmosphere of Am-
monia, 628.
Porter, W. T., elected Resident
Fellow, 613 ; accepts Fellowship,
614.
Pringsheimia scutata, 243.
Pritchett, H. S., elected Resident
Fellow, 613.
Psycho-Physical Laboratory, 599.
Publication, Committee of, Report
of, 605, 625.
Publications, Appropriations for, 607,
626.
Putnam, F. W., Archaeological Work
of J. H. Blake, 612.
Putnam, H., Delegate to Bodleian
Library Commemoration, 620;
elected Associate Fellow, 618;
accepts Fellowship, 620.
Radiation from Carbon, The Visible,
71-118, 612.
Records of Meetings. 599-628.
Rhacomyces Dolicaontis, 39.
Glyptomeri, 39.
Oedichiri, 38.
Rhipocephalus Phoenix, 245.
Rhynchobolus dibi'anchiatus, 551-
562.
Richards, T. W., Grant from Income
of Rumford Fund to, 602, 624,
626 ; Modifications of Hempel's
Gas- Apparatus, 271-277, 615;
Table of Atomic Weights, 630';
The Possible Significance of
Changing Atomic Volume, 1-17,
397-411, 612; The Probable
Source of the Heat of Chemical
Combination, and a New Atomic
Hypothesis, 397-411, 617; The
Standard of Atomic AVeights,
175-181, 615 ; Thomson-Joule
Experiment, 602, 624.
Richards, T. W., and Archibald, E.
II., The Decomposition of Mer-
curons Chloride by Dissolved
Chlorides : a Contribution to
the Study of Concentrated So-
lutions, 345-361, 615.
Richards, T. W., and Ileimrod, G.
W., On the Accuracy of the
Improved Voltameter, 413-443.
Richards, T. W., and Merigold, B.
S., A new Investigation con-
cerning the Atomic Weight of
Uranium, 363-395, 615.
Richthofen, F. Freiherr von., elected
Foreign Honorary Member, 611;
accepts Membership, 613.
River Terraces, 619.
Robinson, B. L., Diagnoses and Syn-
onymy of some Mexican Sper-
matophytes, 628 ; Flora of Cocos
Island of the Pacific, 628; Re-
vision of the Galapagos Flora,
617.
Rotch, A. L., Report of Librarian,
606, 622.
Rowland, H. A., Death of, 599.
Rumford Committee, Report of
(1900-01), 601, (1901-02), 623.
INDEX.
713
Rumford Fund, 600, 621 ; Appro-
priations from Income of, 607,
624, 626; Papers published by-
Aid of, 71, 159, 397.
Rumford Medals, Presentation of,
614 ; Replicas, 002, 607.
Rumford Premium, 703; Awards of,
604 (Complete List from 1839
to 1900 inclusive), 607, 624, 628.
Safford, T. II., Death of, 613; Notice
of, 654-656.
Sappinia, 335.
pedata, 335.
Sappiniacea?, 334.
Sargassum bacciferum, 248.
lendigerum, 248.
platycarpuin, 248.
vulgare, 248.
vulgare forma ovata, 248.
vulgare var. foliosissimum, 249.
Schizothrix coriacea, 240.
Mexicana, 240.
Scudder, H. E., Notice of, 619, 657-
601.
Scudder, S. II., Report of Committee
of Publication (1900-01), 605,
(1901-02), 625.
Scytonema Arcangelii, 241.
conchophilum, 241.
crispum, 241.
densum, 241.
Ilofmanni, 241.
Javanicum, 241.
ocellatum, 241.
Searle, A., Biographical Notice of
Truman Henry Safford, 654-656.
Sedgwick, W. T.,'and Winslow, C-
E. A., Experiments on the Effect
of Freezing and other Low Tem-
peratures upon the Viability of
the Bacillus of Typhoid Fever,
with Considerations regarding
Ice as a Vehicle of Infectious
Disease, 619 ; Statistical Studies
on the Seasonal Prevalence of
Typhoid Fever in Various Coun-
tries and its Relation to Seasonal
Temperature, 619.
Sense Organs of the Proboscis of
Rhynchobolus, 551-562.
Silver, Electrochemical Equivalent of,
438.
Siphonocladus membranaceus, 247.
tropicus, 247.
Soils, Ionization of, 628.
Solieria chordalis, 253.
Solutions, Concentrated, 345-361.
Sorophoran, A Preliminary Enumera-
tion of the, 331-344.
Spatoglossum Schroederi, 249.
Specific Heat of Hydrocarbons, 537-
549.
Spectra, Arc, of Iron, Zinc, Magne-
sium and Tin, 628.
Spectra of Gases, 6 19.
Spectrophotometer, 87.
Spectrophotometric Observations,
103.
Spectrum of Hydrogen, The Arc, 159-
174.
Spermatophytes, Diagnoses and Syn-
onymy of some Mexican, 628.
Spermothamnion Gorgoneum, 258.
Turneri var. variabile, 258.
Sphaleromyces Chiriquensis, 40.
Indicus, 41.
Quedionuchi, 39.
Spirogyra decimina, 242.
Spyridia aculeata. 259.
filamentosa, 259.
Standing Committees appointed, 611,
627.
Standing Votes, Amendment of,
619.
Statutes, Amendments of the, 608,
616.
Statutes and Standing Votes, 693.
Stichomyces, 37.
Conosomae, 38.
Stigeoclonium tenue, 242.
Striaria attenuata, 248.
attenuata var. ramosissima, 218.
Strobel, E. II., elected Resident
Fellow, 618; accepts Fellowship,
620.
Stubbs, W., Death of, 599.
Stypopodium lobatum, 249.
Swain, G. F., Secretary pro fern,
615.
Symploca hydnoides var. genuina,
240.
hydnoides var. fasciculata, 240.
Teratomyces insignis, 36.
petiolatus, 30.
Zealandica, 35.
Thaxter, 11., Preliminary Diagnoses
of New Species of Laboulbeni-
aceae, IV., 19-45, 612 ; V., 628.
714
INDEX.
Thayer, J. B., Death of, 618; Notice
of, 628, 679-681 ; Obituary No-
tice of John E. Hudson, 612.
Thayer, J. 11., Death of, 615 ; Notice
of, 619, 661-664.
Thigniotaxis, 187.
Thomson, E., Rumford Medal pre-
sented to, 614; Rumford Pre-
mium awarded to, 607.
Tin, Arc Spectrum of, 628.
Toy, C. H., Biographical Notice of
Joseph Henry Thayer, 619, 661-
664.
Treasurer, Annual Report of (1900-
01), 599, (1901-02), 620.
Tribrombenzol, 629.
Trowbridge, .1., The Spectra of Gases
at High Temperatures, 619.
Turbinaria trialata, 248.
Typhoid Fever, 619.
Udotea conglutinata, 246.
flabellata, 246.
Ulva fasciata, 242.
Lactuca var. rigida, 242.
Uranium, Atomic Weight of, 303-
395.
Valonia aegagropila, 246.
ventricosa, 246.
verticillata, 247.
Van der Vries, J. N., On the Mul-
tiple Points of Twisted Curves,
628.
Voltameter, Accuracy of the Im-
proved, 413-443.
Vries, J. N. Van der. See Van der
Vries, J. N.
Walcott, H. P., elected Vice-Presi-
dent, 618, 620.
War, Art of, 618.
Warren (C. M.) Committee, Report
of (1900-01), 605, (1901-02), 625.
Warren (C. M.) Fund, 601, 622;
Appropriations from Income of,
607, 626 ; Paper published by
Aid of, 563.
Webster, A. G., Grant from Income
of Rumford Fund to, 623.
Weinhold, K., Death of, 617.
Whitman, C. O., accepts Fellowship,
612.
Williams, F. H., elected Resident
Fellow, 616.
WTilson, E. B., elected Associate
Fellow, 616 ; accepts Fellowship,
617.
Winslow, C.-E. A. See Sedgwick,
W. T., and Winslow, C.-E. A.
Wolff, J. E., and Palache, C, Apatite
from Minot, Maine, 515-528, 615,
617.
Wood, R. W., Grant from Income of
Rumford Fund to, 623.
Wrangelia Argus, 252.
Xenococcus Schousboei, 239.
Yale University, Two-hundredth An-
niversary, 613.
Zinc, Arc Spectrum of, 628.
Zoological Laboratory of the Mu-
seum of Comparative Zoology
at Harvard College, Contribu-
tions from, 183, 551.
New York Botanical Garden Librar
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