Proceedings of the American Academy of Arts and Sciences

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PROCEEDINGS

OF THE

AMERICAN ACADEMY

OF

ARTS AND SCIENCES.

Vou. XLVIII.

FROM MAY 1912, TO MAY 1913.

BOS TON:
PUBLISHED BY THE ACADEMY
1913

The Cosmos Press

EDW. W. WHEELER

CAMBRIDGE, MASS.
||

CONTENTS.

PAGE
On the Ultra Violet Component in Artificial Light. By Louis
BELL : Ἐν Sb On eS Ἐς 1
Alexander Agassiz. By Henry Ρ. Waucotr 31
A Theory of Linear Distance and Angle. By H. B. PxHtnures
and C. L. E. Moors Serta aes τ 3)
Preliminary Diagnoses of New Species of Chaetomium. By A.
H. CHIVERS 81
A Study with the Echelon Spectroscope of Certain Lines in the
Spectra of the Zinc Arc and Spark at Atmospheric Pressure.
By Norton A. Kent 91
The Impedance of Telephone Receivers as affected by the Motion
of their Diaphragms. By A. E. KennEtLyY and G.W. Pierce 111
New or Critical Laboulbeniales from the Argentine. By Routanp
THAXTER - 155
Culture Studies of Fungi producing Bulbils and Similar Propaga-
tive Bodies. By J. W. Hotson + 225

Thermodynamic Properties of Liquid Water to 80° and 12000
Kgm. By P. W. BripGMan

Preliminary Descriptions of New Species of Rickia and Treno-
myces. By Rontanp THAXTER

The Space-Time Manifold of Relativity. The Non-Euclidean
Geometry of Mechanics and Electromagnetics. By EH. B.
Witson and ἃ. N. Lewis :

On the Existence and Properties of the Ether. By D.L. WEBSTER

The History, Comparative Anatomy and Evolution of the Arau-
carioxylon Type. By E. C. Jerrrey

iv CONTENTS.
XIV. The Action of Sulphur Trioxide on Silicon Tetrachloride. By
C. R. Sancer and E. R. Rirceu ot 3 ἡ εν een OS
XV. An Electric Heater and Automatic Thermostat. By A. L.CLuarK 597
XVI. Cretaceous Pityoxyia from Cliffwood, New Jersey. By Rutu

FGEDENS em) τα Bole he ices eee ey Ubi ρον mL
XVII. On the Scalar Functions of Hyper Complex Numbers. By
ἘΠΕ ΝΕ YGe GRABER: 91S oe Wa ed ets PLS Doty ΣΉ 099

XVIII. Preliminary Study of the Salinity ue Sea Water in the Bermudas. ihe ἼἼ |
By ΠῚ Marx . Bue eee ail eee Unie ee

XIX. On Certain Fragments of the Pre-Socratics: Critical Notes and
Hiuctdations. By W.:A.. HEIDEL: τ. (0 4. 40 a) ee ῸΠ

XX. The Structure of the Gorgonian Coral Pseudoplexaura crassa
Wright and Studer, “By W: M.<C@HESTER). 2 τ 4% τ [ὲὺ

XO HR ECORDS) OF) IVERETINGS, τ Ὁ. ἐπι ton ιν δος Τ᾽

BIOGRAPHICAL NOTICES:

oben Amonys “By Re ΕΠ BYEZ. 4, πὸ VY eines es), by OS
Abbott Lawrence Rotch. By R. DrC. Warp ei dees Shay att OU
Charles*hovbert μηδ, Βυ. ΘΟ Ἶ. JACKSONUs) Mor ea). gee en ee
OrxiceRs*aNp Commirtenms FOR 1913-14" wh. i ee 3) en B28
List oF FELLOWS AND FormnIGN Honorary MEMBERS .. .. . 825
STATUTES ANDI STANDING ΘΟ Sy h lel geet) ) pale) --πππΠᾷ.ΠπΠ 990
IVUMEORDEEREMLUNIN SG oc) a) nt-n. teen eee el oe bie ea, Wadeeae se kom Ὁ

]GSA0 Tbe Ta Aen a OS tem eB ema each | νον πυν Bene ΝΘ

Proceedings of the American Academy of Arts and Sciences

Vou. XLVIII. No. 1.— May, 1912.

ON THE ULTRA VIOLET COMPONENT IN ARTIFICIAL
LIGHT.

By Louis BELL.

WiTH Two PuaTEs

INVESTIGATIONS ON LIGHT AND Herat PUBLISHED WITH AID FROM THE

Rumrorp Funp.

THE ULTRA VIOLET COMPONENT IN ARTIFICIAL LIGHT.

By Louis BELL.

Presented March 13. Received March 25, 1912.

Purpose of the Investigation. —The fundamental purpose of this
study has been definitely to evaluate the amount of energy given by
various artificial illuminants in the ultra violet portion of the spectrum.
In particular, beside determining the general proportion of ultra
violet rays and their actual amount in each lamp investigated, the
writer has determined in absolute measure the ultra violet energy
delivered by each light source for unit illuminating value. Assuming
that each of the artificial lights studied is to be used to produce a
certain given illumination, the amount of. ultra violet radiation in-
cidental to that illumination has been set down in absolute terms of
ergs per second per sq. c. m. This classification of illuminants, which
has not hitherto been made, is important in view of the possible
harmful effects of radiation of short wave length which have been
repeatedly discussed during the past few years. The amount of such
possibly injurious radiation given by any particular lamp is a matter
of small importance except as it is correlated with the illuminating
power of the lamp, so that one may know to what amount of possibly
harmful radiations he is exposed in securing a required degree of
ilumination.

Nature and extent of Radiations under Suspicion as harmful. — There
has been much discussion concerning the effects of radiations of
different wave lengths upon the eye. Without going extensively
into an examination of the literature, which is very scattered and
extensive, or of the physiological facts, some of which the writer now
has under careful investigation and which will be reported later, it is
sufficient here to say that the investigators of this matter may be
divided into somewhat divergent schools. All agree that the extreme
ultra violet rays, those of wave length less than 300 uu, which are
absorbed by the cornea and so do not penetrate to the inner parts
of the eye, produce when in sufficient intensity more or less serious
damage to the corneal ephithelium, resulting in acute irritation,
always accompanied by conjunctivitis, and sometimes by cloudiness
of the cornea and other symptoms which go to make up the complex

2 PROCEEDINGS OF THE AMERICAN ACADEMY.

injury which has come to be known as ophthalmia electrica. It is in
effect a superficial sunburn of the eye and is often accompanied by a
similar sunburn in the vicinity of the affected eye. Whether this
particular sort of effect is produced also by ultra violet rays of slightly
greater wave length, say up to 320 μμ or 330 up, is a matter of some
dispute, but most investigators have held this particular region under
suspicion on account of the phenomena of snow blindness, which
closely resemble those of the so-called ophthalmia electrica, and cannot
be produced by the extreme ultra violet rays since the solar spectrum
owing to atmospheric absorption is extremely weak at and below 300
mm, very near to which point it is wholly cut off. It is, however,
fairly rich at 320 to 330 uy, the cutting off by atmospheric absorption
being rather sudden, as shown in a, Plate 1.

Now while the cornea cuts off only rays of wave length less than
300 μμ the lens of the human eye ordinarily absorbs the whole ultra
violet, it being substantially due to this absorption that we are unable
to see beyond the violet. This absorption extends to about wave
length 380 yu and in old persons in whom the lens gets slightly yellow
even as far as wave length 420 μμ. In early youth there is a very
slight transmissibility of the lens in the region 315 to 330 up as
shown by Hallauer.t Now potentially the rays which are absorbed by
a medium may produce changes in it and the ultra violet rays up to
and including the extreme violet have been reputed by various writers
to produce a large variety of lesions, including retinal injury due to the
rays which may filter through the lens. The list of reputed dangers
is a very long one including erythropsia, color scotomata, cataract
and other serious results. The situation from the point of view of the
ophthalmologists who seem to be really in fear of ultra violet radia-
tions is well summed up by Schanz and Stockhausen.? Other writers
like Best ὃ and Voege? attach relatively little importance to the effect
of the ultra violet as such and are inclined to attribute some of the
phenomena to over-intense radiation of ordinary light or to causes
not connected to radiation at all.

A third group, of which Birch-Hirschfeld® is a representative,
holds an intermediate view. It should be noted that the permanent

1 Klin. Monatsbl. f. Augemheilk., Dee. 1909.

2 Ztschr. f. Augenheilk., May 1910.

3. Klin. Monatsbl. f. Augenheilk., May 1909.

4 Die Ultravioletten Strahlen der modernen kuenstlichen Lichtquellen und
ihre augenbliche Gefahr fiir das Auge. Berl., 1910.

> Ztschr. f. Augenheilk., July 1908, and elsewhere.

BELL. —~ ULTRAVIOLET COMPONENT IN ARTIFICIAL LIGHT. 3)

injuries ascribed to ultra violet rays, like cataract and retinal degen-
eration, are charged to the radiations running even up to the visible
spectrum, while the extreme ultra violet, absorbed by the cornea,
produces only superficial lesions generally recovered in a few days.

From the standpoint of the present investigation it did not seem
justifiable to attempt to pass without further investigation on the
validity of any of the divergent views here noted, but to deal with
the radiations of short wave length as a whole, including in the possibly
injurious group all those radiations which have been under serious
suspicion on clinical evidence by reputable investigators. The line
has therefore been drawn between the ordinary lighting radiations
and radiations of short wave length in the extreme violet and ultra
violet of the spectrum, where the lighting value of the rays is negli-
gible and their actinic value notably high.

Separation of the Ultra Violet from the Visible Spectrum. — Having
determined on such a separation of the radiations under grave sus-
picion of injurious action from the rest of the spectrum, it was next
in order to find a suitable screen for making just this division of the
spectrum, so that it would be possible to measure the energy in the
two portions of the spectrum directly and as a whole, without a
resort to the extremely difficult and troublesome measures of the
energy in separate spectrum lines, a task of great delicacy when
discontinuous have to be compared with continuous spectra. After
considerable investigation a suitable medium was found in the so-
called Euphos glass. This glass, which has been strongly recom-
mended by Schanz and Stockhausen as eliminating completely all the
harmful ‘rays and which was prepared under the direction of one of
them, cuts off the ultra violet spectrum with remarkable definiteness
while showing relatively little absorption of the general luminous
rays.

Plate 1, b, c, d, shows the nature of this absorption very clearly.
Spectrogram ᾧ of this Plate is the spectrum of the mercury quartz
arc put on merely for reference, the group at 365 wu being at the right
of the figure and the brilliant green line exactly in the centre of the
plate. Spectrogram c shows the spectrum of the magnetite are which
is very rich in the ultra violet and d shows the same as absorbed by a
Euphos glass screen 2 mm. thick. The exposure in each case was one
minute with a rather wide slit and a very brilliant grating. The cut
off of the shorter wave lengths by the Euphos glass in the ultra violet
is very clean and sudden at wave length 390 uu, practically just at
the end of the visible spectrum as seen by the average eye. The

4 PROCEEDINGS OF THE AMERICAN ACADEMY.

absorption continues slightly on into the violet, gradually fading away
until the transmission becomes nearly complete for the bright blue
mercury line (4385 pu).

In examining b, c and d of Plate 1 it must be remembered that the
second order ultra violet overlaps the first order so that the group
near 365 wu appears in the first order at the extreme right of the figure
and in the second order at the extreme left. In d of this Plate the
arc spectrum fades off on the left, not from absorption but from the
weakening of the photographic action. The Euphos glass is ex-
tremely transparent to the radiations throughout all except the ex-
treme violet of the visible spectrum, and well into the infra red, as
will hereafter be seen. The results here obtained for its absorption
of the ultra violet are altogether parallel with those shown in the
paper by Schanz and Stockhausen ® and also by Hallauer.?. The
Euphos glass thus enables a particularly clean partition of the visible
spectrum from the ultra violet and extreme violet to be made.

If it were possible to obtain an equally good absorbent for separat-
ing the infra red from the visible spectrum radiometric measurements
of efficiency would be greatly facilitated. It should here be noted
that Euphos glass appears in various shades and some imitations of
it are now upon the market, so that a sample of such glass should be
tested in the spectrograph before use for such a purpose as the present,
inasmuch as in some of the shades the cut-off of the ultra violet is
much less sharp and complete. The sample here used was the original
No. 1, 2 mm. thick.

Method of Investigation. —'The method taken for the evaluation
was the familiar one of measuring the radiation directly by means of a
thermopile connected with a sensitive galvanometer in a manner
familiar in recent experiments on the efficiency of illuminants in the
visible spectrum, 6. g., Lux,® Féry.2 The thermopile was chosen as
the radiometric instrument merely as a matter of convenience. The
instrument actually used was a Rubens linear thermopile, having 20
constantin-iron couples with a total resistance of 4.6 ohms. It was
mounted as shown in Figure 1, in a vacuum tube with a quartz window
immediately in front of the couples. The inner body of the instru-
ment, containing the couples, was taken out of its original mounting
and set up in a tube about 37 mm. in diameter, through the upper
end of which was sealed a pair of leading-in wires.

6 Zts. f. Augenheilk., May 1910, Table VII, figure 3.
7 Archiv. of Ophthal., Jan. 1910, Plate I, figure 3.

8. Zts. f. Beleuchtungswesen, Heft 16, 1 p. 36, 1907.
® Bull. Soc. Franc. de Physique, p. 148, 1908.

BELL. — ULTRAVIOLET COMPONENT IN ARTIFICIAL LIGHT. 5

These were firmly clamped in the binding posts of the instrument by
working through the side tube attached for the reception of the quartz
window. The thermopile was then pushed up exactly opposite the
side tube and wedged in place with cork and cotton wool attached
with shellac. The end of the side tube was flanged out and ground
flat for the fitting of the quartz window and after the shellac had dried
out thoroughly the window was fastened in place and the lower end
of the tube drawn out for the attachment of the pump. The tube
was pumped to the high vacuum usual in an X-ray tube, and was then
sealed. It was mounted as shown in a block of wood to which was
secured the disconnecting terminal, reached by a long handled plug,

Figure 1. Vacuum thermopile. Figure 2. Quartz cell.

and the whole was then surrounded by a pasteboard case having a
hole just opposite the quartz window, and packed full with loose
cotton wool. The galvanometer was of the D’Arsonval type, having
a sensibility of 210° ampere per mm. scale deflection. Its period
for the attainment of a complete deflection, was, under the ordinary
conditions of its use, 1 minute.

The galvanometer deflections were read by a scale and telescope,
the scale being a special one bent to 1.5 meters radius. The thermo-
pile indications were calibrated in absolute measure by observations

6 PROCEEDINGS OF THE AMERICAN ACADEMY.

on the radiation of a standard incandescent lamp supplied by the
Bureau of Standards. After applying the proper correction for stray
thermal losses and spherical reduction factor and reducing the read-
ings as taken to the standard distance of 50 cm. employed throughout
this investigation, the constant of the thermopile galvanometer
system was found to be 1 mm. = 1 scale division = 35.3 ergs per
second per square em. By this constant the observed deviations
were reduced to absolute dynamical measure.

As a matter of convenience and to establish an approximate ratio
between the ultra violet radiation from the various sources studied
and the radiation in the visible spectrum, an absorption cell which

8

Transmission
i

500 700 900 1100 1300 1500
μμ

Figure 3. Absorption curve of water.

eliminated nearly all the infra red was kept in front of the thermopile
window. This cell, Figure 2, was of glass, ground flat and exactly 1 em.
thick, 44 mm. external diameter and 35 mm. internal diameter. The
glass ring was provided with a hole for filling and was closed by two
quartz plates cut across the axis, each 2.25 mm. thick and 44 mm.
diameter. These were fastened with hard shellac to the glass cell,
and the cell in use was filled with distilled water. The absorption of
a layer of distilled water of this thickness is shown in Figure 3 taken
from Nichols’s experiments.’ Quartz has no material absorption in
the part of the infra red spectrum transmitted and neither quartz nor

10 Nichols, Physical Review, Vol. 1, p. 1.

BELL. — ULTRAVIOLET COMPONENT IN ARTIFICIAL LIGHT. 7

distilled water in this thickness has any material absorption in even
the extreme ultra violet up to the limit investigated.

The use of this cell therefore could produce no sensible effect on
the accuracy of the ultra violet measurements, while it did serve the
extremely useful purpose of limiting the total amount of energy to
be measured and of eliminating any difficulties that might arise owing
to absorption in the further part of the infra red, all the absorbing
media incidentally used being, as compared with water, practically
entirely transparent to all the radiations that got through the water
cell. It would have been convenient if some substance cutting off the
infra red sharply at 750 uu or 800 μμ had been available. Unfortu-
nately, there is no such substance, so far as has yet been discovered,
the very few substances less transparent than water in the region
800 to 1300 μμ being useless for the purpose of this investigation on
account of opacity in the ultra violet and generally in the visible
spectrum as well. Iron ammonium alum used by Lux (loc. cit.)
and the copper salts used by Féry (loc. cit.) are open to this objection
and the same is true of all the otherwise useful and promising sub-
stances discussed in the very thorough and valuable researches of
Coblentz."

In some of the experiments a second similar quartz cell was used,
particularly in work on are lamps. In this case the Euphos glass
used to cut out the ultra violet portion of the spectrum was perma-
nently affixed to one of these cells and either the plain quartz cell or
the Euphos-quartz cell was thrust into the beam so as quickly to get
differential readings. In order to avoid the somewhat large correc-
tion due to reflection of energy which would have been produced by
the introduction of a plain slip of Euphos glass to cut out the ultra
violet the following expedient was adopted.

The Euphos glass was attached to the surface of the quartz cell by
spring clips with the addition of a thin capillary film of pure glycerine
between the quartz and glass surface. Glycerine is immensely trans-
parent to all radiations, including the extreme ultra violet, to which
Canada balsam and gelatine are quite opaque. Its index of refrac-
tion, 1.47 for D, is sufficiently near that for quartz and the various
glasses to reduce the loss of light at the surfaces to an entirely negligi-
ble amount. As the Euphos has a slightly less index of refraction
than quartz, there was a minute residual gain in the total transmis-
sion of the system when the Euphos glass was added, in the right
direction to compensate for the minute losses by absorption in the
glycerine film.

1 Bull. Bureau of Standards, Vol. 2, p. 619.

8 PROCEEDINGS OF THE AMERICAN ACADEMY.

As a check on the possible magnitude of this virtual absorption by
the glycerine film readings were taken on a tungsten lamp through
the quartz cell alone, and through the quartz cell plus a disc of optical
crown glass 2 mm. thick secured with glycerine in the ordinary man-
ner. The absorption of this crown glass is shown in Plate 1, e, f, g, in
which e is the spectrogram of the quartz arc taken with a wide slit
and 2 minutes exposure, f the spectrogram through the crown glass in
question, and g through the Euphos glass. In spite of the fact that
there is a slight absorption by the crown glass in the region near
300 up, the addition of the crown glass and glycerine film reduced the
galvanometer deflection by barely 0.5 %, an amount scarcely out-
side the errors of observation. ‘The energy cut off from the spectrum
of a tungsten lamp by the crown glass would be of course very
_ small, but perhaps not negligible, since as Schanz and Stockhausen
have shown (loc. cit. table VIII, figure 6) the tungsten lamp spectrum
goes quite down to 300 μμ in sufficient strength to give a clear photo-
graphic effect. At all events it is evident that the use of the glycerine
film involves no material errors.

In the ordinary experimentation in using steady sources, sets of
readings were taken alternately with and without the Euphos glass,
the glass being either added to the clear cell with the glycerine film,
or removed and the film quickly washed away with distilled water.
With sources which give trouble from unsteadiness the second quartz
cell was brought into play as previously mentioned. Aside from a
slight drifting of the zero point, which is generally observable in
measurements with a thermopile, the method adopted worked very
smoothly. The drift, however, was usually small and slow and satis-
factorily taken care of by a time correction. With proper attention
to this, the readings, although necessarily slow, were nearly as consis-
tent as would be found in ordinary photometric measurements.
The following string of deflections forming a single group of 5 readings
is typical of those obtained under ordinary conditions.

Scale readings from bare quartz lamp through quartz cell only.

cm.

36.17
36.10
36 .27
36 .36
36 .16
Av. = 36.21

BELL. ——~ ULTRAVIOLET COMPONENT IN ARTIFICIAL LIGHT. 9

The mean departure of a single reading from the average here given
is slightly less than 4%, so that the errors of observation, of which
this is a fair sample, showed that the thermopile observations are
about as reliable as those with a photometer. Some preliminary
experiments made on Euphos and other glasses showed that the
transmission of the Euphoa glass aside from its absorption in the
violet and ultra violet was exceptionally high for such rays as got
through the layer of distilled water. In fact the total transmission
of energy with Euphos glass was greater than with the ordinary
samples of clear glass and was only exceeded by a single sample of
optical crown which showed extraordinary transparency to all these
radiations, so great that the losses were practically only those charge-
able to actual reflection at the surfaces.

Measurements on various Illwminants. — With these preliminaries
the apparatus was set up permanently and work begun on commercial
illuminants. Readings of current and voltage on the electric lamps
were taken by Weston instruments freshly calibrated, and the quantity
readings on the gas lamps tested were obtained from a newly adjusted
standard meter.

100 Watt Tungsten The first source of light investigated was an
ordinary 100 watt tungsten lamp, taking actually .951 amperes at
113 volts, i. e. 103.38 watts, and giving 79.4 ο. p. in the direction of the
thermopile. With this lamp the mean difference of deflection due
to energy cut off by the Euphos glass was 1.9 em. The ultra violet
energy cut off, including such losses in the extreme violet as are indi-
cated by Plate 1,d, was 6% of the total energy transmitted by the
quartz cell.

100 Watt Gem. — The second source studied was anordinary 100
watt Gem lamp, taking 100 watts at 114 volts and giving in the marked
direction 39.25 c. p. This lamp of course gave a spectrum relatively
weak in the ultra violet, but as will be seen from its spectrogram in
Plate 2,6, the ultra violet region down to wave length 330 μμ is by no
means negligible. The total differential deflection due to the ultra
violet was in this case only 0.61 em., 2.6% of the total deflection.
These readings confirm the extraordinarily small absorption of Euphos
glass throughout the longer wave lengths, since the transmission ob-
served with the known cut off of a very perceptible amount in the
ultra violet, leaves no room for any material selective or general
absorption elsewhere.

It should here be noted that while quartz transmits with extraordi-
nary freedom, so far as absorption is concerned, all rays which are

10 PROCEEDINGS OF THE AMERICAN ACADEMY.

allowed to pass by a cm. thickness of distilled water, it still exercises a
slight selective action by reflection. The index of refraction of quartz
for the longer wave lengths of the visible spectrum is 1.54, while for
rays in the further ultra violet this figure rises to about 1.6, hence in
accordance with Fresnel’s formula (2>;) 2 there is a small amount of
selective stopping of the ultra violet rays by reflection. This occurs
both at the quartz water cell and at the quartz window in front of the
thermopile so that the total selective effect is proportional to the
fourth power of the difference due to the change in the index of re-
fraction for a single surface of transmission. This difference amounts
to approximately 2% as between the red rays and the further part
of the ultra violet. The result is to cause a slight under estimation of
the ultra violet. No account has been taken in any of these experi-
ments of this very small and troublesome correction, which amounts
in ordinary cases to only a small fraction of 1% of the total ultra
violet. The existence of the effect should, however, be noted as it
has a tendency toward causing a slight under estimate rather than an
over estimate of the ultra violet component.

Cooper Hewitt Tube.—'The next source investigated was the
Cooper Hewitt tube. One of the ordinary commercial 22 inch tubes
was used, the particular tube having previously been used in another
research and very carefully photometered. A section of this tube,
giving 100 c. p., was screened off so that the length might be so re-
duced that the energy from the whole,section taken could fall freely
upon the thermopile without causing a material angular error or
forcing one to depart widely from the standard distance of 0.5 meter.
The horizontal radiation normal to the tube was of course taken, the
reflector being removed. The corrected deflection due to the ultra
violet amounted to 1.64 em. which corresponded to 41.7 % of the total
energy passing through the quartz cell. The lamp was singularly
steady and easy to work with, with the exception of producing an
inconveniently small total deflection. The result, however, can be
regarded as fairly precise in spite of the small magnitude, the mean
deviation of a single reading amounting to barely over .5% in the
total deflection. In this lamp the ultra violet energy is nearly all
between 365 μμ and the visible spectrum, the extreme ultra violet
being entirely cut off by the glass of the tube and the few lines of wave
length between 365 and 300 μμ being reduced by the absorption to
very feeble intensity. The total deflection produced by this lamp,
of which the portion exposed radiated 100 ec. p., was only 17 % of the
deflection given by the Gem lamp of the previous experiment, which
gave less than 40 ec. p.

BELL. — ULTRAVIOLET COMPONENT IN ARTIFICIAL LIGHT. ΠῚ

Quartz Mercury Lamp. — Following the examination of the ordi-
nary glass Copper Hewitt tube, the next source investigated was the
quartz mercury lamp. Two tubes were available, each of the ordi-
nary commercial 220 volt type rated at 3.5 amperes. One of these
tubes, which is here referred to as the old mercury lamp, was made by
the French Cooper-Hewitt Company and_had been already used for
experimental purposes for about a year and had seen rather hard
service, having often been worked above its rated amperage. The
second lamp was entirely new, made in the Cooper-Hewitt factory in
this country and was not at any time worked above its rating. The
spectrum of the quartz lamp is extremely rich in certain portions of
the ultra violet, particularly in rays of wave length less than 300 μμ.
It is well shown in Spectrum e of Plate 1. The brilliant lines in this
spectrum, counting from the violet, have wave lengths as follows: —

4077 .84 2967 .27
4046 .55 2925 .38
3983 .96 2893 .60
3906 .47 2752 .80
3663 .27 2698 .88
3662.88 | 2655 .14 |
3654 .83 2653 .70 }
3650 .14 2652 .07 |
3341 .48 2536 .52
3131 84] 2483 87
3131.56 } 2482 76
3125 .67 2482.07
3027 .49 2399 .81
3025.61 | 2399 .43
3023 .43 2378 .39
3021 .50 2302 .65

The wave lengths here are taken at the value assigned by Stiles ”
in A. u. It willbe observed that a number of the lines are associated
in close groups which with small dispersion mass into heavy lines.
The relative intensity of the lines, as is well known, shifts consid-
erably with the degree of excitation of the tube, so that the relative
intensities given by Stiles do not agree with the spectrograms taken
from the quartz arc for the same reason that Stiles’ arc and spark
intensities do not agree. The quartz arc spectrum resembles Stiles’
are spectrum much more closely than it does the spark spectrum.

12 Astrophysical Journ., Vol. XXX, p. 48.

12 PROCEEDINGS OF THE AMERICAN ACADEMY.

In particular the quartz are spectrum displays a very striking gap
between wave length 334.14 μμ and the double line at wave length
313.1 up. Save for the very faint haze of continuous spectrum that
characterizes the radiation from the quartz tube this part of the
spectrum is blank. Indeed the line 334.14 uy itself is far from strong
relatively to those in the further part of the ultra violet and there is.
very little effect of radiation between wave length 313.1 μμ and
365.2 μμ. This gap is of some significance in interpreting the results:
of bactericidal experiments, since any failure of bactericidal action in
the region between wave length 350 wu and wave length 313 μμ
observed in working with the quartz lamp may be due to the absence
of any strong radiation in this region as well as to lack of specific
bactericidal power in rays of this particular wave length if they existed.

In the radiometric investigations on the old quartz lamp it was run
at 3.7 amperes and about 80 volts, an average of about 260 watts,
without an external globe. Under these circumstances the corrected
deflection due to the total ultra violet was 16.7 cm. The deflections:
were not quite so steady as in the case of the ordinary Cooper Hewitt
tube, but still the average departure of a single reading was within 1%.
After the deflection due to the total ultra violet was determined
another set of readings was taken with the bare lamp and quartz
cell and then with the Euphos glass replaced by the crown glass:
of which the absorption spectrum is shown at f, Plate 1.

This glass in effect cuts off substantially the whole of the extreme
ultra violet spectrum, letting pass in practically undiminished strength
only the lines of greater wave length than 300 wu. This separation
is of some importance with respect to the bactericidal power of the
lamp in water purification and similar work. The result was to show
that the transmission of the crown glass was 54.7 % of the transmission
found for the Euphos glass. In other words, nearly one half of the
total ultra violet energy in this lamp was of wave length below 300 yu.
Of the remaining half the spectrum shows, as just indicated, that by
all odds the larger part lies between 365 μμ and the visible spectrum.

The new quartz lamp without its globe was then tested, the input
in this case being 350 watts. The ultra violet output was greater
than in the old tube, the total deflection reduced to the standard
distance rising to 32.1 cm. In this case 65.1 % of the energy trans-
mitted by the quartz water cell was cut off by the Euphos glass.
Following up the radiometric measurement further, the Euphos
glass was replaced by the light crown glass as before with the result
of showing that substantially one half, 49.9 %, of the total ultra violet

BELL. — ULTRAVIOLET COMPONENT IN ARTIFICIAL LIGHT. i153

was cut off by the crown glass and hence substantially this proportion
was of wave length less than 300 wu.

In running quartz lamps without their globes, as was done in these
experiments, the energy output is considerably diminished by the
cooling of the tube and the light-giving properties of the lamp are very
much reduced. Both the old and the new quartz lamps herein noted
were photometered. The lamps were compared against a tungsten
secondary standard by means of a Simmance-Abady flicker photo-
meter. Thee. p. normal to the length of the tube and in a horizontal
direction, was for the old quartz lamp 415, for the new quartz lamp
348, in each case without any enclosing globe. Both lamps were very
steady and easy to work with, both on the photometer bar and with
the thermopile.

Finally the new quartz lamp was fitted with its regular diffusing
globe and tested with the thermopile. In working with the globe
the tube operated at a higher temperature and far more intensively,
the wattage rising to 400. With the Euphos glass in, the total change
in deflection amounted to only 3.7 em. although the lamp tested on
the photometer as in the previous case reached 820 c. p. in the hori-
zontal direction. In percentage the amount of energy cut off by the
Euphos glass was 42.5. These figures plainly indicate that the globe
absorbed the further ultra violet very strongly, more strongly than
the crown glass already referred to. In fact the deflection due to the
ultra violet energy which passed through the globe of the lamp was
extraordinarily small with respect to the ec. p. of the source, very much
smaller than in the case of any other illuminant investigated. With-
out the globe the quartz are is a very powerful source of radiation
in the extreme ultra violet, below wave length 300 uu. With its
ordinary globe on, all this energy in the extreme ultra violet is cut off
and the small remaining amount, mostly in that part of the ultra
violet nearest the visible spectrum, becomes quite insignificant.

The Welsbach Mantle— At this point study of the radiation from
the Welsbach light was taken up. The particular form used was a
Graetzin street lamp with a single large inverted mantle fitted with a
clear glass globe, which obviously eliminated whatever of extreme ultra
violet might be present. This burner took 6.4 feet of gas per hour at
3 inches pressure and gave 75 c. p. in the horizontal direction. Its
total deflection was slightly greater than that produced by the quartz
lamp with its globe tested immediately before. The addition of the
Euphos glass cut down the deflection by .924 c. m., an amount equiva-
lent to the absorption of 8.4 % of the total radiation recorded. The

14 PROCEEDINGS OF THE AMERICAN ACADEMY.

lamp proved fairly easy to work with in point of steadiness and the
average variation of a single deflection from the mean was still less
than 1%.

Acetylene Flame. — Following the trial of the Graetzin lamp a
series of measurements was made on an acetylene flame fed from a
Prestolite tank. This flame gave on the photometer in the direction
of measurement 27.35 c. p. and its change in deflection on interposi-
tion of the Euphos was .524 cm., corresponding to a cut off of 4.5%
of the total energy. It proved very amenable to measurements and
was quite as steady and easy to work with as the mantle burner pre-
viously used. The spectrum of the acetylene flame reaches well
down into the ultra violet as shown by Schanz and Stockhausen."
It reaches, in fact, approximately wave length 310 wu, but the further
portion of the spectrum is comparatively weak. The spectrum of
the Welsbach mantle with a clear globe, given by the same authorities
(loc. cit.), is cut off at about wave length 320 μμ, but is notably bright
in the part of the ultra violet toward the visible spectrum. These
results are fully checked by the spectrograms taken of the particular
burners here indicated.

The Carbon Electric Arc. — Next in order the various are lamps
were taken up for investigation, beginning with the are between
carbon electrodes. On account of the relative instability of the ares
the method of experimentation was modified. A second quartz cell
similar to the one already in use was constructed and filled with
distilled water. The ratio of the absorption between this new cell
and the old cell was then determined. From a slight difference in
thickness or in polish of the quartz plates the new cell was found to
give about 1% more absorption than the original quartz cell and a
correction for this difference was introduced in the subsequent meas-
urements. The two quartz cells were mounted in recesses in a sliding
screen so that either could be brought quickly in front of the thermo-
pile window. The Euphos glass screen was then mounted with a
glycerine film on one of the quartz cells so that the cells with and
without the Euphos could be rapidly interchanged in the beam from
the lamp under test and the absorption thus determined without
having to depend on the constancy of the lamp for any considerable
time.

The times of observation were regulated by means of a stop watch
so that a time correction for shift of zero could be readily made, and

13 Zts. f. Augenheilk., V. XX XIII, plate 8.

BELL. — ULTRAVIOLET COMPONENT IN ARTIFICIAL LIGHT. 15

by taking several preliminary swings, so as to give the thermopile
chance to settle into a steady state, the rate of shift of zero was kept
pretty steadily and the corrections were easily applied. It was also
necessary to photometer the ares in the actual condition in which
they were under test. To this end the apparatus was set up as shown
in Figure 4. Here A is the are lamp, B the thermopile, C the galva-
nometer, D the telescope and scale, EK an adjustable rotating sector
dise just in front of the are, F the quartz cells in their sliding screen
in front of the thermopile window, G a silvered plate glass mirror
which could be quickly interposed in the beam between the arc and

©

waz A”

D

\ ve Tl pores es H
ΘΟ ΖΜ Φ oe eat

Figure 4. Arrangement of radiometric apparatus.

the thermopile so as to deflect the rays into the portable photometer
H, set up on the other side of the photometer room. The coefficient
of reflection of the mirror had previously been many times determined
as the mirror had been in use for photometric work. The photometer
was ready for use at any time simply by closing the switch on the
standard lamp. When in course of a series of thermopile measure-
ments it was desired to test the ec. p. of the lamp the disc was
started, the mirror swung into place and readings were then taken on
the portable photometer.

16 PROCEEDINGS OF THE AMERICAN ACADEMY.

The carbon are was first attacked and it proved to be a difficult
subject for investigation. The particular lamp used was of the en-
closed type, having the globe fitted with a short side tube and a quartz
window so as to keep the arc as steady as possible without losing the
ultra violet. To the same end it was found desirable to adjust a
magnet behind the are so as to keep it burning on the side of the
carbons next the thermopile instead of wandering round and round
the carbons in the usual manner.

The are thus operated gave a prodigious amount of ultra violet
radiation, showing a continuous spectrum far down into the ultra
violet and the three enormously intensive carbon bands usually
ascribed to cyanogen, one of them in the extreme violet and the other
two near wave lengths 380 yu and 360 μμ respectively. Reduced to
the standard distance the deflection due to the ultra violet cut off by
the Euphos glass amounted to 74 em., being 30 % of the whole energy
which passed through the quartz cell. It has, of course, been long
known that the naked electric are gives off very powerful ultra violet
radiations and its effect in the production of ophthalmia electrica
has been known for more than half a century, but in this case the
extent of the ultra violet activity was somewhat unexpected.

It was undoubtedly considerably enhanced by the intensive cyano-
gen bands as regards that portion of the radiation lying near the visible
spectrum, but on the other hand the extreme ultra violet, wave length
300 uu and less, is unquestionably stronger in the case of an open are
than in the enclosed are on account of the very intense continuous
spectrum emitted from the crater, which is much lessened when the
are is enclosed. No separation between these parts of the ultra
violet was attempted with the lamp under consideration since its
unsteadiness was a constant source of annoyance and the ordinary
variations of independent readings from the mean amounted to 5
or 6%. It was sufficiently evident, however, that a powerful en-
closed are in a globe which permits all the radiations to pass is an
enormously powerful source of ultra violet light. The carbon arc,
however, is rapidly passing out of general use so that attention was
next directed to the luminous are.

Magnetite Arcs. — The magnetite are is one of the commonest and
most generally useful outdoor illuminants. It gives a very intense
nearly white light due almost wholly to the arc stream itself. The
spectrum of this, the active electrode being composed almost wholly
of the oxides of iron and titanium, is immensely complicated, contain-
ing thousands of bright lines so closely packed as almost to obtain

BELL..— ULTRAVIOLET COMPONENT IN ARTIFICIAL LIGHT. 17

the effect of a continuous spectrum. The actual character of the
spectrum photographed with a fairly wide slit, is shown in Plate 2, d.
Here, with the quartz are spectrum for reference at a is shown the
radiation from the magnetite are through a quartz window and below
it the spectrum of the same are taken through its ordinary globe. A
quartz window was used merely to insure steadiness of the light, which
would have been lost by taking off the globe. A glance shows that
this spectrum is exceedingly rich in powerful lines all through the
ultra violet clear down to wave length 230 wy. The glass globe cuts
off the spectrum quite sharply near wave length 300 up, as in Plate 2, ὁ,
but from this region to the visible spectrum lies an almost continuous
mass of strong lines, very intense in the region where the quartz mer-
cury are is conspicuously weak, say from the group at wave length
313 yu to the group near wave length 365 μμ.

For radiometric measurements the magnetite are, which was oper-
ated at 6.6 amperes and about 80 volts, proved much more steady
than the carbon are, showing more small and quick fluctuations, but
fewer of the large and relatively slow variations which interfered most
with the readings. As a consequence the deflections obtained agreed
more closely, the average variations of a single setting running be-
tween 3 and 4%. For the magnetite arc through the quartz window
the cut-off of Euphos glass amounted to 29 em., 28% of the total
deflection. Through the ordinary glass globe the deflection was
reduced to 22.4 cm., 22.5% of the total deflection. The difference
between these results shows that while there is a large amount of
energy of short wave length produced by the magnetite arc, most of
the ultra violet energy is of wave length greater than 300 uu. As
compared with the quartz mercury are used without its globe the
magnetite are gave relatively about 60% less energy of wave length
below 300 uu and about 40% more energy in the wave lengths above
300 wu. The candle power in the horizontal direction as measured by
the method just described amounted to 760 in the run with the quartz
window, and 700 in the run with the ordinary globe.

The Nernst Lamp. — Finally a series of readings was taken on the
Nernst lamp. The lamp investigated was of the single glower type
for 220 volts, taking 91 watts and giving a downward ec. p. of 68. As
the spectrum of this source runs to less than wave length 300 μμ and
reaches that vicinity with somewhat material strength an attempt
was at first made to run the Nernst glower without a globe. 11
proved so difficult to get steady deflections under these conditions,
on account of the effect of air currents, that this measurement was

18 PROCEEDINGS OF THE AMERICAN ACADEMY.

abandoned and the readings taken with the globe on, which proved
reasonably easy, the precision being comparable with that obtained
with the ordinary incandescent lamps. But even then the lamp
proved very sensitive to small changes of voltage and only by very
careful regulation of the current could consecutive series of readings
be held in reasonably close agreement.

In the average the deflection due to the ultra violet in the Nernst
lamp with its globe was 1.81 em. and the percentage of energy thus
cut off was 5.2. This completed the radiometric investigation of
ordinary illuminants. Two others which it seemed desirable to
investigate, that is the ordinary flame arc, and the are between iron
electrodes as used by Finsen were studied on the spectrograph, since
their fluctuations were of a character to make their study by means
of a galvanometer of so long period as that used in this investigation
quite impracticable. The peculiarities of these sources will be referred
to in discussion of the general results.

Sun Light. — Finally it seemed advisable to take some comparative
readings on sunlight as a source of ultra violet radiations, particularly
with reference to the amount of ultra violet energy with respect to the
intensity of the light. Of course the solar radiation in absolute amount
has been investigated with great thoroughness, but the ultra violet
has received less attention than the rest of the spectrum. In general
the sun radiates energy substantially like an incandescent black body
at about 6000 degrees C. except in so far as its energy, particularly
in the ultra violet, is cut off by the absorption of its own and the
_ terrestrial atmosphere. It behaves then, like an enormously hot
incandescent body shining through a medium that cuts off all the
ultra violet of less wave length than about 295 wu and greatly dimin-
ishes the shorter radiations even into the violet of the visible spec-
trum. One would expect therefore to find relatively little total ultra
violet per unit of illumination so far as the direct light of the sun is
concerned. On the other hand as Schuster ' and others have shown,
much of this cutting off of the ultra violet is due to scattering of the
short waves by the molecules of the atmosphere and. small bodies
suspended in it. In other words, the violet and ultra violet are not
wholly lost, but appear in radiation from the blue sky. Ἷ

Of the energy thus radiated from the sky the maximum lies almost
in the edge of the ultra violet. The arrangement of the apparatus
for experiments on sunlight is shown in Figure 5. Through the

“Nature, XXXI, p. 97.

ULTRAVIOLET COMPONENT IN ARTIFICIAL LIGHT. 19

BELL.

courtesy of the Director, this part of the work was done in the Rogers
Laboratory of Physics where the conditions for getting natural light
were good. In Figure 5, A is a porte lumiére receiving the light from
the sun and forming by means of the iris diaphragm B, stopped to
3 mm. diameter, an image of the sun on the thermopile front at C,
before which was placed the usual quartz cell D. The thermopile
was connected with the galvanometer F, read by the telescope and
scale G. By the use of the diaphragm, forming a species of “pin
hole” image on the face of the thermopile, at a distance of 3 meters,

Figure 5. Apparatus for solar radiation.

the light and energy were cut down so as to be readable with compara-
tive ease.

To measure the intensity of the illumination a Simmance-Abady
flicker photometer H was set up close alongside the thermopile so
that the solar image could be quickly moved so as to fall squarely
on the photometer disc. On the other side of the photometer at I
was an 80 watt tantalum lamp which was previously calibrated, in
terms of the current flowing through it, against a standardized Gem
lamp. From the source of supply the current was taken to this lamp
through an adjustable rheostat J and a mil-amperemeter K. In
measuring the light-intensity of the beam which was allowed to fall
on the thermopile, it was simply shifted from the face of the thermo-
pile to the face of the photometer and by means of the rheostat J

20 PROCEEDINGS OF THE AMERICAN ACADEMY.

a flicker balance was established. The current read on K and re-
ferred to the standardization curve at once gave the ec. p. of I, so that
the illumination could be computed.

The mirror at A was an electrolytic nickel surface highly polished,
inasmuch as nickel gives a considerably higher coefficient of reflection
near the end of the solar spectrum than does silver, which is particu-
larly weak at this point. To separate the extreme violet and ultra
violet as before and on exactly the same basis, the solar readings
were taken with simply the quartz cell and then with the Euphos
glass and a glycerine film. The cut off of violet and ultra violet pro-
duced by the Euphos glass in the first day’s readings was 16.2 % and
in a second day’s reading 17.9%, both days being brilliantly clear
and cold in late December at noon. The average energy therefore
cut off was substantially 17% uncorrected for the coefficient of re-
flection of the nickel mirror, or approximately 21 % after the correc-
tion for the variation in reflection as between the ultra violet and the
visible spectrum.

This figure is somewhat large as compared with the data ordinarily
quoted for the ultra violet component of the solar spectrum, but it
should be noted that this comparison is not with the spectrum as a
whole but with that portion of it transmitted by a quartz cell filled
with distilled water which cuts off a large part of the infra red. Also
the absorption of the Euphos glass extends into the violet as has been
previously noted, and finally the observations were taken in cold
winter weather when the aqueous vapor, which is important in the
absorption of the atmosphere, is pretty well frozen out.

The observed difference of deflection in these experiments on the
sun due to the cut off of the ultra violet was 2.28 em. and the observed
intensity of the illumination was equivalent to 101 foot candles.
These readings show precisely what the general theory indicates, that
the solar light must be regarded as received from an enormously hot
and hence very efficient radiator which has been robbed by atmos-
pheric scattering and absorption of a considerable part of its shorter
wave lengths. :

REcoRD OF GENERAL RESULTS.

In these experiments the following artificial sources of light were
investigated with respect to the ultra violet component of each as
separated from the rest of the spectrum by a disc 2 mm. thick of
Euphos glass ¥1:—G. E. M. lamp; tungsten lamp; Cooper Hewitt

BELL. — ULTRAVIOLET COMPONENT IN ARTIFICIAL LIGHT. il:

tube; quartz lamp of the French Cooper Hewitt Company without
globe; quartz lamp, American, without globe; quartz lamp, American,
with globe; Graetzin mantle burner; acetylene flame; carbon electric
are through quartz window; magnetite are through quartz window;
magnetite are with ordinary globe; Nernst glower. In addition, a
study was made of sunlight with the thermopile for comparative
purposes and spectrographiec studies were also made of the ordinary
yellow flame are and of the are between iron terminals such as is used
for therapeutic purposes. The Euphos glass was chosen as the
medium for the partition of the ultra violet from the rest of the spec-
trum for the reason that it cuts out and was intended to cut out by
its designers all the rays of any illuminant which are under indictment
as having specific harmful action on the eyes.

Broadly, the accusations of short wave lengths as injurious to the
eye involve the entire ultra violet from the furthest point reached by
natural or artificial illuminants up to and into the chemically active
rays of the violet. Τῇ on the one hand it is the rays in the extreme
ultra violet, wave length 300 μμ and less, which are absorbed by the
cornea, that are held responsible for the ordinary phenomena of
ophthalmia electrica, it is the rays of ultra violet of greater wave length
than this, extending clear into the violet, that have been regarded
by some recent investigators as producing perhaps serious lesions of
the retina and of the lens. Note Schanz and Stockhausen.” The
former class of injuries which have to do with the radiations absorbed
by the cornea are wholly superficial and, according to Van Lint 15 the
prognosis is generally good and the recovery rapid. Injuries to the
retina and the lens, in-so-far as they take place, involvea far greater
danger of permanent injury. Glass-blowers cataract is one of the
typical injuries which has been ascribed to ultra violet radiations lying
adjacent to the visible spectrum by Schanz and Stockhausen, Birch-
Hirschfeld and others. Obviously, the temperature of melting glass
(1400° C) is too low to give rise to any material amount of energy in
the extreme ultra violet.

The present investigation, therefore, took account of the whole
body of radiations of short wave length. So far as possible injury
from the ultra violet component in any artificial light source is con-
cerned it is obviously dependent on the amount of actual energy
delivered by the source in the ultra violet region and not upon the

Ztschr. f. Augenheilk., Mai, 1910.
16 Accidents oculaires provoqué’s par |’électricité, p. 100.

22 PROCEEDINGS OF THE AMERICAN ACADEMY.

percentage relation of this energy to the whole input. It is quite clear
that in order to do any injury to the eye a certain amount of energy
must be spent upon it and must be delivered at a rate in excess of
the power of the eye to repair damages. One receives injury from
excessive exposure to ultra violet rays just as he receives it by exces-
sive exposure to heat rays. In either case the delivery of energy at
a very high rate for a considerable time does damage.

TABLE I.
Source Input Totalu.v. w.v. per watt
100 Watt G. E. M. 100 PNG: 2 15 ΧΟ ΠΩΣ
Glass Mercury Lamp (3 length taken) 96 77, 6.02 x 107
Nernst (with globe) 91 640 1203.<0g
100 Watt Tungsten 103 670 6.50) <atOu!
New Quartz Lamp (with Alba globe) 460 1305 2234 Χ 100

Old Quartz Lamp (without globe) 260 5920 22S. SOs

Magnetite Arc (with globe) 530 7900 145,95 Ν ΠΣ"
Magnetite Arc (no globe) 530 10240 ΠΟ xa
New Quartz lamp (without globe) 350 11350 327 e
Carbon Are (quartz window) 495 26200 πὸ ὦ =a 10m

At a moderate rate and for a moderate time the constructive forces
of the organism are not over balanced by the destructive forces of the
radiations. Hence the first application of the data obtained from the
sources investigated was to determine the actual rate at which ultra
violet energy was delivered by them. Table I shows for all the electric
sources of light, of which the input could be readily measured, the
gross input in watts at the lamp terminals, the total ultra violet radia-
tion in ergs per second per square cm. at the standard distance of
half a meter and finally, this ultra violet output in terms of ergs
square cm. per second per watt input. This last column is propor-
tional to the efficiency of the source as a producer of ultra violet
radiations in terms of the gross input.

In Table I the highest ultra violet output per watt of input is reached
by the carbon are operated in the manner already described. The
next highest figure is given by the quartz lamp operated without its
globe, a condition of relatively low luminous efficiency which would
only be found in cases where the are was being used for bactericidal
purposes or other special tasks where ultra violet radiations are

BELL. —- ULTRAVIOLET COMPONENT IN ARTIFICIAL LIGHT. 23

important. The very high ultra violet output reached by the carbon
are is as has already been pointed out largely due to the very intensive
cyanogen bands about in the middle of the ultra violet spectrum
and the output of wave length below 300 μμ is materially less than it
is in the quartz lamp operated without its globe.

At the other end of the list stand the G. EK. M. lamp and the ordinary
Cooper-Hewitt tube, the former showing a very low ultra violet
output by reason of its relatively low temperature and the latter
by reason of the fact that the extreme ultra violet is entirely cut off
sby the tube, and the middle ultra violet being very weak in the
mercury spectrum, the main body of the energy is of wave length
greater than 365 wu. In fact since the spectrum of the G. E. M.
lamp runs down nearly to wave length 300 yu, and is strong only
between say 360 and the visible, the energy distribution of the spectra
of these two illuminants is singularly similar, considering their wide
difference in character.

The Nernst and tungsten lamps produce rather more total ultra
violet than the Cooper-Hewitt tube, most of the output being toward
the visible spectrum. The Nernst lamp operated without its globe
gives a spectrum relatively stronger in the further ultra violet, reach-
ing wave length 300 μμ with a considerable degree of strength and
stretching beyond it. All the lamps running with glass globes show
a weak spectrum in that region. For this reason the quartz lamp
with its regular diffusing globe shows an ultra violet output per watt
almost as low as the G. E. M. lamp, the cut off of the globe in the
ultra violet region being very striking. The magnetite are both with
and without its globe gives a considerable ultra violet output. The
globe cuts off much less ultra violet than in the case of the quartz
lamp, the latter being relatively rich in the rays which the glass most
effectively absorbs.

Table II shows the percentage of energy cut off by the Euphos glass
in each of the illuminants investigated as compared with the total
energy which was transmitted by the quartz water cell, and also the
relative horizontal c. p. of the sources dealt with. The percentage
ratios of ultra violet are therefore numerically higher than they would
be in the case of admitting the whole infra red to the thermopile.
The relative composition of the various sources, however, is well
expressed by the data.

24 PROCEEDINGS OF THE AMERICAN ACADEMY.

TABLE II.
% of energy Candle power

Source cut off by euphos (horizontal)
100 Watt G. E. M. 2.6 39.25
Acetylene Flame 4.5 27 .35
Nernst (with globe) τ ῶ 68 .0
Tungsten (100 wt.) 6.0 79.4
Graetzin Gas Lamp 8.4 75 ἢ)
Sunlight Zien 272 . (equivalent)
Magnetite Arc (glass globe) D2 700 .0
Magnetite Are (quartz window) 28 .0 760.0
Carbon Arc (quartz window) 30.0 720.0
Mercury Are (glass) 41.7 100.
New Quartz Lamp (with Alba globe) 42.5 820
Old Quartz Lamp (no globe) ὌΝ ἢ 415.
New Quartz Lamp (no globe) Gaul 348 .

It will be noted that the smallest percentage of ultra violet is shown
again by the G. E. M. lamp, with the acetylene flame standing second.
The Welsbach mantle of the Graetzin lamp runs materially higher
than any of the electric incandescent lamps in spite of the fact that
this lamp was tested with its globe on. Next higher than the Graetzin
lamp, and approximating the are lamps, comes sunlight, standing
between the incandescent sources which give a continuous spectrum
and the arcs of various sorts which give highly selective radiation.
At the other end of the list is the quartz lamp worked intensively
without its globe. These ratings of the various illuminants are
instructive as showing the distribution of the energy as between
ultra violet and the remainder of the spectrum, but they are not
significant as regards the extremely practical matter of illumination.
If the ultra violet component of artificial light involves any risk of
injury to the eyes the one important thing to find out in comparing
sources of light is how much ultra violet.they deliver for a given
illumination. In other words if one desires to light a room, say to
an intensity of five foot candles, with what illuminant can he obtain
this intensity while receiving the minimum amount of ultra violet
radiation? It is not of the slightest practical consequence from the
standpoint of good and safe illumination whether a given light source
produces much or little ultra violet per watt, provided it produces an
insignificant amount per foot candle, hence the luminous efficiency

BELL. — ULTRAVIOLET COMPONENT IN ARTIFICIAL LIGHT. 25)

of the source is in the last resort the thing which determines the pres-
ence or absence of ultra violet radiation in material amount. In
other words the more efficiently the energy supplied to the illuminant
is transformed into light the less important does the ultra violet
radiation become in considering the source as a practical illuminant.

TABLE III.

Deflections due Ultra violet ergs per sec.

Source tou.v.incem. per cm? per foot candle
Quartz Are (Alba globe) 3.70 4.3
Graetzin Gas Lamp 92 Aad.
G. E. M. Lamp 61 14.8
Cooper-Hewitt (glass) 1 .64 15.5
Sunlight (direct) 2 .28 1061
Acetylene Flame 52 18 .4
Tungsten Lamp 1.90 22 a
Nernst Lamp (globe) 1.81 Ὁ Ὁ ὦ
Magnetite (glass) 22 .40 30.3
Magnetite (quartz) 29 .00 90. Ὁ
Old Quartz Lamp (bare) 10 77 38.3
New Quartz Lamp (bare) SDAA) 87 .6
Carbon Are (quartz) 74 .00 91.0

Table III assembles the commercial light sources tested, with
respect to the ultra violet energy accompanying a given illumination.
The first column of the table gives merely for the purpose of record
the actual deflections found to be due to the ultra violet energy, and
column two the total ultra violet radiation in ergs per second per
square cm. per foot-candle of illumination. At the head of the list
stands the quartz mercury are with its diffusing globe. Of the com-
mercial illuminants tested this gives by all odds the smallest propor-
tion of ultra violet per foot candle. As the previous tables show, the
ultra violet energy of this source so equipped is small from any point
of view. Its unique position, however, is due largely to the fact that
the light-giving radiation, which lies practically at the very peak of
the luminosity curve for vision, is produced at enormous efficiency,
according to Buisson and Fabry ΤΠ not less than 55 candles per watt
for the green line at wave length 546 which supplies nearly two thirds

1 Comptes Rendus, Vol. 153, p. 254.

26 PROCEEDINGS OF THE AMERICAN ACADEMY.

of the total light and at almost as high efficiency for the pair of yellow
lines which supply nearly all the rest. Next in the list, a rather bad
second, comes the Graetzin gas lamp, its position again being due to
the somewhat selective radiation that gives it a very high luminous
efficiency. ‘Third, comes the G. E. M. lamp which, from its relatively
low temperature, gives a small absolute amount of ultra violet radia-
tion, although its luminous efficiency is not great.

At the other end of the line comes the special enclosed are with
91 ergs per second per square cm. per foot candle, and next to it the
quartz lamp without its globe. Of course the quartz lamp without
its globe is never used for illuminating purposes, but only for such
work as sterilization of water and the like in which the ultra violet
rays are the things sought. Operated for this purpose it undoubtedly
is the most efficient powerful source of extreme ultra violet. To test
this feature of the matter energy measurements were taken on the
two quartz lamps without their globes and on the magnetite lamp
free from its globe while using as a screen instead of the Euphos glass
a disc of the very light crown glass previously referred to, which practi-
cally effects a separation at wave length 300 uy absorbing substan-
tially all the energy below this point and transmitting at almost full
intensity the rest. The result of this test, measuring the extreme
ultra violet and reducing it to the mean spherical output of ultra
violet, showed for the extreme ultra violet efficiency of the new quartz
lamp 4.07 % and for the efficiency of the old quartz lamp 3.14 %.
A similar measurement of the magnetite are showed an extreme
ultra violet efficiency of 1.13%. These figures may be properly com-
pared with the tests for the ultra violet efficiency of the quartz lamps
made by Fabry and Buisson. [ἢ this case two mercury lamps showed
respectively extreme ultra violet efficiencies of 6.4 and 4.7%, the
ultra violet separation being effected by the screens used by Fabry
and Buisson at wave length 320 uu. The values obtained by the
French investigators and in this study therefore check each other
closely, showing that in the quartz mercury lamp 4 to 5% of the total
input is returned in the form of extreme ultra violet radiation when
the lamps are operated, as they are for sterilization purposes, without
their globes. The lighting power of the lamp falls off very greatly in
this condition.

When operated with the globe the total proportion of ultra violet
becomes both absolutely small and extremely small relatively to the

15 Comptes Rendus, Vol. 153, p. 93.

BELL. — ULTRAVIOLET COMPONENT IN ARTIFICIAL LIGHT. 27

light given. In this connection the position of sunlight in Table IIT
is not without importance. On the face of the returns it has a less
amount of ultra violet with respect to the illumination than most of
the artificial illuminants. This is due to the very high temperature
of the source, which insures high luminous efficiency, in connection
with strong ultra violet absorption in the atmosphere. Unfortu-
nately one can apply Planck’s law to very few practical sources
of light. The sun is ruled out by the very erratic and highly selective
absorption which produces the Frauenhofer lines and also by an
unknown absorption of the extreme ultra violet which may take place
in the earth’s atmosphere or near the solar surface or in both places.
Incandescent lamps involve absorption by their globes and also in
the case of more recent ones a certain amount of selective radiation.
The whole tribe of ares which yield in a greater or less degree discon-
tinuous spectra, for which Planck’s law does not hold, are also thereby
eliminated, so that this
otherwise very — useful
guide to the distribution
of radiation ceases to have
exact significance.

The ultra violet com-
ponent of sunlight has
been considerably — dis-
puted. It has been held
by some investigators like
Dr. Voege that sunlight
contains more ultra violet
than the are light, while
Schanz and Stockhausen ”°
take the opposite view. 800 40 500 600 700 s00uu
In a sense both are right Figure 6. Curves of Sun and sky energy.
and both wrong. Sun-
light undoubtedly contains only a very modest proportion of ultra
violet per foot candle of illumination when one considers direct sun-
light alone. If, however, one considers the total daylight effect,
including skylight under favorable circumstances, the situation takes
on a totally different aspect. The light diffused by the blue sky is
mainly violet and ultra violet, being substantially that light of which
the direct sunbeam is robbed by scattering. Figure 6 shows in curve

19 The Illuminating Engineer, Lond., Vol. II, p. 205.
20 The Illuminating Engineer, Lond., Vol. I, p. 1049.

28 PROCEEDINGS OF THE AMERICAN ACADEMY.

A the distribution of energy in the directly received solar light.
Curve B shows the distribution of energy in the diffused light of the
blue sky when the total of this diffused energy equals 20 % of the
total directly received solar energy, a not uncommon proportion. It
will be noted that the maximum for this curve is in the far violet near
the edge of the ultra violet. Curve C is the summation of A and B
and it will be seen at once that the proportion of ultra violet is some-
thing like three times as great as in the case of the direct solar rays.
This proportion would raise the ultra violet activity of daylight to
a point higher per foot candle than that reached by any ordinary
artificial illuminant.

Weisner *! in photographic observations of light received on hori-
zontal surfaces states for example, “For solar altitudes less than
19 degrees the chemical intensity of the sunlight as compared with
diffused daylight is negligible, with increasing solar altitude it gains
in comparison with the diffused daylight. * * * Since the intensity
of the direct beam may reach twice that of the diffused, the total
combined chemical effect may be three-fold that of the diffused light.”

Daylight, therefore, varies very greatly in ultra violet energy, rang-
ing from the low value given in Table ITI for direct sunlight to values
which would exceed almost all artificial light sources. The chief claim
of sunlight to serious consideration from the standpoint of ultra violet
energy, however, lies in the very large amount of energy which the
sun delivers. There is considerable doubt as to the exact amount of
solar radiation outside of the atmosphere, but that which gets through
the atmosphere is pretty well determined and its amount, from the
data given by Abbott ” amounts practically, under favorable condi-
tions, to not less than 1 kw. per square meter, which is 0.1 watt per
square cm. If one assumes that only 10% of this is in the ultra violet
region, an amount which may be exceeded at times, the total ultra
violet radiation rises to 10° ergs per second per square cm., several
times that given by the most powerful artificial sources of ultra violet
at even a distance of so short as half a meter.

Considering this very large flux of ultra violet energy it is small
wonder that troubles from sunburn and snow-blindness are not
infrequent. Did we not habitually shield our eyes by interposing the
rim of the hat or the brow and by systematically looking away from
the direct sunlight ocular troubles would be common and severe.

21 Denkschriften Wien. Akad., Vol. 64, 1897.
22 “The Sun”, Chapter VII.

ULTRAVIOLET COMPONENT IN ARTIFICIAL LIGHT. 29

BELL.

Snow is a good reflector of ultra violet radiations, at least throughout
the limits of the solar spectrum. At two meters distance a square
meter of snow surface may reflect to the eye as much as 10% ergs
per second per square cm. If even one tenth of this is in the ultra
violet then a square meter of snow in the field of vision at two meters
distance would deliver about 1000 ergs per second of ultra violet per
square cm., which is in excess of the greatest amount which would be
given at this distance by any of the artificial sources of light here
investigated.

Fortunately the sun is weak in the extreme ultra violet, but the
very large amount of radiation which can be reflected to the eye from
a snow covered surface is quite sufficient to account for all the phe-
nomena observed, even although the ultra violet per foot-candle in
the sunbeam is rather exceptionally low.

Two sources of light, not here measured for reasons already stated,
should not be forgotten. One of these is the iron arc used for thera-
peutic purposes, of which the spectrum is shown along side of the
mercury spectrum in Plate, 2, g. It will be observed that it is enor-
mously rich in lines, even to the extreme ultra violet, and as the light
giving power between iron terminals is not high, this source would
stand very near the bottom of Table III. The yellow calcium fluoride
arc, of which the spectrum is similarly shown in Plate 2, 7, would un-
questionably stand near the quartz arc at the head of the list, owing
both to its very high luminous efficiency and to the comparatively
weak lines in the extreme ultra violet.

In conclusion it may be confidently stated that no commercial
illuminant radiates for any ordinary working value of the illumination
enough ultra violet energy to be at all harmful, provided one exercises
ordinary discretion is keeping unpleasantly bright visible light out
of the eyes.

Bett.— ULTRAVIOLET Component IN ArtTiFiciAL LIGHT. Pirate 1.

Te Ια}:
ΤΣ
| |

Proc. Amer. Acapv. Arts Ano Sciences. Vor. XLVIII.

Bett.— ULTRAVIOLET ComPONENT IN ArtiFictAt LIGHT. PLATE 2.

Proc. Amer. Acapo. Arts AND Sciences. Vor. XLVIII.

Proceedings of the American Academy of Arts and Sciences.

Vout. XLVIII. No. 2.— June, 1912.

ALEXANDER AGASSIZ.

By Henry P. Watcort.

32 PROCEEDINGS OF THE AMERICAN ACADEMY.

whither she had removed from Neuchatel to the company of her
own relatives. Alexander came here into contact with Professor
C. T. E. von Siebold, whose character and great scientific attain-
ments did not fail to make a deep impression upon him. Soon after
his mother’s death in 1848 he came to this country and joined his
father at Cambridge. He was prepared for college in the high school
of that city and was graduated from Harvard College in the class of
1855.

He received degrees from the Lawrence Scientific School in 1857 and
again in 1862, the studies pursued there were Chemistry, Civil Engi-
neering and Zodlogy. ‘This choice of studies shows that at this time
he was not yet settled in his mind as to his life work — he had for a
short time an interest in a Pennsylvania coal mine, and had thought
of taking up the occupation of railroad engineering. He was appointed
assistant in the United States Coast Survey in 1859 and was em-
ployed in charting the mouth of the Columbia River, Oregon; and in
the survey of the northwest boundary, he found time in the intervals
of his official duties to study the marine life of San Francisco harbor
and to make collections at other points on the Pacific coast for the
Museum at Cambridge.

Whatever his own plans may have been, powers beyond his control
had been at work to determine his career, he vainly thought it might
be in fields remote from those in which his father had labored, but
indulgent fates brought him back to the natural sciences and here he
remained for that part of his activities in which he found his highest
satisfaction. He had lived all his life in an atmosphere of science, he
had an inheritance from both father and mother of the mental qual-
ities that promised him successes in these fields.

Louis Agassiz’s second marriage, in 1850, to Elizabeth C. Cary,
brought into the family a very strong and happy influence in the
same direction, and ultimately the valued companionship for Alex-
ander Agassiz which nearly reached the span of his own life.

Another important influence in his preparation for life is to be
found in the state of Cambridge social life at this time. The native
and unstinted hospitality of the father aided by the gracious manner
in which Mrs. Agassiz received his guests brought to this open house
every traveler of scientific prominence. The college society of the
fifties and the association with the neighboring city could not easily
be found elsewhere; some idea may be formed of its quality by
reading the lines in which Lowell pictures the scenes, from which his
great friend had been recently removed by death. There was no

WALCOTT.— ALEXANDER AGASSIZ. 99

place there for mere wealth, riches were prized only where their
possession had contributed to the improvement or happiness of man-
kind, and the man without a definite occupation in life was practically
unknown. It was avery simple life according to the standards of the
present day but it yielded results which our larger material resources
have not proportionately multiplied.

After a year’s absence upon the Pacific coast, he returned to Cam-
bridge in accordance with his father’s earnest wishes and definitely
entered upon the work of the Museum. His marriage in 1860 to Miss
Anna Russell, sister of the wife of Theodore Lyman, his classmate and
associate at the Museum, made this place also his home. His methodi-
cal habits and financial prudence were of great value to his father in
the administration of the business of the establishment and he early
became indispensable there. The visitor to the modest quarters of
the Museum of those days would probably have failed to discover
in-the quiet assistant intent only on the work of the laboratories and
of the Museum, the power which was destined in a few years to place
these collections in halls commensurate with their value and that by
resources won by himself in the fierce struggle for the wealth buried
in the depths of the earth.

In 1859 was published his first scientific paper which was read
before the Natural History Society of Boston, upon the mechanism
of the flight of Lepidoptera — a subject hardly to be expected from
one who was subsequently to gain his great honors in very different
departments of zodlogy. Before the age of thirty he had published
more than twenty (20) papers upon scientific subjects, all of which
displayed originality and covered a variety of topics. He published
in 1865 with his stepmother, Mrs. L. Agassiz, a book of popular charac-
ter under the title “Seaside Studies in Natural History.” He became
much interested in 1867 in the dredging operations of his friend Louis
F. de Pourtalés, who on the Coast Survey Steamer “Corwin’”’ had
successfully brought up material from the then unusual depth of 850
fathoms along the course of the Gulf Stream between the Florida
coast and the Bahamas. He assisted in the arrangement and descrip-
tion of the collections. He thus early became interested in the study
of the ocean bottom — the problems of which were to occupy so
prominent a place in all his work for the rest of his life. The influence
of this favorite pupil of his father and his own life long friend is
acknowledged in the appreciative notices which were presented to the
American Academy and to the National Academy after the death of
Pourtalés.

34 PROCEEDINGS OF THE AMERICAN ACADEMY.

“The Revision of the Echini,”’ which appeared in the years 1872-74,
is the best known work of Agassiz and was at once recognized as the
performance of a master and made him the leading authority on the
subject. The thoroughness of his methods is shown by this extract
from a letter to afriend from Leuk, Switzerland, August, 1870, “I have
done now with my examination of the Echini collections, having seen
them all.” It was of this work that Jeffries Wyman spoke when he
said that the son had done a piece of work that would live as long as
anything accomplished by the father.” The manner in which the
work was performed by Agassiz is well shown by the quotation from
his letter given above — he saw every specimen that was worth seeing
before he felt justified in stating his own conclusions.

The activity that marked these early years down to 1873 was-a
marvel to all — he was intensely busy, and capable of undertaking
the most strenuous physical and mental labors, his working day was
habitually more than half of the twenty-four hours.

In 1869 came a serious illness from which modern surgery might
have brought a more satisfactory cure than that which he obtained.
Some of the consequences of this illness affected his mode of life
permanently — he avoided thereafter, so far as possible, our New
England winters.

The end of the year 1873 was a time of great sadness for Agassiz.
His father and his wife died within ten days of each other. He as-
sumed the direction of the Museum and for 37 years labored for its
development and administration, a serious task, if it had been his
sole occupation.

Louis Agassiz had opened a school for natural history studies on the
island of Penikese in Buzzards Bay in the summer of 1873. His
immense capacity for teaching, his love for it and success in it
carried the school through the first season, but it was the last great
effort of his life. In the succeeding year Alexander Agassiz reluctantly
took up the burden, he had not shared his father’s enthusiastic belief
in the possibility of carrying on a school at this remote point. He
loyally made the attempt, however, and when it became evident that
the necessary financial support could not be obtained, he characteris-
tically did not hesitate to drop the enterprise and pay the deficit from
his own pocket.

A few years after the closing of the Penikese school he built in the
vicinity of his house at Castle Hill, Newport, an excellent marine
laboratory with the required accommodations for about 12 students.
Here much valuable work was done by a number of men whose names

WALCOTT.— ALEXANDER AGASSIZ. 35

have become well known throughout the scientific world. During
his long service at the head of the Museum and under a variety of
titles, he expended from his own resources for collections and the
buildings to hold them, more than $1,200,000, not including very
considerable sums contributed to other allied interests or to the general
purposes of the University. At the end of the year 1874 he set out on
the first of the many distant expeditions which were made at intervals
through the rest of his life. This journey took him to Chile and Peru,
and during the course of it he made the exploration of lake Titicaca,
an account of which is given in our proceedings for the year 1876.

His quick eye showed him at Tilibiche in Peru, a fossil coral reef
at an elevation of nearly 3000 feet above the sea and 20 miles inland,
and he noted with a certain satisfaction the evidence that Darwin’s
observations had caused on his part an underestimate of the amount
of recent elevation of this coast.

He now entered upon that series of deep sea investigations which in
some form had always been of exceeding interest to him. He directed
three expeditions in the Atlantic on board the U. 5. Steamer “ Blake”
and three in the Pacific on the “ Albatross.”” The vast material col-
lected on these trips was, with combined wisdom and generosity and
in obedience to the rule of the Museum laid down in his father’s time,
distributed for purposes of description and study to those scientific
men everywhere who were best qualified for the work.

Sir John Murray says, and no living authority is better able to
make the statement, “If we can say that we now know the physi-
cal and biological conditions of the great ocean basins in their broad
general outlines — and I believe we can do so— the present state of
our knowledge is due to the combined work and observations of a
great many men belonging to many nationalities, but most probably
more to the work and inspiration of Alexander Agassiz than to any
other single man.”

In these later years he was also much interested in the study of
the coral reefs. He organized many expeditions to all parts of the
world — to the Maldives, to Australia and to remote portions of the
Pacific. He saw, explored, and accurately described every important
coral reef region on the globe and having done so he felt that he was
ready to give his own views to the world.

Darwin saw but one atoll and upon that founded his theory of coral
building. Agassiz was at work in his last days upon the publication
-which would have given to the world the well considered conclusions
acquired by the studies of nearly a lifetime. Though his own final

36 PROCEEDINGS OF THE AMERICAN ACADEMY.

results cannot be surely known, his vast material still exists for some
more fortunate investigator. He had written and rewritten his
sketch of the book upon this subject and a few days before his death
said to his friend, Sir John Murray in London, that it was his intention
to practically rewrite the book during the year for the fourth and last
time, leaving out all criticism of the work of others and stating exactly
what he had himself observed and his own views. It should be
understood that Darwin’s theory of the coral reefs belonged to his
younger years and has no bearing upon his later published theory of
natural selection. What Agassiz’s views were, upon this and other
theories conveniently grouped under the title Darwinism, cannot be
accurately stated. It is true that he found much that was objection-
able in the opinions maintained by some of Darwin’s German followers.
No one who knew him, however, can doubt his ability to weigh dis-
passionately any evidence, which could be produced for this or for any
other doctrine, though it might run counter to opinions long enter-
tained by him or by those whom he delighted to honor.

Some intimations of his views upon the position of the Zodlogist
of today as compared with that of the great men of an earlier genera-
tion may be found in the remarks made by him as representative of
his class at the Commencement at Harvard in 1905, that being the
50th anniversary of his graduation. He called attention to the incon-
veniences and the primitive appliances which hampered the work of
the student of natural history in his own student days and added,
“The change in scientific thought is most striking — fifty years ago
authority was the powerful factor — scientific dictators were not
uncommon — now authority as such is no longer recognized beyond
the point at which it can be controlled. Successful experiment has
taken its place, and while recognizing the value of imagination and
of pleasing speculations, men of science no longer accept the dicta
of their leaders.”

As John Hunter said to his pupil Jenner, who had asked for the
explanation of some perplexing phenomenon, “‘I think your solution
is just; but why think, why not try the experiment.” So with Agassiz,
discussions had little interest for him when it was not possible to put
the conclusion to the test of observation or experiment.

The bibliography of his own scientific papers contains 248 titles
which cover a great range of subjects and procured for him marked
distinctions throughout the world. No man among men of science
promoted the interests of zodlogy so generously as he. In 1910 the
54th volume of the Bulletin and the 40th volume of the Memoirs

WALCOTT.— ALEXANDER AGASSIZ. oF

of the Museum of Comparative Zoélogy were coming from the press.
These publications began to appear in 1863-64 and in the number of
important and finely illustrated papers which are presented there,
they have been excelled by few only of the great and most active
scientific societies of the world, yet the expense of producing them
was largely borne by Agassiz.

Much has been said about the great sums of money spent by him
upon the monument he raised in filial piety to the memory of his father,
and which he duly commemorated in that characteristically simple
inscription upon the walls of the Museum “ Alexander, son of Louis
Agassiz, to his father.”’ The voice of the public has named it the
Agassiz Museum — father and son were both content to call it the
Museum of Comparative Zoédlogy. Whatever legally that title may
be, the memory of these two lives will possess a force greater than the
statute, and will preserve for generations to come the name common to
the enthusiastic founder and to the wise, patient and munificent
builder. Whatever Agassiz’s contributions in money may have
been and others, not he counted them up to sums exceeding any thus
far made to the University, yet he gave a greater still in the devotion
of himself to the task of developing and making secure the future activi-
ties of the Museum. All the material successes he had won in other
fields he pledged to the support of the Museum after he had satisfied
the reasonable requirements of his family, but of his own labors he
made no reservation. The Museum had all that he could bestow.

On the pages of the quinquennial catalogue of Harvard College are
enumerated the distinctions conferred upon him by universities,
learned societies and foreign governments, they are a sufficient proof
of the esteem in which he was held throughout the world. Such dis-
tinctions sometimes reveal a more than passive recipient, but they
came to him absolutely unsought. His intimates even had little
knowledge of the honors bestowed upon him, and rarely obtained it
from himself.

The great gold Victoria Research Medal given to him in 1909, was
shown to his friends, but this was more for the exquisite beauty of
the workmanship of the Medal, than for the pride in receiving it. He
had a keen appreciation of anything that had artistic merit and sur-
rounded himself in his home with many beautiful objects of art col-
lected in his travels from all parts of the world. In addition to the
Victoria Research Medal of the Royal Geographical Society, he had
received the Walker Grand prize of the Boston Society of Natural
History and in 1878 the Serres prize of the French Academy of
Sciences, the first foreigner to be so honored.

38 PROCEEDINGS OF THE AMERICAN ACADEMY.

From 1865 onwards in addition to the scientific work of the Museum
he was developing and managing most successfully the largest copper
mine in the world. He did not rest content with the development of
the mine as a problem in engineering, but always mindful of the
just obligation of capital to labor, he employed experts for the purpose
of securing good conditions of living, caused careful measures to be
taken for the protection of life and limb in this hazardous occupation,
and secured the formation of pension and aid funds for the benefit of
disabled and aged employees to which the corporation made liberal
contributions. No workman was so far removed from the authorities
in control that his complaint passed by unheard. The whole con-
duct of the mine is one of the bright spots in the much beclouded
world of such enterprises and must still be reckoned among the more
satisfactory attempts to bring the workman and his employer into
harmonious relations with each other.

A pleasing instance of his thoughtfulness with regard to the popula-
tion of this mining community is related by one of his friends, the
physician who took care of him through a fever which might have
been acquired during one of his visits to the mines at Calumet. The
physician was asked one day whether he suspected that the disease
could have been brought from that place. If that were so, there was
something to do at once and that was to take such measures that his
work people should be protected from a like danger. Upon this
suspicion, possibly unfounded, a thorough overhauling of water supplies
and systems of sewerage was at once undertaken there while Agassiz
was still confined to his house.

He was early called to service upon the governing boards of Harvard
College, he was elected a member of the Board of Overseers in 1873,
became a member of the Corporation in 1878, resigned his place there
in 1884, and was promptly elected to the Overseers in 1885, was again
transferred to the Corporation in 1886, and definitely gave up his
place there in 1890, when he found it necessary to free himself
from some of his many occupations. During all the period of his
connection with these boards he was an active, much interested and
far sighted helper in all the departments of the University. The
Jefferson laboratory owed much to him for the friendly codperation
with which he promoted the intentions and plans of the generous
founder. He gave valued aid to the Observatory, to the Botanical
Museum, the Mineralogical Cabinet and the Peabody Museum of
American Archaeology and Ethnology.

He interested himself in the attempt to secure for women a share

WALCOTT.—— ALEXANDER AGASSIZ. 39

in the medical instruction offered by the University. He took a
generous part in many of the subscriptions for the general purposes
of the College. He witnessed with interest the development of the
collections of the Arnold Arboretum under auspices not unlike those
with which he was himself so familiar. The members of his College
class have given expression to their warm feelings of friendship for
one who never forgot his college associates and had a genuine pleasure
in all his meetings with them.

The secretary of the class closes a feeling notice of Agassiz’s death
with these words of appreciation, “No one of the class will miss him
more than the secretary does who never went to him in vain for aid
in the many common undertakings which bound the class together.”

He did not forget his early debt to the public schools of Cambridge
and willingly accepted service upon the school committee, and while
a member of that body devoted all his special knowledge to the
service of the city. This appears to be the only public office, subject
to election by the people, which he at any time held.

Agassiz was elected a member of the Academy of Arts and Sciences
Nov. 12, 1862, he was then in his twenty-eighth year. It was
possibly in remembrance of this early election that he suggested in
his last note to President Trowbridge the propriety of bringing in to
this association a larger number of the younger scientific men than had
hitherto been customary. He presented his first paper the next year
and made in all thirteen communications, generally upon special sub-
jects in zodlogy. A very interesting account of his work at Lake
Titicaca is an exception, and has an added claim to our attention
from the fact that it was made at a time when the death of his wife
had left him disconsolate, but it is also an evidence of how resolutely
he turned again to the occupations which he followed to the end.

The series of publications put forth by the Museum of Comparative
Zodlogy received the records of his scientific labors after the date
of the last communication made to the Academy. When President
Cooke died in the summer of 1894, a feeling soon became manifest
that Agassiz was the most fit member for the succession. The Vice-
President of that year was Augustus Lowell and he was the prompt
and enthusiastic leader in the preliminaries usual to an election.
Agassiz as might have been expected was very reluctant to allow the
use of his name and probably would not have done so, but for the
insistence of Mr. Lowell, whose influence was all the greater from the
fact that he was one of the earliest friends acquired by Agassiz when
he landed a stranger among people speaking an unknown tongue.

40 PROCEEDINGS OF THE AMERICAN ACADEMY.

He received a unanimous vote in one of the largest meetings ever
held by the Academy; he faithfully performed all the duties of the
office interrupted only by the winter vacations which his illness of
1869 made necessary for him. In this place it is a satisfaction to
remember that no one of his many and great distinctions gave him a
greater pleasure than did this. It was a most unexpected revelation
to him of the hold he had upon the respect and good will of his
fellows.

It is not possible to escape from some comparison of the two great
men of science who have borne this name, and there can be nothing
unbecoming in the attempt to make it.

The son was the pupil of the father and different as the two men
seemed to be, the son was ever conscious of the debt he owed to his
father.

Louis Agassiz came to this country with a great and well deserved
reputation fairly earned among the world’s great men.

He did more than anyone to encourage the study of the natural
sciences here. Endowed with every social attraction — persuasive,
a leader and fond of his leadership, great in acquirement, quick
in apprehension, rich in imagination, fertile in illustration, a teacher
beyond compare. He found listeners in the market place as well as in
the halls of the Colleges and of the Legislatures. He laid in magnifi-
cent hope the foundation of an establishment so extensive that he had
no just right to expect that either he or his son could see its completion.

Alexander Agassiz, patient seeker after truth, skilful organizer of
scientific methods, unwearied in researches, prudent, self-denying,
pursuing his great ends to a successful issue with silent determination,
not eloquent and always reluctant to attempt persuasion by spoken
words, he leaves behind him, in the opinion of many competent
judges, a more permanent and more important mass of completed
work in the study of the natural sciences than fell to his father’s lot.
He, moreover, by his own exertion completed the structure which
his father could only have seen in some prophetic vision.

It is not easy to speak of the personal qualities of Alexander Agassiz.
Men expected to find in him the counterpart of his father, and in such
intercourse as they may have had with him they met with disappoint-
ment. They regarded him as one holding himself somewhat aloof
from his fellows, not much interested in their doings and slightly
affected by their misfortunes. This conception of his character
showed little acquaintance with the real man; beneath the quiet and
reserved, certainly not austere demeanor, there lay a nature quick

WALCOTT.— ALEXANDER AGASSIZ. 41

in feeling, sympathetic and tender, not given to verbal expression,
but capable of great generosity not in money only, but in the things
that money never buys.

They knew him in the serious work of life, wise, fearless and of an
indomitable energy, quick and fiery in temper, but harboring no
sullen enmities. Many a victim of some sudden expression of a
vigorous disapproval had found to his surprise in some future and
unmerited trouble no warmer friend or if occasion required more
strenuous advocate than Alexander Agassiz.

His emotions were never under his complete control and he steadily
avoided the public occasions that might lead to their manifestation.
They were always, however, the emotions of a sensitive, generous and
strong nature.

His actions often seemed hasty if not premature, but this was
in appearance merely, for his whole life long he thought for himself
and by himself, and when action came it was true that few, if any,
had knowledge of the long and patient thinking that led up to the
result.

His intimate friends were comparatively few in number, but to
those who had earned his confidence, he showed no reserve, and had a
simple charm which made intercourse with him the delight of a life-
time.

The unworthy things in life, or such that seemed so to him, moved
him to quick and impetuous judgments and expressions, but if cooler
thought led him to believe that he had made a mistake, it was quite
certain that any wrong that might have been done would be fully
repaired.

His wealth, whatever it may have become, had little effect upon a
life simple and free from display. The man who was known all over
the world in the assemblies of the great men of science walked unrecog-
nized through the streets of Cambridge, and he would not have had it
otherwise. He was modest, somewhat diffident and shy, but he was
by no means unconscious of his powers and the recognition of them
by his peers was a source of legitimate satisfaction to him. He was
courageous, independent and quite ready to fight if need be, for the
losing cause. He was not a willing critic of the work of other men,
unless it dealt directly with subjects to which he had himself given
much attention. He was ever ready to recognize with unselfish praise
the results of any honest and thorough investigation. All the re-
sources of the Museum were at the disposal of him who could effec-
tively make use of them.

42 PROCEEDINGS OF THE AMERICAN ACADEMY.

He suffered without complaint any criticism of his own opinions,
but was sure to be roused to instant wrath at any suggestion that he
had incorrectly reported observations or experiments. His declaration
of scientific faith was his father’s adage, that a physical fact was as
sacred as a moral principle.

One instance of his fine generosity may well be noted here. Some
years since it was announced that a notice of his father was about to
be published. Mrs. L. Agassiz and he had reason to believe that the
work was not in friendly hands. The printer’s proofs of the paper
came into Agassiz’s possession, together with the intimation that any
change he might wish to make would receive serious consideration.
He requested a trusted friend to read over the proofs and mark such
passages as might appear to him unfitting. The friends met to com-
pare notes, they agreed in substance with the exception of one passage
that seemed to the friend mischievous if not: malevolent. Agassiz
said at once, “As to the spirit in which this statement is made I
_ quite agree with you, but it is a scientific question, and any scientific
man has the right to criticise my father’s scientific views.” The
passage remained.

The lessons of the narrow circumstances of his youth and early
manhood never left him. He could be apparently reckless in discard-
ing machinery and tools which had served their purposes or were infe-
rior to newer inventions, but it was always with the object of getting
a larger return or a better product. For himself he never sought
luxuries, but lived without ostentation in the dignified manner that
became his station. He cast aside all the lessons of thrift, however,
when he turned to the human agencies in his employment. He
never discharged an employee who had been long in his service and
who was still capable of doing enough work to appear to be doing
something.

One of Agassiz’s most remarkable characteristics was the systematic
and accurate disposal of his time, he might be making a journey to
the Maldives or it might be to the barrier reef of Australia. The
date of his return was fixed, and punctual to the day he made his
appearance at the Museum, and quietly resumed his accustomed
occupations there. He made such thorough preparations for these
trips, and provided so carefully for any possible mishaps, that the
usual uncertainties of ocean voyages for him at least ceased to exist.
Many men take measures against the larger accidents, and forget the
trifles. Agassiz kept the great emergencies in mind but never neg-
lected the small things of life.

WALCOTT.— ALEXANDER AGASSIZ. 43

No native born citizen ever carried to Europe a more pronounced
spirit of personal independence than he did. His stories of experiences
with officials on the other side of the Atlantic were a source of much
entertainment for his friends. In the later years of his life his thoughts
turned more willingly to the other shores of the Atlantic, he had made
warm friends there, and he looked forward with much satisfaction
to the few weeks in Paris which generally were the end of his foreign
excursions for the winter. Here in the company of kindred spirits —
Associates in the Institute of France and others — he spent days of
real enjoyment, speaking the language which belonged to his father
if not to his mother and which never had become at all unfamiliar to
him. The theatres of the better sort attracted him and his distance
from the demands of his active life here left him free to indulge in his
always temperate pleasures.

Notwithstanding the very serious illness of his early life his originally
slender but vigorous frame bore him safely through a life of more than
the usual exposures in the varied hardships of a mining camp and
journeys which were often perilous. He was spared the usual defects
of advancing years and carried to the end a clear head, unimpaired
senses and an active body. On Easter morning, March 27th, 1910,
on board the Steamer Adriatic in mid ocean he passed from sleep to
death without a struggle and the last great mystery was revealed to
him who had dealt with the immensities of time and space in all the
oceans of the globe.

It was well known to some of Agassiz’s friends that he had bestowed
much thought upon a plan for giving to this Academy a more satis-
factory house than any it had yet had. He had made provision
in his will for a bequest to the Academy which would have given
it a substantial aid in this direction. He, however, had promised
himself a more immediate gratification of this wish and on 16 October,
1909, wrote to President Trowbridge offering to erect upon the land
already owned by the Academy and the adjoining lot which he had re-
cently purchased a building which should become, to use his own words,
“a scientific and literary Club,’’ while remaining the domicile of the
Academy. He had caused plans to be prepared by Mr. 5. F. Page,
for a building to be erected on this spot — not merely a house for the
Academy but a home for its members, a place to which they would
gladly at all times come, to which they might bring their friends and
associates from other parts of the country or.from foreign lands. It
was quite clear to those who were most familiar with his plans, that
the house was destined to have all the attractive features which

44 PROCEEDINGS OF THE AMERICAN ACADEMY.

he knew so well to give to his own dwellings. His sons in quick
response to the father’s wishes with a generous piety have carried out
his plans. Mr. Page, the architect, had submitted his sketches to
Mr. Agassiz and had had frequent conferences with him before he
left the country in December, 1909. His death on March 27, 1910, of
necessity caused some delay in the progress of the work, but the plans
had been so fully developed that there seemed no doubt as to his inten-
tions and the architect under the direction of the sons and of your
committee has faithfully and successfully brought the building to
completion.

Kings and ambitious noblemen have in other lands and other times
been patrons of learned societies and have provided sumptuous
accommodations for them. Our house is believed to be the only
abode of a scientific society built by a member of the body and devoted
to the unrestricted uses of his fellows. If Agassiz had lived to see the
completion of this house, it is safe to say that neither his name not his
features would have appeared upon these walls. What his singular
modesty would have forbidden to him living has been done in the one
instance by the authorities of the Academy, and in the other by the
loving hands of one of his own family.

In the great Museum at Cambridge is the monument of two great
men of science laboring in the service of science alone. Here in this
pleasant house and home may their associates and successors for
all time remember the gracious spirit of him who asked only of his
fellows a kindly remembrance.

May we not speak of him in the words which our own poet used in
describing another of our greatest and best loved associates,

The wisest man could ask no more of fate
Than to be simple, modest, manly, true,
Safe from the many, honored by the Few;

To feel mysterious Nature ever new;

To touch, if not to grasp, her endless clue,
And learn by each discovery how to wait.
He widened knowledge and escaped the praise;
He wisely taught, because more wise to learn,—
He toiled for Science not to draw men’s gaze,
But for her lore of self denial stern.

O friend of this house and all who gather here, not of a day but for
long years to come may your place still be here to welcome by this
visible presence the generations of this Academy, till this solid struc-
ture which you have built and all that it contains shall sink in dust.

Proceedings of the American Academy of Arts and Sciences.

Vou. XLVIII. No. 3.—Juty, 1912.

A THEORY OF LINEAR DISTANCE AND ANGLE.

By H. B. Patures anp C. L. E. Moore.

A THEORY OF LINEAR DISTANCE AND ANGLE.

By H. B. Puruurres anp C. L. E. Moore.

Presented May 8, 1912, by H. W. Tyler. Received May 6, 1912.
INTRODUCTION.

1. In a recent article! we developed for the plane a theory of
distance and angle such that points equally distant from a fixed
point lie on a line and lines making a given angle with a fixed line pass
through a point. On account of this property we have called this
distance linear. In the present paper we extend this theory to higher
dimensions. Because of the increased complexity, the synthetic
method of the previous discussion cannot be used here and since we
know none better we have adopted that of Grassmann. In the first
part of the paper we have shown how the extensive quantities of
Grassmann can be regarded as matrices and the progressive and re-
gressive multiplication interpreted as simple operations performed
upon these matrices. In this way we develop as much of the Grass-
mann analysis as is needed for our purpose. We then determine for
any two spaces R, R’ of the same dimension, a distance or angle
R R’ having the property that if this invariant is constant and either
of the spaces fixed, the other satisfies a linear relation and such that
for three spaces R, R’, R’”’ of a pencil

RR + RR’ + ROR =O.

Any distance between points that has these properties is expressible
in terms of a hyperplane and a linear line complex. The plane is the
locus of infinitely distant points and the complex the locus of minimal
lines. If the complex does not degenerate, the hyperplane and line
complex in n dimensions determine a point and n — 2 other complexes
forming altogether mn elements which we use for a reference system.
This system of elements forms a group under outer multiplication

1An Algebra of Plane Projective Geometry, Proceedings of the American
Academy of Arts and Sciences, Vol. 47, p. 737.

46 PROCEEDINGS OF THE AMERICAN ACADEMY.

in the sense that any product of these elements is equal to a numerical
multiple of a third one. In terms of this fundamental system we
define the angle between any two spaces. Each of the complexes of
the fundamental system is an infinite locus for spaces complimentary
to it. The entire system is invariant under a group of collineations
of the same order as the Euclidean group of motions. Degenerate
cases are obtained by taking sections having a special relation to the
fundamental system.

Matrices IN THREE DIMENSIONS.

2. Progressive Matrices. Werepresent a point A in three dimen-
sions by a set of four homogeneous coordinates a;. These coordinates
determine a matrix

A = || αι a a3 a4 || = || a; ||

which may be used to represent the point. Two matrices of this
kind will be called equal when their corresponding elements are equal.
The matrix is zero if all its elements are zero. If a; = k δ; we shall
write
A=kB.

In this case the matrices A and B represent the same point but with
different magnitudes. A linear function of A and B is defined by the
matrix

AA + B= || Xa, + pd; ||.

In a similar manner we define any linear function of points or matrices
A, B,C, ete. If the result does not vanish it represents a point in
the space determined by 4, B, C, ete. If it vanishes and the coeffi-
cients are not all zero those points lie in a lower space than a like
number of points usually determine.

The coordinates of the line joining A and B are proportional to the
two-rowed determinants in the matrix

|
|

Van Gp as a |

| bs by bs ba |

αι Ay ||

|
δι be ||”

[1.9] —

We shall call the elements of this matrix the two-rowed determinants

| Gi δ

1b Oy

[This is not in conformity with the usual definition which makes
element equivalent to coordinate a; or b; but is the only definition

PHILLIPS AND MOORE.— LINEAR DISTANCE AND ANGLE. 47

which has a value in the present discussion.| The matrix is zero when
all its elements are zero. In that case the points A and B have
proportional coordinates and hence coincide. If the matrix is not
zero it represents the line A B in the sense that from the matrix can
be obtained the coordinates of the line. Conversely if the line is
given a matrix can be formed by taking any two points on the line.
Different matrices representing the same line are multiples of any
one. For if A, B and P, Q are pairs of distinct points on the line

P=hA+AB,
Ο Ξ μι 4 -- μ. 8,

re DAS
[Pg =|“
μι μὰ
Thus a two-rowed matrix in addition to representing a line, has a
definite size.
The matrix [4 B] is in reality a set of six determinants

and

[4 B].

a; ah,

δι δι

taken in some definite order. . It can then be considered as a one-
rowed matrix of six terms

[A B] = || a; δι --- a 5; ||.

The sum of two matrices [A B] and [C D] is then a complex matrix,
each element of which is the sum of corresponding elements in [A δ]
and [CD]. In general this sum cannot be represented as a single
two-rowed matrix, just as the sum of corresponding Pliicker coordi-
nates of two lines are not in general coordinates of a line. For analy-
tical purposes we express this sum by simply writing the two matrices
with an addition sign between them. If, however, the lines 4 B and
C D intersect in a point P, we can find points Q and R on those lines

such that wey = ΙΡ QI,
Then Ὁ π᾿
[4 8] - [0 Τ] -- [Ρ 4] -Ε1Ρ Ε1Ξ 8 tty ||= P@+ Bl

We can consider [A B] as a product of A and B. For

PACS ΟἿ ΞΖ ΙΕ {50]

Γ

as we have just seen in the case of [P(Q + R)]. The process of multi-
plication consists in placing the second matrix under the matrix A

48 PROCEEDINGS OF THE AMERICAN ACADEMY.

to form a two rowed matrix [A B]. We shall call this the progressive
product. From the definition it is evident that

[A B] = — [B 4]
and [A Al 30:

3. If the points A, B, C are not collinear, the coordinates of the
plane A BC are proportional to the three rowed determinants in
the matrix
CG a2 a3 dal
δι be bs by

Cl Co «(3 οἰ

[A BC] =

This matrix represents the plane in the sense that from it we can
determine the coordinates of the plane. Conversely to represent any
plane as a matrix we take three non-collinear points of the plane and
form the matrix from them. The elements of such a matrix are the
three-rowed determinants belonging to it. In reality we are consider-
ing this as a one-rowed matrix of four terms (equal to the three-rowed
determinants in [A BC]) arranged in some definite order. Two
matrices of this kind will be called equal if corresponding elements
are equal and are added by adding corresponding elements.

If P, Q, R are any three points of the plane determined by A, B, C,

P=A+rAB+ AC,
9 Ξ μι. Ὁ μ. Β-Ή pC,
R=7y,A+”»,B+ 2»3C.
Consequently
Ay Ag Az |
[P QR] = | us μὲ μὲ [A Β ΟἹ.

IS |

Thus a matrix [PQ R] in addition to representing a plane has a
definite size. The vanishing of [PQ R] signifies that P,Q, R lie
on a line.

The matrix [A B C] can be regarded as a product of [A B] and C,
A and [B C] or of A, B and C, the process of multiplication consisting
always of placing the first matrix at the top and the others in order
under it to form a single matrix.?

2 In this multiplication each matrix must have four columns. If instead of
[A δῚ we have a complex the operation must be performed distributively on
each two-rowed matrix of the sum. For purposes of addition we regard our
quantities as matrices of one row but for purposes of multiplication as matrices
or sums of matrices of four columns.

PHILLIPS AND MOORE.— LINEAR DISTANCE AND ANGLE. 49

From this definition it is evident that

Venola= (48-04 = (AB Cl,
aC!) ν {ἰδ Ὁ [AB DI,
Pepa (46 8) [0418]:

The sum of any number of three-rowed matrices can be expressed
as a single three-rowed matrix [PQ R]. In fact let A; δι Ci and
4: B, Cz cut in aline PQ. Then

[Ay B, σι = li Q Ril,
[4: Β. C.] = [PQ Ry].
Hence

[41 B, Cy] + [42 Bz C2] = [P Q Ri] + [PQ Ry]
= [PQ (Rit R)] = [PQ Rl,

R = Ry, 4. Rs.
From four points A, B, C, D we can form a four rowed matrix or
determinant

where

a, Ag Ag a4
b; bs bs by
C1 Ὁ C3 Ca\”

dy ds ds ds

(A BCD) =

This matrix has only one element and hence we write it as a determi-
nant. A matrix of one element is analytically equivalent to a number.
We use the parentheses to indicate this fact. Square brackets are
used to represent matrices which do not reduce to numbers. The
vanishing of (A B C D) is the condition that the four points le in a
plane.

The quantity (A BC D) can be regarded as a product in a number
of ways. From the definition it is evident that

(A BCD) =(A4A-BCD) =(AB-CD) =—(ABDOC).
4. Regressive Matrices. We can consider space as generated by

planes as well as by points. If its coordinates are a;, a plane a is
then represented by a matrix

a || a1 Q2 a3 as ||.

The same plane may be represented by a matrix [A BC]. Then the

50 PROCEEDINGS OF THE AMERICAN ACADEMY.

coordinates a; are proportional to the coefficients of a; in the determi-
nant |A BC X|.3

If a; is equal to the coefficients of x; in that determinant we shall write
ΞΡ 0}

Thus a three-rowed matrix is for our purpose equivalent to a one-rowed
matrix in contragredient variables.

The line of intersection of two planes a and β can be represented
by a matrix

|

ge | a a2 a3 4
le Bl=|\ 6 Be Bs Bs

The coordinates of the line are here

If the same line is the join of two points A and B we know from analy-
tical geometry that the coordinates git are proportional to the co-
τ By
Yi Yk |
If gi, is equal to the coefficient of |; y,| in the determinant we
shall write

efficients of the minors in the determinant | 4 BX ΥἹ.

[a 6] = [A Bl.

This amounts to saying that in the determinant [A Ba], each
minor in the first two rows is then equal to its algebraic compliment
(coefficient in the expansion of the determinant).

Similarly we represent the point of intersection of three planes by a
matrix [a8 y]. The coordinates a; of this point A are proportional
to the coefficients of & in the determinant [Ea]. In particular
if a; is equal to the coefficient of &; in that determinant we write

A= [αβγ].

In this case each term of the first row in the determinant (A a8 1)
is equal to its algebraic compliment.

There is a determinant [a 8 y ὃ] of four planes just as of four
points. These quantities [a 6], [a8 y], (aBy δ) can be regarded
as products formed according to the same laws as the products of
points. These products of matrices expressed in plane coordinates
we shall eall regressive.

3 It is to be observed that here X is written last. If we take the coefficients
of X; in the determinant |X A δὶ ΟἹ they will have different signs from the
coefficients used here. a

PHILLIPS AND MOORE.— LINEAR DISTANCE AND ANGLE. tat

Matrices in Hyperspace.

5. We shall call the order of a space the number of homogeneous
coordinates of a point in that space.* Thus a point is of order one,
a line of order two, etc. A space of order n can be generated either
by points or by hyperplanes of order n-1. A space Rh of order r <n
can be determined by a set of r points A, giving rise to a matrix.

5.6 δ' ᾽. 6 ene e (0) «

This matrix represents the space R in the sense that from the matrix
can be determined the coordinates of the space. ~The same space Rh
can be determined as the intersection of n—r hyperplanes a; determin-
ing a matrix

| | Gr41, 1 Gr41,2----Aryiin |

| | %r+2, 1 Or42,2- ++ Aran) |) _
| =? Ια p12. nl.
| S5e. cilowG\ors Oks τ τ τ Of ©
| On 1 Gn, 2: ---τἰς Gann

The condition that these matrices represent the same space is that in
the determinant

44 Diogenes: fin |
4 Cpe. ea Ce,
Orit,1 ἄγει, 2. ++ ταν, n|
An, 1 OF PG 5 op oO Ann

the minors in the first r rows be proportional to their algebraic compli-
ments.° If in the determinant each minor of the first r rows is
equal to its algebraic compliment we shall write

[Ay Ag. * _A,] = [ap α,.5... On|.

The r-rowed determinants of a matrix of r rows we call the elements
of the matrix. To add such matrices we add corresponding elements.
If there exists a matrix of x columns whose elements are the corre-

4 Cf. Whitehead, Universal Algebra, page 177.
5 Cf. Bertini, Geometria Projettiva, p. 33.

Sy PROCEEDINGS OF THE AMERICAN ACADEMY.

sponding sums, it represents the sum of the given matrices. If no
such matrix exists the sum is complex. In that case we write the
result as an algebraic sum and do not attempt to express it as a single
matrix. If some of the matrices are expressed in point coordinates,
the others in hyperplane coordinates we replace those of one kind by
their dual forms or at least imagine them so replaced. This amounts
to adding elements of the former to their algebraic compliments in
the latter and considering the result as a term of the first kind.

6. A matrix in which the number of rows is equal to or less than
the number of columns can be regarded as a product. If the matrix
is expressed in point coordinates we call the product progressive, if
in hyperplanar coordinates regressive. To multiply two such matrices
(of the same kind) the sum of whose rows is equal to or less than n,
we write the second matrix under the first to form a single matrix.
If one of the factors is complex we apply the process distributively
to the separate matrices of the sum. From the definition it is evident
that such products are distributive and associative and that the
interchange of two points or hyperplanes (according as the product
is progressive or regressive) changes the sign of the result.

If a matrix of r rows vanishes, all the minors of order r in that matrix
are zero. There is then a linear relation between the rows of the
matrix.® If the matrix represents a progressive product of r points
there is a linear relation between the points of that product and they
therefore lie in a space of order less than r. If the matrix represents a
regressive product of r hyperplanes they satisfy a linear relation and
therefore intersect in a space of order greater than n—r. If the matrix
is not zero the progressive form represents the space containing its
factors and the regressive the space common to its factors.

The most general product is the result of a succession of operations
each consisting of multiplying two factors. If the total number of
rows in two matrices of the same kind (progressive or regressive) 15
less than n, the two are multiplied together according to the rule
already given. If the total number of rows is greater than n, the
product as previously defined gives a matrix of more rows than
columns. For such a matrix we have no interpretation. In that case
we replace each factor by its equivalent in contragredient variables.
The total number of rows in the new product is less than n and we form
the product by the previous method. If the total number of rows
is equal to n the result is the same whether the matrices are taken in

6 Bécher, Introduction to Higher Algebra, p. 36.

PHILLIPS AND MOORE.— LINEAR DISTANCE AND ANGLE. 53

point or hyperplane coordinates. If the matrices are of different
kinds we replace one of them by its contragredient form in such a way
that the new matrices have a sum of rows equal to or less than n.
Thus in every case of a product there is a definite result that has a
meaning. We call this the product of those factors.

7. Reduction formulae. We have just found that in expressing
the product of two matrices when the sum of the rows is greater than
nm, we must change to contragredient forms. We shall now derive
certain reduction formulae by which we obtain the same results
without that change. For this purpose let

[Ay Ag. 506 vl) = ἴα τ Qni2--- An |

[8ι Bo. 310 Bi] a [Bo Bos - εν ‘Balk

We shall now prove that in the determinant

ayy 492 aon a CATA ΞΕΞ ΞΕ 610 Seb oes Oi
Api Ap2 - Ayn 4M, + Apo ΞΕ Ayn |
On+1,1 Qn+1, 2 Anil, n 0 0 0
A = Qn, 1 Ans 2 Qn, ἢ 0 0 0
0 0 0 by Dip Din
0 0 0 ben eu oe |
am Bou, ie Bret 2 ar 5. n βι111 Bow 2 Bex, n |
Dae διά way ct oi te od eure ee at oh eve haste oh caavey Sheu caval re te senith al deh ch wed) ey Seaitecten el Metiotadernte al © |
|
=e [Si-4 1 GS Bre Ze ayers a B,, n Br 1 Bri. 2 κεν Bn, n

each minor from the n — p rows of a’s and n —q rows of 6’s is equal to
its algebraic compliment. To prove this we first show that if such a
minor 77 contains a product of a minor A whose order is n — p in the
a’s by a minor B of order n —q in the @’s, then the algebraic comple-
ment of M contains a product of minors respectively equal to A
and B. Since A is contained in the principal minor | ay... .ann|,
if B is in its complement | by... .By,|, the result is obvious. For
the algebraic complements of A and B respectively in those prin-
cipal minors are the terms required. If B is not contained entirely
in the principal minor, there is a minor B’, in | by... .8,,| containing
the same letters as B and in the same order (but having perhaps
different signs). In the algebraic complement of a minor M’ contain-
ing A, B’ is then a term C D = A Β' where C is a minor of p rows of
a’s and D a minor of ῳ rows of b’s. If now we permute the columns

δ4 PROCEEDINGS OF THE AMERICAN ACADEMY.

contained in B’ but not in B with their correspondents of the same
suffix, this term will pass over into a term of the complement of 77.
In this process C and D are not changed for each a, in C is either not
changed at all or replaced by the same letter and no letter of D can be
in a column so moved. Furthermore the sign is correct for there are
as many minus columns introduced as interchanges made. The same
argument shows that for every product of minors in the algebraic
complement of M there is an equal product in MW. Therefore MW is
equal to its algebraic complement.

Suppose now p+qsn. Then

ρει Queene

We expand the determinant A in terms of minors of the nth order
taken from the first n and the last » columns. The part of the ex-
pansion which contains all the a’s and 6’s in the minor from the first
n Yows 15

Δ, = 2 (4, 4.. 56 al B, By. ἮΝ" Bi) {ἘΠ 5. Ὁ als Antl-+-+- αῃ
Bost > o% 5B.)

the summation being for every combination of n—gq A’s in the first
factor with the remaining p + q— _n in the second factor so arranged
that the two groups in the order written constitute a positive permuta-
tion of A; to A,. The form of this expression is evident since the
B’s cannot occur in the same factor with a’s and β᾽5 (the other factor
then containing a row of zeros). The sign of the term written is
positive since it is obtained as a product of principal minors given
by moving 4 rows of B’s past n — p rows of a’s and p-+ qg—n rows
of A’s, interchanging first x and last n columns and changing n — q
minus signs. The result should therefore have a sign

(— 1) το» +p +a—n) +n? +n—¢ ΞΞῚ

The signs of the other terms then follow, since any positive rearrange-
ment of A’s should not change the sign of the term.

Now in the expression of A each minor formed of n — p rows of a’s
and ἢ —q rows of 6’s is equal to its coefficient. Furthermore A,
contains all of the terms inAgiven by such minors taken from the
first n columns. Therefore in A, each minor of the matrix
[αρε1- - «αι Byii---B»] is equal to its coefficient. These coefficients
constitute the matrix

> (4, te Aner B, εν .B,) ea nite! fe val

PHILLIPS AND MOORE.— LINEAR DISTANCE AND ANGLE. δ

σι

which is therefore equal to the former. We can write this result in
the form 7

leper +O Garin Br = [Ay Ay. nA By By. 2 BJ = = (C Bin B,) D (1)

C being the product of any combination of n —q of A’s and D the
product of the others such that

[A, Ap....A,] = [CD]
If p+q<n we take the part of A which contains all the A’s and
B’s in one n-rowed minor. The result is
Ao= (anu s+ «An [Serre D0 .Ββ,)[41 “1 Sly, B, Ὁ Be Bot 5. ὃ “Brea:

Hence we have

tee Al, Bien eD al ΞΞ πα, 8:.τ β,] = Σ Ια ἃ ©) yi (2)

where 6 is any combination of p B’s and y the remaining ones so
arranged that

[Besa . 1Bnl = ley δ].

If instead of the determinant A we use the determinant

| (111 (Πρό: jn 0 Oreste! 0
|
] ον τ ὦ o- oho) (ere © © λον Οὐ πὲ σα ΟΣ
| Apt CUR coe Petia Gon 0 ὃ ΣΙ ΣΕ
] Gps 1 Andy 2 Ansty ἡ ΞῈ Ap+1) 1 Qp+1s 2 = Ap n
=

Δ΄ΞΞ ] Qns 1 απ» Qs +22 ees Ann An} Gn? Qnn
= bi; += bis cau anoad = by, 11 Dy 3610 690.6 Din
σὰ τὸ ub που κε οτος
ede eee tr pcauree 2: wl Ves ay ἘΣ ΡΠ ae fo
+b, a ba ΤΠ τὰ Ἐν ΤΙ Ὁ ἘΞ by. n bat by Dan
| 0 Ome τὺ 0 Bort 1 Bort, 2 Bots n
| 5 8 Roky AE OE Ramage ch oh a Se a
τῷ 0 0 Baa Broan tease Brn

when p + q > n, we obtain the expression in the form
WA Absa τις B, Bee do = DCA Jaloye «Ale DYE. . (3)

where D is any combination of n—p letters B and C the remaining ones
so arranged that

[B, By...B,] = [0 Ὁ].

7 Grassmann, Gesamelte Werke, Vol. I, p. 83; Whitehead, Universal Alge-
bra, p. 188; H. B. Philips, Proceedings of ‘the American Academy of Arts and
Sciences, Vol. 46, p. 909. In this last article the formula obtz tined may havea
different sign from the one here given.

56 PROCEEDINGS OF THE AMERICAN ACADEMY.

When p+ q < ἢ this determinant gives

[apt εὐ τας Bost ες Brl =2 (γ 5: : 5.) ὃ ᾿ἢ . (4)

where Ὑ is any combination of qg a’s and ὃ the remaining ones so
arranged that
[α 81 oan Ay] = Ly δ].

Symbolic notation.

8. The determinants in the matrix representing a space S are
the coordinates 5; of S. Of σ is a space complimentary to S, we
consider it as represented by a matrix of the same kind as S. It has
then a like number of coordniates 7; (algebraic compliments of 5;
in the determinant |so7|). Then

(S σὴ == δὲ Fj.

This is a linear function of the coordinates s; and by a proper choice
of σ (perhaps complex) can be made any linear function of those
coordinates. To obtain a bilinear function of the coordinates r;, s;
of two spaces R and S we take matrices Pp and © complimentary to
Rand Ὁ. then

(Rp) So) = 2p, 7; 5. : . (ὃ)

In order to obtain the most general bilinear function
Σ Ay, Ty δὲ

we consider the above as a symbolic representation in which p; σι,
is to be replaced by az. Thus (Rp) (So) represents symbolically
any bilinear function of the coordinates 7;, δ. Any lmear relation
connecting the symbolic quantities (R p) (S ©) will be satisfied by the
bilinear functions Σ᾽ a, 7; s,. This is the symbolic representa-
tion so much used by Clebsch.

We can consider (Rp) (So) as resulting from an expression p 7
by operating on the first factor with R and on the second with S.
This product p © is the dyadic of Gibbs.8 It may be considered as a
distributive product of p and σ. It is called the indeterminate ϑ
product. In it the order of factors must be preserved. In fact there
is no general functional relation between Pp 7 and @ p. The dyadic

8 Vector Analysis, Gibbs-Wilson, page 265.
Ci ΕΠ Bs Phillips: locsent:

PHILLIFS AND MOORE.— LINEAR DISTANCE AND ANGLE. ou

po represents a transformation which changes a space complimentary
to p into a space (Rp) σ which is given by the locus of S in

(Rp) (So) = 0.

Linear Distance and Angle in Three Dimensions.

9. Linear distance between two points. We define the dis-
tance between two points A, B as such a function A B of their
coordinates that (1) if one is fixed the other lies in a plane, and (2)
for points A, B, C on a line

AB + ΒΟ- CA=0. ; : d (6)
From the first condition the distance must be of the form
Ap alas) (7)
Fy (A, B)

where F, and F, are bilinear functions of A and B. Putting A, B
and C equal in the second condition we get

AA=0.

Hence
F, (A, A) = 0 . . δ : (8)

In this last equation replacing A by A + B and cancelling the terms
F, (A, A) and F, (B, B) we have
F, (4, B)+ F, (BSA e— 0 . δ . (9)

The numerator of AB must then change sign when we interchange
Aand B. In (6) putting C = B we have

AB+BA=0.
This shows that
F, (A, B) = F, (B, A) . . δ . (10)

or the denominator of AB is symmetricin A and B. Let C= A+B.
Then (6) becomes

Fy τ FP, (B, A) =f Fy (B, B) ae FP, (A, A) -Ξ Fy (B, A) =
Ἐς (A, B)

F, (B, A) + F,(B,B) " F(A, A) + F,(B, A) ©
Making use of (8), (9) and (10) this becomes

Fy (A, B) [F2 (A, A) Fo (B, B) — F; (A, B)?] = 0.

58 PROCEEDINGS OF THE AMERICAN ACADEMY.

Then either
ΤΠ ΞΘ

or

Py» (A, Be ἘΞ FP, (A, A) Fs (B, B).

This last equation shows that F, (A, B) factors into a function of A
times a function of B. Calling this function (¢ A), and writing

F, (A, B) = 3 [F (4, B) — F, (B, 4)] = (2 A) (8 B) — (α Β) (8 A),

we have

aq . (2 4) (BB) — (@B) (8 A)

( A) ( B)
Using the identity (3) this takes the form 10
(@8-AB) _ (qg-AB)
(φ A) (6B) (@ A) (φ BY’
where we put gq in place of the two rowed matrix (α A].

10. Angle between two planes. We define the angle between
two planes as such a function af of their coordinates that if the angle
is given and one of the planes fixed, the other passes through a point
and for three planes of a linear pencil

ab+pyt+tya=0.
By the same argument as for the clstcaunes between two points we
obtain for the angle

AB=

ae (p-a B)
(F a) (FB)

where p is a fixed complex and F a fixed point.

Distance is a relative invariant under the group of collineations
that leave the complex q and the plane ¢ fixed. Similarly angle is a
relative invariant under the group leaving p and F fixed. In order
that fixed relations may exist between distances and angles we wish,
if possible, these groups to be the same. We assume that the complex
q does not degenerate into a line. Then the only complex and point
determined by g and ¢ is the complex ῳ itself and the polar point of φ
with respect to it. Hence we have

p=4%
F= we PI.

10 We consider ὯΝ 1 Β) as a regressive produel (a.B.A B), in which we
expand the product (B.A B) and then multiply by a.

PHILLIPS AND MOORE.— LINEAR DISTANCE AND ANGLE. 59

We choose the unit angle such that ἃ = 1. Then
F = [¢ pl.

[F pl] = [φΦ».»] -- (yp. ρ)φ = φ

if we choose the magnitude of p such that

also 11

(p p) = 2.

The relations between ¢ and F are then symmetrical.
Our formulae are now

—._ _—(pAB) -

B= 6 4) (¢ B) oe
— ἀΑἀ(φ-αβ[) ;
ap = (F a) (FB) a) (FB) : ‘ : : (12)

with the condition that F = [¢ p], 6 = [F p] and (pp) = 2.

The ratio of two distances or of two angles, also the product of a
distance and angle are invariant under the seven parameter group
of collineations leaving the complex p and the plane ¢ fixed. If one
of these transformations leaves a distance or angle unchanged it
leaves all distances and angles unchanged. Those quantities then
are invariant under a six parameter group. Any tetrahedron can
therefore be transformed into an equal tetrahedron (one having equal
length of sides) by a collineation leaving distance and angle invariant.

From the formula for the distance between two points, it is seen
that distances along a line of the complex p are zero provided neither
of the points lies on ¢. The distance along a line of p to ¢ is inde-
terminate but along any other line it is infinite. Similarly the angle
between two planes intersecting in a line of p but neither passing
through F is zero. If one of the planes passes through F, the angle
is indeterminate or infinite according as the other plane does or does
not cut it in a line of p.

11. The locus of points y at a distance from the point αἱ is a plane

11 The formula [ p+ p] = 3 (p p) Φ can be proved as follows. Let

p=aB+ γδ.
Then (pp) -- 2(αβ γδ)
and [p-p] = [φία β΄ γδ)- (@B + γ8)}

= (pa B8) y— (ba By) ὃ + (φ α ὃ β)α -- (pyda)B
Ξ Φ(αβ γδ) -- ὦ (pp) >.

60 PROCEEDINGS OF THE AMERICAN ACADEMY.

E intersecting ¢ on the polar plane of x with respect to p. The corre-
spondence between x and & is a correlation. From the equation

τ See ee
cama On) ian
or λ (φ “) (Py) — (pry) = 0,
it is seen that the locus of y is
E= (ox) φ -- [pa] oe ee ome Cs)

Similarly the locus of planes ἢ making a given angle ἃ with the plane &
is a point such that the line connecting it to F passes through the
polar point of € with respect to p. The locus of planes making with
ἕξ an angle — 2 is

z= —A(F&) F — [pi].
Substituting in this the value of € from (13) we get
z= (F px) F —2 (φ 4) [pg] + [p-p2]
since (Ff ¢) = 0, F being a point of ¢. Using the conditions
[Fp] = 4, [dp] =F, and [p-pa]=3(pp)zr=e
we get Z=2

Hence the correlations determined by a distance » and by an angle
— are inverse. Now the correlation set up by an angle — ἃ is
inverse to that determined by an angle X\. Hence the equations

Δ Ξε δ,

Ξ
where x and ἕ are given, y and 7 variable, set up the same correlation.
Through a correlation
=

x 1

Sc

to 2; and x» correspond the planes

λ (φ αἱ) 6 — pay,
d (φ x2) 6 — p Xo.
The angle between these planes is
(p [A ( a1) 6 — pa] [A (Φ a2) — p x)
ΤᾺ (φ a) 6 — pal} (F [A (φ a2) 6 — pal}

PHILLIPS AND MOORE.— LINEAR DISTANCE AND ANGLE. 61

Since [F ¢] and [φ φ] are zero this gives

—) [(h a1) (ρ- bp x2) + (p a2) (p-p αι" Φ)ὴ + (p:p ay: p x)]
(F pai) (F p 22)

hes d {(G 21) (φ 29) + (φ 29) (x1 φ)} + (p αἱ 19)
(F pai) (F p x2)

ΕΞ (p xy 19)
(φ x1) (φ ao)

Hence the correlation changes 21, 22 into two planes &, & such that
£1 & = x1 ὅλ.

In particular if ἃ = 0, the correlation between x and é is the null
system determined by the complex p. The distance between any
two points is therefore equal to the angle between their polar planes
with respect to the complex p.

12. Angle between twolines. We define the angle between two
lines r, s as such a function rs of their coordinates that, one of them
being fixed and the angle constant, the other satisfies a linear relation
(ἡ. ὁ. belongs to a linear complex) and for lines r, 8, t of a plane pencil

rst+tst+tr=0.
By the same argument as for distance between two points we find

fi (r, s)
fs (r, Oh

fi (r, 8) r= -- ἢ (s, r)

and [5 (r, 5) factors into a linear function of r times the same linear
function of s. Hence

rs=

(ar) (ὦ 5) — (as) (Ὁ 7)
(cr) (ὁ 5) :
where a, b, ὁ are matrices of two rows and ab a dyadic setting up a

correspondence between lines or complexes. The numerator of rs
can be written in a different form. In fact

(A Br) (CDs) —(CDr) (ABs) =
[486 -τ- Ὁ 5] — [ABD -r-Cs] + [BCD-r- As] — [ACD-r-Bs]},

as is seen by expanding the right hand member. The expression

15 ΞΞ

62 PROCEEDINGS OF THE AMERICAN ACADEMY.

in the parentheses may be regarded as gotten by operating on the
collineation (dyadic)

1{[A BC] D—[ABD|C+ [BCD] A —[ACD]B}
with 7, s. For this collineation the linear invariant
Z{(ABCD) —(ABDC)+ (BCD A) — (ACD B)} ac)

Such a collineation has sometimes been called normal. By summing
we get

(ar) (ὖ 5) — @s) (Ὁ Ὁ) = (ar-As)
where a A is a collineation such that
(aA) — 0:

Conversely if a A is any normal collineation
ία ἢ 1 ἢ) ΞΞ ἴα ar 0

r being any line or complex. Replacing r by r + s we have
(ar-4s)+ (as-Ar) =0,

showing that (a r-A 5) changes sign with interchange of r and s and
is hence of the type
(7) (05) (07

aa (ar-As)
(cr) (ὁ 5)

It is to be noticed that this formula determines an angle between two
complexes as well as between two lines. In particular the angle is
zero if the complexes coincide.

The system of lines s making a zero angle with a line r = [Ὁ D]
may be constructed as follows. Let the correspondents of C and D
through the collineation a A be

ἘΞ ΟῚ
Di Din) eAe

We therefore have

(14)

Then s is determined by an equation

(ar-As) = (a-CD-As) = (aD) CAs) — (aC) DAs)
= CDEC Naa (Cl IDS) =

PHILLIPS AND MOORE.— LINEAR DISTANCE AND ANGLE. 63

In particular any line of the congruence cutting D’ C and C’ D has
the required property. We may use instead of C, D any two points
of the line. If then CD and C’ D’ do not intersect this gives us an
infinite number of congruences generating the complex to which s
belongs.

13. For a general collineation a A these lines r, s making with
each other zero angles have an interesting geometrical interpretation.
It is well known that a general collineation whose linear invariant
(a A) vanishes has a system of tetrahedra A, B, C, D such that each
point is carried by the collineation into a point of the opposite face.
Two opposite edges A B and C D of such a tetrahedron determine a
zero angle. For in this case since C’, D’ are in the planes A B D and
A BC, the lines C’ D and C D’ cut A B.

Conversely if A B and C D are two non-intersecting lines making
with each other a zero angle and those lines are not left entirely
invariant by the collineation we construct a tetrahedron upon them
as follows. Join A’ and C’, the correspondents of A, C through the
collineation a A, to CD and A B respectively and let these planes
determine on A B and C D respectively the points B and D. Then
B will pass into a point B’ such that A B’ cuts C D (i. 6. a point of
ACD). Similarly for D. Thus, with the possible exception of
fixed lines, the entire system of non-intersecting lines making with
each other a zero angle consists of the opposite edges of these particular
tetrahedra associated with the normal collineation a A.

If P, Q, R, S are any four points it is seen on expanding the right
side that

(ab) ΤΠ =] ah O-ARS —«¢PRAO See SAO RI

Hence if x is any point and é any plane (a2) (A &) is expressible as
a sum of terms of the form ar-As. Under any collineation leaving
all angles invariant this last expression must be covariant. Hence
the form (a x) (A δ) must also be covariant.

Collineations leaving angle invariant must then leave the complex
ὁ invariant and the collineation aA fixed. We wish these angles
to be invariant under the group of transformations that leave distance
fixed. In that case c must coincide with p. There is a transforma-
tion of this group changing any distance x y into any equal distance
xy’. Since to a there can correspond through a A only one point y,
this point must be fixed under all the collineations. Therefore to
each point x corresponds the point F. Hence

aA=fF

64 PROCEEDINGS OF THE AMERICAN ACADEMY.

where 2 is aplane and Fapoint. Dual considerations show that ? is
fixed under all the collineations, i. e. coincides with ¢. Hence by a
proper choice of units we have

Pie ae (or-F 5) = (φ 5-Ε r)
(pr) (ps) (pr) (ps) 5),

The angle between two lines is zero if they cut a line through F in the
plane ¢. The angle is infinite if one of them belongs to the complex
p and they are not cut by a line of the plane ¢ passing through the
point F.

14. We have seen that

xy=R
sets up acorrelation. To x and y correspond planes
Ao x) φ — pa,
Moy) > — py.
To x y corresponds the intersection which can be written
A[p-xy-F] + (pry) p — ἃ (pp) [ry]
Hence to lines r and s correspond lines
A\lor-F] + @r) --τ,
Alo s:F] + (ps) -- 5.
The angle between these lines is |
(φ {Alo s:F] + (ps) p—st Fid[or Fl] + (pr) -- τῇ)
(pith [o S F] + (ps) p—s}) @idlor F] + (Wr) Ὁ τ)
(ὦ. 7)
τ (pr)

Hence the angle between two lines is equal to that between the lines
corresponding to them through the correlation.
: a aN
In particular when ἃ = Ὁ we see that the angle between two lines
is equal to that between their polar lines with respect to the complex p.
15. Distance from point to plane. We wish to determine a

function Aa of the coordinates of a point and plane such that if
either is fixed the other satisfies a linear relation and such that

= ῳ

ee

PHILLIPS AND MOORE.— LINEAR DISTANCE AND ANGLE. 65

is a necessary and sufficient condition that A, a be transformable
into A’, a’ by a motion leaving distance invariant. Such a function

is

ΣΕ os See ae ΠΩΣ

Let a be a plane BCD. Then
ria (ABC Dy 2 (A BCD) (pp)

A
©" (¢4) (FBCD) (¢ 4) (@p-BCD)
This expression can be written

(pA B) (pCD)+ PAC) (pDB)+ (DAD) DBC)

(6 A){(o B) (pC D) + (@C) (PD B)+ @D) (pBC)}
_ AB‘ CD+AC-DB+ AD: B.C
ἦ 0 eC ΠΕ

(17)

That A a is invariant under the transformations leaving distance
unchanged is shown by the last form. Conversely if

4« -- 4’ α'
we take in a a triangle BCD and in a’ a corresponding triangle
B’C’D’ such that
HOG IR, Ξ GS TO GN
LO SD SOT Od

Then the above equation shows that
BD’ = BD.
The two tetrahedra have all their edges equal and hence the one is
transformable into the other.

This quantity Aa we call the distance from the point A to the
plane a. It has many of the properties of euclidean distance from
point to plane. Thus if the point lies in the plane (point not in @
and plane not through F) the distance is zero. If the plane is held
fixed and the distance kept constant the point lies in a plane cutting
aon @. Ifthe point is held fixed the locus of the plane is a point on
the line joining the given point to F.

If aN

66 PROCEEDINGS OF THE AMERICAN ACADEMY.

the point corresponding to A (enveloped by a) is
B = λ (φ A) lie A.
The distance from A to B is

———— edie 3s A?
4B WA Ge)
— (φ 4)

Thus 4 B= Aa. This shows that 4 a is the distance, measured
along A F, from A to the point of intersection of a with A F.

16. Distance from point to line. We define the distance from
a point A to a line r as such a function of their coordinates that one
of the quantities being fixed and the distance held constant, the other
satisfies a linear relation and such that this distance is invariant
under the transformations leaving distance between two points un-
changed. Such a function is

λ.

(18)

If r joins two points, B, C this can be written
5. _ (ABC-op) _ (Ad) (BOD) + (BS) (CAp) + C9) (ABD)
(A φ) (BC p) (A 6) PBC)

Dividing numerator and denominator by (4 ¢) (B@¢) (C4), this
becomes

a Bb CO=- CA AB
Ar =
Bie

(19)

This expression shows that Avr is invariant under the distance
transformations. Conversely of

A A oa

there is a transformation changing 4r into A’r’. For let B, C
be two points of r. Take on r’ two points δ΄, C’ such that

ANB ΞΞΟ a
AC=A'C’,
then piers
ΞΡ

and a transformation of the kind desired can be obtained.

PHILLIPS AND MOORE.— LINEAR DISTANCE AND ANGLE. 67

The distance from a point to a line is zero if the point lies on the
line or if the plane of the line and the point pass through F (assuming
that the point does not lie in ¢ and that the line does not belong to p).

Since the order of A and r is immaterial in the formula for A r we write
Arr rns

17. Angle between line and plane. Dual considerations give
for the angle between a line r and a plane a, the expression
Se ee "

(F a) (pr)

Let a be the plane at distance ἃ from A and r the line all points

of which are at distance ἃ from s. Then

a=)(¢A)o— pA,
; — Nous | = (ps) 5.
Hence
τὴς φ A) ¢ -- pA} ἰλ|φ ΕἸ] + (ps) p -- 5}}
(F {\(¢A)6—pA}) (p ἵλ Φ5Ε + (ps) p—s})
_ (—[pAli@s) F—s4}) (05) @ 4) + @A)-@ 8) |
(φ A) (ps) (¢ A) (ps)
But [p A-s φ] = [p {(4 6) s— As φ]],
and {p[A-¢ = (A-s-¢ p) = (As F).
Ξ πον UPAS) -
Hence oa ΠΕΡΙ Σ Ton ΞΞΙ Ὁ:

Therefore the angle between a line and plane is equal to the distance
between the line and point corresponding to them through the dis-
tance correlation. In particular for \ = 0, we see that the distance
between point and line is equal to the angle between their polar plane
and point with respect to the complex p.

18. Line Area of a triangle. We define the area of a triangle

ABC as a function A BC of three points such that if the vertex is
fixed and the base moved along its line, the area is proportional to the
base. Hence if A is the vertex of the triangle and s the line on which
the base BC lies

68 PROCEEDINGS OF THE AMERICAN ACADEMY.

where kis a function of A and s. This gives on applying formulae
(11) and (18) after replacing s by [B C]

---- (F ABC)
nC = Ξ ες sie
(φ A) (φ B) @ C)

The areas of two triangles having the same vertex and base line are
then proportional to the quantities

CAR Oe
(φ A) ( (φ B) (φ C)

By a series of operations consisting of moving one side of the
triangle along its line and keeping the opposite vertex fixed we can
move the triangle into coincidence with any other having the same
area. Under each of these operations the area is proportional to the
above quantity. Hence any two areas are to each other as those
quantities. Then by a proper choice of unit we have

Ἔν = eS OS ene
(φ A) (¢ B) (φ C)

Writing F = (¢ p) we have
ἜΣ. (pp-ABC) _ (ΦΑ) (pBC) + (B) (pCA) + (¢C) (pAB)

~ (pA) (@B) (¢C) ($A) (6 B) (6 ΟἹ
= B CAS CANA B= ποι τ Ste eee on)

ς : o . :
Thus the line area of a triangle is equal to its perimeter.
Dually we can find as the trihedral angle between three planes

Ὁ: 9. Ys

τ ἐξ (φ αβ γ)
' (F a) (F θ) (Fy)

Sy SG ey easy Ge, ee et

19. Volume of a tetrahedron. Similarly we define the volume
of a tetrahedron A BC D as such a function A BCD of the four
points that given the vertex and plane of the base, the volume is
proportional to the area of the base. From the definition we have

ABCD=kBCD-Aa
= k(FBCD)-(Aa) A peels a B CD) ts
(φ B) (6C) (6D) (φ A) (Fa) (φ A) (φ B) (φ C) (¢ DY’

PHILLIPS AND MOORE.— LINEAR DISTANCE AND ANGLE. 69

where a represents the plane BC D, in which the base lies and i
is afunction of A anda. By aseries of motions consisting of moving
one triangle of the tetrahedron in its plane it is seen that the tetra-
hedron can be moved into any other having equal volume. These
motions keep the volume constant and therefore k is an absolute
constant. Hence choosing our unit so that ἢ = 1, we have

(A BCD)
(φ A) (φ B) @C) @D)
From the definition we have
ABCD=BCD-Aa=BCD-A(BCD)
= 0 00-hy τ ὁ
: ΠΡΟΣ ΟΠ 25 ID Te
ΞΡ DUC peel De BG στ΄ 25)

From (24) we see that if the vertex A lies in the plane A BC the
volume is zero. Hence applying this to (25) we have

AB-CD+AC-DB+AD-BC=0

ABCD= (24)

as a relation connecting four points lying in a plane. This relation
is seen to be identical with the relation connecting the Pliicker co-
ordinates of a line. From this a theory of plane quadrilaterals could
be built up.

20. Summary. We have defined a bilinear function of any two
spaces in three dimensions. In case one of these spaces is a point
we call this function a distance otherwise an angle. We have also
defined certain areas determined by three elements and volumes
determined by four. These functions are all invariant under a six
parametered group of collineations projectively equivalent to the
group of collineations leaving euclidean volume invariant. Under
the correlation

xy = const.
each of these functions is equal to the dual function of the transformed
elements. The expressions for these functions are

aa (p A B)

eee
ᾧ 4) ᾧ Β)

Πῶς -Φ πὶ

(F a) (F B)

70 PROCEEDINGS OF THE AMERICAN ACADEMY.

(p S:Fr)

Tiga Ta CS ΜΌΝΟΣ
Aa= ΠΡ : : : (16)
ree (F Ar)
Eigen ue)
some OTe)
eS NN τ
ΣΕΡΊΟΙΞ τε} τος (Di)
@ ΑἹ @B) 0)
Fe ae Oa
P= το σ᾿
(4 BCD)
Aub) — : : 2:
(@ A) @ B) ᾧ ΟἹ @D) ie
ἀπ = Ὁ ἘΠῚ J sais

“ (Fa) (FB) (Fy) (Fa)

21. Tetrahedron. The angles of a triangle will now be expressed
in terms of the sides. For the angle C A B of the triangle A B C we
have

(¢ A B-FC A)
(p A B) (pC A)
TG A) EAB)
— (pAB)(pC A)
Replacing F by [¢ p] and applying (3) we have
(φ A) (6 p-A BC)
(p A B) (pC A)

_ (6 A) LG A) WBC) + @ ΒΥ (PCA) + (@C) DAB)}
(p A B) (pC A)

Dividing numerator by (¢ A)? (¢ B) (¢ C), this becomes
C26 CA 2 28
AB τ C A

Angle CAB=CA-AB=

CA, AB=

CA; AB =

PHILLIPS AND MOORE.— LINEAR DISTANCE AND ANGLE. iil

If we use A, B, C for the angles and a, b, ὁ for the sides opposite
this becomes

Hanke +b+e (26)
be
Similarly we have
a= ete ει Τὴ

In the tetrahedron if a, β, y, 6 are the planes opposite the vertices
A, B, C, D we have for the angle

apa 2 BCDCDA) _ @CD)(BCDA)

(FBCD)(FCDA) (FBCD) (FCDA)
_ODBCDA
EOD. CA

This gives for the volume

BOD CMA ano

BCD A ——
CD

28)

That is the volume of a tetrahedron is equal to the product of the
areas of two faces and the dihedral angle between them divided by the
length of the common edge.

The trihedral angle a @ ¥ is given by

aBy=af+By+ya

_@D-BCDA DA-CDAB , DB-ADBC
BCD-CDA'CDA-DAB ADB-CDB
(PABCE 1 BCD DAF CDADB) Oo
ΒΩ Cp ἢ ΠΡῸΣ,

= BCDA

This formula solved for B C D A will also express the volume in terms
of the trihedral angle and the three face triangles and three edges
which meet at its vertex.

The volume can also be expressed in many other forms.

1 PROCEEDINGS OF THE AMERICAN ACADEMY.

Linear distance in hyperspace.

22. The argument by which we derived the formula for the distance
between two points in three dimensions applies without change to
higher dimensions. The formula for distance is then always

(q A B)
(φ A) (φ B)

where 4 is a complex matrix of order n —2 and ¢ ahyperplane. Sim-
ilarly the angle between two hyperplanes is

ΕΝ
" Fa) BY

where p is a complex matrix of order two and F a point. We wish
these quantities to be invariant under the same group of collineations.
This will happen if ¢ and q are determined by F and p and conversely.
We shall therefore consider the system of complexes determined by
a point F and a complex p of the second order. The details of this
discussion depend somewhat on whether the space is of even or odd
order. We consequently consider these cases separately.

23. Space of order ἡ = 2m. The progressive products of a
complex p with itself give a system of complexes [p p], [p p p] ete.
we shall denote these by the symbols p’, p? ete. In the present case
p™ is represented by a sum of determinants of order n and hence is a
scalar. We assume that this quantity is not zero. Such for example
is the case if

WE =

oA Ay Ag Aste = eo ee lo
and the points 4; do not lie in a hyperplane. For then
na Ala eA oan Am):

Since p” is not zero none of the lower powers are zero.
We take as a fundamental system the quantities

E> p, 'F p, ee pee,

consisting of the powers of p and those powers multiplied by F. We
shall find that this system forms a group under progressive and regres-
sive multiplication, in the sense that the product of any two is either
zero or a numerical multiple of a third in the system.

To form products it is sufficient to recall that p is a sum of products
of two points and hence in linear (distributive) operations behaves like
a simple product of two points. Furthermore to multiply regressively

PHILLIPS AND MOORE.— LINEAR DISTANCE AND ANGLE. 73
R by a product of points S we take from S all combinations D of
points such that D is complimentary to R, arrange the others in a
product C such that S = CD, and form the sum 2(RD)C. To
obtain the product
[pp]

by resolving the second factor, we must take the sum of products,
of p by all but two letters of any term of the second. factor times the
product of those two. Those letters will occur in a combination p?

Ω

[05 Ξ τς ") αν —(2 ie < ᾿ - (m— 1) ΝΕ Ὁ;

the second term being subtracted because in

ii 1 ee
( 9 ) ἘΠῚ

ΐ eee ἘΠ 1]
and this combination may be selected in ( ) ways Hence

occur 2 % ἯΙ ᾿ terms of the form p”-p, whereas there should be
m — 1 in the expansion of [p?-p” 1]. Simplifying the above expression
we get, since ΡΞ 2}
er m— 1
ie Ul oe CL
m
Similarly
ae r -ῷ 9 τ) v
teal a pip ps2 (5) ἘΠ}. Ὁ.
= ἈΦΞΕΊΞ ΣΙ, ἘΞ ΤΕΣ. Dupe:
m

Since p” is a scalar, we may solve this last equation for p”!. Chang-
ing r into r + 1 in the result we have,
m |p" pr |
p™ (r+ 1) (m—r)’
the equation holding for r = 0 if we take p? = 1. Thus we have an

expression for p” in terms of p’!. Expressing p™! in terms of ρ 2,
etc., we have finally

r

| ie

= ( m ae »"
pe [ὦ +1) r+ 2)... μι] (μι --- γ)!

74 PROCEEDINGS OF THE AMERICAN ACADEMY.

If we choose the magnitude of p such that

™m

p™ = m!
m-)
d let a aa ey)
ail (m — 1)! :
this equation may be written
ὯΝ Grime
= : : Ξ ς 90
r! (m — r)! Be)
woerewa— ἡ d9 seam.
Again we have
[F p™ | = πὸ 1} Ὁ F-p]
and
[piel er pee aha Pp me.
Hence
τ 3 = r(m—r z
[pF pl] = Fp" p']— [pr F- pt] = 29 om (Fp,

Solving this for [F p”!] and changing r into r + 1, we have
m [p™*-F pl),
p™ (m —r—1)(r +1)’

a formula holding for r = 9. By continued application of this for-
mula we finally get

[F p"| =

[F p’) 5 ει: F pes) ; Ἂ:
r! (m —r—1)!(m —1)!
Let
ep]
(m — 1)! i
Then
[F 71] φ ἡ ΤΣ
= : : δ 91
r! (m—r—1)! oe
where Ul ee aio Ale

24. Space of order n = 2m-+ 1. In this case p” is of order
n—1 and hence represents a hyperplane. Since the product p” is
progressive this product must contain p (i. e., p can be expressed
as D Ax [A; A;], the points A; being contained in ¢). Hence,

[p-p™] = 0.

PHILLIPS AND MOORE.— LINEAR DISTANCE AND ANGLE.

We assume that
LF pe] 4 0.

Then p” and [F p"], r = m, are not zero.

~I
Or

Since [p:p”] = 0, there can be no terms in the expansion of

[p-F p™| which have F outside the parenthesis.

p (F p™) = m(F p™) p+ i Leper sp | τὸ (

Consequently
m

= 2 To 1 m
Pip" p= 2 = Cp Zep.

Similarly

LEP De () Dry π acme

Ree ial)

77}

Solving this for p” ! and changing r into r + 1, we obtain

om [F php

r

(5) — Gp") po

Co) p=

Pp

Repeated use of this formula gives finally

~ (Fp™ (r+) (m—n)

7: Ὁ ε- τὴ
2] Ep )

If we choose the magnitudes of F and p such that

(F p™) = m!
and let
aa
(m — 1) ie
jij ne
m!
we have
Ὁ 3, πὸ φ]
r! (m—r)!
wherer = 0,1, .. 2m.

Letting r = Ο in (32) we have
m! = η7 -φ

m! (am fal r)!

(A)

(B)

76 PROCEEDINGS OF THE AMERICAN ACADEMY.

Hence q” is not zero. Now q” is a point, and since 4 contains F
as a factor, must be the point F. Also

ΠΠΞΞ Ὁ}
Consequently
σα στ ς 0)
m!
again from (32) we have
[φ ἢ |
-------». : : : Be
(m— 1)! - On

The equations (A), (B), (C) and (A’), (B’), (C’) show that F, p are
related to ¢, gq in the same way that the latter are to the former.

Hence
pees aA UE Aa be Dues)

r! (m—r)!

Where πῆρ De nares

The formulae (30), (31), (82), (83) show that the system of quanti-
ties p’, F p” is generated in the same way from F, p or from 4, q.
If the product of two of these quantities is progressive the factors can
be associated and the result is either zero or equal to a third. If the
product is regressive we replace p” and F p” by their expressions in
terms of ¢ and q. The product in this form is represented by a sum
of matrices (in hyperplane coordinates) having a smaller number of
rows than columns. The factors can therefore be commuted and
associated giving a result which is number times a quantity of the form
q’ or ¢q’. Hence the product of any two quantities of the funda-
mental system is a numerical multiple of a third.

Let
So, a - |
γ
ge τὰ
27:1 —_ Ἢ ᾿
where r = 0, 1, 2, ...m. Dually we have the quantities o; such
that,
ager a)
σὰν; aT |
bq’ } : : “ See a)
O21 = |

PHILLIPS AND MOORE.— LINEAR DISTANCE AND ANGLE. 77

where r= 0, 1, 2, ...m. Equations (30), (31), (82), (83) show
that

ΟἿ᾽ SS Str . δ . . δ (36).
25. Distance and angle. The distance between two points
A, ‘Bris
See
(φ A) (¢ B)

Similarly we define the angle between any two spaces R, T of the
same order r by the equation
ΞΑ (q- σ, 1 R-o,4 7)

RT a R-o.1 1)
(σ, Π) (σ, 1)

σα being the complex which multiplied by R and T respectively give
points. This expression can be put into two other forms which we
shall now obtain. We consider three cases depending on the form
of Or+1-

yk
(1) If or = δ
we have
Ἐ Πρ" ἬΝ alp peel:
[o,,1 Εἰ = aie = =n = [p-o,4 ΠῚ.
Then
τ (p:oy4 Tos 1.) -- (0,41 R-o,-4 ἽΝ
De
Fok
Or = ! 7 I
then

GPR) F [pF OR!
εἰ Capit

ἰσ, ει R| τε

Since in this case ¢,_; also contains F, we have
(peop I στ) ΞΞ (Gan Roa ΤῊ
In both of the preceding cases
πα, τῆ, 1) = (= (Gael).
[¢q"]

k
(3) Hf σιμι is of the form τ Oleg by the dual of the preced-

»
UL.

78 PROCEEDINGS OF THE AMERICAN ACADEMY.

ing reasoning we have, since the sign must be positive in the first
and negative in the second case
(Ga Ro T= (Ay Ss Ge Beg eae)
= (= 1)" (σε R-o,.1 Τὴ:
For every case the following equation holds:

ies (pie hoa 17) ἣν (q:o -aR-o,1T) ae

(G41 τσ» 1)
(σ, R) (σ, Τ) (σ, R) (σ, 7)

(σ, R) (σ, 1)

It is evident from the definition that

0. eS hi

This together with the linearity of the expression, the factored form
and symmetry of the denominator, shows that three spaces R, R’, π΄
of a pencil determine angles such that

PR RR ROR 0!

To prove this directly it is only necessary to place
RY ΞΧ ΠΕ eR,
in the expression for the above sum and clear of fractions.

26. Distance and angle in a section of hyperspace. A space
R of our space of order n intersects the complexes S; of the funda-
mental system in a set of complexes. For spaces contained in R we
can define distance and angle relative to these last complexes. We
wish now to show the relation between those invariants and the cor-
responding invariants relative to the complexes §;.

First consider the section made by a hyperplane a. This deter-
mines with the complex p a point

F, = [a pl,
and with the complex [F p], a complex
pi = [a-F pl.
We can write this last expression in the form
pi = (a F) p — [a-p- F).

If we multiply this by itself r times, since the last term is a line, this

PHILLIPS AND MOORE.— LINEAR DISTANCE AND ANGLE. 79

last term cannot appear more than once as a factor of any term of the
result. Hence :
: presario (a) arp 5. 0.51}
-Ξ- 8) (al) per la-p-F <p").
(orl): Ὁ 2. pl,
provided that 2r +1 =n. Multiplying the first of these values of
pm’ by δὶ = [a p], since [a p] is already a factor of the second term,
we get
(ct) laze |
r+]
provided that 2r +2=n. Dividing the above expressions for py,”
and [F; ρι7] by r!, we get

[Fi pr] = (a F)" [a p-p"] =

5

poe Gl) ep ]
r! r! (37)
[Fin] (@ Flap] | me
r! (r+ 1)! ;

these expressions being valid if the order of the left side is equal to
or less than that of a hyperplane.
We next find the intersection of a second hyperplane 8 with the
system of complexes p,", [Γι]. Let
Fy (8 pil = 16 a: Fp]

oe edi pal 2 1B Ὁ}
x (a F) PAA)

By the same argument as before we get

OES ΤΠ

r! (a F)"
[Fs : bento 1}: Deve
rf (a F)’ (r+ 1)!

Using the values of ρι and [F; ρι7] in (37) we have

bo
Ss
bo

st
ΞΟ

po (Bap) eB op! 1]
r! CPi”
ae (Ga: F pt]

\ 3
γ! r!

80 PROCEEDINGS OF THE AMERICAN ACADEMY.

these expressions being valid if the order of the left member is equal
to or less than that of [0 a]. Similarly we obtain the intersection of
this system with a hyperplane y, ete. We thus get finally.

Fy = [R Sys],
JON ΞΞ [R Sy 2].

as point and complex in a space R of order n — ἃ. For these we
have the equations

Ry = PX = (RS,)R- Seal |
: ; (38)
Fr r

Ro) = Ls’ = (RS))[R- Sons]

these expressions being valid for values of r such that the orders of
the left members are equal to or less than n — X.
If (R δ.) # 0 we choose the magnitude of R such that

(R S,) ΞΞ 1.
Then the above equations become

RS Rss se a

We consequently have

[Ri»a2 A BIR _ [RS,,ABIR
tee A] ee B| [R δ. 1 Al [R S,1° 8]
AB Reh ole RC sik

er ee ee Ce)

provided that A B is contained in R.!*
Hence we have

“ἘΠ eae
(δ ἢ A) Sine B) bare A] ene B|

We may consider R as the unit quantity in the space R. Then the
right side of the above equation is the expression for distance relative
to the system of complexes in R. Thus whether we take distance in
R relative to the fundamental system of complexes S; or relative to
the sections R; in R, the result is the same. Similar relations of the
angles between other spaces in R relative to S; and R; can be shown.

MASSACHUSETTS INSTITUTE OF TECHNOLOGY.

12 Cf. Grassmann, Gesammelte Werke, Vol. I, theil 2, page 91.

Proceedings of the American Academy of Arts and Sciences.

Vou. XLVIII. No. 4.—Jutny, 1912.

CONTRIBUTIONS FROM THE CRYPTOGAMIC LABORATORIES
OF HARVARD UNIVERSITY.—No. LXVIII.

PRELIMINARY DIAGNOSES OF NEW SPECIES OF
CHAETOMIUM.

By A. H. CHIvErs.

CONTRIBUTIONS FROM THE CRYPTOGAMIC LABORATORIES
OF HARVARD UNIVERSITY.—No. LXVIII.

PRELIMINARY DIAGNOSES OF NEW SPECIES OF
CHAETOMIUM.

By A. H. CHIvers.
Presented by R. Thaxter. Received, June 16, 1912.

For a considerable time the writer has been engaged in the prepara-
tion of an illustrated monograph of the genus Chaetomium but owing
to unavoidable interruptions, and delay caused by the preparation
of plates, he has thus far been obliged to defer a final publication.

At the time when this work was begun, the only comprehensive
paper on the subject was the well known monograph of Zopf (Nova
Acta Acad. Leop.-Carol. 42. 1881), but after it was well under way a
paper by Bainier appeared in the Bull. de la Soc. Myc. de France
(Vol. XXV. Fase. 4. p. 191. 1910) in which a considerable number
of new forms were described and illustrated, some of which prove
to be American. Up to the present time, however, there has been no
further attempt to make a comprehensive review of the genus or to
collate the American forms with the exception of the revision of the
Chaetomiaceae in volume III of the “Flora of North America” by
H. L. Palliser, who enumerates seventeen species including three
unpublished names.

In the course of his work upon these widely distributed fungi the
writer has been able to examine a very large series of specimens from
various herbaria and exsiccati, and to cultivate many species from
diverse sources on various media and through many successive genera-
tions. As a result of this examination numerous forms have been
added to those previously recorded from America, and a number of
new species have been recognized of which it seems desirable to
publish the following preliminary diagnoses. In this connection it
may be mentioned that all of these forms with two exceptions have
been extensively cultivated in a pure condition and that it has been
possible to determine with accuracy their range of variation as well
as their salient, specific characteristics.

84 PROCEEDINGS OF THE AMERICAN ACADEMY.

Chaetomium subspirale, sp. nov.

Griseum vel roseo-griseum. Peritheciis majoribus, longioribus,
314 X 213 μ (800-337 X 206-224), sporidiis irregulariter conglobatis
gerentibus; pilis lateralibus numerosis, tenuibus, regulariter et dis-
tinete septatis, levibus, basi rectis, apice arcte spiraliter convolutis;
pilis terminalibus tenuibus, obscure septatis, pallide-olivaceis, levibus,
primum arcte dein laxe spiraliter convolutis; ascis clavatis, octosporis,
45 X 9.7, p. sporif. 24 μ; sporidiis subdistichis, pallide olivaceis,
limonuformibus, utrinque apiculatis, 6.4 Χ 5.2-5.6 μ.

Frequent in cultures of various substrata from New England.
Appearing in cultures of dung from Holland and South America.

The species may be distinguished by its characteristic hairs; the
lateral ones of which are short, straight, dark below; tightly coiled,
hyaline and refractive at the tips; the terminal slender, at first
tightly coiled in a delicate spiral, later elongated, twisted rather than
coiled and giving the appearance of wooly threads.

Chaetomium sphaerale, sp. nov.

Griseo-flavis, olivaceo-flavis, aetate aureo-flavis. Peritheciis maj-
oribus, subglobosis, basi rotundatis, apice subconstrictis, 312 Χ 276 u
(800-3829 X 262-300), sporidiis regulariter conglobatis gerentibus
vel cirrhis instructis; pilis lateralibus numerosis, gracilibus, levibus,
regulariter et distincte septatis, successive olivaceis, aureoflavis,
pallide flavis, hyalinis, apice collabentibus; aliis subrectis, longiori-
bus, 1-2-ramosis, basi 3.7 uw diam., aliis flexuosis, brevioribus, non
ramosis, basi 2.8 «4 diam.; pilis terminalibus longis, gracilibus, pilis
lateralibus concoloribus, levibus, irregulariter flexuosis vel subspiral-
iter convolutis, 1—5-ramosis, basi distincte septatis, apice obscure
septatis vel subcontinuis; ascis clavatis, octosporis, 48 X 13 μ, p.
sporif. 26 μ᾽ sporidiis subdistichis, dense olivaceo-brunneis, utrinque
umbonatis, limoniformibus, 7.3-8.1 Χ 6.4 μ.

In a culture of caterpillars from Reading, Mass.

The perithecium, globose below, with a tendency to narrow above
into a neck, distinguishes this species from all others which the writer
has studied. The slender delicate hairs and the entire absence of
differentiated rhizoids are also significant characteristics.

CHIVERS. — NEW SPECIES OF CHAETOMIUM δὴ

Chaetomium quadrangulatum, sp. nov.

Griseum. Peritheciis majoribus, longioribus, 403 & 294 uw (333-
456 X 243-350), cirrhis longissimis instructis; pilis lateralibus
numerosis, tenuibus, rectis, regulariter et distincte septatis, basi
olivaceo-fuscis, asperulis vestitis, apice hyalinis, levibus; pilis termi-
nalibus biformibus, aliis spiraliter convolutis, irregulariter pauci-
septatis, asperulis vestitis, basi olivaceo-brunneis vel atris, apice
dilute coloratis, aliis subrectis, undulatis vel convolutis, irregulariter
pauciseptatis, asperulis vestitis, ramosis, basi olivaceo-brunneis vel
atris, apice dilute coloratis; ascis clavatis, octosporis, 39 Χ 9.7
p. sporif. 21 4; sporidiis pallide olivaceis, a fronte visis subquadrangu-
latis, a latere ovatis, 7.3 Χ 6.3 μ (6.4-8 X 5.6-6.4).

Cultivated on dung from Cambridge, Mass. Appearing also on
dung from Chile and from Little Swan Island, Gulf of Mexico (R.
Thaxter).

The species may be easily identified by the spores which, when seen
in face view, are four sided and four angled but, when seen in profile,
are oval. Chaetomium quadrangulatum and Chaetomium trigono-
sporum are the only species known to the writer which possess spores
with angles, the former having spores clearly quadrangular, the latter
clearly triangular.

Chaetomium convolutum, sp. nov.

Cyano-griseum. Peritheciis magnitudine mediis, globosis, 244 Χ
232 μ (236-254 Χ 224-240), cirrhis instructis; pilis lateralibus paucis,
gracilibus, rectis, regulariter et distincte septatis, basi olivaceo-flavis,
asperulis vestitis, apice hyalinis, sparse asperulis vestitis; pilis termi-
nalibus undique asperulis vestitis, olivaceo-atris, subcontinuis vel
irregulariter pauciseptatis, 8-10 spiraliter convolutis, ad ipsam apicem
convolutionibus terminalibus regulariter successive minoribus; ascis
clavatis, octosporis, 56.4 X 10 4, p. sporif. 27.4 uw; sporidiis pallide
olivaceis, ovatis vel limoniiformibus, utrinque obtusis, subapiculatis,
8-8.4 X 6.4 yu.

Cultivated on mouse dung from Germany.

Apparently a rare species having appeared but once. The species
may be identified by the distinct blue color of the plant when seen
with the naked eye or a hand lens, and by the long spreading terminal
hairs whose long series of coils taper abruptly to a blunt point.

86 PROCEEDINGS OF THE AMERICAN ACADEMY.

Chaetomium spinosum, sp. πον.

Aureo-flavum. Peritheciis magnitudine mediis, subglobosis, 290-
224 (273-318 X 206-262), cirrhis instructis; pilis lateralibus
numerosis rectis, rigidis, acutis, irregulariter et parum distincte sep-
tatis, basi atrobadiis, asperulis vestitis, apice hyalinis, levibus; pilis
terminalibus rectis, rigidis, acutis, asperis vestitis, ramosis, ramis
ramulisque dilute olivaceis; ascis clavatis, octosporis, 41 Χ 7.5 μ,
p. sporif. 22 4; sporidiis subdistichis, pallide olivaceis, oviformibus,
5.9 X 3.9 u (5.6-6.4 X 3.2-4).

Growing in cultures of dung from Buenos Ayres (R. Thaxter).

This is, apparently, a rare species having appeared but once. The
egg-shaped spores and the branched terminal hairs are peculiar to
the species. From the dark, stiff, spine-like shafts or the terminal
hairs arise slender, delicate, irregularly swollen and constricted
branches, from which secondary branches arise. As the cirrhus of
spores forms the branches rise in the form of a column and in this way
a support is formed for the spore mass.

Chaetomium ampullare, sp. nov.

Ochraceum. Peritheciis majoribus, longissimis, 489 147 μ (456-
532 Χ 137-167), sporidiis irregulariter conglobatis gerentibus; pilis
lateralibus paucis, gracilibus, regulariter et distincte septatis, basi
rectis, olivaceo-fuscis, asperulis vestitis, apice collabentibus, levibus;
pilis terminalibus longis, gracilibus, distincte et regulariter septatis,
successive aureo-brunneis, aureo-flavis, hyalinis; levibus, ramosis, in
fila hyalina elongatis; ascis clavatis, octosporis, 45 Χ 9.7 μ, p. sporif.
23 u; sporidiis subdistichis, laete olivaceo-flavis, utrinque umbonatis,
limoniiformibus, 8.1-8.9 X 6.4 u.

On culture of sail cloth from Lowell, Mass. On dung from North
Carolina (R. Thaxter).

The species is clearly characterized by the very much elongated
bottle-shaped perithecium, and by the terminal hairs which are drawn
out into long, hyaline, tangling, easily collapsing threads.

Chaetomium aureum, sp. nov.

Griseum, pallide-olivaceum, lutescens, demum aureo-flavum. Peri-
theciis minutis, globosis, 127 & 115 μ (110-140 & 105-123), cirrhis
instructis, pilis lateralibus numerosis, tenuibus, rectis vel flexuosis,

CHIVERS. —_NEW SPECIES OF CHAETOMIUM. 87

regulariter et distincte septatis, olivaceo-flavis, asperulis vestitis;
pilis terminalibus olivaceo-flavis, regulariter septatis, asperulis vestitis,
arcuatis, apice subrectis vel incurvatis; ascis clavatis, octosporis,
42 X 10 uw, p. sporif. 26 μ; sporidiis olivaceo-brunneis, irregulariter
ovatis, utrinque apiculatis, 9.8 Χ 5.4 μ (9.4-11 Χ 4.7-5.6).

On paper, dung and other materials of various kinds from New
England. In cultures of old paper from Java (R. Thaxter).

The small size and characteristic golden yellow color clearly dis-
tinguish this species from all others except Chactomium. trilaterale
and Chactomium fusiforme. From the former of these it differs in
that the spores are discharged in long black cirrhi, in the comparative
obscurity of the perithecial hairs at maturity, in the incurved tips
of the terminal hairs, and in the irregular, oval shape of its spores.
From the latter it differs also in producing long black cirrhi, in the
incurved extremities of its terminal hairs, and in the size of its spores
and their irregular oval shape.

Chaetomium fusiforme, sp. nov.

Griseum vel pallide olivaceum. Peritheciis minutis, subglobosis,
120 X 102 (116-123 X 101-125), cirrhis carentibus; pilis latera-
libus numerosis, tenuibus, flexuosis, regulariter et distincte septatis,
olivaceo-flavis, asperulis vestitus; pilis terminalibus crassioribus,
asperulis vestitis, olivaceo-brunneis, regulariter et distincte septatis,
arcuatis, apice circinantibus vel subconvolutis; ascis clavatis, octo-
sporis, 48 X Τῇ μ, p. sporif. 324; sporidiis laete olivaceo-flavis,
vel olivaceo-brunneis, longis, angustis, subfusiformibus, apice rotunda-
tis vel apiculatis, 15.8 X 5.4 uw (15-16 Χ 4.8-5).

On paper from Alabama (Herb. R. Thaxter).

The long narrow spores distinguish this form from all other species
of Chaetomium. In general characteristics it most nearly resembles
Chaetomium aureum and Chaetomium trilaterale, but differs from both
in the long, slender, fusiform spores.

Chaetomium trilaterale, sp. nov.

Olivaceo-flavum. Peritheciis minutis, subglobosis, 106 Χ 94 u
(100-110 90-97), cirrhis carentibus; pilis lateralibus numerosis,
gracilibus, longioribus, regulariter et distincte septatis, aureo-flavis,
basi rectis, asperulis vestitis, apice 1-3 spiraliter convolutis, levibus;
pilis terminalibus irregulariter septatis, olivaceo-brunneis, asperulis

88 PROCEEDINGS OF THE AMERICAN ACADEMY.

vestitis, arcuatis, apice 1-8 spiraliter convolutis; ascis clavatis,
octosporis, 50 X 9.5 4, p. sporif. 26 4; sporidiis subdistichis, laete
olivaceo-flavis, forma sphaerasectoris praeditis, utrinque subapicu-
latis, 9.5 X 5.5 p (8.9-9.7 X 5.2-6).

On paper from New England (Herb. R. Thaxter).

This species has certain characteristics in common with Chaeto-
mium aureum and Chaetomium fusiforme. From the former it differs
in the more numerous, stout, 1-3 spirally convolute, terminal hairs;
the spirally coiled lateral hairs; the smaller size and unusual shape of
the spores. From the latter it differs in the convolute lateral hairs;
the shape of its spores and their smaller size.

Proceedings of the American Academy of Arts and Sciences

Vout. XLVIII. No. 5.—Aveust, 1912.

A STUDY WITH THE ECHELON SPECTROSCOPE OF
CERTAIN LINES IN THE SPECTRA OF THE ZINC
ARC AND SPARK AT ATMOSPHERIC PRESSURE.

By Norton A. ΚΕΝΤ.

WITH Two PLATES.

INVESTIGATIONS ON LicguT AND HEAT MADE AND PUBLISHED WITH AID

FROM THE RuMFORD FUND.

A STUDY WITH THE ECHELON SPECTROSCOPE OF CER-
TAIN LINES IN THE SPECTRA OF THE ZINC ARC
AND SPARK AT ATMOSPHERIC PRESSURE.

By Norton A. ΚΕΝΤ.
Presented by Charles R. Cross. Received June 19, 1912.

In November, 1907, the writer published, in collaboration with one
of his graduate students, an article + attempting to meet certain
objections made by Keller? to the method of procedure adopted by
the writer in certain former work ? upon the question of the relative
wave-lengths of certain lines in the spectrum of titanium and zinc as
developed by the are and spark discharge in air at normal pressure.
That displacements of the spark lines to the red from the position of
the corresponding arc lines actually existed on the photographic plates
obtained, is regarded by the writer as unquestionably proven. It is
certain, also, that the displacements were not due to any incorrect
experimental procedure.

It appeared to be worth while to study the matter further, seeking
to ascertain, if possible, the cause of these displacements. As the
echelon spectroscope had revealed structure in the lines of metal-
lic spectra both in Pliicker tubes and in the are in vacuo and at
normal atmospheric pressure*, it seemed advisable to use this in-
strument to study the spark, noting the change in the form of the
image as a function of the constants of the electric circuit. The
titanium lines AA 3900 and 3913, formerly studied in detail, presented
difficulties because of their short wave-lengths; therefore, it appeared
best to concentrate the work upon zinc.

A brief survey of the most important results in the case of this metal
recently obtained by various observers is thus in order.

1 These Proceedings, 43, No. 11, Nov. (1907).
2 Ueber die angeblicke Verschiebung der Funkenlinien, Inaugural Disserta-
tion, Christian Keller. ;
3 These Proceedings, 41, No. 10, July (1905).
4 Janicki, Annalen der Physik, 19, 36-79, Jan. (1906).
Nutting, Astrophysical Journal, 23, No. 1, Jan. (1906)
Nutting, Bulletin Bureau of Standards, 2, No. 3, Dee. (1906).

92 PROCEEDINGS OF THE AMERICAN ACADEMY.

HISTORICAL SURVEY.

Houston ® who notes the changes which take place in the reversal
system as seen by an echelon when a zine arc “begins to hiss,” speaks
of the “striking forms of reversal,” the distances between the different
components in the line varying in the different parts of the are.
With one of his ares and a small amount of vapor, he obtained the
three blue lines of zine “without reversals.’’ Under certain condi-
tions the three blue lines were “all doublets with components of
equal intensity.”

Janicki δ in his inaugural dissertation (1905) states that “an exami-
nation by the echelon of the lines of the zine spectrum developed in a
capillary tube of 0.3 mm. diameter with external electrodes at a temp-
erature of about 460° showed them to be single lines.”

Nutting,’ in a paper on line structure, mentions the fact that Pliicker
tube spectra of rarefied gases moderately excited show narrow lines
of the simplest structure, “but with a heavy current or capacity in
parallel, if the pressure be greater than 3 or 4 mm. the lines broaden,
and finally, with a spark in series with the tube, widen into a continu-
ous spectrum, with the peculiar fluted appearance characteristic of
spark lines.”

He states further that “sparks between metallic electrodes give
lines far too broad for use as monochromatic sources. They are
never less than half a tenth-meter broad. The effect appears to
depend chiefly upon the amount of capacity used, and is greatly
heightened by the use of another spark in series; that is, it 7s due to
the steepness of the wave-front of the current wave. Inductance weakens
the wings produced by capacity, and sometimes channels them, but
never reduces a line to a simple structure. Occasional lines will
appear to simply broaden out under the violence of the discharge, but
ordinarily it is simply a case of the dark background — between
spectra οἱ different order — becoming luminous.”

“Using a small current (0.02 amp.) of low voltage (5000) and low
frequency (60) and a minimum of capacity, and electrodes of iron
and brass, the spark lines were found to be still broad and diffuse.
Lines due to impurities (sodium, for example) occasionally appear

5 Philosophical Magazine, 7, May (1904).

6 See Annalen der Physik, 19, 36-79, Jan. (1906).
7 Astrophysical Journal, 28, No. 1, Jan. (1906).
8 The italics are the writer’s.

KENT.— SPECTRA OF THE ZINC ARC AND SPAPK. 93

fairly sharp on but a faint background, but a number of tests in-
dicated that it is impracticable to obtain narrow lines by introducing
impurities into the spark.”

Further, when discussing are spectra in general, he writes: “The
structure which a line exhibits depends primarily upon its intensity;
that is, upon the amount of a substance vaporized and the intensity
of its excitation in the are”’; and specifically, in the case of zine:

“ All four zine lines are rather diffuse, and are usually found double
or triple.* * * The blue lines, 4810, 4722, 4680, are broad and diffuse,
and show a trace of structure on reversal.” -

In a general discussion attention is called to the fact that the
structure of any one line is very variable, so much so that “we may
hardly speak of any line as having a fixed definite structure, even with
a minute specification of conditions of production.”

Types of lines are classified according to structure and behavior,
and the general conclusion drawn that to explain certain types — lines
which, when single, under some conditions become double or triple,
symmetrically or unsymmetrically, with receding components of
various relative intensities — the old absorption theory of reversal
is not satisfactory.®

In another paper !° covering the results of a search for intense and
yet “pure” light standards, Nutting, sketching the development of
the typical normal line in either the open air arc or at pressures less
than atmospheric, states:—‘“‘with increase of intensity the line
broadens, and finally separates into two; * * * with further increase
the two components continually broaden and separate”; and of
highest “rank as to purity are the composite lines produced in the
vacuum tubes measured between extreme components.”

In a paper?! on relative intensities of spectrum lines an attempt is
made to show that the changes produced in spectra by varying current,
capacity, inductance, temperature and pressure, may be accounted
for by a single variable, or at most, two. He writes: —

“Several years ago the writer!? gave the steepness of the wave-
front through a gas as condition for the preponderance of the secondary
over the primary spectrum. Crew 15. almost at the same time con-

9 Nutting advances a theory of broadening, doubling and reversal in the
Astrophysical Journal of April (1906).

10 Bulletin Bureau of Standards, 2, No. 3, Dec. (1906).

11 Nutting, Astrophysical Journal, 28, 66 (1908).

12 Astrophysical Journal, 20, 135 (1904).

13 Ibid., 20, 284 (1904).

94 PROCEEDINGS OF THE AMERICAN ACADEMY.

cluded that a ‘high E. M. F., rapidly changing, is a probable conditio
sine qua non for the appearance of spark lines in arc spectra.’ Both
might better have expressed their results in terms of potential gradi-
ent.” * * * “The lowest gradients are obtained in heavy current
arcs and Pliicker tubes with wide capillary; in the former case the
low gradient is due to the heavy current, in the latter to low ga»
pressure. Higher potential gradients are obtained in ares with very
small current, Pliicker tubes with fine capillaries and sparks with
small capacity and large inductance. The highest potential-gradients
are found in sparks and other interrupted arcs, the gradient increasing
with the amount of capacity in circuit and with the impressed voltage.
Gradients vary from about 20 to 80 volts per cm. in ordinary ares and
tubes up to thousands of volts per cm. in condensed sparks.” * * *
“Inductance reduces the gradient down to a minimum, beyond
which it is inoperative.” * * * “In the condensed spark without
inductance, the front of the pilot discharge must have a potential-
gradient not much below the dielectric strength of the intervening
gas. The remainder of the discharge is probably at a very low
gradient, approaching that of a direct-current are. Hence such a
spark gives both spark and arc lines. Inductance and resistance
lower maximum gradients by smoothing out the current wave. The
spectrum of a spark rendered dead beat by series resistance can
scarcely be distinguished from that of a low direct-current are.”

In 1909 Janicki 14 writes on the structure of spectrum lines, giving
the results of a study made with the Lummer-Gehrcke plate, the source
being an arc at low pressure (0.1 mm. or less) in a special form of
apparatus having an anode of the desired metal.

The three zinc lines in the blue are described as sharp and simple.
They appeared at 0.3 amp., were good at 0.4 amp., and at more than
0.7 amp. were reversed in part.

In certain calcium lines the change of position of their satellites
with increase of current is noted, and attention called to an unsym-
metrical broadening and reversal. Somewhat later reference is
made to the,work of Exner and Haschek on the displacement of
spark lines.

“They traced these displacements, directed mostly toward longer
wave-lengths, to the different density of the metallic vapor. With
good reason Eder and Valenta objected that these displacements were
only apparent. * * * They photographed are and spark lines im-

14 Annalen der Physik — Band 29 (1909).

KENT.— SPECTRA OF THE ZINC ARC AND SPARK. 95

mediately above one another with different exposure times. The long
exposures seem to give a different center of intensity from the short,
if a line is unsymmetrically broadened to one side; whereas on the
other hand the real center remains clearly in the same position only
in the case of sufficiently short exposures. The long and short ex-
posures play the same réle, however, as a greater or smaller density
of metallic vapor; therefore the shifts observed by Exner and Haschek
are to be considered only as apparent. Exner and Haschek then
tried to maintain their theory by referring the cause of the shifts to
changeable satellites, which cannot be resolved by a Rowland grating
and might therefore produce a shift. They studied the arc lines of a
series of elements by means of a 15 plate echelon and made the aston-
ishing discovery that a satellite often appeared upon the red side of
the line, especially when the are flickered. With the plane parallel
plates at my disposal, which are more efficient than a 15 plate echelon,
I have been unable to verify the satellites which they reported.” * * *
“Tt is possible that the satellites seen by Exner and Haschek with the
flickering of the arc arose from impurities in the carbon and the metal.
It is more probable, however, that they must be regarded as ghosts.
Ca \ 4527 is supposed to be simple, but with a satellite arising on the
side of greater wave-length upon the flickering of the are; whereas I
found no satellite near this strong line. On the contrary, I observed
a weak satellite of greater wave-length near Ca ἃ 4586, while Exner
and Haschek did not. Ca 5270 is supposedly a triplet, in which
with weak current the middle line is the brightest; with strong current
the two lines toward the red are the brightest. All my photographs
show this very strong line to be single; furthermore, Cu ἃ 5218 is
supposed to have a red companion which grows more rapidly than the
head-line as the current is increased; I always found this very strong
line to be single. This very line seems to me proof that Exner and
Haschek were deceived by ghosts in their echelon. For if the head-
line is not very strong, the ghost can scarcely be seen; if the main
line becomes stronger, the ghost comes out more strongly; with
further increase in intensity, the main line, however, seems to gain less
rapidly than the ghost, since the eye (Exner and Haschek make
visual observations only) cannot distinguish differences in great
intensities so accurately as in the case of small ones. Nutting has
also used the ordinary arc for creating spectrum lines and worked
with an echelon of 30 plates, of 14 cm. thickness. The same remarks
as above made are valid in case of the use of the carbon arc.”

Janicki reviews Nutting’s results, characterizes them as extraor-

96 PROCEEDINGS OF THE AMERICAN ACADEMY.

dinary; states that they should have aroused Nutting’s suspicion
and regards them as due to ghosts which become visible when the
intensity of the source is sufficiently great. He writes: —

“Thus, according to Nutting, the red Cd line, the red and the blue
Zn lines form triplets; whereas, even with the greatest intensity and
the most varied sources of development, it is just these very lines
that have always been found to be unquestionably single by Michel-
son, Fabry and Perot, Hamy, Gehrcke and van Baeyer, and myself.
* * * Nutting’s echelon had about the resolving power of the plane
parallel plate C and did not approach that of plate H, so that the
objection cannot be raised that he was able to make closer observa-
tions by reason of having a finer instrument. According to him all
five prominent silver lines are compound, and indeed, both triple and
quadruple, while the plate H even with the greatest intensity shows
no sign of satellites. * * * The characteristic line-structure remains
the same, no matter how the spectrum is produced. This is confirmed
by the agreement of the observations of the lines of Cd and Zn, where
it makes absolutely no difference with whatever instrument one
observes and no matter how the spectrum is produced. * * * That
the designation of the brightness of the satellites sometimes varies,
as in Cd ἃ 4800, is immaterial, since the satellites are weak and the
differences in their intensity very slight.”

Here follows a discussion of unsymmetrical broadening noted with
the Rowland grating by Kayser, Rowland and others. Thestatement
is made that “a good Rowland grating would not resolve an unsym-
metrical reversal the components of which, like the chromium line,
are 0.043 Angstrom units apart, and the resultant apparent shift
about 0.02 Angstrom units.” There follows a reference to the work
of the writer who, with Avery, made certain measurements upon two
titanium lines. He writes: —

“They found an average shift of 0.019 and 0.018 Angstrom units
for the two titanium lines \\ 3900.7 and 3913.6. In the mean taken
from both observers, the minimum and maximum shifts for the line ἃ
3900.7 are found to be 0.009 and 0.038 Angstrom units. This very
circumstance seems to me to indicate that Kent and Avery were
dealing here with unsymmetrical reversals like those of chromium and
calcium, reversals which their grating would not resolve and which
appeared to them as line-shifts.”

KENT.— SPECTRA OF THE ZINC ARC AND SPARK. 97

GENERAL DESCRIPTION AND ARRANGEMENT OF APPARATUS.

An echelon spectroscope and a constant deviation spectroscope of
the Hilger pattern were ordered of A. B. Porter of the “Scientific
Shop,” the echelon having 33 plates, a 1 mm. step, 34 mm. height of
plate and about 15 mm. thickness, and the lenses of the constant
deviation and echelon spectroscopes being of 13΄ and 2’ diameter
and 17” and 202” focal length, respectively. The constant deviation
prism proved to be of insufficient aperture to fill the echelon, and was
therefore sent to Hilger for a new prism.?°

The echelon itself finally appeared to be a poor instrument and
wholly unfitted for first-class work; for, upon final adjustment, the
green mercury line \ 5471 showed a false pattern and there also ap-
peared in certain zine spark lines a distinct pattern which the writer,
in view of the false satellites in the mercury line, at first deemed
likewise spurious, inasmuch as a smaller and less powerful echelon
made by Petitdidier, and kindly loaned by Professor Goodwin of the
Massachusetts Institute of Technology, did not show it. This was
later identified with Nutting’s “peculiar fluted appearance, character-
istic of spark lines’’.1®

The Porter instrument was finally sent to Petitdidier for over-
hauling. Three plates were taken out and all were adjusted so that
the step was more uniform. The instrument again showed both
patterns, the mercury line pattern being false. Many months were
thus lost with these various difficulties. At length it was decided to
continue the work with the borrowed Petitdidier echelon, an excellent
instrument, although of only 20 plates, total aperture 27 & 153 mm.,
step ξ mm. and 14? mm. thickness of plate.

The apparatus generally employed was, then, the Petitdidier
echelon and Porter constant deviation spectroscope with a prism
fitted by Hilger.

The spark was generated by a Holtzer-Cabot motor-generator set,
the alternator of 4.5 K. W. giving 60 complete cycles per second and
feeding a 5 K. W. transformer (of ratio of transformation 110 to 30,000)
in the secondary of which was a condenser of 0.0226 microfarads,
which discharged, at times through various inductances, over a spark
gap generally set horizontal.

Two methods of producing the are were employed, one giving what

_ 15 Professor Porter died within a short time after the instrument was de-
livered.
16 Nutting, Astrophysical Journal, 23, No. 1, Jan. (1906).

98 PROCEEDINGS OF THE AMERICAN ACADEMY.

we may call the Pfund arc,!” between two iron rods, the upper, the
negative terminal, being 5 mm. in diameter and pointed somewhat,
and the lower, the positive, being 16 mm. in diameter, the current
varying from about 1 to 9 amp. and the E. Μ. F. of the circuit being
220 volts; and the other a 110 volt circuit are between carbon termi-
nals, the lower being positive, and the values of the currents used
being within the above limits. In both cases the positive terminal
was supplied with small pieces of the necessary metal, ordinary com-
mercial zinc. The echelon image was magnified about 3? diameters
by a Bausch and Lomb microscope.

Two shutters were used, at first a very light wood and wire arrange-
ment, having two sets of openings of three and two openings respec-
tively, placed in the focal plane of the echelon spectroscope; and
finally a shutter of cardboard, having two sets of openings of two and
one openings respectively, placed over the slit of the constant devia-
tion spectroscope (this method giving good results, as the echelon
spectroscope slit was set accurately in the focal plane of the telescope
of the constant deviation spectroscope). The echelon was cevered with
a cotton lined box to prevent temperature changes, which were never
more than 0.1° C during any one set of exposures and usually much less.
The photographic plates generally used were Seed Gilt Edge * 27, in
some cases double-coated; the developer generally normal rodinal
solution.

In adjusting and testing the echelons a Cooper-Hewitt mercury
lamp, kindly loaned by Mr. William Sawtelle of Harvard, was used.

The two inductance coils used were as follows: —

(a) A coil having three layers as described on page 186 of the Astro-
physical Journal for October, 1905.

(Ὁ) A commercial coil of annunciator wire, weight about 8 lbs.,
size of wire ¥18 5. W. G.

The arrangement of the apparatus is shown in the figure.
E
eo) we Ss τ ee ees
Fo 0 0
0

S, S, slits; P, prism; 0,0,0,0, lenses; G, echelon grating; EK, eye.

17 Pfund, Astrophysical Journal, 27, 296, May (1908).

KENT.— SPECTRA OF THE ZINC ARC AND SPARK. 99

GENERAL METHOD OF PROCEDURE.

Before describing the work in detail it may be stated that the
general procedure was to set the echelon at the position of greatest
efficiency, such that its axis was parallel to that of the collimator
and telescope.

A vertical arc or horizontal spark image was thrown upon the slit and
studied visually under numerous and widely different conditions.
When a photographic comparison of the two sources was desired, a
shutter was used.

DETAILS OF THE INVESTIGATION.

PRELIMINARY COMPARISON OF SPARK AND ARC. At the outset an
attempt was made to compare the position of the image of a highly
disruptive spark with that of the are. This was soon found to be
impossible because of the fact that the lines given by a disruptive
spark between terminals of the pure metal were not sufficiently
monochromatic. Their images given by the Petitdidier instrument
cannot be distinguished from those given by the corresponding region
of the spectrum of a Nernst lamp (see Plate 1, 52) and the position of
the maximum intensity is a function of the condition of the echelon
whether purely of a single or purely of a double order nature at the
temperature of the instrument. The only cases in which this method
would apply are those in which the spark line is more nearly mono-
chromatic and the condition is absolutely that of a single order.
Even then the form of the intensity curve for white or not fully mono-
chromatic light would have to be known.

VIsUAL sTuDY OF aRc LINEs.!®8 As the conditions in the are and
the resulting structure of the lines of the spectrum often change very
rapidly, it appeared to be of interest to study these three strong zinc
lines visually. A study of this sort was made, an assistant keeping
the are image on the slit and recording the structure of the line as
dictated to him. From various sets of observations, many of which
are mutually confirmatory, the conclusions given below may be drawn,

18 These visual observations were made in a wholly unprejudiced state of
mind for, although the papers of Nutting and Janicki referred to had been
read when they were first published, the details of the same had been quite
forgotten by the writer of this paper.

100 PROCEEDINGS OF THE AMERICAN ACADEMY.

these being, of course, modified by the condition of the echelon,
whether of absolutely single or double order, or part way between the
two. However, interpreting the pattern is a simple matter in either
case. The echelon was so placed that in the field of the microscope
the lower orders lay at the left, the higher at the right.

Zinc 4810. Upon starting the are after a fresh piece of zinc was
put in, the whole field resembled that of a polychromatic source,
except that the normal diffuse echelon image was marked by several
fine lines similar to the pattern shown in Plate 1, 12, whether the posi-
tion of the echelon for monochromatic light be that of single or double
order. This structure always accompanied the are when noisy, and
was present in 4722 and 4680, as well as 4810. It is clearly visible
in are lines with the Petitdidier instrument and is similar to the
“fluted appearance”’ of spark lines. At low current and the single
order condition, eight components were visible in 4810, the two outer-
most poorly marked; the two innermost the sharpest of all. As the
vapor became less dense, the structure became less extensive. There |
appeared two lines strongly marked, lying between two other wider,
less intense and less sharp satellites. Then the two outer satellites
faded, the stronger, inner pair at times receded from each other and
then again approached. Finally the reversed region (if, indeed, we
are justified in speaking of the phenomena as a “ reversal’’) disappeared
and the two lines merged into one, which eventually became a single,
narrow line.

The above phenomena were noticed in the Pfund are at 2.5 amp.,
with the upper pole (in error) positive. The condition was the
double order one, the lower order being slightly stronger. The same
phenomena appeared, however, at single order condition, and with
lower pole positive.

At 3.4 amp. at another temperature such that the condition was
nearly single order, and with the lower terminal positive, the same
general phenomena appeared, but when the two line structure was
present and the vapor density was decreasing, the right component
became weaker than the left; whereas when judged by the fact that the
adjacent order was stronger, it should have been the stronger of the
two. However, the right component sometimes appeared stronger than
the left and was generally broader. At this point the current was re-
duced to 1.1 amp. and the right component, although visible near
the lower, or positive terminal, disappeared at the center of the are,
the line there being single.

At 5.5 amp. and the lower pole negative, the phenomena of 2.5

KENT.— SPECTRA OF THE ZINC ARC AND SPARK. 101

amp. were noted, but upon change of polarity and in the single order
condition, the fluting changed into three components, the one lying
toward the red being the faintest of the three; moreoever, at times
six components appeared, the four toward the red being well marked.

At 8.8 amp. the changes were sudden and well defined. The con-
dition was nearly that of the single order, the higher order being
slightly stronger. The central component was lacking and the four
side components appeared far apart, the two innermost being the
strongest. Then at times the central line appeared, attended by two
hazy satellites, the left one of which was often the strongest of all three
lines. A sudden change here occurred to a very broad image, show-
ing no structure. New zine was then supplied and there eventually
appeared two well-marked lines far apart; these gradually approached
each other, a line developed between them, and all three of these lines
were at times of the same intensity. Finally, with lessening vapor
density, the central component became stronger and the two outer
ones shrank toward it.

Zine 4722. Current 1.3 amp. single order condition. The same
general phenomena obtained following the first fluting, which was
poorly marked. There appeared two lines, the left a little stronger
than the right. These eventually reduced to a single line.

At 2.5 amp. there appeared a single line between two faint satellites.
The right component of the three was stronger than the left at certain
times; whereas, the arrangement of the orders was such that it would
be weaker. With low vapor density the system became a single line.

At 3.5 amp. three lines of nearly equal intensity appeared, the
two on the outside somewhat fainter than the central one, which
last was the sharpest of all. The outside components often became
broader and finally there resulted one single, sharp line with a faint
suggestion of side lines at times of greatest brilliancy.

At 5.5 amp. and nearly a double order condition, a central compo-
nent and two broad satellites were found.

At 8.8 amp. and using carbon terminals, in the single order condi-
tion, at first the field showed no structure, then followed the fluting,
then there appeared three lines, the right and left strong, the central
one weak and diffuse. Finally the left component disappeared, the
central one became as intense as its fellow; then the two merged into
a single fine line.

Zinc 4680. At 1.2 amp. and a nearly double order condition,
after the fluting there followed a condition marked by two components
nearly equal in intensity, followed by a single line.

102 PROCEEDINGS OF THE AMERICAN ACADEMY.

At 2.5 amp. the left component appeared a little weaker and the
lines were less sharp than with less current. At low vapor density
there appeared a single line, slightly hazy on both sides. With small
amount of vapor and in double order condition, the lines appeared
hazy, and no reversal was to be seen. This line, 4680, has, however,
been observed at this current in single order condition as a single
line with two side components which broadened at certain times, all
three lines broadening and receding from each other.

At 3.5 amp. the two components were far apart, and equal in inten-
sity. With small amount of vapor the reversal was less well marked.

The results of this visual study of the are may be summarized as
follows:

(1) All three lines are at times single.

(2) All have been observed “reversed” but,

(3) 4810 and 4680 are generally double or quadruple, while 4722 is
generally triple, and,

(4) All are still more complex at times and show asymmetry, but
this asymmetry is no more often marked by stronger red satellites
than violet.

VISUAL STUDY OF THE INDUCTANCE SPARK LINES. A visual study
of the spark with inductance showed that the conditions could in this
case be more easily controlled and were more steady.

4810, in a nearly single order condition, the right order of the
three being stronger than the left, with coil (b) as inductance in the
condenser discharge circuit, showed two lines, the right component
distinctly weaker than the left when the arrangement of the orders
would, if the two components were intrinsically of the same intensity,
make this right component the stronger.

The central part of the image was under observation. This right
component, however, appeared stronger when the end of the spark
image was thrown upon the slit. With no inductance the fluting
was faintly visible (it had not been observed previously with the
Petitdidier instrument?®) for the gap was small so that the spark
burned quietly.

4722 showed the fluting more clearly than 4810, and with inductance,
the condition being nearly single order, there appeared two bright
central lines which were nearly equal at times. Whenever unequal,
however, the left line was the stronger. At the end of the image near
the terminals the line broadens out and resembles the disruptive spark.

19 See page 97.

KENT.— SPECTRA OF THE ZINC ARC AND SPARK. 103

4680 in the double order condition showed the fluting faintly at
times, while with inductance the line appeared almost single, the
“reversal” being almost invisible.

This visual work with the spark shows: —

(1) That at high inductance 4810 and 4680 are generally double;
(4810 has been photographed as quadruple, and, with less inductance,
as a quintuplet and a triplet) and 4722 triple.

(2) That here we have a definite asymmetry, controllable and regu-
lar, a relative increase in intensity of the red satellites when the end
of the spark gap is used. This is fully confirmed by the photographic
study. (See discussion below and Plate 1, 71 (a), (c), and 111 (b).)

PHOTOGRAPHIC STUDY OF ARC AND SPARK LINES AND A COMPARISON
OF THE TWo.?2 Among others the following photographs were taken
with the Porter echelon:—

The “ fluting”’ not visible in all disruptive spark lines.

12. 4722. Spark without inductance. Center of 4 mm. gap.
Shows fluting.

16. Zn4924. Without inductance. Center of 4mm. gap. Shows
no fluting. This may be an “air” line, however.

The following photographs were taken with the Petitdidier echelon:

A general comparison of the images of a line as given by different
sources.

28. 4810. Pfund arc through two of the openings of the five open-
ing shutter; spark through three openings. Arc current, 0.9 amp.
Spark without inductance. Gap 2 mm. and in series an auxiliary gap
of 4mm. Exposures: are 20 seconds, spark 2 minutes. Compares
the pattern and position of are and spark images, under the double
order condition. Confirmed by other similar photographs. However,
we cannot tell with the echelon a disruptive spark from an arc burning
on a heayy current, as is shown by 36.

32. 4680. Similar to 28. Compares the are and spark images
under single order condition. Confirmed by other similar photo-
graphs.

36. 4810. Inside 110 volt arc of about 10 amp. between Pfund
terminals and very dense vapor. Outside Pfund arc, 1 amp. Com-
pare 28.

52. 4810. Center of 4mm. gap of disruptive spark, inside open-
ing of three opening shutter; Nernst lamp (in neighborhood of 4810),
outside openings. Exposures: Nernst, 1 minute; spark, 15 seconds.
Shows that the two cannot be distinguished.

20 For the photographs which have been reproduced see Plates 1 and 2.

104 PROCEEDINGS OF THE AMERICAN ACADEMY.

Inductance spark structure.

70 (a). 4810. Single order condition. Center of3mm. gap. Coil
(Ὁ) in circuit. Exposure: 30 seconds. Notice four components,
the two outermost faint.

Inductance spark structure and power in circuit.

81 (b) and (d). 4810. Single order condition. Center of 1.5
mm. gap. Three layers of coil (a) as inductance. Two exposures
of 30 seconds each: (b) at 20 amp. and 1 hectowatt; (d) at 50 amp. and
2 hectowatts. These show that approximately doubling the current,
and the power in the primary of the transformer has little, if any,
effect upon the structure. This is confirmed by another photograph
in the case of 4722.

Inductance spark structure as a function of the part of the image viewed.

71 (a). 4722. Single order condition. Electric conditions asin
70 (a). Exposure: 25 seconds. Three components are apparent
on the original negative, but the one toward the red is very weak.

71 (c). 4722 Same as (a) but near end of image. Exposure:
35 seconds. Notice new component toward red not due to inequality
of exposure, for the main component is just as bright in 71 (a) as in
71 (ce). This effect is confirmed for 4810 by another photograph and
still further by :—

111 (b). 4810. Center of photographic plate, central part of 4
mm. spark gap; outside of plate, end of gap. Coil (b) as inductance.
Notice the new component to red in the exposure of the end of the
gap. The original negative shows still another component toward the
red. Note further that despite the fact that the photographic image
of the central part of the gap is the denser of the two, the components
appearing are but two in number. Single order condition with the
left of the three central orders slightly stronger than the right, giving
a condition unfavorable for the appearance of components to the
right! This is confirmed by three other sets of exposures.

Effect of using an alloy.

88 (a). 4810. Single order condition, center of 1.5 mm. disruptive
spark between brass terminals. Shows that the line structure is
simple although a continuous pattern is present with it, and that dis-
ruptiveness in itself is not the only controlling factor. Other ex-
posures with 5 and 9 mm. gaps gave the same results.

89 (0). 4810. Sameas 88 (a) except that three turns of inductance
were inserted. The result is a single fine line.

89 (c). 4722. Same as 89 (b). Two fine lines, just separated,
appearing on the original negative. Photographs 89 (b) and 89 (ce)

KENT.— SPECTRA OF THE ZINC ARC AND SPARK. 105

thus show that with an alloy and inductance the structure is rendered
very simple and the light even more monochromatic than with the
lower voltage are.

Comparison of arc and disruptive spark.

48 (c). 4680. Pfund are at low current shown by two openings
of the five opening shutter: end of image of a disruptive spark of
3 mm. gap with a 4 mm. auxiliary gap in series, shown by three
openings. Double-coated Seed, gilt edge 27 plate. Hydrochinone
developer. Exposure: are, 15 seconds, spark 1 minute. Note that
there is structure in the spark and that it lies to the right, the
region of longer wave-lengths. See especially the middle of the
five shutter openings. This is confirmed by two other sets of ex-
posures. The reproduction is poor, owing to the fact that the
structure is not strongly marked, and is obscured by a continuous
pattern.

Comparison of are and inductance spark.

85 (a). 4810. A comparison of an inductance spark outside
(inductance, three layers of coil (a); exposure, 30 seconds; and
center of gap) with Pfund arc inside (low current and exposure 5
seconds). Single order condition but with the stronger of the two
adjacent orders toward the violet. Notice that the maximum in-
tensity of the structure lies toward the red in the spark in comparison
with the are. This is confirmed by another set of exposures in which
the are was given relatively greater exposure time. Of course if
another part of the are had by chance been used, the result might
possibly have been different. And again, greater are current might
have made some difference in the structure and further, as the rapidly
fluctuating conditions in the are change the structure, the distribu-
tion of energy might at another instant have been different. But
further exposures are confirmatory with respect to 4810, and show
a like phenomenon in the case of 4722; and still others are confirma-
tory with respect to 4722, and show a like phenomenon in the case of
4680. Further, two other sets of photographs taken some days later,
confirm these results for all three lines; and two more using carbon
terminals and a 3 amp. current show the same effects in all three lines.
And again four other sets taken upon still another day, with a 220
volt, 3.3 amp arc between carbon terminals, give in every case the
same results for these three lines.

Such agreement proves that the effect cannot be fortuitous. How-
ever, as the inductance spark is steadier and easier to control, it is
well to compare sparks having different inductances in circuit: —

106 PROCEEDINGS OF THE AMERICAN ACADEMY.

Spark line structure as a function of the inductance.

78 (c). 4810. Between single and double order condition. Center
of 1. mm. gap. Three layers of inductance coil (a). Exposure:
1 minute. Two main components. Note that the right component
of the quadruplet is as strong as, or stronger than the left, when the
position of orders is such that it would be weaker. This fact is con-
firmed by other exposures.

79 (6). 4722. Between single and double order condition. Elec-
tric conditions as in 78 (c). Exposure: 1 minute. Shows three main
components.

80 (a). 4680. Between single and double order condition. The
electric conditions are as in 78(c) and 79(e). Two main components.
Exposure: 1 minute.

65 (b). 4810. Single order condition. Center of 4mm. spark gap
under different conditions. Outside, no inductance, 5 seconds:
inside coil (b) in circuit, 45 seconds. Notice the two side components
in the inductance spark image.

68 (a). 4722. Single order condition. Electric conditions, simi-
lar to 65. Note inequality of intensity of inductance line components.
Exposures: 30 seconds with inductance and 3 seconds without.

94 (c), (d), and (6). 4810. Single order condition. Center of a
very small gap—less than 2 mm. Three, two and one layers of
coil (b), respectively.

96 (ce), (4), and (6). 4680. Double order condition. Same set
of operations as in 94. Notice in both plates a continuous increase
of intensity of the old components lying toward the red and the
development of new ones as the inductance is decreased. Another
photographic plate (numbered 95) clearly confirms this for 4722. On
all three, 94, 95 and 96, there were also taken shutter comparisons
showing the relative positions of the components given with one,
_two and three turns. These all show that the component coming
up with decrease of inductance is the one toward the red: the com-
ponent toward the violet retains its position while its intensity be-
comes relatively less. The effect of removal of inductance is similar
to that obtained by moving up to the end of a somewhat longer gap
leaving the inductance the same. (See 111b).

The conclusions to be drawn from the photographic study are:—

1. That it is impossible by means of the echelon grating to com-
pare the positions of maximum density of any but quite monochro-
matic sources, whether the condition be either double or single order.

2. That it is impossible in general to distinguish the images given

KENT.— SPECTRA OF THE ZINC ARC AND SPARK. 107

by a Nernst lamp, an arc of great vapor density, and a highly disrup-
tive spark between terminals of the pure metal.?! These sources give,
in fact, nothing but the so-called “diffraction” as distinguished from
the “interference”’ pattern.

3. That inductance, even in small amounts, is extremely efficient
in reducing the intensity of the continuous or diffraction pattern and
producing structure in the spark image.

4, That the structure varies with the part of the inductance spark
image used whether end or center; the end showing an enhancement
of the intensity of the components lying toward the red.

5. That as the value of the inductance is increased, the red com-
ponents in the structure become less intense.

6. That even a disruptive or non-inductance spark between brass
terminals shows structure in the zinc lines studied and that, if in
addition inductance be inserted, the resultant lines are as sharp, or
even sharper, than those given by a low current arc.

7. That a small amount of vapor in the arc, even with fairly high
current (e. g. 8 amp.) produces conditions favorable to structure other
than the fluting which occurs when the are is heavily charged with
vapor and is noisy.

8. That on all plates obtained upon which the positions of the
components of the spark with small inductance are compared with the
positions of the components of the are at low current (about 3.3 amp.)
the center of gravity of the spark structure lies further toward the red
than that of the are.

GENERAL CONCLUSIONS.

That conflicting results were obtained by Janicki and Nutting is
probably due to the fact that different sources of light were employed.
The structure Nutting describes is unquestionably real. Certainly
echelon gratings may give ghosts.. That the Petitdidier instrument
used in this investigation is free from such, is shown by the fact that
the green line of mercury shows no false lines.

Further, from the visual observations made upon are lines, it is
perfectly clear that the “ghost” argument will not explain the en-
durance of a satellite or its increase in intensity, when a formerly
brighter line grows fainter or disappears entirely, nor, specifically,
Oe | ὃ ὃ

21 This is true of the spark only when the echelon is not powerful enough
to resolve the components of the fluting.

108 PROCEEDINGS OF THE AMERICAN ACADEMY.

a case such as that recorded on page 101 under Zn 4722 at 8.8 amperes.
It is impossible for the main line to disappear and the ghost remain;
and again, even if ghosts were present, there is no reason why these
should appear in the case of any one line with the spark as a source,
and not with the are. The presence of neither a symmetrical nor
unsymmetrical ghost structure could produce the enhancement of
the red satellites in the spark.

A certain objection may, however, be made: namely, that the
presence of the diffraction pattern between the orders when the
instrument is in a double order condition, might cause satellites which
are of low intensity to appear (when otherwise they would not) in
much the same manner as fogging a photographic plate will carry the
exposures of “low lights” up along the intensity curve so that they
will become visible.22. In response to this objection, it may be said
that the satellites in question are not always of low intensity, either
visually or photographically; and they even come up on the right
side when the diffraction pattern lies to the left.

We must conclude, then, that there exists for some unknown reason
a fairly progressive increase in the intensity of the red satellites of
these three zine lines with decreasing inductance. There follows at
once the unsymmetrical broadening to the red of the images given by
instruments of less resolving power, namely, prism or grating spectro-
scopes.

The unsymmetrical satellite system may be produced by the high
potential gradient in the spark; why, the writer, of course, cannot
state. Disruptiveness is not a determining factor, for in the same
spark we obtain from different parts of the gap different line structure.
Vapor density probably does not of itself determine structure, but may
influence the potential gradient. In the are high density seems to
produce a tendency toward complexity of structure, but not an asym-
metry of a regular or enduring type.

All the writer’s observations, both visual and photographic, confirm
the results obtained by Nutting, dealing with are structure. The
results of this study also confirm the shifts found by the writer? to
exist at lower dispersion, shifts,— great at the end of a fairly large
gap of a non-inductance spark between terminals of the pure metal,
lessened or removed entirely by the addition of inductance, and by
the use of the central region of the gap; and lessened also by the use
of an alloy. In this former work the standard of reference employed

22 R. W. Wood actually used this method.
23 Astrophysical Journal, 22, No. 3, Oct. (1905).

KENT.— SPECTRA OF THE ZINC ARC AND SPARK. 109

was a carbon arc of somewhat greater current than here used, but the
amount of vapor was never great, only small bits of metal being in-
serted in the arc, and the exposure always being made when it was
burning quietly. These two sets of standards were probably much
the same. Still, assuming them different, if the potential gradient
determine the enhancement of the red satellites and we accept Nutt-
ings classification of gradient, from low to high the order being, (1)
heavy current are, (2) low current are and inductance spark, (3) high
capacity and non-inductance spark, then the assymmetry of satellites
(and resultant shift) obtained in this investigation with low current
ares as standards would be even less than that found with the some-
what higher current arcs previously used. However, as stated above,
in the arc there seems to be no regular, controllable nor enduring
enhancement of either red or violet satellites.

Janicki’s suggested explanation of the shifts obtained — namely, as
“unsymmetrical reversals like those of chromium and calcium,
reversals which their grating would not resolve and which appeared to
them as line-shifts’” must then be replaced by this enhanced satellite
theory.

The distances between the satellites in Plate 2, 48 (c) are approxi-
mately 0.05 Angstroms. We may then say that the removal of two
layers of inductance in coil (a) has shifted the center of gravity of the
line at least 0.02 Angstroms. In the extreme case then, with no
inductance in the circuit, the shift might easily be in the neighborhood
of 0.032 Angstroms, as formerly obtained.

The writer wishes to record his appreciation of the kindness of
Professor Goodwin of the Massachusetts Institute of Technology in
loaning his Petitdidier echelon. To the Rumford and Bache Com-
mittees, and a personal friend, Mr. J. DeL. VerPlanck, the writer is
indebted for funds which made this investigation possible. In the
actual work of obtaining the results he wishes to acknowledge the
faithful assistance rendered by various students, especially Messrs.
Walter F. Burt, Russell T. Hatch, Charles H. Smith and Carl K.
Springfield.

Puysics LaBporatory, Boston UNIVERSITY,
JUNE, 1912.

Kent. — SpPecTRA OF THE ZINC ARC AND SPARK

—
to

mid
πῶνν

δ"

510

The following negatives, on Plates 1
and 2, represent approximately a three-
fold enlargement of the image as pho-
tographed or a twelve-fold enlargement
of the echelon image.

The region of longer wave-lengths
lies to the right.

12 and 16 were taken with the Porter
echelon; 28 to 96e with the Petitdidier
instrument.

Much of the detail existing upon the
enlarged negatives is not apparent in
the reproductions herewith shown.

814 718

ΕΒΈΛΤΕΙ 1.

16

716 1110

[9]
rroc. Amer. Acap. Arts ano ϑοιένοεβ, VoL. XLVIII.

Kent. — Spectra OF THE ZINC ARC AND SPARK. Pirate 2.

88a 89b 89c

786 796 80a 65b 68a

96¢ 96d 96e

946 944 9468

Proc. Amer. Αοαῦ. Arts AND Sciences. Vor. XLVIII.

THE IMPEDANCE OF TELEPHONE RECEIVERS AS
AFFECTED BY THE MOTION OF THEIR
DIAPHRAGMS.

By A. E. KENNELLY AND G. W. PIERCE
Received July 16, 1912.

I. INTRODUCTION.

THE writers have made a series of measurements of the resistance
and inductance of several forms of telephone receivers over a wide
range of frequency of current. In the course of the measurements
some interesting results have been obtained, which form the subject
of this paper.

As the period of the e. m. f. used in the measurements approaches
the natural period of the diaphragm, the note emitted by the telephone
receiver increases markedly in loudness, and the resistance and in-
ductance of the receiver undergo wide deviations from values obtained
when the diaphragm is prevented from vibrating by being damped.
That is to say, the motion of the diaphragm has an effect upon the
resistance and inductance of the receiver, and this effect grows rapidly
as the electrical period approaches the mechanical period.

In the tests to be described, the resistance and the inductance of a
given receiver were measured, first with the diaphragm free and sound-
ing, and, second, with the diaphragm damped, or arrested. The values
when the diaphragm is free may be called free values; the values when
the diaphragm is damped may be called damped values. The difference
obtained by subtracting the damped values from the corresponding
free values may be called the motional values of resistance, inductance,
ete.; since such differences are due to the motion of the diaphragm.

It is found that when the impressed frequency differs widely from
the natural frequency of the diaphragm, the motional resistance and
inductance are very small. In the neighborhood of resonance, which
is often very sharply marked, these motional values become relatively
large, and one or both pass through a change of sign, in such a manner
that, when the motional impedance for different frequencies is drawn
vectorially from a fixed point as origin, all the points given by the
observations lie upon a circular graph, which may be called the mo-

116 PROCEEDINGS OF THE AMERICAN ACADEMY.

was repeated with the diaphragm of the telephone 7 at rest and silent.
The damping was effected usually by lightly pressing upon the dia-
phragm with the finger, but in some cases it was affected by inserting a
light wedge (a quill) between the diaphragm and pole, when this opera-
tion was permitted by an open structure telephone. The balance,
when the diaphragm was damped, gave practically complete silence in
the head-telephones H, and the settings of resistance and inductance
were consistent within about 4 of 1%. The balance, on the other
hand, when the diaphragm was in motion, was not so good. In this
case, difficulties were introduced by parasitic notes probably due to
currents of higher frequency generated by the motion of the telephone
diaphragm. It was usually possible, however, to balance out the
fundamental tone, with adjustments consistent within 1 or 2 ohms.

III. PartricuLars OF THE TELEPHONES TESTED.

Several telephones were submitted to measurements. Four of the
instruments, for which the results are presented in the present account,
were: —

1. A Western Electric Bipolar Bell Telephone, Type 122, here
designated “Ry”,

2. A Western Electric Bipolar Watch-case Telephone receiver,
designated ‘“ Watch-case,”

3. An experimental specially-constructed monopolar receiver,
here designated “ Experimental monopolar,” and

4. An experimental bipolar telephone receiver, provided with
exploring coils, and here designated “ Experimental bipolar.”

The following table (Table I) contains some of the mechanical
particulars of these instruments.

IV. ExprrIMENTAL Data AND RESULTS.

The data obtained by measurements of the resistance and inductance
of the first three of the above receivers are contained in Tables II to
VI. The data with the “experimental bipolar” receiver are not
tabulated, as they were taken for the specific purpose of determining
the angle of lag of magnetization of the iron behind the actuating
current and this subject is discussed later.

Explanation of Tables.— A brief explanation of Table II, obtained
with the bipolar Bell “R,” with 0.3 effective volts applied at its
terminals, will be given as typical of all the tables. The first column

KENNELLY AND PIERCE.— TELEPHONE RECEIVERS. 117

contains the frequency in cycles per second. The second column
gives the corresponding angular velocity in radians per second. The
third column gives R’ the resistance free, at each frequency, as meas-
ured on the Rayleigh bridge; while the fourth column gives R the
corresponding resistance obtained with the diaphragm damped. The

TABLE I.

MECHANICAL CONSTANTS OF RECEIVERS.

Watch- | Exp. Exp.
Bell Ro. case. Monopolar.| Bipolar.

| * | *
Area of each pole in em. xem. |1.4 x .225,1.61 x .16,0.53 x0.53}1.17 x0.38

Distance separating poles in |
cm. ; .80

External diam. of diaphragm |
in cm. [oie .48

Diameter of clamping circle, |
cm. | “1 81
Tchikness of diaphragm, em.

Weight of diaphragm, grams

Direct-current resistance of
coils, ohms, at 20° C.

* Laminated poles.

fifth column, headed “motional,” gives R’ — R; or the difference be-
tween the free and damped resistances with a proper sign for the
difference. The three remaining columns contain the corresponding
reactances, as obtained by multiplying the inductances observed on
the Rayleigh bridge by the angular velocity ὦ in each case. The final
column, marked “motional,” gives the excess of free reactance over
damped reactance, with proper sign.

Tables III to VI contain data similar to those in Table IT, but with
different applied voltages or different receivers.

An examination of these tables shows that there are two independent
phenomena of interest; namely,

First, the effect of the frequency on the resistance, reactance and
inductance of the receiver when damped; and

118 PROCEEDINGS OF THE AMERICAN ACADEMY.

TABLE ΤΊ:

RESISTANCE AND REACTANCE OF BipoLAR BELL RECEIVER Rp, AT DIFFERENT
FREQUENCIES.

0.38 voLT aT TERMINALS.

Frequency. Resistance, Ohms. Reactance, Ohms.

n. w =2rn | | ]
Cycles | Radians | Damped | Motiona | Ὶ | Damped Motional
ἣ R. R

per

per — R. .| X= Lo. | Llwo— Lo.
Second. | Second. ] |

440 2760
512 3220
600 o770
670 4210
704 4420
720 4520
744 4660
754 4730
770 4830
778 4880
4900
4960
4970
4970
4970
4975
4980
5050
5080
5160
5180
5180
5190
5190
5220
5280
5450
5590
5600
5730
5900
6283
6650
7250
7850
10350
15500

bo 00 COT κα
bo OO ee OO

σι σι σι σι

OYE KR σὺ στὴν ROWE
MOGCONS © NORONOMBRWMO

NOOCNSOMWMOOOUNUNDROMNOORNUWHOWRWHONRAONOSO

NRNWNHRPOUOSO

KENNELLY AND PIERCE.— TELEPHONE RECEIVERS. 119

Second, the effect of the motion of the diaphragm. These two effects
will be treated in order.

Change of Damped Resistance, Inductance and Reactance
with Change of Frequency.— Figure 2 shows the damped resis-
tance, inductance and reactance of the bipolar receiver “ R),”’ plotted

HENRY
ΘῈ

(000

048
S O44
Ξ
2 τς
3 Ξ
Ε 036 2
3, aon
ξ .032 5
9 μι
Ξ 028
Ἔ
$ 024
Ω
020
016
0120
0080
0040

2000 4000 6000 8000 10000 12000 14000
Angular Velocity in Radians Per Second

Ficure 2. Curves of damped resistance, inductance, and reactance plotted
against angular velocity, for Bell bipolar receiver, with 0.3 volt at terminals.
The dots are observed points; circles calculated; crosses belong to reactance
curve.

against the angular velocity of the current used in the measurements.
Figure 3 contains the corresponding curves for the bipolar “watch-
case” receiver. In each case the resistance and reactance of the
telephone when damped increases with increase of frequency, while
the damped inductance decreases with increase of frequency. The
following empirical relations approximately hold.

For the bipolar Bell “Ry,” at 20° C, and with 0.3 volts at its termi-

120 PROCEEDINGS OF THE AMERICAN ACADEMY.

TABLE III.

RESISTANCE AND REACTANCE OF BELL BIrpoLAR RECEIVER Rp At DIFFERENT
FREQUENCIES.

0.42 Votts at TERMINALS OF RECEIVER.

Frequency. | Resistance, Ohms. Reactance, Ohms.

- —|-= = - == ae -Ξ- ἮΦ

Damped | Motional

|
Lw. | L’'w— Le.

σι. ω |

Cycles | Radians Free Damped | Motional| Free
per | per Ἂς R. R’—R. ΄

Second, | Second.

428
548
704

4885
4976
5060

KENNELLY AND PIERCE. — TELEPHONE RECEIVERS. 129}

nals, the damped resistance as a function of the angular velocity is
expressible by the equation

R= 71+ 0.0234 ὦ — 0.456 X'10w? ohms, (1)

in which R is the damped resistance, and ὦ is the angular velocity in
radians per second.

TABLE IV.

RESISTANCE AND REACTANCE OF WATCH-CASE RECEIVER, AT DIFFERENT
FREQUENCIES, WITH 0.3 VoLtT aT TERMINALS OF RECEIVER.

Frequency. Resistance, Ohms. Reactance, Ohms.

n. ω

Cycles | Radians | Free Damped Motional | Damped | Motional
per per Tis ΤῸ Tee Ieee X’—X.
Second. | Second.

<

451 | 2834
550 | 3456
653 | 4102
702 | 4410
712 | 4474
753.5| 4738
804. 5052
849.5 5340
884.3, 5554
0903 Ι 5674
913 5736
9293. | 5800
934 | 5868
940 5906
945 | 5938
957 | 6014
968 | 6082
980 | 6158
993 6240
1020 6408
1084 | 6812
mez | 7270
1250 | 7854
1846 | 11600

|
=

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omen
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TW - OUST OO © οι σι ὧι δι δι δι NT
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For the bipolar “watch-case,” at 20° C, and with 0.3 volts applied,
R = 81.4 + 0.0214 w — 0.505 & 10-%w? ohms. (2)

In these equations, 71 and 81.4 are the respective resistances of the
two instruments to steady currents; the other constants of each

22, PROCEEDINGS OF THE AMERICAN ACADEMY.

equation were determined by using two of the observed points on each
of the resistance-frequency curves.

Another more interesting fact, obtainable from the experimental
curves, is that the product of the damped resistance by the damped

OHM HENRY
.0560

-0520

0480,

Resistance and Reactance -
Inductance

2000 4000 6000 8000 10000 12000
Angular Velocity

Fiaure ὃ. Curves of damped resistance, inductance, and reactance vs.
angular velocity, for watch-case receiver, with 0.3 volt at terminals. Dots,
observed; circles calculated.

inductance, for each of the two telephones, is approximately a constant
independent of the frequency. That is, for the bipolar “Rp,” at 0.3
volt,

6.25
Ξε henrys (8)
and for the “ watch-case”’ at 0.3 volt
a = henrys. (4)

The degree of accuracy with which these formulas accord with the
observations is shown by the damped resistance and inductance

KENNELLY AND PIERCE. — TELEPHONE RECEIVERS. 123

curves of Figures 2 and 3, where the observed points are indicated by
ΕΣ «

black dots, and the points calculated from the formulas are represented
by the circles. The agreement between the calculated points and the
curve of observations in the case of the watch-case instrument (Figure

2)

3) is within about 1%. In the case of the Bell instrument “ Ry,” in

TABLE V.

RESISTANCE AND REACTANCE OF EXPERIMENTAL MONOPOLAR RECEIVER,
witH 0.3 VottT at TERMINALS OF RECEIVER.

Frequency. Resistances. Reactances.

= Free | Damped | Motiona Damped |
Cee ara | er eRe aa Χ Bie | eas

Motional
xX ©

6240 | 158 | 140 | 39: 365,
6360) | e205) 143
6390 | 266 | 142
6400 | 161 | 142
6410 | 207 | 142
6410 | 195 | 143
6428 | 248 | 144
6436 | 291 | 143
6454 | 211 | 143
6454 | 175 | 143
6435 | 148 | 144
6440 | 303 | 143
6444 | 331 | 143
6448 | 321 | 143
6450 | 291 | 143
6460 | 238 | 144
6480 | 1385 | 144
6508 | 175 | 144
6586 | 146 144
6603 | 134 | 144
6624 | 140 | 145

|
|
]

ὡς σι ΘΟ συῦτην ὁ -τἰοῦ MMO

MONO WOH NTR OO ROTO WO 00 CO 9

Song

order to have sufficient range of frequency, the writers had to use
some of the earliest observations, taken before they had learned the
precautions required for accurate results. But in this case also, the
values calculated by the formulas (1) and (3) agree closely with the
curves that best represent the observed points except in regions where
the latter are uncertain.

As a further illustration of the approximate constancy R X L taken
with the telephone damped, reference is made to Table VII, which
contains this product at different frequencies for receiver Rp with 0.42

124 PROCEEDINGS OF THE AMERICAN ACADEMY.

volt at its terminals. At this voltage, the product for this telephone
averages 6.21, and within the range of frequencies between 428 and

TABLE VI.

RESISTANCE AND REACTANCE OF EXPERIMENTAL BIPOLAR RECEIVER PRO-
VIDED WITH ExpLorING Corts, WitH 1 Vout at TERMINALS.

Frequency. Resistance, Ohms. Reactance, Ohms.

τι. ω.
Cycles | Radians Free Damped ] protons Free Damped | Motional
᾿ς: 5 R’ — R. xe XE X’—X.

per per Χ'

Second. | Second.

1007 6370
1020 6410
1020 6410
1023 6430
1026. 6450
1027 6450
1027 6450
1027 6452
1027. 6455
1028 6458
1030 6470
1030 6470
1033 6492
1033 6492
1033 6492
1036 6510
1036 6510
1037 6520
1038 6525
1039 6530
1039 6530
1039.5) 65383
1041 6540
1042 6546
1042 6546
1048 6560
1045 6570
1047 6580
1051 6600
1051 6604
1054 6624
1059 6660
1064 6686
1084 6812

WwW N ὁ κα

J : b
NOWOWOOWARONNOONWAWWONNWUNOODWOONANEO

AAWWWWOSDSHOSOSCOSOSCOSCOCSOOCONOOHNHHOHDINAW
NW NOWNNWAOUIIROARWNOWUNAOHUIDROARBOMNOH

DOMWEROCOHOOOOCOCOCOCODWOWROOCNNHDONWORH
SCNNOMWNIMNOWHONPEUROONOURORNONOQNUNNEHA

CDHODDOOONSOSSOOSOMNONNSOCOCORCCONAE
SSOSOSCOCOPNHOWROHANUNMHNIMDORWOOCOWRONEE

890 cycles per second, the product does not depart from the average
by more than 2%. There is no march of the product within this range.

KENNELLY AND PIERCE. — TELEPHONE RECEIVERS. 1S)

When, however, the computation is extended to a single observation
at 2464 cycles per second, a departure of 5% is obtained.

A third interesting fact shown by the experimental tables is that
the damped reactance is approximately equal to the damped resis-
tance for the telephone “Ry’* over a wide range of frequency. This
may be seen, for this telephone, at 0.3 volt, by a reference to Figure 2
and by a comparison of the observed reactance values, marked by
crosses, With the observed points on the resistance curve marked by
black dots. 'The damped reactances and damped resistances are seen
to be nearly the same throughout the range of frequencies between
451 cycles per second (ω = 2834) and 1250 cycles per second (w =
7850). Within this range the damped resistance and the damped
reactance both nearly double and yet remain within a few percent
of equality with each other. For the telephone Ry» at 0.42 volts, the
same approximate equality holds within the range of frequencies
between 428 and 2464 cycles per second, as may be seen by a reference
to the fourth and seventh columns of Table III. It is to be noted,
however, that this same equality cannot persist at low frequencies,
for the damped reactance at zero cycles is zero, while the resistance
of this instrument at zero cycles is 71 ohms. As a corollary, it may be
observed that within the range of equality of damped resistance and
damped reactance, the damped angle of lag of current behind impressed
6. m. f. is 45°, and the damped impedance is V2R. With the other
instruments tested, the equivalence of damped reactance and damped
resistance was not obtained; but, as may be seen by reference to Figure
3, the curves of damped reactance and damped resistance for the
watch-case instrument run nearly parallel and within 10 ohms of each
other, for a considerable range of frequencies.

It would be interesting to discuss the relations expressed in equations
(1), (2), (8), and (4). Since, however, at this time the primary pur-
pose of the writers is to present an account of the effects of the motion
of the diaphragm in modifying the resistance and reactance of the
telephone receivers, a further discussion of the relations (1) to (4)
will be deferred.

The Effects of Motion of the Diaphragm on the Resistance
and Reactance of the Receivers.— As stated in the introduction,
the motion of the diaphragm of a telephone receiver has a marked effect
on its resistance and reactance. This effect is best shown by sub-
tracting the damped resistance from the free resistance, and the
damped reactance from the free reactance and plotting the differences,
called respectively motional resistance and motional reactance, against

126 PROCEEDINGS OF THE AMERICAN ACADEMY.

the frequency in radians per second (angular velocity). This is done
in Figures 4, 5, and 6. Taking Figure 4 plotted from Table IV
obtained with the watch-case receiver, as typical, it will be seen that
the Figure contains curves of motional resistance, motional reactance,
motional power, and phase angle of motional impedance, marked
respectively Resistance, Reactance, Power and Phase. These quantities
are all plotted against angular velocity. The black dots are observed
points, and the circles are computed values, or derived values. Begin-
ning with the resistance curve, and remembering that this curve
represents the excess of free resistance over damped resistance, that
is to say, the effect of the motion, it will be seen that, starting at a
value slightly below zero at 2834 radians per second, the increment
of resistance due to motion (motional resistance) increases up to 23
ohms at angular velocity 5674, then descends rapidly to minus 25
ohms at angular velocity 5938 and then increases again toward zero.
The motion of the diaphragm markedly increases the resistance at
certain frequencies and markedly decreases it at other frequencies.
The formulas for computing the motional resistance values are given
under heading V below.

Next, let us examine the motional reactance curve. The effect of
the motion of the diaphragm is chiefly to decrease the reactance so that
the free reactance is less than the damped reactance, giving usually a
negative motional reactance, amounting to — 44.7 ohms at angular
velocity 5800. The motional reactance is not always negative but
shows small positive values in the neighborhood of angular velocities
4500 and 7000.

The resemblance of the motional resistance curves and the motional
reactance curve of Figures 4, 5, and 6 to the curves of optical index
of refraction and optical absorption plotted against frequency, in the
neighboring of an absorption band, will at once strike the attention of
the reader familiar with theoretical optics. A difference, however,
exists on account of the hysteretic behavior of the iron in the telephone
theory, as will be pointed out in the treatment under heading V below.

Effect of Motion of Diaphragm on Draft of Power.— Attention
is next directed to the curve marked Power in Figure 4. This curve
shows the excess of power sent into the telephone when freely vibrat-
ing over the power sent into it under the same impressed e. m. f. when
damped. The excess of power (i. e. motional power) is plotted in
microwatts against angular velocity of impressed e. m. f., and is seen
to be different for different angular velocities corresponding to different
frequencies. The maximum of motional power is in the neighborhood

KENNELLY AND PIERCE. — TELEPHONE RECEIVERS. 127

of angular velocity 5820 radians per second, and this is the period of
the diaphragm, as is shown later by other methods of analyzing the
data. The impressed e. m. f. in this experiment was maintained
throughout at 0.3 effective volt.

MICRO-
© - oy WATTS
= 0- “ 60
it
Ξ at ἰῷ
‘sat ye ate
Ξ ο τι Φ
2 hap Ε
ἘΠΕ ae 40 ὦ
βι Ξ ποι 3
Ὁ “πὸ Ξ
τ 3 20 8
4 =)
© 20
Ξ
= 10
5
Ξ 0
&
o
oO
[-
ij
--
τη
o
a
Ε
S
Ξ
ο
=
-b0 -
τ 8000 4000 5000 6000 7000 8000

Angular Velocity in Radians Per Second

Ficure 4. Curves of motional resistance, reactance, power, and phase,
plotted against angular velocity, for watch-case receiver at 0.3 volt. Dots,
observed; circles calculated.

The method of obtaining the motional power curve was as follows:
Table III contains measurements of resistance and reactance of this
receiver at different frequencies both while free and while damped.
The square root of the sum of the squares of resistance and reactance
gives directly the impedance. Dividing the impedance into the e. m. f.
gives the effective current. The square of the free effective current
multiplied by the free resistance gives the free power. Likewise, the
square of the damped current multiplied by the damped resistance
gives the damped power. The free power minus the damped power
gives the motional power. These are tabulated for two receivers, for
three series of measurements, in Tables VIII, [X and X.

128 PROCEEDINGS OF THE AMERICAN ACADEMY.

It is not necessarily true that all of the motional power goes into
energy of motion. The term means merely the excess of input when

TABLE VII.

SHOWING PRopuct or R AND L For ΒΙΡΟΙΑΒ RECEIVER Rp wit 0.42 Vout
AT TERMINALS.

Frequency Damped | Damped |
Cycles per | Resistance | Inductance : ΠΡΟΆΓΕΙ,
Second. n. | &. Ohms. L. Henry. -

Average

sounding over input when damped. Asa matter of fact, the motional
power is negative at some frequencies, as is shown in some of the curves

KENNELLY AND PIERCE. —- TELEPHONE RECEIVERS. 129

(e. g. Figures 5 and 6). Always, however, at consonance of the im-
pressed 6. m. f. with the period of the diaphragm, the motional power
TABLE VIII.

ΝΑΙ ΕΒ OF Power. Bett Breowar Rp at 0.3 Vout.

Frequency. Power in Microwatts.

n, | ω,
Cycles Radians Damped. Motiona .
per Second. | per Second.

“I

2760
3220
3770
4210
4420
4520
4660
4730
4830
4880
4900
4960
4970
4970
4970
4975
4980
5050
5080
5160
5180
5180
5190
5190
5220
5280
5450
5590
5600
5730
5900
6283
6650
7250
7850
10350
2468 15500

308.
303
297.
283 .
275.
271.
266.
265.
261.
262.
266.
209.
209.
270.
259.
260.
259.
209.
257.
256.
254.
250.
253.
253.

WRTORPNNWEENNOMOOURNWOOWOONDOUBHONONUE
Ἐ τῷ WMH HE AOONARODOMNOONNSOHODHONWINMAWDOOOUOR

HWM OHAWNORWDOOOCOCOUNWNONNODNNRONNHONOSE

ROR Dh σι

has a large positive value, which is no doubt correlative with the large
amount of sound produced under this condition. With the receiver

130 PROCEEDINGS OF THE AMERICAN ACADEMY.

giving the curves of Figure 4 (the bipolar watch-case — cf. Table X)
the motional power at resonance is 62 microwatts, which is 20% of the
total free input (809 microwatts) and 25% of the total input at the
same voltage with the diaphragm damped (247 microwatts). In the

~

case of the bipolar Bell receiver Ry at 0.8 volt (see Figure 5 and

Motional Resistance and Reactance

3000 6 4000 5000 6000 7000 8000
Angular Velocity in Radians Per Second

Ficure 5. Curves of motional resistance, reactance, and power, vs. angular
velocity, for Bell bipolar, with 0.3 volt. Dots, observed, circles calculated.

Table VIII) the motional power at resonance was 179 microwatts,
which is 41% of the free input and 69% of the damped input. At
0.42 volt with receiver Ry (see Figure 6 and Table [X) the motional
power was 338 microwatts at resonance, amounting to 40% of the
total power input with diaphragm free and to 68% of the power input
under the same 6. m. f. with the diaphragm damped. That is to say,
if one holds his finger on the diaphragm so as to damp it, and measures
the power supplied to this receiver at 0.42 volt, the frequency being
resonant with the period of the diaphragm, and then takes his finger

off, the telephone emits a loud sound and the power input jumps up
68%. :

KENNELLY AND PIERCE. — TELEPHONE RECEIVERS. Lod

An examination of the curves of Figures 4, 5, and 6 shows how this
occurs. The effective resistance of the receiver, with the e. m. f. at
resonance, is not very different when it is sounding and when it is
damped; that is, the motional resistance is nearly but not quite zero.
What causes the large consumption of power at the resonant frequency

fo}
io
25
Motional Power in Microwatts

Motional Resistance and Reactance

3000 4000 5000 6000
Angular Velocity in Radians Per Second

FicurE 6. Same as Figure 5, but with 0.42 volt at terminals of Bell bipolar.
Power points, calculated; other dots, observed; circles, calculated.

is the low value of the effective inductive reactance of the receiver at
this frequency and the consequent large draft of current from the
source. As we go away from the frequency of e. m. f. resonant with
the period of the diaphragm, the motional power consumption may be
due either to excess of free resistance over damped resistance or to
the excess of free current incidental to a decrease of inductance by the
motion.

Effect of Motion on Phase.— The phase angle of the motional
impedance for the watch-case receiver is shown in the curve marked

2, PROCEEDINGS OF THE AMERICAN ACADEMY.

Phase in Figure 4. The angles plotted in this curve were obtained by
taking the antitangent of the ratio of motional reactance to motional

TABLE IX.

Vatues oF Power. Brett Breouar Rp at 0.42 Vout.

Frequency. Power in Microwatts.

Cycles per | Radians per Free. Damped. | Motional.
428 2690 677 666 11
548 3446 556 609 — oe
704 4425 520 530 ll)
710 4468 527 528 = 1
722 4540 539 520 19
733 4610 539 518 21
744 4680 546 518 28
754 4740 538 518 | 20
4810

resistance and plotting the result, which is phase of motional imped-

ance, against angular velocity. The meaning of this phase angle will

be made plainer in the discussion of the circular graphs to follow.
Application to Sound Experiments.— It may be noted, in pass-

KENNELLY AND PIERCE. — TELEPHONE RECEIVERS. 133

ing, that the effect of the reaction of the motion of the diaphram in
modifying the electrical properties of the telephone receiver is of im-
portance in experiments on sound, where an electrically driven tuning
fork or telephone is used as the source of sound, because the power
consumed in producing the sound may change with the change of the

TABLE X.

VALUES OF PowrER. WartTcH-cASE RECEIVER AT 0.3 VOLT.

Frequency. Power in Microwatts.

Ns Radians
Cycles per per
Second. Second.

Motional.

|
|
|

451 2834
550 3456
653 4102
702 4410
712 4474
754 4738
804 5052
849. 5340
884 5554
903 5674
913 57386
923 5800
934 5868
940 5906
945 5938
957 6014
968 6082
980 6158
993 6240
1020 6408
1084 6812
1157 7270
1250 7854
1846 11600

ον ρος

stationary sound-wave system in the room. [ἢ our experiments, the
sound emitted from the test telephone was reflected from the various
walls of the room and formed a stationary system with nodes and
loops at various parts of the room. As an assistant walked about the
room while the measurements were being made, it was found that the
bridge, previously balanced, was thrown successively in and out of
balance as the reflection and absorption of the assistant’s clothing

134 PROCEEDINGS OF THE AMERICAN ACADEMY.

changed the stationary sound system when he walked through the
room. Professor Sabine, in some experiments not yet published, had
previously noticed the effect of a shift in the stationary wave system
in modifying the draft of power by an electrically-driven tuning fork
kept vibrating at constant amplitude. In accordance with the pres-
ent experiments and as Professor Sabine previously suggested in

Figure 7. Circular graph for bipolar Bell receiver R, with 0.3 volt at
terminals. Diameter 103 ohms. Depression angle (28) 70.5°. 9 = 4885
radians per sec. A = 200. Small circles observed. Internal ring numbers
computed.

conversation with one of the writers, the phenomenon is seen to have
its explanation in the change of resistance and reactance of the coil
of the fork due to the variously affected motion of the fork.
Circular Graphs of Motional Impedance.— A very interesting
result is obtained by plotting the motional reactance of a telephone as
ordinate against the motional resistance as abscissa. The result is a
point on the R X plane, and the point is different for different values
of the angular velocity used in the measurement. The locus of this
point, as the angular velocity is varied, is a circle passing through the
origin; that is, through the point of zero motional resistance and zero
motional reactance. Stated otherwise, if the motional impedance,
(R’ — R) + 7(X’ — X), is plotted vectorially from a point as origin,

ae

- veo

KENNELLY AND PIERCE. — TELEPHONE RECEIVERS. 1.35

the vector for any given frequency is the cord of a circle through the
point. As the angular velocity of the impressed e. m. f. increases from
zero to infinity, the free end of the vector impedance passes once around
the circle. Circular graphs of this character are plotted in Figures
7 to 11 for different instruments or for different values of impressed

Figure 8. Circular graph for bipolar Bell receiver Ry with 0.42 volt at
terminals. Diameter 103.5 ohms. Depression angle (28), 73°; 9 = 4940
radians per second; Δ = 200. Small circles observed. Internal ring num-
bers computed.

e.m.f. These several circular graphs are on different scales, and are
summarized to the same scale in Figure 12.

On each of the circular graphs, all of the observed points, for a given
receiver with a given impressed e. m. f., are plotted as small circles.
The measured angular velocities of the impressed e. m. f. for the
observed points are printed at the outside of the circular locus. To
avoid crowding, not all of the points are designated with angular veloci-
ties, and in the selection of the points to bear numerical designation of
angular velocity, those points were chosen, for which the measure-
ments were made with especial precaution as to voltage and frequency.

The numbers placed inside of each of the circular loci are computed
values for the theoretical distribution of angular velocities around

136 PROCEEDINGS OF THE AMERICAN ACADEMY.

Figure 9. Circular graph for watch-case rec@iver with 0.3 volt at terminals.

Diameter 47 ohms. Depression angle

second. A= 150! Small circles observe
Panes ee)
bas a 3
Sale
30 “Ost
| δ,
Fiaure 10.

volt at terminals.
#) = 6448 radians per second.
ring numbers computed.

A = 20

(28) 93°. wo = 5820 radians per
d. Internal ring numbers computed.

ἘΠΕ

ΤΕΣ
eae ΠΕ
me, ——

be
LJ

Circular graph for experimental monopolar receiver, with 0.3
Diameter 185.4 ohms.

Depression angle (28) 21.5°.

. Small circles observed. Internal

—— αὶ ὩΣ. ἃ

ὔἶ ιν ὦ

KENNELLY AND PIERCE. —- TELEPHONE RECEIVERS. 137

ὧν»

ἘΣΤΙ
ἘΞ
aa
Pale
Pale
ἘΞ
[alle
ἌΝ

ζ : w

Ων

Figure 11. Circular graph for experimental bipolar receiver, with one
volt at terminals. Diameter 10.9 ohms. Depression angle (28) 26.5°.
ὧν = 6465?; A = 20?.

Figure 12. Circular graphs collected to one and the same scale. The
largest circle and the smallest circle are graphs with experimental receivers.
Two light circles near together are graphs with bipolar Bell receiver. Broken
circle is graph with watch-case.

138 PROCEEDINGS OF THE AMERICAN ACADEMY.

the circular graphs. The formulas by which this distribution has been
computed are derived under heading V below.

The quantities of theoretical and practical importance in these
circular graphs are:

1. The length of diameter of the circular graph for a particular
receiver.

2. The dip of the diameter below the axis of resistance.

3. The rate of change of angular velocities around the circle.

4. The angular velocity at the end point of the Giameien remote
from the origin, and

5. ‘The impedance at this point.

The significance of these several quantities will appear in connection
with the discussion of the theory of the problem, which follows.

V. THeory oF THE REAcTIVE Errects oF ΜΌΤΙΟΝ OF THE [)1«-
PHRAGM ON THE ELECTRICAL CONSTANTS OF THE RECEIVER.

An exact treatment of the electrical properties of a coil containing a
magnetic core in proximity to a moving magnetic membrane offers
great difficulty. If, however, we confine our attention to terms of the
first order, we can obtain a sufficiently close approximation to a solu-
tion, to permit an interpretation of the preceding experimental results.

Assumptions Regarding Mechanical Magnitudes.— To this
end we shall assume, so far as concerns the fundamental mode of
vibration of the diaphragm,

(1) That the elastic restoring force of the diaphragm is all concen-
trated at the center of the diaphragm, and 15 proportional to the dis-
placement;

(2) That the motion is opposed by a frictional force proportional to
the velocity and also concentrated at the center of the diaphragm: and

(3) That the actual distributed mass of the diaphragm may be
replaced by an equivalent mass concentrated at the center of the
diaphragm.

Motion of the Center of the Diaphragm under a Pull Main-
tained Sinusoidal.— As a first step toward the solution, let us
assume the diaphragm to be solicited by a force which is maintained
sinusoidal; then (cf. Figure 13)

st + ra + mx =f = Fé 2dynes Z (5)

2 The sign aw following fi unit “adnate fiat ane equation should be inter-

preted vectorially, or in complex quantities.

KENNELLY AND PIERCE. — TELEPHONE RECEIVERS. 139

in which

x = the displacement of the effective mass of the diaphragm from its
position of rest (cm.),

= the displacement velocity (cm/sec),

Σ = the displacement acceleration (em/sec?),

the elastic force per unit displacement (dynes/em),

the resisting force per unit velocity (dynes per cm. per sec.)

ἢ;
2
8
r
f = Fé, the impressed moving force measured in the direction of x
toward the poles (dynes),

w = ὥπη, the angular velocity of the impressed force (radians per
second), and

n = the frequency of the impressed sinusoidal force (cycles per
second).

5

bas,
I|

Fiaure 13. Diagram of receivers. N is number of turns. F is force on
diaphragm with direction of arrow; / is normal gap length; and x displace-
ment toward poles.

The solution of equation (5) for velocity of displacement, after a
steady state has been attained, is well known, and may be written in
the form

: Feit
—— ! = " = 2 em/sec Ζ (6)
: 8 5 5
Reed (mo —2)
Ww
in which
z=rt+ j( ms — Ἂ dyne sec/em Ζ (7)

The quantity 2 may be called “vector mechanical impedance” from
its analogy to vector electrical impedance.

140 PROCEEDINGS OF THE AMERICAN ACADEMY.

We may further write for abbreviation

l2| = Jet (ne =e =) dyne sec/em (8)

(69)
and

Q | radians (9)

The quantities entering in the above equations, and their analogous
electrical quantities, are tabulated below.

Mechanical Quantity. Electrical Quantity.

Velocity of displacement 7 } Current
Mechanical force Electromotive force

Resistance (i. e., force of re- Resistance (i.e., e.m.f. of re-
sistance per unit velocity) sistance per unit current)

Effective mass (1. e., force per | Self-inductance (i. e., 6. m. fe
unit time-rate of change of per unit time-rate of change
velocity) | of current)

Elastic force per unit displace- | Reciprocal of capacity (i. e..
ment (1. e., per unit time- e.m.f. per unit time-integral
integral of velocity) 1/C | οἵ current)

Vector mechanical impedance Z Vector electrical impedance
Mechanical Impedance |Z| | Electrical impedance
Mechanical phase-angle θ Electrical phase angle

Mechanical inertia reactance Lw | Electrical inductive reactance

Mechanical elastic reactance (1/Cw)| Electrical capacity reactance

Circular Graph of Velocity.— By equation (6) x is seen to be
sinusoidal, with amplitude ΠῚ and lagging by an angle a behind the

impressed force. A geometrical representation of the amplitude and
phase of ὦ is given in Figure 14. In the left hand part of the figure
Op is a representation of the vector mechanical impedance z. As w
changes from zero to infinity, the point p moves along the straight
line Xp from minus infinity to plus infinity, parallel to OY. In the
right hand part of the figure, the circle is the vector graph of Fz,
which is given in magnitude and direction by OP. This circle is
obtained by taking the reciprocal of the straight line locus of the vector

KENNELLY AND PIERCE. — TELEPHONE RECEIVERS. 141

z and multiplying the reciprocal by F, which gives a circle of diameter
F/r symmetrically disposed with reference to the axis of reals.

The use of this circle is as follows. For a given value of ὦ find the
angle a by equation (9) and lay off this angle negatively at O; then

the length of the chord OP of the circle gives the amplitude — of a,

[5]

Ficure 14. Left straight line graph of z. Right, circular graph of F'/z.

for the given w, and the angle is the angle of lag of x behind the
impressed force. As w changes from zero to infinity, the point P
moves negatively once around the circle from O, through X, back to 0.

Magnetic Flux as Dependent on Current and Mechanical
Displacement.— In the problem under consideration, the pull f act-
ing on the diaphragm is determined by the magnetic flux through the
air gap, or air gaps, of the receiver. If ¢ is the mean flux through
the active part of the magnetic circuit, we have, for a bipolar receiver,
approximately

φ--: = “= 88 maxwells (10)

¢—-_%= ae Ee maxwells (11)

in which

F = the total m. τη. f. due to the permanent magnet and to the
current ὦ in the coils (gilberts),

δ. = πη. m. f. due to permanent magnet alone (gilberts),

142 PROCEEDINGS OF THE AMERICAN ACADEMY.

Ὁ = total reluctance of the magnetic circuit (oersteds),
%, = reluctance of circuit exclusive of that of the gaps (oersteds),
N = total number of turns in the receiver coils,

7 = instantaneous current in the coils assumed to vary sinusoidally,
or according to the real part of [ε΄ (absamperes),

1 = normal air-gap between poles and diaphragm (cm.),

δ = mean flux density in the air gap (gausses), and .

S = area of one gap (em”).

The Equations of Current and Motion.— We can now express
the pull on the diaphragm in terms of the flux. It is a well known
fact, which may be derived from energy relations, that the pull on the
diaphragm is

f= ὡς for a bipolar receiver dynes (12)
and

af

= ἧς for a monopolar receiver dynes (13)
If now f; is used to denote the part of the pull due to the current 2,

and if this is small in comparison with the pull due to the perma-
nent magnet, we may write

ip==2 | dynes Ζ (14)

which by substitution from equations (12) and (10) becomes

ened Uy,
EE Cries

2No. 2N%X,. :
Ne ὶ -- "i fora bipolar dynes Z (15)
RS δὲ

and
NX.
fi Ξ --- Ὑ tor a monopolar. dynes Ζ (16)
ot

In equations (15) and (16) %, has been substituted for 8, since the
increment in 93, due to 27, when multiplied by ἢ, is assumed to be a

second order effect.
In order to avoid carrying through separate discussions for the

area ees

KENNELLY AND PIERCE. —— TELEPHONE RECEIVERS. 143

bipolar and for the monopolar receiver, and in order to simplify the
equations, let us write
2N%8, : ae
A = ~~ for the bipolar receiver, and dynes/absampere (17)
οἷ
A = τ “ for the monopolar receiver; dynes/absampere (18)
οἱ

then, for either instrument,
fi = Δι dynes Z (19).

Equations (15), (16) and (19) assume that the pull on the diaphragm
due to ἢ is in the phase with ὁ; but with hysteresis and eddy currents
present, the electromagnetic force will lag? behind the current 7 by an
angle 31; whence the force on the diaphragm due to the current 7
becomes, by eq. (19),

7 Ξ A 8) dynes Z (20)
Consequently, by equation (6),
Ἢ ἘΞ 4:1 δι em/sec Z (21)
z

The e. m. f. induced in the coils by the motion of the diaphragm
will be, in the absence of hysteresis,
dp _ noe :

axe abvolts, Z (22)

Ee oe reas aie:

and by differentiating equation (10) or (11), equation (22) gives
to a first approximation

2N Rox :
@ = = Ab abvolts, Z (22a)
and by substitution from equation (21)
ΡῈ
θᾳ = το abvolts Z (28)

However, it should be noted that there is also a hysteretic lag of
flux with change of gap, and this will cause the induced e. m. f. to lag
by a certain angle (2 behind 2, so that equation (23) should be changed
to

a a abvolts Z (24)

3 On the question of Constancy of 4; see VI below.

144 PROCEEDINGS OF THE AMERICAN ACADEMY.

If L and R are the inductance and resistance of the receiver when
damped, the impedance of the damped receiver will be
Z=R+jlw absohms Ζ (25)

and if ὁ is the instantaneous value of the impressed e. τη. f. of the type

Eé*', we shall have
Ὁ ΞΘ iW abvolts Z (26)

But owing to the influence of the e. m. f. of motion, the last equation
becomes modified to

Ὁ ΞΖ abvolts Ζ (27)
or
e=iZ+e, abvolts Z (28)
That is by equation (24)
e= if Z+ -- B+ . ΞΞ 12. abvolts Z (29)

where Z’ is the free impedance of the receiver.
This means that the impedance of the receiver has become increased,
through the vibration of the diaphragm, by a motional impedance:

ies a

z

\Ai + Bo absohms Z (30)

This motional impedance, being the reciprocal of the vector equation
of a.straight line with w as variable, is a circle for variable w, and has a
2

diameter =, depressed below the axis of reals by an angle \3; + β..

As to the relative values of 8; and β0 it seems reasonable that
whether the change of flux of a circuit is caused by a small change of
current, changing the m. m. f., or by a small change of gap-length,
changing the reluctance, the angle of lag of flux behind the cause is
the same; that is 6; = βι = βὶ (Say). This is borne out by one of our
experiments to be described below (see VI). With this equivalence
substituted in equations above, we obtain,

oe

Le 2| absohms Ζ (31)

-
Ὁ

Consequently, if we vary ὦ from 0 to + %, keeping the impressed
e. m. f. and all other quantities constant, the motional impedance
Z' — Z has a circular graph through the origin, with its principal

KENNELLY AND PIERCE. — TELEPHONE RECEIVERS. 145

: A? : ς
diameter of length — depressed 23 below the axis of reals. Equation
r

(31) is the theoretical equation to the circular graphs of Figures 7 to 12.
Replacing the vector z of equation (31) by its absolute value [2
and angle a, we have

Z—ZL= a 8 +a absohms Ζ (32)

Squation (32) may be analysed into

Ὁ
ihe Π τὸν (238+ a) absohms_ (33)
E — A®.,
a Aue sin (28 + a) absohms (34)
in which
a= Je + (me -- ΣῪ, absohms (35)
and
( 8
mo — —
Ὁ ΞΞ᾿ tae: Ξ es radians (36)

are functions of w. The quantity A, involving & and %, might be
expected to vary with variation of w, but an examination of the
experimental results shows that, with the excitations employed, not
much error is introduced by considering A and also independent of w.

Equations (82), (33), and (34) are in convenient form for computa-
tion, and permit an easy determination of some of the important
mechanical constants of the diaphragm.

For example, if we let wo be the angular velocity of impressed
mechanical force for which the sustained vibration of the diaphragm
is In resonance, we see from equation (6) above that

Ww =| radians /sec. (37)

m

Now, if w, the angular velocity of the impressed electromotive force in

the telephone circuit, is equal to wy = 1 it is seen by equation (36)
m

146 PROCEEDINGS OF THE AMERICAN ACADEMY. Ἑ
that a becomes zero; hence the value οὗ w, which in the experimental
circular graphs of Figures 7 to 10 lies at the remote end of the principal
diameter is the w = wo for which the diaphragm in sustained vibration
is resonant. This gives a simple and accurate method of determining
wy for a telephone diaphragm.*

Again, let A be the logarithmic decrement per second of the dia-
phram, if vibrating under no external force, then by the theory of
elasticity,

— numeric/sec. (38)
2m
whence from (36)

numeric/sec. (39)

ω tana

Differentiating (89) with respect to a, we obtain

dw w daw :
Ae tana + wsec?a = —— numeric/sec. (40)
aa a

see a= 0,
[2] -- Δ; numeric/sec. (41)

That is, in the experimental circular graphs, the rate of change of w
with change of a, at the remote end of the principal diameter, is the
logarithmic decrement per second of the diaphragm. This quantity
cannot, however, be obtained with the precision with which w can be
obtained.

Another method of obtaining A is by taking the values of w; and
w» which lie respectively 45° below and 45° above the principle diame-
ter,— these angles being measured at the origin, not at the center.
For these points tan a is respectively + 1 and — 1; whence from (39)

9
2Aa == wy = ONE
= 2Ao2 = Ww” — we"

and by subtraction and division by 2 (w; + ws),

A = ——— numeric/sec. (42)

4 For another method of finding ) from the humming tone of a telephone
receiver, see a paper by A. E. Kennelly and W. L. Upson, Proc. Am. Phil. Soc.,
1908, ‘“‘The Humming Telephone.”’

ee ee ee ee a μων.

KENNELLY AND PIERCE. — TELEPHONE RECEIVERS. 147

Thus we have methods of determining both wy and A. The experi-
ments, on the ether hand, do not permit a direct determination of the
quantities m, r, and s; but it would seem that by adding a known
mass, as a small load, to the center of the diaphragm and repeating
the series of measurements, these quantities should be capable of
determination.

VI. Comparison oF EXPERIMENTAL RESULTS WITH THEORY.

An examination of the experimental results with the aid of the
theory above developed gives the following results, which may be
called the characteristics of the several receivers (Table XI):

TABLE XI.

SUMMARY OF CHARACTERISTICS OF RECEIVERS.

Watene | Experi- Experi-

Bell Rp | Bell Rp.| case | | mental | montar

at at at
| | lar at at
0.3 Volt. | 0.42 Volt.) 0.3 Volt. 0:3 Voli.| 1 Volt.

| Bipolar | Bipolar

Diameter of motional im- |
pedance circle in ohms. é | oe [0

Depression angle (28) in |
degrees 26.5

ὡρ in radians per second S82 ; | 6465 ?

Log. dec. per second. (Δ) p | | 20 ?

The method of obtaining these characteristics was as follows:
The circular graphs of Figures 7 to 11 were plotted. The diameter
of the motional impedance circle and the angle of depression of this
diameter below the axis of R’—R could be measured off at once on the
diagram. The value of w at the free end point of the diameter could
also be read_or obtained by interpolation; this ὦ is the w, of the dia-
phragm. The logarithmic decrement per second A could have been
obtained by either of the two methods derived in the discussion of the
theory, equations (41) or (42); but a third method was employed;
namely, by the use of the more general equation (39), in which several
values of a and the corresponding values of w from the circular graphs
were substituted, and the values of A so obtained were averaged.

148 PROCEEDINGS OF THE AMERICAN ACADEMY.

Having now obtained the constants of Table XI, the theoretical
distribution of angular velocities around each of the circular graphs
of Figures 7 to 11 were calculated by equation (39), and these theo-
retical values are designated by numerals on the inside of the circular
graphs.

The values of R’—R and of X’—X corresponding to these theo-
retical values of w were then plotted as the circles on the rectangular
graphs of motional resistance and motional reactance in Figures 4, 5,
and 6. It is seen that the agreement of the computed and observed
points in these Figures 4 to 6, while not exact throughout the entire
range, is yet sufficiently good to show that the theory is essentially
correct.

Another significant point in the theory is the interpretation we have
given to the depression angle 2 of the circular graphs. We inter-
preted 3 to be the angle by which the magnetic flux lags behind the
magnetizing current in the telephone receivers. ΤῸ test this point,
this angle of lag of magnetic flux behind magnetizing current was
independently measured with the experimental bipolar receiver.
This receiver had a separate secondary, or exploring, coil wound
around the ends of its poles, near the diaphragm. The e. m. f. gen-
erated in this exploring coil is in phase with the time rate of change
of flux; and the phase of this e. m. f. was compared with the phase
of the alternating current in the exciting coils in two ways (1) by a
three-voltmeter method and (2) by an alternating current potentio-
meter.

In the three-voltmeter method, a known resistance was put in
series with the exciting coils, and one end of the exploring coil was
connected to the point between the exciting coil and the known resis-
tance. With the frequency and the e. m. f. about the telephone kept
the same as that used in the bridge measurements (i. e., the e. m. f.
of 1 volt, and the frequency near the resonant frequency of the dia-
phram) voltages were measured about the known resistance (20 ohms),
about the exploring secondary, and about the two in series. These
voltages, being small, were measured by a crystal rectifier in series
with a galvanometer,® — the galvanometer and rectifier having been
calibrated immediately before and after the experiment by an a. 6.
potentiometer operating at the frequency employed.

The readings of voltage were very consistent, and were as follows
in a typical case:

5 G. W. Pierce: Phys. Review, 25, p. 31, 1907; ibid., 28, p. 153, 1909.

KENNELLY AND PIERCE. — TELEPHONE RECEIVERS. 149

Voltage about 20 ohms = 0.129 volt
‘““ ~ about secondary = 0.125 “
“about both = 0.196 “
“about both with secondary reversed = 0.161 “

Substitution of the first three of these values in the formula for an
obtuse-angle oblique triangle gives 79°, as the angle by which the
secondary voltage leads the primary current. This is the angle
by which the time derivative of the magnetic flux leads the primary
current. The flux itself lags its time derivative by 90°, and therefore
lags the primary current by 90°—79° = 11°.

Again, a substitution of the first, second, and fourth value of above
table in the formula for an acute-angle oblique triangle gives for the
flux lag angle the value 11.5°.

This angle of lag of flux behind the magnetizing current was found
to be nearly independent of the frequency. ΤῸ illustrate this, and as
a further confirmation of the result obtained by the three-voltmeter
method with the crystal rectifier and galvanometer as voltmeter,
a second measurement was made by an entirely different method;
namely, by the use of a Drysdale alternating-current potentiometer,
with a 60-cycle current, and with a vibration galvanometer as indi-
cating instrument. The method employed in this experiment con-
sisted in first measuring the magnitude and phase of the primary
current, and then the magnitude and phase of the voltage in the
secondary winding. The difference between these two phases, sub-
tracted from 90°, gives the required angle of magnetic flux lag. Bal-
ance was in each case indicated by getting a zero deflection of the
vibration galvanometer. This method gave 12.5° as the angle by
which the flux in the telephone lags behind the magnetising current.

The three values obtained by direct measurement for the flux lag,
which should be the angle @ according to the theory above proposed,
are 11°, 11.5°, and 12.5°; whereas half the depression angle, for this
telephone, which, according to the theory, should also be the angle £,
is 13.2°. The agreement is not as good as might be desired for a
perfect confirmation of the proposed theory; but in view of the diffi-
culty of measuring small angles of lag in circuits containing voltages
of the order of 0.1 volt, and in view of the fact that the experimental
telephone receiver constructed for this purpose had to be complicated
by auxiliary secondary windings and also unfortunately had a dia-
phragm mounted in such a way as to have a very large temperature
coefficient of vibration period, which rendered difficult an accurate

150 PROCEEDINGS OF THE AMERICAN ACADEMY.

determination of the points of the circular graph, the writers believe
that the departure of a degree or two in the value of β, as obtained
by direct measurement from its value as obtained by the circular
graphs, is not unsatisfactory.

VII. Summary or REsutts.

1. The resistance and inductance of several telephone receivers
were measured over a wide range of frequencies with their diaphragms
both free and damped.

2. The damped resistance is approximately a quadratic function
of the angular velocity of impressed e. m. f. (see equations (1) and (2) ).

3. Although the damped resistance and the damped inductance
both change with the frequency of e. m. f., their product is approxi-
mately constant, independent of the frequency, over a considerable
portion of the range of audible frequencies (see eq. (3) and (4) and
Table VII).

4. The damped reactance of one form of standard bipolar Bell
receiver is approximately equal to its damped resistance, over a con-
siderable range of frequency; so that the current lags the e. m. f. by
45° (see Figure 2).

5. The free resistance and reactance of telephone receivers go
through marked changes with changes in frequency of constant e. m. f.
in the neighborhood of the natural frequency of their diaphragms
(cf. Figures 4-6).

6. The motional resistance and motional reactance (by which is
meant excess of free resistance of reactance over damped resistance
or reactance) conform accurately to certain simple laws as follow:

I. The motional reactance plotted as ordinates against the
motional resistance as abscissas, as the frequency of constant
impressed e. m. f. is changed from zero to infinity, gives a
circular locus, with various interesting characteristics
(cf. Figures 7-12).

II. The rectangular plots of motional reactance and motional
resistance against angular velocity of constant impressed
e. m. f. give curves somewhat analogous to the curves of
index of refraction and absorption of light in an optical
medium in the neighborhood of an absorption band (¢f.
Figures 4-6).

7. The power taken by a telephone receiver when sounding at 0.3
volt applied voltage may exceed by 68% the power taken from the

KENNELLY AND PIERCE. — TELEPHONE RECEIVERS. Τ51

same 6. m. f. when the diaphragm is damped (Figures 4—7 and Tables
ΥΠ|-Χ).

8. A theoretical explanation of the phenomena is given, and com-
putations are submitted in comparison of experiment and theory
(Headings V and VI).

9. The vibration constants of the diaphragms of the several re-
ceivers are deduced and collected (Table XI).

Harvarpb UNIVERSITY, CAMBRIDGE, Mass.
Juuy 16, 1912.

Proceedings of the American Academy of Arts and Sciences.

Vou. XLVIII. No. 7.—SeEpremsBer, 1912.

CONTRIBUTIONS FROM THE CRYPTOGAMIC LABORATORIES
OF HARVARD UNIVERSITY.—No. LXIX.

NEW OR CRITICAL LABOULBENIALES FROM THE
ARGENTINE.

By Rouanp THAXTER.

CONTRIBUTIONS FROM THE CRYPTOGAMIC LABORATORIES
OF HARVARD UNIVERSITY. — No. LXIX.

NEW OR CRITICAL LABOULBENIALES FROM THE
ARGENTINE.

By RoLanp THAXTER.
Presented April 10, 1912. Received July 28, 1912.

THE rapid accumulation during the past six years of Laboulbeniales,
which have come to me from various parts of the world and now
include some hundreds of new species and genera, has forced me to
abandon my intention to figure all new forms as they were published;
and it has again become necessary to resort to preliminary diagnoses,
a third series of which is entered on with the present paper. It is,
however, my purpose to illustrate all the species described in this
series as soon as the necessary figures can be prepared and published.
The exotic material which is now available is not only very varied,
but is in far better condition than that which has formerly been
obtained from dried specimens of insects, for the reason that a majority
of the hosts have been collected directly into alcohol and the parasites
removed before drying.

The examination of large series of forms in good condition has
inevitably led to some modification of my views in regard to the limita-
tions of certain genera and species, and while it has in some instances
made clearer relationships or differences that were formerly in doubt,
it has at the same time served to break down distinctions which were
formerly regarded as more or less crucial, so that it has seemed best
to modify the treatment of certain genera and species. Thus in the
present paper, the limits of Corethromyces, for example, are consider-
ably extended to include several genera hitherto kept distinct, and
other changes will be noticed applying both to species and genera,
which have seemed advisable in the light of a more complete knowledge
of numerous forms.

The materials here considered were collected in Argentina, chiefly
in the Buenos Aires region, the host insects having been captured

156 PROCEEDINGS OF THE AMERICAN ACADEMY.

for the most part by myself in the Parque 3-de-Febrero, at Palermo,
a suburb on the river above Buenos Aires: in the grounds of the
Escuela Regional de Santa Catalina near the station of Llavallol,
where a small planted wood of various trees affords a good collecting
ground already familiar to mycologists, by name at least, from the
large number of fungi collected there and described by Prof. Carlos
Spegazzini, to whom I am much indebted for guiding me to this
locality as well as to the Isla de Santiago near La Plata, where I spent
two days collecting. Many hosts were also obtained in the grounds
of the Quinta Mackern, at Temperley, a town about ten miles south
of Buenos Aires, where I spent several weeks in the spring of 1906.

To Dr. Propile Spegazzini I am greatly indebted for numerous
miscellaneous beetles which he kindly collected for me at La Plata
and in Tucuman, both during my visit and after my return to the
United States: to the Director of the Museo Nacional at Buenos Aires,
and to Dr. J. Bréthes I am under obligations for various courtesies
and for the privilege of examining the entomological collections of the
Museum. For the determination of certain of the hosts I am indebted
to Mr. Samuel Henshaw, Dr. Fenyes, Dr. Max Bernhauer, M. Pic,
Dr. Malcolm Burr, Dr. Erno Csici and Col. Casey. To all these
gentlemen I desire to express my appreciation of their kindness in
thus assisting me.

With the exception of perhaps a half dozen species, of which the
material is either too scanty or not in condition for description, the
following enumeration includes all the forms obtained. As will be
seen, a majority of them are hitherto undescribed, but it has seemed
desirable also to append a list of the species obtained which are
already known, and are listed below in alphabetical order. Of these
there are in all forty-nine species, while of the new forms sixty-eight
are included, with nine new generic types.

Dimeromyces Anisolabis nov. sp.

Male individual, quite hyaline. Receptacle consisting of four
superposed cells obliquely separated, except the upper; the basal
subtriangular, larger than the two subequal cells above it, of which
the upper always bears an antheridium, while a second may often
arise from the cell next below it. The antheridia rather stout and
short, the venter and stalk-cells about as long as the abruptly dis-
tinguished stout neck, which is bent abruptly outward distally.
Appendage consisting of three superposed cells subtended by a more

THAXTER.— ARGENTINE LABOULBENIALES. 157

or less conspicuous somewhat prominent red-brown septum; the tip
of the appendage hardly extending to the tip of the antheridium.
Total length to tip of antheridium, including foot (7 4), 58m. Ap-
pendage 20 μ. Receptacle, exclusive of foot, 18-20. Antheridium,
including stalk-cell, 31 Χ 8 μ.

Female individual, almost hyaline, the perithectum becoming
faintly yellowish. Receptacle consisting of five successively smaller
cells superposed obliquely, except the uppermost which subtends the
primary appendage, and from which it is separated by a red-brown
septum, the subterminal cell also bearing a similar somewhat larger,
usually five-celled appendage, distinguished from its small subtending
cell by a red-brown septum; the subbasal cell of the receptacle bearing
a still larger appendage, the somewhat irregular subtending cell of
which projects on its inner side and is distally and externally separated
from the slightly divergent and inflated portion of the appendage by a
narrower deeply blackened isthmus, which includes a portion of the
subtending cell, and more than half of the basal cell of the appendage
proper. Perithecium usually single, a second rarely developed from
the terminal cell of the receptacle, arising between its two appendages;
long slender slightly enlarged distally, the tip not clearly distinguished,
tapering slightly, inflated at the apex. Perithecia 75-100X14 μ.
Receptacle, exclusive of foot, 25-30X20y. Primary appendage
about 40 μ. Lowest appendage, including its subtending cell, 60-70 μ.
Total length to tip of perithecium, including foot, 100-150 μ.

On the inferior surface of the abdomen, near the tip, of Anzsolabis
annulipes Luc., Palermo, No. 1682.

This species is very closely allied to D. Forficulae, and may prove
only a variety, although the abundant material does not indicate
that the form is variable. The male is most readily distinguished by
the presence of only one suffused septum in its appendage, as well as
by its shorter stouter form and outcurved antheridial necks. The
two appendages arising in the female of D. Forficulae from the terminal
cell of the receptacle, are replaced by only one, and the character of the
lower appendage, and the form of the perithecium are also different.
A third closely allied form is known to me from the Amazon region.

Dimeromyces Corynitis nov. sp.

Male individual, straw-yellow, the receptacle straight, or but slightly
curved, consisting of a single series of from three to eight superposed
cells, the basal usually larger; the rest small, broader than long, all

158 PROCEEDINGS OF THE AMERICAN ACADEMY.

bearing antheridia and separated by horizontal, or but slightly
oblique, septa; the series terminated by a unicellular mitriform
appendage, somewhat variably inflated, symmetrical, broader than
the axis which it terminates. Antheridia nearly horizontal, straight,
two to seven in number, arising on one side in a single series from all
the cells of the receptacle except the basal, their stalk-cells relatively
long, sometimes exceeding in length the body of the antheridium,
which is short and broad, the discharge tube short, straight and stout.
Total length (including foot, 16 μὴ) about 50-609 uw. Appendage-
cell 14-20 10-12 uw. Antheridia about 35 μ, the stalk-cell 9-186 μ,
the venter 10X12 μ.

Female individual, pale straw-yellow. Receptacle similar to that
of the male, consisting of four or five superposed cells terminated by
a mitriform sterile appendage-cell, the cell immediately below it
usually giving rise laterally to an erect, or slightly divergent, appen-
dage of usually five or six successively smaller somewhat inflated
cells; the first perithecium usually arising from the cell next below,
one or two more perithecia rarely developed from the cells immediately
below the first. Perithecium usually solitary, relatively large, its
axis nearly at right angles to that of the receptacle or curved upward
from it; usually slightly broader distally, the tip not clearly dis-
tinguished, the apex blunt, slightly suleate. Spores (in perithecium)
609 uw. Perithecium 150-215) 380-40 u, the sporogenous portion
100-135 p. Appendage 60-1008 yw. Receptacle to tip of primary
appendage-cell, including foot, 80-100 μ.

On the elytra of Corynites ruficollis Fabr., La Plata, No. 1459.

A clearly distinguished species, most readily recognized by its
mitriform sterile appendage-cell. Both sexes appear to grow ap-
pressed on the elytra, the antheridia and perithecia projecting upward
nearly at right angles.

Dimorphomyces Meronevae, nov. sp.

Male individual, relatively large, nearly hyaline, or with faint
reddish brown suffusions at the base of the appendage. Basal cell of
the receptacle rather large, subtriangular, distally in contact with the
outer half of the wedge-like base of the long antheridial stalk-cell;
somewhat obliquely separated from the squarish subbasal cell; the
appendage relatively short, not extending beyond the base of the neck
of the antheridium, its basal cell rounded, somewhat longer than
broad, sometimes nearly as large as the whole receptacle and dis-

THAXTER.— ARGENTINE LABOULBENITALES. 159

tinguished from it by a marked indentation, distally narrower below
the small squarish subbasal cell the terminal cell cylindrical, hyaline.
Antheridium large, its slender stalk-cell as long as the inflated venter,
the neck somewhat shorter than the stalk and venter combined, and
slightly curved. Receptacle including foot, 40X23 u. Appendage
17 wu. Antheridium 32-35 uw; neck 15 μ, venter 10 μ, stalk-cell 9 μ.

Female individual. Receptacle relatively small, the subbasal cell
larger than the basal (without its secondary extension), squarish,
distinguished by a deep indentation from the basal cell of the appen-
dage which is subequal, tinged with vinous brown, and rounded in
form; the rest of the appendage bent strongly to one side, more
deeply suffused, small, blunt or pointed, its two cells not distin-
guishable. Perithecium relatively large and long, the region below
the tip conspicuously suffused with vinous brown, its inner margin
concave, the tip hardly distinguished, more faintly suffused, somewhat
asymmetrical, as is the hyaline blunt apex; the rest of the perithe-
cium slightly inflated above, more faintly suffused, except the narrow
hyaline base. Secondary appendages subcylindrical, somewhat less
than half as long as the perithecium, two-celled, the basal cells thick-
walled, about half as long as the thin-walled blunt terminal cell.
The secondary receptacle narrow, horizontal, or nearly so; its four
to eight cells bordered by the narrow extension of the basal cell of the
receptacle, the one to three erect perithecia and the appendages
rising vertically from it. Perithecia 65-70X12-15 uw. Spores (in
perithecium) 141.5 uw. Receptacle, including foot, 18 u. Sec-
ondary receptacle 18-35 yw. Primary appendage 18X9 u.

On the legs of Meroneva Sharpi L. A., Temperley, No. 1503, in
company with Monoicomyces nigrescens.

A very clearly marked species which was found but once, and is
described from four pairs of mature individuals.

Dimorphomyces verticalis nov. sp.

Male individual, relatively small, tinged with blackish brown, the
basal cell small, very obliquely separated from the slightly longer
narrower subbasal cell which extends downward nearly to its base,
and upward to the end of the stalk-cell of the usually single antheri-
dium, which is erect, the venter but slightly inflated; with the short
rather stout hardly tapering neck abruptly distinguished. Appendage
parallel to the antheridium, or but slightly divergent, consisting of
three cells: the basal longer than broad, and distally rounded to the

160 PROCEEDINGS OF THE AMERICAN ACADEMY.

very small much narrower squarish subbasal cell; the terminal cell
hyaline elongate slightly inflated below, tapering distally; sometimes
extending to or beyond the tip of the antheridium. ‘Total length,
including foot, 60 wu. Antheridium, including stalk-cell, 35 μ; its
neck 8 uw. Appendage, 20-30 μ.

Female individual, becoming dark blackish brown, the primary
appendage erect, consisting of a larger basal cell hardly twice as long
as broad, a narrower subbasal cell broader than long, and a terminal
cell, hyaline or paler distally, longer than broad, inflated or degenerat-
ing. Perithecia usually not exceeding three in number, elongate,
straight or curved, blackish brown, very slightly inflated; the tip
bluntly rounded, or asymmetrical and snout-like, when viewed later-
ally: the hyaline apex subtended, on the inner side, by a darker shade.
The secondary appendages of two or three superposed cells, hardly a
third as long as the perithecia, alternating with them, or somewhat
irregular in position, especially above; the series of cells which bears
them, and the marginal extension of the basal cell of the receptacle
nearly erect, or diverging from the appendage at an angle of not more’
than 45°. Perithecia 75-100 15-20 uw. Secondary appendages 25-
30 uw. Total length to tip of highest perithecium 100-200 y; to tip
of secondary receptacle 75-120 μ.

On Atheta sp., Palermo, Nos. 1690, 1965, and 1966.

This species, which was found not infrequently, appears to vary
considerably; the older and better developed individuals becoming
very dark, and attaining a considerable size. Such individuals,
which usually occur on the abdomen, do not appear to be separable
from smaller and paler forms which occur, usualiy, on the legs, an-
tennae and head.

Rickia Lispini nov. sp.

Receptacle short and stout, the basal cell small, hardly longer than
broad; the main body consisting of a central cell lying between a pair
of marginal cells superposed on either side of it, the two lower united
below it and separating it completely from the basal cell; while its
extremity lies in oblique contact with the lower half, or less, of the
perithecium; the upper marginal cell on one side cutting off one to two
small appendiculate cells which subtend the base of the perithecium;
the upper marginal cell on the opposite side, bearing two or three
to six simple appendages, their origins often lying nearly horizontally,
one to five of them arising from single small cells successively separated

THAXTER.— ARGENTINE LABOULBENIALES. 161

from above downward (within outward), one, however, always sub-
tended by two minute cells placed not always next the perithecium,
and representing the primary and originally terminal appendage.
Perithecium short and stout, but slightly longer than its contained
spores, subellipsoid to ovoid, the tip hardly distinguished, the apex
truncate-papillate. Spores 28X4u. Perithecia 40-50 27-31 μ.
Receptacle 60-75 X 28-35 μ. Appendages 20-55 μ. Total length
75-120 μ, average 90-100 μ.

On the abodmen ete. of Lispinus tenellus Er., Llavallol No. 1502.
Also from Los Amates, Guatemala, No. 1625 (Kellerman).

Were it not for the fact that the genus Rickia, as illustrated by the
material accumulated from various parts of the world, proves to be
a large and very varied one, I should be inclined to separate the present
form under a special generic name; and, although it seems best to
treat it as a very simple type of Rickia, it differs from all others in the
fact that all its appendages come from the two distal marginal cells.
In a few specimens I have seen a structure associated with the appen-
dages which may be an antheridium; but, in a majority of individuals
these organs seem to be quite absent. This appears to be the case
also in other and more typically developed species of the genus.

Rickia Melanophthalmae πον. sp.

Hyaline. Perithecium long-ovoid, with a broad truncate apex
which may be flat or slightly suleate, the lumen of the basal wall-cells
obliterated, their thick walls forming an ellipsoid cavity in which the
spores, which nearly equal it in length, lie somewhat obliquely, and
above which the three upper tiers of small subequal wall-cells persist.
Receptacle broad and compact, multicellular above the single basal
cell; the cells in three vertical series, two lateral and one median; one
of the outer consisting of a single somewhat elongated cell, which may
rarely be divided into two or three cells, above which lie the three
visible basal cells of the perithecium, which are subequal and form an
integral part of the receptacle in no way distinguished from it; the
marginal series on the opposite side consisting of two to four cells,
usually rather narrow, each usually cutting off a small cell obliquely,
distally and externally, the uppermost subtending a hardly distin-
guishable antheridium, the rest developing neither appendages nor
antheridia and often becoming wholly obliterated; the series termi-
nated by a small cell which bears the small short stout primary append-
age of the usual type; the median series consisting of three superposed

162 PROCEEDINGS OF THE AMERICAN ACADEMY.

cells, the two lower larger, the upper lying beside the base of the
perithecium. Perithecium 35-4323 4. Spores about 40X2.5 μ.
Receptacle 4027-31 u. Total length 75-85 μ.

On the elytra of a minute beetle belonging to the genus Melanoph-
thalma. Llavallol, No. 1980.

This curious little form is distinguished by the apparent absence
of any secondary appendages, the cells which are separated to subtend
them in other species, developing nothing more than mere rudiments,
and often becoming quite obliterated by the general enlargement of the
receptacle, the cells of which may become somewhat displaced. On
the perithecial side the usually single marginal cell cuts off no subtend-
ing cell even when it becomes divided. Like the preceding species
this form is distinctly aberrant.

Monoicomyces Caloderae nov. sp.

Straw-colored, the perithecia and older appendages becoming tinged
with amber-brown. Basal cell of the receptacle stout, squarish, the
subbasal cell less than half as large, pale straw-colored or nearly
hyaline. Primary appendage concolorous with the receptacle,
elongate, its tip often extending above the tips of the perithecia;
tapering slightly to a blunt extremity, simple or usually producing
one or two branches from the third or fourth cells on the inner side.
The two primary fertile branches variously complicated by successive
proliferation of the secondary branches, the branchlets of which may
be of the second or even the fourth order, the perithecia subtending
the antheridia. Antheridium of the usual type, its tiers and append-
ages somewhat variably developed, but resembling in general those
of M. Homalotae. Perithecia rather short and stout usually symmétri-
cal, inflated below, conical above; the apex small, blunt; the basal
cell-region not distinguished from the ascigerous region; the stalk-cell
well defined, its basal half usually slightly constricted and suffused
with vinous amber-brown. Spores 38X4yu. Perithecia, including
basal cell-region, 80-90 30-35; the stalk-cell 25X12 4. Receptacle
about 25X20y. Primary appendage 150-175. Appendages 75-
100 uw. Antheridium 90 X 35 μ.

Usually on the abdomen of Calodera sp. Nos. 1504, 1515, 1691
and 1991, Palermo, Temperley and Llavallol.

Although very common this species is seldom if ever found in good
condition, perhaps owing to certain peculiar habits of its host. The
appendages are usually broken off entirely and the development of

THAXTER.— ARGENTINE LABOULBENIALES. 163

the fertile branches may be very irregular. Although perhaps a dozen
perithecia may be formed on a single individual, many are apt to be
broken and but few ever mature. The species is most nearly allied to
H. similis and H. Homalotae from both of which it is distinguished by
the character of its primary appendage and by the proliferous habit
of its fertile branches. The genus of the host has been determined
by Dr. Fenyes.

MOoNOICOMYCES INFUSCATUS Speg.

Receptacle very small, the basal cell becoming more or less suffused
with smoky brown, broader than long, the hyaline subbasal cell
hardly distinguishable. Primary appendage stiff rigid upcurved,
black externally from its base upward, simple or producing a single
branch above its subbasal cell which may be similarly blackened.
Fertile branches usually producing a single perithecium and antheri-
dium, more rarely two by proliferation, suffused, especially externally,
with blackish olive-brown; the two distal tiers forming a well defined
rounded enlargement, terminated by two erect blackened rigid
appressed hyaline-tipped appendages. Perithecium hyaline or faintly
olivaceous, slightly asymmetrical, subfusiform, the tip hardly dis-
tinguished, the apex blunt, the narrower basal cell region not dis-
tinguished, the basal cells relatively large, the stalk-cell short and
broad, not abruptly distinguished below the basal cell-region. Spores,
in perithecium, about 20X2.7 uw. Perithecia 90X26 μ, the stalk-cell
18X12 uw. Antheridium 45-70 μ, its appendages 45-70 μ. Primary
appendage with its branches, 110 u. Receptacle 18X12 μ.

On the abdomen of Xantholinus Andinus Fauv., No. 1689, Palermo,
No. 1988, Llavallol.

A small and apparently rare species, very closely allied to M.
nigrescens and distinguished especially by its rigid black primary
appendage.

Mimeomyces nov. gen.

Receptacle consisting of two superposed cells, the upper bearing
terminally the single appendage and the stalk-cell of the single peri-
thecium. Appendage consisting of a basal cell and several cells
superposed above it, the lower bearing single free compound antheridia
on the inner side, the upper bearing sterile branches. The antheridia
consisting of a group of apparently six similar antheridial cells and
originating directly from the slightly swollen extremity of a short

164 PROCEEDINGS OF THE AMERICAN ACADEMY.

stalk-cell and discharging at the same level into the efferent tube.
Perithecia stalked and normal.

_ The characters of this genus correspond exactly to those of Core-
thromyces Quedionuchi which occurs with it on the same host, and in
general to that section of Corethromyces formerly separated under
Sphaleromyces, except that the lower branches of the appendages
bear conspicuous, typically developed compound antheridia. It
seems altogether probable that certain of the species hitherto placed
in Sphaleromyces, and in which the presence of antheridia has not
yet been definitely recognized, may find a place in the present genus
when their antheridial characters are known. A careful reexamination
of my material of these species has, however, failed to show any indi-
cation of the conspicuous antheridia which occur in the present
instance.

Mimeomyces decipiens nov. sp.

Perithecium pale translucent yellowish, the basal cells relatively
large and clearly distinguished, the ascigerous part usually bent
slightly toward the appendages, distally slightly inflated, symmetrical,
conical; the tip hardly distinguished, terminating in a small sub-
truncate apex: stalk-cell short, broader than its length. Basal cell
of the receptacle elongate, rather abruptly broader distally, con-
colorous with the perithecium or more or less deeply and completely
suffused with blackish brown, sometimes quite opaque; the subbasal
cell small, subtriangular. Appendage consisting of from four to five
obliquely superposed cells, subequal in length, the distal ones smaller,
the basal without appendages, the subbasal and often the cell above
it bearing each a single compound antheridium on a short stalk-cell.
Perithecium (sporogenous portion) 55-65X 24 yw, including basal and
stalk-cells 75-95 uw. Main appendage 50-55 yu, its longest branches
60 uw. Receptacle 50-70 μ, basal cell (longest) 60 u. Total length to
tip of perithecium 125-150 uw. Spores about 302.5 (measured in
ascus).

On legs and abdomen of Quedius sorecocephalus Bernh. (nov. sp.),
Llavallol, No. 1520.

The general form and coloration of this species is very similar to that
of Corethromyces Quedionucht which may occur with it, but the color
and the form of the tip of the perithecium, as well as the conspicuous
antheridia distinguish it at a glance. One or more accessory anther-
idia are sometimes present near the base of the appendage. The host
has been determined as a new species of Quedius by Dr. Bernhauer.

THAXTER.— ARGENTINE LABOULBENIALES. 165

Cantharomyces permasculus nov. sp.

Perithecium becoming dark amber-brown with a smoky tinge,
subsymmetrical, or usually straighter externally with the inner margin
somewhat convex, broadening distally; the short pale rather abruptly
subconical tip usually bent outward, the pore subterminal and ex-
ternal, an inner lip-cell forming the small papillate rounded apex:
the basal cell region not distinguished, the basal cells extending up
about the ascogenic region; the stalk-cell consisting of an upper sub-
triangular portion, distinguished more or less abruptly by a variably
developed constriction from its narrower basal portion, which may
equal the distal part in length, and is somewhat obliquely inserted on
the receptacle. Receptacle more or less deeply tinged with dirty
amber-brown, the basal cell nearly straight and variably elongated, as
is the more deeply colored subbasal cell, the base of which is modified
by an annular prominence of darker color. Appendage becoming
somewhat divergent and curved away from the perithecium, the axis
of which coincides in general with that of the receptacle, consisting of
five or six superposed cells, the basal one sterile and modified distally
by an annular darker ridge similar to that at the base of the subbasal
cell of the receptacle, the two to four cells immediately above it
becoming compound antheridia, the uppermost or the two uppermost
of which may bear a usually simple branch distally, or a pair of such
branches arising from opposite sides; the several terminal cells of the
appendage bearing distally usually two simple opposite branches
which greatly exceed the tip of the perithecium. Perithecia 135-160
40-50 μ, the stalk-cell 45-60 uw. Spores 70-75X4 uw. Receptacle
100-155X40 yw. Main appendage 200-275 μ, its longer branches
250 uw. Total length to tip of perithecium 275-875 μ.

On a large species of Parnus, commonly on the elytra. Palermo,
No. 1686.

This species is readily distinguished from the following by the form
and color of the perithecium and its short stalk-cell, by the annular
prominences of the receptacle and appendage, which are without
striations, by its usually more elongate straight receptacle the axis
of which coincides with that of the perithecium, not of the appendage
as in (Οὐ. Bruchi, and by its much more highly developed appendage,
which may produce more antheridial cells than are known in any other
of the Laboulbeniales. In its antheridial characters this species, as
well as its ally, depart distinctly from the usual type of Cantharo-
myces, which possesses but one antheridium. It should not be sepa-

166 PROCEEDINGS OF THE AMERICAN ACADEMY.

rated, however, and is connected with the more normal type by a
species, as yet undescribed, which occurs on Parnus in north tem-
perate regions. Sufficient material of both species in good condition
has been examined and leaves no doubt as to their distinctness.

Cantharomyces Platensis nov. sp.

Perithecium subsymmetrical, more or less tinged with amber-brown,
the venter somewhat inflated above its base and more deeply suffused,
the distal portion subconical tapering to a rather broad blunt apex,
the basal cells small, the outer extending somewhat upward, the region
not distinguished from the body of the perithecium; the stalk-cell
but slightly suffused, straight erect somewhat divergent from the ap-
pendage, the axis of which coincides with that of the receptacle, as
long as, or much longer than, the body of the perithecium, the distal
end contrasting with and as broad or broader than the darker base of
the perithecium; from which it is separated by a horizontal septum
more deeply suffused and often abruptly narrower, or distinguished
by a pseudo-articulation where it is inserted on the receptacle. The
receptacle somewhat darker amber-brown, its basal cell irregularly
triangular, geniculate, the subbasal cell usually hardly longer than
broad, an annular secondary wall extending around its base and
marked by very fine vertical striations. Appendage straight, erect;
its basal cell concolorous with the receptacle, its base broad somewhat
oblique; the whole cell broader than long, distally modified like the
base of the upper cell of the receptacle, and with the same longitudinal
striations; usually not more than two of the cells immediately suc-
ceeding it, squarish and modified to form antheridia, and succeeded
by two or three narrower superposed cells all of which may bear a
single erect straight branch; the terminal one often furcate, the
branches short or sometimes extending as far as the tip of the peri-
thecium. Perithecia 125-180. . 892-44 μ, its stalk-cell 135-235 25-
35. Spores 60X4u. Receptacle 60-75 35-40 wu. Main append-
age 110-135, its longest branches 200 μ. Total length to tip of
perithecium, about 400μ (350-470 μ).

On the elytra of a smaller species of Parnus ?, Palermo, No. 1685.

This species differs from the preceding in its long-stalked more
slender perithecium, in its shorter receptacle and appendage, in the
smaller number of its antheridia which are never appendiculate, and
in the striation and absence of elevation which characterises its
peculiar annular secondary walls. Closely allied to C. Bruchi Speg.
which is half as large and otherwise different.

THAXTER.— ARGENTINE LABOULBENIALES. 167

Amorphomyces Ophioglossae nov. sp.

Male individual, relatively long and slender, nearly straight, the
basal and subbasal cells nearly equal, the antheridial cell as long as
both combined. The subbasal cell deep reddish brown, contrasting
with the hyaline basal cell and the straw-yellow slightly asymmetrical
antheridium, the neck of which is about as long as the symmetrically
inflated venter. Total length, including foot, 55-655 μ, the antheri-
dial cell 28-32 X 6-7 uy.

Female individual. Basal cell hardly longer than broad, hyaline;
its base slightly broader, contrasting with the deep red-brown base
of the perithecium above it; the short deeply suffused stalk-cell, and
the minute basal cells of the perithecium hardly distinguishable at
maturity: the body of the perithecium pale straw-yellow, short,
stout; the inner margin straight or concave; the outer strongly con-
vex, tapering from near the middle about equally to the base and apex;
the latter broad, flat or somewhat rounded, subtended externally by a
reddish brown suffusion, the short tip often slightly bent outward,
giving it a snout-like habit. Basal cell 8X8 yu. Total length, includ-
ing foot (7-11 μ), 100-120X30-35 μ.

On the head and tip of abdomen of Ophioglossa sp. Llavallol, No.
1500, and Tucuman, No. 1935, (P. Spegazzini).

A common species at Santa Catalina.

Amorphomyces rubescens nov. sp.

Male individual. Basal cell hyaline, somewhat longer than broad;
subbasal cell red-brown, hardly longer than broad; antheridium
relatively large, at least twice as long as the two basal cells combined,
exclusive of the foot; the venter shorter than the neck, prominent
distally on one side, tinged with red-brown below, slightly inflated;
the neck erect, clear reddish straw-color. Total length, including
foot, 65 u. The two basal cells 16-18X6 μ. Antheridium 35-379 μ,
the neck 19-20 μ.

Female individual, relatively slender, the basal cell broader than
long, smaller than the foot, hyaline, contrasting. The perithecium
tinged throughout with reddish brown, the suffusion deep at and
toward the basal and stalk-cells, the latter somewhat shorter than the
relatively long narrow basal cells above it. The body of the perithe-
cium straight, relatively narrow, subsymmetrically and_ slightly
inflated, the apex broad, slightly rounded, the tip asymmetrical or

168 PROCEEDINGS OF THE AMERICAN ACADEMY.

bent outward. Basal cell 7X94. Total length, including foot, 140—
165X 25 μ.

On the abdomen of Diestota sp. Temperley, No. 2007, and Llavallol,
No. 1498 on Homalota sp., the genera doubtfully determined by Dr.
Fenyes.

Tetrandromyces nov. gen.

Male individual consisting of four superposed cells the uppermost
bearing a crown of four simple antheridia.

Female individual. General structure as in Dioicomyces.

Although the perithecium of the female in this genus is unlike that
of any of the species of Dioicomyces in external form, it corresponds
to this type almost exactly in other respects, so that the genus is
based upon the characters of the very peculiar male individual, in
which the antheridia are not only grouped, but of a distinctly different
type from those of Dioicomyces, recalling those of Synandromyces or
of some species of Stigmatomyces.

Tetrandromyces Brachidae nov. sp.

Male individual stout, faintly suffused with brownish olive, basal
cell nearly hyaline, longer than broad, the three cells above it subequal
or successively smaller, the distal cell triangular or otherwise shaped
according to the point of view. Antheridial cells as large as the basal
cell, the stout suberect and subsymmetrically arranged brown necks
but slightly curved. Antheridia 238 y, the group 164 wide. Total
length including foot 60 μ.

Female individual. Receptacle faintly yellowish, the basal cell
small, about as long as broad; the subbasal cell triangular; minute
but clearly distinguished; the subtending cell of the appendage narrow,
oblique, the terminal cell stout, distally rounded, deep black-brown.
Perithecium relatively very large, the stalk-cell rather short and stout,
faintly yellowish; the basal cell and basal wall-cell regions not dis-
tinguished externally, and forming an evenly slightly inflated base,
or the external basal cell forming a rounded slightly blackened promi-
nence; the second tier or wall-cells marked by a slight inflation
distally, not distinguished from the slightly asymmetrical dome-
shaped region of the third tier, above which the short and abruptly
narrower tip is abruptly distinguished, being subtended by the slightly
elevated blackened insertion of the trichogyne; the hyaline apex
slightly asymmetrical, bluntly rounded or slightly pointed, subtended

THAXTER.— ARGENTINE LABOULBENIALES. 169

by two rounded tooth-like prominences from two adjacent wall-cells
of the terminal tier. Spores, in perithecium, male 28-304-5 μ,
female about 40 uw. Perithecia 200-235 50-65 μ, the subterminal
prominence 8 yu long, the stalk-cell 60X20 yw. Sterile appendage-cell
20X12 4. Total length to tip of perithecium 250-280 μ.

Near the tip on the superior surface of the abdomen of Brachida
Reyi Shp., Llavallol, No. 1989.

Although in fully matured turgescent individuals the distinction
between the basal cell and basal wall-cell regions becomes obliterated,
the basal cells, especially the external one, may be distinctly promi-
nent in younger or partly collapsed individuals. The ascogenic cell
produces great quantities of asci and spores, unlike the forms of
Dioicomyces. The general form of the perithecium recalls that of the
conventional “fat pig.” The host has been determined for me by
Dr. Fenyes.

Dioicomyces Formicellae nov. sp.

Male individual rather slender, the foot-cell slightly broadened,
blackish or concolorous with the basal cell of the receptacle which is
grey brown and usually separated from it by a hyaline line; basal
cell a little more than twice as long as broad; the subbasal usually
nearly square; the third cell shorter; the antheridial cell somewhat
longer than broad; the neck terminal at one side, slender slightly
bent. Total length including foot and neck 60-70 u; basal cell 20
8 μ.

Female individual variously curyed, sometimes sigmoid, sometimes
curved throughout, or the perithecium alone somewhat bent. Basal
cell of the receptacle hardly longer than the foot, suffused with brown,
the subbasal cell almost obsolete; the sterile appendage-cell short,
rounded distally, tinged with brown. Perithecium large, yellowish
brown, deeper at the tip and in the middle, strongly curved; the
successive wall-cells on the convex side distinguished by slight eleva-
tions and depressions, the third wall-cell on the concave side slightly
elevated; the venter somewhat inflated; tapering slightly to the
coarse bluntly rounded or roughly truncate apex; the basal celi
region sometimes abruptly narrower or not distinguished; the stalk-
cell elongate, narrower at its base, tinged with yellowish or brownish.
Spores, male 355 μ, female 40-428 yw. Perithecia 145-165 45-
50 μ; stalk-cell 140-18025 μ. Receptacle, including foot and
appendage-cell, 40-65 μ.

On the elytra of Formicella strangulata Pic, Palermo, Llavallol,
and Temperley, No. 1692.

170 PROCEEDINGS OF THE AMERICAN ACADEMY.

Although its host was very common in the Buenos Aires region,
this species was seldom met with. It is the largest species of the
genus thus far described, but is otherwise without striking peculiari-
ties.

Dioicomyces malleolaris nov. sp.

Male individual, consisting of three superposed cells and a terminal
antheridium, relatively small and stout; the basal cell nearly hyaline,
twice as long as broad, the subbasal cell but slightly longer than
broad, the third cell much shorter than broad; the antheridium
relatively large, slightly suffused, distally somewhat asymmetrical,
the well developed neck terminal at the side. Length about 45x
ΤΠ) Γῆς

Female individual, hammer-shaped: the basal cell of the receptacle
very small, suffused with blackish brown; the subbasal minute, flat;
the appendage-cell blunt-conical, faintly yellowish. Perithecium
horizontal, its upper outline straight; the axis of its main body lying
at right angles to that of the long, very thick-walled, slightly curved
stalk-cell, the lumen of which may be nearly obliterated; the position
of the basal cells and basal wall-cells so abnormal that the rounded
ascigerous region projects free on one side corresponding to the free
tip which projects somewhat further on the other; the whole supported
by two cell-series that diverge abruptly from the end of the stalk-cell;
on one side, as seen laterally, consisting of two basal cells, on the other
of one basal and two squarish wall-cells; the whole including the
stalk-cell more or less suffused with pale smoky yellowish brown;
the tip tapering slightly to a blunt slightly asymmetrical apex. Spores
28-30X3.5 uw. Perithecia 99-100 26-32 uw. Stalk-cell 65-90 16 μ.
Appendage cell 15-16 u. Receptacle including large foot 28 μ.

On the tip of usually the right elytron of Anthicus parvus Pie,
Palermo and Llavallol, No. 1513.

This very curious and rather rare species grows more or less ap-
pressed, the perithecium lying at right angles to the axis of the elytron.
Like all the species of the genus herewith described, the spores begin
to germinate normally before discharge and are twice septate when
they emerge, with a well developed black foot.

Dioicomyces umbonatus nov. sp.

Male individual almost hyaline or faintly yellowish brown externally,
rather slender, straight or slightly curved inward, the basal cell as

THAXTER.— ARGENTINE LABOULBENIALES. 171

long as the portion above it; the foot small, the subbasal cell slightly
larger than the cell above it, the antheridial neck usually erect, rela-
tively long. Basal cell, including foot, 204. Total length to base
of neck 35X5 uw. Neck 12 μ.

Female individual dirty straw-colored with a brownish tinge, the
perithecium and the outer margin of the receptacle and appendage
becoming somewhat darker. Basal cell of the receptacle larger than
the foot, the subbasal flattened, concave below. Basal cell of the
appendage hardly distinguishable, the terminal cell blunt pointed,
evenly pale yellowish brown. Stalk-cell of the perithecium nearly
straight, rather short and stout, deeply constricted just above its
origin, about the same diameter throughout; the perithecium short,
stout, strongly curved, so that the tip is horizontal, the basal cell
region hardly distinguished from the body; one of the basal wall-
cells on the convex side forming a conspicuous umbonate projection;
the apex broad, slightly suleate, asymmetrical. Perithecium, from the
base to the horizontal edge of the tip, 70-7840-43 uw (including
umbo), the stalk-cell 40-4212-15 uw. Receptacle to tip of append-
age, including foot, 42 u. Total length 135-145 μ.

At the base of the elytra near the inner margin of several specimens
of Anthicus parvus Pic; Temperley, No. 15138C.

This species is nearly related to D. Anthici, and to the following
species from which it is most readily distinguished by the umbonate
prominence resulting from the inflation of one of the basal wall-cells.
A single specimen was found growing at the base of the anterior
leg of one host.

Dioicomyces angularis nov. sp.

Male individual relatively short and stout, rather deeply suffused
with olivaceous brown, especially externally; the foot relatively large,
the basal cell slightly longer than the rest of the series, the subbasal
cell hardly larger than the cell above it; the antheridial cell hardly
longer than broad, the antheridial neck slightly divergent. Length,
exclusive of neck, 306 μ. Basal cell, including foot, 19.5 u; neck8 μ.

Female individual much as in the preceding species, the receptacle
and appendage more deeply suffused. Stalk-cell of the perithecium
elongate, somewhat broader distally, slightly curved distally or near
the base. Perithecium rather clear pale straw-yellow, straight or very
slightly curved, its axis diverging slightly from that of the stalk-cell,
subtriangular, or more or less strongly angular externally owing to a

72 PROCEEDINGS OF THE AMERICAN ACADEMY.

prominence corresponding to the point of separation between the basal
and subbasal wall-cells, the perithecium tapering thence to the sym-
metrically rounded apex of the relatively narrow tip; the basal cell-
region distinguished on the inner side only, by a slight indentation
marking the base of the lower wall-cell. Perithecium 80-94 35-42 μ;
the stalk-cell 98-120X15 yu. Receptacle to tip of appendage 38 μ.
Total length 185-125 μ.

On the tips of the elytra and the adjacent free portion of the abdo-
men of Anthicus parvus Pic., Temperley and Llavallol, No. 1513A.

Distinguished from D. Anthici, to which it is very closely allied,
chiefly by the angular or triangular form of it perithecium.

Autophagomyces nov. gen.

Male individual, attached to the basal cell and foot of the female,
consisting of several superposed cells and bearing terminally and
laterally from one to several large flask shaped simple antheridia.

Female individual consisting of a single basal cell from which the
stalk-cell of the perithecium arises distally. Ascogenic cell single,
spores 1-septate.

Although five species of this type have been examined and several
individuals destroyed in an attempt to isolate the spores, I have
found it impossible to determine whether the male and female spores
are more definitely associated than in the other unisexual genera of
this type. It is therefore possible that what I have assumed to be a
male individual may be an antheridial branch, which arises from the
base of the basal cell of the female, although such a condition seems
improbable. The relationships of this genus are evidently with
Dioicomyces, the species of which also occur, for the most part, on
Anthicidae, and with Amorphomyces which the female very closely
resembles, except for its septate spores.

Autophagomyces Platensis nov. sp.

Male individual consisting of three or four superposed cells exclusive
of the foot and bearing one to three antheridia. Total length to tip
of terminal antheridium 53-605 uw. Antheridia 25 μ.

Female individual. Basal cell slightly broader than long, somewhat
suffused with brownish below. Stalk of the perithecium short and
stout, broader distally, concolorous with the hyaline or faintly yel-
lowish perithecium; which is slightly but distinctly curved through-

THAXTER.— ARGENTINE LABOULBENIALES. 178

out; its axis at ἃ 5Π0}: angle to that of the stalk; its outline somewhat
irregular distally, owing to the presence of slight elevations and
depressions which correspond to the successive tiers of wall-cells;
the tip bluntly rounded, asymmetrical and not well distinguished.
Perithecium 106 28-32 μ, its stalk-cell 14-1810-14 μ. Basal cell
9X 10.5 uw exclusive of foot.

On the elytra of Tomoderus forticornis Pic, Llavallol, No. 1982.

The base of the stalk-cell is in some specimens slightly constricted
or so modified that a very small cell may appear to be separated at
its base. There is no indication in this or the succeeding species of
any sterile cell which might be formed from the terminal spore-seg-
ment. I am indebted to M. Pic for determining the host which he
finds to be new.

Autophagomyces nigripes nov. sp.

Male individual, slender, usually consisting of three superposed cells
bearing a single terminal, or rarely also a subterminal, antheridium.
Total length to tip of antheridium 60-70%3.5 uw. Antheridium 26 μ.

Female individual. Basal cell relatively large, three to four times
as long as broad, slightly broader distally, uniformly suffused with
blackish brown, contrasting with the perfectly hyaline stalk of the
perithecium; which is slightly longer, broader distally, where it is
abruptly bent so as to turn the perithecium at right angles to its axis.
Perithecium rather slender, its outline somewhat irregular, bent
upward slightly distally; the tip large, broad, well distinguished,
blunt-pointed and oblique above; or with the outer, upper lip-cell
somewhat prominent. Perithecium 106X 26 u, stalk-cell 26-28 16 μ.
Basal cell exclusive of foot, 269 μ.

On the inferior surface of the abdomen of Tomoderus forticornis Pic.

Cryptandromyces nov. gen.

Receptacle consisting of two superposed cells, the upper bearing a
solitary stalked perithecium, and an appendage formed by a simple
series of superposed cells without branches; several consecutive cells
of this series at first functioning as antheridial cells, from which sperm-
cells appear to be discharged directly through perforations of the wall
on the inner side. Perithecia normal, a single ascogenic cell present
in the type.

The determination of the characters which distinguish this genus,

174 PROCEEDINGS OF THE AMERICAN ACADEMY.

of which several species are known to me on related hosts, has given
much difficulty; since the antheridia appear to be functional only at
the moment when the trichogyne is receptive, and the openings
through which the sperm cells appear to issue are soon obliterated;
the antheridial cells also losing the peculiar densely granular appear-
ance which at first distinguished them. It is only in very few speci-
mens that I have been able to make out these perforations through
which there actually seems to be a passage of sperm-cells of the usual

type.
Cryptandromyces geniculatus nov. sp.

Wholly hyaline. Receptacle straight, the basal cell becoming
broader distally, often longer than its greatest width; the subbasal
cell usually angular or subtriangular, slightly larger than the basal
cells of the appendage. Appendage slightly divergent, variably de-
veloped; sometimes distally elongate and tapering, but often rather
short and stout; consisting of usually three to five cells below the
antheridial cells, with evenly rounded lumens, the antheridial cells
above them, which may be as many as six in number, terminated by a
bluntly pointed, slightly incurved cell, or the appendage in some cases
becoming long slender and distally attenuated. Stalk-cell of the
perithecium slender, two or three times longer than broad, often
narrower subterminally; perithecium relatively large short stout, its
axis at an angle, sometimes at right angles, to that of the stalk-cell,
its inner margin often straight or concave, the outer strongly convex;
the tip hardly distinguished, sometimes slightly bent upward, the
obtuse apex minutely papillate or slightly suleate. Spores relatively
large 28X3.5 wu. Perithecia 50-70 25-30 μ; stalk-cell 20-268 μ.
Receptacle 26-35 12-16 uw. Appendage 509 yp, the more elongate
130 μ.

On the elytra ete. of Connophron nov. sp. Temperley, No. 2001.

The material of this species is sufficiently abundant, and though I
at first suspected that it was a unisexual form and that the male had
been overlooked, a more careful examination shows that the indi-
viduals bearing perithecia are often paired. This host has been
kindly determined for me by Col. Casey.

Synandromyces nov. gen.

Receptacle consisting of two cells forming, in conjunction with
the basal cell of the appendage, a compact structure in which the

eee

THAXTER.— ARGENTINE LABOULBENIALES. 175

subbasal cell of the receptacle occupies a central position, bordered
on one side by the subbasal cell, on the other by the basal cell of the
appendage, both of which thus tend to become marginal extending
to or toward its base. Perithecium relatively large, with a single
ascogenic cell, and five wall-cells in each row; the short stalk-cell
forming a narrow isthmus between the broad base and the receptacle.
The appendage, above its adherent basal cell, forming a compact
free structure consisting of a flattened basal cell in some species
obliquely divided, which is surmounted by two cells both bearing
single simple antheridia; one surmounted by a spine, or bearing also
a small cell which subtends a third antheridium, on which the lateral
spine is borne; the antheridia arising close together in a characteristic
group; their venters closely approximated, their stout necks distally
somewhat divergent. Trichogynes bicellular above their insertions,
the distal cell elongated at right angles to the basal cell on both sides,
and distally beset by numerous vesicular receptive prominences.

The above diagnosis is based upon the examination of several
species of this genus which are known to me from various regions,
only two having been obtained in the Argentine. It is most nearly
related to Acompsomyces.

Synandromyces Telephani nov. sp.

Perithecium erect, relatively very large; becoming tinged with
amber-brown, straight; the main body, including the basal cell
region, symmetrically inflated, subfusiform, but often somewhat
more tapering above and rounded at the base; the four cells of the
first and second tiers of wall-cells separated by a corresponding num-
ber of more or less distinct prominences; a terminal portion rather
abruptly distinguished from the main body, and often subtended
by slight prominences, straight, narrow, isodiametric above, more
deeply suffused, as a rule, than the main body, but nearly hyaline
below, slightly inflated distally immediately below symmetrical hya-
line truncate or slightly papillate and sulcate apex: the stalk-cell
small, constricted to form a short slender isthmus, which is bent
sidewise and connects laterally with the basal cells of the perithecium.
Receptacle short and compact, its axis straight, the basal cell narrow,
clavate above; the subbasal cell extending nearly to the foot, slightly
enlarged distally, very narrow below; the basal cell of the appendage
extending not quite so low as the subbasal cell, which it closely re-
sembles, though distally more abruptly broadened to form the hori-

176 PROCEEDINGS OF THE AMERICAN ACADEMY.

zontal insertion of the free appendage. Appendage compact, rounded,
subsymmetrical, amber-brown; the flat basal cell undivided, about
equalling the pair of cells above it, from which arise two antheridia,
and, externally, a small cell bearing laterally a spinose antheridium;
the necks of the antheridia lying side by side, erect and parallel, or
bent slightly inward and in contact, except distally. Spores 40X6 u.
Perithecia, including basal cells 235-310 45-58 μ, its rostrate termi-
nation 80yu. Receptacle including foot 45-6035 yu. Appendage,
free part including antheridia, 45-50 20 μ.

On the elytra, prothorax and other parts of Telephanus sp., Temper-
ley and Llavallol, No. 1992.

Synandromyces geniculatus nov. sp.

Similar in general to the last. Perithecium relatively smaller,
the main body tinged with deeper smoky brown, and lying horizontally
at right angles to the axis of the receptacle; asymmetrical, the distal
portion short, rostrate, tapering more or less to the short hyaline
tip; which is often abruptly somewhat narrower, sometimes slightly
inflated, irregularly papillate; the base inserted laterally on the
short, abruptly bent, constricted stalk-cell. Receptacle as in the
previous species, but relatively longer, strongly curved below. The
free portion of the appendage relatively smaller, tinged with smoky
brown. Spores 30X5 μι Perithecia 135-155X45-60 μ, rostrate
termination 45-50 uw. Appendage including antheridia, free portion,
30X 20 μ.

On the superior surface of the tip of the abdomen and less frequently
on the adjacent tips of the elytra, often with the last, on the same host,
Telephanus sp. Temperley and Llavallol; Nos. 1508, 1992.

This species grows, usually somewhat crowded, in the position
indicated, and I have not seen it on the elytra except at the very tips,
where S. Telephani may also occur. It can thus hardly be regarded
as a variety due to its position of growth. It may be easily distin-
guished from S. Telephani, even with a hand lens, from its darker
color, smaller size, and sigmoid habit.

Stigmatomyces Anoplischii nov. sp.

Faintly yellowish olivaceous with conspicuous brown shades near
the base of the appendage on the inner 5146. Perithecium relatively
very large and long, the venter greatly elongated, but slightly inflated;

THAXTER.— ARGENTINE LABOULBENIALES. 177

the neck slightly narrower, squarish or slightly inflated, subtended
by a slight elevation; the tip narrower and somewhat shorter than
the neck; the apex broader, terminated by four hyaline projections
which taper from broad flat bases to blunt, slightly divergent tips,
often symmetrical; the two upper basal cells extending upward, and
not distinguished from the base of the venter; the stalk-cell very
small, often shorter than broad, and bulging externally, separated
from the lower basal cell by a marked constriction. Stalk-cell of the
appendage narrow, lying in contact with the basal cell of the recep-
tacle; its pointed base reaching nearly to the foot, similar to and
symmetrical with the somewhat smaller subbasal cell, which lies
beside the narrow enclosed prolongation of the basal cell which reaches
nearly to the base of the free appendage. Basal cell of the appendage
free, tinged with reddish brown on its inner side, becoming divided
into two sometimes subequal cells, the outer sterile or bearing an
antheridium, the subbasal cell often as large as the inner division
of the basal, its wall red-brown on the inner side, bearing a single
antheridium externally, which may or may not be subtended by a
small cell; the cell next above smaller, subtriangular, bearing one
external and two lateral antheridia, the terminal cell becoming an
antheridium, the neck of which is subtended externally by a stout
blunt brown spinous process; antheridia tinged with brown, the
venters subtriangular, the necks abruptly distinguished, slender,
curved, as long as the venters. Spores 60-658 yu. Perithecia,
including stalk-cell (8 μ), 280-33045 uw. Appendage, exclusive of
stalk-cell, 50-6025 μ (at base): antheridia 25X12. Receptacle,
including stalk-cell of appendage, 50-5526 u. Total length to tip
of perithecium 310-390 u; to tip of appendage 130u. >

On the elytra of Anoplischius sp., Buenos Aires, No. 2028, La
Plata, No. 1518.

A well marked species most nearly related to S. virescens, but differ-
ing In various essential points. The arrangement of the distal anther-
idia recalls that seen in Helminthophana.

Zeugandromyces, nov. gen.

Receptacle consisting of two superposed cells, the upper bearing
a perithecium and antheridial appendage. The appendage consisting
of a stalk-cell and a series of superposed cells above it, the lower basal
cells clearly distinguished, or not differentiated from those above it
and like them, bearing on the inner side a vertical double series of

178 PROCEEDINGS OF THE AMERICAN ACADEMY.

paired antheridia, the terminal cell or cells of the series sterile, or
converted directly into antheridia. Perithecitum usually solitary,
normal, with a well developed stalk-cell; the short trichogyne arising
from the base of the prominent free portion of the trichophoric cell.

Were it not that sufficient material is available of two other species
of this genus which occur on allied staphylinids, one in Borneo and
the other in New England, I should hesitate to separate this type
from the very large and varied genus Stigmatomyces. The antheridia
recall those of Idiomyces, in which I have described an arrangement
of antheridia in three vertical rows. I have not felt satisfied, however,
that this was the actual condition, and a reexamination of fresh
material of this curious type may show that here also the antheridia
are in two and not in three vertical rows.

The Argentine material is for the most part in poor condition, only
one of the dozen or so specimens being fully matured. The perithecia
do not greatly resemble those of Stegmatomyces, having well developed
stalk-cells, while the distinction between venter, neck and tip is not
well marked. The apex, in all three species, is rather characteristi-
eally shaped, flat-conical, without projections or papillae. There
appear to be four ascogenic cells in all cases.

Zeugandromyces australis nov. sp.

Perithecium nearly symmetrical and straight, rather elongate, rich
amber-brown, paler distally; the base inflated, tapering thence
gradually to the blunt conical apex; the stalk-cell stout, broader
distally, faintly yellowish or hyaline, in the type bent abruptly near
the base. Receptacle subtriangular, nearly symmetrical, broader
distally where the septum is horizontal; subbasal cell somewhat
broader, much smaller, irregular. Appendage tinged with brown,
the terminal and basal cells darker, the stalk-cell subtriangular,
broader externally, the basal cell more or less clearly distinguished
from the five to seven cells above it, and like them bearing relatively
large antheridia with long appressed upcurved necks; the terminal cell
sterile, subtriangular, turned inward, externally spiniferous. Peri-
thecium 15544 μ; the stalk-cell 1627 μ (distally). Appendage,
including stalk-cell, 44-54 uw. Antheridia about 20 μ. Total length
to tip of appendage 90 μ; to tip of perithecium 250 μ.

On Scopaeus laevis Sharp. No. 1695, Palermo.

Found on a single specimen of the three hosts collected.

~J
em)

THAXTER.— ARGENTINE LABOULBENIALES 1

CORETHROMYCES ‘Th.

A comparison of new material from various parts of the world has
led me to the conclusion that the scope of this genus should be con-
siderably extended. Although those forms which, like the type,
occur on Cryptobia are all similar and are readily grouped in a section
by themselves, owing to the uniform characters of the appendages,
there are other closely related forms or groups of forms, like those on
δε οὶ, as well as various undescribed species on somewhat varied
hosts, that do not seem to be distinguished from the type with suffi-
cient clearness to justify the erection of new genera for their reception.
As a result of this extension, it seems desirable, moreover, to discard
the genus Rhadinomyces, which, though sufficiently well defined in
its typical conditions, varies to forms too near Corethromyces for
proper separation. That this union might prove necessary, I have
already mentioned in my second Monograph (p. 317).

A further complication in this connection has been encountered in
connection with the species of Sphaleromyces, a type in which the
antheridial characters are little known. The genus was based on ὃ.
Lathrobii in which the antheridia appear to be solitary, but in a
majority of the species which have been described under this generic
name these organs have not been seen at all, or have been but doubt-
fully recognized: for the reason that the material has all been obtained
from dried insects, and was consequently for the most part in poor
condition. Among the South American forms are several which would
have been placed in this genus had it not been possible to determine
from the fresh alcoholic material, that the antheridial characters
were those of Corethromyces. The striking form for example,
described below from material growing on Pinophilus, is undoubtedly
congeneric with the two species formerly discovered on hosts of this
staphyline genus, namely S. occidentalis and S. indicus; but several
of the younger specimens obtained, in which the antheridia still per-
sist, show clearly the intercalary nature of the latter. S. Quedionuchi
was also obtained both in Chile and in the Argentine, and although
the appendages here are densely tufted and small, a seriate disposi-
tion of the antheridia seems also to be present. Since, apart from the
supposed antheridial distinction, there are no essential differences
between Sphaleromyces and Corethromyces, the former genus must also
be abandoned.

The genus Corethromyces thus modified, may be considered to
include those forms in which a two-celled receptacle gives rise to a free

180 PROCEEDINGS OF THE AMERICAN ACADEMY.

stalked perithecium, normally solitary, and to a single appendage
consisting of a main axis of several superposed cells from some of
which ramiferous cells are separated on the inner-side, the branches
variously developed, the subbasal cell and sometimes the cell above
it bearing antheridial branches; the antheridial branchlets them-
selves, which really form the distinctive feature of the genus, some-
times associated with sterile branchlets and bearing antheridial cells
typically arranged in series of two or more superposed members, one
or more of which occupy an intercalary position in the series. That
even this character may be obscured, or is at least not always recog-
nizable, is evident from an examination of the peculiar series of forms
parasitic on species of Stilicus of which several additions are herein
included. Although in more than one species of this very individual
and peculiar group of forms, the seriate arrangement is well marked,
instances occur in which it is rarely or perhaps never present. Thus
in Corethromyces Stilicolus, which I formerly referred provisionally
to Stichomyces, it is only after the examination of much additional
material, that examples have been found in which the characteristic
seriate arrangement occurs, the antheridia usually tending to become
solitary or at least free, even when grouped: although in the light of
further knowledge of this type there can be no question that it is
congeneric for example with C. Stilici and others of this series, in
which one or more of the antheridia may be intercalary.

The conclusion thus seems unavoidable that both Rhadinomyces
and Sphaleromyces should no longer be maintained as distinct genera,
but should be merged in Corethromyces, which, in addition to the
species previously described under this name and the new forms
described below, may be regarded as embracing the following spe-
cies: Corethromyces cristatus and C. pallidus formerly placed in
Rhadinomyces; C. Stilicolus formerly included in Stichomyces; C.
Lathrobii, C. occidentalis, C. Indicus, C. atropurpureus, C.
Brachyderi, C. Chiriquensis, C. Latonae, C. obtusus, C. pro-
pinquus and C. Quedionuchi formerly placed in Sphaleromyces.

That further changes in the disposition of the last mentioned forms
may become necessary, when better material of the other species
related to C. Quedionuchi has been: examined, is suggested by the
characters of the new genus Mimeomyces described above, which are
exactly those of the group referred to, except for the presence of well
developed compound antheridia. C. atropwpureus, for example, might
well belong to the new genus, but in the type material, no signs of
compound antheridia can be found.

THAXTER.— ARGENTINE LABOULBENIALES. 181

Owing to the difficulties which are met with in determining the
exact nature and association of the antheridia in many forms included
in the genus it may be assumed that all those in which a two-celled
receptacle bears distally a single perithecium on the one hand and a
single main appendage on the other, bearing branches on its inner face
and terminally, should be sought under Corethromyces, when it pos-
sesses no characters which would exclude it from the genus.

Corethromyces Argentinus nov. sp.

Perithecium becoming very large, elongate, asymmetrical; the
outer margin more prominent; the region of the subbasal wall-cells
greatly elongated, usually distinctly suffused with purple-brown,
and more or less inflated; or the whole perithecium of nearly the same
diameter to the tip; which is well distinguished, blunt-conical, the
apex flat, papillate, subtended by a slight elevation: the basal cell-
region relatively short and compact, concolorous with the part above,
the stalk-cell hyaline, but externally opaque at its base, short and
about twice as long as broad. Receptacle small, the basal cell trans-
lucent, reddish, broader above than the opaque subbasal cell. Primary
appendage opaque below and externally indistinguishable below from
the subbasal cell of the receptacle; consisting of three superposed
cells, the two lower translucent along their inner margins, their limits
barely indicated externally by a slight elevation, the subbasal cell
associated with two unequal cells on its inner side; the lower larger
than the subbasal cell itself, inflated, and bearing paired erect branches,
which produce branchlets arising near the base only, the two lowest,
usually, short, opaque, contrasting, directed obliquely outward; the
rest suberect, more or less suffused with purplish or nearly hyaline,
coarse, straight or curved toward the perithecium, the tip of which
they may exceed when unbroken, the longer branches not numerous
(six or more), simple, stout, septate, tapering slightly to blunt tips:
the third, terminal cell of the main axis, very small, mostly translu-
cent, bearing distally one or two short branches. Perithecium 100--
290 40-55 μ, ascigerous part 165-270, stalk-cell 40-60 20-30 μ.
Spores 403.5 μ. Primary axis of appendage 50; total length to
tip of branches, longest 370; larger branches 8 yu in diameter.
Receptacle 40 X 8 μ.

On legs and abdomen of Cryptobium sp. Palermo, Nos. 1703-4.

This species was very common on a dark almost black Cryptobiwm
with yellow legs which frequented the low ground in the park. It is

182 PROCEEDINGS OF THE AMERICAN ACADEMY.

well distinguished by its very large and long perithecia, and the stout,
erect and elongate simple branchlets of the appendage, certain short
oblique branchlets below their origin being alone deeply suffused.

Corethromyces Ophitis nov. sp.

Perithecium rather slender, translucent reddish brown, tapering
but slightly to the hyaline blunt papillate tip; the basal cell well
developed, hyaline, distinguished above by a slight constriction, the
lower large; the stalk-cell relatively small, narrow, hyaline distally,
but otherwise rich red-brown, its insertion very oblique, its suffused
portion united to the basal cell of the appendage. Basal cell of the
receptacle translucent brown, pale, somewhat longer than broad,
slightly bent; the subbasal cell somewhat narrower below than the
basal, nearly or quite opaque. Basal cell of the appendage opaque
like the upper portion of the receptacle, and distinguished from it
only by an external well defined rounded prominence; its second and
third cells also opaque, both distinguished by a similar rounded promi-
nence: the subbasal separated by an oblique septum from the basal
and associated with two cells which occupy its whole inner surface; a
lower, subtriangular, nearly equalling it in size, extending from its
base for about three fourths of its length and bearing a red-brown
ramiferous cell on either side; the upper much smaller and ramiferous;
all the branches arising from these cells hyaline, two to four times
subdichotomously branched, the ultimate branchlets longer, tapering,
erect, the tips often abruptly recurved, some of them extending
beyond the tip of the perithecium; the third cell of the main append-
age subisodiametric, darker and abruptly constricted externally
above its subtending prominence, a crest-like series of branchlets
(usually broken) arising from its broad distal surface, the most external
opaque or basally suffused. Perithecium 175 X28 yu including basal
cell-region (20 μὴ). Main appendage 70 μ, to tips of branches 170 μ.
Receptacle including foot 50u. Total length to tip of perithecium
209 jh

On Ophites Fauvelii, in the Museo Nacional Collection. Collected
at Palermo by Dr. J. Bréthes.

Several specimens, only one of which is well matured, have been
examined. ‘The species belongs in the section of the genus the mem-
bers of which occur on Cryptobia. It is most nearly allied to C.
purpurascens, but is readily distinguished by the characters of its
appendage.

THAXTER.— ARGENTINE LABOULBENIALES. 183

Corethromyces Platensis nov. sp.

Perithecium becoming translucent amber-brown; usually straight,
subconical, tapering more or less from the variably swollen venter to
the blunt hyaline apex; the tip more or less clearly distinguished above
a slight enlargement; the basal cells rather large; the stalk-cell
variably, often greatly, elongated, and tapering somewhat to its
insertion. Appendage consisting primarily of three superposed cells;
the basal, and sometimes also the others, more or less deeply black-
ened; the subbasal cell bearing distally from its inner side a pair of
antheridial branches, one or both of which often become more or less
highly developed through monopodial branching, forming two main
axes of obliquely superposed cells; the lowest producing on the inner
side fan-like antheridial branches, the ultimate branchlets consisting
of two or three superposed antheridial cells; the rest bearing externally
simple or branched, sterile, upcurved, appressed branchlets, the lower
mostly blackened: the third cell of the primary appendage variably
developed; often very small bearing distally and from its inner face,
which may become outcurved and recurved, a variable number of
simple bristle-like black branches, the lowest external one originally
terminal (usually broken off), one of the others often greatly developed
by successive monopodial branching, replacing the main appendage
and consisting of from three to twelve obliquely superposed cells,
each of which bears distally and externally, usually simple branch-
lets, for the most part short, three-celled, becoming more or less deeply
suffused with black or blackish brown, upcurved, more or less closely
appressed; the two or three uppermost hyaline, long, multiseptate.
Basal and subbasal cells-of the receptacle hyaline, small, subequal,
or the subbasal larger. Perithecium, including basal cell-region,
118-125X3440 yp, the sporiferous part 75-1004; the stalk-cell
40-60X 12-20 4. Spores 24X2.5y. Greatest length of whole ap-
pendage 150-360 yu. Receptacle, including foot, 4020p. Total
length to tip of perithecium 85-235 μ.

var. gracilis nov. var. Perithecium and its stalk-cell longer and
more slender than in the type. Appendage divergent, slender, its
primary axis consisting of three superposed cells; the basal hyaline
below, blackened and slightly constricted above; the subbasal hya-
line, rarely externally suffused, nearly twice as long as the basal cell,
a small cell separated from its inner distal angle forming a rounded
prominence from which arise right and left paired antheridial bran-
ches, wholly hyaline, spreading, several times closely branched; an-

184 PROCEEDINGS OF THE AMERICAN ACADEMY.

theridial cells single or two to four of these superposed; the third
cell bearing distally one to usually not more than three branches;
the outer, primary branch, shorter, slender, hyaline; the others, if
present, hyaline, stouter, longer, sometimes once furcate above the
basal cell. Perithecium 100-156 X 20-35 μ, including basal cell-region;
stalk-cell 175X20 yu. Greatest length of appendage 150-430 μ. Total
length to tip of perithecium 180-385 μ. .

On Lathrobium niti'um Er., Palermo, Temperley and Llavallol,
Nos. 1687, 1688, 1998;

The type of this species occurs on various parts of the host and when
its appendage is well developed is a very striking form. It is very
variable in size and in the development of its appendage, and near the
tips of the legs assumes a small, compact stout habit quite unlike
the usual form. The variety corresponds exactly to the type formerly
distinguished as Rhadinomyces, and occurs on the elytra, usually,
or at the base of thelegs. It differs from the type in its slender form,
the absence of sterile branchlets on the antheridial branches, and of
the black bristle-like branches of the rest of the appendage. The
examination of a sufficient series, however, appears to show that the
two are not specifically separable.

Corethromyces Scopaei nov. sp.

Perithecium hyaline becoming faintly tinged with yellowish, rela-
tively rather large, usually slightly asymmetrical owing to an out-
ward curvature, tapering but slightly above the basal portion which is
not prominently inflated; the tip short, conical, subsymmetrical; the
small rounded papillate apex prominent; the basal cells forming a short
compact group not distinguished from the base of the perithecium,
the stalk-cell broad hyaline narrower below, set obliquely or sidewise
on the small nearly isodiametric hyaline subbasal cell of the recepta-
cle; the basal cell of which is about the same size but of characteristic
form, rounded outward, its thick outer wall passing into and not dis-
tinguished from the broad undifferentiated hyaline or slightly purplish
foot. Appendage wholly hyaline, the basal cell hardly longer than
broad, the outer wall greatly thickened and in contact below with
the basal cell of the receptacle; the subbasal cell somewhat narrower,
the outer wall greatly thickened; the distal portion of the appendage
occupied by a more or less crest-like series of hyaline branches
derived from the end of the subbasal cell and from one or perhaps
more terminal cells which become displaced and appear to be external,

THAXTER.— ARGENTINE LABOULBENIALES. 185

their cavities obliterated by their thickened walls, the outer branches
short, directed outward and upward, the inner (from the subbasal
cell) stouter, longer, once or twice branched near the base and ex-
tending not much beyond the middle of the perithecium. Peri-
thecium 65-75: ascigerous portion 55-70; the stalk-cell 2812 yu.
Receptacle 20X16 u. Total length of appendage including branch-
lets 60-80 u. Total length to tip of perithecium 95-120 4. Spores
18 xK:3 in. AK

On superior abdomen of Scopaeus frater Lyach. No. 1698 and No.
1702, Palermo.

A small pale species chiefly peculiar from the fact that no foot is
distinguished from the peculiar rocker-like basal cell of the receptacle,
which is usually quite hyaline. The species bears more resemblance
to the Stilicus-inhabiting forms than to the more typical members
of the genus.

Corethromyces brunneolus nov. sp.

Perithecium pale reddish brown with a yellowish tinge, usually
rather strongly bent inward distally; the basal cells very small not
distinguished from the base of the ascigerous portion, which tapers
but slightly to the blunt rounded hyaline apex; the tip not distin-
guished; the small basal cell-region clearly distinguished by a distinct
constriction from the stalk-cell, which may be nearly straight, or
strongly curved, distally broader or slightly inflated, about twice as
long as broad; the stalk-cell and the appendage very asymmetrical
in their relation to one another and to the small receptacle; which
consists of two subequal cells, concolorous with the perithecium. Basal
cell of the appendage relatively large, symmetrically inflated; the
subbasal cell, at maturity and through displacement, appearing to
bear directly a more or less fan-like series of short, rather stout, some-
what incurved hyaline branches, which may be once or twice branched
near the base. Spores 222.5 yu. Perithecia 58-62204y; asci-
gerous portion 54-58y; the stalk-cell 23-3012. Receptacle
24X16 uw including foot. Appendage, total length including branches,
longer, 100 μ; the basal cell 20X16 μ.

On the elytra of Stilicus sp., Nos. 1511 and 2012, Temperley.

This pale species appears to be very rare, only a very few specimens
having been obtained. It is quite unlike any of the other forms
which occur on Stilicus and appears to be most nearly allied to the
preceding species.

186 PROCEEDINGS OF THE AMERICAN ACADEMY.

Corethromyces Stilicolus nov. comb.
Stichomyces Stilicolus Thaxter.

This species which, in view of its single free antheridia, I formerly
placed provisionally in Stichomyces, was found frequently in the
vicinity of Buenos Aires on several species of δέ οι, and an examina-
tion of sufficient material shows that, although the species tends to
produce its antheridia singly, or free in groups, the intercalary arrange-
ment also occurs, and there can be no doubt but that the form is con-
generic with the other Stilicus-inhabiting species of the genus. The
Argentine specimens are similar in all respects to those first obtained
on Stilicus at Arlington, Mass.

Corethromyces pygmaeus nov. sp.

Perithecium becoming rather deeply suffused with dull reddish
amber-brown, asymmetrical; the basal cell-region small and hardly
distinguished, one of its cells usually bulging externally to form a
distinct prominence; the ascigerous portion, usually rather abruptly
inflated externally, the apex of the curvature forming a more or less
well distinguished hump, the inner margin usually straight; the tip
broad not distinguished, the apex truncate, subtended externally by
a rather abrupt rounded prominence: stalk-cell suffused, becoming
concolorous with the perithecium, usually strongly curved inward,
distally broader below the base of the perithecium, from which it is
distinguished by a very slight constriction, and which it nearly equals
in length. Axis of foot at right angles to that of the basal cell of the
receptacle, which is twice as large as the somewhat flattened subbasal
cell; externally strongly concave, its inner margin convex, sometimes
distally constricted on its inner side, a deeply suffused outgrowth
arising from its outer upper angle; almost uniform in width above its
narrower base, extending outward then upward abruptly beside the
two basal cells of the appendage, sometimes bent inward near its
rounded tip. Basal cell of the appendage large, nearly spherical;
the subbasal cell small and surmounted by several hyaline branches,
one or two of which may extend nearly to the tip of the perithecium.
Perithecium 58-66 X 24-28 μ: stalk-cell 40-6020 μ. Spores 26X
2.5 w (measured in perithecium). Receptacle 20X 12 μ, its outgrowth
20-305 uw. Total length of appendage 30-40 uw. Total length to
tip of perithecium 100 μ.

THAXTER.— ARGENTINE LABOULBENIALES. 187

On head and labium of Stilicus sp., No. 1963B, Palermo.

This small species was found only once in the park at Palermo but
was also obtained on a similar host at Corral, Chile, No. 1902. It is
allied to C. Stilici, from which it differs in the form of its perithecium
and receptacle, as well as in the character of the outgrowth from the
latter.

Corethromyces sigmoideus nov. sp.

Axis from tip of perithecium to foot, describing an even sigmoid
curve, the lower curvature much shorter. Perithecium strongly
curved outward, translucent amber-brown; the basal cell-region
concolorous, often slightly distinguished from the ascigerous part, the
basal cells well. developed and triangular; the apparent apex formed
by a blunt outgrowth directly continuous with the ascigerous portion,
of which it forms the bluntly rounded slightly asymmetrical termina-
tion; the apex proper having its pore lateral in position and hardly
distinguishable: stalk-cell but faintly suffused, broader distally, and
distinguished from the basal cell-region by a slight constriction;
abruptly curved near the base, the axis of which is directly con-
tinuous with the subbasal cell of the receptacle. The’ latter slightly
suffused, relatively large, extending on the perithecial side downward
nearly to the foot, and obliquely separated from the externally deeply
suffused basal cell; which is of about the same diameter throughout,
including its upward extension which, lying beside the subbasal cells,
extends beyond the base of the first cell of the appendage to which it
is adherent, forming a rounded prominence; the upgrowth larger
than the basal cell proper, and not distinguished from it. The basal
cell of the appendage subelliptical, concolorous with the subbasal cell
of the receptacle, its long axis nearly at right angles to that of the rest
of the appendage which is curved across the stalk-cell of the perithe-
cium; the subbasal cell small, flattened or rounded, bearing on its
inner surface a smaller ramiferous cell, and distally a much larger one,
often several times longer than broad, and bearing distally numerous
branches; the latter more or less branched, all the branches tapering
somewhat, slightly suffused below, hyaline above; the two or three
longer ones curved downwards. Perithecia 70-85 23-27 μ: stalk-
cell 60X18 μ. Receptacle including foot 40 u. Total length to tip
of perithecium 135-170 μ. Spores 263 μ.

On the superior right lateral margin of the prothorax of Stilicus
elegans Lynch. Llavallol, No. 1994.

188 PROCEEDINGS OF THE AMERICAN ACADEMY.

Closely allied to the last species, which grows in a similar position
on another species of Stilicus; but readily distinguished by its sigmoid
habit, and the different structure of its appendage and perithecium.

Corethromyces uncigerus nov. sp.

Perithecium rather bright translucent reddish amber, somewhat
concave and more deeply suffused on the inner side, rather strongly
convex externally, the basal cells clearly defined, subtriangular in a
compact group, the basal cell-region not distinguished from the asci-
gerous portion, which tapers distally to its peculiarly modified tip,
the blackish suffusions of which extend to an opaque, hook-like pro-
longation which, bending at right angles, forms a lid immediately above
and often partly concealing the hyaline apex: the stalk-cell nearly
hyaline, variously, often greatly, elongated, curved, or often straight
and erect; distally broader than the basal cell-region, from which it
is thus separated by a more or less pronounced constriction. Subbasal
cell of the receptacle relatively large, hyaline, subtriangular, the
basal cell narrow below, smoky, extending obliquely upward to the
base of the appendage where it is continued by a deeply suffused
broad straight erect upgrowth, which is flattened against the ap-
pendage, and extends to or beyond its subbasal cell. Basal and
subbasal cells of the appendage subisodiametric and subequal, or
the basal larger and longer, the subbasal appearing to bear from its
broad distal surface, a small tuft of hyaline, rather short branches
and branchlets. Spores 26X2.8 uw. Perithecia 70-85X20-26 u;
its stalk-cell 50-125 15 μ, distally, 20 u broad. Appendages, we
75 wu. Receptacle, including foot, 30-40 μ, its outgrowth 30-60 μ
Total length to tip of perithecium, 150-250 μ.

On the posterior legs of Stilicus elegans Lynch, No. 1994, not
uncommon at Llavallol, and easily distinguished by the peculiar tip
of its perithecium which recalls that of Chitonomyces psittacopsis or

of C. Bullardt.

Corethromyces armatus nov. sp.

Perithecium nearly uniform dull purplish amber-brown, the basal
cell-region not distinguished, or somewhat paler and very slightly
narrower than the ascigerous part above; the inner margin slightly
convex, the outer strongly so distally, the tip broad undifferentiated;
the apex broad, flat, subtended internally by a rounded projection

THAXTER.— ARGENTINE LABOULBENIALES. 189

and externally by a prominent conical outgrowth extending obliquely
upward and outward and narrower toward its blunt, often slightly
contracted, apex: the stalk-cell hyaline, shorter than the perithecium,
straight or outcurved, often slightly enlarged on the inner side below
the perithecium. Subbasal cell of the receptacle triangular, hyaline,
the basal cell abruptly curved at right angles, wholly suffused with
blackish, but not opaque; obliquely related to the subbasal cell,
and continued below and just beyond the base of the appendage by an
external outgrowth which is not free, even at its tip, being adherent
to the basal and subbasal cells of the appendage. The basal cell of
the appendage nearly hyaline, bent almost at right angles, and thus
turning the rest of the appendage across the stalk-cell of the perithe-
cium; the subbasal cell often abruptly narrower, hardly twice as long
as broad, bearing distally a few external branches and a large appen-
diculate cell, from which arise elongate tapering branches, two or
three of which may exceed the perithecium and its stalk-cell in length.
Spores 32X3 u. Perithecium 60-70X 20-23 μ, its terminal projection,
upper margin 28 μ, lower 40 μ; stalk-cell 30-45X12-18 μ. Recep-
tacle 30-40 u. Longest appendage 175 yu. Total length to tip of
perithecium 120-150 μ.

On the upper surface of the prothorax near the right margin of a
species of Stilicus, Palermo, No. 2012, and Temperley; No. 1992,
Tucuman.

This species, which was met with rarely, always occurred in exactly
the same position, and is easily distinguished by its appendiculate
perithecium, and the peculiar position of its appendage.

Corethromyces rhinoceralis nov. sp.

Perithecium dirty pale brownish amber, a deeper patch of amber-
brown involving the subterminal wall-cell on the inner side; subclavate
in form, the gradual distal enlargement extending to the subterminal
wall-cell; distally curved outward to the subhyaline apex which is
slightly cleft, and subtended on the inner side by a long, straight,
rather slender unicellular spine-like process which tapers slightly to a
blunt apex and projects at right angles; basal cell-region well devel-
oped, concolorous, not distinguished from the ascigerous part, nar-
rower below where it connects with the rather slender free, subcylin-
drical stalk-cell. Receptacle concolorous with the appendage and
perithecium, the basal and subbasal cells of about equal length, the
subbasal cell half as broad as the basal, except immediately above the

190 PROCEEDINGS OF THE AMERICAN ACADEMY.

latter, and obliquely separated by a curved septum from the basal
cell of the appendage which lies beside it and extends but slightly
above it: the rest of the appendage rather slender, rigid, its axis of
four or five successively smaller superposed cells, each bearing distally,
from the inner angle, a short hyaline branch, seldom persistent and
producing large bottle shaped antheridia singly or in series of two,
one terminal and the other intercalary. Spores (in perithecium)
about 45X6y. Perithecium, including basal cell-region, 240-250
46 w: the subterminal spine 80-90 uX8-10 uw near base; the stalk-cell
6015 u. Receptacle including foot 704. Free portion of append-
age 135 μ.

On the inferior surface of the abdomen of Pinophilus suffusus Er.,
No. 1977, Llavallol.

Closely allied to C. Indicus, from which it differs chiefly in the
clavate form of the perithecium, and in the highly developed spine
which springs from a projection of one of the subterminal wall-
cells. The species appears to be very rare, for although very many
specimens of its host were obtained it was found in only two instances.

Corethromyces macropus nov. sp.

Nearly hyaline. Perithecium asymmetrical; the outer margin
convex, the inner straight below the incurved tip; the basal cell-region
not distinguished from the slightly and symmetrically inflated body,
which tapers slightly to the undifferentiated tip; the latter slightly
suffused with brownish, and rather abruptly bent inward, one of its
lateral wall-cells deeply suffused with brown, and forming a free
truncate projection immediately beside the flat-conical, hyaline,
slightly geniculate apex: stalk-cell small, not distinguished from the
basal cells, one of which lies beside it extending nearly to its base.
Receptacle relatively large more or less strongly curved, the foot
large and long, tapering from a large bulbous portion to its pointed
extremity: the basal cell more or less deeply suffused with smoky
brown, paler above, rectangular, somewhat longer than broad, dis-
tinguished by a horizontal septum from the small subbasal cell, from
which the perithecium and appendage arise asymmetrically. The
appendage consisting of about five superposed cells; rigid, straight,
divergent, nearly hyaline; the basal and subbasal cells not appendicu-
late, the rest bearing short branches distally on the inner side. Peri-
thecia, including stalk- and basal cells, 100-110X25 μβ. Receptacle,
including foot, 55X18 u. Appendage 50-55X8-10 yu. Total length
to tip of perithecium 150-1804. Spores 30 μ.

THAXTER.— ARGENTINE LABOULBENIALES. 191

On Heterothops nov. sp., No. 1987, Llavallol.

This curious form is most clearly distinguished by the peculiar
conformation of the tip of the perithecium and its relatively large
receptacle and foot; but is included only provisionally in the present
genus owing to the fact that the antheridia are not distinguishable
in any of the specimens. The host has been determined as a new
species by Dr. Bernhauer.

Corethromyces rostratus nov. sp.

Perithecium tinged with pale brownish, long, slender, erect and
straight, symmetrical; the basal cell-region distinct from the more or
less inflated basal ascigerous part; the mid-region sometimes rather
abruptly narrower and elongate; the tip not distinguished, symmet-
rical; the apex narrow subsymmetrical, hyaline, abruptly papillate:
stalk-cell small, concolorous, rather broader than long. Receptacle
externally prominent below the insertion of the appendage, the basal
cell large, subtriangular, suffused with smoky brown, externally
opaque, its broad distal surface obliquely separated from the small
flattish subbasal cell. Appendage somewhat divergent, consisting
of five or six superposed cells; the basal nearly hyaline; those above
it more distinctly suffused, and each bearing a branch from its distal
inner angle; the branches once to several times divided, the subbasal
cell of the lowest branch, in conjunction with the bases of its two or
three branchlets, rather characteristically inflated; the ultimate
branchlets slender, hyaline, cylindrical, associated with usually single
(?) antheridia. Perithecia, above basal cells, 120-135X20-22 μ:
the stalk-cell 6XSu. Receptacle 55-58 u. Spores 30X3 yu. Append-
age 95-100 12-14 μ its longest branches 155 uw. Total length to tip
of perithecium 200-230 u.

On various parts, usually the abdomen of [eterothops sp., Temperley,
No. 2000, Llavallol, Nos. 1985 and 1987. .

It seems difficult to obtain this species in very perfect condition,
and though I have examined material from a number of different
individuals, I have been unable, even in the younger specimens, to
determine the exact nature of the antheridia which appear to be
solitary near the bases of the lower branches of the appendage. It is
possible that I have mistaken short branches for these organs, and
in any case the reference of the form to Corethromyces as above emended
must be considered provisional.

A well marked variety was also found having a hyaline obconical

192 PROCEEDINGS OF THE AMERICAN ACADEMY.

basal cell, separated by a straight horizontal septum from the small
triangular cell above, its perithecium and appendage closely approxi-
mated.

Stichomyces Catalinae nov. sp.

Perithecium rather stout, nearly hyaline; the basal cell-region well
developed, slightly broader than the base of the ascigerous region;
the latter becoming gradually and but slightly broader to the broadly
conical, symmetrical, or slightly bent, distal region, from which it is
distinguished by a slight double corrugation on one or both sides;
the apex small, often bent sidewise, rathér abruptly distinguished,
symmetrical, rounded, hyaline and subtended by dark brown suffu-
sions which often appear like paired rings; the stalk-cell well dis-
tinguished, broader than long, distally bent abruptly upward from
its insertion which is lateral, from the distal end of the subbasal cell
of the receptacle. Receptacle deeply suffused with brown, except
its narrow hyaline base just above the small foot; the basal cell
broader distally, hardly twice as long as the somewhat broader sub-
basal cell. The appendage consisting of an axis of four superposed
cells not distinguished from the receptacle, and concolorous with it;
the subbasal cell bearing from its upper inner angle a group of
hyaline branches, which reach to or beyond the tip of the perithe-
cium; the terminal cell smaller, hyaline, and bearing a few hyaline
branches. Spores 201.5 μ (measured in perithecium). Perithecium
50-60 X 15-20 μ. Receptacle, including foot, 30-55X9-12 uw. Main
axis of appendage 30-35 12 μ; total length to tip of longest branch-
lets, 75 uw. Total length to tip of perithecium, 90-125 μ.

On Conosoma testaceum Lat., No. 1984, Llavallol.

The branches of the appendage in this species are usually badly
broken, and even in those which are still intact, are so beset by masses
of bacteria, that it has not been possible to make out the antheridia
with certainty, although they appear to arise in small groups some-
what as in S. Conosomae. The character of the perithecium and of
its apex, and the dark continuous axis formed by the receptacle and
main appendage, are characteristic of the species, although a few
specimens were obtained that are smaller and in which the successive
cells of the receptacle and appendage are less evenly continuous.

THAXTER.— ARGENTINE LABOULBENIALES. 193

Laboulbenia Lathropini nov. sp.

Receptacle relatively stout and small, cells I and II faintly suffused,
subequal in length; the latter broader, sometimes longer; the rest
of the receptacle and the perithecium deeply suffused with dirty
olivaceous brown; cells III and IV subequal; the upper angle of cell
V free between the perithecium and the slightly oblique insertion-cell,
which is thick but rather small. The simple outer appendage enor-
mously elongated, distally hyaline, the cells several times longer than
broad, all similar; the first three or four somewhat shorter than the
rest; the basal cell of the inner appendage very small, bearing an
antheridial branch consisting of one to two small cells, terminated
by one to two antheridia, one of which may be replaced by a long
simple sterile branch. Perithecium relatively large, not wholly free,
slightly and evenly inflated; the wall-cells strongly spiral and marked
by fine irregularly parallel lines; the tip deeply suffused, the lip-edges
hyaline, subequal, the apex suleate and turned strongly inward.
Spores 75X8 uw. Perithecium 150-175X45-50 yw. Receptacle 120-
155 μ. Longest appendage 90016 μ at base. Total length to tip
of perithecium 90016 wu.

On the upper surface of the abdomen of Lathropinus fulvipes Er.,
No. 1975, Llavallol.

A species of the simpler “polyphaga”’ type, most nearly allied to
L. Oedodactyli, and distinguished by its enormously elongated outer
appendage and spirally twisted, longitudinally striate wall-cells.
The host was found rarely in decaying wood.

‘

LABOULBENIA FUNEREA Speg.

This form which is very abundant on species of Anaedus in the
vicinity of Buenos Aires, especially in the woods at Santa Catalina,
is, in my opinion, best regarded as a variety of L. polyphaga. It
is characterized by its small size, averaging about 175 u to the tip
of the perithecium, the receptacle being usually rather short, about
95-100 μ, although cell II is occasionally considerably enlarged.
Cell I is always hyaline, cell II often so, though frequently in-
volved by the characteristic blackish olive-brown suffusion of the
rest of the receptacle, which is concolorous with the perithecium
except for a small hyaline patch usually present below the insertion-
cell. The outer appendage is usually furcate above its subbasal
cell, the two branches distally hyaline and tapering; the small basal

194 PROCEEDINGS OF THE AMERICAN ACADEMY.

cell of the inner appendage bearing one or two short branches, the
lower cells of which bear a few antheridia. The perithecium is
straight, very slightly inflated, the tip clearly distinguished, deeply
blackened, the lips hyaline, turned slightly outward, separated by a
slight apiculus.

Laboulbenia hemipteralis nov. sp.

Receptacle rather short and stout, the basal and subbasal cells
subequal in length; the former hyaline; the rest of the receptacle
more or less deeply tinged with olivaceous, especially the relatively
broad distal portion; cell VI (stalk-cell) small, triangular, its oblique
contact with cell II not extending to the end of the latter; the basal
cells of the perithecium obsolete; the ascigerous cavity lying immedi-
ately above the stalk-cell. Perithecium olivaceous, tapering, its
distal half, only, free; the tip conspicuously blackened and bent
slightly inward; the apex subsymmetrically rounded, or slightly
pointed, concolorous with the tip; the pore turned inward. Insertion-
cell relatively very broad, lying somewhat higher than the middle of
the perithecium, the basal cell of the outer appendage bearing a single
branch, consisting of a single cell externally suffused at its base, bent
inward slightly, producing four or five closely successive branchlets
externally, the lowest of which is distinguished by a thin darkened
septum and bears about four secondary simple branchlets in a simi-
lar fashion, the lowest of which is more slender and suffused especially
at its base, usually projecting subhorizontally, the others hyaline;
the remaining primary branchlets hyaline, simple or fureate, often
spirally curved above: the basal cell of the inner appendage giving
rise normally to an outer and an inner and two lateral branches,
consisting of single short cells, each bearing a large terminal brown
antheridium, which may be replaced by a sterile branch bearing hya-
line branchlets like those above the base of the outer appendage. Peri-
thecia 6620-23 uw. Spores 222.6 (in perithecia). Receptacle
85X23 uw. Appendages to tips of longest branchlets, 105 yu. Total
length to tip of perithecium 100-120 μ.

On the legs and inferior surface of Velia Platensis Berg., Palermo,
near Belgrano,'No. 1951 along the margin of a pool. (Van Duzee
det.)

This very clearly distinguished form which was found with the fol-
lowing species. is the first of the genus thus far reported on Hemiptera.
The material is abundant and in good condition.

THAXTER.— ARGENTINE LABOULBENIALES. 195

Laboulbenia Veliae nov. sp.

Receptacle dirty olivaceous, concolorous with the perithecium,
cells I and II forming a stout elongate stalk about five times as long
as the scarcely broader distal portion. The insertion-cell broad and
thick, deep reddish, not quite opaque; the outer and inner basal cells
of the appendages subequal; the appendages but faintly suffused
or subhyaline, once or twice somewhat irregularly branched; the
branches divergent, the two or three lowest cells short, slightly in-
flated, distinguished by dark thin septa. Perithecium not wholly
free, narrow, geniculate below the tip, the pore lying laterally on the
inner side in the angle formed between the small rounded hyaline
prominent inner lips and the greatly enlarged outer lip-cells, which
are deeply suffused externally on the side above the pore, above
and beyond which they form a characteristic large blunt erect slightly
bent process, which terminates the perithecium, Spores 507 xz.
Perithecia 125-130X24 u. Receptacle 235-200 μ; cells I and II
20018 u. Appendages including longest branchlets, 2004. Total
length to tip of perithecium, largest, 350 μ.

On the superior surface of the thorax of Velia Platensis Berg.,
No. 1951, Palermo near Belgrano.

A very distinct species, remotely resembling L. ceratophora and its
allies. A small group of adult specimens was found on the same
individual with L. hemipteralis.

Laboulbenia Lacticae nov. sp.

Receptacle hyaline, becoming very faintly tinged with brownish
yellow; cells I and IJ subequal, nearly as broad as the much reduced
distal portion; cells III, IV and VI not greatly different in size, the
insertion-cell occupying but half of the distal surface of cell IV, the
rounded outer half of which is free externally. Basal cells of the
appendage involved by the opacity of the insertion-cell, and indis-
tinguishable; the outer bearing a compact group of six or eight
suberect branches in two radial rows, or more irregularly placed,
which bear short branchlets on their inner sides, and consist of two
parts; a basal, seated on an almost hyaline cell and composed of
rather short cells deeply suffused with blackish brown and constricted
at the septa, and a distal portion suffused only at its base, above which
it is quite hyaline rigid and tapering: basal cell of the inner appendage
bearing one or two short branches on which one or two antheridia

196 PROCEEDINGS OF THE AMERICAN ACADEMY.

may be produced, the latter sometimes occurring on the inner branches
of the outer appendage also. Perithecium wholly free, concolorous
with the receptacle, narrow, but slightly inflated, the tip nearly as
broad as the body, and clearly distinguished by blackish suffusions;
the lip-cells large rounded and bent slightly inward. Spores 453.5 μ.
Perithecium 90-100 X 24-28 μ. Receptacle 80 15-155 X22. Longer
appendages 135-150 u. Total length to tip of perithecium 175-280 μ.

On the tips of the elytra, wings and abdomen of Lactica varicornis
Jac. or a closely allied species. Palermo, No. 1462.

LABOULBENIA BLECHRI Spegazzini.

Receptacle slender, hyaline, the basal cell not symmetrically
adjusted to the subbasal, which is slightly prominent above it on the
posterior side, while the basal bulges below the subbasal on the ante-
rior side; the subbasal somewhat longer than the basal, hardly
broader; cells III, IV and VI subequal and subisodiametric, cell V
very small. The insertion-cell, black, rather thin, not very broad; the
outer appendage erect, simple, its three lower cells rather deeply tinged
with olivaceous, especially externally, subequal, each somewhat
broader distally and thus rather abruptly distinguished from one
another; the rest of the appendage quite hyaline, tapering slightly:
basal cell of the inner appendage much smaller than that of the outer,
producing the usual branch on either side, each once or twice branched;
the whole forming a group of four to six branchlets olivaceous below,
which are relatively very stout, short, bent inward or across the
perithecium, the longest extending just above its tip, the lower cir-
cinate distally. Perithecium colorless, straight, its axis somewhat
divergent from that of the slender receptacle, the basal cell-region
forming an external rounded prominence, the junction of the basal
and subbasal wall-cells also prominent; the tip, rather stout, sub-
tended by a slight external prominence, the apex broad, the hyaline
lips outwardly oblique, subtended by an olivaceous patch on the inner
side. Spores 35X3 yu. Perithecium 62-7020-22 μ. Receptacle
80-100 yp. Appendages, longer, inner 55 yw, outer 110 yw. Total
length to tip of perithecium 140 μ.

On Blechrus sp., at the tips of the elytra. Llavallol, No. 1979.

A single specimen of the host was found bearing this species which
is most readily distinguished by its relatively very large incurved
inner appendages. The perithecium may become suffused with age,
but in the specimens examined it is quite hyaline, although they are
sufficiently mature to have produced spores.

THAXTER.— ARGENTINE LABOULBENIALES. 197

Laboulbenia Monocrepidii nov. sp.

Cells I and II hyaline or faintly olivaceous, narrow, cell IT rather
abruptly broader distally, and obliquely separated from cell III by
an incurved partition; the distal portion of the receptacle deeply
suffused with olive-brown, deeper externally below the very thick
dark insertion-cell; cell V paler. Basal cells of the appendage
suffused, subequal, each bearing a short single simple rarely once-
branched erect similar appendage, the basal cell of which is subhyaline
or more faintly suffused, and distinguished above and below by a
constriction and by a blackened septum, the rest of the appendage
short hyaline, tapering to a blunt point, the inner appendage single
short simple, replacing a single small short antheridium found in
younger specimens. Perithecium about three quarters free, deeply
tinged throughout with olive-brown, slightly inflated; the tip long,
not abruptly distinguished, suffused with blackish, the black shades
extending downward separated by pale areas; the lips asymmetrical,
the edges irregular, outwardly oblique, hyaline. Spores 754.5 uw.
Perithecia 120-135X40-45 μ. Receptacle 150-225. Longest ap-
pendage 80-110 μ. Total length to tip of perithecium 250-325 μ.

On the elytra etc. of Monocrepidius sp., Palermo, No. 1683 and also
at Llavallol.

A clearly distinguished species, the first as yet recorded on a mem-
ber of this family (Elateridae).

Laboulbenia fuscata nov. sp.

Receptacle tapering evenly to the small foot, dirty olive brown,
cells I and II paler, cell ΤΥ externally rounded and prominent below
the rather broad insertion-cell which is but little darker than the cells
below it. Basal cell of the outer appendage roundish or bell shaped,
deep reddish brown, hardly larger than the inner, the appendage
externally blackened and curved abruptly outward above it, short,
separated by an opaque septum from its deeply suffused reddish
brown basal cell, and bearing two to three suberect or incurved short
branches; the inner basal cell bearing two deep reddish brown,
somewhat bell-shaped cells, terminated by a single short erect usually
simple appendage. Perithecium free, except at the very base, dark
translucent yellowish olive, subsymmetrical, curved slightly outward,
twisted one quarter so that the tip is viewed at right angles to its
normal position; the tip large, characteristically and slightly inflated,

198 PROCEEDINGS OF THE AMERICAN ACADEMY.

especially its inner basal half, externally margined with black, the
apex nearly opaque, broad, symmetrically bilobed. Spores copious
75X4.5 μ. Perithecium 156X48-55 uw. Receptacle 20075 μ. Total
length to tip of perithecium 330-350 u. Longest appendages 120 μ.

On legs of a small species of Pterostichus taken on flats outside
the docks at Buenos Aires, No. 1968.

A peculiar form, of which four fully developed specimens were
obtained, which does not appear to be nearly allied to any of the
described species.

Laboulbenia granulosa nov. sp.

Receptacle becoming more or less uniformly tinged with dark olive,
the suffused area coarsely granular-punctate, the dark granulation
involving the distal portion of the otherwise hyaline basal cell; cell
II narrow, very obliquely separated from cell VI which extends nearly
to its base, cells ΠΠ| and IV subequal. Insertion-cell broad and thick;
cell IV protruding but slightly below it; basal cell of the outer append-
age sometimes twice as large as that of the inner, both becoming
concolorous with the receptacle; the outer appendage usually furcate
above its subbasal cell; the basal cell of the inner appendage produc-
ing a branch on either side, usually once branched; the branchlets
of both appendages hyaline, eventually curved inward across and
beyond the terminal portion of the perithectum. Perithecium evenly
olivaceous, a few coarse scattered maculations on the basal third;
somewhat inflated in the middle, the tip not abruptly distinguished,
rather stout and broad; the apex asymmetrical; the outer lip-cell
somewhat more prominent, the inner subtended by a blackish suffu-
sion. Perithecium 11040 u. Receptacle 13540 uw. Total length
21D) Me

On the legs of Argutor Bonariense Dej. (thus named in the Museo
Nacional) No. 1460, Isla de Santiago, near La Plata.

This species bears a distant resemblance to L. scelophila, but is
distinguished by its more slender abruptly curved appendages and
the blackish powdery granulation of its suffused portions. The host
appears to be the same which is called by Spegazzini Argutoridius
oblitus, which Mr. Henshaw informs me should be placed in Ptero-
stichus.

THAXTER.— ARGENTINE LABOULBENIALES. 199

Laboulbenia subinflata nov. sp.

Receptacle rather long but variable, cells III and IV becoming
olivaceous, the rest pale dull yellowish, the upper half or more of cell
II characteristically swollen, broader than the receptacle above it,
from which it is separated by a distinct indentation on one or both
sides; cell III relatively large, sometimes twice as large as cell IV, the
outer half of which lies external to the insertion-cell, below which it
is thus prominent and obliquely rounded outward. The insertion-
cell black, rather thick and narrow; the basal cell of the outer append-
age several times as large as that of the inner, the subbasal cell similar
and subequal, both becoming olivaceous; the latter bearing regularly
two parallel branches distally, the outer usually shorter; the whole
appendage erect or slightly divergent and reaching a short distance
beyond the tip of the perithecium: the small basal cell of the inner
appendage bearing a short erect branch on either side, from the base
of which arises a unicellular antheridial branchlet terminated by two
to three antheridia. Perithecium relatively small, the lower wall-cells
and the upper basal cells becoming tinged with olive, distinguished
from the part above by a more or less pronounced elevation, later
obliterated, from which a darker area of olive-brown extends hori-
zontally across the perithecium, which above it is pale amber-brown;
the tip relatively narrow, abruptly distinguished externally above a
conspicuous rounded prominence, its concave external margin broadly
blackened; the lips outwardly oblique, coarse, the inner more promin-
nent, rounded, subtended by a blackish patch. Spores 555 u.
Perithecium 175-185 45-50 uw. Receptacle 310-415 X 62-78 μ; larg-
est subbasal cell 187X75y. Appendages 200 μ, longest 215 μ.
Total length to tip of perithecium 350-585 μ.

On the left margin of the prothorax, superior, of “ Argutor Bonarien-
sis Dej.”; Buenos Aires, Nos. 1512 and 1962; Llavallol, No. 2032.

This species was found on a number of individuals of its host, and
always in exactly the same position, sometimes in company with all
of the six other species, including L. polyphaga, which occur on this
host, from which it may be easily distinguished by its perithecium,
appendages and inflated subbasal cell.

Laboulbenia Bonariensis nov. sp.

Large, long, slender, and as a rule evenly curved from base to apex.
Receptacle becoming more or less evenly suffused with olive brown,

200 PROCEEDINGS OF THE AMERICAN ACADEMY.

the base of cell I hyaline, the distal part more deeply suffused than the
rest of the receptacle; cell II somewhat longer anteriorly than cell I,
cell IV somewhat obliquely prominent below the insertion-cell,
which is relatively narrow and thick: appendages slender, the basal
cell of the outer very slightly longer than broad, somewhat larger than
that of the inner, becoming deeply suffused with age, bearing a single
slightly divergent branch, the slightly smaller basal cell of which bears
two to three branchlets distally, its deep external suffusion continu-
ous with that of its short slender outer branchlet, its one or two inner
branchlets radially placed, simple hyaline erect, extending to or above
the tip of the perithecium: basal cell of the inner appendage bearing
one or two branches, sometimes once branched, hyaline, erect, similar
to the adjacent branches of the outer appendage. Perithecium bent
inward, becoming rich brown with a slight olivaceous tinge when fully
mature; the base, above the basal cells, sometimes rather abruptly
distinguished and slightly paler; the tip rather long, broad, hardly
distinguished, sometimes bent very slightly outward; the apex broad,
blunt, often symmetrically rounded; or the lips slightly prominent,
subhyaline and subtended by a deeper shade on the inner side. Spores
70X6y. Perithecium 13535 to 210*55y, average 17542 μ.
Receptacle 235-335 50-70 uw. Longest appendage 200yu. Total
length to tip of perithecium 300-500 wu.

On “ Argutor Bonariense Dej.’’ Usually growing in a single group
not far from the base of the outer margin of the left elytron, but occur-
ring less frequently on the legs and inferior surface. Llavallol, No. 2032;
Temperley, No. 1512; Buenos Aires, No. 1962; La Plata, No. 1460.

A species usually distinguishable with a hand lens from its large
size and localized position on the left elytron. In one group of indi-
viduals examined there is some variation from the type described,
cell I being short, cell II much enlarged and separated from cell VI
by a conspicuous indentation, so that the receptacle is subgeniculate;
the tip is more prominently distinguished and bent inward, the lips
broader and more prominent. The variations in size are considerable
and almost straight individuals of the normal type sometimes occur.

Laboulbenia lutescens nov. sp.
“ Laboulbenia fumosa,”’ Spegazzini, Fungi Chilenses, p. 135.

Receptacle more or less deeply, though not uniformly suffused with
clear olive brown, especially along the margin below the appendages,
the basal cell small, hyaline below; cell II but slightly longer; cells

THAXTER.— ARGENTINE LABOULBENIALES. 201

II and VI subequal, the latter somewhat shorter; cell IV abruptly
prominent externally below the insertion-cell. Insertion-cell deeply
suffused, rather thick; the basal cell of the outer appendage somewhat
smaller than that of the inner, externally opaque, bearing distally two
branches radially placed; the outer branch strongly divergent to
horizontal or even slightly recurved, almost wholly opaque, its opacity
continuous with that of the basal cell; bearing above several subhya-
line branchlets; the inner branch erect, once or twice branched, its
basal cell and the outer primary branchlet arising from it, more or less
deeply suffused externally: basal cell of the inner appendage slightly
longer than that of the outer, bearing two erect slightly olivaceous
branches, one on either side, which are usually twice branched; the
ultimate branchlets hyaline, rigid, bluntly tipped, the longest scarcely
reaching the tip of the perithecium. Body of the perithecium slightly
and more or less evenly inflated, broadest in the middle, rich amber
yellow, sometimes becoming tinged with olivaceous; usually, but not
invariably, twisted one quarter, so that the tip is viewed at right angles
to the normal position; the tip more or less deeply suffused with black-
ish olive, short, rather abruptly distinguished, bent distinctly inward,
its outer margin nearly straight, its inner strongly indented, the apex
usually broad, horizontal, symmetrically bilobed; the lip-edges hya-
line and evenly rounded; if the twist is absent, oblique, or sometimes
four-lobed if the twist is one eighth. Spores 78X7u, Perithecium
125-145 35-40 uw. Receptacle 100-135 4. Total length to tip of
perithecium 225-275 μ, average 250 μ.

On the outer margin of the left elytron of “Argutor Bonariense Dej.”
Buenos Aires, No. 1962, No. 1431 in Museo Nacional; also at Temper-
ley and Llavallol.

This species does not appear to be nearly allied to L. fumosa to
which it has been referred by Spegazzini who found it on “ Argutori-
dius” at Santiago, Chile. It was found by me on the same host at
the Bafios de Apoquindo, near Santiago.

Laboulbenia asperata nov. sp.

Hyaline becoming pale straw- or amber-yellow. Receptacle
normal, the subbasal cell variably elongated, rarely minutely corru-
gated; cell V parallel to cell IV and slightly longer. Appendages
hyaline, the insertion-cell transparent, faintly suffused with reddish,
the basal cell of the outer appendage usually distinctly larger than
the inner, broader than long and forming a more or less prominent

202 PROCEEDINGS OF THE AMERICAN ACADEMY.

rounded or angular external projection variably developed below the
usually solitary elongate branch or simple appendage which arises
from it and is erect, sometimes divergent or even pendent, especially
if it is associated with a second branch within; the basal cell of
this appendage, sometimes its subbasal cell, inflated, broader than
long, more or less deeply constricted at the very faintly suffused
septa: the basal cell of the inner appendage producing two branches
which may be simple or once branched at the base, usually slightly
exceeding the tip of the perithecium, and sometimes elongate like
the outer appendage. Perithecium subhyaline to yellowish, rather
narrow, slightly divergent distally, the external basal wall-cell more
or less conspicuously roughened by fine transverse ridges; the tip
hardly distinguished, tapering very slightly; the apex broad, sub-
tended on the inner side by a small faintly suffused patch, the lips
evenly oblique outward, hardly prominent. Perithecia 11040 μ.
Longest appendage 250 μ. Receptacle 100-235 yp. Total length to
tip of perithecium, 150-350 μ, average 235 μ.

On the elytra ete. of Tachys sp., Palermo, No. 1696.

This species is nearly allied to L. Tachyis and to L. marina Picard,
but differs from both in the characters of its appendages and insertion-
cell, as well as by the characteristic external roughening of the outer
basal wall-cell of the perithecium.

Laboulbenia australis nov. sp.

Receptacle indistinctly punctate, cells I and II becoming dirty
yellowish, often contrasting with the frequently deeply suffused
yellow-brown distal portion which often becomes somewhat olivace-
ous. Insertion-cell horizontal, rather thick; the appendages rather
copiously branched the branches subparallel in a rather compact
group, usually erect or the whole bent slightly toward the perithecium;
the basal cell-of the outer appendage twice as long as the inner, not
distinguished from the cells above it, the appendage once or twice
branched or sometimes simple: the basal cell of the inner appendage
producing an erect branch on either side each once or twice branched,
the antheridia arising singly or two together even from the third
cells of the branches, so that they may lie opposite the tip of the
mature perithecium. Perithecium free, except at its very base,
usually straight, or concave externally and strongly convex inwardly,
especially immediately below the tip, so that the whole perithecium
is bent strongly outward distally in a characteristic manner; the tip

THAXTER.— ARGENTINE LABOULBENIALES. 203

short, abruptly distinguished, laterally deeply suffused especially
externally; the lips rounded, more or less symmetrically, translucent
or hyaline. Spores 45X3.5 μ. Perithecia 98X35 uw. Appendages
to tips of longest branches 155 uw. Receptacle 125-275 μ. Total
length to tip of perithecium average 250-275 μ (150-300 μ).

On all parts of a species of Apenes. Tucuman, No. 1940
(P. Spegazzini).

This species of which abundant material is available, is somewhat
similar to L. Oopteri, but differs in its characteristically and more
strongly curved perithecium, and in the absence of dark septa in the
outer appendage, the basal cell of which is never as highly developed,
in the present species. Individuals growing on the legs are smaller,
stouter and darker. .

Laboulbenia flexata nov. sp.

Yellowish to hyaline, with variable brown shades; the perithecium
becoming uniformly rich translucent brown. Form rather slender,
evenly curved throughout, but more or less distinctly geniculate
between the basal and subbasal cells of the receptacle which are
rather long and about equal in dimensions. Cells [V and V somewhat
enlarged and divergent, carrying the very broad and thick black
insertion-cell free from the base of the perithecium. Appendage
consisting of an outer and an inner branch of the type of L. Texana;
the outer stout, or curved somewhat away from the inner, and con-
sisting of four to six large subequal cells, each bearing a simple branch-
let like those of L. Texana, subtended by a small cell from which it is
separated by a deeply blackened septum; the small terminal cell of
the series bearing two such branchlets: the inner appendage consisting
of two branches which spring from a common basal cell; one of them
unicellular and terminated by a single antheridium, the other strongly
curved across the perithecium, and consisting of five or six small
superposed cells, each bearing a simple branchlet similar to those of
the outer appendage. Perithecium rather narrow, curved toward
the appendage, its middle opposite the insertion-cell; its tip abruptly
distinguished, narrow, prominent, opaque, contrasting abruptly with
the hyaline symmetrically rounded apex. Perithecium 155-200
48-55 wu. Receptacle 275-390 uw. Outer appendage 135-155x40 μ
at base, longest 20050 uw: inner appendage 50-6012 μ; longest
branchlets 120-140 μ.

On the inferior left margin of the prothorax of Brachinus sp., No.

204. PROCEEDINGS OF THE AMERICAN ACADEMY.

1457, Isla de Santiago, La Plata; No. 1426 in Museo Nacional, no
locality; No. 2030, La Plata (P. Spegazzini).

The present species adds still another form to the well marked
series of the L. Texana group, all of which occur on the inferior surface
or legs of species of Brachinus, and which I have hitherto preferred to
treat as varieties of L. Texana. Sufficient material of several of
these forms which is now available, indicates clearly that the members
of this series are better regarded as species, which correspond among
themselves in a fashion very similar to that which may be seen in the
much more numerous species which have developed on the allied
host-genus Galerita in the Western Hemisphere. Among these forms
Laboulbenia Oaxacana, alone, has not been found in the Argentine
region, although Laboulbenia pendula is known only from Monte-
video, and but a single specimen of what appears to be the typical
L. Texana was obtained at the Isla de Santiago.

Of the other members of the group the following were obtained.

Laboulbenia incurvata exactly resembling the types, was found
on a large Brachinus in the Museo Nacional, No. 1427, labeled
“Argentine”; on several specimens of a Brachinus taken on the Isla
de Santiago, La Plata, and on a Brachinus collected in Tucuman by P.
Spegazzini.

Laboulbenia retusa, which was first found in Florida, was again
obtained on Brachinus from the Isla de Santiago near La Plata, No.
1457, as well as from Tucuman No. 1939.

Laboulbenia tibialis, also first obtained in Florida, occurred in
good condition on a Brachinus collected by P. Spegazzini in Tucuman,
No. 1939. All the seven species of this group occupy more or less
definite positions on the host, and none of them ever occur, as far as
has been observed, on the upper surface; although L. Brachini,
which is often associated with them, may be found in any position.

Laboulbenia inflecta nov. sp.

Basal cell of the receptacle hyaline or faintly suffused above, much
longer than broad, the receptacle above it uniformly dull yellowish
olivaceous and compact, the cells not greatly different in size; cell III
extending upward sometimes almost to the insertion-cell. Insertion-
cell somewhat oblique, thick, deeply suffused; outer and inner basal
cells of the appendage subequal, the outer externally rounded and
suffused, the axis of the outer appendage consisting of about five
obliquely placed cells; those above the basal cell small, their branches

THAXTER.— ARGENTINE LABOULBENIALES. 205

stout, relatively short, divergent; the main axis of the inner appendage
consisting of five cells, the lower bearing relatively small stalk-cells
terminated by single large stout antheridia. Stalk of perithecium
hyaline, contrasting, very short, constricted; its axis coincident with
that of the perithecium and bent inward at a slight but definite angle
to the axis of the receptacle; the body of the perithecium translucent,
nearly symmetrical, becoming deeply suffused with clear, slightly
reddish olive-brown, subsymmetrically inflated throughout, the tip
rather narrow, abruptly distinguished, more deeply suffused; the apex
hyaline or becoming suffused, nearly symmetrically rounded or slightly
irregular. Perithecium above stalk 110-128X35-38 μ, the stalk
8X15-20 uw. Receptacle 9840-45 μ, its basal cell 45-5020 μ.
Main appendages 20 μ, their branches 50-75 uw. Antheridia 20 μ,
their stalk-cells 10-12 μ.

On the mid left elytron of a black species of Galerita (from two speci-
mens), La Plata No. 2021, P. Spegazzini.

This species resembles small forms of L. punctata, but differs in
the complete absence of maculation, as well as in other minor points.

Laboulbenia marginata nov. sp.

Basal cell of the receptacle hyaline, cells JI and III opaque and
indistinguishable, forming above a broad black margin extending
upward so that the free distal margin is on a level with the insertion-
cell; cell IV inwardly yellowish, obliquely elongated, externally dark
brown, separated from the upper part of cell III by a clear oblique
septum; cell V triangular, similarly suffused externally; both these
cells, as well as the rest of the receptacle, transversely punctate. Cell
VI and the cells above it subhyaline, soiled with dirty brown: the
stalk of the perithecium hyaline, the main body deeply suffused, ex-
ternally nearly straight and translucent, indistinctly punctate below,
inwardly distinctly convex and opaque; the tip abruptly distinguished
on both sides, opaque below the asymmetrical suleate apex; the inner
lips prominent, broad, rounded, the outer much smaller, lower, the
pore turned obliquely outward. Insertion-cell indistinguishable
from the opaque basal cells of the appendages, the blackened portion
curved outward and upward and forming a free rounded prominence
subtending the first outer branch; this blackened area larger than the
hyaline compact main appendages, the cells of which are very narrow;
those of the outer seven or eight in number, including the basal cell,
somewhat obliquely associated in a but slightly oblique series; the

206 PROCEEDINGS OF THE AMERICAN ACADEMY.

cells of the inner appendage more obliquely superposed, six or seven
in number, the three lower bearing antheridial branches consisting
of single basal cells terminated by single antheridia; the simple sterile
branches of the upper cells extending to about the middle of the peri-
thecium. Perithecium 250-275 Χ 52 uw exclusive of the stalk (58X30 μ).
Receptacle 190-20090 μ. Appendages to tips of branches about
175 μ; the antheridia 24 μ, their basal cell 204. Total length to tip
of perithecium average 500-510 μ.

On the inferior surface of the abdomen of Galerita Lacordairii.
Museo Nacional, No. 1428, “Argentina.”

Laboulbenia sordida nov. sp.

Resembling L. perplexa; rather slender; the basal cell of the recep-
tacle hyaline, the rest becoming irregularly suffused with dirty olive
brown; the region below the insertion-cell becoming nearly opaque,
the subbasal cell sometimes lighter or hyaline distally; cell IV sepa-
rated from cell III and V by parallel septa at an angle of 45° to the
axis of the receptacle. Insertion-cell broad, thick, horizontal, opaque;
the opacity involving the outer basal cell of the appendage which is
externally prominent upward. The outer appendage consisting of a
series of seven or eight obliquely superposed cells, coherent through-
out with the inner appendage, short; all, including the basal cell, bear-
ing erect branches, the two basal cells of which are dark brown, the
rest of the branch nearly hyaline and extending to or slightly above
the middle of the perithecium: the inner appendage consisting of a
series of usually five cells on either side above the basal cell, the
distal one bearing a short erect branch, while the four lower bear
antheridial branches consisting of a well developed brown basal cell,
bearing distally a pair of divergent, brown, somewhat curved antheri-
dia. Stalk of the perithecium clearly distinguished, about as long as
broad, hyaline, contrasting; the main body deep olive brown, straight,
asymmetrical, very slightly inflated below; the tip slightly darker,
short, asymmetrical, more or less well distinguished, its outer margin
oblique; the apex translucent, obliquely rounded outward, subtended
on the inner side by an opaque suffusion. Perithecium, exclusive of
stalk, 215-235X45~47 μ, the’ stalk 27-31X27 uy. Receptacle 215X
66 μ. Appendages, to tips of branches, longest, 1604. Antheridia
23-27 X6 p.

On the tips of the elytra of a black Galerita, La Plata, No. 2021.

This species is most nearly related to L. perplexa, from which it is

THAXTER.— ARGENTINE LABOULBENIALES. 207

best distinguished by the short coherent primary appendages, short
branches, and numerous paired antheridia.

Laboulbenia Heteroceratis nov. sp.

Uniformly pale straw-yellow, very variable in form. Receptacle
usually rather elongate, but sometimes short and stout, the subbasal
cells larger than the basal, cells [IV and V subequal. Insertion-cell
concolorous with the cells below it, the primary outer appendage
short, simple, cylindrical, hyaline, becoming distally flaccid; the
inner consisting of a few ill defined short flaccid branches; the in-
sertion-cell becoming very variably modified by secondary divisions,
which may also involve the basal cells of the appendages so that the
primary outer appendage may even become completely surrounded by
small cells bearing either branches or curved antheridia, the branches
sometimes forming a tuft of some length. Perithecium asymmetrical,
the inner margin usually straight or slightly concave, the outer
strongly convex; tapering to a snout-like tip so turned (in the Argen-
tine material) that it is viewed sidewise and shows a blunt symmetri-
cally rounded apex, subtended by a purplish shade. Perithecium
110-120X35+40 uw. Receptacle 156-235 uw. Appendages 50-60 μ.
Total length to tip of perithecium 220-340 wu.

Growing in various positions on species of Heteroceros sent from
La Plata by P. Spegazzini in 1907, Nos. 1679-80. Also found on
species of Heteroceros sent from Kansas by Dr. A. Stewart.

This very peculiar form varies greatly in general habit, and from
the secondary divisions of its insertion-cell and the basal cells of its
appendages may assume an appearance very similar to that of some
of the aquatic forms on Gyrinidae. Its relationships seem to be
evidently with the forms found on Clivina and its allies; although a
similar production of sessile antheridia from proliferous cells such as
occurs in the present instance is not seen in other forms. The above
description is based in part on material obtained from American
species of Heteroceros which were found among a small collection of
beetles kindly procured for me by Mr. Alban Stewart in Kansas City.
The measurements given above are from the Argentine material.
The Kansas specimens show the slightly oblique asymmetrical tip
of the perithecium from the usual point of view.

208 PROCEEDINGS OF THE AMERICAN ACADEMY.

Laboulbenia funeralis nov. sp.

Dull blackish olive becoming opaque, except the basal and subbasal
cells of the receptacle which are translucent dull olive, subequal,
forming a curved or sigmoid stalk not abruptly distinguished from the
rest of the receptacle, which is relatively narrow; the basal cell-
region of the perithecium bulging externally, and forming a rounded
flat, but usually distinct, prominence; above which the narrow
perithecium tapers very slightly and evenly to the very broad tip,
which is not distinguished; the apex partly hyaline bearing an inner
shorter tooth-like appendage, and an outer which is longer and usually
irregularly fureate. Appendages not very numerous, erect, septate
at the base; the hyaline slender tapering distal portion extending to
or beyond the apex of the perithecium. Perithecium 110-155 35-
40 »; the longer terminal appendage (longest) 20 uw. Total length
to tip of perithecium 235-350 μ; greatest width 38-66 uw including
elevation at base of perithecium.

On the margins of the elytra of a species of Gyrinus, No. 1957, in a
pond near the railroad station at Palermo.

This species which seems constant in specimens from a considerable
number of different individuals, is very closely allied to L. Gyrinidarum
from which it differs more especially in its smaller size, in the color
and conformation of its basal and subbasal cells which have no yellow-
brown tint, are similar and subequal; both being much longer than
broad; in the marked prominence below the perithecium, the tip of
which is not distinguished even on the inner side, as well as by its
terminal usually furcate apical appendage.

Rhachomyces Argentinus nov. sp.

Rather slender. Cells of the receptacle tinged with pale brown,
small, about as long as broad, ten or twelve of the lower visible; the
remainder wholly concealed by the closely appressed, rather slender,
copious black appendages; those about the base of the perithecium
somewhat stouter with hyaline tips, closely appressed about the
perithecium, nearly uniform in length, and extending nearly to its
tip, which projects free beyond them. Perithecium straight, sym-
metrical, brown, the tip nearly black, the apex subhyaline, flat-
conical or bluntly pointed. Perithecium 12040-4383 yw. Longest
appendages about 95 uw. Total length to tip of perithecium 310-425 μ
(longest).

THAXTER.— ARGENTINE LABOULBENIALES. 209

On the legs of a small carabid beetle resembling Casnonia. Jujuy,
Northern Argentine, No. 1480, Museo Nacional.

This species is most nearly allied to R. Javanicus, from which it is
distinguished by its more slender, copious and closely appressed
appendages, which conceal the axis of the receptacle distally, as well
as by the somewhat pointed apex of its perithecium. The material
includes two small specimens not more than 200 u in length.

Scaphidiomyces nov. gen.

Axis consisting of a primary receptacle of two superposed cells,
the subbasal bearing a primary branched appendage terminally, and
subterminally a secondary receptacle consisting of an indeterminate
series of superposed cells, which give rise alternately to stalked
perithecia and to branches similar to the primary appendage. An-
theridia simple, terminal on short branches. Perithecia normal.

This type, of which two other species are known on scaphidians,
from the Argentine and West Africa, appears to be related to the
Compsomycetaceae although the number of spores in the asci has
not been definitely determined. Some of the branches of the second-
ary receptacle when young, show the same peculiar oblique septation
characteristic of one of the appendages in Compsomyces; but this
may not be significant, and the perithecium has but a single stalk-cell;
the alternate production of branches and perithecia, and their associa-
tion on the indeterminate secondary axis, have no parallel in any
other genus. The characters of this type are nevertheless not clearly
defined, and a definite conception of its limitations cannot be arrived
at until sufficient material of other species is available.

Scaphidiomyces Baeocerae nov. sp.

Colorless, the perithecia becoming amber-brown at maturity,
rather short and stout, somewhat inflated, subsymmetrical, narrowed
distally to the broad tip; its apex broad, bluntly rounded or sub-
truncate; the basal cells similar, rather small, projecting slightly;
the region hardly distinguished from the body, and concolorous with
it: the stalk-cell hyaline, but slightly longer than broad, narrower
below. Basal cell of primary receptacle longer than broad, narrowed
and suffused with blackish brown just above the foot. The primary
appendage consisting of two to three superposed cells, bearing dis-
tally short few-celled branches and branchlets. Secondary receptacle

210 PROCEEDINGS OF THE AMERICAN ACADEMY.

continuous with and not distinguished from the primary, its axis
of similar cells of approximately the same size, superposed more or less
regularly in a somewhat zigzag fashion, the successive cells bearing
with more or less regularity appendages similar to the primary append-
age, and stalked perithecia of which there may be from one to four or
five in various stages of development produced on the same side or
alternating on opposite sides of the axis. Perithecia 75X35 μ, the
stalk-cells 15-18 u. Appendages to tips of branchlets 704. Total
length to tip of primary perithecium 150-310 wu.

On elytra of an undescribed species of Baeocera, a small scaphidian
feeding on Corticia under moist logs. Llavallol. (Determined by

Dr. Csiki.)
Scelophoromyces nov. gen.

Main axis consisting of a basal and subbasal cell forming a primary
receptacle, and a series of cells superposed above it; the subbasal cell
producing a lateral branch of several superposed cells,-terminated by
the primary perithecium: the upper cells of the axis, above the sub-
basal cell, producing more or less copious branches on the inner side
and terminally; while one or more secondary perithecia with single
stalk-cells may arise from the lower. The lower cells of the primary
perithecial branch, and sometimes the subbasal cell of the receptacle,
giving rise to slender supporting outgrowths, which curve down toward
the substratum. Antheridia (?) simple, and formed terminally from
the lower branchlets.

This genus is erected with some reluctance, since the nature of the
antheridia is somewhat doubtful. The latter appear to be terminal
cells of short lower branchlets from the main branches that arise from
the upper cells of the axis above the subbasal cell, and which may be
regarded as a primary appendage, or, since it gives rise to perithecia,
as a secondary receptacle. Although numerous specimens are avail-
able, and the form has also been obtained from the Amazon region,
the branches are for the most part not well preserved, even in the
youngest individuals. The several-celled stalk of the primary peri-
thecium would suggest that the relationships of the genus might be
with the Compsomyceteae, while the production of what may be re-
garded as a secondary axis suggests Clematomyces and Scaphidiomyces.
The adventitious branches which grow downward from the lower cells
toward the substratum undoubtedly act as buffers, like those of Cer-
atomyces rhizophorus described below, and Hydrophilomyces digitatus,

THAXTER.— ARGENTINE LABOULBENIALES. 211

described recently by Picard to which further reference is made below
under Ecteinomyces.

Scelophoromyces Osorianus nov. sp.

Pale straw- or amber-yellow, concolorous, becoming dirty amber-
brown with age. Perithecium subsymmetrical; main body distin-
guished from the slightly broader basal cell-region; of nearly equal
diameter throughout, or but slightly inflated, the short stout tip
abruptly distinguished, bent slightly outward; the apex broad and
nearly truncate; the basal cells subequal, large, slightly prominent;
two to six cells superposed to form the perithecial branch; the sup-
porting branches simple, septate, tapering throughout to pointed
extremities; two to four in number, one of them usually derived
from the subbasal cell of the receptacle on the side opposite the peri-
thecial branch. Main appendage, or secondary receptacle, consisting
of eight to ten superposed cells, terminated by a more slender portion
similar to the branches, which arise distally from cells obliquely sepa-
rated on one or both sides of the upper cells of the main appendage;
the branches more or less copiously branched, the ultimate branchlets
forming more or less characteristic tufts, and curved toward the main
axis: one to three of the lower cells usually producing a corresponding
number of secondary perithecia similar to the primary one. Dimen-
sions very variable. Perithecia, above hasal cells, 95-110 30-40 yu,
the perithecial branch 25-120 μ, total length, including branch, 130-
250 μ; basal cell-region 20-40 25-30 u. Total length to tip of long-
est branchlets (largest) 400 4. Supporting outgrowths 100-275 μ.

On abdomen and elytra of Osorius sexpunctatus Bernh., Palermo,
No. 1693, and Isla de Santiago, La Plata, No. 1972. Also from the
Amazon, (Mann), on a very large Osorius.

EcTEINoMYCcES Thaxter.

I have called attention in my second monograph to the uncertain
position of this genus, as well as of Hydrophilomyces; and also to the
similarity between these two and Misgomyces. Although the exami-
nation of fresh American material of Misgomyces Dyschirii from
Kansas, recently received in moderately good condition, appears to
show that this is a distinct genus more nearly allied to Laboulbenia,
a further study of forms allied to Ecteinomyces and Hydrophilomyces
has forced me to the conclusion that it is inadvisable to retain both

212 PROCEEDINGS OF THE AMERICAN ACADEMY.

these names, and that all the species are best united under the first.
The antheridial characters are doubtful in all the species, and it is
still uncertain whether the structures described as simple antheridia
in both cases are actually functional as such; since no actual discharge
has been observed from them. In these, as in other cases in which
the antheridia are not clearly distinguished, either by their position
or form, it is often very difficult to distinguish them from young sterile
branchlets, unless the material is examined while still fresh, so that
the discharge of sperm-cells can be observed. I have therefore con-
cluded to drop the name Hydrophilomyces, using Ecteinomyces to

include the three new forms below described, as well as E. rhynco-
phorus and Εἰ, reflexus.

Hydrophilomyces digitatus Picard on Ochtebius marinus from France
described in the Bull. Myc. Soc. de France, Vol. X XV, p. 244, 1910,
should also be changed to Ecteinomyces digitatus Picard, since it
evidently belongs in this group.

Ecteinomyces rhyncophorus was found at Palermo on a small hydro-
philid, and has also been obtained from Guatamala; the material in
both cases corresponding in all respects to that originally obtained
from Florida.

Ecteinomyces filarius nov. sp.

Wholly hyaline. Perithecium rather long and narrow, straight,
hardly inflated, the tip rather long-conical with straight margins,
subtruncate or rounded, the apex symmetrical and subtended ex-
ternally by a distinct prominence; the basal cell-region not distin-
guished, its cells flattened around the ascogenic cells; borne on a
distinct short stalk-cell. Receptacle filamentous, slender, elongate,
consisting of many (about forty) superposed cells; the distal ones
becoming slightly broader, and occasionally cutting off a small cell
subterminally or laterally; the axis continuous with an erect primary
appendage of similar character, consisting of about six superposed
cells, and lying close beside the perithecium and slightly exceeding it in
length, bearing distally the remains of one or two branchlets. Spores
(in perithecium) 30-35X3 yu. Perithecium 70X14 uw; the stalk-cell
8X10 uw. Receptacle 230-275X7-9 μ. Total length 290-340 μ.

On the elytra of Coproporus rutilus Er.; Tucuman, No. 1934,
(P. Spegazzini).

The antheridia of this species have not been seen, and the types
show only the bases of what appear to have been rather short branches

THAXTER.— ARGENTINE LABOULBENIALES. 213

from the end of the appendage. Its hypha-like receptacle is even
more striking than that of EF. Trichopterophilus, from its greater
length and more evenly cylindrical form.

Ecteinomyces Thinocharinus nov. sp.

Wholly hyaline. The receptacle usually tapering continuously
from above to the minute foot, its axis continuous with that of the
perithecium and consisting of from six to twelve more or less flattened
cells, which may occasionally be divided longitudinally; the foot-cell
of some individuals developing an upcurved appendage, deeply
blackened except along its inner margin, of variable length, thicker
and bluntly rounded at its tip. Perithecium clearly divided into a
nearly symmetrical oval venter and a long, stout, nearly straight,
isodiametric neck-portion, the base of which is subtended on the outer
margin by a more or less distinct prominence formed by the slightly
protruding extremity of the outer basal wall-cell; the tip hardly
distinguished, tapering but slightly to the blunt symmetrical apex.
Appendage slightly divergent, consisting of six or more superposed
cells, the basal larger, angular, in contact on its inner side with the
small basal and stalk-cells of the perithecium; the terminal cells
bearing a group of rather coarse branches, once or twice branched,
the ultimate branchlets not reaching to the tip of the perithecium.
Spores, in perithecium, 20X2.5 w. Perithecia 120-130X 23-27 “μ.
Receptacle 55-65 yw. Foot-appendage 18 uw. Appendage 35-50 μ,
its branches 75-90 μ.

On the abdomen ete. of Thinocharis exilis Er., Temperley, No. 2004,
and Palermo, No. 1701.

The curious black outgrowth from the foot of this species, occurs
in about half the specimens; but while in these it is well developed,
there is no trace of it in the others, even when fully matured and
growing in the same position.

Ecteinomyces Copropori nov. sp.

Hyaline or faintly tinged with yellowish. Receptacle consisting of
from ten to twenty superposed cells some of which may become
irregularly divided by one or two longitudinal septa, the cells usually
flattened, often irregular, the basal cell subtriangular and deeply
suffused with blackish brown above the small foot. Appendage at
first not distinguished from the receptacle and continuous with it,

2

214 PROCEEDINGS OF THE AMERICAN ACADEMY.

slightly divergent when mature, consisting of a variable number
(eight to twelve) of superposed cells, the series tapering distally, some
or most of the cells cutting off one or two small cells on the inner side,
sometimes also on the outer side from which branches arise as well as
antheridia (?) which are irregularly flask-shaped, single and sessile or
borne one or two together on short branchlets; the sterile branches
usually broken and not copiously developed. Perithecium nearly
straight, its axis usually continuous with that of the receptacle, a
venter neck and tip more or less clearly distinguished, the latter bent
very slightly inward, the apex blunt and usually becoming minutely
six-papillate; the outer, lower wall-cell slightly prominent below the
neck; the two upper basal cells extending upward beside the venter,
the stalk-cell short and subtriangular. Perithecium 140-200X38-
44 μ, smallest 100X 25 μ, stalk-cells and lower basal cells 20 u. Spores
in peritheclum 35X3.5 uw. Receptacle average 200 μι Appendage
60-100 μ. .Total length to tip of perithecium about 325 μ.

On the abdomen of Coproporus rutilus Er.; Tucuman, No. 1933,
P. Spegazzini. Also from Los Amates, Guatemala, No. 1614 (Keller-
man).

The material of this species is not in very good condition and it is
difficult to determine the character of the appendages and antheridia
from them. The Guatemalan material includes only three specimens
in which the perithecia are mature, and in these the papillation of
the apex is either indistinct or lacking; but, although the individuals
are somewhat larger, the perithecia more divergent, and the cells of the
receptacle shorter and broader than the Tucuman material, the two
forms seem identical.

Autoicomyces bicornis nov. sp.

Pale yellowish with a smoky tinge, deepest at the base of the peri-
thecium. Basal and subbasal cells of the receptacle rather large, of
about equal length. Appendage usually straight, somewhat diver-
gent, comparatively slender; consisting of six or more superposed cells,
and bearing a few small branchlets. Perithecium nearly straight
externally, its inner margin convex; the tip lying in the fork formed
by two outgrowths which arise symmetrically just below it from the
wall-cells on either side; the outer shorter, rather closely septate,
tapering to a blunt apex, and curved inward; the inner two or three
times as long, usually septate only at the base, curved away from the
perithecium and tapering to a blunt point. Perithecium 95-110X

THAXTER.— ARGENTINE LABOULBENIALEFS. 215

40-45 μ, its longer appendage 60-200 μ, the shorter 70-78 μ. Ap-
pendage 1385. Receptacle 80X35 4. Total length to tip of peri-
thecium 175-190 uw; to tip of inner appendage 310-370 μ.

On the inferior surface of the abdomen of Berosus sp. or a closely
allied genus. Palermo near Belgrano, No. 1944.

A species readily distinguished by its paired perithecial appendages,
but conforming strictly to the type so clearly marked in this genus.

Ceratomyces rhizophorus nov. sp.

Receptacle small, hyaline, normal; the second and third cells
broad and much flattened. The appendage long, of nearly equal
diameter throughout, composed of numerous short flattened cells
bearing scattered branches. The basal cell, and one or more of the
upper cells of the receptacle, developing short rigid curved simple
outgrowths, which grow downward to the substratum. Perithecium
stout, tapering distally to a well distinguished, abruptly narrower,
bluntly rounded tip; each marginal row of wall-cells comprising about
twenty cells. Perithecium 10040 μ. Appendage 135X 16 (broken).
Receptacle 50 μ, the foot 204. Total length to tip of perithecium
150 μ.

At the tip of the left anterior leg of Tropisternus sp. Palermo, near
Belgrano, No. 1645.

All but two specimens of this small and peculiar species were unfor-
tunately destroyed by accident, while they were being mounted, so
that it has been necessary to base the above description on a single
nearly mature, and one younger individual. It is, however, so pecu-
liar, and so well characterized by its supporting outgrowths that it
has seemed safe to give it a name. The outgrowths are evidently
buffers, similar in function to those described in Ecteinomyces
(Hydrophilomyces) digitatus Picard, and of Scelophoromyces described
above.

Ceratomyces ventriosus nov. sp.

Receptacle relatively long, the subbasal cell and the cell above it
deeply blackened laterally, the suffusion extending upward and involv-
ing the outer margin or half of the cell which subtends the appendage.
Appendage long and relatively slender, bearing a few scattered
branches, the lower cells somewhat flattened and becoming divided
by a few oblique septa. The receptacle, appendage and base of
perithecium pale yellowish, or with a reddish-amber tinge. Peri-

216 PROCEEDINGS OF THE AMERICAN ACADEMY.

thecium relatively very large and long, about forty-five cells in each
row of wall-cells; more or less evenly curved away from the append-
age, deeply rich red amber-brown, except at its pale narrower base,
of the lower half characterized by a belly-like enlargement; the upper
half of nearly the same diameter throughout; the tip subtended
externally by a vesicular enlargement of one of the wall-cells, its
hyaline apex pointed and bent inward toward the concave base of
the long appendage, which is usually abruptly curved at its base,
more or less deeply suffused or opaque below, tapering very slightly,
consisting of about twelve cells, the lowest of which is comparatively
small, and not extending above the apex of the perithecium. Peri-
thecium 550-700X 100-110 uw (lower half) and 65-75 uw (upper half),
the appendage 250-350 30 μ.

On the inferior surface of the abdomen, near the tip on the left side
of Tropisternus sp.; Palermo, near Belgrano, No. 1949.

The long appendage of this remarkable species is very similar to
that of the last, to which it seems to be most nearly allied, but from
which it is easily separated by the form of its receptacle and its enor-
mous pot-bellied perithecium.

Ceratomyces marginalis nov. sp.

Uniform dirty translucent amber-brown. Receptacle small, the
foot and basal cell opaque and indistinguishable; the two cells above
greatly flattened, the subbasal partly involved below by the suffusion
of the cells above. The appendage small, short, consisting of four or
five superposed cells, terminated by a few branchlets, erect, appressed
against the perithecium or but slightly divergent. Perithecium rel-
atively large, about eight wall-cells in each row, straight, but slightly
and rather evenly inflated; the tip not distinguished, but terminated
by an erect hyaline nearly cylindrical slender blunt apical prolonga-
tion, subtended by a relatively very large sigmoid appendage, which
curves toward and beyond it, thence bending and tapering upward,
and composed of a series of eight or nine superposed cells of about
equal length, sometimes terminated by a few short colorless branch-
lets. Perithecium 90-110 35-45 μ, the longest appendage 100 μ.
The receptacle, including foot, 55-6030. Appendage 60X7 μ.
Total length to tip of perithecium 135-150 μ, to tip of appendage
ΦΦ Ὁ yt,

Beneath the margin of the elytra of a small pale hydrophylid.
Palermo, near Belgrano, No. 1952.

THAXTER.— ARGENTINE LABOULBENIALES. 217

In general habit this species is not unlike C. minisculus from which
it is at once distinguished by its large perithecial appendage.

Ceratomyces intermedius nov. sp.

Receptacle faintly tinged with amber-brown, rather short, externally
opaque above the basal cell to the base of the appendage, the blacken-
ing involving the outer half or less of the cells concerned; the cell sub-
‘tending the appendage slightly prominent externally, below the latter.
The perithecium and appendage usually divergent at the base of the
latter, which is faintly tinged with amber-brown, stout, curved out-
ward; consisting of a series of cells smaller distally, about six of the
lowest very broad and flattened, becoming divided more or less irregu-
larly by oblique partitions, and bearing a few scattered branchlets
on the inner side. Perithecium large, stout, deeply tinged with dull
amber-brown, paler at the base where it is distinctly narrower, the
distal two thirds of nearly the same diameter throughout, or the middle
third somewhat inflated; the tip short abruptly distinguished exter-
nally, being subtended by a rounded prominence in which the series
of wall-cells below it ends, its apex hyaline, asymmetrically rounded
or outwardly oblique; the simple perithecial appendage becoming
deeply suffused or opaque except at its bluntly pointed tip, erect or
bent inward, consisting of from about six to eight successively smaller
cells, the lower becoming deeply suffused; the basal cell very large,
concave within, convex externally, the whole assuming a sigmoid
curvature as it matures. Perithecium 310-39080-105 yu, the base
50-60 4; the appendage 105-170yu. Receptacle 74-82X75-78 μ,
without foot (304). Appendage 2004548 μ at base. Total length
to tip of perithecial appendage 660 yu.

On the left anterior margin of the thorax of Tropisternus sp.; Pal-
lermo, near Belgrano, No. 1946.

A large and clearly distinguished species, intermediate between
C. mirabilis, which it more nearly resembles in its perithecial char-
acters, and C. cladophorus, which has a similar though somewhat.
more highly developed appendage.

Synaptomyces nov. gen.

Receptacle indeterminate, consisting of a series of superposed cells;
the uppermost of this series followed by two cells placed side by side,
one of which is separated by a single small cell from the basal cell of

218 PROCEEDINGS OF THE AMERICAN ACADEMY.

the appendage, while the other forms the base of the outer series of
wall-cells of the perithecium. The appendage consisting of a series
of superposed cells bearing scattered branchlets. Perithecium many-
celled, indeterminate, without distinction of venter and neck, ap-
pendiculate on the inner side below the tip.

This genus, of which two other species are known on Hydrocharis,
one from North America, and another from Africa, appears to be
intermediate between Ceratomyces, which it resembles most nearly
in the characters of its perithecium, and Rhyncophoromyces, which ἡ
possesses a similar indeterminate receptacle. Although in the present
species, which is taken as the type, several appendages develop in a
compact group below the apex of the perithecium, in the African form
there is only one which is very similar to that seen in species of Cera-
tomyces. ‘The North American form, of which I have only one un-
developed individual, shows that the sperm-cells -are developed
exogenously exactly as in Rhyncophoromyces.

Synaptomyces Argentinus nov. sp.

Receptacle consisting of a series of about twenty superposed, much
flattened, cells; surmounted by two somewhat unequal cells separated
from one another by an oblique septum; a transversely elongated
rounded cell lying obliquely between the anterior of the two and the
basal cell of the appendage, which is more or less conspicuously
indented externally. The appendage somewhat broken in the types,
its basal or subbasal cell giving rise to a simple branch, the main axis
of undivided superposed cells proliferating to form several slender
branches, which arise from its tip. Perithecium relatively large and
stout, hardly inflated above the base, slightly narrower distally, the
papillate tip abruptly distinguished; the apex broad and asymmetri-
cally rounded, the perithecial appendages arising in a group just below
the tip on the anterior side, usually three being superposed; their
extremities free, their bases laterally coherent, some of them proli-
ferating to form slender terminal hyaline branchlets: Perithecium
335 X80-390-105 μ; its appendage without terminal branchlets 110--
120 μ. Receptacle 250-27 70-80 μ distally. Appendage (broken)
160 15-18 μ. Total length to tip of perithecium 700-750 μ.

On the left inferior margin of the thorax of Hydrocharis sp., No. 948,
Palermo, near Belgrano.

THAXTER.— ARGENTINE LABOULBENIALES. 219

In addition to the new forms above described the following species
were found, and also a few others that are not determinable.

Acompsomyces brunneolus Th. <A species closely allied to the North
American form, was obtained at Palermo on a small Corticaria (?)
The conformation of the tip of the perithecium is very similar, but
the latter is shorter and stouter, its broad base abruptly distinguished
from the somewhat longer narrower straight stalk-cell. The stalk-
cell of the appendage is also quite hyaline. Since the type form has
been found only once, its variations are not yet known, and it seems
inadvisable to separate the Argentine form until further material of
both is available.

Camptomyces melanopus Th. Several well matured and _ typical
specimens of this species were found on the abdomen of Sunius sp.,
No. 2002, at Temperley, but although very many specimens of Suni
were examined it was not again met with.

Chaetomyces Pinophili Th. was found very rarely on Pinophilus
suffusus Er., although its host was very common at Llavallol. The
material differs in no respect from that obtained in North America.

Ceratomyces mirabilis Th. was very common on T'ropisterni at
Palermo, near Belgrano, the specimens exactly like those from New
England.

Ceratomyces ansatus Th. was also common, and as usual did not
occur on the wholly black species of T'ropisternus.

Ceratomyces filiformis Th. Several typical specimens were ob-
tained growing at the tip of the posterior legs of several Tropisterni.

Ceratomyces minisculus Th. was found once on a species allied to
T. lateralis.

Compsomyces verticillatus Th. was found rather rarely on species
of Sunius at Temperley and Llavallol, Nos. 1995 and 2002, the
individuals differing in no essential respect from the North American
type.

Corethromyces purpurascens Th. This species was found very
commonly in the vicinity of Buenos Aires on an evenly, rather pale
brown species of Cryptobiwm, and appears to be very constant in its
characters, varying only in the luxuriance with which the branches
of the appendage are developed.

Corethromyces Stilici Th. This species was found in abundance
on several species of Stilicus, the normal form like that first collected
at Interlaken, Switzerland, being sometimes associated with one in
which the stalk-cell of the perithecium is enormously developed, the
body of the perithecium being at the same time more elongate, its

220 PROCEEDINGS OF THE AMERICAN ACADEMY.

wall-cells more markedly spiral and with the appendage somewhat
reduced. Although perhaps worthy of varietal rank, it has not
seemed desirable to separate this form specifically.

Dichomyces furciferus Th. was found several times at Palermo and
at Temperley on Philonthus hepaticus Er., No. 1960.

Dichomyces vulgatus was met with rarely on a large Philonthus at
Llavallol, No. 1490 and 1936, and occurred on a Philonthus collected
by Propile Spegazzini in Tucuman.

Dichomyces princeps Th. was found rarely at Palermo on a species
of Philonthus, No. 1958.

Dichomyces Homalotae Th. Typical material of this species was
found several times at Palermo, No. 1964, and at Temperley, No.
2008, on Atheta sordida Marsh.

Dichomyces sp., a species apparently unlike the North American form
on Xantholinus, was found on a small species of this, or a closely
allied genus at Llavallol, No. 1497, at Temperley, No. 2003 and at
Tucuman, No. 1931 (P. Spegazzini), but the material is too scanty to
make a positive determination possible.

Dimeromyces Labiae Th., was found in abundance on Labia minor,
No. 1974, in the park at Palermo, the specimens corresponding exactly
to those obtained at Cambridge.

Ecteinomyces rhyncophorus Th., on a small hydrophilid at Palermo.

Eumonoicomyces Papuanus Th. A form which does not appear to
differ essentially from the Papuan material of this species was found
occasionally on the legs of a species of Oxytelus (?) at Temperley. This
appears to be the form described as E. Argentinensis Speg.

Herpomyces Paranensis Th. was found in abundance on the an-
tennae of a large roach (Blabera ?) inhabiting the roof of the Museo
Nacional at Buenos Aires.

Kleidiomyces furcillatus Th. This peculiar species, formerly known
only from a single complete specimen, was found in perfect condition
and not uncommonly on species of Aleochara at Temperley, Llavallol,
and the Isla de Santiago. An examination of abundant material
shows conclusively that its separation from Monoicomyces is inevit-
able owing to the quite different character of its antheridium which is
furnished with a lateral pore.

Laboulbenia Aspidoglossae Th. on Aspidoglossa sp. (?) was common
in the park at Palermo and resembled the North American material
in all respects.

Laboulbenia bicolor Th. This small species was found abundantly
on the elytra and legs of a black Galerita, No. 2021, collected at La

THAXTER.— ARGENTINE LABOULBFNIALES. 221

Plata by P. Spegazzini, and also on the legs of G. Lacordairii, No.
1428, in the Museo Nacional. It resembles the type form from Vene-
zuela in that the basal cell of the outer appendage is similarly modified
but lacks the constriction, so characteristic in the type, above the
basal cell of the receptacle. In the latter respect it approaches more
nearly the distinctly larger Brazilian specimens obtained on G.
carbonaria, in which, however, the basal cell of the outer appendage
is unlike that of the type.

Laboulbenia Brachini Th. was again obtained abundantly from
various species of Brachinus, and from different regions in the Argen-
tine.

Laboulbenia Clivinae Th. on Clivina sp. and entirely typical was
found on a specimen in the Museo Nacional, No. 1430, “ Argentina.”

Laboulbenia compacta Th., was found but twice on Bembidia outside
the docks at Buenos Aires, No. 1969 and 1967.

Laboulbenia cristata Th. was found but once on Paederus sp., No.
2029 La Plata.

Laboulbenia geniculata Th. Several specimens of this species, which
correspond exactly to the type, were obtained with several other
species on a black Galerita collected at La Plata by P. Spegazzini.

Laboulbenia decipiens Th. was found on a black Galerita, No. 1439,
from Tucuman, in the Museo Nacional.

Laboulbenia Mexicana Th. a pale and variable species, usually found
only on the mid-elytra, occurred on two species of Galerita, Nos.
2020 and 2021 from La Plata, and Llavallol; also on a species from the
Pampa Grenada, No. 1442 and from Jujuy, No. 1445, both in the
Museo Nacional.

Laboulbenia Oedodactyli Th. was found repeatedly on Oedodactylus
fuscobrunneus Fairm. No. 1976, at Llavallol and at Temperley. The
material is in good condition and in a majority of individuals the
outer appendage is greatly elongated, almost as much so as in L.
Lathropini, which is its nearest ally, but from which it is distinguished
at once by the character of its wall-cells which are neither striate nor
spirally twisted.

Laboulbenia pedicillata Th., occurred rather rarely on Bembidiuwm
at Buenos Aires. No. 2016.

Laboulbenia Philonthi Th. was very common on various species of
Philonthus throughout the whole Buenos Aires region.

Laboulbenia polyphaga Th. The forms allied to this species and to
L. flagellata were numerous on many genera of Carabidae. The whole
series needs much careful study of abundant material. Nos. 1506,

222, PROCEEDINGS OF THE AMERICAN ACADEMY.

2019, 2022, 2023, 2024, 2025, 2026, 2027, 1445, 1444, 1970, 1997,
2010, 2014, 2017, 2022.

Laboulbenia Pterosticht Th. was found occasionally on carabids, all
allied to Pterostichus, near Buenos Aires.

Laboulbenia punctata Th. was found on the head of a large Galerita
with red prothorax, from Tucuman No. 1441, the individuals for the
most part immature and somewhat smaller than the type, but other-
wise identical with it.

Laboulbenia Pygmaea Th. was obtained on Galerita sp. from Jujuy,
northern Argentina, in the Museo Nacional, occurring on the tip of
the abdomen. The species seems to vary chiefly in the relative width
of its receptacle which may be considerably narrower than it is repre-
sented in my Monograph, Part II, Plate LXII, fig. 6.

Laboulbenia sigmoidea Spegazzini. This well marked species which
is most nearly allied to L. elegans Th., was found on the left inferior
margin of the prothorax of a carabid named in the Museo Nacional
Argutor Bonariense, but referred to by Spegazzini as an Argutoridius
in his original description, Fungi Chilenses, p. 134 (Buenos Aires,
1910). It was found by me near Santiago, Chile, and in several
localities in the vicinity of Buenos Aires, but although the host is
common it was rather rare. The host-genus is Pterostichus.

Laboulbenia Tachyis Th., or a very closely allied form, was found
repeatedly on a Bradycellus sp. in the park at Palermo, No. 1697, also
at Temperley, No. 1517, and at Llavallol, No. 1996.

Laboulbenia Texana Th. A single immature individual that appears.
to belong to this species was obtained on a species of Brachinus on
the Isla de Santiago, La Plata. The other forms heretofore grouped
as varieties of this species, are referred to above (p. 56). Among these
L. incurvata, L. retusa and L. tibialis were again found in the Argentine.

Laboulbenia variabilis Th. was common about Buenos Aires, as it
appears to be everywhere else in South America, Nos. 1433, 1435,
1443, 1446 etc.

Laboulbenia vulgaris Th., which appears to have been described as
L. Chilensis by Spegazzini, is everywhere common on Bembidia
in Chile and the Argentine. There seem to be no characters indicated
either by Spegazzini’s description or figures which would suggest
that L. Chilensis should be considered distinct. (Spegazzini, Fungi
Chilenses, p. 133.)

Moniocomyces Homalotae Th. A few typical specimens of the
smaller form of this species on Atheta sp., No. 1510, were found
at Palermo. Another species closely allied to M. Homalotae, was

THAXTER.— ARGENTINE LABOULBENIALES. 223
”
found on Ophioglossa sp., but the material is not sufficient for
description,

Monoicomyces nigrescens Th. A form corresponding in all respects
to the North American material of this species was found abundantly
in the Buenos Aires region on the tip of the abdomen of Meroneva
Sharpi L. Arrib., No. 1503, Palermo, Temperley and Llavallol.

Rhyncophoromyces rostratus var. similar to that which is figured in
my first Monograph, Plate XXIV, fig. 26, was found several times at
Palermo on the margins of the elytra of a pale Hydrophilid. This
form will probably have to be separated from the type, eventually.

Stigmatomyces virescens Th., which is probably cosmopolitan,
having been received from Borneo, as well as Brazil and the West
Indies, was obtained on a dull coccinellid collected by P. Spegazzini
at La Plata.

Zodiomyces vorticellarius Th. The monstrous Argentine form
previously recorded from Rosario, Argentina, was again met with at
Palermo, on a large Hydrophilus, and the normal type was also found
on smaller hydrophilids. A form perhaps specifically distinct was
also found on a small hydrophylid, but sufficient material was not
obtained.

Note. Since the present paper was in type I have received from Professor
Spegazzini his “‘Contribucién al Estudio de las Laboulbeniomycetas Argen-
tinas,” Buenos Aires, June, 1912, and have made such alterations in my own
account as seemed absolutely necessary; reserving further comment on the
paper for some more convenient time.

Proceedings of the American Academy of Arts and Sciences.

Vor. XLVIII. No. 8.—Ocroser, 1912.

“

CONTRIBUTIONS FROM THE CRYPTOGAMIC LABORATORIES
OF HARVARD UNIVERSITY.

No. LXX.—CULTURE STUDIES OF FUNGI PRODUCING
BULBILS AND SIMILAR PROPAGATIVE BODIES.

By Joun WI.LurAM Hotson.

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CONTRIBUTIONS FROM THE CRYPTOGAMIC LABORATORIES

OF HARVARD UNIVERSITY.

LXX.— CULTURE STUDIES OF FUNGI PRODUCING BUL-
BILS AND SIMILAR PROPAGATIVE BODIES.

By Joun Wiuu1aAm HortTson.

Presented by Roland Thaxter. Received June 19, 1912.

CONTENTS.

Introduction Ξ

Review of Literature

Sources of Material

Culture Methods

Systematic Consideration of the Forms studied .
Discomycetous Forms .

Cubonia bulbifera n. sp.

Lachnea theleboloides (A. & i) ) Sace.

Peziza species, Zukal Γ
Pyrenomycetous Forms :

Melanospora papillata n. sp.

Ἂ cervicula τι. sp.
anomala τι. sp. .

Melanospora Gibelliana Mattirolo
Melanospora globosa Berl.
Sphaeroderma bulbilliferum Berl.
Ceratostoma species (Bainier)

Forms doubtfully Referred to the Pyre homyeetes
Papulospora candida Sace. :
Acrospeira mirabilis B. & Br.

Basidiomycetous Forms.

Grandinia crustosa (Pers.) Fr. ᾿

Corticium alutaceum (Schrader) Bresadol: Ne

Papulospora anomala n. sp. ἜΣ

‘‘Bulbil No. 200” . Shade.
Bulbils not yet Connected with ; any Perfect Forms and

in the Form-Genus Papulospora
Papulospora
{{

({

immersa 1. Sp.
pannosa ni. sp.
irregularis τι. sp.
spinulosa τι. sp. .
coprophila (Zukal)
rubida τι. sp. J
sporotrichoides n. sp.

Included

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PROCEEDINGS OF THE AMERICAN ACADEMY.

Pace

Papulospora cinerea Τ᾿. Sp. . ὦ a IP Cet ah hs, "=
parasitica (Karsten) eld, en Pee td See eee ED

i asnengullijonaiss πσνοἔὁΕΨσννσἔἘΕσηςἝἘοψἅ δ δ)262}ὸῸὺῦυῸό᾿π“τ-- -οτιτἙ«:᾿ῸὸῈὸ-

MY POLYSPOTG MN. SPie tks Apes eles) ee ee See

Other recorded Bulbiliferous Forms _. στ U0
Compound Spores and other Structures which resemble Bulbils . . . 297
fhe Morphological-Sienificanceiof Bulbils ~~ =). e209
DistrbutionyandsOccurrenceyoh Bulbilses 2 9s 2 a ee OIL
Key to the Species of Bulbils ΠΥ Ma LA π Ὁ}
List of Literature ons Sad el a. ao ee ee eee ὃ"

INTRODUCTION.

Tue term “bulbil” was first employed in connection with Fungi
by Eidam in 1883 to designate certain sclerotium-like bodies, some-
what definite in form, and capable of reproducing the plant. They
vary greatly in appearance, some consisting of a compact mass of
homogeneous cells clearly distinguished from certain others which
surround them. The latter form a single layer or in some cases
several layers of cells, which may or may not become empty and
colorless and which correspond, in a general way, to the pseudospores
or accessory spores of certain smuts, while the cells which they sur-
round are functional spores and capable of germination. Bulbils
are the predominant type of reproduction in certain fungi, and in
some cases the only means at present known. The most typical
bodies of this nature are readily distinguished from sclerotia by their
smaller size, more definite structure, and peculiar methods of develop-
ment. There are other types, however, that seem to approach more
nearly true sclerotia; while others again resemble very closely the
“spore balls” of such forms as Tuburcinia, Urocystis, ete., among the
Ustilaginales, or even the compound spores of such forms as Stem-
phylium, Mystrosporium, etc., among the Hyphomycetes; but from
the first they are definitely distinguished by their method of germina-
tion, while in general they are readily separated from the last two
by their mode of development. They thus seem to possess morpho-
logical characters that would place them in an intermediate position
between sclerotia, on the one hand, and compound spores of the
dictyosporic type on the other, with examples of transitional forms
which grade into the former and others that are almost indistinguish-
able from the latter.

Bulbiferous conditions among the fungi have, in general, been
described under the following genera of the so-called “Fungi Imper-
fecti’’: Papulospora, Helicosporangium, Baryeidamia and Eidamia;

ee

HOTSON.— CULTURE STUDIES OF FUNGI. 229

but in a few instances, in which their association with other and more
definite types has been reported, they have been included under the
generic name applied to the latter as, for example, Dendryphium or
Haplotrichum. There seems to be little or no uniformity or agree-
ment among the writers on this subject, especially among the earlier
ones, regarding the morphological significance of bulbils. Preuss,
who was the first to describe bodies of this nature in 1851, considered
each bulbil a single compound spore and placed the genus Papulo-
spora, which he had created for their reception, in the “ Bactridiaceae”’
of Corda, a family not now recognized, which was established to
include fungi like Trichocladium Harz, bearing compound spores and
with prostrate fertile hyphae. On the®other hand, Karsten (’65) re-
garded the bulbil-like bodies which were associated with his “ Helico-
sporangium”’ as an ascus-producing structure, which was included by
him among the Erysipheae. Again, Eidam (’83) was of the opinion
that the two genera, Papulospora and Helicosporangium, occupied an
intermediate position between Ustilagineae and Erysipheae, while E.
Fischer is inclined to place them among the Monascaceae. De Bary,
in his “Morphology and Biology of Fungi,” considers them briefly
and includes them in a category which he calls “ Doubtful Ascomy-
cetes’’ and suggests that “the plants should be further investigated.”
In considering these forms at a later period, Harz (’90) included all
structures of this nature then known under a new order, the “ Lep-
toomycetes’”’ and expressed the opinion that they are somewhat
closely related to the Oomycetes and coordinate with them and the
Zygomycetes.

Inasmuch as these bulbils have received very little attention, our
knowledge of their morphology, development, and taxonomy is very
meagre. These forms are not as rare as has been generally supposed
but are, on the contrary, widely distributed and of common occur-
rence. Substrata which have produced bulbils have been obtained
from various parts of Canada and the United States; from Guatemala,
Mexico, and West Indies; from South America and Europe. Their
small size, the nature of the substratum on which they grow, and their
failure to form a conspicuous fructification in a majority of cases,
account to some extent for the fact that they are generally overlooked
in the field and in laboratory cultures.

The results of the present investigation emphasize the fact, more
recently brought out by several mycologists, that these fungi do not
belong to any one of the Natural Orders, nor do they in any sense
form a group by themselves, but occur without regularity as imperfect

230 PROCEEDINGS OF THE AMERICAN ACADEMY.

forms among the main groups of Higher Fungi. The forms associated
with bulbiferous conditions which are herewith enumerated include
among the Discomycetes, a new species of Cubonia; among the
Hypocreales, three species of Melanospora; and among the Basidio-
mycetes at least four types; while nine species of Papulospora as
yet unconnected with a perfect form are added to those already known.
Among the latter also, Papulospora candida Sace. has been found to be
associated with a second and well marked imperfect form, namely
Verticillium agaricinum var. clavisedum. In the life histories that have
been worked out, the results have been obtained from pure cultures
which, in many eases, have run for a number of years, and care has
been taken to avoid any errors resulting from contamination.

In view of the very general occurrence of bulbils, it is somewhat
surprising that more attention has not been given to them. The
literature on the subject is quite limited and the accounts given often
conflicting. Preuss, Karsten and Eidam did their work at a time
when Mycology was in a more or less transitional condition, the
emodern bacteriological methods had not yet been applied to the
cultivation of fungi, a fact which may account to a certain extent for
the varied and often conflicting opinions of these earlier writers.
Certain more recent contributions, however, have given us more
accurate information as to certain isolated forms and the investiga-
tions of Mattirolo, Berlese, Bainier and Lyman have suggested or
demonstrated the actual relationships of certain forms to species
among the Ascomycetes and Basidiomycetes, of which they prove
to be imperfect conditions. There has been no attempt, however,
so far as the present writer is aware, to investigate the general subject
of bulbiferous fungi.

The need of further examination of the morphology and develop-
ment of bulbils was suggested by Professor Roland Thaxter, under
whose direction and supervision the work has been conducted. The
problem was begun and finished in the Cryptogamic Laboratories of
Harvard University, some culture work and collections of material
being done in California while the writer was connected with Pomona
College.

It is a pleasant duty for the writer to acknowledge, at this point,
his indebtedness to those who have rendered him assistance in carry-
ing on this research: especially to Professor Thaxter are grateful
acknowledgments due, for suggestions, kindly advice and encourage-
ment, and for placing at the writer’s disposal many dried specimens
and tube cultures of bulbils which had been collected by him, and for

eee Δ. ἃ. ὦ

eae:

HOTSON.— CULTURE STUDIES OF FUNGI. 231

the use of a number of papers belonging to his private library; to
Professor Elias J. Durand of the State University of Missouri, for
the description and naming of Cubonia bulbifera; to Professor W. G.
Farlow for material and the use of several articles from his private
library.

REVIEW OF LITERATURE.

The literature relating to bulbils is, as has been already indicated,
by no means extensive, and deals with less than a dozen described
forms, some of which do not appear to have been recognized by
mycologists since their original publication. In order to give a
clearer idea of the present state of our knowledge of the subject, it
seems desirable, before proceeding further, to give a brief summary
of the more important papers, which may be conveniently considered
seriatum under the following heads:

(a) Helicosporangium, (Ὁ) Papulospora, (c) Pyrenomycetous
Forms, (d) Discomycetous Forms, and (6) Basidiomycetous Forms.

(a) Helicosporangium.

The genus Helicosporangium was first described by Karsten (’65)
and was based on a form said to be “parasitic” on beet roots,
which he named H. parasiticum. According to his description the
fertile branches of this fungus tend to become erect, and are septate
like the rest of the hyphae. In the process of development they coil
up spirally at the end to form the bulbil. This character suggested
that they might be closely related to such hyphomycetous forms as
Helicoma Corda, Helicosporium Nees, Helicomyces Lk., Helico-
trichum Nees, ete. In fact, it was this spiral development of the
fructification, held in common with these forms, that suggested to
Karsten the name, Helicosporangium.

At maturity these bulbils are described as almost spherical, with
one large central cell which is surrounded by a single layer of colorless
cortical cells which form a complete wall. Karsten believed that one
of these cortical cells produced a short protuberance on the inner side,
which extended into the large central cell, in which he says a “nu-
cleus” soon appeared and enlarged quite rapidly. He further ob-
served that the contents of the central cell soon became somewhat
differentiated and divided into a number of small cells, usually eight
in number, but varying from seven to ten, which gradually enlarged
to form free, hyaline, elliptical spores; and, after escaping from the

232 PROCEEDINGS OF THE AMERICAN ACADEMY.

central cell, divided, forming compound spores of two cells. On
germination each cell produced a germ tube.

Karsten believed that the contents of the cortical cells entered
directly, or by diffusion, into the large central cell and that only after
the contents intermingled were the spores formed. This suggested
the possibility of sexual differentiation of certain cells which made
up the coil, the end-cell, in his opinion, acting as an oogonium and
the second or even the third or fourth cell acting as an antheridium.

It will thus be seen that in Karsten’s opinion the peculiar structures
which he described in Helicosporangium were neither bulbils nor
homologous with other non-sexual propagative bodies, and although
it is possible that he may have been dealing with some form allied to
Monascus, in which a sexual process was actually present, it seems
not improbable that he was misled by what he saw. Since, however,
this subject will be further discussed below in connection with a form
which appears to be identical with Karsten’s species, it need not be
further considered in the present connection.

Eidam (’77, 783) described and figured a bulbil obtained from
moist turnips which he referred to Helicosporangium parasiticum
Karsten, but, as has been pointed out by Karsten himself (88),
Harz (90), and others, it seems probable that he was dealing
with a fungus different from that which Karsten described. Eidam’s
fungus is said to be saprophytic, producing numerous conidia borne
on characteristic bottle-shaped sterigmata and having two kinds of
bulbils which do not contain endospores. In these respects it is said
to differ from that described by Karsten. This matter, however,
will be referred to again below.

De Bary (87) accepted in general the views expressed by Eidam
(83) regarding H. parasiticum, but Karsten (88) maintained that
he did so because he had not read the original article, but formed his
opinion on information obtained from “Eidam’s unfortunate review
of τ᾽ (88), and in conclusion ironically gives the name Baryeidamia
to Eidam’s fungus, in recognition of what he considered the combined
blunders of these two mycologists in dealing with this form.

A third species referred to the genus Helicosporangium was de-
scribed under the name of H. coprophilum by Zukal (’86) and was
found by him on horse dung associated with Stysanus stemonites Cd.
According to Zukal’s description, this bulbil consists of two to eight
large central cells with thick walls of a dark-red color, which are
surrounded by a layer of smaller cortical cells of a lighter color. The
form and manner of development of this bulbil are said to vary con-

HOTSON.— CULTURE STUDIES OF FUNGI. 200

siderably. “Indeed,” he says, “there are hardly two to be found
which are exactly alike.”’

Zukal (86) also describes a yellowish-brown bulbil under the name
of Dendryphium bulbiferum, found on birch twigs, the mycelium of
which is said to grow up, tree-like, and to branch monopodially, the
ultimate branches terminating in rows of small hyaline ellipsoidal
cells. At maturity these little cells become brownish and, when they
are abstricted, form a dusty mass. The bulbil associated with them
is almost spherical and bears a very close resemblance to Helicosporan-
gium parasiticum Karsten, both in its mode of development and in its
general appearance.

On decayed fruit of Lycopersicum esculentum Mill. Zukal (86) has
reported the occurrence of bulbils closely resembling, both in appear-
ance and development, the two types above referred to, but which
are said to differ in their greater variations and irregularities, and
also in the fact that they are associated with the conidia of Haplo-
trichum roseum Lk. (Oedocephalum glomerulosum Bull.). It should
be mentioned in this connection, however, that since Zukal did not
apparently deal with pure cultures and no such bulbils have been
found, as far as the writer is aware, by others who have cultivated this
very common Hyphomycete, his statements must be accepted with
some reserve. It may be stated at this point that in none of the pub-
lished accounts of Helicosporangium is there any evidence that pure
cultures were used, and thus the possibility of contamination renders
these results largely untrustworthy.

(b) Papulospora.

Of the several species which have been placed in this genus the first
was described by Preuss (61) from material found growing on decayed
pieces of apple and was said to be connected with chlamydospores
which resembled those of Sepedonium. He therefore named _ his
species P. sepedonioides. These bulbils are described as irregularly
arranged on lateral branches, white at first and later becoming rust-
colored, with the cortical cells differentiated. from the central ones.
Preuss regarded this bulbil as a single multicellular spore and not as a
cluster of single spores, because they never break up into individual
cells, although he thought the cortical layer probably bursts at the
time of germination.

Eidam (’83), in the paper already referred to, described a second
bulbil found quite abundantly on straw, weeds, dung, ete., which

>

234. PROCEEDINGS OF THE AMERICAN ACADEMY.

appeared, in his opinion, to be so closely related to the form described
by Preuss that he placed it in the same genus; since it was, however,
not associated with chlamydospores like those of Sepedonium, but
with an Aspergillus-like fructification, he named it P. aspergilliformis.
Two kinds of bulbils were described as connected with this fungus,
which resembled each other in color but differed in their mode of
development. Of these two types, one is said to be large, sclerotium-
like, without any differentiation into central and cortical cells, while
the other is small and consists of several large central cells surrounded
by a row of colorless cortical cells resembling those of Helicosporan-
gium parasiticum, mentioned in the same paper.

In connection with this fungus Eidam described conidia which,
he states, were produced on exceedingly delicate, colorless, conidio-
phores resembling somewhat those of Aspergillus albus Wilhelm,
but the sterigmata are usually flask-shaped. These conidia were also
borne individually on the sides of ordinary hyphae, being abstricted
in chains from flask-shaped sterigmata and resembling those described
by Eidam as associated with the form which he referred to Heltco-
sporangium parasiticum.

“Chlamydospores”’ were also described by Eidam in connection
with his P. aspergillformis. “This form of reproduction,” he says,
“seems to be by far the most common one connected with Papulo-
spora and often is the only one. I have found, in great abundance,
mycelia with only chlamdospores and no trace of bulbils or conidio-
phores.”” On account of the presence of these chlamydospores which
resemble the spores of Acremoniella, Lindau (’07) has redescribed this
species under the name of Hidamia acremonioides Harz. The criti-
cism that was offered as to the reliability of Eidam’s investigation of
Helicosporangium may equally well be applied here. Bainier (’07)
is of the opinion that he mistook the conidia of Acremoniella atra
Sace. (Acremonium atrum Corda) for chlamydospores belonging to
Papulospora, as these two species are often found associated with each
other.

Bainier (’07) found a fungus abundantly on straw, paper, cardboard,
etc., which he calls P. aspergilliformis. His description of the conidia
and conidiophores is practically the same as that given by Eidam (88).
His fungus, however, does not produce acremonium-like chlamydo-
spores, as did that of Eidam, but, on the other hand, developed pari-
thecia with long necks, which he refers to the genus Ceratostoma.
The asci, which are very transitory, even disappearing before the
maturity of the spores, are ovoid with eight simple brownish spores

HOTSON.— CULTURE STUDIES OF FUNGI. 235

somewhat variable in shape and grouped together, forming a sort of
ball. Moreover, he considers that the bulbils of Helicosporangiwm
parasiticum described by Eidam are merely abnormal forms of P.
aspergilliformis, such as are often found among other Mucedineae.

Another Papulospora, which was found in the tubers of Dahlia,
has been described under the name of P. dahliae by Costantin (᾽ 88).
The bulbils of this fungus are spherical, brownish-red in color, with
two or three large central cells. All the cells are said to contain
granular protoplasmic material at first, but the central cells soon
become strongly colored violet and more densely filled with granular
material and oil globules, and eventually the peripheral cells become
empty and transparent. There were found associated with this
fungus colorless septate spores which taper at both ends and corres-
pond very closely to those described by Saccardo (Michelia I, p. 20)
under the genus Dactylaria. Here again there is little evidence that
the investigation was carried on with pure cultures and it is doubtful
that the conidia and the bulbils described belong to the same fungus,
since they were only found associated and not actually connected.
It would thus appear that the only contribution on Papulospora
that shows any evidence of work with pure cultures is that of Bainier
(07).

(c) Pyrenomycetous Forms.

The first evidence of the definite association of a bulbil with one of
the Pyrenomycetes as an imperfect form, is found in the description
of Melanospora Gibelliana, published by Mattirolo in 1886,— although
Zukal (’86) a few months previously had announced that he had
found bulbils in connection with Melanospora fimicola Hansen, and
M. Zobelii Corda, but gave no description of them. The fungus
studied by Mattirolo was found growing abundantly on decayed
chestnuts and was said to produce not only perithecia of Melano-
spora but also bulbils, conidia and chlamydospores. In appearance
and development these bulbils are said to resemble closely those of
Baryeidamia, but with more variations. Their color is pale yellow
when young, brownish-yellow at maturity, and they are often 100 μ
in diameter. Mattirolo considered them immature perithecia, but,
although he employed the most varied methods of experimentation,
he was unable to make them develop into melanosporous perithecia.
The conidia said to be connected with this fungus are described as
small, colorless, spherical spores, on bottle-shaped sterigmata, resem-
bling closely those mentioned by Eidam as belonging to Baryeidamia.

236 PROCEEDINGS OF THE AMERICAN ACADEMY. .

The chlamydospores referred to this fungus are said to have very
rough, thick walls, resembling somewhat those of Sepedonium. Al-
though Mattirolo is of the opinion that these chlamydospores form
a phase of the life history of M. Gibelliana, he admits that he has not
absolutely proven it. He states he has “cultivated these forms
without ever being able to establish unquestionably their origin and
relation.”

Berlese (’92) described a bulbiferous fungus producing perithecia,
which he named Sphaeroderma bulbilliferum. This fungus he found
growing abundantly on dead leaves of Vitis, Cissus and Ampelopsis.
It is said to have several modes of reproduction, such as (a) micro-
conidia, which appear in chains and which resemble those figured
by Mattirolo as belonging to Melanospora Gibelliana and by Eidam,
to Helicosporangium parasiticum; (b) chlamydospores, which varied
somewhat in size — (these were ovoid, usually smooth, and golden-
yellow in color, each with a septum near the base, which divided the
chlamydospore into two unequal cells); (c) golden-yellow bulbils,
which resembled those described and figured by Mattirolo in Melano-
spora Gibelliana and which seem to be short-lived and, under the
most favorable conditions, could not be made to produce mycelia;
(d) perithecia, which were represented as almost spherical and when
mature measured from 400-500 uw in diameter. They remain without
an ostiole almost to maturity and consequently there is no formation
of a neck. The color of the young perithecium is yellowish but
becomes darker as it grows older, until at maturity it is almost a tan
color. The asci are club-shaped with deep smoke-colored spores,
ovoid and prolonged at the poles into short obtuse papillae.

Another pyrenomycetous form producing bulbils has been reported
by Biffen (701, ’02), and is said to be connected with Acrospeira
mirabilis Berk., which was originally found on sweet chestnuts
(Castanea vesca, Gaertn.). By the use of pure cultures, Biffen claims
to have succeeded in obtaining not only the chlamydospores, as de-
scribed by Berkeley and Broome in the Annals and Magazine of
Natural History for 1861, but also what he calls “spore-balls”’
(bulbils) and definite perithecia.

The spore-balls, which he says so closely resemble Urocystis violae
that he “could not find a single characteristic to separate them by,”
were obtained by sowing the ‘chlamydospores’ on a watery extract
of chestnuts. Greater difficulty was experienced in producing the
perithecia, but finally, by sowing the chlamydospores and bulbils on
sterilized chestnuts, he records the following results: — “The ‘ chlamy-

HOTSON.— CULTURE STUDIES OF FUNGI. 237
dospore’ infections gave a crop of ‘chlamydospores’ only; the
spore-balls gave spore-balls and small reddish-brown, hard-walled
perithecia. The walls of the perithecia were smooth and without
bristles and the ostiole was small and flush with the surface, i. e., not
raised on a papilla or forming a neck... .Berkeley’s A. mirabilis thus
turns out to be one of the stages in the life history of a Sphaeria.”’

The investigations on the pyrenomycetous forms show more careful
work than those under the two preceding headings. In all these there
is evidence that pure cultures were used more or less, but in most cases
it is uncertain how far the results were thus obtained.

(d) Discomycetous Forms.

There have been two fungi described which produce bulbils asso-
ciated with discomycetous fructifications, one by Zukal (’85, ’86)
and the other by Morini (’88). Zukal found two kinds of primordia
in connection with his fungus; one, he says, consisted of two or three
small mycelial branches which wound about each other and eventually
produced reddish-brown bulbils with a cortex of small colorless,
almost transparent, cells. The other primordium was made up of a
number of hyphae massing themselves together and becoming quite
large and, under proper conditions of nutrition, developing into
apothecia of the Peziza type; but he does not give a name to this form.
This fungus produced conidia abundantly on erect, branched coni-
diophores. The conidia are spoken of as colorless, ellipsoidal, smooth,
and they appear in clusters upon the ends of short sterigmata. Zukal’s
cultures were grown on absorbant paper saturated with Leibig’s
extract, but there is no evidence in his article that these were pure
cultures, or that the life history of the fungus was carefully traced
from ascospore to bulbil.

Morini (’88) describes “ bulbil-like”’ bodies associated with Lachnea
theleboloides (A. & S.) Sace. in old cultures. Since these occurred
only in cultures that had run for a long time, in which the nutrient
was probably largely exhausted by the previous growth of the fungus,
and since the development was largely the same as that of the apothe-
cium, Morini considers that the bulbils of L. theleboloides are abortive
apothecia and, further, that they are analagous to the similar struct-
ures described by Eidam, Karsten, et al. He apparently has used
pure cultures in his investigation, but to what extent his results were
obtained from such cultures could not be determined from his paper.

238 PROCEEDINGS OF THE AMERICAN ACADEMY.

(e) Basidiomycetous Forms.

The only account, as far as the writer is aware, of the definite
association of bulbils with Basidiomycetes is given by Lyman (’07)
in connection with his culture-studies of Cortictum alutaceum (Schra-
der) Bresadola, his results having been obtained from pure cultures
made of the basidiospores of this fungus. ‘The bulbils,’”’ he says,
“are reddish-brown or chocolate-colored clusters of cells, more or less
globose in shape, and usually 65-80 μ in diameter, although ranging
as high as 220 y....They are frequently very irregular in shape, due
to the unsymmetrical arrangement of the cells, and to the bulging
of the free outer walls. There is no distinction between internal and
external cells of the cluster.”’ Besides the basidiospores and bulbils
this Corticium also produces conidia which are of the Oidium-type.
Occasionally whole hyphae break up into chains of spores of this type.

Lyman also mentions two other bulbiferous fungi which were
referred to the Basidiomycetes, being recognized as such by the clamp-
connections of their hyphae, although the basidiospores were not
obtained. :

Lastly, it may be well to mention an article by Harz (’90), in which
he describes a fungus found growing on material obtained from the
reservoir of a factory and which he names Physomyces heterosporus
(Monascus heterosporus (Harz) Schréter). Although this fungus is
probably a true Monascus, as Schréter has indicated, yet since it has
been associated with bulbils, and since the ascocarps of Monascus in
general bear a superficial resemblance to them, it may be well at least
to mention it in passing. Harz has associated this form closely with
Helicosporangium parasiticum Karsten, and created a new family
Physomycetes — for the reception of these two genera. As, however,
these two forms will be referred to again in connection with H. para-
siticum Karsten, a further consideration of them will be deferred until
that time.

It will be seen from the foregoing brief review of the literature that
much of it is quite vague and untrustworthy. This perhaps is what
one would expect from investigations which were carried on during
a period prior to the adoption by mycologists of the bacterial methods
of handling pure cultures. This is especially true with regard to
polymorphic forms, like some of those under consideration, where it
is so necessary to adopt these methods in order to be absolutely sure
of the different steps in following the life history of the fungus from
spore-form to spore-form. The contributions of Lyman and Biffen

HOTSON.— CULTURE STUDIES OF FUNGI. 239

on this subject show undoubted evidence that their investigations were
carried on with pure cultures and that the life history from spore to
bulbil was closely traced. It is probable that Bainier, Morini, Berlese,
and Mattirolo also used pure cultures more or less, but there is little
evidence in their writings that there was careful tracing of the fungus
from spore to bulbil.

Sources OF MATERIAL.

Before recording the results obtained from the study of the various
bulbiferous fungi cultivated by the writer, it will be well to refer
briefly to the sources of material and the methods used in this
investigation.

In 1907, at the suggestion of Dr. Thaxter and with a view to obtain-
ing as much material as possible for examination, the writer began
collecting substrata of various kinds from widely different localities.
This material was placed in moist chambers in the laboratory and as
bulbils appeared pure cultures were made of them. The methods
employed in doing this will be referred to later. Most of the material
from which bulbils were obtained was collected either in the vicinity
of Cambridge, Mass., or Claremont, Calif.; but bulbils were also
procured from substrata received from other portions of New England
and California, from Kentucky, Canada, Mexico, Guatemala, Cuba,
Jamaica, Bermuda Islands, the Argentine Republic, Italy, ete.

The substrata on which these fungi were found were very diverse.
The most productive were various kinds of excrement (dog, rat,
mouse, rabbit, pig, horse, goose, goat, etc.), dead wood (Acer, Lathy-
rus, Quercus, Eucalyptus, ete.), decaying vegetables (squash, onions,
etc.), straw (wheat, oats, barley, rye, alfalfa, etc.). A number were
found on paper and old cardboard, as well as on a variety of other
substrata. Of many hundreds of such cultures about two hundred
yielded bulbils.

CuLTuRE METHODS.

The moist chambers used for the cultivation of these materials were
usually crystallizing dishes covered with pieces of glass. A large
amount of this material was grown in the laboratory and from time
to time was carefully examined through the glass top with a hand lens.
When bulbils were observed, one of them was picked out by means of
fine dissecting-needles under a dissecting microscope, and after thor-
ough washing in sterilized water on a flamed slide, was transferred to
a test-tube containing sterilized nutrient material — usually potato

240 PROCEEDINGS OF THE AMERICAN ACADEMY.

agar. In the case of some melanosporous forms the transfer was made
by carefully touching the long cirri of ascospores, produced by the
perithecia of this genus, with a piece of nutrient agar on the end of a
sterilized platinum needle. The ascospores adhering readily to the
agar, a pure culture was easily obtained.

Bacteria sometimes gave trouble in some transfers, but as a rule
these were gotten rid of either by picking out separate bulbils carefully
and washing several times before growing them in acidulated nutrient
agar, or by keeping the impure tubes at a temperature of 15-20° C.
The growth of the bacteria being retarded either by the cold or acid,
the mycelium producing the bulbil soon grew out beyond the affected
region, and by gouging out a few of the ends of the hyphae with some
of the agar and transferring to another tube, a pure culture was readily
obtained.

When these were secured the fungus was cultivated on various
kinds of nutrient agar media, some growing better on one medium and
some on another. The following were used most frequently: potato,
onions, sucrose of different percentages, bran, rice, cornmeal, straw,
plums, prunes, grapes, figs, bread, squash, Spanish chestnuts, wood,
various kinds of dung, etc. These were usually used with agar, but
some materials like wood, dung, straw, nuts, etc., were sterilized in
bulk with plenty of water and without using agar while in some
instances decoctions were used. In Claremont, California, they were
grown in the laboratory at an average temperature of 25-30° C.
In Cambridge many were grown in an oven kept at various constant
temperatures, 20-25° C. giving the best results.

The vessels used for these cultures were usually medium sized test-
tubes, Erlenmeyer flasks of one and two litres, or preserve-jars with
cotton plugs. These were filled about one-third full of nutrient agar
and usually slanted to give more surface. On this nutrient the fungus
would usually grow well for several months, and results were often
obtained from pure gross cultures which could not be secured from
the smaller ones.

In the germination of the spores and bulbils, Van Tieghem cells
were used very freely. For this purpose cover glasses of one inch
and two inches in diameter were used and carefully sealed, plenty of
sterilized water having previously been put in the cells which corre-
sponded in dimensions with that of the cover glasses. The large
Van Tieghem cells afforded an opportunity of using cultures of con-
siderable size which were usually composed of decoctions of different
kinds of nutrient material, sometimes with agar to make them solid,
while at other times the decoctions were used as hanging drops.

HOTSON.— CULTURE STUDIES OF FUNGI. 241

In cases where the transfer of conidia, only, was desired, two
methods were employed to avoid getting either bulbils or pieces of
mycelium. If the conidia were quite plentiful or were on erect stalks
so that they were somewhat separated from the rest of the mycelium,
this could be accomplished by means of a piece of nutrient agar on
the end of a sterilized platinum needle. By careful manipulation
and with the aid of a dissecting microscope, they could be touched
with the agar to which they adhered readily, and after exami-
nation under a microscope to determine if there were only conidia
present, they were immediately transferred to a new tube or a Van
Tieghem cell, as the case required. In instances where the above
method could not be used, or where cultures from individual conidia
were required to verify the relation between a conidial form and
the bulbil, Barber’s spore-picking apparatus (’07) was employed.
Plate-cultures were also used to advantage in some instances for
separating the conidia from the bulbils.

Throughout this investigation, as already stated, the results ob-
tained are based upon pure culture methods and every precaution
has been taken to avoid error as a result of contamination.

It perhaps should be mentioned at this point that it is the intention
of the writer to deposit living cultures of most of the forms described
with the Centralstelle fiir Pilzculturen.

SYSTEMATIC CONSIDERATION OF THE ForMS STUDIED.

As has already been indicated, “ Bulbils” must in all instances be
regarded as representing imperfect conditions of the higher fungi;
and like the members of other more or less clearly defined “ form-
genera”’ may be associated with perfect conditions included in wholly
unrelated genera of the Ascomycetes and Basidiomycetes. They
may, moreover, not only represent conditions of such perfect forms,
but may be further associated with one or more additional imperfect
forms. There may thus be present in some instances a succession
of three or even four distinct reproductive phases which together
make up the individual life-cycle.

It has been the aim of the present investigation, therefore, to
endeavor not only to obtain further information as to the occurrence,
morphology, and development of these comparatively little known
structures, but by means of careful and extended work with pure
cultures to make some further contribution to our knowledge of their
actual relationship in different cases.

242 PROCEEDINGS OF THE AMERICAN ACADEMY.

Bulbils, as a rule retain their vitality a long time so that they
germinate readily after a year or more. Their maximum longevity
has not been precisely determined, but in some instances, as in
Grandinia and Corticium, they have been germinated after three
years. This fact of the extensive longevity of bulbils is of immense
importance to the fungus, enabling it to withstand long periods of
unfavorable conditions, the perpetuation of the species being thus
comparatively well assured.

In arranging the materials available for systematic consideration
it has been found most convenient to group the forms under four
main divisions, namely: those which are known or supposed to be
connected with perfect forms belonging to the Discomycetes; those
thought to be connected with Pyrenomycetes; those which appear
to be imperfect conditions of Basidiomycetes, and lastly those the
actual relationships of which are still undetermined. It has seemed
best to consider the last group under a single form-genus, Papulo-
spora, this name having been the first which was applied to bodies
of this nature, and the variations in the morphology and development
in the different species being such that a separation into more than
one form-genus does not seem advisable.

DISCOMYCETOUS FORMS.

Previous investigations have brought to light but two bulbiferous
Discomycetes; an unnamed species of Peziza observed by Zukal
(85, ’86), and Lachnea theleboloides (A. & 8S.) Sace. reported by
Morini (’88). To these is added a species of Cubonia now reported
for the first time, specimens of which were sent for identification to
Professor Elias J. Durand of the University of Missouri, to whom the
writer is indebted for the following diagnosis:

Cubonia bulbifera n. sp.
ῬΙΆΤΕ 1, Figures 1-28.

“Plants single or gregarious, often crowded, sessile or narrowed to a
stem-like base, turbinate, 3-10 mm. in diameter. Disk cupulate or
saucer-shaped, the hymenium pale fawn-color, even when young, but
in old specimens wrinkled in a cerebriform manner, externally much
darker, becoming almost black with age, smooth or grumous; margin
irregularly lacerate-dentate. Consistency subgelatinous, excipulum
pseudoparenchymatous throughout, of nearly rounded cells, 20-25 μ

HOTSON.— CULTURE STUDIES OF FUNGI. 243

in diameter, the cortical cells blackish, often protruding in groups.
Asci clavate, apex rounded, not blue with iodine, 125 & 15 4. Spores
8, uniseriate, hyaline, smooth, spherical, 12 u diameter. Paraphyses
slender, hyaline, only slightly thickened upward. . Mycelium giving
rise to numerous rounded, black bulbils, 75-100 μ diameter, composed
of rounded cells about 20 μ᾽ diameter.”

Cultivated on nutrient agar. Found on dog dung from Jamaica,
Paestum (Italy), Guatemala and California, and pig dung from
Guatemala.

This fungus was first obtained by Dr. Thaxter on dog dung from
Jamaica and has been kept growing in pure tube-cultures for twenty
years; since then he has found it on the same substratum from Paes-
tum, Italy, and from Guatemala. It was also secured from gross
cultures of pig dung and of dead flowers believed to be of the genus
Criosanthes from the last named locality, while the writer has found
it on gross cultures of dog-dung from Claremont, California, from
which a pure culture was obtained in a manner similar to that already
described. This was not difficult, since the mycelium grows with
great rapidity and the bulbils are produced in abundance. The fungus
Was grown, on a great variety of media until the mature perfect form
was obtained. The mycelium grows well on nearly all media, pro-
ducing numerous dark-colored, almost black, bulbils. The best sub-
stratum for producing apothecia is bran, or rat or dog-dung, although
they developed quite readily on sweet-potato agar or on Irish potato
agar with a little sugar; but it was found that after the fungus had
been cultivated for a long time on artificial media, it failed to produce
mature apothecia.

On appropriate substrata such as bran, dung, etc. the rate of
growth of the mycelium is remarkably rapid. The average of several
measurements made of this fungus, grown at the temperature of the
laboratory is as follows: 1 em. in 24 hrs., 24 em. in 50 hrs., 33 em. in
74 hrs., and 5 em. in 120 hrs. It is white and somewhat flocculent,
and does not grow in a “zonate fashion” like that of the Peziza de-
seribed by Zukal, but spreads out quite evenly over the surface of the
substratum. In older cultures the hyphae become quite large, often
over 10 w in diameter, and densely filled with granular protoplasm, but,
as they reach their limit of size, they lose their contents. Frequently
when a hypha becomes broken or a portion of it is killed, there seems
to be a stimulus for growth at the free end, somewhat similar to that
in higher plants which are subjected to wounding. This injury of the
hyphae appears to cause a sort of damming up of food material, which

244 PROCEEDINGS OF THE AMERICAN ACADEMY.

is evident from the sprouting out of several small hyphae, not only
from the end but also from the sides near the end of the injured part;
and these often twine about each other in such numbers, that it gives
the appearance of a broom-like structure.

The bulbils— Often within forty-eight hours, dark bodies, which
eventually become black, may be observed with a hand lens, scat-
tered over the substratum or in it; they are most abundant near the
point of inoculation, from this point extending out as the peripheral
growth of the mycelium increases thus exhibiting a progressive forma-
tion. These black bodies are bulbils which soon become very numer-
ous, forming a blackish crust over the substratum and usually giving
the whole culture a black aspect. This is especially true when it is
grown on such media as potato agar made very hard with about forty
grams of agar to the litre. In such cases the mycelium is quite scanty
and procumbent, and the bulbils thus become very conspicuous;
while on media like rat dung, where there is an abundance of myceli-
um produced, they are not so readily seen, since they are usually
formed on or in the substratum. In the development of these struc-
tures which are produced so abundantly, two or three intercalary
cells become enlarged and filled with granular nutrient material, as

shown in Figures 11-14, Plate 1. From these cells others are produced .

by budding, or short branches are formed which surround the prim-
ordial cells, and which in turn become enlarged so that eventually
there is produced an almost spherical bulbil somewhat flattened,
75-100 μ in diameter, the cells in the center, usually considerably
larger, but all filled with protoplasm, without any definite differentia-
tion of cell-contents between internal and external cells. Not infre-
quently, however, the marginal cells of old bulbils lose their contents,
although they retain the dark color in the wall, but this is probably
due to age. As a result of the unequal production of marginal cells,
the bulbils may vary considerably in size and some become quite
irregular in outline. Frequently the bulbils or the primordia of im-
perfect ones, especially as the cultures become old, heap together and
form conspicuous dark elevations scattered over the substratum.
These structures eventually assume a yellowish color, probably due
partly to fading and partly to the immature bulbils that compose
them.

The apothectum.— Occasionally there is found a spiral primordium,
as shown in Figure 1, Plate 1, produced on short lateral branches
which usually divide dichotomously, sometimes of the second or third
order, the ultimate branches of which coil up spirally (Figures 1+,

— δικόν,

HOTSON.— CULTURE STUDIES OF FUNGI. 245

Plate 1). Ordinarily there are about one and a half to two turns in
the spiral, but occasionally there are as many as four. If a lateral
branch fails to divide, as it often does, only one primordium is pro-
duced (Figure 4, Plate 1). Frequently after the first dichotomy,
one of the branches does not divide again, but coils up immediately,
while the other may divide once or twice before coiling ‘(Figures 2-3,
Plate 1). Thus, according to the number and regularity of these
dichotomous divisions, there may appear one, two, or more primordia
which are more or less closely related to each other. Usually, however,
the pedicels on which they are formed elongate, and thus they may
become separated from each other. When this primordium has made
about two turns, sometimes as many as four, small branches are pro-
duced from the sides of the coils (Figures 5-6, Plate 1), which at this
stage often become separated from each other, as shown in Figure 6.
It is, however, a very obscure structure, the further details of which
are difficult to follow.

Occasionally on media like potato, more frequently on bran, Spanish
chestnuts, sweet potato, etc., and quite freely on rat and dog dung,
little white patches of hyphae are seen scattered over the substratum.
These are the young apothecia. The fine, white, wool-like hyphae
become thickly matted together and form a white superficial dome-
shaped structure with fine filaments growing out on all sides (Figure 7,
Plate 1), and asthese become older, they lose their contents and as-
sume a brownish color. Shortly a circular opening appears at the apex
(Figure 8, Plate 1), apparently due to the rapid and extensive growth
of the inner portion of the apothecium. This opening gradually
increases in size, often exhibiting a conical depression in the center
which, as the hymenium enlarges, becomes flat and then slightly con-
vex. Microtome sections, made at the time of the opening of the
apothecium or shortly before, show the upper region closely crowded
with long narrow paraphyses, nearly uniform in thickness, which a
little later, slightly enlarge at the ends, forming the somewhat even
surface of the hymenium (Figures 9-10, Plate 1).

A short distance below the center of the apothecium, when about
the age of that represented in Figure 8, Plate 1, a large cell containing
deeply staining material is seen in microtome sections. This appears
to be the ascogonium and from it very narrow hyphae, which also
stain deeply, grow up between the sterile cells of the apothecium, and
eventually produce the asci. At maturity the apothecium is brown-
ish, measuring 3-10 mm. in diameter and 3-5 mm. in height; often in
groups and occasionally with a short stem-like base.

246 PROCEEDINGS OF THE AMERICAN ACADEMY.

When a portion of the hymenium containing some of the large
cells below the sub-hymenium was put in a sterilized Van Tieghem
cell in an endeavor to induce the ascospores to germinate, it was found
that frequently these large cells, which measure 20-25 yp in diameter,
sent out germ tubes, or turned brown, secreted thick walls about
themselves and resembled considerably chlamydospores (Figures 26,
27).

Germination of the ascospore.-— The mature asci are quite uniform,
clavate, with the apex rounded, opening by a lid, 125 w in length and
15 w in diameter at the widest place. The ascospores are hyaline,
spherical, 12 μι in diameter, and arranged in a single row. At maturity
all the spores from each ascus are ejected with considerable force
blowing off the lid at the apex in a manner somewhat similar to that
of Ascobolus, and thus are thrown in a bunch for several centimeters,
and, by means of the protoplasmic material which surrounds them,
adhere readily to any glass surface with which they may come in
contact. These spores were allowed to strike a sterilized cover glass
and then supplied with nutrient material and cultivated in a Van
Tieghem cell, which had previously been thoroughly sterilized. Not
only were the spores alone used as just stated, but frequently a por-
tion of the hymenium with the asci was gouged out with a sterilized
platinum needle and hanging drops made of 11. In an effort to get
these spores to germinate, various kinds of media were used, such as —
potato, prunes, bran, horse dung, dog dung, Spanish chestnuts,
carrots, etc., either as a decoction, or more often solidified with agar.
In spite of these varied efforts, the spores could not be made to germi-
nate. The writer some time ago succeeded in getting the spores of
Ascobolus to germinate in Van Tieghem cells by first crushing them
lightly between two glass slides, and it occurred to him that the same
method might be successful here also. Accordingly hanging drops
were made as before, using different media, but the spores were first
crushed with a sterilized platinum spatula on the cover-glass. This
method proved successful. These spores are composed of a thick
brittle episporium and a thin flexible endosporium; the object in
crushing was to break the former without injuring the latter. Many
of the spores thus crushed were totally destroyed, and broken por-
tions of the episporium were scattered over the culture; but in a few
cases, where the pressure was sufficient just to break the episporium
without injuring the endosporium, it was found that germination
took place in from 24 to 48 hours (Figures 22—24, Plate 1). When
this occurs the endospore pushes out, forming a germ tube which is

-
HOTSON.— CULTURE STUDIES_OF FUNGI. 247

only a little smaller in diameter than that of the spore itself (Figure
22), and frequently when it has grown a short distance, broadens out
as much as 14 uw in diameter (Figure 29). Thus the primary hypha
from the ascospore is very large (7-14 uw in diameter), well filled with
food material, and grows quite rapidly under favorable conditions.
The culture of these germinating spores was carried on in Van
Tieghem cells until bulbils were produced on the mycelium.

Germination of the Bulbil— The bulbils, unlike the ascospores,
germinate with great readiness within twenty-four hours and any
of the cells that contain protoplasmic material may send out a germ
tube, which shortly produces other bulbils from intercalary cells, as
described above. When the bulbils are crushed, the contents of each
of the large cells escapes surrounded by an endosporium (Figure 19)
and germinates readily in Van Tieghem cells. Little significance can
be attached to this fact, however, as not only are nearly all bulbils
similar in this respect, but it is a common occurrence among spores
which are surrounded by a thick episporium, such as the ascospores
just considered.

In prolonged cultures of this fungus no other spore forms have been
observed.

LACHNEA THELEBOLOIDES (A. & S.) Sace.

The association of this species with bulbil-like bodies is reported
by Morini (’88) but it is not clear from his account whether the
structures seen were true bulbils, or abortive apothecia, as he believed
them to be. The apothecia, which he describes and figures, are very
similar to those of Cubonia bulbifera but the spherical spores of the
latter distinguish it at once.

The bulbil-like structures which he describes were found only in
old cultures in which the nutriment was more or less exhausted, and
are described as irregularly globose, 160-220 μ, and rather hard.
In many cases large cells of somewhat spiral form were visible in
these bodies which Morini considered “rudimentary ascogonia.”
The protoplasm of the external cells, is said to be replaced by an
aqueous liquid and the walls become thick and brownish-red in color.
A large number of the superficial cells, as in the case of the developing
apothecium, give rise to short, often septate setae, which cover
nearly the whole surface. When these “bulbils’’ were transferred
to fresh substrata, only those with better developed “ascogonia”
continued their development until they formed apothecia identical
in character with those produced normally. In all other cases,

248 PROCEEDINGS OF THE AMERICAN ACADEMY.

especially those in which the so called “ascogonium” had completely
disappeared, Morini observed no further development, except that in
rare cases, a few paraphyses were found.

He is of the opinion that these “bulbil-like” bodies are degenerate
apothecia, analogous to the bulbils of Eidam, Karsten, etc., and
concludes his article by saying that “the forms heretofore called
‘bulbils’ or ‘spore-bulbils’ are to be considered as exactly homologous
to apothecia of which they represent forms more or less degenerate
or modified during many generations of unfavorable conditions.”

ῬΈΖΙΖΑ, species; not determined.

A species of “Peziza’”’ found by Zukal growing on a laboratory
culture may be here referred to, which according to his account is
associated with small bulbils 30-40 uw in diameter, reddish brown in
color, and produced by “two or three small hyphal branches which
wind about one another like serpents or twist, screw-like.” The
primordium of the apothecium is somewhat vaguely described. The
ascospores are said to be elliptical, hyaline, smooth, about 9 X ὁ μ,
obliquely monostichous, germinating readily in from twenty-four to
thirty-six hours. Since this form does not appear to have been studied
by means of pure cultures its connection with the bulbils described
must be regarded as somewhat doubtful.

PYRENOMYCETOUS FORMS.

In the review of the literature a number of pyrenomycetous forms
that produce bulbils were mentioned, which have been referred
either to the genus Melanospora or to the allied genera Sphaero-
derma or Ceratostoma. More than twenty different gross cultures
made by the writer of various substrata, such as onions, straw of
various kinds, paper, pasteboard, Live Oak chips, rotten planks,
tubers of Dahlia, old leather gloves, ete., have produced bulbils
which in pure cultures have yielded melanosporous perithecia. In
a few cases the perithecial form was found on the original sub-
stratum and cultures were made from the cirri of discharged asco-
spores, which on nutrient agar produced bulbils.

In addition to bulbils, all of these forms also produce ovoid, hyaline
conidia borne on characteristic bottled-shaped sterigmata. ‘The
ascospores are yellowish brown, becoming black or smoke-colored,
asymmetrical, more or less crescent shaped. They vary but little

HOTSON.— CULTURE STUDIES OF FUNGI. 249
in size, the measurements of Melanospora papillata and M. cervicula
averaging 10 X 25 4 while those of M. anomala are slightly larger,
12 X 28 uw. These variations, however, are so small that they could
not alone be considered as specific. The size and shape of the asco-
pores also correspond quite closely with those of Melanospora Gibel-
liana and Sphaeroderma bulbilliferum. At maturity the ascospores
appear as an irregular black mass in the center of the perithecium. As
in all the species of Melanospora the asci are very evanescent. The
walls become gelatinous and swell by the absorption of water, which
increases the volume to such an extent that the mucilaginous mass
protrudes from the ostiole, carrying out with it the embedded spores.
If the atmosphere is somewhat humid, this mass of spores, as they
are forced out, aggregate in a spherical mass at the mouth of the
ostiole; but if the air is dry as they are pushed out, they adhere to-
gether into a long, twisted, tendril-like filament, something like
the paint as it is squeezed out of an artist’s paint-tube. These cirrose
structures may measure from 10-18 mm. in length, and twist up into
a variety of shapes. The spores not infrequently germinate while
still in the cirrus, giving it a white appearance.

Microtome sections show no paraphyses between the asci, but from
the walls there grow out more or less conspicuously into the cavity
above the asci, numerous hyphal branches, as paraphyses, which con-
verge radially and extend upwards towards the ostiole. These prob-
ably aid in the formation of the neck when it is present.

In general the culture methods used were the same for all. Gross
cultures of the various substrata were made in crystallizing dishes
which were half-filled with sphagnum and covered with white filter
paper, on which the substratum was placed. The whole was then well
supplied with water and covered with a piece of plain glass and set
in a place in the laboratory where it would be protected from the
direct sunlight. When bulbils were observed, individual ones were
carefully picked out under a dissecting microscope and cultures made
from them, until a pure culture was obtained. ‘These were grown on
various kinds of media until perithecia with the characteristic long
cirri of ascospores, were obtained. Transfers of the ascospores were
then made by touching one of the aerial cirri with a piece of nutrient
agar on the end of a sterilized needle. In all cases pure cultures of
ascopores obtained in this way produced bulbils.

The germination of the ascopores was followed in Van Tieghem cells
until bulbils were again produced on the mycelium, thus demonstrat-
ing the connection between the ascospore and the bulbil.

250 PROCEEDINGS OF THE AMERICAN ACADEMY.

In these forms the very young perithecium can be readily distin-
guished from the bulbil, not only by its mode of development when
that is different, but also by the color. The bulbils turn brownish
at a very early stage in their development, such as is represented,
for example, in Figure 2, Plate 2, while on the other hand, the peri-
thecia frequently remain colorless, or nearly so, until they are beyond
the size of the average mature bulbil, and the ascogonium usually can
be distinctly seen in the form of one or two large cells lying towards
one side of the young perithecium.

The question of sexuality in connection with the formation of the
ascogenous primordia has not been worked out. Structures have been
observed that might well be taken for antheridial branches, but their
attachment was not constantly or certainly observed, so that this
phase of the problem will have to be left for future consideration.

Among the twenty bulbil cultures from different sources which have
been found by the writer to produce melanosporous perithecia, at
least three distinct species appear to be distinguishable. Although
these forms possess ascospores that show little if any variation, the
differences in their perithecia, bulbils and secondary spore-forms are
such that they cannot be included in a single species. Moreover, the
characteristics are believed to be sufficiently distinctive to warrant
their consideration as separate species. They have therefore been
named Melanospora papillata, M. cervicula, and M. anomala. There
thus appear to be several closely related Melanospora-like forms, in-
cluding Sphaeroderma bulbilliferum, Melanospora Gibelliana and M.
globosa all of which give rise to bulbils.

The differences which distinguish the perithecia of these forms may
be summarized as follows:

Melanospora Gibelliana; neck of perithecium long and tapering,
with terminal setae, asymmetrical ascospores.

M. globosa; neck of perithecium longer than M. Gibelliana, no well-
defined terminal setae, symmetrical ascospores.

M. papillata, τι. sp.; perithecium with a distinct papilla only with
terminal setae, asymmetrical ascospores.

M. cervicula, τι. sp.; perithecium with a short neck, terminal and
lateral setae, asymmetrical ascospores.

M. anomala, τι. sp.; perithecium more or less definitely papillate,
with occasional indications of abortive terminal setae, asymmetrical
ascospores.

Sphaeroderma bulbilliferum; perithecia without papillae or setae.

The species of “Sphaeria “mentioned by Biffen as associated with
Acrospeira mirabilis and the species of “Ceratostoma’”’ connected

HOTSON.— CULTURE STUDIES OF FUNGI. 201

with bulbils by Bainier may also be melanosporous and will be re-
ferred to later on.

Melanospora papillata n. sp.
PLaTE 2, Figures 1-26.

Perithecia scattered or gregarious, superficial, membranous, semi-
translucent, straw-colored to light brown, globose to pyriform,
350-450 uw X 400-500 yp, papilla surmounted by erect, somewhat
divergent, continuous setae, 100-170 ww in length; primordium a
group of one or more intercalary cells; ascospores asymmetrical,
somewhat crescent-shaped 10 X 25 yp, yellowish brown becoming
black; conidia abundant, hyaline, spherical to ovoid, on flask-shaped
sterigmata; bulbils yellowish brown, irregular in outline, 50-60 μι in
diameter, sometimes considerably more than this.

On Live Oak bark (Quercus agrifolia Née) from Pomona, Cali-
fornia.

A pure culture of this species was easily obtained by making a
transfer of the ascospores in the manner already described, on rich
nutrients, fairly soft, with about 20 gm. of agar to the litre, and both
perithecia and bulbils were produced abundantly. On substrata,
however, poorly supplied with nutrient material, such as sterilized
agar-agar, or even on a medium well supplied with food material if
made very hard (about 40-50 gm. of agar to the litre) the bulbils are
very sparingly produced if at all, the mycelium is quite inconspicuous
and the perithecia appear scattered over the surface more or less
abundantly. In its capacity to retain its power of producing peri-
thecia this species resembles M. cervicula, while it is in sharp contrast
to some other melanosporous forms studied in which, after long
artificial cultivation the bulbils tend to become the dominant mode
of reproduction and the perithecia are produced sparingly if at all.

The bulbils. The hyphae, which vary in diameter from 4-7 p, are
hyaline, with numerous oil globules and prominent cross walls, and
are usually very scantily developed. The bulbils make their appear-
ance as small straw-colored bodies scattered somewhat sparingly
and usually in small patches over the surface of the substratum.
In the process of development, which was carefully followed in Van
Tieghem cells and in pure cultures in test-tubes, hyphae divide up
into short intercalary almost isodiametric cells, one or more of which
enlarge (Figure 1, Plate 2) while the contents becomes densely granu-
lar and filled with oil globules. At this stage these enlarged cells are

252 PROCEEDINGS OF THE AMERICAN ACADEMY.

colorless or opalescent with a comparatively thick wall and look
much like chlamydospores. The adjacent cells of the filament on
either side of them become stimulated and also enlarge to some
extent, but remain colorless longer than the others, although they are
eventually incorporated into the bulbil. The primordial cell or cells
soon become brownish and produce others by gemmation, which in
turn produce still others (Figures 2-5, Plate 2), so that the mature
bulbil finally consists of one or two, occasionally more, large central
cells with shghtly thickened walls, surrounded by a number of smaller
less highly colored ones, with thinner walls. The mature bulbils
measure from 50-60 uw in diameter, although they may vary consider-
ably.

Sometimes three or four intercalary cells enlarge and take part in
this process, producing an elongated, somewhat irregular bulbil,
while at other times there are as many as eight or ten such cells;
but in this latter case they seldom go farther than the production of
a few lateral cells which soon become empty and colorless, as is
shown in Figure 7, Plate 2.

Not infrequently the terminal cell or series of terminal cells becomes
the primordium (Figures 24-25), the further development of which
is the same as the one already described. In Van Tieghem cell-
cultures, bulbils are sometimes produced with more central cells than
ordinarily occur in tube-cultures, and these, which are usually spheri-
eal, contain oil globules which give them a peculiar, somewhat
opalescent appearance. The cortical cells in such cases are somewhat
flattened, as indicated in Figure 22, Plate 2, a condition which may
be due to the pressure exerted by the increased number of the central
cells.

The perithectum.— The form of the primordium of the perithecium
is essentially the same as that of the bulbil but the former, as has
already been stated, can, even in the early stages of its formation, be
readily distinguished from the latter by the fact that it is colorless.
It can be distinguished also from the primordium of the perithecium
of M. cervicula, which in many respects it resembles, by the fact that
the latter turns brownish at a much earlier stage in its development,
producing a large number of radiating hyphae, so that its outline is
soon indistinguishable.

Usually one, rarely two, intercalary cells take part in its formation,
and from these, two or three large cells are produced laterally by
budding (Figure 8, Plate 2). From the intercalary cells, or, more
frequently, from the adjacent ones of the hypha, branches are sent

HOTSON.— CULTURE STUDIES OF FUNGI. 252

up which eventually enclose this group of large cells. These branches
which divide up into short cells, form the wall of the perithecium.

Sometimes, as in the case of the bulbi!, a terminal cell may become
the primordium, as is evidently the case in Figure 10, Plate 2, where
there are two large cells which have originated from a terminal one.

The mature perithecium is straw-colored, globose or slightly pyri-
form, measuring 400-500 uw in diameter, but often much smaller than
this, the variations in size are largely due to the character of the
medium on which it grows. It is surmounted by a crown of setae
which surround the ostiole and are colorless, 100-170 j in length,
stiff, erect, straight, and tapering to a point. There are no lateral
setae of this nature, but frequently superficial cells near the base of
the perithecium may send out filaments which serve as attachments
to the substratum. The perithecia often occur grouped in consider-
able numbers and not infrequently two or three are found which have
more or less fused during their development, having no doubt arisen
from primordia which were in close contact with each other. Some
time after their formation the cirri of ascospores begin to assume a
whitish appearance which is due to the presence of numerous germi-
nating spores producing many abnormalities. A very common form
in such cases is shown in Figure 14, Plate 2 where, instead of a regular
germ tube, a large opalescent, spherical body is formed at the end of
the spore, which contains a great deal of granular material and stains
deeply. Occasionally a second such body is produced, and from
these one or more lateral branches may arise (Figures 18-20, Plate 2).
Not infrequently a series of these swollen cells appears terminating a
branch and these become spherical and form a bulbil-like structure
(Figure 17) such as issometimes met with in Van Tieghem cell cultures
(Figure 21). One of the most striking features of these germinations
is the copious formation on the germ tubes of ovoid conidia which
arise from bottle-shaped sterigmata and usually adhere in short
chains, although they sometimes cohere at the tips of the sterigmata
in a spherical mass. As already mentioned conidia similar to these
are also quite frequently met with on the mycelium in all parts of
the culture, and when the spores collect in masses the fructification
might readily be mistaken for that of Hyalopus.

In some cases the outer cells of the bulbils increase in numbers
until the whole structure is about half the size of a perithecium,
although very irregular and sclerotium-like. In each case, however,
the cells of the original bulbil retain their deep tan-color, while those
which have resulted from this secondary growth are distinguished

254 PROCEEDINGS OF THE AMERICAN ACADEMY.

by light colored walls resembling those of the typical perithecium.
The occurrence of such abnormal forms, which may be quite frequently
produced on media rich in nutriment such as bran-agar for example,
and their resemblance to young perithecia, suggested the possibility
of a direct development of perithecia from bulbils similar to that
suggested by Bainier (’07), and an effort was accordingly made to
determine this point. Individual bulbils showing this tendency were
isolated and their further development watched in Van Tieghem cells,
while others were transferred to different kinds of media, moist
cotton, moist filter paper, ete., but in no instance could they be in-
duced to develop into perithecia, although when the moisture was
sufficient, they produced numerous germ tubes which grew out
forming the typical mycelium.

Melanospora cervicula, n. sp.
PLATE 3, Ficures 16-24.

Perithecia scattered or gregarious, superficial, membranous, semi-
transparent, straw-colored to brownish, globose to pyriform, 350-
450 Χ 450-550 μ, with a definite neck 85-140y in length, terminal
setae 100-170 uw in length, erect, somewhat divergent, continuous,
sharp, subulate; lateral setae on the neck and upper part of the peri-
thecium; ascospores asymmetrical, somewhat crescent-shaped 10 Χ
25 μ, yellowish brown becoming black; conidia common in tube
cultures, hyaline, spherical to ovoid, on flask-shaped sterigmata;
bulbils yellowish brown, irregular, normally 50-60 mw in diameter,
sometimes 100 yu, primordium one or more intercalary cells. This
form is also said to produce conidia on secondary “ Harzia-like”’
heads, and chlamydospores resembling those of Acremoniella atra.

On rabbit dung, Cambridge, Mass.

This melanosporous fungus was obtained from Dr. Thaxter who
had grown it for some time as a pure culture. It was originally found
on a gross culture of rabbit dung from the vicinity of Cambridge,
Mass., and has proved to be of special interest on account of its differ-
ent methods of reproduction.

In addition to perithecia and bulbils, this fungus seems to have
associated with it two other spore forms, chlamydospores resembling
those of Acremoniella atra and also conidia produced on secondary
heads resembling those of the genus Harzia. Alcoholic material
furnished by Dr. Thaxter was used for the study of these two modes
of reproduction. This material was the result of a series of transfers

HOTSON.— CULTURE STUDIES OF FUNGI. 255

of the cirri of ascospores and therefore probably pure. The writer
has under cultivation transfers of this same fungus but although it
has been grown on various kinds of media, both very rich and very
poor in nutrient material, and hard and soft, ete., yet thus far he has
not succeeded in obtaining either the chlamydospores or the “ Harzia-
like” fructification. This is probably due to the fact that the pro-
duction of these structures is secured under certain peculiar conditions
not readily controlled.

In general this fungus resembles M. papillata in form and habit of
growth. The predominant type of reproduction in both is by asco-
spores the production of bulbils being scanty, while in some cases, as
on attenuated agar cultures, they are not produced at all. The peri-
thecium of MW. cervicula which is usually 400-500 μι in diameter, has a
definite neck 85-140 yw in length, while MW. papillata which is slightly
smaller, seldom reaching 500 in diameter, has no neck but often
a papilla-like structure from which the setae arise. Moreover, the
former probably produces conidiophores of the “Harzia type’? and
also chlamydospores which resemble those of Acremoniella atra.

The Bulbils— The mycelium is colorless, procumbent or only slightly
aerial, growing evenly over the surface of the substratum. The
hyphae, which are copiously septate, measure 5-7 μ in diameter, but
often large swellings occur in them which seem to act as storage organs
and from which several branches may grow out as shown in Figure 21,
Plate 8. These are found not infrequently on attenuated artificial
media such as agar alone without any nutriment, on which the mycel-
ium is very scanty, being barely visible even with the aid of a hand
lens. On such media, it should also be noted that as in M. papil-
lata, bulbils are not produced. It further resembles the latter in
the mode of development of the bulbils, the primordium consisting of a
group of intercalary cells. It is, however, subject to considerably
greater variation and many irregular, incomplete or imperfect forms
appear. Since the mode of development is essentially the same as
that described for M. papillata, it will be unnecessary to repeat
the description here. They are, however, produced very sparingly
on most media, and on some, such as that just mentioned, do not occur
at all, although on a rich substratum not too hard, such as sugar,
chestnut or bran agar they are produced quite abundantly.

The perithecium.— In general the perithecium resembles that of
M. papillata, but is clearly distinguished by having a definite neck.
They, however, vary considerably in size, sometimes reaching 550 μ
in diameter, their form often being somewhat contorted, with only

256 PROCEEDINGS OF THE AMERICAN ACADEMY.

a slight difference in size between the neck and body, while at
other times several may be grown together. The neck is short, 85-
140 uw in length surmounted by a group of terminal setae of about 100-
170 μ in length. The mode of development of the perithecia is some-
what variable. Although at times they seem to be produced from in-
tercalary cells, yet more frequently a short lateral branch is produced
which may form a close coil of one or two turns, and occasionally even
a definite spiral is found as is shown in Figure 19, Plate 3. The
young perithecia turn brownish at a much earlier stage of their devel-
opment than either those of M. papillata or M. anomala. This fact,
together with the large number of radiating hyphae that are produced
from the initial cells, a condition not occurring in either’ species
just mentioned, make it very difficult to follow the early development.
When the perithecium is young before the neck is produced, filaments
with thick brownish walls, apparently stiff and with prominent septa,
are seen scattered sparingly over the surface and radiating from it.
They are formed by the outgrowth of some of the peripheral cells,
and as the perithecium becomes older, as has already been stated,
their number increases and some grow down into the substratum and
act as hold fasts.

The “ Harzia-type”’ of reproduction.— This mode of reproduction
which was studied from material preserved in alcohol appears in
small tufts scattered over the surface of the substratum. Short
lateral branches become swollen at the end after the fashion of
Oedocephalum or Aspergillus, and from this head a number of flask-
shaped sterigmata are produced, on the ends of which occur secondary
heads crowded with hyaline conidia which are usually spherical and
sessile but occasionally more or less ovoid and furnished with short
stalks (Figure 24, Plate 3). The secondary heads seem to vary con-
siderably in size, and being so completely covered with conidia it was
difficult to determine at all times the exact relation of the different
parts of this fructification. In several cases there appeared to be
little or no swelling of the secondary head, but with the limited amount
of material at hand this could not be determined with certainty.
Occasionally the head instead of being spherical is somewhat elongated,
and the bottle shaped stalks, on which the secondary heads are
formed, are scattered along the margin of this as shown in Figure 23,
Plate 8. This fungus also ‘produces numerous spherical conidia on
bottle-shaped sterigmata along the margin of the hyphae, similar to
those described for the other melanosporous forms.

The chlamydospores.— On the preserved material already referred

HOTSON.— CULTURE STUDIES OF FUNGI. 257

to, there were also found associated with the “ Harzia-like”’ fructifiea-
tion, chlamydospores which are ovoid, smooth, brownish, thick-
walled, and have the distal end rounded. They are produced usually
on short lateral branches which taper towards the tips and may be
continuous or septate. ‘The mature spores are quite uniform in size,
about 17 X 21 μ, although there were some that appeared to be mature,
which were slightly smaller than this. These spores resemble both
in color and form those of Acremoniella atra Sace. There are certain
other fungi that produce imperfect forms of the “Harzia”’ and
“Acremoniella”’ type which will be further considered below in
connection with P. aspergilliformis.

Melanospora anomala n. sp.
PuLaTE 2, Figures 27-30; Puate 3, Figures 1-15.

Perithecia scattered or gregarious, superficial membranous, straw-
colored or light brown, globose or subglobose, 250-350 μ. Χ 350-
450 μ, ostiole formed in connection with a definite but inconspicuous
papilla without setae, primordium a spiral of 4 or 5 coils; ascospores
asymmetrical, somewhat crescent-shaped 14 Χ 28 μ, yellowish brown
becoming brownish black; conidia, hyaline, spherical to ovoid, on
flask-shaped sterigmata: bulbils yellowish brown, variable in size
70-140 u in diameter, sometimes elongated ones 1804 in length,
primordium a group of intercalary cells.

On Spanish chestnuts in laboratory culture.

Gross cultures of Spanish chestnuts, which were imported probably
from Spain obtained by the writer in the Boston market, produced
numerous brownish colored bulbils when cultivated in moist chambers.
By using the general methods already described, separate bulbils
were transferred to sterilized nutrient-agar tubes and, after a few
transfers, were obtained pure.

The mycelium of this fungus is white and more or less aerial, vary-
ing according to the media in which it is grown. When grown on soft
chestnut agar, it becomes quite flocculent, while on chestnut decoc-
tion it forms a more or less felted layer over the surface, assuming the
brownish color of the liquid; but on potato agar its growth is rather
scanty. The diameter of the hyphae varies from 2.5-7 μ.

The bulbils.— Scattered over the aerial hyphae and on the substra-
tum are seen numerous small yellowish-brown bulbils, which, when
examined microscopically, are found to vary considerably in size and
outline, many of them nearly spherical, others somewhat elongated.

258 PROCEEDINGS OF THE AMERICAN ACADEMY.

Usually there is no differentiation between the cortical and central
cells, but in old bulbils several empty cells, which may or may not
be colorless, are often found loosely attached to the periphery. The
central cells are often larger than the more superficial ones, but this
is not always true, since in many instances they are perfectly uniform
throughout. These bulbils are usually developed from a lateral
branch which divides up into short cells. These produce short
secondary branches (Figures 27, 29, 30, Plate 2) which also divide up
into short cells and may produce others by a process of gemmation.
Sometimes the primordium consists of a group of intercalary cells
(Figures 28, Plate 2, and Figure 14, Plate 3) which may produce other
cells by budding in a manner somewhat similar to that of M. papil-
lata. At maturity the bulbils are irregularly spherical, about 70-
140 μ in diameter, but where several interealary cells have taken part
in its formation, the long axis frequently measures 180 μ. This bulbil
may be distinguished from M. papillata or M. cervicula by the fact that
the cells are usually homogeneous throughout, while in the latter two
there is a more or less definite cortex. The margin is also often more
irregular in the bulbil under consideration as is shown in Figure 15,
Plate 8. In the immature bulbils which show this uneven outline
more markedly than the mature ones do, there sometimes appear
short branches of two or three seriate cells which extend beyond the
others.

The perithectum.—In an effort to induce this fungus to produce the
perfect form, it was grown on various kinds of media. Decoctions of
potato, bran, corn meal, Spanish chestnuts, ete., were hardened with
agar-agar, some hard, some soft, but nothing except variations in the
size and development of the bulbil could be obtained. Finally, after
removing the shells of some fresh, sound chestnuts, the kernels were
sliced up and used for cultures. On this medium perithecia were
produced in abundance. These are almost spherical in form and vary
from 300-400 u in diameter, no ostiole being developed until they are
nearly mature, at which time a few cells about the opening form a
definite, though inconspicuous papilla. Terminal setae are wholly
absent, and only rarely do the superficial cells produce lateral filaments.
Frequently, however, short projections are observed from some of the
cells that compose the papilla, as if an attempt were being made to
produce setae. The perithecia are light yellowish-brown in color,
much lighter than that of the bulbils, and so translucent that the
spores can be readily seen grouped together in a black mass in the
center (Figure 12, Plate 8).

HOTSON.— CULTURE STUDIES OF FUNGI. 259

Development of the perithectum.— The primordium of the perithecium
is quite different from that of the bulbil. In this case a short lateral
branch coils up spirally, usually making about four or five turns, but
in some cases as many as eight. Figures 1 to 8, Plate 3, represent
successive stages in the development of the spiral. Usually the second
and part of the the third turn become enlarged while branches are
given off from the first or from the cells below it. These branches grow
up around the spiral and often send secondary branches in between
the swollen lower coils so that they are forced apart (Figures 7, Plate 3).
The branches continue to grow until they have enveloped the whole
spiral, which soon loses its characteristic form. It would appear
that the upper portion of the spiral either becomes a disorganized mass
of mucilaginous material or not infrequently seems to be pinched off
and ejected during the formation of the wall of the young perithecium,
as is shown in Figure 7, Plate 8. By the time the wall is completed
all that can be recognized of the spiral are two or three large cells
which come to lie free in a cavity usually towards one side of the peri-
thecium and which stain deeply (Figures 9-10, Plate 3). Sometimes
branches seem to come off from each of the coils, so that one finds the
spiral with a number of very short lateral branches produced from its
outer surface. Occasionally also the lateral branch that produces the
spiral, while making its first coil, divides into short cells and sends off
secondary branches from these, as shown in Figure 3, Plate 3.
Whether either or both of these develop into perithecia or bulbils, or
are to be regarded as abnormalities, could not be determined, since
they were of rare occurrence.

Conidia on bottle-shaped sterigmata, similar to those produced by
M. papillata also occur in this species (Figure 13, Plate 3). Germi-
nating ascospores particularly, produce them abundantly in a dry
atmosphere, but they are more sparingly developed on the mycelium.

This fungus resembles somewhat a form described by Berlese (92)
under the name of Sphaeroderma bulbilliferum, which is referred to
below. The former has, however, a slightly smaller perithecium
(300-400 yw in diameter) with a papilla about the ostiole, while the
latter is 400-500 yu in diameter, and has no papilla, the ostiole being
flush with the surface. The Sphaeroderma moreover is said to have
connected with it large two-celled chlamydospores, which have not
been found associated with M. anomala although the writer has re-
peatedly searched for them. Berlese does not describe the method of
development of the bulbils, but states that “the sporeballs resemble
those described by Mattirolo as belonging to Melanospora Gibelliana,”’

260 PROCEEDINGS OF THE AMERICAN ACADEMY.

The bulbils of the latter are not unlike those of M. anomala in size,
color and mode of development.

The species of “Sphaeria,”’ referred to by Biffen (’02) in connection
with Acrospeira mirabilis, also resembles somewhat M. anomala. It
differs from the latter, however, in several important respects. The
perithecium has no papilla about the ostiole, the ascospores are sym-
metrical and the primordium of the bulbil is a spiral.

Again the mode of development of the perithecium from a spiral
primordium resembles somewhat that of Melanospora stysanophora
described and figured by Mattirolo (’86). The mature perithecia
however, are different, M. stysanophora having a distinct neck. The
latter is also said to be associated with a Stysanus-like fructification.

MELANOSPORA GIBELLIANA Mattirolo.

This species was found by Mattirolo on a gross culture of decayed
chestnuts in moist sand, and besides melanosporous perithecia and
bulbils it also produced chlamydospores and conidia on bottle-shaped
sterigmata.

The perithecium, which develops from a spiral primordium, 15
somewhat pyriform with a long neck surmounted by terminal setae.
The neck, however, is considerably longer than that described for
M. cervicula. The ascospores are brownish-black and asymmetrical,
somewhat similar to those described for the other melanosporous
forms.

The bulbils are said to be nearly spherical, pale yellow to brownish-
yellow, and often 100 μ in diameter, with a colorless cortical layer of
cells resembling somewhat the appearance of Papulospora coprophila.
In its development a short lateral branch divides and forms a number
of short secondary branches which intertwine forming an irregular
spherical body varying considerably in size.

This species also is said to have associated with it chlamydospores
somewhat resembling Sepedonium, as well as conidia on bottle-
shaped sterigmata.

MELANOSPORA GLOBOSA Berl.

In the same article in which he describes Sphaeroderma bulbilli-
ferum (’92) Berlese also describes Melanospora globosa which he found
growing on small pieces of decaying wood and herbaceous material.
The perithecium of this species is, as the name indicates, globose,
250-280 μι in diameter and 360-450 uw (rarely 500 μὴ long. The neck

HOTSON.— CULTURE STUDIES OF FUNGI. 201

is well developed, 110-200 μ in length. The ascospores differ from
those, already described, in being symmetrical. The other forms
have asymmetrical ascospores which are somewhat crescent-shaped.

Besides the perfect form this species is said to have: microconidia
which resemble those of Acrostalagmus; chlamydospores that are
of the type of Acremoniella atra; and bulbils which he considers of
the same nature as similar structures described by Mattirolo. Berlese
succeeded in obtaining bulbils on the mycelium produced from asco-
spores but he failed to find any perfectly developed.

SPHAERODERMA BULBILLIFERUM Berl.

This species which is described by Berlese (’92) was found growing
on dead leaves of Vitis, Cissus, and Ampelopsis. It is said to have
several kinds of reproductive bodies, such as ascospores, bulbils,
conidia and chlamydospores.

The perithecium is globose or sub-globose, 400-500 uw in diameter,
without any neck, setae or papilla. These characteristics distinguish
it from any of the melanosporous forms already referred to. It
resembles M. anomala but is slightly larger and has no papilla. The
ascospores are brownish-black and asymmetrical.

The bulbils are yellowish, nearly spherical, 80-150 μι in diameter,
consisting of polyhedral cells and surrounded by a layer of empty
cortical cells. They are said to resemble quite closely those described
in connection with Melanospora Gibelliana.

The conidia occur in chains on bottle-shaped sterigmata resembling
those of the melanosporous forms already referred to.

The chlamydospores, which measure 32-40 X 24-25 μ, are described
as yellow, oval, smooth, composed of two unequal cells, and formed
terminally on the ends of short lateral branches.

“CERATOSTOMA”’ sp. indet.

Bainier (’07) has reported that he has determined the connection
of a perithecium of the genus Ceratostoma with Papulospora asper-
gilliformis. He is of the opinion that the bulbils in this instance are
immature perithecia and that, under proper conditions as regards
nutriment and moisture, they may be induced to complete their
development.

In this form, the bulbil is produced by a short lateral branch
which coils up spirally, the coils becoming quite compact. One or
more of the terminal cells enlarge and eventually become filled with

262 PROCEEDINGS OF THE AMERICAN ACADEMY.

conspicuous food material. The cells below the spiral send out
branches which divide and may, in turn, produce others. These
grow up around the spiral and completely envelop it, thus forming
a somewhat spherical mass of cells. In a moist atmosphere these
are said to develop into sclerotium-like bodies. By transferring
these large bulbils to pieces of moist bread, Bainier succeeded in
inducing them to develop into perithecia which he refers to the genus
Ceratostoma, although it is not evident why this form should not also
be referred té Melanospora. This subject will be further dealt with
below under Papulospora aspergilliformis.

In connection with pyrenomycetous forms it will be well to con-
sider briefly two additional species which may be regarded as doubt-

fully pyrenomycetous.

FORMS DOUBTFULLY REFERRED TO PYRENOMYCETES.

Papulospora candida Sace., parasitic on Geoglossum, has been re-
ported by Dr. Thaxter to be connected with hypocreaceous perithecia
found on specimens of the host obtained in South Carolina; but this
material was, unfortunately, not available for examination, and
since pure cultures of this fungus grown on different media have thus
far failed to produce any perfect form, its position must, for the present
at least, remain more or less uncertain. The fact, however, that the
bulbil is definitely connected with a Verticillium would seem to afford
strong evidence of its hypocreaceous nature. A second doubtful
form is Acrospeira mirabilis (Beck ἃ Br.), with which Biffen (’02)
has associated a species of “Sphaeria,’’ but since he was unable to
obtain the bulbils or “chlamydospores” as he terms them, of Acro-
speira from pure cultures of the ascospores, his conclusions must be
accepted with some reserve.

PAPULOSPORA CANDIDA Sacc.
Piate 4, Figures 1-47.

This fungus was first found by Ellis who collected it in New. Jersey
and distributed it by N. A. F. No. 3673. The species appears to be
common and distributed from N. Carolina to Maine. The material
for the present investigation was found growing abundantly as a
parasite on Geoglossum glabrum in a maple Sphagnum swamp near
Walnut Hill, Mass. It was first described (Mich. II, p. 576) as
Papulospora candida, by Saccardo who also mentions that Verti-

HOTSON.— CULTURE STUDIES OF FUNGI. 263
cillium agaricinum_Link, var. clavisedum (Mich. II, p. 577) is asso-
ciated with it.

A large number of specimens of Geoglossum, with plenty of Sphag-
num and leaf mould about each, were collected — some infected,
others not — and were grown under bell jars or in a large germinating
vessel with a glass top. It was thus kept growing for nearly two
months, until it could be determined whether the Papulospora would
grow as a saprophyte on artificial media. A number of tube cultures
were made of the bulbils on various kinds of media, the most success-
ful of which were the ascoma of Geoglossum itself. About a dozen
large specimens of these with long stalks were selected and each put
in a test-tube which had previously been supplied with about half
an inch agar. These were then sterilized in an autoclave, the object
of the agar being simply to hold the specimen in place and thus lessen
the chances of contamination in making the transfers, ete. On this
medium a pure culture was eventually obtained, which was then
transferred to other media such as potato, corn meal, chestnut,
horse dung, ete., hardened with agar. This fungus grows fairly well
as a saprophyte, better on hard than on soft media such as potato
and bran, but very slowly on horse dung, on which, after a month,
it had not grown much more than an inch from the point of inocula-
tion. Associated with the Papulospora on the ascoma were found,
among other fungi, specimens of Plewrage anserina (Rabh) Kuntze
and Verticillium agaricinum Link, the latter producing in pure cul-
tures very large and conspicuous, brownish sclerotia.

On its natural host Papulospora candida forms conspicuous white
blotches spreading over the upper portion of the ascoma (Figure 47,
Plate 4), and if not too wet, extending down the stem. Although the
host is usually found in damp sphagnum swamps, the parasite is
largely confined to those specimens that grow tall, so that their tops
are comparatively dry. The mycelium is white, procumbent, branch-
ing copiously, but soon becoming indistinguishable as such, even with
a good hand lens, mainly on account of the large number of bulbils
that are formed which give the whole fungus a powdery appearance.
When examined under a microscope the mycelium is opalescent,
owing to the presence of numerous oil globules (Figures 42, 44, Plate 4)
and other colorless material in the cells. The cultures become com-
pletely covered with the white powdery bulbils which a little later
assume a characteristic cream color.

The bulbils— During the process of development of the bulbil a
short lateral branch divides up into a number of cells and the end

264 PROCEEDINGS OF THE AMERICAN ACADEMY.

one enlarges and usually also the second or third (Figures 29-37,
Plate 4). From these, other cells are then produced by budding,
the lateral walls of which eventually adhere closely to those ad-
jacent, so that there comes to be from two to six large central cells
surrounded by a number of smaller ones, all filled with granular proto-
plasm, the only apparent difference being in their size. As they
mature, however, the inner and outer cells become markedly differ-
entiated. The former, which are large with conspicuously granular
contents and with numerous oil globules, secrete a thick hyaline wall,
while the latter, which become empty and spherical, adhere to each
other loosely, their contents probably being absorbed by the central
cells (Figure 41, Plate 4). Although the terminal cell is usually the
most prominent in producing the larger central cells, yet one or both
of the two adjacent cells may take the lead and, owing to their lateral
growth a somewhat crosier-like coil may even occasionally be produced
by one or more of these secondary branches.

Germination of the bulbils.— For the purpose of studying the germi-
nation, bulbils in different stages of development were placed in Van
Tieghem cells. In about twelve or fifteen days the marginal cells of
those that were immature — that is, those whose superficial cells
still contained protoplasm — began to send out vegetative branches,
one or two from each cell (Figure 42, Plate 4); but the central cells
were not observed to produce tubes at this stage. After about a
month the mature forms begin to germinate, but very sparingly, each
of the large central cells usually sends out a single germ tube which
readily pushes aside the loosely adhering peripheral cells. The germ
tubes or vegetative hyphae, as the case may be, usually divide up into
short cells which become swollen with the protoplasmic contents and
more or less constricted at the partitions (Figure 42, Plate 4).

The conidia.— The erect septate conidiophores of the so-called
Verticilium agaricinum (Link) Corda, var. clavisedum Sacc., already
referred to, are invariably associated with the bulbils in pure cultures,
and are thus shown to be not, as Saccardo supposed, accidentally
concomitant but a regular phase of the life cycle. Figure 45, Plate
4, shows bulbils and the Verticillium fructification definitely connected
on the same erect hypha. This phenomenon 15 of so frequent occur-
rence that there is no possibility of error. The conidiophores are
simple or branched, with the sterigmata in whorls, varying greatly in
number, commonly in threes and frequently clustered at the apex.

The mature conidia are ellipsoidal to oblong and rounded at both
ends, varying considerably in size, the average measurements being

HOTSON.— CULTURE STUDIES OF FUNGI. 265

14 X 15 μ, although the length may vary from 12 to 15 yu. In this
respect it differs from [΄. agaricinwm in which the conidia are smaller
and ovoid in shape. Both of these forms have been cultivated in
pure cultures for some time and seem to be absolutely distinct, the
one, V’. agaricinum, producing ovoid conidia often clustered at the
apex of the sterigmata as well as an abundance of large brownish
sclerotia not associated with bulbils, while the other has oblong coni-
dia, rounded at both ends, somewhat larger than the former, and on
germination the mycelium invariably gives rise to bulbils, without
any trace of the sclerotia.

The germination of the conidia of P. candida was carefully followed
in Van Tieghem cells, using different kinds of nutrient media. In
these cultures many interesting variations were observed, as is shown
in Figures 1-12 and 15-27, Plate 4, all of which have the same magnifi-
eation. Figures | and 2 show the variation in the size of the conidia.
During the first twenty-four hours they enlarge by the absorption of
water, becoming almost spherical (Figure 4), in which condition they
are ready to germinate, the diameter at this stage varies from 12-18 μ.
The germ tube, which may appear at one or both ends (Figures 7, 20)
or from one or both sides of the conidium (Figures 6, 8), sometimes
grows out to form a mycelium (Figure 10) on which bulbils and the
conidial fructifications are produced; but more often, in Van Tiegham
cells at least, it rounds up and forms another large cell. Several
large cells may be produced in a similar way, which become almost
spherical in shape and densely filled with granular protoplasm and oil
globules, and from these acting as central cells, other smaller ones
are formed laterally by budding, and in about sixteen days a bulbil
consisting of two to six large central cells surrounded by a layer of
smaller ones, all containing protoplasm, results.

ACROSPEIRA MIRABILIS (Berk. and Br.).
Puate 5, Figures 18-23.

Acrospeira mirabilis (Berk. and Br.) appeared on a gross culture of
Spanish chestnuts obtained from the Boston market. It was from
this same material that Melanospora anomala was obtained but from
other gross cultures. The former was first described by Berkeley
and Broome in 1861, a more detailed account being given by
Berkeley in his “Introduction to Cryptogamic Botany.’ Massee
(03) refers to it as a very destructive parasite doing a great deal of
damage to chestnuts in Spain, but states that “nothing as to the life

266 PROCEEDINGS OF THE AMERICAN ACADEMY.

history of the parasite is known.” Before Biffen (’02) examined this
species, the only method of reproduction known was by its so-called
“chlamydospores”’ which at maturity consist usually of one large,
thick-walled, chocolate-brown, warty cell and three or more colorless
cells adhering closely to it. By the use of pure cultures Biffen claims
to have succeeded in obtaining not only the “chlamydospores,” as
described by Berkeley and Broome, but also what he calls “spore
balls”? (bulbils) and definite perithecia.

The mycelium of Acrospeira is fine, colorless, procumbent, more or
less sparingly developed, and produces large numbers of reproductive
bodies, which, in their development and structure, are bulbils rather
than “chlamydospores.” They are so abundant that the whole
surface of a culture, which would otherwise be white, assumes a
brownish aspect. The readiness with which these bulbils are pro-
duced makes it comparatively easy to trace their development,
which, in brief, is as follows: an erect lateral branch usually divides
into three secondary branches (Figure 18, Plate 5) each of which coils
up much like that of Papulospora parasitica, to be considered below.
They make about one to one-and-a-half coils and divide into three
cells by cross septa. The middle one of these three, as a rule, en-
larges rapidly, forming the functional spore (Figure 21, Plate 5) (the
central cell of P. parasitica), but occasionally the end cell (Figure 20,
Plate 5) more rarely the third, is the one that functions in this respect;
while the other cells of the coil, ordinarily three or more in number,
grow less rapidly and eventually lose their contents, become colorless,
and adhere to the side of the large cell. If the marginal cells should
increase in number so as to enclose the large cell completely, there
would be practically the same condition as exists in P. parasitica
(Figures 16, 17, Plate 5). In the present form, however, the large
cell becomes dark brown in color and develops a thick wall, which
eventually becomes warty, and measures 25-30 uw in diameter. Fig-
ures 18-23, Plate 5, illustrate the stages in the development of this
bulbil. Thus in Acrospeira we have a structure that is only slightly
-Jess complex than that seen in P. parasitica, a form in which many
imperfect bulbils can with difficulty be distinguished from some of
those of Acrospeira, their only difference being due to the absence of
a warty episporium. ‘These bulbils were grown on various kinds of
sterilized nutrient material, and most of the experiments described
by Biffen were repeated. The culture conditions were varied with
regard to media and other conditions of growth, in many. of these
experiments, but more bulbils of the same kind were always produced

HOTSON.— CULTURE STUDIES OF FUNGI. 267

and never, so far as the writer has observed, have any indications
been seen of the development of “spore balls,” or perithecia such as
have been described by Biffen.

BASIDIOMYCETOUS FORMS.

As has already been mentioned (p. 238), bulbils were first reported
among the Basidiomycetes by Lyman (707), who not only definitely
connected one form with Corticium alutaceum (Schrader) Bresadola,
which is dealt with briefly below, but also refers to two other kinds of
bulbils, the mycelia of which have well marked clamp-connections;
but basidiosporic fructifications were not produced abundantly
enough to allow of their identification. Dr. Lyman has kindly
supplied the writer with specimens of these forms for the purpose of
comparison, which will be referred to under their respective species.

The methods used here were much the same as those already de-
scribed, except that more gross cultures of wood were used with
different amounts of moisture. The best results were obtained from
decoctions of bran in one or two litre Erlenmeyer flasks with pieces of
rotten wood that extended considerably above the liquid, so that the
mycelium could obtain the degree of moisture that best suited it.

In order to keep the pieces of wood in place and thus lessen the
chances of contamination a quantity of agar was sometimes put in
the bottom of the flasks.

GRANDINIA CRUSTOSA (Pers.) Fr.
Puate 6, Ficures 1-10.

Bulbils of this species were obtained from at least ten different
sources, mostly on substrata such as rotten chips of Live Oak (Quercus
agrifolia Née), old canvas, paper, cardboard, ete., from Claremont,
California. It has been found also by Dr. Thaxter on gross cultures
of rabbit dung from Mass. and on rotten wood from Buenos Ayres,
and is probably the same as that referred to by Lyman (ΟἿ, p. 166),
which was obtained by Mr. A. H. Chivers on a gross culture of bits
of wood, paper, etc.

The mycelium, which shows quite marked clamp-connections,
is colorless, procumbent, producing numerous white fibrous, rope-
like strands of hyphae which radiate conspicuously in all directions
from the point of inoculation. The white mycelium, however, soon
takes on a light straw-colored aspect, owing to the formation of bul-

268 PROCEEDINGS OF THE AMERICAN ACADEMY.

bils in large numbers, which gradually become darker as they mature.
When grown on nutrient agar in large receptacles like Erlenmeyer
flasks, after the mycelium has covered the whole substratum with
powdery bulbils, new centers of growth-activity occur at different
points on the surface of the culture, and the radiate development
of the hyphae and the subsequent formation of bulbils are repeated
on the top of those first formed. If the flasks have plenty of nutrient
and do not dry up, this process may be repeated two or three times,
the amount of mycelium, and consequently the number of bulbils
formed, decreasing each time, so that eventually there appears a
thick powdery mass with here and there large, white, rope-like strands
of hyphae persisting, which is all that can be distinguished of the
mycelium.

The bulbils are usually more or less spherical in shape, varying
from 52 to 88 uw in diameter, although often exceeding this size, espe-
cially when the primordia of two happen to be so close together that
their hyphae intertwine, thus forming a large irregular body. The
individual cells are large, densely filled with granular material and
oil globules, spherical at first; but the central .ones soon become
angular by pressure, while the marginal ones retain more or less their
original form. There is no differentiation of a cortical layer; the
cell wall and contents are uniform throughout, except that occasion-
ally some of the peripheral cells which project beyond the others lose
their contents, but this is the exception and is probably due to age.

The bulbils— The hyphae which take part in the formation of the
bulbils become enlarged, conspicuous, and more or less contorted on
account of the prominence and swollen nature of the clamp-connec-
tions, which often occur at short intervals. The lateral branches
from these divide up into short cells, so that there comes to be a
number of almost spherical hyaline cells with fairly thick walls and
filled with granular material and oil globules (Figures 4-9, Plate 6).
During the formation of new cells, which are also spherical in shape
and produced by budding from the marginal ones, the central cells
gradually lose their original form and become angular, as a result of
the lateral pressure or resistance offered by the outer cells. When
the bulbils are nearly mature, they assume a light straw or “rusty-
cinnamon” color. Figure 10, Plate 6, represents a mature bulbil,
drawn on the same scale as the other mature forms. This method of
development follows very closely that described by Lyman (707) in
connection with Corticium alutaceum, considered briefly below.

Formation of basidiospores.— The basidiosporic fructification of

OE .ἀδνν ἁανα

ee τὰ

ΘΟ δ. οι νὰ.

HOTSON.— CULTURE STUDIES OF FUNGI. 269

Grandinia has been produced on gross wood cultures of this bulbil
and also on test-tube cultures of bran-agar of about 40 gm. of agar to
the litre, by three or four of the ten cultures from different sources
under cultivation. Preparatory to its formation, the mycelium ceases
to produce bulbils and forms a sort of incrustation, chalk-white in
color and becoming pustulate by the time the spores are formed,
Figure 1, Plate 6. The pustules on examination are found to be made
up of more or less thickly interwoven branching hyphae, which have
become enlarged and densely filled with granular material and oil
globules, the ultimate ramifications of which form the hymenium
(Figure 2, Plate 6). The basidia, which form a somewhat loose hy-
menium, each produce four spores, which are ellipsoidal to oblong in
shape, measuring about 4 X Sy. These spores were germinated in
Van Tieghem cells and the growth of the mycelium followed until the
formation of new bulbils, which were transferred. to nutrient agar
media, where they produced mycelia and bulbils like the original
culture.

On tube cultures this fungus occasionally produces typical sclerotia,
which are formed by the massing together of many hyphal branches
which remain colorless for some time and thus are easily distinguished
from the bulbils. Moreover, they are larger, 400-500 u in diameter,
irregular in shape, somewhat darker in color at maturity, and com-
posed of smaller, compact cells.

Grandinia also produces conidia of the Oidium-type on slender
clampless conidiophores, such as are described by Lyman (’07) for
Corticium alutaceum.

CorRTICUM ALUTACEUM (Schrader) Bresadola.

The bulbils of this species were obtained from Dr. Farlow, who found
them on a piece of rotten oak bark collected at Chocorua, N. H. It
was comparatively easy to get a pure culture, as the bulbils are pro-
duced in large numbers and germinate readily. This form has been
carefully compared with specimens of Corticiwm alutaceum obtained
from Dr. Lyman and they proved to be the same. The development
of the bulbil and the character of the conidia are practically identical
with those described for Grandinia and, as these have been well worked
out in pure cultures by Lyman (’07), it is not necessary to repeat the
results here, a detailed description of which may be obtained by con-
sulting his article, pp. 160 and 196. The mode of development of the
bulbils and the character of the conidia, however, have been carefully

270 PROCEEDINGS OF THE AMERICAN ACADEMY.

verified. Lyman obtained his cultures from the basidiospores collected
on old rotten oak logs in the field and pure cultures from these produced
bulbils. The writer began his cultures with bulbils, also collected
in the field, and, after a great number of unsuccessful attempts, finally
succeeded in obtaining a basidiosporic fructification similar to that
described by Lyman. This was accomplished by using gross cultures
of partly decayed wood in two litre Erlenmeyer flasks with sufficient
agar to hold them in place. The mycelium, as usual, produced bul-
bils profusely on the agar and wood, but after six or eight weeks near
the top of the pieces of wood conspicuous patches of white mycelium
appeared, which eventually produced the hymenium and basidiospores
of C. alutaceum.

Papulospora anomala n. sp.
Plate 6, Figures 11-19.

This form, which was obtained from four different localities,—
three from the vicinity of Claremont, California, found on Live Oak
chips, and one on an old paper from Cambridge, Mass.,— has been
grown on a variety of substrata in the hope that it would produce its
perfect form, but thus far all these efforts have failed. That it belongs
to the Basidiomycetes is shown by its clamp-connections, which,
however, are not so prominent as those in the two preceding forms,
from which it is further distinguished by the dark brown, opaque,
almost black color of the bulbils, the compact nature of their cells,
and their mode of development. The mycelium is white, procumbent,
scanty, slightly aerial on some substrata, with a large number of con-
spicuous oil globules, and not infrequently contains swollen intercalary
cells, which are also densely filled with food material and probably
act as storage organs.

The bulbils— The primary hyphae are small, seldom more than
3 uw in diameter, and do not produce bulbils; but scattered over the
secondary hyphae, which vary greatly in width, often reaching 10 μ
and under some abnormal conditions 14 μ, are seen slightly swollen,
colorless, intercalary cells, quite different from those mentioned
above, about 4 or 5 uw in diameter, sometimes projecting considerably
and resembling short stunted branches; at other times the base of a
short lateral hypha swells slightly and forms the primordium (Figure
12, Plate 6). From the primordial cell or cells branches are sent out
in different directions, the basal cells of which become spherical and
in turn may produce other similar branches (Figures 13-15, Plate 6).

HOTSON.— CULTURE STUDIES OF FUNGI. pain

The lateral walls of these basal cells adhere firmly to each other and
the cells become incorporated into the bulbil.

Figures 11-15, Plate 6, illustrate the early stages in the develop-
ment, and Figures 14 and 15 show the formation of the spherical
cells at the center, around the initial cell or cells, while Figure 16
represents a little later stage, which is composed of small hyaline cells
with very indistinct walls and forming almost a spherical body with
few, if any, cells projecting beyond the others. About this stage, or
usually a little later, it would appear that the bulbils cease to form
new cells, or, if any, very few, and that the further increase in its size
is chiefly due to the enlargement of the individual cells which compose
it and which, up to this period, have been small, hyaline, with in-
distinct walls. As these cells enlarge, there is quite a strong lateral
pressure exerted, which tends to make the walls angular, which in the
meantime have become more prominent and gradually assumed a
brownish tint, that later becomes a dark brown, almost black. As a
result of this mode of development, the bulbil at maturity has a
clear-cut, even margin, without any appendages or sharp projections,
nearly spherical in form, except where some cells in the process of
enlargement increased faster than others or in cases where two pri-
mordia were formed close together and their early branches became
intertwined, forming an elongated, compound structure. The color,
which becomes so deep that even the cell walls cannot be distin-
guished, may be bleached out by placing them in potassium hydroxide
for a few hours. The mature bulbils (Figure 17, Plate 6) vary in
size, usually measuring from 125 to 175 μ in diameter, although occa-
sionally some are even larger.

BuxBit “No. 200.”

This form was obtained from Dr. G. R. Lyman and was originally
found by Dr. G. P. Clinton in the vicinity of Cambridge, Massachu-
setts, on a fragment of an old newspaper in a field. In general this
species resembles Grandinia in the mode of development of the
bulbils, the presence of conidia and the clamp-connections of the
hyphae. The bulbils, however, are much darker and the mycelium
does not form the white, fibrous, radiating strands that are so charac-
teristic of Grandinia.

On gross cultures, especially of wood or horse dung agar, the hyphae
mass together in conspicuous papilla-like elevations, which are
much more prominent than the fructification of Grandinia. These

2.7. PROCEEDINGS OF THE AMERICAN ACADEMY.

elevations are composed of closely compacted basidia-like structures.
Unfortunately thus far the writer has observed only a few scattered
basidia with basidiospores so that it has been impossible to obtain a
specific determination.

BULBILS NOT YET CONNECTED WITH A PERFECT
FORM AND INCLUDED IN THE FORM-GENUS
PAPULOSPORA.

Key to the Species of Papulospora.
I. Primordium interealary.
AC vibulloils. folache ks tl ete aire Se Bins ote ners eee cas P. pannosa n. sp.
B. Bulbils yellowish to dark brown.
1. Bulbils, brownish-yellow, central cells 28-55 » in diameter.
P. immersa τι. sp.
2. Bulbils straw-color, central cells 10-20 μ in diameter.
P. irregularis τι. sp.
Bulbils dark psoray hyphae with clamp-connections.
P. anomala τι. sp.

ΕΣ
vo.

II. Primordium one or more lateral branches.
A. Primordium normally a single lateral branch.
1. Primordium a spiral.
a. Cells of bulbil heterogenous, definite cortex.
i. One central cell.
a.’ ‘Cortex* completes, 21.24 Aes eee P. parasitica.
τ imcomplete 2% 4.2.45 Acrospeira mirabilis.
ii. More than one central! cell.
a. Spiral in one plane, cortical cells spinulose.
P. spinulosa τι. sp.
8. Spiral in more than one plane, 2-6 central cells.
(a) Bulbils a dark brown......... P. coprophila.
(b) ΠΕΡΙ ΘΕ. P. rubidan. sp.
b. Cells of bulbil homogenous.
i. Bulbils brown 21-36 win diam... P.sporotrichoides τι. sp.
il. ‘‘ steel gray 21-36 » in diam... ..P. cinerea τι. sp.
2. Primordium not a spiral.

a. Bulbils large, 100-7504 in diam.....P. aspergilliformis.

|b). = ΘΟ ΞΘΡ π ἴπτα. cream colors eee eee P. candida.
B. Primordium two or more lateral branches forming a spherical aggre-
ration of:cells.at the tops can: <2. epee teen P. polyspora n. sp.

Heretofore fungi producing bulbils have been referred chiefly to the
form-genera Papulospora and Helicosporangium, but the characters
on which these two have been based are not clearly defined, and as
already stated, it does not seem desirable to recognize more than one
form-genus.. Since Papulospora was the name first employed to
represent bodies of this nature, all the fungi that the writer has ex-
amined that produce bulbils, the perfect form of which has not been
determined, are placed in this form-genus which may be described
as follows.

HOTSON.— CULTURE STUDIES OF FUNGI. 273

Papulospora.

Mycelium extensive or scanty, flocculent or procumbent, usually
white but sometimes dark colored. Reproduction by means of
bulbils, i. e., reproductive bodies of more or less definite form, com-
posed of a compact mass of homogeneous or heterogeneous cells
which may be few or many, but are always developed from primordia
of more than one cell. Other modes of reproduction may be present.

For convenience bulbils may be grouped under three heads: those
which form an intercalary primordium of several cells; those which
typically originate from a primary spiral; and those that are pro-
duced by a perpendicular branch or branches which do not form a
spiral.

As has already been pointed out the distinction between simple bul-
bils and compound spores on the one hand, and the more complex bul-
bils and sclerotia on the other, is not always definite, and in certain
instances it is difficult to determine to which category a given struc-
ture belongs. Compound spores are reproductive bodies of more than
one cell, having a more or less definite form, and are usually the result
of a successive or simultaneous division of a single cell. On the other
hand, sclerotia are compact bodies capable of reproducing the plant
and formed rather by the massing together of vegetative filaments,
forming a pseudoparenchymatous tissue, but not developed from a
group of more or less definitely related cells. Moreover, the individual
cells of a sclerotium are not at all spore-like or independent of each
other. Bulbils, are reproductive bodies, more or less definite in form
and mode of development, and normally derived from primordia of
more than one cell, rather than the result of successive or simultaneous
divisions of a single cell, and their individual cells are more or less
independent and spore-like.

Papulospora immersa n. sp.
PuaTE 10, Figures 17-25.

Mycelium white, septate, scanty, procumbent, growing in or on
the substratum; bulbils, light brownish-yellow, irregular, 88-150 μ
in diameter, but very variable, sometimes the long axis exceeding
260 μ, often immersed; central cells large 28-55 w in diameter,
angular, with conspicuous oil globules; 50-70 cells in surface view,
but in irregular forms 100 cells, no differentiation of internal and
external cells. No other mode of reproduction at present known.

274 PROCEEDINGS OF THE AMERICAN ACADEMY.

On horse and dog dung from Cambridge, Massachusetts, and rabbit
dung from Innerkip, Ontario.

Both the bulbils and the mycelium usually grow more or less below
the surface of the substratum. The former are often found immersed
more than a centimeter. It is easily distinguished from P. polyspora
by its mode of development and from P. pannosa by its color, the
latter being black. It resembles most nearly P. irregularis, from
which it may be distinguished by its darker color, the size and con-
spicuous contents of the cells of the bulbils and the fact that the
latter become more or less imbedded in the substratum.

The mycelium, since it is formed largely in the substratum, is in-
conspicuous in tube-cultures and is composed of large swollen hyaline
cells, densely filled with oil globules and often much contorted
(Figure 17, Plate 10). In older cultures the cells lose their contents.

This fungus was grown on different kinds of media, but could not
be induced to develop any other mode of reproduction. It grows
well on bran and horse dung agar, the bulbils often becoming very
large and numerous just below the surface of the substratum, forming
almost a continuous layer, and often producing a more or less hard
crust. In contrasts of mycelia in plate cultures, a marked heaping of
the hyphae occurs where the two mycelia come together, and the
bulbils seem to be somewhat larger, and more irregular in this region,
but no other marked difference was observed.

The bulbils— The primordium of the bulbil consists of one or more
intercalary cells which become much enlarged. For example, Figure
17, Plate 10, a later stage of which is seen in Figure 23, shows several
such cells, all of which would have taken part in the formation of a
somewhat elongated irregular bulbil, such as is shown in Figure 23.
On the other hand, Figure 18 represents a primordium which consists
of a single cell, and Figures 19-22 are further stages in its develop-
ment. In the latter case a more or less spherical bulbil is the result
(110-148 » in diameter), while in the former it is more irregular,
often exceeding 260 μ through the long axis. The method of enlarge-
ment, however, is exactly alike in both cases, that is, short lateral
branches are produced from the bases of which are cut off a series
of short cells which enlarge, becoming spherical at first and later, as
the bulbil increases in size and the cells are subjected to lateral pres-
sure, forming a compact angular mass in the center. Occasionally
the branches are replaced by cells which, arising as lateral buds,
become spherical and in turn give rise to other buds, the lateral
walls of which adhere closely and ultimately form a more or less

ore

HOTSON.— CULTURE STUDIES OF FUNGI. Sle

spherical or elongated bulbil with a fairly even margin, the central
cells of which soon become angular. In either case all the cells are
filled with conspicuous oil globules. At maturity there is no differ-
entiation of central and cortical cells, but all are uniformly filled with
food material, the central ones being larger, 28-35 μι in diameter,
“and more angular than those nearer the periphery.

Papulospora pannosa n. sp.
Puate 6, Figures 20-25; Piate 8, Figures 28-31; Pate 9,
Figures 18-20.

Mycelium white at first, becoming dark smoke-colored, 8-10 u
in diameter, somewhat shaggy; bulbils black, irregular, variable in
size and outline, sometimes 350 μι in diameter, but usually consider-
ably less; cells homogeneous throughout, 200-300 cells in surface
view; primordium, a group of intercalary or terminal cells. No coni-
dia observed.

On laboratory cultures of rabbit and goat dung, and on corn-cobs
from Claremont, California.

Pure cultures of this fungus from about fifteen different sources
were obtained and grown on various kinds of media and the mycelium
from the different sources contrasted with each other, but thus far it
has not developed any other mode of reproduction than the bulbils.
This species is easily distinguished from most of the others by the
color of its bulbils. The only other black form is that of Cubonia
bulbifera from which it differs in size and the character of its outline,
which is quite even and regular in the latter, as well by the fact that
the hyphae are black at maturity.

The bulbils—The mycelium which grows well on a variety of
media in tube-cultures, appears somewhat shaggy, is white at first,
gradually becoming dark smoke-colored, with prominent cross walls
which remain rigid when the cells collapse (Figure 31, Plate 8). The
hyphae which are 3-4 » in diameter when young and hyaline, gradually
increase in size until they are 8-10 μ in diameter, and have already
become dark in color at the time the black bulbils are produced.
During the formation of the latter, the hyphae become much dis-
torted, and divide into a series of short, somewhat inflated cells which
are separated by constriction at the septa (Figure 24, Plate 6), some-
what after the fashion of Cubonia bulbifera, but the successive cells of
these series are much more irregular and of greater diameter. These
enlarged cells send out lateral branches (Figure 18, Plate 9), from

276 PROCEEDINGS OF THE AMERICAN ACADEMY.

which are cut off short basal cells which assume a spherical form,
‘become swollen and may produce other branches similar to the primary
‘ones. This mode of development is illustrated by Figures 20-24,
Plate 6, and Figures 18-19, Plate 9. Instead of the enlarged cells
producing branches, however, other cells may arise laterally from
them by gemmation, become spherical, and may in turn give rise
to others in a similar fashion. In either case the lateral walls of
adjacent cells eventually adhere firmly, thus forming a compact
group, each cell of which is almost spherical at first, but later be-
comes irregular. The further multiplication of the peripheral cells
is subject to considerable variations. Not infrequently the primary
or secondary branches, owing to local variation, grow much faster
than others and thus produce more cells in that region of the bulbil.
If there are several of these points of special activity, the mature bul-
bils may be quite irregular in outline. Occasionally a bulbil is formed
from a single lateral branch (Figures 28-30, Plate 8), new cells being
formed by a process of budding or by short branches as in the other
cases. Ordinarily, at maturity, they are more or less spherical or
somewhat elongated, their margins roughened by projecting cells
(Figure 20, Plate 9) and are very variable in size, sometimes as large
as 350 in diameter. There is no differentiation between the inter-
nal and external cells as far as contents are concerned. The central
cells are, however, as a rule, larger and more angular.

Papulospora irregularis n. sp.
Pirate 9, Figures 11-17.

Mycelium white, more or less procumbent; bulbils hyaline, be-
coming light straw-color, somewhat spherical (140-170 μ᾽ in diam.)
to irregular in outline (250-300 uw in diam.), margin very uneven;
primordium a group of intercalary cells.

On rat dung, Kittery Point, Maine.

A pure culture of this species was comparatively easy to obtain.
In the hyphae, which are hyaline, procumbent and inconspicuous,
certain intercalary cells become enlarged and, by a process of budding,
these give rise to other cells which in turn may produce still others.
Sometimes short lateral branches are produced, the basal cells of
which enlarge and take part in the formation of the bulbil (Figure 15,
Plate 9). The young bulbils are colorless, covering the substratum,
but in older cultures they turn light straw-color. They are usually
somewhat spherical in form, measuring 140-170 » in diameter, but

HOTSON.— CULTURE STUDIES OF FUNGI. 277

frequently run into irregular sclerotium-like bodies, 250-300 w in
diameter. In old cultures the hyphae often form a felted mass over
the substratum. This mode of development is similar to that of P.
pannosa, from which, however, it is easily distinguished by the color
of the mycelium and bulbils, those of the latter species being black.
It also resembles P. immersa, but it is lighter in color and does not
have such large cells with conspicuous oil globules and the bulbils
are not immersed in the substratum. Figures 11-17, Plate 9, illus-
trate the mode of development of this bulbil.

Papulospora spinulosa, n. sp.
PLATE 9, Figures 1-10.

Mycelium white, scanty, septate, procumbent, becoming slightly
brownish when old, 3.5 uw in diameter, the old hyphae somewhat
larger; bulbils hyaline until well developed, at maturity light choco-
late-brown, somewhat spherical, 55-88 » in diameter, 50-60 cells in
surface view; primordium a coiled lateral branch which remains
prominent throughout the development, becoming empty and show-
ing slight thickenings in the walls. No other means of reproduction
known.

On rat dung, Kittery Point, Maine.

This fungus was found on a gross culture of rat dung obtained from
Kittery Point, Maine, and has been grown for about three years on
various media without producing any reproductive body other than
bulbils. The mycelium is white and grows quite -sparingly on most
media. It has been found that bran agar or rat dung agar is the
best nutriment on which this species will grow.

The bulbils.— During their early stages of development the bulbils
are hyaline until they are about half grown, at which time they begin
to turn a light brown and at maturity assume a chocolate-brown
color, often covering the whole substratum with several layers, so
that all appearance of hyphae is lost sight of, except around the
margin where a white zone about 5 mm. in width indicates the
actively growing region of the mycelium and the formation of new
bulbils. In the process of development a short lateral branch coils
up, usually crosier fashion (Figures 1-4, Plate 9), although ocecasion-
ally the tip somewhat overlaps, as shown in Figure 3, Plate 9. The
primary loop varies greatly in size, as may be seen from a compari-
son of Figure 1 with the other figures representing the development,
all of which are drawn on the same scale, but even these large open

278 PROCEEDINGS OF THE AMERICAN ACADEMY.

primordia form eventually quite close coils. The helix which consists
of one to one and one-half turns, divides into cells from which short
lateral branches are produced, usually growing towards the center,
rarely outward (Figures 5-7, Plate 9). These branches twine and
intertwine, the lateral walls adhering firmly so that eventually a
somewhat spherical body is formed which superficially resembles the
sporangium of afern. The cells of the original spiral are more promi-
nent than the others, usually slightly elevated with well marked walls,
and correspond to the annulus, as will be seen from Figures 9-10,
Plate 9. Figure 10 is a view of an immature bulbil, looking down
on the “annulus,” while Figure 9 is a side view of the same. At
maturity the bulbil, which is nearly spherical, is 55-88 yp in diameter.
The cells of the primary coil usually become empty and lighter
colored, showing slight thickenings scattered over their surface, oc-
casionally projecting slightly, thus giving the’ appearance of minute
spines.

Sometimes a lateral hypha divides dichotomously and each branch
coils up and produces a bulbil. Similar branches may be produced
directly from the superficial cells of a bulbil (Figure 8, Plate 9). The
mode of development in this form resembles that of certain species of
Urocystis, such as U. cepulae, the common onion smut, in which a
lateral branch coils up, making about one turn, and this divides
into cells from which secondary branches are given off. Figures 4,
5, 6 and even 7, Plate 9, might almost equally well illustrate the
development of Urocystis cepulae.

Papulospora coprophila, nov. comb.
Helicosporangium coprophilum Zukal (’96).

PLATE 10, Figures 1-16.

Mycelium white, septate, flocculent, abundant, persistent; bulbils,
dark brown, more or less spherical, 30-40 uw (rarely 60 μ) in diameter,
with one to four (sometimes as many as 10) large central cells sur-
rounded by a cortex of empty colorless or slightly brownish ones;
primordium spiral, of one to four turns, the end cell usually becoming
a central cell. Conidia on bottle shaped sterigmata, frequently in
white tufts scattered over the surface of the substratum.

On onions, straw, horse dung, ete., Cambridge, Massachusetts,
and California.

Onions have proved very productive as a substratum for bulbils.
Some onions obtained from the Boston market which had been shipped

a

HOTSON.— CULTURE STUDIES OF FUNGI. 279

from New York State, produced several different kinds and among
them P. coprophila which has been secured from at least ten differ-
ent sources, not only on onions, but frequently on horse dung and
straw. It grows readily on potato and bran agar, but, like many of
the other species, after continued artificial cultivation the mycelium
becomes scanty and the bulbils few. In such cases it can be re-
juvenated by growing on a gross culture of sterilized fresh horse dung,
on which the mycelium is developed luxuriantly and becomes floccu-
lent, producing bulbils and conidia abundantly.

This species appears to be the same as that described by Zukal (’86)
under the name of Helicosporangium coprophilum which he found
growing on horse dung. The general appearance of the bulbils of
these two forms, their size, color, and at least one phase of their
development seem to be identical. The form under consideration,
however, differs from the description given by Zukal in producing a
copious supply of flocculent hyphae. This may be due to the differ-
ences in the conditions of cultivation. P. coprophila resembles in
mode of development the species referred by Eidam to Helicosporan-
gium parasiticum Karsten, but the bulbils of the latter are brick-red,
with yellowish cortical cells which, judging from the figures, are much
less prominent than in the present form. The only other close allies
are P. parasitica and P. spinulosa, the former easily distinguished by
its single large central cell, the latter by its mode of development,
and the presence of slight thickenings in the walls of the cortical cells.

This form develops sparingly on very moist substrata. On nutrient
potato agar containing sugar, however, or on fresh horse dung, it
grows well. Contrast cultures of mycelia from different sources
yielded nothing more than additional variations in the filaments and
bulbils. The former grew much more luxuriantly at the points of
contact of the two sets of mycelia.

The bulbils— A short lateral branch coils up, making about one or
one and a half turns, the end cell enlarges, becomes spherical and
frequently turns brownish. As it continues to increase in size its
two lateral faces protrude more or less conspicuously and may even
become subpendent, as in P. parasitica (Figure 4, Plate 5). These
projections, however, often behave differently from those of the
latter, since they are frequently cut off and thus form other enlarged
central cells. Sometimes the second or even the third cell of the coil
enlarges and takes part in the formation of the central cells. Those
that do not enlarge grow out laterally over the surface of the central
cell or cells and eventually completely enclose them. Figures 13-15,

280 PROCEEDINGS OF THE AMERICAN ACADEMY.

Plate 10, show what appear to be arrested forms of this mode of
development, all of which have brownish walls. These conditions
resemble somewhat the mode of development figured by Zukal (’86).

About three or four days after inoculation on fresh nutrient agar
which contains sugar, there frequently appears a spiral primordium
of three or four turns, as shown in Figures 1-6, Plate 10, which
divides into cells from which short secondary branches are produced,
or other cells are formed by gemmation, so that eventually the spiral
is enclosed by them. The cells of the spiral enlarge and usually lose
their characteristic form. The lateral walls of the superficial cells
adhere firmly together, so that eventually there comes to be one to
four (sometimes as many as ten) large central cells, surrounded by a
cortical layer of empty and often colorless cells (Figures 10-11, Plate
10). The development of the spiral may be checked at nearly any
stage of its formation and thus certain variations in the form and
number of the central cells of the bulbil may result. This variability
in the formation of the spiral seems to be largely due to the character
of the medium which, when favorable, usually produces quite regular
primordia with the maximum number of coils, while under less favora-
ble conditions, or after the substratum has been once run over with the
hyphae, many variations are found. Some of the spirals are loosely
coiled (Figures 1-2, Plate 10), while others are close and compact
(Figures 4, 6, Plate 10). Although the primordium usually loses its
spiral form early in its development, it is occasionally found surrounded
by an irregular layer of cells, as shown in Figure 8, Plate 10. These
bulbils resemble somewhat the primordium of a perithecium, like
that of Melanospora as shown in Figures 5-6, Plate 3. On account
of this resemblance an effort was made to induce them to develop into
some perfect form, but although many and varied kinds of experi-
mentation as to media, moisture and temperature, were tried, all
efforts proved unsuccessful.

There are also associated with this bulbil spherical or slightly ovoid
conidia, on bottle shaped sterigmata, identical with those found in
connection with the melanosporous forms. These conidia, which
frequently appear on conspicuous white tufts of hyphae scattered
over the surface of the substratum, may be formed individually, in
chains, or occasionally in a moist atmosphere may cohere at the ends
of the sterigmata in a spherical mass. Although, as a rule, the
sterigmata occur laterally on the walls of the hyphae, they are often
found clustered on irregularly swollen branches and exhibit all the
variations referred to below in connection with P. aspergilliformis,

HOTSON.— CULTURE STUDIES OF FUNGI. 281

although the characteristic ‘“ Aspergillus-like” fructification illus-
trated in connection with.the latter has never been observed. These
conidia were picked out with Barber’s apparatus and transferred to
nutrient tubes where they germinated and produced mycelium on
which bulbils developed. In this respect they differed from those of
P. aspergilliformis, which, although repeated efforts were made,
could not be induced to germinate.

When these bulbils are crushed the contents of the large central
cells escape, surrounded by a thick endosporium (Figure 11, Plate 10).
These cells germinate readily in Van Tieghem cells (Figure 12, Plate
10).

Papulospora rubida n. sp.
PuaTE 8, Figures 12-27.

Mycelium white, procumbent or slightly aerial on some media;
bulbils more or less spherical, 30-40 yw in diameter, with 2-5 large
central cells surrounded by a layer of empty cells which usually
retain their yellowish red color, at maturity the whole culture has a
brick-red aspect; primordium a spiral, with many modifications;
conidia on bottle-shaped sterigmata, but not formed in white tufts.

On dog dung from Buenos Ayres.

This species was obtained from a pure culture received from Dr.
Thaxter, which he has had growing for a number of years. It was
originally found on dog dung from Buenos Ayres. In general it
resembles P. coprophila in size, form, and mode of development.
It is easily distinguished, however, bythe appearance of the culture.
The mycelium is more or less procumbent and the bulbils give the
whole substratum a brick-red aspect, in old cultures forming a leathery
incrustation which often cracks as the medium dries up. The my-
celium of P. coprophila, on the other hand, is flocculent, filling the
whole lower part of the test-tubes in slant cultures, and the bulbils
give the culture a dark brown appearance. The cortical layer is
colorless and more definitely marked in the latter species.

The hyphae of the form under consideration vary from 3-14 μ in
diameter and, especially in old cultures, have well marked cross walls.
Large swollen intercalary cells (Figure 24, Plate 8), are often formed,
which seem to act as storage cells, as they are densely filled with
granular, protoplasmic material and oil globules.

The bulbils— A short lateral branch coils up Gili usually mak-
ing one to one and a half turns (Figures 12-15, 21, 22, 27, 25a, Plate
8) and divides up into cells all of which become more or less swollen.

282 PROCEEDINGS OF THE AMERICAN ACADEMY.

One or more of these cells, as a rule the first or second or both of them,
increase in size beyond the rest, becoming densely filled with granular
material and oil globules, while the other cells grow out laterally
(Figure 16, Plate 8) and eventually enclose the enlarged cells in a
manner similar to that of P. coprophila and P. parasitica. It some-
times happens that when the end cell enlarges, protuberances are pro-
duced from the lateral sides, which may even become subpendent, as in
P. parasitica (Figure 26, Plate 8). The development of the cortical
cells is shown in Figures 16, 21, 22 and 27, while Figure 25 is a median
section and Figure 18 a surface view of the mature bulbil. Thus at
maturity the bulbil is more or less spherical, 30-40 w in diameter
with 1-5 (usually 2 or 3) large central cells each of which varies from
10-14 w in diameter (Figures 16, 25, Plate 8), surrounded by a cortex
consisting of a single layer of empty cells, rarely more, which is often
incomplete. The walls of the cells of this cortical layer usually retain
their color.

Occasionally the short lateral branch instead of making but one or
one and a half turns continues the spiral until from three to five turns
are formed (Figures 17, 20, Plate 8). From the cells of the spiral are
produced others laterally by budding, which eventually adhere to
each other laterally, thus forming a wall about the spiral. This is
similar to the process observed in connection with P. coprophila.

This species also produces conidia on bottle-shaped sterigmata
similar to those described in P. coprophila, but they do not, as far as
the writer has observed, occur in white tufts scattered over the sub-
stratum as they do in the last named species.

Papulospora sporotrichoides n. sp.
PLaTE 12, Figures 1-41.

Mycelium white, procumbent, usually scanty; bulbils dark choco-
late colored, somewhat spherical or flattened, 21-36 u in diameter,
primordium a spiral of one to two turns, with conspicuous oil globules,
the spiral sometimes not well marked. Conidia and conidiophores
of the Sporotrichum type.

On Live Oak chips (Quercus agrifolia) and corn cobs from Clare-
mont, California, and Maple chips from Newton, Massachusetts.

The bulbils—In the development of the bulbil a short lateral or
terminal branch coils up, divides into a number of short cells with
walls well distinguished, forming a close spiral of two or, rarely, three
turns. This process is illustrated by Figures 1-9, Plate 12. During

Ee ee

were ee Oe

HOTSON.— CULTURE STUDIES OF FUNGI. 283

the very early stages of development, the primordia are colorless,
somewhat larger than the ordinary hyphal threads with more granular
material. The walls, however, begin to turn brown shortly after
division takes place. In Figure 5, for example, the walls are dis-
tinctly colored. In the mature bulbil the spiral form can sometimes
be recognized (Figure 8, Plate 12), but more frequently, owing to the
unequal enlargement of the cells composing the coils, or some modi-
fication in the development which will be spoken of later, all trace of
it is lost.

The development of these bulbils was carefully followed in pure
Van Tieghem cell cultures, and many interesting modifications were
observed. Quite frequently, as illustrated in Figures 12-14, Plate 12,
before the spiral has completed one turn or the walls of the individual
cells thickened, one of the cells, usually the third or fourth from the
tip, grows out into a vertical branch and coiling divides into cells
similar to the first. The second coil may repeat this same process,
so that two or three or even four coils like that which is shown in
Figure 14, Plate 12, are formed one above the other, each producing
a separate bulbil. These usually continue their development inde-
pendently of each other, but not infrequently the primordia overlap
and a single “compound” bulbil of two or three spirals, as the case
may be, is the result. Occasionally this secondary branch is_pro-
duced on the opposite side of the cell so that it grows into the concave
portion of the first coil as shown in Figure 15, Plate 12. In some in-
stances a single coil only may be formed, the cells of which enlarge as
usual (Figures 19-25, Plate 12) becoming divided during the process,
by thin cross partitions which are at first hardly visible without stain-
ing. The multicellular bulbil thus produced, does not become dark at
once like the normal type but remains hyaline for some time, slowly
changing color and only after it has become fully mature does it
assume the dark brown tint of the more common type from which,
however, it is eventually indistinguishable.

The Conidia——A conidial form of reproduction, which usually
appears on old cultures after a large number of bulbils have been
produced, is also connected with this fungus. These conidia are of
the Sporotrichum type and were obtained from pure cultures by the
transfer of individual bulbils. It seemed desirable, however, to
obtain the bulbil-type from germinating conidia in order to eliminate
all chance of error; but this was found unexpectedly difficult for the
reason that single spores isolated by Barber’s apparatus refused to
germinate although cultivated in varied media. The conidial form

284 PROCEEDINGS OF THE AMERICAN ACADEMY.

is as a rule scantily developed in older cultures only, but by using a
special nutrient composed of a decoction of bran, Spanish chestnuts,.
horse dung and rotten wood hardened with agar, an abundant pro-
duction of conidia was obtained after two months, the conidiophores
(Figures 35-36, Plate 12) rising well above the substratum at the mar-
gin of the culture, so that large quantities of spores were readily
obtained in an absolutely pure condition. Cultures of these yielded
about two per cent of germinations after twenty days.

The development of these germinating conidia (Figures 38-41,
Plate 12) was continuously followed in Van Tieghem cells until
bulbils were produced on the mycelium derived from them.

The conidiophores (Figures 35-36, Plate 12) which are colorless at
first but become light grayish brown at maturity, are larger (3.54 μ
in diameter) than the other hyphae from which they arise, with quite
irregular walls producing numerous lateral conidia which rest either
upon short stalks or upon little projections of the wall of the conidio-
phore, or are completely sessile. The conidia, which are also colorless
at first, but become the same color as the conidiophore, are ovoid,
4X 7 u, with smooth, fairly thick walls. During germination, they
swell so as to be almost spherical in shape (Figures 39-41, Plate 12).

Papulospora cinerea n. sp.
PLATE 8, Figures 1-11.

Mycelium white, septate, procumbent, forming a felted mass over
the substratum; bulbils steel-gray or slate-colored, somewhat spheri-
cal and flattened, 21-36 μ in diameter, with three or four large angu-
lar central cells, and a layer of fairly regular cells forming a cortex,
but of the same color as the others; the primordium a spiral of one
or two coils. No conidia known.

On gross culture in the laboratory, Cambridge, Mass.

This fungus was found running over a gross culture in the Crypto-
gamic Laboratories at Harvard University by Dr. Thaxter and has
been kept growing as a pure culture for more than ten years. It is
easily distinguished from any of the others by the steel gray or slate-
color of the bulbils, which are round, somewhat flattened in form, and
measure 21-36 μ in diameter, in which respects they resemble those
of Papulospora sporotrichoides. The mycelium is white, procumbent,
forming a felted mass over the substratum, the slate-colored bulbils
being scattered among the white hyphal filaments, finally giving the
whole culture a bluish gray or steel-gray appearance. When young

HOSTON.— CULTURE STUDIES OF FUNGI. 285

the hyphae are closely packed with oil globules which escape into the
water when the filament is ruptured, and might be mistaken for spores.

The bulbils— A short lateral branch coils up, usually making one
or two turns, rarely more, and frequently less than two, and divides
into a number of short cells from which secondary branches are pro-
duced, or from which individual cells are formed by budding (Figures
7-8, Plate 8). In either case, spherical cells which gradually increase
in size, are developed, and the lateral walls adhere closely to each
other. The original coil, the cells of which in the meantime have
become much enlarged and filled with granular material and oil
globules, is thus eventually completely surrounded. At maturity
three or four large central cells may be distinguished which have
become angular by pressure, surrounded by a layer of fairly regular
cells which are also usually somewhat angular except the outer walls.
It often happens that when one turn is made by the primordial coil,
the secondary branches begin to form, while at other times two or
more turns are formed before this happens. Between these two.
extremes a number of variations are found. Not infrequently the
lateral branch becomes divided into four to eight cells and may or
may not be coiled at the end, and from these, secondary branches
are produced which coil around each other and around the original
branch, dividing and subdividing, the lateral edges eventually adher-
ing closely, and producing a more or less elongated bulbil (Figures
4—6, Plate 8). This process also inhibits the further growth of the
coil. An extreme instance of this is shown in Figure 6, Plate 8,
where several cells are seen to take part in the formation of lateral
branches. Bulbils formed from a primordium of this type are elon-
gated, irregular, and larger than those formed in the usual way.

Although this species was grown on a great variety of nutrient
media, it could not be induced to develop any perfect form or even
another imperfect type.

Papulospora parasitica nov. comb.
Syn.: Helicosporangium parasiticum Karsten. (nec Eidam.)
ῬΙΑΤΕ 5, Fiagures 1-17.

Mycelium septate, white, flocculent; bulbils light brown, nearly
spherical, 15-21 μι in diameter, with a single large central cell sur-
rounded by a single layer of empty colorless cells; primordium a
spiral, coiled crosier-fashion.

286 PROCEEDINGS OF THE AMERICAN ACADEMY.

On bread, Cambridge, Massachusetts; mouse dung, Duarte, Cali-
fornia.

This form which appears to be identical with Helicosporangium
parasiticum Karst. was found by Dr. Thaxter on bread in Cambridge,
Massachusetts, and kept as an herbarium specimen, but was too old to
be resuscitated. The writer also found it on a gross culture of mouse
dung in an old paper bag obtained from Duarte, California. This
culture was so overgrown with Penicillium and other foreign material
which grew so much more rapidly than the bulbiferous fungus that it
was difficult to get it pure. This was finally accomplished by using a
gross culture of sterilized peas on which the mycelium of the bulbil
grows quite rapidly.

The bulbils— The development of the bulbils, which are produced
in large numbers, agrees in all essential points with the original de-
scription and figures of Karsten (65). Short lateral branches of the
hyphae coil up crosier-fashion and, although quite open at first, soon
close up, forming a close coil which divides into short cells, all of which
increase in size to a certain degree. One of these, usually the end cell,
but not infrequently the second, enlarges more rapidly than the
others and becomes a “central cell,” the remaining members of the
coil forming a ring or “annulus” around it and becoming firmly at-
tached to the side of the original lateral branch. As this central cell
increases in size more rapidly than those of the coil, considerable
lateral pressure is exerted and consequently protuberances usually
appear on each side of it which usually becomes subpendent and
subsequently may divide into two or three lobes (Figures 4, 5, 9, 10,
Plate 5). As this tension is released, probably through the inerease
in size of the “annulus,” the large central cell loses its lobed appear-
ance and assumes a spherical form (Figure 11, Plate 5) and may later
become somewhat angular.

In the meantime the cells composing the
out laterally, extending over the surface of the large central cell, and
in the mature bulbil completely corticating it, the walls adjacent
adhering laterally. Sometimes there is a small pore left at one or
both of the centers of the lateral faces of the central cell and through
them at germination the germ tube grows, but this is the exception and
is probably one of the incomplete stages of development that will be
spoken of later.

During the early stages of development and even until they have
almost reached their full development these bulbils are cclorless, but
eventually they become light brown. At maturity they are nearly

‘

‘annulus”’ begin to grow

HOTSON.— CULTURE STUDIES OF FUNGI. 287

spherical in form, consisting usually of a single large central cell about
10-14 μ in diameter, densely filled with granular material and oil
globules, and surrounded by a single layer of empty colorless cells,
the whole bulbil measuring 15-21 μ in diameter. Although the
foregoing description of the mode of development of the bulbil is
the characteristic one, the process may vary considerably in differ-
ent cases. Occasionally there appears a tendency to form a helix, at
other times a protuberance from the central cell develops only on one
side or not at all, and quite frequently the “annulus” is incomplete,
or the cortical cells that are derived from it fail to cover the whole
central cell. It would thus appear that the development of the
bulbil may be arrested at nearly any stage, and these arrested forms,
under proper conditions, will germinate almost immediately.

In Van Tieghem cells these bulbils germinate in 24-36 hours and
send out one or two germ tubes, as shown in Figures 15-16, Plate 5,
which arise from the central cell only. The germ tubes usually
proceed from that region where the marginal cells meet or, as some-
times happens fail to meet, leaving two small pores, as already men-
tioned. In incompletely developed bulbils, the germ tube seems to
come out from any point offering the least resistance.

Conidia-like bodies were occasionally found connected with this
fungus when grown on straw. A short lateral branch, which not
infrequently becomes septate (Figure 17b, Plate 5), enlarges at the
end and from it an ovoid cell (4.5 XK 6.5 μ) is abjointed. Unfortu-
nately these were produced so rarely that their germination and
further development could not be observed. Figure 17, Plate 5,
however, shows a direct connection between these “conidia’’ and a
bulbil.

This form agrees in all respects with the original description and
figures of Helicosporangium parasiticum (Karsten ’65) except that it
is saprophytic and that no “endospores” are found in the central cell.
As already stated, Karsten was of the opinion that the contents of the
cortical cells passed into the central cell, either directly or by diffusion
and as a result of the union of these different protoplasmic bodies the
spores were formed. If the account given by Karsten is correct, in
all its details he was not dealing with a bulbiferous form at all. It
would seem, however, that later writers are probably correct in
considering them as such, since Karsten may have been misled by the
presence of more or less regular oil globules, such as occur in this and
other species and which might easily have been mistaken for endo-
spores. On the other hand, it is by no means impossible that he was

288 PROCEEDINGS OF THE AMERICAN ACADEMY.

dealing with a form related to Monascus, which has not been recog-
nized by subsequent investigators. Since, however, the morphology
and development of his “Helicosporangium”’ corresponds so exactly
with that of the bulbil under consideration and since also the “ para-
sitism”’ of his plant on “beets,” seems at least very questionable,
the writer feels little hesitation in concluding that he was dealing with
a bulbil, in all probability identical with the one under consideration.

Harz (’90), in his account of Physomyces heterosporus (Monascus
heterosporus (Harz) Schréter), is of the opinion that this plant is
closely related to Helicosporangium parasiticum Karsten, and further
suggests that Papulospora sepedonioides Preuss, belongs near this
fungus also, the difference consisting in the fact that the central cell
of the latter is said to contain but one or only a few “ endospores.”’

The bulbils described and figured by Zukal (86), under the name of
Dendryphium bulbiferum, also resemble this form in appearance and
mode of development, except that it does not produce the lateral
protuberances from the developing central cell, at least they are not
mentioned or figured, and that it is described and illustrated as being
intimately connected with hyphae producing spores of the genus
Dendryphium.

In this connection it may also be mentioned that the spores of
Stephanoma strigosum Wallr. (Asterophora pezizae Corda, Syntheto-
spora electa Morgan, Asterothecitum strigosum Wallr.) show stages
that resemble quite closely certain. conditions in the development
of P. parasitica. Figure 35, Plate 5, for example, is an abnormal
spore of Stephanoma and, except for its size and color, might easily
be taken for an imperfectly developed bulbil of the form under con-
sideration, such as is represented by Figure 14, Plate 5.

A corresponding resemblance may also be seen between imperfectly
developed bulbils of the present species, in which the cortical cells
have failed to surround the central cell completely, and the immature
bulbils of Acrospeira mirabilis described above.

PAPULOSPORA ASPERGILLIFORMIS Eidam.
PLATE 7, Figures 1-20.

This bulbil was obtained from several different sources, chiefly on
onion leaves, wheat chaff, and oat straw from the vicinity of Cambridge,
also on straw from Claremont, California. It is not at all rare and
can easily be obtained by placing straw in a moist chamber. It is
readily distinguished by its relatively large, irregular, sclerotium-like

HOTSON.— CULTURE STUDIES OF FUNGI. 289

bulbils. Pure cultures from a half-dozen different sources were made
by the methods already described, and kept under cultivation on a
variety of media.

The septate mycelium grows very slowly on nearly all substrata,
producing the best results on bran agar, and on sterilized fresh horse
dung on which it becomes somewhat flocculent. The primary
mycelium grows on the top of the substratum, or just below the surface,
and sends up lateral branches into the air. It is these lateral branches
that produce its peculiar Aspergillus-like fructification. The primary
mycelium becomes very large, usually somewhat contorted and packed
full of granular material and oil globules. The hyphae, which an-
astomose readily often forming a sort of network, measure as much
as 11 μ in diameter, and some of the swollen lateral branches 17 μ
(Figure 4, Plate 7). Occasionally, especially in the young hyphae,
there occur large swollen intercalary cells containing oil globules and
other food material (Figures 17-18, Plate 7). These seem to be cells
for the storage of food.

The bulbils—The mycelium grows out evenly in all directions from
the point of inoculation. In about two or three weeks (on horse
dung, in about a week), small brownish-red spots appear near the
margin of the mycelial growth. These are young bulbils, and on
closer examination they are found to develop as follows. A short
lateral branch (Figures 2-3, Plate 7) well filled with nutrient material,
sends out branches which twine about each other. The former
sometimes coils at the tip but this seems to be incidental. These
secondary branches may come off near the base of the lateral branch
(Figure 3, Plate 7), and by twining about the primary hypha may
incorporate it into the bulbil. More often, however, the secondary
branches come off a short distance from the hypha (Figures 2, 4, 6,
Plate 7), so that, especially in the early stages, it is evident that they
are on short pedicels. The secondary branches intertwine with each
other, and divide up into short cells, their lateral walls adhering
firmly to those of their neighbors and eventually forming a compact
mass of uniform cells. At maturity these bodies superficially resemble
true sclerotia perhaps more nearly than they do typical bulbils, but
they are developed from a group of cells composing the primordia,
and not from a mass of interwoven hyphae from different sources.
They vary considerably in size and shape, some of them being nearly
spherical, about 100 in diameter; but most of them are irregular
in form, reaching in old cultures 570 X 750 4. There is no differentia-
tion between the marginal cells and the central cells. Microtome

290 PROCEEDINGS OF THE AMERICAN ACADEMY.

sections show that the bulbil is uniform throughout (Figure 20, Plate
7) all the cells containing protoplasm, and under favorable conditions
capable of sending out germ tubes. In this respect it differs from the
typical sclerotium, which usually has a compact layer of several cells
in thickness (the rind) which forms the margin. The primordia are
colorless at first (Figures 2-4, Plate 7), then light-yellow, later ruby-
red, and finally reddish brown and opaque.

In this as in most other bulbils the process of development may
vary greatly. Figure 1, Plate 7, shows the primordia of three bul-
bils, two of which and possibly the third also, would probably have
grown together, forming a large, irregular, sclerotium-like body.
This phenomenon occurs quite frequently, giving rise to a variety of
forms, which vary with the number of the initial primordia taking
part in their development, their proximity, and the inequality of
their development. In such cases each primordium develops in-
dependently, until its lateral branches intertwine with those of one
or more that lie adjacent to it, a compound bulbil finally resulting,
in which the several origins are indistinguishable.

Aspergillus-like fructification. Conidia are frequently produced
both on Aspergillus-like heads and also laterally, on the sides of the
hyphae (Figures 10-11, Plate 7). The latter are usually isolated,
sometimes irregularly grouped. The conidiophores arise from erect
lateral branches, and are frequently septate; rarely branched. They
are very minute, so that one can detect them only with difficulty,
even with a good hand lens. The length of the conidiophore varies
greatly, some being quite short, others so long that it is difficult to
trace them to their origin. The swollen head of the conidiophore is
usually spherical, or nearly so, and on it are arranged somewhat
irregularly numerous simple sterigmata. These vary slightly in size
and shape, but always have a broad base and taper more or less
gradually, often to a point, at the distal end. The relative length of
the vertical and transverse diameters of the swollen base varies some-
what, so that one may find gradations in shape from almost spheri-
cal to napiform. The conidia are nearly spherical, sometimes ovoid,
smooth, colorless, minute, occurring in chains, and dropping off very
readily; but in moist atmosphere the conidia, instead of being pro-
duced in a chain, frequently adhere and form clusters much like those
of Hyalopus.

There are many variations in the arrangement of these conidia,
which may, for example, arise, as is shown in Figure 9, Plate 7, termi-
nally and laterally on irregularly clavate extremities of hyphae.

HOTSON.— CULTURE STUDIES OF FUNGI. 291

Occasionally a conidiophore may form an intercalary swelling with
conidia on it, as if it were a secondary head (Figure 10, Plate 7).

Chlamydospore-like bodies occur quite frequently. They are
mostly intercalary but sometimes terminal (Figures 13-16, Plate 7).
When young they are colorless, or opalescent, slightly swollen, ovoid
cells, filled with granular material. At maturity they are usually
more spherical and have thick brown walls (Figures 13, 15, Plate 7).
Occasionally more than one cell takes part in the formation of these
spore-like bodies. Figure 16, Plate 7, shows two such cells and
Figure 5, Plate 7, a large number of “ chlamydospores”’ closely packed
together.

There are several forms that have Aspergillus-like fructifications,
similar to those just described and which may be considered briefly
at this point. As has already been noted, Eidam (’83) describes
these structures in his account of Papulospora aspergilliformis, and
also chlamydospores resembling those of Acremoniella atra Sace.
(Acremonium atrum Corda.) such as are produced by Melanospora
cervicula. Eidam, however, described two types of bulbils in P.
aspergilliformis, a small one that develops in a manner similar to
the form examined by the writer, and a large one, the primordium of
which is spiral, resembling that described by Bainier (07). Τ is quite
possible that Eidam has here confused the primordia of two species
the larger of which corresponds in all essentials to that studied by the
writer. On the other hand his smaller bulbil would correspond more
closely with that studied by Bainier.

Bainier (07), in his article on Papulospora aspergilliformis also
refers to its “Aspergillus-like” conidial fructification. According
to his account the primordium of the bulbil consists of a short lateral
branch which coils up spirally and eventually produces a more or less
spherical bulbil. Under certain conditions of nutrition and moisture,
however, the latter are said to produce large sclerotium-like bodies,
which in turn may be induced to develop further and form perithecia,
which are referred to the genus Ceratostoma. This form described
by Bainier seems to be different from the one under consideration,
since the bulbils of the latter do not develop by means of a spiral
and are large and sclerotium-like. The present form, moreover, has
been grown for nearly three years and during that time it has never
been observed to produce any other type of bulbil than the one de-
scribed. It has, however, produced in abundance conidia on Asper-
gillus-like conidiophores which sometimes occur in direct connection
with the bulbil (Figure 8, Plate 7). This species has been compared

292 PROCEEDINGS OF THE AMERICAN ACADEMY.

with material received from Professor Bainier by Dr. Thaxter, and
the two forms have been grown on many and varied kinds of nutrient
material for nearly three years during which time, as already men-
tioned, the American material has never been observed to produce
small spherical bulbils; nor has the form received from Bainier
developed the large sclerotium-like bodies which he describes, al-
though every effort has been made to obtain them.

There is also a marked difference in the method of growth in these
two forms. The mycelium of the American form grows very slowly
on bran or corn agar, but fairly rapidly on horse dung, while Bainier’s
species grows rapidly on a variety of media. There is also a marked
difference in the general appearance of the two while growing in
cultures; the mycelium of the former being quite inconspicuous at
first and often two or three weeks elapse before bulbils are produced.
The two forms thus appear to be very probably distinct and there
seems little doubt but that Bainier was mistaken in referring his
species to P. aspergilliformis. Neither of these forms has associated
with it Acremoniella-like Chlamydospores, such as Eidam describes
and it seems not improbable that Bainier is right in believing that
these spores do not belong to P. aspergilliformis, but are those of
“Acremonium atrum” which although frequently associated with it
are not a part of its life cycle.

The writer has under cultivation about a dozen pure cultures of
Acremoniella atra obtained from different sources, some of which were
closely associated with bulbils, and these have been grown for nearly
three years under varying conditions of temperature, moisture, and
nutrient material, the different mycelia having been contrasted on
plate-cultures under various conditions. In no instance, however,
have bulbils or Aspergillus-like conidiophores been produced.

Harz (11) has described a form under the name of Monosporium
acremonioides that produces chlamydospores and _ conidiophores
similar to those of P. aspergilliformis Eidam, but not associated with
bulbils, and states that the conidia were produced on secondary
heads either sessile or short-stalked, like those of Melanospora cer-
vicula. This latter character has been used by Costantin (88) as the
basis of a new genus, Harzia, into which he puts the foregoing species
under the name of Harzia acremonioides. Later, in referring to
Papulospora aspergilliformis Harz (’90) calls attention to the striking
resemblance between the two spore-forms of this fungus and those of
Monosporium acremonioides Harz, and suggests that, if they are the
same, the name should at least be Papulospora acremonioides, although

i iat ti

7. δὰ

HOTSON.— CULTURE STUDIES OF FUNGI. 293

he takes exception to the generic name on the ground, as will be seen
later, that it does not correspond with the description of the genus by
Preuss.

Lindau (’07) apparently is of the opinion that these two forms are
the same and he creates a new genus, Eidamia, for their reception
under the name EF. acremonioides (Harz).

The conidial form of Melanospora cervicula resembles quite closely
Harzia acremonioides in having its conidia on secondary heads and in
producing Acremoniella-like chlamydospores, but:differs in possessing
bulbils and melanosporous perithecia. It is quite possible, however,
that the two are identical. It is possible also that the so-called
“Harzia type” of fructification, as seen in M. cervicula and the
“ Aspergillus-like” type as seen in P. aspergilliformis, are modifica-
tions of one and the same mode of reproduction: since on several
occasions the writer has found in connection with the conidial fructifi-
eation of M. cervicula instances in which secondary heads seemed
to be lacking, but, owing to the fact that there was only a limited
amount of material available, this point could not be absolutely
determined. The perithecium of this form, however, is clearly
of the melanosporous type, and can hardly be the same as the Cerato-
stoma described by Bainier.

The writer has under cultivation the Mycogone ulmaniae Potebnia,
(07) (Chlamydomyces diffusus Bainier) obtained by Dr. Thaxter
from Liberia and kept in cultivation for over fifteen years. In addi-
tion to its large two-celled, warty, chlamydospores, this species also
produces conidia on “Aspergillus-like” conidiophores similar to
those of P. aspergilliformis.

Conidial forms similar to those above mentioned are also described
by Moller (98) in connection with the garden fungi of certain species
of ants in the tropics.

Again, large chlamydospores, somewhat similar to those of Melano-
spora cervicula except that they are divided into two unequal cells,
have been described by Berlese (92) in connection with Sphaeroderma
bulbilliferum. They differ from those of Mycogone ulmaniae, how-
ever, in being smooth.

Papulospora polyspora, n. sp.
PuaTeE 11, Figures 1-13.

Hyphae septate, hyaline, scanty, procumbent, 5-7 μι in diameter
(sometimes as much as 9 μὴ); bulbils dark red-brown usually with a

294. PROCEEDINGS OF THE AMERICAN ACADEMY.

thin mucilaginous film about each, eventually becoming a dry powdery
mass, completely concealing the mycelium, more or less spherical,
119-122 μ in diameter, composed of closely compact angular cells,
150-200 cells visible in a surface view; cells homogeneous throughout.
Individual cells of the bulbil eventually forming spherical spores, 17—
22 win diameter loosely held together. No other spore-form known.

On straw, old paper, from California and cotton flowers from Cuba.

This fungus has been obtained from at least three different sources.
It was found by Dr. 'Thaxter running over a gross culture of the flowers
of Cuban cotton and also by the writer on gross cultures of barley straw
from Claremont, California, and on old paper from Duarte, California.

The usual methods of obtaining a pure culture were employed here,
after which the fungus was grown on various kinds of nutrient material,
but it could not be made to produce any perfect form. Mycelia from
widely different sources were contrasted in Petri dishes but no results
were obtained except the production of certain abnormal enlargements
and contortions of the hyphae, such as may frequently be observed in
contrasting forms of even widely different species.

The mycelium of this fungus is white, inconspicuous, procum-
bent, the hyphae densely filled with coarse granules or oil globules.
At a short distance from the margin of growth small white pustules
are seen, which gradually become larger and more frequent as they
approach the point of inoculation. These soon turn tan-colored, and
are frequently associated with small drops of liquid of nearly the same
color, which may often be seen surrounding a bulbil. At maturity
these bulbils are almost spherical, 119-122 μ in diameter, composed
of closely compacted angular, often irregular cells, uniform throughout,
there being no distinction of a definite cortex. They occur in large
numbers heaped together, covering the whole substratum and obliter-
ating completely the naturally scanty mycelium. In older cultures
they become a dry powdery mass.

The bulbils.— The formation of this bulbil is different from that of
any of the others thus far considered, since they result not from the
development of a.single primordium but from the combined activities
of several primary branches. One or more procumbent hyphae send
up vertical branches which twine about each other (Figures 1+,
Plate 11). Usually several of these branches arise simultaneously at
a given point (Figure 3, Plate 11) and as the bulbil increases in
size, more and more of these take part in its formation, their extremi-
ties combining to produce the bulbil proper, while just above the
substratum there may form a sterile supporting base, often with a

HOTSON.— CULTURE STUDIES OF FUNGI. 295

diameter nearly equal to that of the bulbil itself and composed of
interlacing hyphal strands, which are partly made up of branches from
the procumbent hyphae and partly by the branching of the original
vertical ones. These supports or “stalk-like” structures vary in
length, some being quite long (100 μὴ, while at other times the bulbils
appear to be almost sessile on the horizontal branches. The primor-
dia that are produced later, are hindered in their upward growth by
the presence of the first formed bulbils, which, however, are soon
broken away from their attachments and pushed up so that eventually
several irregular layers of independent spherical bodies are produced,
the oldest ones being on the surface. Whether the vertical hyphae
first formed fuse at the apex could not be determined. They evidently
receive some stimulus, for they begin to send out short branches in
different directions, which in turn divide and subdivide, and these
intertwine among themselves and, with other hyphae that grow up
from the original horizontal branches, form an interlacing weft which
becomes more and more compact, producing a hyaline, spherical body
in which the walls are very thin and almost indistinguishable except
after staining. As they increase in size they assume a brownish tint
and finally a rich tan-color, during which time the walls gradually
become more definite and eventually are well marked.

Since liquid media appeared to have a peculiar affect on the develop-
ment of these bulbils, cultures were tried in large flasks on pieces of
wood partly immersed in bran decoction, so that the effect of different
degrees of moisture might be observed, as the mycelium spread from
the liquid medium toward the dryer portions of the wood. Under
these conditions it was found that the bulbils formed on the wood
about three or four inches above the liquid, began to assume a paler
aspect and soon became light straw-colored, instead of the dark tan of
the normal bulbil. On examination it was found that the cells com-
posing these pale bulbils, instead of being compact with angular walls
as in the normal form, had rounded up and become spherical (17-22 μ
in diameter), adhering very loosely by means of a mucilaginous mate-
rial that had evidently been secreted by them, so that a very slight
pressure would separate them into individual spores (Figure ὃ,
Plate 11). The germination of these “spore-masses” was followed
carefully in Van Tieghem cells — some crushed, others not — and it
was found that nearly all the spores germinated in twenty-four hours,
some producing one, others two germ tubes, which were hyaline and
septate, becoming much branched (Figures 9-10, Plate 11). When
allowed to remain adherent, the spore-mass sent out germ tubes in all

296 PROCEEDINGS OF THE AMERICAN ACADEMY.

directions which shortly forced the individual spores apart. The
bulbils were also germinated in Van Tieghem cells, but their germi-
nation was much slower and they produced comparatively few germ
tubes which seemed to be chiefly from the superficial cells.

In water cultures the hyphae are usually larger and more densely
filled with granular material, with numerous large swollen intercalary
or terminal cells (Figures 9b-13, Plate 11). These cells are grouped
together irregularly as if attempts were being made to form bulbils
but they do not become compact. ‘They often grow very large, as
may be seen by a comparison of Figures 90--[8, Plate 11, all of which
have the same magnification.

This development and final fate of the bulbil of P. polyspora,
suggest a similar condition that is found in Aegerita. In Aegerita
Webbert Fawcett (10) the “sporodochia”’ which measure 60-90 μ in
diameter, consist of an “aggregation of conidia-like, inflated, spherical,
cells, 12-18 μ in diameter,” resembling the conditions described for
P. polyspora. The development of the latter on the other hand
recalls also that of the sporodochium of A. candida Persoon (Penio-
phora candida Persoon) as described and figured by Lyman (07) and
it is possible that the two structures may be similar in nature.

OTHER RECORDED BULBIFEROUS FORMS.

In addition to those above enumerated several other bulbils or
bulbiferous forms have been recorded, some of which have already
been referred to, but which may here be again mentioned.

Papulospora Dahliae Costantin (88). This species was found by
Costantin on roots of Dahlia. Its bulbils appear to be somewhat
like those of P. coprophila, brownish-red in color, with two or three
large central cells surrounded by a layer of empty cortical cells.
Conidia belonging to the genus Dactylaria are, however, said to be
associated with these bulbils, although it is not evident that the species
was cultivated in a pure condition.

Dendryphium bulbiferum Zukal (86) has been mentioned on page 233,
and also in connection with P. parasitica. The bulbils described and
figured by Zukal are said to be directly associated with the conidia of
a Dendryphium; but here, as in other forms studied by this author,
there is no evidence that pure culture methods were used in studying
the fungus.

“ Haplotrichum roseum Lk.” is also stated by the same author (’86)
to be associated with bulbils said to be very similar to those of the

HOTSON.— CULTURE STUDIES OF FUNGI. 297

Dendryphium just mentioned; but here again pure cultures do not
appear to have been used. As far as the writer is aware, moreover,
this common hyphomycete has never been seen to be thus associated
by any other observer.

Papulospora (Stemphylium) Magnusianum (Sacc.), (Michelia,
I, 132) a form collected by Magnus in the Tyrol, distributed in Vester-
gren, Micr. Sel., No. 1150, and also figured by Saccardo in Fungi
Italici, No. 934, should be mentioned in the present connection, since
it is a typical bulbil and by no means a compound spore like that of
species of Stemphylium.

Clathrosphaera spirifera Zalewski (88), is a form which the author,
although his observations are concealed in Polish text, appears to
regard as bulbiferous, or as producing bodies comparable to bulbils,
which are also associated with a species of Helicoon.

The writer has himself observed various other more or less ill de-
fined types of bulbils, which have not been above enumerated, since
they do not appear to be sufficiently well marked to warrant a definite
name. “No. 170” for example (Figures 24-34, Plate 5), was found
in California on straw from Claremont, and on old paper from Duarte.
The fungus is characterized by an abundant white mycelium, the
hyphae of which produce bulbil-like bodies consisting of a few cells
each, as indicated in the figures. Their characters and development,
however, are not constant and their exact nature is somewhat doubt-

ful.

COMPOUND SPORES AND OTHER REPRODUCTIVE
STRUCTURES WHICH RESEMBLE BULBILS.

Reference has already been made to the close resemblance which
exists between the so called “spore-balls”’ of some of the Ustilaginales,
and the structures under consideration; in fact it would be quite
impossible to differentiate the spore-balls of Urocystis or Tubercinia
from bulbils, as far as concerns their gross structure and method of
development which may be exactly similar. They are, however,
clearly distinguished in other ways; since in bulbils, spore formation is
never preceded by any nuclear fusion, so far as is known; and further-
more the germination of bulbils in no way resembles that of the smuts;
and there is never any indication of the formation of anything corre-
sponding to a promycelium.

Attention has also been called to the fact that the compound spores

298 PROCEEDINGS OF THE AMERICAN ACADEMY.

which are associated with the imperfect forms of many of the higher
fungi, may bear a close resemblance to bulbils. Although compound
spores may in general be distinguished by the fact that they normally
arise as the result of the septation of a single cell, while in the pro-
duction of bulbils two or more cells are primarily involved, to which
others are added by a process of budding which may also be combined
with secondary septation, it is not always possible to separate them
with certainty. Spores like those of Stephanoma, referred to else-
where, in which the empty superficial cells arise by budding, serve,
however, to break down this distinction.

On the other hand, the more complicated types of bulbils are easily
comparable to the simpler types of sclerotia, such as occur for example
in Penecillium Italicum, Verticilltum agaricinum and similar forms.
Such sclerotia, however, result from the irregular and indefinite
massing together of vegetative filaments, the densely compacted
cells of which do not partake of the nature of spores, while the func-
tional cells of bulbils are usually spore-like and act independently of
one another at the period of germination.

Among the compound spores formed in connection with the imper-
fect conditions of higher fungi, several may be mentioned which have
bulbil-like characteristics.

Stephanoma strigosum Wallr. a parasite on Peziza hemispherica
which, as Dr. Thaxter informs the writer, occurs also on Genea
hispidula in this country and is connected with an undescribed hypo-
creaceous perithecial form, might very well be regarded as a bulbil of
a simple type, since not only are its spores similar in their develop-
ment, but, when mature, are hardly distinguishable from the more
simple bulbils which are often produced, for example, by Papulospora
parasitica.

Stemphylium macros poroideum Sace., which has been examined from
cultures kept in the Cryptogamie Laboratories, produces a compound
spore consisting of one large functional cell to which, at maturity, two
or more empty ones are attached. In this condition it resembles very
closely the bulbil of Acrospeira mirabilis; but in view of the fact that
it develops as a result of the successive divisions of a single terminal
cell, it must be regarded as a compound spore. Certain other forms
also of Stemphylium as well as of Mystrosporium might well be mis-
taken for bulbils.

Hyalodema Evansu P. Magn., which von Hohnel has referred to
Coniodyctium Chevaliert H. & Pat., produces a hymenium-like layer
bearing compound spores which, except in color, are very like the

HOTSON.— CULTURE STUDIES OF FUNGI. 299

bulbils of Papulospora sporotrichoides. Their development, however,
is clearly that of compound spores and not of bulbils.

Eleomyces olei Kirchner (’88) a fungus found growing in poppy oil,
produces a compound spore which consists at maturity of a large
thick-walled functional cell, surrounded by several empty coherent
cells, the whole resembling the bulbil of Acrospeira. If, as suggested
by Kirchner, this body results from the coherence of several adjacent
cells, it might well be regarded as a bulbil and not a compound spore.

Various other spore-forms might be mentioned which bear more or
less resemblance to bulbils, but those above enumerated are sufficient
for purposes of illustration. Before leaving bulbil-like forms, how-
ever, two or three additional types may be mentioned, the nature of
which is not altogether clear, since they are neither compound spores
nor typical sclerotia.

Aegerita Webberi Fawcett (10), a fungus attacking scales on Citrus,
produces, under certain conditions, bulbil-like bodies which consist of
loosely coherent spore-masses closely comparable to those of the
aberrant Papulospora polyspora, the development of which, under
moist conditions, has been described above.

Sorosporella Agrotidis Sorokin (’88, ’89), which attacks the larvae
of Agrotis, fills the latter with loosely but definitely coherent cell-
groups which might also be compared to those of P. polyspora.

Lastly, among structures which bear a striking resemblance to bul-
bils, the peculiar spore-balls of Spongospora subterranea (Wallr.)
Johnson should be mentioned; which, although they might readily be
taken for a species of Papulospora, have been shown to belong to the
life-cycle of one of the Mycetozoa.

THE MORPHOLOGICAL SIGNIFICANCE OF BULBILS.

Opinions concerning the morphological significance of bulbils differ
widely. Preuss (’51), Eidam (’83), DeBary (’86), Mattirolo (86)
all regarded them as normal structures which function as auxiliary
methods of reproduction; while Karsten (65), Zukal (’86), Morini
(88), and Baineir (07) looked upon them as immature ascogenous
fructifications of either perithecial or apothecial forms, believing
that their arrested growth was due to unfavorable environment, and
that, with proper nutriment, they might be able to complete their
development.

Although it is possible that the last mentioned view may be correct
in some instances, it is quite certain that in many cases, where both

300 PROCEEDINGS OF THE AMERICAN ACADEMY.

bulbils and ascocarps are present, this cannot be the case, since the
primordia and development of the two are widely different. Thus in
Cubonia bulbifera, for example, the bulbil is produced from a group of
intercalary cells, while the primordium of the apothecium is a spiral.
In like manner Melanospora anomala develops bulbils which arise
from intercalary cells, somewhat as in Cubonia, while the perithecia
arise from free spirals.

It is quite possible, however, that in other cases, as for example in
M. papillata, where the primordium of the bulbil and that of the
perithecium are similar, they may be homologous. But even in
such cases, the two primordia are distinguishable so early in their
development, that it is more than probable that here, also, they cannot
be regarded as immature ascocarps. Various attempts have been
made by the writer to induce the bulbils of various species to continue
their development and produce ascocarps. Many bulbils of ἢ.
papillata for example, that had grown larger than the more normal
types, were isolated and placed on different media where they were
exposed to different degrees of moisture, with this end in view. Simi-
lar attempts were also made with the bulbils of P. coprophila, in
which the spiral bulbil-primordium might be supposed to suggest its
ascogonial nature. In no instance, however, was any evidence ob-
tained that would seem to point to the conclusion that they were to be
regarded as anything but independent non-sexual propagative bodies,
except that, in some instances they increased in size, sometimes be-
coming approximately half as large as perithecia. This enlargement,
however, was unassociated with any structural differentiation such
as always characterizes the developing perithecium.

Although Bainier reports that he was successful in inducing the
bulbils of Papulospora aspergilliformis to develop directly into peri-
thecia which he refers to Ceratostoma, the writer has been as un-
successful with this species as with others, even when using material
derived from a living culture received from Bainier by Dr. Thaxter.

In view of the careful and long continued experiments made by the
writer in this connection, and his entire failure to obtain positive
results, the assumption seems justified that ordinarily, at least, bulbils
are not to be regarded as abortive ascocarps, but rather as an auxil-
iary method of reproduction that has been interpolated in the life
history of certain fungi without definite relation to other forms of
reproduction which they may possess; or if they have in reality been
derived from some other reproductive body, that this was more
probably some type of compound non-sexual spore, rather than the
primordium of an ascocarp.

HOTSON.— CULTURE STUDIES OF FUNGI. 301

DISTRIBUTION AND OCCURRENCE OF BULBILS.

It is evident from the foregoing account that bulbiferous types
are not only widely distributed, but are very readily obtained if sought
for, and, like so many other types among the Fungi Imperfecti, have
been independently developed by a variety of species wholly unrelated
and belonging to widely separated groups among the Pyrenomy-
cetes, the Discomycetes and the Basidiomycetes. Such bulbiferous
conditions, therefore, cannot in any sense be regarded as forming any-
thing in the nature of a Natural Group. If one may judge from our
actual knowledge of these forms, it would appear, on the contrary,
that the bulbiferous condition was a specific one, the habit having
been developed by certain species, only, in genera, the other members
of which have no such secondary means of propagation: just as the
habit of producing sclerotia of a characteristic type, has arisen in a
few species, only, of Penecillium, like P. Jtalicum. The same princi-
ple is well illustrated in the large genus Corticium many species of
which have been tested by means of pure cultures. Here again one
finds a single species, only, which possesses the bulbiferous habit, namely
C. alutaceum, pure cultures of which become completely covered by its
dark brown bulbils.

In view of the wide distribution and common occurrence of bulbil-
producing forms, it is not a little surprising to find such scanty refer-
ences to them in mycological literature; and from the experiences
of the writer in studying them, it seems certain that further attention
to this subject will not only yield numerous other forms, but will show
connections with “perfect”? conditions even more varied than is at
present indicated.

KEY TO THE SPECIES OF BULBILS HEREIN
CONSIDERED.

According to their method of development bulbils may be grouped
in three more or less well defined categories namely: those which
originate from a primary spiral; those which develop from an inter-
calary primordium of several cells, and those which arise from a group
of vertical hyphae. Using these characters as a fundamental basis
for separation, the species above enumerated may be distinguished as
follows.

302 PROCEEDINGS OF THE AMERICAN ACADEMY.

Key to the Species of Bulbiferous Fungi. ὦ

A. Primordium normally involving more than one cell.
I. Bulbils black or smoke-colored.
1. Bulbils 75-100 in diam. margin even........ Cubonia bulbifera.
2. ~ 200-3002." — * ‘irregular. . Papulospora pannosa.

Il. Bulbils yellowish red to dark brown.
1. Hyphae showing clamp-connections.
1. Bulbils dark brown or chocolate colored.
i. Bulbils 65-80. in diam. clamps conspicuous.
Corticium alutaceum.
11. “125-1754 “ “5. margin even, clamps incon-
SPICUOUSs rare cesta Ce eee ke Papulospora anomala.
2. Bulbils yellowish or hight brown.
i. Bulbils light yellow, hyphae radiating conspicuously.
Grandinia crustosa.
ii. Bulbils brownish yellow, hyphae formed evenly.
“No. 200.”
2. Hyphae not showing clamp-connections.
1. Bulbils scanty, perithecia usually present.
i. Perithecia with neck, lateral and terminal setae.
Melanospora cervicula.
papilla and terminal setae.
Melanospora papillata.
2. Bulbils abundant, perithecia usually absent.
1. Primordium intercalary.
(i). Bulbils brownish-yellow, dente cells 28-55 up

ae {{ “ec

SLOW RL OT: Vat να ν Papulospora immersa.
(1). Bulbils straw-colored, central cells 10-20% in
Gian, ate eee Soe Papulospora irregularis.

il. Primordium one or more lateral branches.
(i). Primordium normally a single lateral branch.
a. Primordium a spiral.
§ Cells heterogenous, definite cortex.
A. One central cell.
x Cortex complete.
Papulospora parasitica.
x * Cortex incomplete.
Acrospeira mirabilis.
B. More than one central cell.
Spiral in one plane, cortical
cells spinulose
Papulospora spinulosa.
* % Spiral normally in more
than one plane, 2-6 central
cells.
a Bulbils dark brown.
Papulospora coprophila.
8 Bulbils brick red.
Papulospora rubida.
§§ Cells homogenous, bulbils 21-36 yu in
diam. brownish producing sporo-
trichum spores.
Papulospora sporotrichoides.

HOTSON.— CULTURE STUDIES OF FUNGI. 303

b. Primordium not a spiral.

§ Bulbils large, 100-750 wu, irregular.
Papulospora aspergilliformis.
70-150 μι, somewhat spherical,

producing perithecia with slight pap-
illa..........Melanospora anomala.
(ii). Primordium two or more lateral branches
forming a spherical aggregation of cells at the
top. Papulospora polyspora.
III. Bulbils white to cream colored, 30-35 » in diam.
Papulospora candida.
IV. «steel gray, 21-86 in diam......... Papulospora cinerea,

ia

HARVARD UNIVERSITY
April, 1911.

LITERATURE.
Bainier, G.
07. Evolution du Papulospora aspergilliformis et étude de
deux Ascodesmis nouveaux. Bul. Trimestriel de la
Société Myc. de France. Tome XXIII, p. 132. 1907.
Barber, M. A.
07. On Heredity in Certain Micro-organisms. Kansas Univ.
Sei. Bulls, Vol TV, Ὁ 1907.
Bary, A. de and Woronin, M.
’66. Ascobolus pulcherrimus. Beitr. z. Morph. u. Phys. der
Pilze. Taf. IV. 1866.
81. Comparative Morphology and Biology of Fungi, ete.
Trans. by Garnsey and Balfour; Oxford. 1887.
Berkeley, M. J.
’46. Observations, Botanical and Physiological, on the Potato
Murrain. Jour. Hort. Soc. of London, Vol. I, p. 9.
1846.
’57. Acrospeira mirabilis. Intr. Crypt. Bot., p. 805. 1857.
60. Papulospora, Preuss. Outlines of British Fungology, p.
354. 1860.
Berlese, A. N.
92, Intorno allo sviluppo di due nuovi Ipocreacei. Malpighia.
Anno V, p. 386. 1892.
Biffen, R. H.
01. Notes on some factors in the spore-formation of Acro-
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Soc. Vol. XI; Pt: I, p. 136s 901.

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703. On some facts in the Life History of Acrospeira mirabilis
(Berk. and Br.). Trans. British Mycol. Soc., Vol. II, p.
17. March, 1903.
Claypole, Mrs. E. W.
91. Baryeidamia parasitica Karst. Bot. Gaz. Vol. XVI, 263.
1891.
Costantin, J.
88. Note sur un Papulospora. Jour. de Bot., Vol. II, p. 91.
1888.
"88a. Les Mucédinées simples, p. 82. 1888.
’88b. Notes sur quelques parasites des Champignons supérieurs.
Bull. Soc. Bot., pp. 251-256. 1888.
Eidam, E.
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Engler und Prantl.
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708. Spongospora Solani, Brunch. (Corky Seab). Econ. Proe.
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OL ΝΣ συ Ὁ συν βιιἐεὺ. ὑπο π

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Johnson, T.
09. Further observations on Powdery Potato Scab, Spongo-
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99. A Text-Book of Plant Diseases. p. 305. 1899.
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XVIII, pp. 121-154, 2 plates. 1886.
Moller, Alfred.
’93. Die Pilzgarten einiger sudamerikanischer Ameisen. Bot.
Mittheilungen aus den Tropen von Dr. A. F. W. Schimper,
Heft 6. 1893.
Morgan, A. P.
’92. Synthetospora electa Morg. Bot. Gaz., Vol. XVII, p. 192.
1892.
92a. North American. Helicosporeae. Jour. of Cincinnati
Soc. Nat. Hist., Vol. XV, p. 39. 1892.

306 PROCEFDINGS OF THE AMERICAN ACADEMY.

Morini, F.
’88. Biografia degli apoteci della Lachnea theleboloides (A. et
5.) Sace. Mem. R. Ace. Scienze ἃ. Istituto di Bologna,
Ser. 4, tom. 9, p. 611. 1888.
Potebnia, A.
07. Mycogone Ulmariae Potebnia, Annales Micologici, Vol. V,
p. 21. 1907.
Preuss, C. G. T.
’51. Papulospora Preuss. Sturm’s Deutchlands Flora, Abth.
Til; Pilze, Heft: 30,’p. 89. Vat. 25: 1851:
Saccardo, P. A.
’86. Sylloge Fungorum. Vol. IV. 1886.
Schroter, J.
97. In Engler τι. Prantl’s Die Naturlichen Pflanzenfamilien.
I Teil. 1 Abth. p. 149. 1897.
Sorokin, N.
’88. Parasitologische Skizzen. Centralblatt. f. Bakter. u. Para-
sitenkunde. Bd. IV, No. 21, pp. 644-647. 1888.
’89. Un Nouveau Parasite de la Chenille de la Betterave, Soro-
sporella agrotidis. Bull. Scientifique d. France et d.
Belgique, Vol. XX, p. 76. 1889.
Ule, E.
701. Ameisengarten 1m Amazonasgebeit, Engler’s’ Bot. Jahrb.
Vol. XXX. Beiblatt 68 : 45-52. 1901.
Wallroth, F. W.
’42. Die Naturgeschichte der Erysibe subterranea Wallr. Beit.
zur. Bot., p. 118. 1842.
’42a. Linnaea, Vol. XVI, pt. 2. p.332. 1842.
Woronin, M.
82. Beitrag zur Kenntniss der Ustilagineen. In De Bary and
Woronin, Beitr. Morph. u. Phys. der Pilze, Ser. 5, p. 5.
taf. 2. 1882. Abhandl. d. Senckenb. naturf. Ges. 12: 559.
Zalewski, A.
88. Prayezynki zycioznawstwa grzybow przez. Krakow. Dru-
karnia uniwersytetn jagiellonskiego. 1888.
Zukal, H.
’85. Mycologische Untersuchungen. Denkschriften d. k. Aka-
demie d. Wissen. (Wien), Bd. 51, pt. 2, pp. 21-26, Taf.
2, Figs. 1-4. 1885.
’86. Untersuchungen iiber den biologischen und morpholo-
gischen Werth der Pilzbulbillen. Verh. k. k. Zool. bot.
Ges. Wien, Vol. XXXVI, pp. 123-135, plate 4. 1886.

EXPLANATION OF PLATES.

The figures of Plates 1-12 were drawn with the aid of a camera lucida using
different combinations of the Bausch and Lomb lenses, All the mature
bulbils were drawn with the same magnification, namely 4 mm. objective
and 3 eye piece, and for the stages of development of the bulbils, 4 mm. objec-
tive and 12 eye piece were used. The plates have been reduced in reproduc-
tion about three-quarters.

PLATE 1.

CUBONIA BULBIFERA.

Ficures 1-6. Different forms of the primordium of the apothecium.

Figures 7,8. Young apothecia.

Figure 9. Section of the mature apothecium.

Ficure 10. Asci and paraphyses.

Fiaures 11-16. Stages in the development of the bulbil.

Figure 17. Mature bulbil.

Figure 18. Contortions of the hyphae.

Figure 19. Portion of a crushed bulbil with the contents of the cells escaping.

Ficure 20. Ascospore.

Ficure 21. The endosporium broken off.

Ficures 22-24. Germinating Ascospores.

Ficures 26, 27. Sprouting vegetative cells from the inner portion of the
apothecium.

Fiaure 28. Germinating bulbil producing spiral primordia directly.

Hotson. —Cucture Stupies oF Funai PLaTe 1.

Proc. Amer. Acapo. Arts ANd Sciences. Vor. XLVIII.

PLATE 2.

MELANOSPORA PAPILLATA.

Figures 1-6. Stages in the development of the bulbil.

Figure 7. A group of Chlamydospore-like intercalary cells.

Fiaures 8-10. Stages in the development of the perithecium.

Ficure 11. pune ot a mature perithecium showing the relative size of the
ulbils.

Figure 12. A group of asci crushed from a young perithecium.

Ficurss 13-20. Germinating ascospores.

Figures 21, 22. Forms produced in Van Tiegham cell cultures.

Fiaure 23. Conidia on flask-shaped sterigmata produced on a hypha.

Ficures 24, 25. Stages in the development of a terminal bulbil.

Fiaure 26. An intercalary bulbil with three large central cells.

MELANOSPORA ANOMALA.
Figures 27-30. Stages in the development of the bulbil.

PLATE 3.
MELANOSPORA ANOMALA.

Fiaures 1-12. Stages in the development of the perithecium.

Figure 12. Mature perithecium.

Figure 13. (a) Germinating ascospore showing a bottle-shaped sterigma.
; (0) Bottle-shaped sterigma on a hypha.

Ficures 14, 15. Other stages in the formation of the bulbil.

Figure 15. A mature bulbil.

MELANOSPORA CERVICULA.

Ficures 16, 17. Primordia of the bulbil.

Figure 18. A bulbil produced from a group of terminal cells.

Figure 19. Primordium of the perithecium and conidia on flask-shaped
sterigmata.

Figure 20. Mature perithecium.

Figure 21. Abnormal forms common among the hyphae.

Figure 22. Chlamydospores of the Acremoniella type.

Figures 23, 24. “Harzia-like”’ fructification.

Hotson. — Cucture Stupies oF Funei. Piate 3.

Sse : SSE

Proc. Amer. Acav. Arts ano Sciences. Vor. XLVIII.

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PAPULOSPORA CANDIDA.

Ficures 1,2. Variation in the size of the conidia.
Ficures 3-12, and 15-27. Stages in the germination of the conidia and the

development of the bulbil from them.

Ficures 28-41. Stages in the development of the bulbil from a lateral

FIGuRE 42.
Ficure 48.
FIGURE 44.
Fi@ureE 45.

FicureE 46.
FIGURE 47.

branch of the hyphae.
Germination of the superficial cells of the bulbil.
Conidiophores of Verticillium agaricinum var. clavisedum.
Portion of the hyphae showing large oil globules.
Showing intimate connection between the bulbil and the
Verticillium.
An irregular primordium of a bulbil.
Ascoma of Geoglossum glabrum attacked by the parasite.

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PAPULOSPORA PARASITICA.

Ficures 1-14. Show various stages in the development of the bulbil.

Ficures 4, 5, & 9, 10. Show the protuberance from the lateral surface of the
large central cell.

Ficures 15, 16. Germinating bulbils.

Figure 17. Conidia-like bodies connected with the bulbil.

Ficures 35b, 36. Swollen intercalary cells.

ACROSPEIRA MIRABILIS.

Fiaures 18-23. Stages in the development of the bulbil.

Figure 20. The end-cell has enlarged to form the central cell.
Friaur& 21. The second cell has enlarged to form the central cell.
FiaureE 22. Several empty cortical cells are shown.

REPRODUCTIVE Bopirs RESEMBLING BULBILS.

Fiaure 24-34. Irregular forms of a doubtful bulbil (No. 170).
Figure 35. Spore of Stephanoma strigosum Wallr.

Hotson. — Cucture Stuoies oF Funai. Prate 5.

Proc. Amer. Acapo. Arts ano Sciences. Vor. XLVIII.

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PLATE 6.

GRANDINIA CRUSTOSA.

Ficure 1. Pustulate habit of the fructification.

Figure 2. Hymenium with basidiospores.

Figure 3. Basidiospore.

Ficures 4-10. Stages in the development of the bulbil.

Fieure 10. Mature bulbil with the same magnification as all the other mature
bulbils.

PAPULOSPORA ANOMALA.

FicurE 11-17. Stages in the development of the bulbil.

Ficure 17. Mature bulbil.

Ficure 18. Two primordia close together.

Fiaure 19. Large intercalary cells densely filled with oil globules.

PAPULOSPORA PANNOSA.

Fraures 20-24. Stages in the development of the bulbil from intercalary
cells.
Fiacure 25. Occasional mode of formation of intercalary primordia.

Pirate 6.

Ευνοι.

Hotson. —Cucture Srtubdle€s ΟΕ

νοι. XLVIII.

Proc. Amer. AcAv. Arts AND SCIENCES.

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PLATE 7.

PAPULOSPORA ASPERGILLIFORMIS.

Ficures 1-4, & 6. Stages in the development of the bulbil.

Figure 5. A group of Chlamydospore-like bodies.

Ficure 7. A primordium that produces a very irregular bulbil.

Ficure 8. ‘Aspergillus-like’’ heads produced directly from the bulbil.
Ficures 9-12. Different forms of the “ Aspergillus-like” fructification.
Fraure 12. Abnormal conditions.

Ficures 13-16. Chlamydospores.

Ficures 17, 18. Large swollen cells, likely storage cells.

Figure 19. Bulbil forming from terminal cells.

Ficure 20. Section of a mature bulbil.

Hotson. — Cucture Stupies of Funai. PLate 7.

Proc. Amer. Acapo. Arts Ano Sciences. Vor. XLVIII.

PLATE 8.

PAPULOSPORA CINEREA.

Ficures 1-10. Stages in the development of the bulbil.
Figures 4, 6, &9. Modifications of the regular mode of development.
Fiaures 10, 11. Mature bulbils.

PAPULOSPORA RUBIDA.

Figures 12-16. Stages in the development of the bulbil.

Fiaures 25a-27a, 21, 22. Other stages in the development of the bulbil.
Figures 17, 20. The spiral primordium that sometimes occurs.
Figure 25. Section of a mature bulbil showing five large central cells.
Figure 18. Surface view of a mature bulbil.

PAPULOSPORA PANNOSA.

Figures 28-30. The development of a bulbil from a lateral branch.
Figure 31. A collapsed hypha showing rigid septa.

wr ef

PLAT

Proc. Amer. Acapv. Arts Ano Sciences. Vor. XLVIII.

PLATE 9.

PAPULOSPORA SPINULOSA.

Figures 1-7. Stages in the development of the bulbil.

Ficure ὃ. Primordia produced from a superficial cell of an immature bulbil.
Ficure 9. Section of a mature bulbil showing the ‘ Annulus.”

Fiaure 10. A surface view of the same looking down on the ‘‘ Annulus.”

PAPULOSPORA IRREGULARIS.
Ficures 11-17. Stages in the development of the bulbil.
Figure 17. A mature bulbil.
PAPULOSPORA PANNOSA.

Ficures 18-20. Stages in the development of the bulbil.
Fiaure 20. A mature bulbil.

Hotson. — Cucture Stupies oF Funai. Pate 9.

Proc. Amer. Acav. Arts ano Sciences. Vor. XLVIII.

renee

PLATE 10.

PAPULOSPORA COPROPHILA.

Figures 1-8. Stages in the development of a bulbil from a spiral.

Fieure 6. An υδύειι condition, the production of conidia directly from the
spiral.

Figure 8. A spiral primordium surrounded by an irregular layer of cells.

Ficure 9. Immature bulbil that has developed like Figs. 14 and 15, and also
a spiral primordium. Ἷ

Fiaure 10. Median section of a mature bulbil with two large central cells.

Figure 1l. A Sg pes with the contents of the large cells crushed out
(Fig. 11b).

Ficure 12. Germination of one of these cells.

Fiaures 13-15. Forms arrested in the process of development.

Ficures 16. Surface view of the mature bulbil.

PAPULOSPORA IMMERSA.

Fieure 17. Irregular hypha densely filled with protoplasm. The primor-
dium of the bulbil.

Figure 18. Primordium consisting of a single intercalary cell.

Figure 19-25. Stages in the development of the bulbil.

10.

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PLATE 11.

PAPULOSPORA POLYSPORA.

Ficures 1-7. Stages in the development of the bulbil.

Figure 7. A mature bulbil.

FicurE 8. Group of spores adhering loosely together.

Ficures 9 & 10. Germinating spores.

Ficures 9b, 10b, 11-13. Modifications that occur when grown in liquid media,

Pirate 11.

Hotson. — Cucture Stupies oF Funct.

XLVI.

Proc. Amer. Acao. Arts AND Sciences. VOL.

ΙΑ ΤΟΣ
PAPULOSPORA SPOROTRICHOIDES.

Ficurms 1-9. Stages in the development of the bulbil.

Fiaure 8. A mature bulbil.

Ficure 9. A side view of an immature bulbil.

Ficures 10, 11. Abortive forms.

Figures 12-16. Modifications in the formation of the spiral.

Figure 17. Anirregular bulbil germinating, magnified more than the others.

Figure 18. Branch of the hyphae showing primordia of the bulbils.

Fiaures 19-25. Modifications in the development of the bulbils which are
hyaline.

Figures 26-28. Semi-diagrammatie representation of the mode of cell
formation in the development of the hyaline bulbils.

Fiaure 29. A section of a mature bulbil.

Figures 30, 31. Large interealary and terminal cells found in the hyphae.

Figures 32-34. Germinating bulbils.

Fiaures 25-26. Conidiophores with conidia.

Figure 37. Conidiophore produced directly from the bulbil in a Van Tieg-

hem cell culture. 5

Fiaure 38. Conidium.

Figure 39. The form the conidia usually assume before germinating.

Fiaures 40, 41. Germinating conidia.

Plate 12.

Hotson. — Cutture Stupies OF Funat.

Vor. XLVI.

Proc. Amer. Acav. Arts AND SCIENCES.

a

ang Proceedings of the American Academy of Arts and Sciences.

Vou. XLVIII. No. 9.—Srprremper, 1912.

CONTRIBUTIONS FROM THE JEFFERSON PHYSICAL
LABORATORY, HARVARD UNIVERSITY.

THERMODYNAMIC PROPERTIES OF LIQUID WATER
TO 80° AND 12000 KGM.

By P. W. Bripeman.

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CONTRIBUTIONS FROM THE JEFFERSON PHYSICAL
LABORATORY, HARVARD UNIVERSITY.

THERMODYNAMIC PROPERTIES OF LIQUID WATER TO
80° AND 12000 KGM.

By P. W. Brip@Man.
Received June 26, 1912.

TABLE OF CONTENTS.

Pace.
πο RTOS pee τιν εἰπε Rn Rn Bums Roe Se Fr meres, Slt τι 510
Method . . Sand |, ease g a Gata ote aoe: Sth IED
Previous Use of the Method ............ . B12
Description of the Apparatus . τυ tree Se ro! μ,
Correction for the Distortion of the Vessel. . . . . . . . . 316
Experimental Procedure . . σι τα ad che” 135140)
In Determining Compressibility Raison ene lac Merah Fra tomes Ce)
Calibration of Meneeun Calling i 2 gs ees See oa
Formulas . . ἀντ Shy ane TN OE
In Determining ilacitionte: ΘΕ νυ Os eee eet ae a 326
he ataan ἢ εἰν AP eer * PAE a aw Aaer Ole
Compr essibility Af law Pressuteas:, )-/ το ον το θέν χα τ:
ΠΤ ΠτΟ τ ΘΠ Ow, ΕΥΘΕΒΌΓΘΗ ο΄... si hea eel nd epee ce yt 390
Compresaibility at High*Pressures: « (.- 4 a, Se, 391
ΤΠ ΡΠ 5 ποτ athens Pressunes: Gs y5\ Gs. Ssh, es, PRS ἢ 5554
PHBE URSIONAGI Le; FueHIMES’ 7) ck Se ae Pues LG GN ate 986
Table of Volumes . . Pe δέον ἡ πλὴν cert ote τ ων OOS
Method of Consttuctiony cal) &: . ΝΣ ας ΤῊΣ 336
Wanous; PhemhodynamicQuantitess). Ut i. wo. kw 357
eS Ov
Compressibility, [ | ον ΡΣ το 840
Dilatation, (2) αν ioc eee ae
OT p
Work of Compression, W = — “Ὁ (5) Cpr. Vliet Dee ony 46
4"
Heat of Compression, Q = — τ AS), AD AN ap fae Σ Oe!
Change of Internal Energy, AE = W a OUI Wes fais ah προ.) 948
Pressure Coefficient, (32 See) NED στο ον 1540
OT /v

Specific Heat at Constant Pressure, Cp τ΄. <=. . 4. . dol

Specific Heat at Constant Volume, (Cs. . . .... . . 9852
Thermal Effect of Compression, (= Ss} eet me mR a
φ
Adiabatic Compressibility, (5) Oe oe Ae τπνῸς λει σοῦ
Volume of Kerosene as a Function of Temperature and Pressure . . 356

Compressibility and Dilatation of Ice VI re Cl Pate Se ake lie. ai eee

310 PROCEEDINGS OF THE AMERICAN ACADEMY.

INTRODUCTION.

Tuts paper is in the nature of a supplement to a former paper on
the properties of water in the liquid and the solid forms.1_ The solid
forms were studied over a range of 20,000 kgm. /cm.?, and from —80°
to +76°, but the study of the liquid reached only from the lowest
temperature of its existence to about +20°. Above 0°, measurements
were made on the liquid at only 20°. The two measurements, at 0°
and 20° were sufficient to give the mean dilatation between 0° and 20°,
but not the variation of dilatation with temperature. It was assumed
in the earlier paper that the variation of dilatation with temperature
became negligible at high pressures, since this seemed to be the most
plausible assumption in view of all the data then available.

In this present paper the study of the liquid has been continued
from 20° to 80°, and to 12000 kgm. The pressure range is greater
than that of the preceding paper by about 2,500 kgm. The range is
not great enough to entirely cover the region of stability of the liquid,
but it is as great as it was convenient to cover with the method used
here, which is different from that of the former work. It has the
advantage of very much greater rapidity of operation, but since it
depends on the complete elastic integrity of the steel pressure cylinders
it is not possible to reach so high pressures with it as with the former
method. [The former limit of 9500 kgm. was set by the freezing of
the liquid and was not due to any limitation of the method.] Never-
theless, it may be hoped that the present temperature and pressure
ranges are both wide enough to give a fairly complete idea of the nature
of the effects to be expected at high pressures with varying tempera-
ture.

Measurements of the dilatation have been made at four tempera-
tures, so that it has been possible to find the variation of dilatation
with temperature at any pressure. Perhaps the most unlooked for
feature disclosed by the measurements is the fact, contrary to the
assumption of the first paper, that the variation of dilatation with
temperature does not become vanishingly small at high pressures, but
reverses in sign. This means that while at low pressures the volume
increases more and more rapidly with rising temperature, at high
pressures the expansion becomes more slow at high temperatures.
\@ The data of this paper are sufficient to completely map out the
p-v-t surface over the domain in question: Both the first and second

1 Bridgman, These Proceedings, 47, 439-558 (1912).

ΟἹ

BRIDGMAN.— THERMODYNAMIC PROPERTIES OF WATER. Old

derivatives are therefore completely determined, so that we now have
all the data at hand for the determination of any one of the thermo-
dynamic properties of the liquid. This means that we are in a posi-
tion to find such quantities as the specific heats, change of internal
energy, adiabatic temperature rise etc., as well as the more easily
determined compressibility and thermal dilatation. The latter part
of the paper, after the discussion of the method and the presentation
of the data in the first part, is occupied with the computation of these
various thermodynamic quantities. The accuracy of some of these
is probably not very great, because the error in the second derivative
of an experimental quantity may be considerable. It has, therefore,
seemed best to give the general view of the nature of the quantities
which is offered by a graphical representation, rather than to give
tables, with the tacit assumption of greater accuracy which usually
goes with a set of tables. In spite of the lower order of accuracy of
some of these thermodynamic quantities, it has still seemed well
worth while to give them, since even the general trend of some of the
quantities, such as the specific heats, has not been hitherto known
with relation to pressure.

The data presented here are only the beginning of a projected
study of the characteristic surface under high pressures for a number
of liquids. The measurements have already been carried through for
twelve other liquids beside water. The purpose of this study is
ultimately the development of a theory of liquids, since it would seem
that a much more intimate grasp of the nature of the forces at work
in a liquid would be afforded by a study over a wide pressure range,
than over the comparatively low pressures hitherto used. It must be
admitted, however, that this broader purpose is not particularly
furthered by this work on water, because of the well known abnor-
malities of this substance. In the previous paper several abnormali-
ties had been shown to exist at low pressures. In this paper, new
abnormalities are found at higher pressures. Water gives the ap-
pearance of becoming completely normal only at the higher tempera-
tures and pressures of the range used here, but of course whether this
is really normal or not cannot be told until the behavior of normal
liquids has been discovered. The full significance of the present
data, in their bearing on such questions as the polymerization of the
liquid, for example, cannot appear until after the discovery of the
laws for entirely normal liquids. The investigation of water before
that of normal liquids was undertaken for two reasons; firstly because
of the desire to complete the work for water already begun, and

312 PROCEEDINGS OF THE AMERICAN ACADEMY.

secondly because in this and the following investigation a new method
for determining the compressibility was to be used, which had not
yet been proved to be reliable, but which could be tested by a com-
parison of the results obtained by this method with those already
obtained by another method at lower temperatures for water.

In addition to the data for liquid water, two other quantities were
determined incidentally in the course of the work, and are given at
the end of the paper. One of these is the experimental measurement
of the compressibility and thermal dilatation of ice VI between 0°
and 20° and 6360 and 10,000 kgm. The other is the measurement of
the volume of kerosene up to 12,000 kgm. and between 20° and 80°.

THe ΜΈΤΗΟΡ.

The method in its fundamental idea is as simple as it would well be
possible to devise. The substance, whose compressibility or thermal
dilatation is to be measured, is placed in a heavy steel cylinder in
which pressure is produced by the advance of a piston of known cross
section. The change of volume, given by the distance of advance
of the piston, is measured as a function of the pressure. The method
is simple, rapid, and above all, applicable to the highest pressures.
But there are a number of corrections which must be made, often
difficult to determine, which doubtless account for the slight use which
has been made hitherto of the method. Apparently, with the excep-
tion of the present work, it has been used recently only by Tammann,?
and by Parsons and Cook. Tammann and Parsons and Cook
applied it only to the measurement of compressibility, reaching
pressures of about 4000 kgm. The author has previously applied
it to the measurement of the thermal dilatation of water at tempera-
tures below 0° C. over a pressure range of about 6500 kgm.

The most serious of the errors which readily occur to one is that of
leak. It is almost essential to the success of the method to secure a
piston absolutely free from leak, and this has hitherto been a matter of
some difficulty at high pressures. Tammann did not entirely secure
this freedom from leak, but avoided it in large measure by the use of
a very heavy oil, such as castor oil, and still further lessened the error
by correcting for the slight amount of leak by measuring the amount
of liquid which escaped past the piston in a given time. This method
would not be applicable to the highest pressures, however, because

2 A. D. Cowper and G. Tammann, ZS. Phys. Chem., 68, 281-288 (1909).
3 Parsons and Cook, Proc. Roy. Soe. A, 85, 332-349 (1911).

BRIDGMAN.— THERMODYNAMIC PROPERTIES OF WATER. 313

of the freezing of the oil. Parsons and Cook were able to secure
entire freedom from leak up to 4000 kgm. by the employment of a
cupped leather washer combined with a brass dise of special design.
It has been the experience of all those who have worked with high
pressures, however, that no leather washer is capable of standing
pressures very much in excess of the limit of 4500 kgm., since the
leather rapidly disintegrates under the pressure. In the present
work the same form of packing was used which was used in the pre-
vious work on the freezing of water and mercury under pressure.
This has been proved in the previous paper to be absolutely free from
leak up to the highest pressures which can be sustained by the steel
containing vessels. In the present work this same packing has
proved itself to be reliable for the purposes of this method.

The question of the method of measuring pressure is also of con-
siderable importance in using this method, since the usual measuring
devices, such as a Bourdon gauge, cannot be applied, for reasons to be
discussed later, and attempts to calculate the pressure directly from
the force required to produce motion of the piston are likely to be in
error because of the friction of the packing. Parsons and Cook did,
however, adopt this latter method, and computed the pressure from
the known force required to move the piston. The effect of the
friction of the packings was allowed for in as large a degree as possible
by taking the mean of the readings during increasing and decreasing
pressure, assuming that the friction remained constant. The results
obtained by Parsons and Cook in this way were surprisingly good.
That the friction did remain fairly constant was indicated by the
constancy of the results and the fact that the curve nearly always
returned to the starting point; but it is doubtful if the method would
work at very much higher pressures because of the increase of friction
due te the flow of the softer parts of the piston. The brass washers
used by Parsons and Cook would almost certainly have upset under
two or three thousand more kgm., and it is the experience of the
author that it is difficult to obtain even steel washers which will
stand much more than 8000 kgm. without taking some set. In fact,
at high pressure there must necessarily be some plastic yield, in order
to follow the expansion of the cylinder. The result of this set in the
washers is that the friction becomes very irregular, and cannot be
assumed to be the same during increasing and decreasing pressure.
Variations in the amount of friction due to this cause of as much as
200 or 300% have been found at the higher pressures of this work.

_ The only escape from the difficulty seems to be to measure the

314 PROCEEDINGS OF THE AMERICAN ACADEMY.

pressure directly inside the cylinder. This was done by Tammann
by connecting a Bourdon gauge directly to the cylinder. But it is
known that the errors of the Bourdon gauge become rapidly more
serious at higher pressures,* due to the increase of hysteresis, so that
this gauge could not be used for the pressures of this experiment.
Furthermore, no Bourdon gauge has up to the present been made of
sufficient sensitiveness which is capable of standing more than 6500
kgm. In the present work the pressure was measured inside the
cylinder by inserting directly into it a coil of manganin wire, which
had been already calibrated against an absolute gauge. This method
of measuring pressure has been fully described in a previous paper.®
It was necessary for the purposes of the present work, however, to
make a somewhat more careful determination of the temperature
coefficient than was done formerly, and this determination will be
described in detail later. The method has shown itself perfectly
satisfactory and reliable in every respect. One coil of wire has been
used almost continuously for over six months, and occasional calibra-
tions have shown no change. These calibrations were made by
measuring with the coil certain fixed temperature-pressure points,
such as the freezing pressure of mercury or of ice VI, at some fixed
temperature.

The apparatus used in the present work is the same in most features
as that used in the former work, a detailed account of which has already
been given in the papers mentioned. Only the points in which this
has been changed will be mentioned here. It was a disadvantage of
the former method that the apparatus consisted of two parts; the
lower part, a cylinder containing the liquid to be measured, was placed
in a thermostat, and the upper part, a cylinder in which pressure was
produced, was exposed to the temperature of the room. When tem-
perature was changed in the thermostat below or pressure was changed
in the cylinder above, liquid passed from the one cylinder to the other,
experiencing in the transition a change of temperature, and so a
change of volume also. This change of volume accompanying a
known change of temperature varies in an unknown way with the
pressure, and to apply the correction it was necessary to make an
independent, set of experiments. In the present form of apparatus
the difficulty was avoided by including everything in one cylinder.
This cylinder contained the liquid under investigation, the pressure
measuring coil, and the piston by which pressure was produced. It

4 Bridgman, These Proceedings, 44, 201-217 (1909).
5 Bridgman, These Proceedings, 47, 319-343 (1911).

BRIDGMAN.— THERMODYNAMIC PROPERTIES OF WATER. 315

was placed in the lower part of the hydraulic press and, together with
the lower part of the press, was placed in the thermostat. The di-
mensions were so small that this could be done without increasing
to an unwieldly bulk the size of the apparatus, the four tie rods of the
press being 1 1/8” in diameter and their centers 6” apart. It is the
same form of apparatus which was used for the measurements on ice
VI up to 20,500 kgm. The present experiments run to only 12,000
kgm., however, since it is evidently an absolute essential to the success
of the method that there should be no permanent distortion of the
eylinder. It would be easily possible to reach pressures much higher
than those reached in this experiment, but it was felt that the risk
and the extra time involved in the probable construction of new
apparatus was not justified at present, when it seemed that the most
important work was to map out the field, obtain data for as many
liquids as possible, and determine the general nature of the significant
problems. Later, if there are crucial points which need the use of
much higher pressures, it will be a comparatively easy matter to obtain
them.

The cylinder used in this experiment was not the same as that used
in the previous work on water. This new cylinder is from a piece of
chrome-vanadium steel made in the electric furnace by the Haleomb
Steel Co., of Syracuse, N. Y. The steel itself is a wonderful product,
and without it the present investigation would not have been so easily
possible. It shows a tensile strength of 300,000 lbs. per sq. in. when
hardened in oil, and an elastic limit of about 250,000 lbs. These
figures are considerably in excess of those for the steel used in the
previous investigation. The steel furthermore is remarkably homo-
geneous, because of its production in the electrical furnace. One of
these pieces was pierced with a hole 1/8’ diameter and 13” long, and
the drill came through concentrically without any variation from the
straight line. The dimensions of the cylinder used in the present
work were 4 1/2” outside diameter, 13’’ long, inside diameter 17/32”
for the greater part of its length, with an enlargement to 3/4’ at the
lower end for the reception of the manganin coil. The original inside
diameter was 7/16’’. The cylinder was prepared for use by hardening
in oil and then subjecting to a pressure much in excess of that con-
templated for the actual experiment. The seasoning pressure was
over 30,000 kgm. Even under this high seasoning pressure the
cylinder showed very little permanent change of internal dimensions,
not stretching as much as 1/32.’ This is less than the amount of
stretch which has been found for any other grade of steel. The

316 PROCEEDINGS OF THE AMERICAN ACADEMY.

effectiveness of the treatment is shown furthermore in the fact that
in over six months of continual use the inside has not stretched by so
much as an additional 1/10000’’.. The hole was enlarged to a final size
of 17/32”, instead of keeping it as small as possible, because of the
difficulty of reaming out the hole so as to give a satisfactorily smooth
surface after the seasoning process. The difficulty was occasioned
by the hardness of the steel, and several attempts were necessary
before the desired result was produced.

The pressure measuring coil was the same as that used in the last
part of the work on ice VI. The construction of the insulating plug
was also the same as that used there. During the course of the work
it was necessary to take this plug apart several timess, because water
had reached the mica washers, and once or twice the mica washers
themselves have given way. These mica washers are the weakest
part of the entire apparatus as at present used, since they gradually
disintegrate and fail by shear after prolonged use, but it is a matter
of only a few hours to replace them. Every time after the insulating
plug has been freshly set up it has been tested for insulation resis-
tance, both during application of pressure and after release. The
resistance was in all cases as high as several hundred megohms, the
limit of the measuring devise. The steel of the insulating plug has
also failed once or twice by the “pinching-off effect”’® after long use.
This also is an easy matter to repair. Failure of this type is attended
with some danger, however, because of the violence of the explosion
with which the ruptured plug is expelled. The surest way of avoiding
this danger is to so mount the apparatus that the plug points at the
floor or other indestructible object.

The hydraulic press, the method of measuring the displacement of
the piston, and the details of the packing of the moving piston, were
the same as that used in the former paper.

In the use of the apparatus to determine compressibility there is
one serious error which did not enter into its use in the determination
of the change of volume during change of state, namely the correction
for the distortion of the cylinder in which the piston moves. At low
pressure the correction is relatively unimportant, and may be com-
puted from the theory of elasticity, if one is willing to assume that
the theory is sufficiently accurate for this type of stress. But at higher
pressures the correction becomes more important, increasing in
percentage value directly with the pressure, and is almost certainly

6 Bridgman, Phil. Mag., 24, 63-79 (1912).

BRIDGMAN.— THERMODYNAMIC PROPERTIES OF WATER. 917

not calculable by the theory of elasticity, because of the entrance of
such effects as hysteresis. ΤῸ determine the correction an auxiliary
set of experiments is necessary. Evidently if the true value of the
compressibility of some one substance were sufficiently well known,
then the apparent compressibility as determined by this method would
give the correction for the distortion of the cylinder. No such com-
pressibilities are known with any high percentage accuracy, but this
is not necessary, provided only that the uncertainty in the standard
compressibility is small in comparison with the distortion of the
vessel. The substance which most readily suggests itself because
of its small compressibility is steel, but this is a solid, whereas the
method is applicable directly only to liquids, so that some modifica-
tion of the procedure is necessary. Such a modification readily sug-
gests itself, and has been used by the author in the previous determi-
nations of the thermal dilatation of water at temperatures below 0°,
and has also been used by Parsons and Cook. The modification is to
replace part of the liquid under investigation by a steel cylinder, and
determine the compressibility of the liquid and the steel together.
The difference of two determinations, the one for the liquid alone,
the other for the liquid and the steel, gives a value for the difference
of compressibility between the liquid and the steel from which the
effect of the distortion of the vessel has been almost entirely elimi-
nated. Furthermore, the compressibility of the steel is so small in
comparison with that of the liquid that the slight uncertainty in the
value for the steel is of no account, so that the compressibility of the
liquid is given directly.

The application of this method would demand, then, that the inte-
rior of the cylinder be filled first with water and the apparent compressi-
bility determined, and then part of the water replaced by steel and
the apparent compressibility determined again. But this demands
that the coil of manganin with which the pressure is to be measured
come directly in contact with the water, which evidently cannot be
allowed because of the short circuiting produced by the water. It
seemed to be necessary, then, to devise some sort of protection for the
coil, which should not occupy so much volume as to introduce a
serious correction, and which should at the same time transmit the
pressure readily to the innermost parts of the coil. Considerable
time was spent in trying to devise such a protection. The scheme
adopted was to surround the coil with a small mass of vaseline enclosed
in a flexible sac, formed from the finger of a silk glove, and rendered
impervious to water by painting it over with several coats of the col-

318 PROCEEDINGS OF THE AMERICAN ACADEMY.

lodion of surgeons. This sac was tied with silk thread directly over
the end of the insulating plug. It was proved by trial that the
vaseline did not become so viscous under pressure as to refuse to trans-
mit the pressure with sufficient freedom, but the arrangement did not
prove itself as trustworthy as was to be desired. The collodion might
leak after several applications of pressure, which made it necessary
to reassemble the insulating plug and redetermine the elastic constants
of the apparatus, because the distortion included in the plug itself
was sufficient to introduce appreciable error. The device probably
could have been made usable with a little more effort, but it would
always have been more or less unsatisfactory, and would have been
applicable only to those liquids which do not attack the collodion,
whereas most of the organic liquids which it was desired to use in the
future do so attack the collodion. The attempt to protect the coil
was abandoned after a month’s work, therefore, and the method re-
placed by another, which at first sight introduced additional com-
plications, but which is really just as simple as the first, and has the
advantage of being applicable with only slight modifications to the
investigation of other liquids.

The modified method used two liquids in every determination, one
beside the one whose compressibility is to be measured. The water
under investigation is placed in a thin shell of steel fitting the inside
of the cylinder. This shell, when in position in the cylinder, is sur-
rounded on all sides and above and below by kerosene, which below
transmits pressure to the manganin coil, and above reaches to the
moving piston with which pressure is produced. In the auxiliary
experiment to eliminate the effect of the distortion of the cylinder, the
shell with water is replaced by a solid cylinder of steel, and the quan-
tity of kerosene remains the same as before. The motion of the
piston due to the change of volume of the kerosene remains the same
in the two experiments, therefore, and the difference of readings of the
two sets gives directly the difference of compressibility between the
water and the steel. The disadvantage of the method is that it is
not possible to use so large quantities of water as in the former method,
because the steel shell containing the water remains invariable in
length under pressure, and enough kerosene must be introduced origi-
nally to take up the change of volume of the water in this shell as well
as the distortion of the other parts of the apparatus. - The reduction
in the quantity of water under experiment is not greater than 30%,
however, and the other advantages more than outweigh this com-
paratively small loss of accuracy.

BRIDGMAN.— THERMODYNAMIC PROPERTIES OF WATER. 319

The procedure in using the apparatus in this finally modified form
is as follows. The manganin coil is first screwed into the lower part
of the cylinder. The rubber washer used to make this plug tight is
one cut with a standard set of cutters, so that all the washers used for
this purpose are always the same in size. This insures that the
distortion due to the compression of the washers shall always be the
same. The steel shell with the water in it is next introduced from
above. The quantity of water is previously determined by weighing.
It is desirable not to fill the shell to closer than 1/4” of the top, ex-
perience having shown that otherwise water is likely to spill out and
find its way to the manganin coil. The kerosene is next introduced
into the cylinder from above. To ensure entire filling of all parts of
the apparatus and the exclusion of air, only part of the kerosene is at
first poured in, the air is then exhausted by attaching the mouth of the
cylinder to an air pump, or simply by exhausting with the lungs, and
then the remainder of the kerosene poured in. The amount of kero-
sene is determined by weighing the dish from which it is poured before
and after filling. Because of the wetting of the dish by the kerosene
it is not always possible to obtain exactly the amount of kerosene
desired each time, but the variation is seldom over 0.02 gm., and the
very slight effect of this discrepancy may be corrected for, as will be
described later. Finally the movable plug is introduced into the
top of the cylinder, taking particular pains not to allow any of the
kerosene to escape in the process. Here again the rubber washer used
has been cut with standard cutters, so that the amount of rubber
used here is also the same in all the experiments. The cylinder is
then placed in the thermostat, and the zero of the manganin coil
read at the temperature of the room. The thermostat is then adjusted
for the desired temperature and the cylinder seasoned for the run by
the application of pressure.

A preliminary seasoning is necessary because of the hysteresis
shown by the cylinder, and this hysteresis is shown with respect to
both pressure and temperature. Many of the early results were
somewhat in error because the necessity of this seasoning for tempera-
ture as well as for pressure was not clearly recognized. The method
of seasoning to be adopted depends on the kind of data which it is
desired to obtain from the run, whether the compressibility at con-
stant temperature or the thermal dilatation at constant pressure.
If it is desired to determine the isothermal compressibility, the season-
ing consists simply in raising the pressure through the entire range
and releasing several times. It was found by experiment that three

320 PROCEEDINGS OF THE AMERICAN ACADEMY.

such preliminary excursions were sufficient; after this the cylinder
settles down into a state in which the normal hysteresis cycles are
retraced with perfect regularity. Of course it is necessary to make
the compressibility determinations immediately after this seasoning,
as the effect gradually disappears with time. The time occupied in
making the final readings to 12,000 kgm. and back with increasing
and decreasing pressure, making in all 20 readings, might vary from
two to three hours. After every change of pressure it was necessary
to wait for the temperature effect of compression to disappear; this
time was from 5 to 7 minutes.

If the thermal dilatation under constant mean pressure is to be
determined, the seasoning consists simply in taking the cylinder once
through the temperature range contemplated as well as through the
pressure range. A word of description as to the general procedure
in determining the thermal dilatation at constant mean pressure will
not be out of place. The general plan is to change the temperature
while the piston is kept invariable in position, and therefore while
the volume is also approximately constant. The rise of temperature
produces a rise of pressure, so that after the rise of temperature it is
necessary to bring the pressure back to the former value by with-
drawing the piston if the change of temperature has been an increase,
or advancing it if the change of temperature has been a decrease.
The amount, by which the piston is withdrawn, as also the new final
pressure, is noted. The temperature is then changed again, and the
same set of readings made again. Thus every observation at any
given temperature involves two readings of the position of the piston
and the corresponding pressure. The slight change of pressure during
the changes of temperature carries with it hysteresis effects, which
it is necessary to avoid by previous seasoning, exactly as for pressure
changes over a wider range. ‘Two processes of seasoning are necessary
for temperature, therefore, one a larger one for the entire temperature
range, and another smaller one for the slight changes of pressure
incident to the changes of temperature. This second seasoning is
made after the first more extensive seasoning simply by running the
pressure back and forth several times through the small range of
pressure to be met with during the temperature changes. This small
range was determined by preliminary experiment.

In the actual calculation of the results there are a number of
corrections to be applied. These will now be discussed in detail
separately. In the first place the temperature coefficient of the
manganin coil has to be determined with particular care. This is

BRIDGMAN.— THERMODYNAMIC PROPERTIES OF WATER. 321

because the pressure changes brought about by changes of temperature
during the determinations of the thermal dilatation are comparatively
slight, so that any change of the pressure coefficient of the coil brought
about by the change of temperature appears in the result greatly
magnified. Thus for the sake of example, we will suppose that a
change of temperature of 20° produces a change of pressure of 400
kgm. at 10,000 kgm. total pressure. This figure is a fair average of
the results to be met with in practice. If now the pressure coefficient
of the coil is changed by 1% by this same rise of temperature, the
pressure will thereby appear to have risen 500 kgm. instead of the
actual 400, introducing an error of 25% for a change in the constant
of the coil of only 1%. In addition to the effect of the temperature
coefficient of the coil, there is an effect due to the change of the zero
of the coil with temperature, but this change can be determined by
observations of the temperature coefficient of the coil at atmospheric
pressure and is easy to measure with the requisite accuracy.

The change in the pressure coefficient of the coil with temperature
is more difficult to determine with the desired accuracy. It would
not be possible to determine this by a direct calibration against the
absolute gauge with which the mean value of the coefficient has been
determined, for the reason that the absolute gauge itself is not accu-
rate to better than 1/10%, and this would still leave a possible error in
the thermal dilatation of 2.5%. To affect the desired calibration,
some standard of pressure must be used which can be relied on to
remain absolutely constant. Such a standard pressure is evidently
afforded by the transition point of the liquid to the solid form of any
convenient substance at some fixed temperature. In previous work
the transition points of both water and mercury have been determined
at various temperatures with an accuracy in the absolute pressure of
1/10%. To make the calibration it is only necessary to keep the pres-
sure constant automatically at this known value by placing in com-
munication with the chamber in which is the manganin coil to be
calibrated another chamber in which are the liquid and solid forms
of the substance whose transition temperature and pressure are
known. This second chamber is to be kept at constant temperature
accurately enough so that slight changes in this temperature will not
produce changes of more than the allowed amount in the transition
pressure. For this purpose the most convenient fixed temperature
seems to be that of melting ice at atmospheric pressure, and the most
convenient substance to use mercury, because of the sharpness of the
freezing, and the ease with which it can be obtained pure.

aoe PROCEEDINGS OF THE AMERICAN ACADEMY.

The actual arrangements in making this calibration for the tempera-
ture coefficient of the pressure coefficient of the coil were as follows.
The upper cylinder of the hydraulic press in which pressure was
produced contained in addition to the moving plunger a steel shell
in which was as large a quantity of mercury as convenient, about
150 gm. This upper cylinder as well as the entire lower part of the
press was surrounded by a tank containing ice and water, by which
the temperature of the mercury could be kept continuously and
accurately at 0°. A heavy nickel steel tube led out of the lower end
of the upper cylinder through the bottom of the tank, and connected
with the lower cylinder in which was the manganin coil under exami-
nation. This lower cylinder was placed in an oil bath with thermo-
static regulation, by which the temperature could be set at and
retained at any desired value. The experimental procedure was as
follows. The temperature of the lower bath was set at any desired
value, and the pressure increased until the freezing point of mercury
at 0° was slightly passed. The mercury then froze, with decrease of
volume, thus bringing the pressure back to the known equilibrium
value at 0°. After equilibrium had been reached, the resistance of
the manganin coil was read. The pressure was then lowered slightly
by withdrawing the piston. This was followed by automatic restora-
tion of the equilibrium pressure, brought about by melting of the
frozen mercury with increase of volume. The transition point was
always so sharp that no difference could be detected in the equilibrium
pressure whether approached from above or below. The temperature
in the lower cylinder containing the manganin was then changed to
another desired value. This change of temperature, if it were an
increase, would naturally carry with it a rise of pressure, but the
pressure is then automatically lowered by the freezing of the mercury.
After a steady state is reached, the new value of the manganin re-
sistance is read, and then the pressure lowered again by slightly
withdrawing the piston, and the value of the resistance noted again
after the equilibrium conditions have been restored from below.
In this way the coil can be calibrated over the entire temperature
range contemplated for the experiments. Of course this calibration
is good only for one fixed pressure, but in view of the proved linearity
of the pressure-resistance relation within 1/10% from 0° to 50°, it
seemed safe to let the calibration go at this one determination, particu-
larly since no effect could be found.

The calibration of the manganin was carried out at five tempera-
tures; 25°, 45°, 65°, 85° and 110°. No appreciable change of the

BRIDGMAN.— THERMODYNAMIC PROPERTIES OF WATER. 323

coefficient could be found for the four lower temperatures, but be-
tween 85° and 110° there is a very perceptible change of 1%. But
since the range of temperature of the actual experiment did reach
over 80°, no correction was applied to the observations for this effect.
It is to be noticed that this result is valid only for this one coil, since
previous work, both by Lisell 7 and by the author, have shown that
different pieces from the same spool of wire may show slight variations -
in the temperature coefficient, which is sometimes positive and
sometimes negative.

In addition to this special calibration for slight relative changes
in the pressure coefficient with temperature, the absolute value of the
pressure coefficient has been checked from time to time during the
course of the experiments. This could be done conveniently with the
apparatus as used for the compressibility determinations by determin-
ing the transition point of ice VI, or of mercury at known temperatures.
These calibrations have shown no change whatever in the pressure
constant of the coil.

It has already been stated that the actual measurements involve
two sets of readings, one with the apparatus filled with water, kerosene
and asmall amount of bessemer steel, and a second set with additional -
steel replacing the water. By subtracting the piston displacement at
any given pressure for these two sets of experiments a value is obtained
which gives approximately the piston displacement for the water alone,
and from which the effect of the distortion of the vessel has in large
measure been eliminated. But a moment’s consideration will show
that the effect of distortion has not been entirely eliminated, and it
is necessary to apply a correction for the slight residual effect. The
correction comes because of the fact that the position of the piston
at corresponding pressures is not the same in the two sets of experi-
ments, so that the subtraction leaves still uncorrected the distortion
due to the part of the cylinder exposed to pressure in the one set of
experiments and not so exposed in the other. This correction can-
not be determined directly, and the only way seems to be to calculate
it by the ordinary theory of elasticity, taking for the constant of the
steel the values under ordinary conditions, which are known not to
vary much even for the most different varieties of steel. There is
undoubtedly some error in the correction as so determined, but the
total value of the correction is at best small, and any such error is
relatively unimportant.

. 7 Lisell, Om Tryckets Inflytande p& det Elektriska Ledingsmotstandet
hos Metaller samt en ny Metod att Mita Héga Tryck (Diss. Upsala, 1909).

324 PROCEEDINGS OF THE AMERICAN ACADEMY.

The compressibility of the steel replacing the water also evidently
enters as a correction factor. This compressibility is relatively slight,
and it has been previously determined over a range of 10,000 kgm.
The value of the compressibility of the steel also changes with the
temperature, but this change has also been shown by direct experi-
ment to be slight, so shght that it can
be neglected. In the present work the
value was assumed to be constant, in-
dependent of temperature and pressure,
having the value 58 Χ 10% per kgm.
per sq. em.

There is also a correction to be
applied for the compressibility of the
kerosene, if the amount does not happen
to be the same in the two sets of ex-
periments, and it was seldom that the
amount was exactly the same. The
variation was very small, however, and
the correction is easy to apply if the

Figure 1. Diagramshowing compressibility of the kerosene itself
the position of the piston. To jis known. This was determined with
Fh ae τ ce be ΣΝ sufficient accuracy for the purpose by
the compressibility. an independent set of experiments,

exactly the same in principle as those
for determining the compressibility of water. The results of these in-
dependent experiments are given at the end of the paper.

The following formulas were used in making the corrections, and
include all the corrections mentioned qualitatively above. Figure 1
shows the position of the piston at different times in the course of
the experiment. The left hand part of the diagram (denoted by the
suffix 1) is for the cylinder when it is filled with kerosene and bessemer
steel only, and the right hand part (denoted by the suffix 2) is for the
cylinder when it contains water, kerosene, and bessemer steel. A and
C are the positions of the piston at the arbitrary zero of pressure in
these two sets of experiments (this arbitrary zero was usually taken
in the neighborhood of 2000 kgm. and will be denoted by p), and B
and D indicate the position at some higher pressure, the same in
the two sets, which will be denoted by p’. We now write down
the expressions for the total volume of the cylinder beneath the
piston.

it 2

BRI DGMAN.— THERMODYNAMIC PROPERTIES OF WATER. 329

ra at eee ae an ee
Ag BOVE ΝΞ ΕΝ

At C, V2 = Κὰ + Vo no + V2.
At D, Vol = Vox! + Vo! no + Τὼ

where the suffixes Καὶ, H»O, or S indicate that the volume is for the
kerosene, the water, or the steel respectively.
Subtracting the equations above from each other, we obtain

(Vy = ‘ee (Vy - V,’ = (Viz = γι) = (Vo, — Vx")
Ἐ τ ( Η0-- Γ' H,0) ΞΕ Fa ar V5’) =< (Vo, ag to °

We now denote by Al the difference of displacements at the two
positions A and C, and by Al’ the corresponding difference at the
positions B and D. We now assume that V; and V2 differ only by
the volume of the cylinder of length Al, and similarly Κι and V2’
differ only by the cylinder of length Al’. This assumption is justified
if only the positions of the pistons at A and C are so far removed from
the end of the cylinder that the end effects in the distortion of the
interior are the same in the two cases. This condition has been shown
_ by the theory to be satisfied when the distance is two or three diameters,
as it always was in these experiments. Hence we may write,

ha va 80 (1+ ap) Al
Vy’ -- V./ = δῇ ( + ap’) Al
where so is the initial section of the cylinder at atmospheric pressure,
and a is the factor of proportionality by which this is changed with
pressure. Now if we call the displacement form A to B, D; and from
C to D, Do, then.
1. - Al = D; + AF

and the above equation may be thrown into the form
Vi — V2 — (Vy — V2!) = — 89(D2 — Dy) (1 + a. p’) + 59 Ala (p — p’)

We now make use of the fact that the total change of volume of
any substance under pressure is proportional to its mass. If Av
(positive for a decrease) is taken as the change of volume of 1 gm.
between p and p’, then,

Vix -ς Vu — (Vo, --- Voy’) ΞΟ ἊΝ UE (muy, -- m2},)

Vo πὸ — Vo π,0 = AtH,0™ Β,0
= Vay = (ie, = Vo, = A 0; (rr, — m2.)

326 PROCEEDINGS OF THE AMERICAN ACADEMY.

This enables us to solve the equations for the compressibility of the
water and the kerosene, giving,

1
AvH,o = Feet (Dz — Dx) (1 + ap’) — δολία (p — p’)
+ Av, (my, — mez) + Av, (m4, — mes)}

and for the kerosene, when the two runs are both made with kerosene,
as in determining the data for kerosene given at the end of the paper,

1
Av, = ———— {5 (D2 — D1) (1 + ap’) — soAla (p — p’) — Ar,
Mor — Mik

(m2, — m5) }

The considerations so far apply only to the measurement of com-
pressibility at constant temperature. The thermal dilatation is deter-
mined in the same way as the compressibility from the difference of
the thermal dilatation as given by two sets of experiments, one with
the water replaced by steel. The piston displacement is not the same
at corresponding pressures here, either, and a correction is to be
applied for the thermal dilatation of the part of the cylinder which is
exposed to pressure in the one experiment and not so exposed in the
other. But this portion of the cylinder to which the correction is
to be applied was seldom more than 1” in length, and the correction
for this amount of steel is negligible in comparison with the thermal
dilatation of the total quantity of water. There is also a correction
to be applied for the dilatation of the steel replacing the water, and
this correction is small but not negligible. It was assumed that the
dilatation of the steel remains independent of the pressure over the
pressure range used, and the value for ordinary mild’steels at atmos-
pheric pressure was employed. This value is 0.000039 for the cubic
expansion per degree Centigrade.

The corrections to the measurements of the thermal dilatation are
not so serious or so important as those for the compressibility, since
the total effect is much smaller and most of the corrections become
negligible. The method of determining the thermal dilatation has
already been explained to be that of observing the change of pressure
brought about at constant volume by a known change of temperature.
From this the change of volume with temperature at constant pres-
sure can be immediately determined if the slope of the p-v curve at

set a3 (x) (= ) Op ov\ .
that point is known, for \ ar = —( — ( Mg ee ers

BRIDGMAN.— THERMODYNAMIC PROPERTIES OF WATER. 327

dently given directly from the curves for compressibility at constant
temperature. The slope of this curve changes somewhat with the
temperature, so that a correction should be applied for this, but the
change is so slight at the higher pressures that for this purpose the
compressibility can be assumed constant. At the lower pressures,
below 2500 kgm., the change cannot be neglected, and another
method of computation must be applied.

The thermal dilatation at low pressures was.determined by taking
directly the difference between the isothermals traced out at different
temperatures. This method is not applicable at high pressures be-
cause the irregularities of isothermals traced at different times is
sufficient to make their difference an inaccurate measure of the slight
change of volume with temperature, but at the low pressures, the
errors introduced by hysteresis and other irregular action of the steel
cylinder are so slight that the method may be used directly to give the
value of the compressibility, and by taking the differences, the value of
the thermal dilatation. In fact it would seem that the method would
be applicable with slight modifications to the determination of the
compressibility of a great variety of substances at low pressures, and
it is very much more rapid than the methods hitherto used.

A special setting up of the apparatus was necessary for the experi-
ments at low pressures, because in order to be able to reach low pres-
sure on release of pressure it is necessary that the friction in the
movable plug be not too high, and if the pressure has once been run
to so high a value as to upset the plug, the friction becomes so great as
not to permit release of pressure to much below 1500 kgm. For these
experiments, then, the plug was made initially a push fit for the hole,
by making it about 0.0015’’ smaller than when used for the higher
pressures, and in performing the experiment the pressure was never
pushed beyond 2500 kgm. In other respects the experiments at low
pressures were the same as those at higher pressures. It was not
necessary to take quite so elaborate seasoning precautions at these
low pressures, however.

With regard to the amount of hysteresis or elastic after-effects
to be met in the experiments, the difference of the displacment with
increasing or decreasing pressure usually amounted at the middle of
the range to 0.03 in. This amount was very uniformly consistent,
indicating that the cylinder had really settled down to a steady be-
havior. The piston always returned to the starting point to within
the limits of accuracy of reading, indicating that there was no leak or
permanent set, or wearing of the packing in appreciable amount.

328 PROCEEDINGS OF THE AMERICAN ACADEMY.

Of course the experiments at low pressures showed very much less
hysteresis, in fact it was so small as to be almost imperceptible. The
effect of hysteresis was eliminated as far as possible by using for the
displacement at any pressure the mean of the results with increasing
and decreasing pressure. The hysteresis was so constant that it
would probably have been sufficient to have used consistently the
results either at increasing or decreasing pressure. The actual pro-
cedure has, therefore, the weight of two independent determinations.
In the determinations of thermal dilatation, on the other hand, the
hysteresis effects were so much smaller, that except for one run initially
to show that there was no effect of this kind, the readings were always
made either only with increase or only with decrease of temperature
for any mean pressure, never with both increase and decrease.

THE Data.

Three independent sets of experiments were performed to give the
change of volume with temperature and pressure over the entire range;
namely the isothermal compressibility at pressures over 2500 kgm.,
the isothermal compressibility and the thermal dilatation at pres-
sures below 2500 kgm., and the thermal dilatation at pressures over
2500 kgm. ‘This is the actual order of experiment, but for the pur-
poses of presentation it will be better to use the natural order, pro-
ceeding from low to higher pressures.

COMPRESSIBILITY AT Low PRESSURES.

The method with the present form of apparatus is not very sensitive
at the low pressures, and not many measurements were made over
this range. Two sets of determinations of compressibility were made,
the first at 20°, 40°, 60°, and 80°, and the second at only 20° and 80°.
Here, just as for the measurements at the higher pressures, there is
always sufficient friction in the packing after the pressure has once
been applied not to permit of close enough approach to the zero to
make an extrapolation back to the zero justifiable. And if the extra-
polation to the zero is to be made from the readings during first appli-
cation of pressure, special effort has to be made to design the washers
so as to avoid small initial distortions. For this reason only the
second of the above sets could be used by extrapolation back to the
zero of pressure. The readings of volume at 20° and 80° were corrected
back to 40° from the thermal dilatation as determined by this same set
of experiments, so that we have from the above two values for the

BRIDGMAN.— THERMODYNAMIC PROPERTIES OF WATER. 329
compressibility at 40° up to 2200 kgm. The first set of readings at
five temperatures is consistent with this latter set above 1000 kgm.,
but at the lower pressures gives values for the compressibility which
are doubtless too high. To find the best value for the change of
volume at low pressures-we now have three sets of data, those of the

TABLE I.

VoLUuME OF WATER AT 40° AND Low PRESSURES BY DIFFERENT Meruops.

Pressure,
kgm.
ΟῚ." Piston. Amagat.

Change of Volume, cm.*/gm.

Final
Mean.

.0000 0000 .0000
.0203
.0376
.0532
.0673

present determination, those of the previous work by the method of
the steel piezometers, and the results of Amagat. The most probable
value for the change of volume has been found by comparing these
three sets of values. These values are given in Table I, as also the
mean selected from them as the most probable value from the data
at present in hand. In taking this mean, the greater weight has been
given to the values of Amagat at the lower pressures, since his method
of measurement was doubtless more accurate for the low pressures
than the present method, which was intended only for high pressures,
but at the upper end of the range in the neighborhood of 2000 kgm.,
more weight has been given to the present determinations. It is to
be noticed that the mean value taken as final is lower than that found
by Amagat. This divergence is in the same direction as that found
by Parsons and Cook, who worked with a method like the present one.
The deviation found by them from the results of Amagat is greater
than that adopted here.

330 PROCEEDINGS OF THE AMERICAN ACADEMY..

DILATATION AT Low PRESSURES.

For the thermal dilatation at low pressures, two sets of determina-
tions were made; one was the series of isotherms at four different
temperatures already mentioned, and the second was by the method
adopted for the higher pressures, namely variation of temperature
at constant mean pressure. The method of calculation for this lower

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Ficure 2. The change of volume of water for intervals of 20° plotted
against pressure.

range was not the same as that employed for the higher pressures,
as already explained, due to the fact that the slope of the isothermals
is not sufficiently independent of temperature at the lower pressures.
The method of computation adopted here was a graphical one, by
plotting the observed volume and pressure points for the different
temperatures and taking the difference between adjacent curves
graphically. The temperatures at which the different determina-

BRIDGMAN.—— THERMODYNAMIC PROPERTIES OF WATER. 991

.tions were made were not exactly the even temperatures desired,
namely 20°, 40°, and 60°, and 80°, but they were in all cases within
a few tenths of a degree of these temperatures. The results were
corrected to these even temperatures by assuming the mean variation
with temperature over the whole temperature range to hold for the
few tenths of a degree on either side. The final result given by the
data is the total change of volume for an interval of 20°; from 20°
to 40°, from 40° to 60°, and from 60° to 80°. The mean of the results
of the two sets of experiments is shown with satisfactory accuracy in
Figure 2, on which are plotted all the values obtained by the different
methods. The results for the low pressures are shown in the full
black circles. These values are seen to extrapolate, without forcing,
to the values already found by other observers for atmospheric pres-
sure, and they also make fairly good connections with the values found
by the other method for the higher pressures. In view of this agree-
ment it did not seem to be necessary to make further determinations
of this quantity.

CoMPRESSIBILITY AT HicH PRESSURE.

The determinations of the isothermal compressibility at higher
pressures extended over a considerable interval of time and are more
numerous than any of the other determinations. In all, twelve deter-
minations of this quantity were made, at five different temperatures.
These determinations include those made during the early course of
the experiment, when the attempt was being made to find the thermal
dilatation directly from the difference of compressibility at different
temperatures. A little work with the method showed that it was not
sufficiently accurate for the purpose, but the results obtained then can
be used to give the compressibility at the standard temperature, 40°,
by applying the temperature correction found from the later more
accurate results. The temperature of 40° was chosen as the standard
because this is the lowest of the 20° intervals at which the water is
liquid up to 12000 kgm.

The results of these twelve determinations, extending over a period
of three months, are shown in Table II. The results as given are
reduced to 40°, but the temperature at which the original measure-
ments were made is given also in the table. Two of these sets of
determinations differ considerably from the others, and were discarded
in taking the mean, although as it happens one of these discarded sets
is too high and the other too low, so that it makes very little difference

PROCEEDINGS OF THE AMERICAN ACADEMY.

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BRIDGMAN.— THERMODYNAMIC PROPERTIES OF WATER. 333

in the final result whether they are included in the mean or not. For
convenience in making the computations the pressure was taken in
units given conveniently by the changes of the manganin resistance,
the intervals of pressure corresponding to a displacement of the slider
of the bridge wire of 5 em.

TABLE III.

CoMPARISON OF REsuLts BY Two MetTuHops ror CHANGE OF VOLUME OF
WATER AT 20°.

Pressure, : Pressure,
kgm.

Piston. Piezometer. cm.” Piston. | Piezometer.

«Ο000 .0814 .0821

.0954 0964
. L078 .1105

. 1190 . 1229

These results, reduced to 20° are shown compared with the results
of the previous determination in Table III. It is seen that the newer
results are lower than the former ones, the difference being about 1%,
except at the higher pressures, where the difference is greater. The
agreement is perhaps not as close as could be desired, but at present
there seems to be no way of choosing between the results. There is
no consistent discrepancy, which would indicate a fundamental error
in the present method, such as in the correction applied for the dis-
tortion of the steél cylinder, for example. If there were any such
error it could be eliminated by so choosing the correction as to make
the present results agree with the former ones. In the absence of
any means of deciding between the two methods therefore, and since
the results by the present method reach over a wider temperature and
pressure range, and since also the method has been used much more
extensively than the former one and with no greater discrepancy in
the individual results, these present results have been accepted as
the best ones. But it must be remembered that the absolute com-
pressibility given here may be m error by as much as 1% at the higher
pressures. This error, however, will not be found to invalidate any
of the conclusions drawn from the data.

334 PROCEEDINGS OF THE AMERICAN ACADEMY.

DILATATION AT HicH PRESSURES.

The determinations of the thermal dilatation at the higher pressures
were made on four occasions. The first two of these were preliminary,
during which was discovered the necessity of seasoning for tempera-
ture as well as for pressure, and also the necessity for the secondary
pressure seasoning over the small range of pressure accompanying
the changes of temperature. These first two determinations, while
confirming the results of the two later ones, were not given much
weight in selecting the final value. The method of computation
adopted in finding the thermal expansion from the data requires
mention. At first an attempt was made to apply the same graphical
method which has been already explained in its application to the
determinations at the lower pressures. This method involves the
drawing of a curve of the same general slope as the compressibility
curve through the two points giving piston displacement against
pressure at each temperature. But it was found that even after the
seasoning for the small pressure range involved here, the points were
too irregular to give good results by this method. The irregularities
may be due to residual hysteresis, but are more probably due to
slight irregularities brought about by the motion of the piston itself.
These irregularities are too minute to have any effect on the com-
pressibility determinations. The best way to avoid them is to utilize
in the computations only those readings during which the piston
remains stationary. This means that only the change of pressure
accompanying a change of temperature is used in making the computa-
tions, the second reading at any temperature by which the pressure is
brought back to the mean value being ignored. The change of
volume at constant pressure for the given change of temperature is
then computed from the known change of pressure at constant volume
and the previously determined change of volume with pressure at
constant temperature. In making this computation it is generally
necessary to make two corrections; one to bring the temperature
interval to the exact 20° desired for the final results, and the second
to correct for the very slight change of measured piston displacement
accompanying the change of temperature. This change of displace-
ment is seldom over 0.003”. It is probably not due entirely to actual
motion of the piston, but partly to temperature changes in the bars
of the press which dip into the thermostat. That this method of
computing the results is preferable to the graphical one previously
mentioned is shown by the fact that this method gives very much

BRIDGMAN.— THERMODYNAMIC PROPERTIES OF WATER. 330

more uniform and consistent results when applied to the same set of
data than the graphical method.

The method of computation adopted was first to calculate inde-
pendently from the individual observations of each set of readings the
thermal dilatation at six mean pressures between 2200 and 12,000 kgm.
Then smooth curves were drawn through these points for each set of
readings, the curves being spaced in the best way so as to give regular
variations with both pressure and temperature. The values given
by the smooth curves of each set of readings were then combined into
the grand mean. In taking this grand mean, as already explained,
almost the entire weight was given to the last two sets of readings.
The agreement between the different sets was best at the higher
temperatures, 60° to 80°, and about equally good between 20° and
40° and 40° and 60°. ΑἹ] four sets of curves, while not agreeing very
well as to the numerical value of the coefficient, do agree as to the
general character of the results, which are, perhaps, not quite what
would be expected. The unexpected feature is the change in the
sign of the temperature derivative of the dilatation at the higher
pressures. At the low pressures the dilatation is greater at the higher
temperatures, but at the higher pressures the thermal dilatation
becomes less at the higher temperatures. This essential feature is
verified on all four sets of curves. There are indications that it may
be an essential characteristic of the behavior of any normal liquid at
high pressures, and that it is not peculiar to water alone. This is
shown by the work on kerosene, and is also indicated by the work at
present being done on still other liquids. This will be taken up in
greater detail later. The other feature not to be expected is the
increase in the value of the thermal expansion between 20° and 40°
at the higher pressures. It is to be distinctly expected that the ther-
mal dilatation will decrease with rise of pressure, as indeed it does for
all the other intervals of temperature, but this rise between 20° and 40°
is shown by all the sets of determinations and seems to be an un-
doubted fact. It is probably connected with some new abnormality
in the behavior of water at the higher pressures, which may be con-
nected in some way with the appearance of the new variety of ice.

The values finally taken as the best values for the thermal dilatation
are the mean of the results of the four determinations, much the greater
weight being given, as already explained, to the two latter determina-
tions. Figure 2 gives these results, as also those of the other methods
at the lower pressures. The agreement of the two best determina-
tions at the higher pressures is about 5% for the lower temperature

336 PROCEEDINGS OF THE AMERICAN ACADEMY.

interval from 20° to 40°, 3% for the interval 40° to 60°, and 2% from
60° to 80°. The order of accuracy to be expected in these thermal
measurements is not so great as that in the compressibility determina-
tions, therefore, but perhaps the accuracy is as great as could be
expected when one considers the smallness of the quantities involved,
and the difficulty of making such measurements at high pressures.
At any rate the absolute value of the coefficient cannot be very much
inerror. This is made probable by the agreement with the known
values at atmospheric pressure. The accuracy is at least high enough
to enable us to expect a fairly good quantitative description of the vari-
ous thermodynamic quantities under high pressure, even those most
sensitive to error. The calculation seems to be worth while carrying
through in some detail, because such calculations seem never to have
been undertaken for any substance, even for the low pressure range up
to 3000 kgm., which is the range over which compressibility determi-
nations have been previously made.

Discussion OF RESULTS.

The first necessity for a calculation of the various thermodynamic
quantities is as accurate as possible a knowledge of the relation
between pressure, temperature and volume over the entire pressure-
temperature plane. It may be shown that this is sufficient to com-
pletely determine the thermodynamic behavior of the substance if in
addition the behavior of the specific heat at constant pressure, for
example, is known in its dependence on temperature at atmospheric
pressure. This may be assumed to be known well enough for the
present purpose. The first and the most important outcome of the
present data is, therefore, the construction of a table giving pressure,
volume, and temperature at sufficiently close intervals. In con-
structing this table the basis of computation was the compressibility
as determined at 40°. This, together with the known value of the
volume at 40° and atmospheric pressure, gave the volume as a function
of the pressure down a line through the middle of the table at 40°.
The values of the volume were tabulated for intervals of the pressure
of 500 kgm., the values found graphically from smooth curves through
the experimental points being so smoothed as to give smooth second
differences. The values of the change of volume for intervals of 20°
now were combined directly with these values to give the volume
as a function of the pressure at 0°, 20°, 60°, and 80°. To find the
intermediate values of the volume, smooth curves were drawn through

BRIDGMAN.—— THERMODYNAMIC PROPERTIES OF WATER. 337

these five points at every constant pressure, and the intermediate
values so chosen as to given smooth values for the second differences
over the entire temperature range. The values for the points below
zero, Which are also given in the table, were taken directly from the
previous work, the values for the dilatation found there being kept
without modification, but the present value for the compressibility
at 0° being used. The differences so introduced may be seen by com-
parison of the two tables to be only slight.

The table gives the volume to only four significant figures, since
this is as many as the variations in the values of the compressibility
would entitle one to, but in making the calculations of the thermal
expansion it was necessary to keep three significant figures for the
expansion, which would mean five figures in the table.

The thermal dilatation per degree rise of temperature was deter-
mined from the values used in the construction of the table for the
differences of volume at 5° intervals by dividing by 5, and using the
result as the thermal expansion at the mean temperature. The values
of the total change of volume for five degree intervals had been
smoothed so as to give smooth second differences, so that the dilata-
tion as found in this way was smooth also with respect to the second
differences, and could be used directly to give the second tempera-
ture derivative of the volume at constant pressure.

The difference of thermal dilatation at different temperatures can
evidently be combined with the known compressibility at 40° to
give the compressibility as a function of the temperature.

These several quantities so determined; the compressibility, the
thermal expansion, and the second temperature derivative of the
volume, in their dependence on temperature and pressure, are the
basis of most of the calculations of the quantities of thermodynamic
interest to be given presently. The accuracy of most of these quan-
tites is not so high but that they can be shown as well in figures as in
tables, and this manner of presenting them has been chosen as giving
the most ready general survey of the facts.

The tables and figures follow. The results are given simply for
themselves, without much comment, except to call attention to the
unexpected features, or those properties which seem to be peculiarly
characteristic of high pressures. It would not be safe to generalize
from the behavior of this one liquid, abnormal at low pressures, to
the general behavior to be expected for any liquid for high pressures
and the bearing on a possible theory of liquids. Such a general
treatment must be reserved for another paper, when the data for
more liquids are in hand.

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PROCEEDINGS OF THE AMERICAN ACADEMY.

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BRIDGMAN.— THERMODYNAMIC PROPERTIES OF WATER. 339

In presenting the results, the quantities have been arranged in
order of simplicity of the thermodynamic formulae, which is also
the order of directness with which they are derived from the experi-
mental data.

Volume, cm.? per gm.

4 oo

aoe 8

60} X "Wo / ᾿πϑν ‘aunssotg
4

a Π ΟἿ 6 8

Ficure 3. Isothermal lines for water, showing volume against pressure.

In Table IV are given the values of the volume for intervals of
pressure of 500 kgm., and intervals of temperature of 5°. The table
does not require comment. It was computed in the way already
described. The values of the volume at intervals of temperature of
20° are shown as a function of the pressure in Fig. 3. The figure
does not show the results as accurately as the table, but enables one
to form a clearer mental picture of the nature of the results. The
curves, on the scale of the figure, do not show any abnormalities to
the eye, except in the neighborhood of the origin, where the well
known negative expansion at 0° results in the curves drawing together.

340 PROCEEDINGS OF THE AMERICAN ACADEMY.

There are various abnormalities besides those in the neighborhood of
0°, however, as will be shown by the other figures. |

With regard to the compressibility there seems to be some variance
of usage, so that it will be well to call attention to the fact that the
quantity used throughout this paper in the sense of compressibility is

Isothermal Compressibility

0.0
42 ἘΠΕ :
tes
HE ΠΗ i
ἘΠΕΒΕΙΤΕ : tt
0.0.41 d et =4t'} ΤΗΣ Tf
iff SHG ἘΒΘΕΤΗ ΒΗ
ἢ ἸΞΈΙ ΠΗ ;
ἘΠΕ ΠΗΞΕΙΕ ΠΗ ΠΗ ΕΣ te

$923 4 - BS

Ol δ ν 4 νὴ G72) 28 9 aa 11 5
Pressure, kgm. / cm.’ x 10°

Figure 4 ‘Theisothermal compressibility of water, (=) against pressure.

Op /t

the derivative (Fe) :
Op t
same sense. Figure 4 shows the compressibility, that is, the analytic

Sometimes the expression : (=) is used in the
t

expression (1 , as a function of the pressure at 0°, 20°, and 80°.
ι

It would have made the figure too crowded to have tried to show the
values for 40° and 60° also. The complete values for the five standard
temperatures are shown in Table V separately, however. The figure
shows the well known abnormality in the compressibility at the low
pressures, namely a higher compressibility at the lower than at the
higher temperatures. This abnormality disappears above 50°, and
from here on the compressibility increases with rising temperature.
The figure shows that at 80° the initial compressibility is higher than

OE ee

BRIDGMAN.— THERMODYNAMIC PROPERTIES OF WATER. 341

at 20°, although it has not yet risen to the value at 0°. In addition
to the abnormality at low pressures, the curve shows also a slight

TABLE V.

ComPRESSIBILITY OF H:O.

(2), em.3/gm.

40°. 60°.

Pressure,
kgm./em,? | —
|

abnormality at the higher pressures in the neighborhood of 6500 kgm.
Here the compressibility at 20° rises and at the melting point of ice
VI, it has become higher than the compressibility at 80°. The thermal
dilatation shows abnormality in the same locality; it would seem to be

342 PROCEEDINGS OF THE AMERICAN ACADEMY.

connected in some way with the appearance of the new variety of ice,
but the exact connection cannot at present be stated.

The large change in the value of the compressibility brought about
by pressure should be noticed, amounting at 12,000 kgm. to a decrease
of five fold. Furthermore the rapid flattening of the curve at the
higher pressures also should be commented on. The curve gives the
appearance, for the pressure ranges used here, of becoming asymp-
totic to some value greater than zero. Of course this cannot really
be the case for infinite pressures, for otherwise we should have the
volume completely disappearing for some finite value of the pressure,
but it may indicate the entrance of another effect at the higher pres-
sures, which may persist in comparative constancy for a greater range
of pressure than will ever be open to direct experiment, such an effect
as the compressibility of the atom, for example. This possibility
has been already mentioned and made plausible from the data of the
preceding paper.

If instead of the compressibility as defined above, the quantity

. (=) , which in this paper will be called the relative compressibility,
t

is plotted, a curve of the same general character as that shown will

be obtained.

The compressibility may also be plotted against a different argument
than the pressure. For many purposes the pressure is perhaps not
the most significant independent variable that might be chosen.
This is because the external pressure is not a measure of what is
happening inside of the liquid. We conceive a liquid as composed of
molecules in a state of constant motion and of collision with each other,
acted on also by attractive forces between each other. The effect of
these attractive forces is to produce at the interior points a pressure
which may be much higher than the external pressure. The external
pressure is equal to the interior pressure diminished by the amount
of the attractive pressure drawing the molecules to the interior at the
exterior surface, where the attraction is an unbalanced action in one
direction. The amount of the unbalanced pressure at the outside
depends in a complicated way on the law of attraction between the
molecules, on their mean distance apart in this surface layer, and on
the distribution of velocities in this layer. The external pressure
required to hold the liquid in equilibrium is, therefore, largely a sur-
face phenomonon, and is connected in a complicated way with the
state of affairs at inside points. A more significant independent
variable, therefore, would be one involving only the condition of the

BRIDGMAN.— THERMODYNAMIC PROPERTIES OF WATER. 343

molecules on the average throughout the mass, and not one depend-
ent on the surface layer. There are only a few such quantities de-
pending on the state of the liquid at interior points. Any quantities
involving in any way the constancy of pressure or of entropy, for ex-
ample, do depend on the complicated action of the surface layer. One
of the quantities which is independent of this surface layer, however, is
the volume. In many theoretical considerations the use of the vol-
ume as an independent variable is known to produce simplifications.

If the volume, instead of the pressure is taken as the independent
variable for the compressibility, curves are obtained of the same
general appearance as when the pressure is used forthe variable.
The compressibility falls with decreasing volume, and the curvature
is in the same direction as when the pressure is the independent vari-
able. The same general characteristics are also shown if the relative
compressibility instead of the compressibility is plotted against the
volume. The two sets of curves, for the compressibility and the
relative compressibility, do show one feature in common, however,
different from the curves when the pressure is used as the variable.
This is the fact that the compressibility is always lower for the same
volume at the higher temperature. This is true throughout the entire
range of volume used; there is no crossing of the curves indicating
abnormalities, such as is the case when the pressure is used as the
variable. This is what one would expect on the kinetic theory. A
liquid, at two different temperatures but at invariable volume, differs
only in the violence of the motion of its molecules. At the higher
temperature, the kinetic pressure due to the motion is greater, and so
the resistance offered to change of volume under a given increase of
external pressure 15 greater when the temperature is higher.

Fig. 5 shows the thermal dilatation as a function of pressure at
various temperatures. The thermal dilatation plotted in the figure

is the expression (2 instead of the expression : (=) , which is some-
»

» ot

times used as the dilatation. The usage adopted here for the dilata-
tion is analagous to that explained above for the compressibility.
The values listed in the figure were obtained from the table of volumes
in the manner already described. The curve at 0° was obtained from
the data of the previous paper for the low temperatures, but in that
paper the mean value of the thermal expansion for the range 0°-20°
was given, whereas here the instantaneous value at 0° is given instead.
The substitution of the instantaneous for the mean dilatation produces
no change in the general character of the curves, however.

344 PROCEEDINGS OF THE AMERICAN ACADEMY.

The points at the higher temperatures were obtained from the data
of this paper alone. There are two striking features that call for
special comment. ‘The first of these is the abnormal behavior of the
curve for 20°. In the initial stages, the dilatation rises with increasing
pressure, unlike normal liquids, but this merely indicates the return
of water to the normal behavior to be expected at high pressures.
At about 3500 kgm. the curve at 20° has reached a maximum and
begins -to descend with increasing pressure, as it does for the curve at
0°. But the descent continues for only a little way, and at 5500 kgm.
the curve begins to rise again, indicating the entrance of a new abnor-

= T [Sanu et + ; +
Senses ται : =: + = ΞΕΞΞΞΞ: rte ht
ἘΞ ΞΕ ἘΞ ΞΕ gee ae errs arse a
Ξε : Fatt nine Ft Ξ
Ξ ΣἘΕΞΞΞΞΞΞΞΞΞΞΕΙ
= th Ht + tH pesees ἘΕΞ port
9. geseaeassazeze: ΞΕΞΞΞΞΕΞΞΒΞΞΞΞΞΞΞΈΞΞΞ: ΞΕ ΞΞΞΞΒΞΞΞΞΞΞΕΣ ett
Ὁ Sete + ΤΙ ΕΗΞΕΞΞΕΕΕΞΉΞΗΤΕ
iy} + a 1353503 + ra 2: res
Ὁ — =
3 . --- τ-ας--- = ++ —
= ΕΣ SE SESE -
oy
= 55:
is] + Ξ
= ΓΕ = psesess
i Ξε
Vv
pi = posses
= adi tuassnasqraetitasvteseerefertae

ΤΥ

as

3° 4 B67 PS 9. 10 aaa eee
Pressure, kgm. / cm.’ x 10°

Figure 5. The dilatation of water, (=) , against pressure.
Pp

mality. The abnormality is not so striking or so great in amount as
that in the neighborhood of 0° and atmospheric pressure. The ab-
normality at 20° continues for about 2500 kgm., up to 8000, where the
curve is terminated by the entrance of the solid phase, but the direc-
tion of the curve has already begun to change, indicating that if it
could be continued, this abnormality also would probably disappear
at higher pressures. As to the question of experimental error here,
there would seem to be no room for doubt as to the actual existence
of this new abnormality, for it was shown by all four of the dilatation
curves, even those taken before the method was got to running satis-

_ ΎΨΜ ΥΥΥ ΨῃΨῃ0ΟΙΝ

BRIDGMAN.— THERMODYNAMIC PROPERTIES OF WATER. B45

factorily, and in which the accuracy was not very high. The curves
at the higher temperatures behave as one would be prepared to expect
in the region of low pressures. The curve for 40° shows vestiges of
the abnormal behavior at the low pressures, namely slight initial
rise of dilatation with rising pressure, followed by a fall, but the
curves at the higher temperatures, 60° and 80°, show the regular
initial decrease with rising pressure shown by all normal liquids. But
at higher pressures, the behavior of all three of these curves, for 40°,
60° and 80° is different from what might be expected. The unexpected
feature consists in the crossing of the curves, all in the vicinity of the
same pressure, 5500 kgm., so that at higher pressures the thermal
dilatation at the higher temperatures is lower than it is at the lower
temperatures. It has been already remarked that there are indica-
tions, both from the present work and from that of Amagat, that this -
may be the behavior for any normal liquid at sufficiently high
pressures. The comparative constancy of the thermal dilatation at
the higher pressures, fs also a matter perhaps not to be expected.
Thus the expansion at 40° remains nearly constant over the entire
range of pressure, while the compressibility has in the same range
dropped from 44 to 9. It was distinctly expected, before these
measurements were taken, that the dilatation would show the greater
variation with pressure, so that the effect of temperature on the
volume would tend to disappear at the higher pressures, but such is
not the case.

The relative thermal dilatation may be plotted against pressure,
as was the relative compressibility. The curve shows no striking
features. The curve plotting relative dilatation against volume has
also been plotted, and this is the same in general character as the
others. The slight differences consist in an accentuation of the ab-
normalities in the neighborhood of 5500 kgm., and the fact that at
the lower volumes, that is at the higher pressures, the dilatation
against volume increases with decreasing volume for 40° and 60°,
but decreases for 80°.

These figures for the thermal dilatation and the compressibility
complete those which are obtainable directly from the table. Other
quantities of thermodynamic interest may be obtained by combining
these, however. Perhaps the simplest of these quantities are those
connected with the absorption of energy when the pressure is changed
at constant temperature. The first of these is the actual mechani-
cal work done by the external pressure in compressing the liquid
at constant temperature. This of course is simply the expression

346 PROCEEDINGS OF THE AMERICAN ACADEMY.

W= ul Dp (= dp+ It was obtained by a mechanical integration
t

from curves similar to the volume curves of Figure 3, drawn on a
larger scale. For this purpose the integrating machine owned by the
mathematical Department of Harvard University was used. The

sae

+

9
8
7
6
δ
4
8
2

7 8 9 10
Pressure, kgm. / cm.” x 10°

Work of compression, kgm. m. per gm.

Ficure 6. The mechanical work of compression at 60°.

actual value of the mechanical work at any pressure is of course de-
pendent on the temperature, but since the variation is so slight that
it would have been impossible to show it in the figure (see Figure 6),
the work of compression is plotted for only the one temperature, 60°.
Although the change of external work with temperature was too slight
to show in the diagram, the change with temperature was nevertheless
taken account of in making the calculations of the quantities depend-
ing on it to be described immediately. After the first 4000 kgm. it is
seen that the curve becomes very approximately linear. The curve
for a substance which retains the same compressibility unchanged
over a wide pressure range, as steel for example, is a parabola, the
work increasing directly as the square of the pressure. That this
curve for water becomes linear, means that the compressibility
decreases so fast with increasing pressure that the decrease in the yield

“ΠΑ. “ὠὰ. σι δ

BRIDGMAN.— THERMODYNAMIC PROPERTIES OF WATER. 347

of the liquid for a given increment of pressure decreases almost at
the same rate that the pressure itself increases.

The total heat given out during an isothermal compression may be

derived from the formula (=) =—T (5) . This quantity is shown
Op/, OT/p

in Figure 7. The figure does not call for especial comment. The

peseasess
Ἑ 40 + eth
Be a
se es
o
a ἢ
3
3)
30 at ἘΠῚ :

= 20 Seas
3 δ
2 satsescssesccsenseees 3
ἩΣΉΉΤΗΣ ἢ

Θ᾽ ees
a ols ξ ΠΕ + HESS:
« 1 ΕΞ : 559.» (οἵ τ + 4 |
>= jan ee a8 ΤΡ se
3 srt :
c=

Ἶ : HTH ΤῊΣ HEE ptt ae
Ol eohes 4 “are 7 85... 9 10 11 15
᾽ Pressure, kgm. / cm.” x 10°

Figure 7. The heat given out by water during an isothermal compression.

rapid change in the direction of the isothermal lines in the vicinity of
the origin due to the abnormal behavior at low temperatures and pres-
sures is manifest from the figure, as also the slight abnormalities at
the upper ends of the 0° and the 20° curves, already commented upon
in other connections. Beyond 5000 kgm. the curves for all tempera-
tures tend to become linear and parallel to each other.

These two quantities, the heat liberated in compression and the
mechanical work, combine to give the change of internal energy along
an isothermal, this change of energy being equal to the difference of
the heat and the mechanical work. The change of energy so calcu-
lated is shown in Figure 8. The change is a decrease, which continues
at all temperatures up to the highest pressures. In the previous
paper a value of this quantity was given, confessedly inaccurate,
since in the computation the mean thermal dilatation between 0° and
20° had been used instead of the actual dilatation at 0° or 205, The

348 PROCEEDINGS OF THE AMERICAN ACADEMY.

curve so obtained had the characteristics of the curve now given for 0°,
but the maximum at the top was much more strongly accentuated than
in the present figure. It was surmised in the previous paper that at
high enough pressures the internal energy of all liquids would probably
increase instead of decrease along an isothermal. This surmise seemed

Ἢ t t
He : 4 tf agesas +H :
ΕΗ : Ht segssesecesssessss
18 : ἘΞ ΕΞ

sasas

HoH
itt +

ἜΤΗ

+H

1 2 8 “ΜΠ 667776284 99 10. 11 10
Pressure, kgm. / cm.” x 10°

Change of Internal Energy, gm. cal. per gm.

Fiaure 8. The decrease of internal energy of water during an isothermal
compression.

plausible because one would expect that at high enough pressures the
energy stored up as strain in the interior of the molecules in virtue of
the extremely high pressures would more than counterbalance the
work done by the attractive forces of the molecules themselves as they
were brought closer together by the action of the pressure. This
present figure shows that this is not the case, however, for the range
of pressure reached here. The lower temperature, 0°, is the only one
at which this reversal of the direction of the change of internal energy
manifests itself, and this change, in comparison with the other curves,
is now seen probably to be an effect of the other abnormalities shown
at low pressures and temperatures. Nevertheless it would still seem
as if at very high pressures the energy must increase instead of de-
crease along an isothermal, but the only indication of it from the

present curves is in the direction of curvature, which is in the direction ©

Ὡς ἐπα i a i i i il i i i ....

BRIDGMAN.— THERMODYNAMIC PROPERTIES OF WATER. 349

to indicate the possibility of a maximum and a reversal of direction
at higher pressures. The pressure for a maximum, however, if there
is one, is much beyond the reach of any at present attainable. Within
the pressure range of these measurements, the attraction between the
molecules still remains the dominant feature, so that the work done
by the attractive forces and liberated as heat much more than suffices
to overbalance the mechanical work of compression.

The internal energy of a substance is one of those quantities which
depend only on the properties of the mass of the substance at interior
points and do not involve the action of the surface layer. Change of
energy plotted against volume shows in the first place that the change
of internal energy is much more nearly a linear function of the volume
than it is of the pressure. The average slope of the isothermal lines
of energy increases rapidly with rising temperature for the lower
temperatures, but the two curves for 60° and 80° run nearly parallel
to each other for their length. Abnormalities are shown at the upper
ends of the 0°, 20° and the 40° curves, and the 0° curve shows the same
maximum as it does when plotted against pressure. The origin, of
course, for the curves at different temperatures does not coincide as
it does for the same quantities when plotted against pressure.

One other quantity may be simply determined in terms of the
compressibility and the thermal dilatation alone, the so-called pres-
sure coefficient, that is, the change of pressure following a rise of
temperature when the temperature is raised by 1° at constant volume.
This quantity is given immediately in terms of the compressibility
and the thermal dilatation by the well known formula,

(se). — &), Ge)

It is shown plotted in Figure 9. The curves for 0° and 20° show
anomalies, as is indicated by the unexpected direction of curvature.
The other curves for the higher temperatures seem to be regular
enough, though of course it cannot be told whether the course of these
curves is the same as that which would be shown by a normal liquid or
not. At the upper ends of the high temperature curves, the curva-
ture is in such a direction that if they were continued far enough the
pressure coefficient would decrease instead of increasing with rising
pressure.

This quantity, the pressure coefficient, has been made the basis
of theoretical speculation. It has been enunciated as a law, approxi-
mately true, by Ramsay and Shields, that the pressure coefficient

350 PROCEEDINGS OF THE AMERICAN ACADEMY.

is.a function of the volume only. This means that if the coefficient
were plotted against volume instead of pressure the curves for all five
temperatures would fall together. That this is not the case for water

at high pressures is shown very distinctly in Figure 10. At the lower

pressures and the larger volumes, the curves for the different tempera-

ζὸ
οι

(ve)
(=)

Coefficient of Pressure

+ +

aon: Beoossas + +H
saan #4

Ἔ jausegges passaassas es mas eg ze:

ΘΟ 1 5 τ π΄, Π XG 7 8, eo Opie 1
Pressure, Kgm. / cm.” x 10°

Figure 9. The pressure coefficient, that is the change of pressure accom-
panying a rise of temperature of one degree, as a function of the pressure.

tures are very widely separated. The abnormality on the curve
at 0° in the neighborhood of the locality where the new variety of
ice makes its appearance is very striking. At the higher pressures
the curves do draw together, but they are not approaching coincidence,
for they cross in the neighborhood of a volume of about 0.85. It does
not seem likely that the entire failure of coincidence throughout the
whole range of pressure can be due to abnormalities, since even at
low pressures water is nearly normal at the higher temperatures, and
certainly at the higher pressures and temperatures we have every
reason to expect that its behavior is quite like that of other liquids.
This completes the list of quantities which can be deduced directly
from the compressibility and the thermal dilatation. Other quanti-

BRIDGMAN.— THERMODYNAMIC PROPERTIES OF WATER. 351

ties of thermodynamic interest involve the specific heats, and these
in turn involve the second temperature derivative of the volume.
The first of these quantities is the specific heat at constant pressure.
Y As
This is given by the thermodynamic equation (=) =—T (=) ἘΠῚ ΠῚ
? : ap), δῖ,
will be seen that only the derivative of the specific heat is given by
the data as directly determined. In
order to obtain the specific heat itself,
the derivative, obtained from the ta-
bles in a manner already described,
must be integrated. This integration
was performed mechanically, in the
same manner as the integration for
the mechanical work of compression.
The results are shown in Figure 11.
The values for the specific heat as a

100 90 80
Volume, cm.° per gm.
function of temperature at atmos- Fieure 10. The pressure coeffi-
pheric pressure were taken from the cient of water as a function of the

Coefficient of Pressure

ΠΗ aed Danse

These values seem to be open to some slight question at the present
time due to experimental work done by Bousfield ° since the publica-
tion of the tables, but in any event the possible error is slight, too
slight to be visible on the scale of the figure. The curves show the
now expected abnormalities at 0° and 20°. The striking feature
about the curves for the higher temperatures is the very rapid increase
of the specific heat with rising temperature at the higher pressures.
The specific heat at first decreases on all the curves except at 0°,
but passes through a minimum, and then increases. The pressure of
the minimum rapidly becomes less with rising temperature, and is
situated at 6500 kgm. for 40°, 5500 kgm. for 60°, and at 1100 kgm.
for 80°. At 80° the specific heat rises rapidly beyond the minimum,
reaching the value 1.17 at 12000 kgm.

Any valid characteristic equation should predict the behavior of
the specific heat at high pressures as well as giving the volume in terms
of pressure and temperature, since from the equation the second tem-
perature derivative of the volume may be found. The equation of
Tumlirz 19 has been mentioned in the preceding paper as giving per-
haps as good agreement as any with the previously known facts over

8 Marks and Davis, Steam Tables. (Longmans, Green, and Co.)
9 W. R. and W. E. Bousfield, Trans. Roy. Soc. (A), 211, 199-251 (1911).
10 Tumlirz, Sitzber. Wien, Bd. 68, Abt. Ila (Feb., 1909), pp. 39.

352 PROCEEDINGS OF THE AMERICAN ACADEMY.

a pressure range of 3000 kgm. This equation would predict a con-
tinuous diminution in the specific heat up to infinite pressures, the
limiting value being very approximately 0.5. It was shown in the
preceding paper that there is some new effect introduced at the high
pressures which does not make itself felt at the low pressures, with the

a HEEEG
ἘΣ gine Ty le

ἘΞ ἘΠΕῚ

ΘΟ 1 5. 8. ἡ τ Ὁ ΒΕ 9. 10 Π| 10
Pressure, kgm. / cm.’ x 10°

Figure 11. The specific heat at constant pressure of water as a function
of the pressure.

result that an extrapolation to infinite pressures from the behavior
for the first 3000 kgm. is not safe. This was shown in that paper by
the behavior of the volume, which tended to decrease more rapidly at
the high pressures than was predicted by the formula. The present
data also show that there is a new effect at the high pressures, and
indicate that the effect, whatever it is, is such as to have a much
greater influence on the specific heats than on the volume itself.
The specific heat at constant volume may be found from the specific

(5),
τς
δῚ ;
(χω,
This quantity, so calculated, is shown in Figure 12. The same ab-
normalities are shown at 0° and 20° as were shown in the curves for
C,. The curves for 40° and 60° decrease for nearly their entire
lengths, although they are just beginning to rise at the very highest
pressures, but the curve for 80° shows the same sharp turning point
and the same rise through the greater part of its length as the curve

heat at constant pressure by means of the formula, C,—C,= —r

EEE ee eee ee eee

BRIDGMAN.— THERMODYNAMIC PROPERTIES OF WATER. 353

for C,. This quantity, the specific heat at constant volume, has more
theoretical significance than the other specific heat, since this repre-
sents the heat going into the rise of internal energy of the liquid when
the temperature rises, and does not involve the work done against
external pressure in expanding the liquid. The external work in-

C,, gm. cal. per

ok ee foe 4 Bee - 6 wR τὸ 0.115
Pressure, kgm. / cm.’ x 10°

Figure 12. The specific heat at constant volume of water as a function
of the pressure.

volves in a complicated and at present unknown way the action of
the surface layer, while the specific heat at constant volume does
not contain this surface effect. This specific heat is therefore one of
the quantities mentioned in the beginning as having significance be-
cause it does not involve the unknown attractive forces between the
molecules as displayed in the surface layer. In order to show this
independence of the surface layer, of course C, should be plotted
against a variable not itself involving the action of the layer. It is
evidently not adequate, therefore, to plot C, against the pressure as
as been done in Figure 12. C, plotted against volume may be ex-
pected to show this independence of the action of the surface layer.
It is shown so plotted in Figure 13. The figure is of the same general
character as that in which it is plotted against pressure, but the
separation of the curves for the different temperatures is greater,
partly because the curves do not start from a common origin. The
minimum on the curves for 40° and 60° comes at a lower pressure
than it does in the former figure, and the upper end of the 80° curve
is perhaps a trifle steeper at the upper end, but there are no essential
differences. The entire behavior of the curves is not what one would

354 PROCEEDINGS OF THE AMERICAN ACADEMY.

expect from the ordinary theoretical considerations, however. It is
usually considered that when the volume of a substance is kept in-
variable all, or else a fixed fraction, of the heat put in during a rise of
temperature goes toward increasing the kinetic energy of the mole-
cules. This is because the temperature is supposed to be proportional

ΞΈΞΞΕΕΣΕΣΕΡΕΣΕΕΣΕΕΣ ΕΕΕΕΣΕΕΣ εετεετεεεέξεας

C,, gm. cal. per gm.
re)
=)

105. LOO +> 9007 30° 85 ? 30
Volume, cm.? per gm.

Figure 13. The specific heat at constant volume of water as a function of
the volume.

to the energy of translation of the molecules, and therefore, because
of the law of the equipartition of energy, to the total energy of the
molecules. We should expect, therefore, that the input of energy
required to raise the temperature by a specified amount would in-
volve only the interval of temperature, and would be independent
of the absolute value of the temperature and of the volume. The
curves show most convincingly that this is not the case. This sug-
gests that in formulating a theory of liquids it would be well to
scrutinize pretty carefully several assumptions that underlie the
above considerations, namely that the temperature is proportional to
the kinetic energy, that a fixed fraction of the total energy of the
molecules is kinetic, and that the law of the distribution of velocities
is independent of temperature.

Another quantity of thermodynamic interest which may be found
in terms of the specific heats is the thermal effect of compression,
that is the rise of temperature in degrees accompanying a change of
pressure adiabatically of one kgm. per sq.cm. This may be computed

Ov
ΠῚ ἣν, τί a)
φ

by the thermodynamic formula (Ξ The results so

Cp

a

— δϑδ

BRIDGMAN.— THERMODYNAMIC PROPERTIES OF WATER. 355

calculated are shown in Figure 14 for the five standard temperature
intervals. The character of the curves is the same as that shown so
many times before, namely a rise to a maximum and then a fall at
0°, the abnormal behavior at the upper end of the 20° curve, and
the more or less regular behavior of the three curves for the higher

+
ΤῊ
ἢ

Rut ταῖν

ΠΡ ἢ 8, Sin4p ee Ρ 6. ἢ ἢ
Pressure, kgm. / cm.’ x 10°

Figure 14. The adiabatic rise of temperature of water against pressure.

temperatures, with the crossing of the high temperature curves below
the low temperature curves at the higher pressures. In the preced-
ing paper only the approximate values for the very lowest tempera-
ture interval could be found. The calculation was based on the
mean value of the dilatation between 0° and 20°. The general
character of the curve was the same as that found here for 0°,
namely a rise to a maximum and then a fall.

Finally it is possible to compute from the quantities in hand the
difference between the isothermal and the adiabatic compressibilities.

This is found from the formula (=) — (=) pe) (ey. The
Ip)» Op/)- Cp \Or/p

results are shown in Figure 15. The general character of the results
is exactly the same as those previously given for the temperature
effect of compression. Here again, the results at the lowest tem-
perature agree with those of the previous paper which were based
on a mean value for the dilatation.

356 PROCEEDINGS OF THE AMERICAN ACADEMY.

PROPERTIES OF KEROSENE UNDER PRESSURE.

In the course of the experiment other data were gathered inci-
dentally which are of interest for themselves, and which will now be
given. First of these is the compressibility and the thermal dilatation
of kerosene. It was not necessary to determine this quantity in

0.0.8

0.0,2

Qo. 1 Se 8) 4 ἰδ 6252 OS. θὲ 10; 115 }5
Pressure, kgm. / cm.’ x 10°

Figure 15. The difference between the adiabutic and the isothermal
compressibilities of water.

order to find the corrections to be made for the distortion of the vessel,
but since half the work was already done in determining the effect
with the cylinder partly filled with kerosene and the other part filled
with bessemer steel, it seemed worth while to make the additional
run necessary to determine the pressure and temperature effects on
the kerosene. Not so many determinations were made of these
quantities for kerosene as were made for the water. The results are
given in Table VI. The curves showing the total thermal change of
volume for 20° intervals are shown in Figure 16. This figure is the
analog of Figure 2 for water. The results are very different. At the
‘lower pressures the dilatation is greater at the higher temperatures,
as it is for all normal substances, but with rising pressure the effect is
reversed, the dilatation becoming greater for the lower temperatures.
This is the same behavior which takes place for water at higher
temperatures after it has regained normality. But above 5000 kgm.
the kerosene shows other abnormalities quite different in their charac-

OO ΨΚ

BRIDGMAN.— THERMODYNAMIC PROPERTIES OF WATER. 307

ter from those of water. This is shown plainly in the figure as a
separation and then a drawing together again of the curves. The
curve for 20°-40° between 6000 and 8000 and the curve for 60°-80°
beyond 9000 accomplish this separation and drawing together again

TABLE VI.

VoLUME OF KEROSENE AS A FUNCTION OF TEMPERATURE AND PRESSURE.
(The volume at 0° and atmos. pressure is taken as unity.)

Pressure, Volume.
kgm.

by rising with rising pressure, exactly as do some of the curves for
water. The abnormality is doubtless due to an entirely different
cause, however. In this case the effect is to be explained by the
delayed freezing of the kerosene. Kerosene is not a simple pure
substance, but is a mixture of several components with different
melting points. Freezing under these conditions is not sharp, but is
spread out over a considerable interval of temperature or pressure as
the case may be. Neither is there any necessity that the freezing

358 PROCEEDINGS OF THE AMERICAN ACADEMY.

should ever be perfectly complete, as indeed it is probably not. This
may be shown at atmospheric pressure by plunging the kerosene into
solid CO:. The effect is to change the kerosene to a white pasty
mass, like white vaseline. The pressure at which this transition
occurs will rise with increasing pressure. The existence of a transi-

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rf. sit:
τε ἘΞΕΗΕ > +
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page T ΤῊΣ

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ἩΤΗΞΕΗΞΗΞΗ ΡΞ ΣΕΤΗ £ +
020 Rss : ΞΕΗΗῚ

ΤῊΣ

Change of Vol. at 20° Intervals

paps

az
ΤΉ ΞΈΣΕΤΗΣΤΕ

11 12

ἐξ

004E= ad eben ee
O° 4 5 Fane δ’ δ 8. ano

Pressure, kgm. / cm.’ x 10°

Fiaure 16. The change of volume of kerosene at constant pressure for a
rise of temperature of 20°.

tion point, if there were one perfectly sharp, would be shown by an
abrupt rise of the curve by an amount corresponding to the change of
volume on freezing. But with the delayed freezing which takes
place here due to the separation out of the separate components
from a solution of varying strength, this abrupt rise becomes con-
verted into a gradual rise extending over a fairly wide pressure range.
Furthermore, the mean pressure at which this rise takes place in-
creases with rising pressure, just as the ordinary freezing point is
raised by increasing pressure. These features are all clearly shown in
the diagram. At the extreme right of the diagram, at pressures over
12,000 kgm., there is evident the beginning of the reversal of the effect,

ον

BRIDGMAN.—- THERMODYNAMIC PROPERTIES OF WATER. 359

that is, the curves are going to cross again, and the thermal dilation
become greater at the higher temperatures. This may possibly
indicate a reversal of the reversal of the effect mentioned above for
liquids, but more probably the meaning is simply that at pressure
above 12,000 the substance is practically a solid, and that for solids
the reversal of the effect found in liquids at high pressures does not
occur.

There is one bearing which these observations have on the previous
data which should perhaps be mentioned. This is in connection with
the delayed freezing. Whenever freezing takes place there is usually
the possibility of subcooling before separation to the solid form takes
place. The amount of subcooling usually taking place depends on
the nature of the liquid. In some it is very considerable, while in
others it is negligible. If such subcooling took place here, it would
produce irregular results, because the change of volume in the kero-
sene transmitting pressure to the water would not always be the same
under the same pressure. The only answer to be made to this ob-
jection is that in this experiment the subcooling was not great enough
to produce sensible irregularity. No discrepancies were found in the
data suggesting that they were due to this effect. It was feared in the
beginning of the work that the effect might be very troublesome, but
such did not turn out to be the case.

Also with respect to the solidification of the kerosene, the experi-
ments showed that the solidification could not be complete, but the
kerosene, even at the highest pressures, must remain a pasty mass like
vaseline in nature, always capable of transmitting pressure nearly
hydrostatically. But that on the other hand the kerosene does
undoubtedly become pretty stiff under pressure has been already
shown in the course of some measurements on the linear compressi-
bility of steel rods.

The second bit of data collected incidentally in the course of the
work was a measurement of the expansion and the thermal dilatation
of the high temperature variety of ice.

Ture CoMPRESSIBILITY AND THERMAL DILATATION OF Ice VI.

Although these data are not directly concerned with the properties
of liquid water, which forms the subject matter of this paper, still
it was so easy to obtain them without any modification in the arrange-
ment of the apparatus, that it was thought worth while to measure
them. In the previous paper on the properties of water and the

360 PROCEEDINGS OF THE AMERICAN ACADEMY.

several varieties of ice, a very rough experimental value for the com-
pressibility was given, as also a computation of the approximate
compressibility, neglecting the thermal dilatation of the ice, for which
no experimental value was found at that time. These measurements
here include a direct measurement of the thermal dilatation, and
two different determinations of the compressibility by two different
methods. The value for the dilatation may be combined with the
already determined values for the volume of the liquid and the change
of volume when ice VI separates out, to give a third independent
value for the compressibility.

The determinations of the dilatation will first be described. This
was found in the same manner as the dilatation of the liquid, by chang-
ing the temperature at constant mean pressure, and measuring the
change of pressure brought about thereby. Three determinations of
this were made for the combination of ice and kerosene, and two for
the combination of kerosene and bessemer. The agreement of the
different determinations was within 2% of the mean. The dilatation
was found between 0° and 20° at a mean pressure of 10,000 kgm. The
correction introduced by the thermal dilatation of the bessemer
cylinder in the control experiment is fairly large here, being about 25%
of the entire effect. The value assumed for the cubic dilatation was
0.000036, which is the value for atmospheric pressure. The effect
of pressure is to decrease this number slightly, which would result
in a larger value for dilatation of the ice. The effect of pressure on
this quantity is, however, very small, and the error so introduced
is probably negligible. The mean dilatation found in this way for the
20° above 0° at 10,000 kgm. was 0.00241 cm.3/ gm., or 0.000120
em.3/ gm. per degree. This is considerably less than the dilatation
of the liquid in this neighborhood, for which the value 0.00040 has
been found previously.

This value for the dilatation may now be combined with the other
data for the liquid and the solid to give the compressibility of the
solid along the equilibrium curve. For this we have the following
data: vol. of 1 gm. of water at 0° and 6360 kgm., 0.8428 em.%, and at
20° and 9000 kgm. (these are the equilibrium pressures at these
temperatures) 0.8160 cm.%. For the change of volume when the
liquid freezes to the solid we have at 0°, 0.0916, and at 20°, 0.0751.
This gives for the volume of ice at the equilibrium pressures at 0°
and 20° the values 0.7512 and 0.7409 respectively. The decrease
of volume of the ice along the equilibrium curve is 0.0103. Part
of this is an increase due to rise of temperature, which according to

BRIDGMAN.— THERMODYNAMIC PROPERTIES OF WATER. 361

the above data is 0.0024. This leaves a decrease of 0.0127 to be
accounted for by the increase of pressure of 2640 kgm. which gives
a mean compressibility over this range of 0.0000048, a little more
than one third of the compressibility of the liquid over the same
range.

The direct determination of the compressibility of the ice was made
by two different methods. One of these was the same as that used
roughly in the preceding paper, that is by finding the difference of
the slope of the curves plotting piston displacement against pressure
above and below the transition point to the solid. The values obtained
in the preceding paper for this were very rough. In these determina-
tions the cylinder was very much more carefully seasoned, and the
readings were made with all the precautions which had been sug-
gested by all the experience of this paper. Two determinations of
this quantity were made at 0° and also two determinations at 20°.
The two values for the difference of compressibility differed by 2.5%
at 0° and by 0.7% at 205. The value found for the difference was
0.0000087 at 0° and 0.0000067 at 20°. Combining with the values
given already for the compressibility of the liquid, this gives for the
compressibility of ice VI 0.0;49 at 0° and 6360 kgm., and 0.0,;43 at 20°
and 9000 kgm. Mean 0.0;46.

The second method for determining the compressibility was exactly
the same as that for finding the same quantity for the liquid, com-
paring the displacements when the apparatus was filled with ice and
kerosene with those when the ice was replaced by bessemer steel.
This determination was made over a wider pressure range, to find if
possible the variation of compressibility with pressure. No variation
with pressure could be found over a range of 4500 kgm. at 0° and 3300
kgm. at 20°. The absolute values do not agree with those found
by the two other methods, however, the figures being 0.0;31 at 0°
and 0.0,35 at 205. The cause of the discrepancy is not clear, but is
probably connected in some way with the hysteresis of the cylinder.
The hysteresis was not regular for these small pressure ranges, being
at times almost negligible, and again being as large as for almost the
entire pressure range from atmospheric pressure to the maximum.
There seems little question but that the greater weight is to be attached
to the values found by the first two methods. This third determina-
tion does show, however, that the variation of the compressibility
with pressure and temperature over this range is so small as to be
beyond the accuracy of these measurements. In selecting the best
probable value for the compressibility the only weight that will be

— ee

362 PROCEEDINGS OF THE AMERICAN ACADEMY.

ee

assigned to this third determination is in slightly lowering the mean
of the other two.

The final most probable values for Ice VI are as follows: for the
compressibility 0.0,45, and for the thermal dilatation 0.000120
cm.?/ gm. over the range 6360-10,000 kgm. and 0° to 20°.

The cost of much of the apparatus used in this investigation was
defrayed by an appropriation from the Rumford Fund of see
American Academy.

JEFFERSON PHysIcAL LABORATORY,
Harvarp UNIVERSITY, CAMBRIDGE, Mass.

Ἢ

Proceedings of the American Academy of Arts and Sciences.

Vout. XLVIII. No. 10.— Srpremser, 1912.

CONTRIBUTIONS FROM THE CRYPTOGAMIC LABORATORY
OF HARVARD UNIVERSITY.

LXXI.— PRELIMINARY DESCRIPTIONS OF NEW SPECIES
OF RICKIA AND TRENOMYCES.,

By Routanp THAXTER.

-

bd

CONTRIBUTIONS FROM THE CRYPTOGAMIC LABORATORY OF
HARVARD UNIVERSITY.

LXXI.— PRELIMINARY DESCRIPTIONS OF NEW SPECIES
OF RICKIA AND TRENOMYCES.

By ον THAXTER.
Received August 19, 1912.

RICKIA.

THE genus Rickia has proved to be a large and varied one, and
although I have enumerated below only those forms parasitic on
Acari which have come under my notice, many others are known to
me on a variety of hosts, an account of which I have reserved for a
future paper. The general habit appears to be very variable, includ-
ing in addition to the condition seen in the type form, others in which
the median cell-series is undeveloped, as well as various species with
a more or less complicated system of branches. . The antheridial
characters, moreover, appear to be equally variable. Not only do
the antheridia which are extraordinarily abundant in some species
seem wholly lacking in others, but their character may vary in differ-
ent cases. In some there may be a single antheridium, only, similar
to that of Peyritschiella, definitely placed at the base of the perithe-
cium; or an antheridium of this type may be associated with others
of the normal habit variously disposed. Again even in forms having
the three characteristic cell series, antheridia may be present like
those of the genus formerly separated as Distichomyces, each anther-
idial cell becoming more or less free in a compact group. Since both
the antheridial characters and those of the receptacle thus appear to
be so variable, it has not seemed desirable to limit the genus to the
type form as illustrated by Rickia Wasmanni, and I have therefore
given it a more liberal interpretation; including under it forms with
two or with three cell-series, whether they be simple or branched, and
whether their antheridia be of the Rickia or the Distichomyces
type. The latter genus is, therefore, abandoned, one species only,
Rickia Leptochiri, being involved in-this change.

366 PROCEEDINGS OF THE AMERICAN ACADEMY.

The only American form, R. minuta, thus far recorded on Acari,
has been described by Paoli (“Redia,” Vol. VII, fase. 2, 1911, repub-
lished in Malpighia, Vol. XXIV, 1912) from immature specimens
with undeveloped perithecia, a practice which it is surely most desir-
able to avoid in the systematic study of a group which presents such
great difficulties as do the Laboulbeniales. I have been fortunate,
however, in obtaining abundant material of this species, fully matured,
from the Amazon region, for which as well as for other hosts, I am
indebted to the kindness of Mr. W. H. Mann who has allowed me to
look over his collections made on the Leland Stanford Expedition
in 1911. I am further greatly indebted to the kindness of Messrs.
T. Petch, Geo. Schwab and J. B. Rorer who have most generously
collected or caused to be collected for me numerous insects, in Ceylon,
Kamerun and Trinidad respectively, from among which a majority
of the following hosts were obtained. I am also indebted for two
species of Acari collected in Grenada to Mr. C. T. Brues and kindly

placed at my disposal; while lastly I am much indebted to Mr.
Nathan Banks for his determinations of the host-genera.

In the following diagnoses I have assumed that the side bearing
the perithecium is “anterior.””’ The spore measurements are for the
most part made within the perithecium.

Rickia furcata nov. sp.

Furcate, sometimes irregularly branched. Basal cell short and
rather stout, the receptacle above it dividing in two straight divergent
branches; an anterior, bearing a perithecium, and aposterior. An-
terior branch consisting of a series of usually eleven cells, the lower
superposed horizontally, the upper obliquely; all cutting off appen-
diculate cells externally; the series extending nearly to the apex of
the perithecium, to which it is united throughout its length; the
second cell of the series extending inward below the base of the latter,
the outline of which is symmetrically subfusiform, the inner lip-cell
protruding as a finger-like process. Posterior branch indeterminate,
formed by a double series of cells which are more or less regularly
paired above the second cell of the outer row, the third cell bearing
the primary appendage on its narrow subtending and long cylindrical
basal cell; many, but not all of the cells above in both rows cutting off
distally and externally small cells which bear well-developed appressed
appendages or antheridia (?). Appendages subcylindrical, 8-16 X
2.5u. Perithecium 30-40 X 8-104, including terminal projection

THAXTER.— RICKIA AND TRENOMYCES. 367

(2.5-3 μ). Spores about 25 X 2.54. Total length to tip of perithe-
cium 40-70 μ, to tip of posterior branch 50-175 μ.

On Euzerconspp. No. 2481, Trinidad; No. 2236, Manaos, Amazon;
No. 2058, Grenada, W. I.

This species, and to a more marked degree the following, depart
greatly from the normal type, and would be placed in a new genus
with little hesitation were it not for the structure which characterizes
various others of the many undescribed species known to me. It is
evident that the “posterior branch”’ is an indeterminate proliferation
beyond the primary appendage, which appears to involve both the
“median” and the “posterior” marginal series of the more normal
forms. The receptacle, especially when a primary perithecium fails
to develop, may become variously branched and more than one
secondary perithecium may be produced. Antheridia of a type
like that of Distichomyces appear to be developed externally on the
posterior branch nearer the base. The specimens from Brazil and
Trinidad seem to be identical, although those from Grenada, though
otherwise similar, are constantly somewhat smaller.

Rickia arachnoidea nov. sp.

Basal cell rather short and stout, the receptacle above it dividing
into two usually fureate arachnoid branches; an anterior on which a
perithecium is produced, and a posterior. Anterior branch indetermi-
nate, consisting of two parallel series of cells usually not opposite,
irregularly appendiculate, furcate at a variable distance from its
base; one of the branchlets sterile, often greatly elongated; the
other short but variable, bearing a perithecium which on one side
is usually united to the upper six cells, some of them appendiculate,
which continue one of the two series forming the perithecial branchlet
which thus extends to the apex of the perithecium, beside which it
terminates in a short brown appendage: the perithecium long, slightly
and nearly symmetrically inflated, the tip bent distally abruptly
sidewise; the other row of the perithecial branchlet ending horizon-
tally or obliquely below the base of the perithecium and consisting
of from three to eight cells, some of which are appendiculate. Pos-
terior branch indeterminate, furcate, usually, just above its first to
fifth pair of cells, the cells of the two indeterminate branchlets not
paired, irregularly appendiculate, indeterminate, usually greatly
elongated: the second cell of the main receptacle below its furcation
bearing the large long nearly cylindrical basal and subtending cells

368 PROCEEDINGS OF THE AMERICAN ACADEMY.

of the primary appendage, which may be on either side. Appendages
suffused with brownish, mostly rather short and stout, 7-18 X 4μ.
Spores 30 X 3y. Perithecia 70 X 18-20. Diameter of branches
8-10 μ, greatest length 460-520 μ, in largest specimens. Basal and
subtending cell of primary appendage 18-20 X 4 μ, the former rarely
divided.

On Discopoma sp. Trinidad, No. 2433; on Trachyuropoda sp.
Trinidad, No. 2429; also an immature specimen from the Amazon
on same host; on Euzercon sp., Trinidad, No. 2482.

When normally developed this curious form appears to be more or
less regular in its structure, as above described, but especially when
injured or when the first perithecium aborts, secondary branching
takes place, and more than one perithecium may be formed. That
there is no significance in “anterior”? and “posterior” as applied to
the main branches of this form, is indicated by the variable position
of the primary appendage beyond which they proliferate. The
plant has a characteristic sprawling habit, its branches resting on the
upper surface of its host, which is its usual position of growth. Unless
it is viewed sidewise, the cell-series bordering the perithecium is not
visible, and may thus be wholly overlooked. The appendages, as
in all the species, are borne from small subtending cells. Among
described species it is most nearly allied to R. furcata.

Rickia anomala nov. sp.

Hyaline, rather strongly curved throughout above the basal cell.
Median cell-series wanting. Basal cell wholly free, longer than
broad, of nearly the same diameter throughout. Anterior series
consisting of three or rarely four cells, subisodiametric, externally
convex, subequal, without appendages. Posterior series of usually
nine cells, the two or three lower larger, rounded; the rest smaller,
subequal, irregularly rounded; the first, third, fifth, and seventh
cells separating distally small cells which subtend appendages, the
second cell subtending the basal cell of the primary appendage, which
is relatively very large, wholly free, constricted at the base, terminated
by a small cell which subtends the appendage proper; the latter
somewhat smaller than the others, but otherwise similar, faintly
brownish, bladder-like, roundish, or somewhat longer than broad.
Perithecium directly continuous with the anterior series, externally
wholly free, rather long and narrow, the tip well distinguished, nar-
rowed, its lower half united on the inner side to the distal cell of

THAXTER.— RICKIA AND TRENOMYCES. 369

the posterior series, which ends in a minute suffused roundish hardly
distinguishable cell; the inner lip-cell forming a finger-like straight
free process. Spores about 25 X 3 yu (in perithecium). Perithecia 30-
35 X 8-10.54. Basal cell 14-18 Χ 5-6.5y. Basal and subtending
cell of primary appendage 16-17 X 7μ. Appendages 9X 4.5-
7X 6u. Total length 48-56 Χ 14-16 xu.

On a minute mite belonging to a new genus, near Iphiopsis.
Trinidad, No. 2440.

Although there are fourteen specimens of this peculiar species in
various stages of development, none of them show any indication of
the presence of an antheridium.

Rickia Discopomae nov. sp.

Hyaline, becoming slightly soiled with dirty brownish throughout.
Basal cell large, twice as long as broad. Main body of the receptacle
of about the same diameter throughout, broadening slightly below
the perithecium, usually rather strongly curved. Cells of the three
cell-series small, subequal, squarish or subisodiametric, arranged in
tiers of three cells each with some regularity; the middle series extend-
ing half way along the tip of the perithecium, its two or three terminal
cells free beyond the base of the primary appendage, which terminates
the posterior marginal row. Cells of the median row fifty to sixty
in number, sometimes less; those of the anterior marginal row thirty
to fifty; of the posterior marginal row fifty to sixty, the cells of both
marginal rows cutting off appendiculate cells irregularly, except
those of the posterior row opposite the perithecium which produce
them uninterruptedly; the appendages and antheridia thus irregularly
and rather sparingly distributed along the margins. Appendages
short and usually inflated. Perithecium rather short and _ stout,
the tip often somewhat bent outward, the apex blunt. Spores 30 X
δμ. Perithecium 48-52 X 18-25. Total length 250-350 Χ 18-
32 μ, measured below the perithecium. Appendages 7-10 X 3-4 u.

On superior surface of Discopoma sp. Peradenyia, Ceylon, No. 2111.

The antheridia of this species are not certainly recognized, but
appear to be of the type seen in “ Distichomyces.”’ The appendages
appear to branch occasionally, becoming fureate, a condition possibly
resulting from the proliferation of old antheridia.

370 PROCEEDINGS OF THE AMERICAN ACADEMY.

Rickia elegans nov. sp.

Basal cell hyaline; cells of median row small, rounded; those of
marginal rows horizontally elongated or their axes directed upward
somewhat obliquely, more than fifty cells in the posterior row, about
twenty-five in the anterior; the cells at maturity in all the rows be-
coming deeply suffused with rich blackish brown and quite indis-
tinguishable; all the cells of the marginal rows cutting off small cells
which remain almost wholly hyaline and bear short appendages,
their cup like bases rich brown, the distal portion hyaline. Peri-
thecium wholly united on its inner side to the median row, the last
two or three free cells of which reach to the middle of the short stout
deeply suffused rather broad tip, which is bent rather abruptly out-
ward; the apex hyaline, or translucent; the body nearly straight,
about the same diameter throughout, rather narrow, rich brown, not
as deep as the tip, the outer margin somewhat irregular, continuous
with that of the receptacle below. The whole plant straight or
curved, tapering gradually from apex to base. Perithecium 65-85 X
20 yu. Appendages about 15 X 4y. Total length 200-220 x 35-
40 μ.

On legs and margin of body of Discopoma sp. Peradeniya, Ceylon,
No. 2110.

This species is very closely allied to R. Berlestana Paoli (Bac.),
differing chiefly in its much more numerous cells, which are smaller
and differently arranged and the total suffusion of the receptacle.
In fully mature specimens, the perithecium is concolorous with the
receptacle, and not distinguishable from it.

Rickia cristata nov. sp.

Basal cell three times as long as broad, its upper half or less included
between the lower cells of the marginal rows. Posterior row crest-
like, the cells radially elongated, each separating several appendiculate
cells, the pointed bases of which are intruded between them nearly
to their bases, the appendiculate cells becoming so multiplied, where
the series curves over against the tip of the perithecium, that the
primary cells are obliterated; the primary cells of this series about
eighteen, the appendiculate cells thirty-six to forty: the anterior
series extending slightly beyond the middle of the perithecium, the
base of which it incloses, consisting of three or four cells from which a
number of appendiculate cells are cut off, as in the posterior series,

ee eee ee ee

THAXTER.— RICKIA AND TRENOMYCES. 371

one or two of the uppermost bearing pointed antheridia: the append-
ages six to eight: the middle series of six flattened cells lying along the
inner margin of the perithecium for a little more than two thirds of
its length. Perithecium rather short and stout, slightly curved,
the apex blunt and opposite the bases of the distal appendages of the
posterior series, the tip well distinguished externally. Spores 30 X
4u. Perithecium 45 Χ 18 μ. Free portion of the basal cell about
18 u; the rest of the plant 60-75 X 48-52 u. Appendages 16-25 X
4, becoming brownish and subtended by the usual dark cup-like
base.

On the inferior surface of a mite parasitic on Prioscelis sp. (?) and
belonging to a new genus near Cilliba. Kamerun, No. 2438.

A species closely allied to R. Coleopterophagi Paoli and R. minuta
Paoli, differing in the form of its appendages and the arrangement of
its cell-series. The single type of R. Coleopterophagi as well as those
of R. minuta, are immature, so that it is not possible to judge of the
perithecial characters in these species. The latter, however, has been
received from Brazil (Mann) on various mites parasitic on Scara-
beidae, and an abundance of well matured individuals are available for
comparison. The species though very variable is quite well distin-
guished from the one above described. The tip of its perithecium is
wholly free; the cells of the middle series vary considerably in number
and extend as far as those of the posterior series, which is more nearly
vertical, the general habit of the plant being more slender; the basal
cell is not intruded between the lower cells of the anterior and pos-
terior series and there are other differences.

Rickia pulchra nov. sp.

Basal cell variably developed, more often short, the upper half
enclosed by the lower cells of the marginal series; or long and very
stout distally. Posterior marginal series consisting usually of four
cells, the lower opaque blackish brown bearing distally a very minute
rounded appendage, the next above somewhat rounded and cutting
off a small cell which subtends an antheridium, the third large tri-
angular, its pointed end directed upward, and cutting off three to
five appendiculate cells which lie external to it; the uppermost small,
flattened, distally pointed, separating a single minute cell which lies
external to it and subtends a small short brownish spine-like append-
age: the anterior series consisting of three cells, similar to and sym-
metrical with the corresponding cells of the posterior series, and

372 PROCEEDINGS OF THE AMERICAN ACADEMY.

bearing an antheridium and appendages in a similar fashion so that
the individual is bilaterally subsymmetrical: the middle series con-
sisting of but two flattened cells, the upper, its broader extremity
free beyond the distal cell of the posterior series, nearly twice as long
as the lower, which is opaque below and forms with the two lower
cells of the two other series a suffused area in which cell-divisions
are not visible and which extends upward so as to involve the lower
half of the perithecium; the tip of which is nearly free, usually bent
slightly toward the anterior series, and subtended anteriorly by a
straight appendage about 15 Χ 3 μ, suffused towards the base, and
apparently the indurated base of the trichogyne. Appendages
nearly symmetrical on either side, long and slender, hyaline, becoming
deeply suffused at and towards the base, cylindrical, tapering slightly
at base and apex. Antheridia normally solitary, borne distally from
the subbasal cells of the two marginal series, hyaline, the necks pur-
plish, curved outward. Spores, in perithecium about 22 Χ 3.5 μ.
Perithecia 35-40 X 15y. Basal cell 18-50 X 6-15. Appendages
35-60 Χ 4-6. Total length exclusive of stalk 48-56 Χ 35-38 μ.

On the inferior surface and legs of Macrocheles sp. and Celaenopsis
sp. Kamerun, Nos. 2488, 2439.

A very beautiful species, quite unlike any other known form. The
specimens on Celaenopsis are somewhat smaller.

Rickia obcordata nov. sp.

Hyaline. Basal cell bent, its pomted upper half filling the sinus
of the slightly asymmetrical obcordate body. The marginal series
consisting of typically six cells each and subsymmetrical with one
another, the posterior shorter, terminated by the slender basal cell
of the primary appendage which, like all the appendages and the
antheridia, projects radially in a more or less regular fashion: basal
cells of the marginal series radially extended, broad and rounded
externally, separating a small triangular cell above, which subtends
an appendage symmetrically placed on either side of the body, the
second and third cells of both series separating externally three to
four small cells which subtend each an antheridium, the necks quite
hyaline projecting more or less radially, usually straight, the third
cell on the posterior side usually bearing an appendage distally: the
fourth and fifth an antheridium and an appendage, or an appendage
only in both series, except in cases where there are but five cells in
the posterior series, the uppermost of which always subtends the

δον EE

ee δὰ, ee τ μὰ μιν...

THAXTER.— RICKIA AND TRENOMYCES. 373

primary appendage; the sixth cell of the anterior series producing
neither appendage nor antheridium. Appendages subcylindrical,
several times as long as broad, faintly suffused aboye the conspicuous
blackened slightly constricted base. Median series consisting of
five cells successively smaller from below upward, the three lower
rounded, the uppermost triangular, its upper face free below the
slightly projecting truncate or bluntly rounded free tip of the peri-
thecium. Thelatter otherwise completely enclosed, vertical or slightly
oblique, and lying almost wholly anterior to the median axis. Peri-
thecium 60 Χ 254. Body 90-100 X 78-85 μ. Basal cell including
foot 28-35 X 15-18 yu. Appendages 24-35 X 5y. Projecting an-
theridia 12 μ.

On a minute mite. Kamerun, No. 2441.

A very minute form characteristic from its obcordate almost sym-
metrical form and radiating antheridia and appendages.

Rickia elliptica nov. sp.

Hyaline, elliptical to nearly circular in outline. Basal cell very
short, sometimes entirely included in the angle between the inner
surfaces of the basal cells of the marginal rows, the foot, only, project-
ing beyond the general outline of the main body. Anterior marginal
row consisting of from five to eight cells subradially elongated, the
two uppermost extending downward to sharp points, all or nearly all
cutting off distally a small triangular appendiculate cell; the append-
age which terminates the distal cell appressed against the free
anterior face of the tip of the perithecitum: posterior marginal row
consisting of from seven to nine cells, similar to the anterior series
except that the upper cells are smaller, the uppermost much smaller,
bearing distally the basal cell of the primary appendage which is
small, narrow, free, not greatly longer than the subtending cell of
the very small appendage; other appendages stouter, short, irregu-
lar with slightly suffused bases. Median series of six to eight cells,
one to three of the terminal ones externally free above the basal cell
of the primary appendage, the successive cells subisodiametric, some-
what irregular in outline, and not greatly differing in size. Peri-
thecium almost wholly inclosed, the tip free externally, slightly
bent outward below the apex which is subtended on its inner side
by an erect finger-like upgrowth, geniculate at its base; body of the
perithecium rather long and narrow, subsymmetrical. Spores (in
perithecium) 22 Χ 2.5. Perithecium 30-40 Χ 10-12 μ, not includ-

374 PROCEEDINGS OF THE AMERICAN ACADEMY.

ing the projection which is 7 X 2u. Basal cell, including foot,
8-16 u. Total length of body 50-66 Χ 35-40 un.

On legs of Discopoma sp. Trinidad, No. 2433.

Although seven specimens in perfect condition and of various ages
have been examined, I have seen no indication of an antheridium.
The base of the trichogyne persists as a minute dark rounded body
below the base of the upgrowth from the inner terminal wall-cell.

Rickia inclinata nov. sp.

Minute, hyaline, of irregularly rounded form. Basal cell forming
a well defined slender stalk, the upper third or half inserted in the
angle between the two basal cells of the marginal rows. Anterior
marginal row not extending above the base of the perithecium, con-
sisting of two radially elongated cells which are subequal and cut off
distally and externally two to three appendiculate cells: posterior
marginal row consisting of seven cells like those of the anterior, exter-
nally convex, the second to the fourth more radially elongate than
those above, which are successively smaller; the basal usually sepa-
rating one, the rest two appendiculate cells distally and externally;
the terminal cell much flattened followed by the broad basal cell of
the primary appendage, which appears to be a member of the series,
its inner margin in contact with the fourth cell of the median series:
median series of four subequal irregularly rounded cells. Perithe-
cium stout, its axis straight and characteristically tilted inward at a
slight angle to that of the receptacle, its base in contact with the
distal cell of the anterior series, externally wholly free; the tip quite
free, bent very slightly outward, the apex broad, flat, each lip-cell
projecting very slightly and somewhat irregularly. Spores 25 X 3y
(in perithecium). Perithecium 38-40 X 11 yu. Basal cell, including
foot, 25 X Su. Total length of body to tip of perithecium 50 X 41-
44. Appendages hyaline, tapering very slightly, 16 X 34, with
clearly defined dark basal septa.

On a minute mite, as yet undetermined. Trinidad, No. 2307.

A characteristic and minute species, distinguished by its tilted
perithecium, which is externally free. It is closely allied to R. Celae-
nopsis, from which it differs in the number and arrangement of its
cells, etc. I have been unable to dete mine the presence of an an-
theridium in either of the two adult types.

a δι νων μ.μ.....

σι

THAXTER.— RICKIA AND TRENOMYCES. 37

Rickia Celaenopsis nov. sp.

Hyaline, minute, somewhat angular in outline. Basal cell forming
a well developed stalk, the upper third or less inserted in the angle
between the two basal cells of the marginal rows. Anterior series
consisting of two cells, the lower characteristically triangular in form,
its outer margin straight and evenly continuous with that of the upper
cell, which is radially elongated and cuts off distally an appendiculate
cell which is relatively very long, its distal half or two thirds pro-
jecting free beyond the margin and subtending a relatively very large
and long antheridium which projects above it just at the base of the
perithecium: posterior series consisting of typically six cells, the basal
like that of the anterior series, triangular, but cutting off distally a
slightly prominent appendiculate cell; the four cells above obliquely
elongated, lying subparallel, and separating distally a conspicuously
protruding upturned appendiculate cell; the terminal cell triangular,
subtending the wholly enclosed sublenticular basal cell of the primary
appendage, the subtending cell of which is free, bell- or dome-shaped,
bearing a rather stout appendage. The appendages subcylindrical,
several times longer than broad, rarely furcate, with the usual dark
subtending base: median series consisting of usually six cells, the
basal and distal somewhat larger, the rest squarish or slightly com-
pressed, subequal, the upper margin of the distal cell free, its oblique
wall very thick and directly continuous with the margin of the tip
and the distal portion of the venter of the perithecium which rise erect
beyond it. Perithecium thick walled, somewhat inflated, quite
free and convex externally, erect or nearly so, the tip symmetrical,
‘truncate conical, the apex flattened or slightly rounded. Spores
20 X 3m (in perithecium). Perithecium 40 X 20μ. Basal cell
including foot 25 X 8yu. Total length of body to tip of perithecium,
50 X 88 μ, largest. Antheridium about 12 uw long.

On legs of Celaenopsis sp. Trinidad, No. 2426.

Closely allied to R. inclinata, but differing in many details of struc-
ture, the triangular form of the two basal cells of the lateral series
giving it a characteristic appearance.

Rickia discreta nov. sp.

Hyaline, rather elongate. Basal cell relatively large and long,
distally symmetrical, but slightly intruded between the lower cells
of the marginal series. Anterior marginal series consisting of three

376 PROCEEDINGS OF THE AMERICAN ACADEMY.

to four subequal obliquely separated cells, the lowest cutting off an
appendiculate cell distally and externally, the upper an antheridium
of the Peyritschiella-type, which subtends the base of the perithecium
from which its hyaline sharply pointed stout extremity projects
obliquely upward: posterior marginal series consisting of usually
seven obliquely separated cells, usually the first, third and fifth, only,
separating a rather large appendiculate cell; the uppermost cell
triangular, its upper margin continuous with that of the distal cell of
the median series, subtending the basal and large subtending cell of
the primary appendage, the two latter subequal, the basal somewhat
broader: median series consisting of normally six successively smaller,
vertically slightly elongated cells. Perithecium erect, slightly curved
outward distally, the tip free, the apex symmetrical, truncate, slightly
papillate. Appendages relatively long and stout, yellowish, sub-
cylindrical, the basal ring black and conspicuous; 15-25 X 3.5 y, the
primary one 30-45 μ, its basal and subtending cells 10 XK 4μ. Peri-
thecium 25 X 9u. Basal cell including foot 20 X 7u. Total length
to tip of perithecium 55-65 X 18-22 μ.

On an undetermined gamasid mite. Trinidad, No. 2308.

This species is well distinguished by its large discrete yellowish
appendages, somewhat elongate form, and large single antheridium.
In one of the nine specimens examined a second antheridium is devel-
oped just below the first.

Rickia spathulata nov. sp.

General form spathulate except for the projecting tip of the peri-
thecium. Basal cell rather stout, its upper half or less inserted in
the sharp angle between the lower cells of the marginal series. An-
terior series consisting of six to eight cells, the lowest irregularly
triangular, externally slightly concave, and without appendage, the
rest usually but not always appendiculate, radially elongated, and
shghtly oblique upward; the subterminal cell bearing also an an-
theridium, the basal cell of which penetrates three fourths of its length;
the terminal cell sometimes separating a second antheridium, its
inner margin in contact with the lower two thirds of the perithecium,
narrow, its extremity broader and convex: posterior series consisting
of ten to thirteen cells, usually eleven, the lowest externally convex
like the rest, the other members of the series each usually cutting off
an appendiculate cell about half their length and lying between them;
the upper ones successively narrower and more elongated radially;

ee

THAXTER.— RICKIA AND TRENOMYCES. oLL

the cells above the second or third curved inward in a somewhat
crest-like series which lies parallel to the median series and the inner
margin of the perithecium, the terminal cell of the series small,
triangular, bearing the large basal cell of the primary appendage which,
with the small subtending cell, forms a free straight projection, its
axis bent inward at an angle of about 45° to that of the receptacle:
median series consisting of eight to ten cells, the two or three lowest
enclosed by the marginal series, the rest lying against the strongly
convex inner margin of the perithecium, the free slightly convex
margin of the uppermost reaching almost to the base of the free tip.
Perithecium rather stout, its outer margin nearly straight, its inner
convex, the outcurved tip, and externally a small portion of the body,
free; the apex flat, protruding slightly externally. Spores 28 Χ 3 y,
in perithecium. Perithecium 40-46 X 16-20 yu. Basal cell, including
foot, 28-33 X 9-llyu. Total length, not including primary ap-
pendage base, 12-16 X 6-Su. Appendages 6 X 2u or smaller,
wholly smoky brown, usually broken off, the dark base not conspicu-
ous.

On legs of Celaenopsis sp. No. 2229, Amazon, “M. ἃ M.”
(Mann No. 41).

A very well marked species peculiar for its more or less regularly
spathulate outline, which is broken only by the projecting tip of the
perithecium and the primary appendage. It is not nearly allied to
other known acarine species, but is perhaps most nearly related to
R. minuta.

Rickia excavata nov. sp.

General form roughly triangular, distally concave. Basal cell
three or four times as long as broad, its distal fourth included in the
angle between the two lower cells of the marginal series. Anterior
series consisting of four cells, the lower three subequal, usually all
appendiculate, the uppermost vertically elongated, externally convex,
extending to the middle of the venter of the perithecium: posterior
series consisting of usually seven cells, the four lower similar to those
of the anterior series, usually all appendiculate, the subtending cells
hardly intruded between adjacent members of the series, the three
terminal cells successively smaller, flattened, their septa at right
angles to the axis of the series which they form, and which is continu-
ous with that of the primary appendage and its basal and subtending
cells, which, together with the two terminal cells of the posterior
series form a free subtriangular projection directed at an angle of

378 PROCEEDINGS OF THE AMERICAN ACADEMY.

somewhat over 45° to the axis of the body of the perithecium: the
median series consisting of usually five cells, the lowest larger, longer
than broad and lying mostly below the base of the perithecium; the
three upper successively narrower, extending to the base of the tip
of the perithecium, forming a series almost symmetrical with that
of the three terminal cells of the posterior series and the primary
appendage, the axes of the two series nearly at right angles. Tip of
the perithecium wholly free, bent strongly inward, the apex abruptly
distinguished, the lip-cells rather prominent, the inner more so,
rounded; the body nearly vertical or inclined very slightly outward,
rather long and narrow and symmetrically rounded basally and
distally. Spores 18 X ὅμ. Perithecium 80 10u. Appendages
subceylindrical, small, about 6 X 2.5. Basal cell 20 X 6u. Total
length to tip of perithecium 75 X 344, not including basal cell of
primary appendage.

On Celaenopsis sp. Trinidad, No. 2427. _

Clearly distinguished from other known species by its general form
and excavated superior margin.

Rickia Euzerconalis nov. sp.

General form short-spathulate, hyaline. Basal cell very small
and short, separating an appendiculate cell distally on the anterior
side. Posterior marginal row consisting of usually eight, often nine
cells, radially and obliquely but slightly elongated; all usually cutting
off an appendiculate cell, except the distal one, which is small, tri-
angular and subtends the large usually outcurved basal cell of the
primary appendage which is free above it, two to three times as long as
broad, and about the same diameter throughout: anterior marginal
series consisting of usually five cells, more rarely four or six, the lowest
separating an appendiculate cell below, which lies between it and the
basal cell of the receptacle; the remaining cells large, each, except
sometimes the lowest, separating an appendiculate cell distally; the
uppermost extending to or beyond the middle of the perithecium with
which its appendiculate cell with the appendage is in contact: median
series consisting of almost invariably six, rarely five or seven, cells,
not differing greatly in size, extending from just below the base of the
perithecium nearly to its apex. Perithecium narrow, erect, its tip
externally free, the inner lip-cell projecting as a short finger-like
process. Appendages stout, yellowish-brown, 7 X 3.54. Spores
25 X 2.5. Perithecia 22-24 * Sy. Basal cell including foot,

THAXTER.— RICKIA AND TRENOMYCES. 379

14-16 X 6-8 u. Total length to tip perithecium 50-70 Χ 24-32 μ.
Basal and subtending cell of primary appendage 12-15 Χ 5 μ.

On Euzercon spp. ‘Trinidad, Nos. 2432 and 2430; Kamerun, No.
2443.

This species is most nearly related to R. Megisthani from which it
differs in its more complicated receptacle, larger size and more or less
evenly spathulate outline. In this, as well as in the following species
(R. Megisthani) the lowest appendage on the anterior side is subtended
by a cell which lies external and inferior in relation to the lowest cell
of this series, instead of distal, and has the appearance often of having
been separated, not from this cell, but from the basal cell of the re-
ceptacle below and it is possible that this is its actual relation.

Rickia Megisthani nov. sp.

Hyaline. Basal cell rather short and stout, obliquely separated
from the basal cell of the anterior series, which is angular, subiso-
diametric and lies immediately below the base of the perithecium,
cutting off an appendiculate cell which sometimes covers its whole
outer margin, or more often lies external and inferior in relation to it;
the series consisting of two other cells which are subequal, elongate;
the base of the upper lying obliquely over the distal end of the lower,
which may or may not cut off an appendiculate cell distally; the cell
above it, sometimes lacking, with or without an appendiculate cell
which lies in contact with the outer margin of the perithecium reach-
ing to its upper third or half: the posterior series consisting of
normally four cells, the lowest more often not appendiculate; the
second and third equal and appendiculate; the fourth vertically
elongated, its upper third or half quite free, straight or distally
slightly geniculate and continued by the long free finger-like slightly
curved basal cell of the primary appendage. Median series of three
subequal cells, vertically placed and extending almost to the apex of
the perithecium. Perithecium rather stout, its inner margin straight,
its outer convex and one half to one third free; the tip very slightly
bent inward; the outer lip-cell forming a small, short, finger-like
projection. Appendages very short and small, 5 X 2.5. Spores
20 X 2u. Perithecia 30-32 8-117 μ. Basal cell, including foot,
16 X 7u. Total length to tip of perithecium 50-60 & 20-304. The
free termination of the posterior series, including basal and subtend-
ing cell of primary appendage 25-40 X 5 μ.

On Megisthanus sp. Trinidad, No, 2435,

380 PROCEEDINGS OF THE AMERICAN ACADEMY.

No antheridia have been seen in the numerous specimens examined.
The species is very closely allied to R. Euzerconalis from which it
differs in its smaller size, simpler structure and more irregular outline.

Var. Trachyuropodae nov. var. Similar in general to the type.
Somewhat smaller, the distal cell of the anterior series extending
cushion-like usually to the tip of the perithecium; the posterior series
consisting of five cells, the distal one wholly enclosed or hardly pro-
truding, directed slightly inward, bearing the more slender base of
the primary appendage which is erect or curved very slightly outward.
Appendages stouter.

On the thin anterior and lateral margins of Trachyuropoda spp. Ita-
coatiara, Amazon, No. 2206, and Trinidad, No. 2429.

Abundant material of both type and variety have been examined
and the differences noted seem constant, though not sufficient for
specific separation.

Rickia Kameruna nov. sp.

Hyaline asymmetrical. Basal cell small and short, abruptly dis-
tinguished from the receptacle and from its broad pointed end, which
is but slightly intruded between the two basal cells of the lateral
series. Anterior series consisting of two cells without appendages,
the upper partly overlapping the base of the perithecium which it
subtends, and which is otherwise wholly free externally, rather long,
its upper half bent slightly inward, the apex, only, free on the inner
side, the outer and especially the inner lip-cell slightly prominent:
the median series erect, consisting of five cells, the lowest not extend-
ing to the base of the perithecium: posterior series consisting of seven
to eight cells, all except the upper one or two cutting off a relatively
large appendiculate cell, the two lower slightly elongated radially,
the rest very similar to those of the median series beside which they
lie; the terminal one bearing terminally and externally the basal cell
of the primary appendage which projects outward obliquely, its
axis parallel to that of the free upper oblique margin of the terminal
cell of the median series. Appendages rather stout, 10 <3. Spores
18-20 X 2y. Perithecium 30-34 X 6-8 yu. Basal cell exclusive of
foot 8 μ. Total length to tip of perithecium 40 X 20 μ. Basal cell
of primary appendage, with subtending cell, 8 μ.

On Euzercon sp. Kamerun, No. 2487.

Although the posterior series in this species is not extended to form
an appendage, it seems as nearly related to R. filifera as to any of the
other species, owing to the small development of its posterior series,

THAXTER.— RICKIA AND TRENOMYCES. 381

which leaves the external margin of the perithecium wholly free as in
R. Celaenopsis. There appear to be two cells in the anterior series,
the upper of which is almost concealed by the base of the perithecium.
I have seen no indication of an antheridium in either of the three
specimens from which the description has been drawn.

Rickia filifera nov. sp.

Small and slender. Basal cell obliquely separated from the lower
cell of the anterior marginal series which consists of two subequal
cells; the upper extending a short distance upward external to the
base of the perithecium: posterior series consisting of a variable
number of cells (eight to fifteen) the basal extending above the base
of the perithecium, the subbasal lying opposite to it; the third extend-
ing beyond its tip; the rest superposed to form a long, slender, erect,
or slightly outcurved appendage, terminated by the undifferentiated
basal cell of the primary appendage: the basal cell of the series, and
many of the others, cutting off a small appendiculate cell distally and
externally: median series consisting of two cells, the lower lying
opposite the upper half or less of the perithecium, the upper in contact
with the third and fourth cells of the posterior marginal series, its
inner margin wholly free. Perithecium slender, the tip well dis-
tinguished externally and bent slightly outward, the inner lip-cell
forming a short projection. Appendages slender, cylindrical, hyaline,
10 X 2u. Spores 24 X 2.8 μ. Perithecia 35-45 X 8-12. Basal
cell including foot 12 X 4-5y. Total length to tip of perithecium
35-45 X 8-12. Longest free flagellum, including primary append-
age, 175 μ.

On a very large mite allied to Megisthanus, on Passali. Kamerun,
No. 2442.

This species varies considerably in size and in the length of the
extension of its posterior marginal row. No antheridia have been
recognized, although material of various ages is available. It is
perhaps most nearly related to R. Megisthani but resembles it only
remotely, and cannot be confused with it on account of its free “ flagel-
lum.”

TRENOMYCES.

This very curious genus was first discovered by Chatton in France
on Mallophaga infesting domestic fowls, and had been received by me
from Dr. Miiller who collected it at Elbing, Prussia, and from Dr.

382 PROCEEDINGS OF THE AMERICAN ACADEMY.

Trinchieri who found it at Naples, before the appearance of the pre-
liminary paper by Chatton & Picard in Comptes Rendus (CXLVI,
p. 208, 1908) was published. It was thus discovered almost simul-
taneously in Italy, Germany and France, and has since been found
in New England and received from various other parts of North
America.

Having been interested to learn something further as to the distri-
bution and characteristics of the species in this genus, I have made a
special effort to accumulate material, and am especially indebted for
an opportunity to do so to the kindness of Prof. V. L. Kellogg, who
has allowed me to go over his very large accumulations of duplicates
in alcohol, and of Mr. M. A. Carriker who put his valuable collection
at my service. Mr. Kirkpatrick has also sent me Mallophaga from
turkeys and pigeons collected for me at the Rhode Island Experiment
Station, for which I am greatly indebted to him, and I have also
obtained material from Guatemala collected by the late Professor
W. A. Kellerman; from the Bahamas, (W. W. Worthington), as
well as from other sources.

The results of my examination of some thousands of Mallophaga
have been somewhat disappointing, since their parasites are generally
rare, and, if the data obtained may be assumed to indicate the actual
conditions, have not found this aberrant group of insects a very
favorable substratum for the development of numerous or character-
. istic species. As will be seen the following enumeration includes
only six additional forms, none of them, with the possible exception
of 7. gibbus, departing very far from the characters of the type-
species. In all a more or less complicated rhizoidal apparatus is
developed, simple in one species, which penetrates the host. The
receptacle consists of two cells terminated by a bicellular apiculate
appendage resembling a spore of Puccinia, the upper giving rise to
fertile branches which grow downward and corticate the lower, the
corticating cells producing perithecia or antheridia according to the
sex of the individual; although in some instances the corticating cells
of the male are hardly developed, the antheridia arising directly from
single cells obliquely separated from the lower margin of the subbasal
cell of the receptacle. As in Dimeromyces and Dimorphomyces, to
which the genus is most nearly related, the basal cells of the peri-
thecium break down, and the cavity of the latter and that of the stalk-
cell become continuous.

a θα ν τ ναληδανηηι

ae

THAXTER.— RICKIA AND TRENOMYCES., 383

TRENOMYCES HISTOPHORUS Chat. & Picard.

This species, which appears to vary greatly in size, has been re-
ceived from Dr. Miiller, from Elbing, Prussia; from Prof. Trinchieri
from Naples, Italy, and I have examined type material kindly sent
me by Professor Chatton. In this country it has been obtained on
species of Menopon and Goniocotes from Kittery Point, Maine, and
from Newton, Mass. (on hosts kindly sent me by Mr. Walter Deane),
on Menopon sp. from Gundlach’s mockingbird, Bahamas; on Meno-
pon from hen, Jamaica, W. I., and Guatemala: in the Kellogg collec-
tion on M. mesoleucum (crow), Palo Alto, California; M. tridens, Iowa;
Menopon sp., No. 256b; on Goniocotes, Guatemala.

A species has been examined from various species of Nirmus,
N. punctatus (Calif.), N. maritimus (N. E. and Cal.), N. olivaceus
(Elbing, Prussia, Dr. Miiller), which seems hardly separable from the
many variations of 7’. histophorus. A variety, which may possibly
prove a distinct species has also been found on Menopon numerosum
(Kellogg, No. 24b), Menopon spp. (Kellogg, Nos. 80b, 256b, 74b),
Docophorus sp. (Kellogg, No. 997). In this form the basal cell and
the upper enlarged portion of the rhizoid are more or less conspicuously
suffused with smoky brown in all cases. The ascogenic cell is usually
near the base of the short stalk, and the distal cell of the appendage
is somewhat more compressed than in the type but there are otherwise
no distinctive characters.

Trenomyces Lipeuri πον. sp.

Male individual. Rhizoid more or less abruptly enlarged immedi-
ately below the integument, the swollen portion variably elongated
and passing below into a rather stout simple, cylindrical prolongation
of variable length. Basal cell of the receptacle bent at right angles
to the rhizoid, horizontally elongated and corticated on the upper
surface by an irregularly double series of small cells, which give rise
to a corresponding series of erect or slightly divergent antheridia,
Stalk-cell of the antheridium very slender, broadened below the basal
cells; the body rather short and stout, subfusiform, the efferent tube
short and slender. Appendage lying horizontally; the distal cell twice
as long as the basal. Length from tip of appendage to last corticating
cell, largest specimen, 42 4. Appendage 15 X 9. ‘Total length of
antheridium including stalk 35 μ; efferent tube 4 long; rest of body
about 18 X 10 u.

384 PROCEEDINGS OF THE AMERICAN ACADEMY.

Female individual. General structure like that of the male; the
base of the rhizoid shorter and relatively broader with very thick walls,
the rhizoid proper, simple. Corticating cells of the basal cell vertically
elongated, closely associated in a double crest-like series, bearing two
or three to fifteen perithecia. The latter yellowish more or less dis-
tinctly tinged with brown, the stalk rather slender and clearly dis-
tinguished, about one third as long as the body of the perithecium
which is rather short and stout, subfusiform; the apex blunt and
relatively broad, crowned by four more or less clearly defined promi-
nences which surround the short rounded or slightly suleate apex.
Perithecium, including stalk, 90-110 yu. The main body 60-80 X
20-28 μ. Total length of rhizoid about 90-100 μ the slender portion
about 7 μ in diameter.

On various parts of [ipeurus sp. on Buzzard, Los Amates, Guate-
mala, No. 1547. On L. celer, Nos. 1564-67, California (Kellogg, Nos.
20a, 684c, 39a).

This species is clearly distinguished by the horizontal arrangement
of its perithecigerous cells and by its simphe rhizoid. It is somewhat
variable in size, the specimens from Guatemala producing a greater
number of smaller perithecia than those from California. The ap-
pendage which also lies horizontally is usually quite hidden or broken
off, and appears to be rather narrow, the distal cell larger.

Trenomyces Laemobothrii nov. sp.

Male individual. Corticating cells extending but slightly below
the subbasal cell, the lower two thirds of the basal cell quite free,
the latter thick-walled, somewhat broader distally, about as long as
broad. Antheridia of the usual form suberect in a compact group,
six or more in number, the stalk-cells rather long, broader distally
and not abruptly distinguished from the body. Appendage relatively
very large, the cells subequal, broadly rounded, the apiculus hardly
distinguishable. Basal cell 18 Χ 18. Appendage 28 X 18m. An-
theridia including stalk 45-50 Χ, the body 12 X 254, including
efferent tube.

Female individual. Basal cell rather large and rounded, more or
less completely corticated, except at the base where the ends of the
corticating branches may be clearly visible. Perithecia about six
in number, rather slender, subfusiform, the stalk relatively short,
not distinguished from the body, the tip large, its margins slightly
convex, but otherwise not distinguished from the main body; the

a 00

o

THAXTER.— RICKIA AND TRENOMYCES. 385

rather prominent suleate apex subtended by four somewhat spreading
bisuleate prominences. Appendage relatively very large, the subequal
cells rounded as in the male. Perithecium, including stalk 140-160
20-25 μι Appendage 30 X 20 u.

On Laemobothrium atrum from Coot, New England. M. C. Z.,
No. 1537.

This species is most easily distinguished by its unusually large
appendage, which resembles a stout spore of Puccinia. It seems most
nearly related to 7. Lipeuri, the perithecia being very similar. The
mode of growth is however, quite different. The rhizoids are entirely
broken off in all the specimens.

Trenomyces circinans nov. sp.

Male individual. Corticating cells few and irregular, producing
usually not more than two to four antheridia. Antheridia of the
usual form, the body bent often at a right angle to the slender stalk-
cell or sometimes recurved, the stalk 18 Χ 4 yu, the body 18 X 14 uz.
Appendage relatively small, the cells about equal, 18 X 114, the
.distal cell blunt pointed.

Female individual. Swollen portion of the rhizoid bearing several
horizontal or upcurved lobes from which arise usually furcate smaller
lobes running to slender threads of no great length. Perithecia two to
four, usually strongly circinate when young, at maturity typically
bent or even recurved, rarely straight, the stalk relatively slender, the
body often rather abruptly distinguished, broader distally below the
tip, which may be subtended by a distinct elevation on one side and is
well distinguished, its margin usually slightly convex, separated by a
slight constriction from the crown formed by four symmetrically
placed somewhat spreading lobes which surround the hardly promi-
nent apex, the whole surface of the stalk and body more or less dis-
tinctly roughened or granular, the walls much thickened. Appendage
relatively small like that of the male. Perithecium including stalk
225-280 X 28-35 μ; the stalk 70-125 X 1ὸ or broader. Appendage
20 X 10-14 uw.

On various parts, especially the head of Lipeurus sp., on pigeons,
Kingston, R. I., No. 1549; on L. baculus, Elbing, Prussia (Dr. Miiller) ;
on Docophorus Californicus, California, No. 1555 (Kellogg No. 666);
on D. Montereyi, No. 1554 (Kellogg No. 264c).

The Californian forms on Docophorus are not quite so well marked
as those from Prussia and Rhode Island which, by their abruptly

386 PROCEEDINGS OF THE AMERICAN ACADEMY.

curved habit, slender stalks, and roughened surface, are clearly dis-
tinguished from other species of the genus. The tip of the perithe-
cium in well developed specimens is not unlike that of Arthrorhynchus
Eucampsipodae, but the conformation varies considerably and com-
paratively few specimens have a well defined subterminal hunch.
Several specimens on Docophorus colymbinus, Nos. 1556-7 (Kellogg,
Nos. 14a and 12a), differ distinctly in that the tip is unmodified and
hardly distinguished, the stalks stouter and less well distinguished.
Further material may indicate that this form is distinct.

Trenomyces gibbus nov. sp.

Male individual unknown.

Female individual. General structure like that of 7. histophorus.
Swollen portion of the rhizoid producing several, horizontal lobes.
Corticating cells very irregular, completely concealing the somewhat
irregular basal cell, giving rise to numerous perithecia. Perithecia
faintly tinged with yellowish, stout elongate, the stalk not distinguished
from the body, the whole indistinctly roughened, and having the
appearance of a goose’s neck and head owing to a subterminal protru-.
sion which causes the tip and apex to be bent to one side at an angle
45° or more; the tip nearly symmetrical above the protrusion, broadly
conical, the apex rather narrow, subtruncate, slightly indented.
Total length of perithecium 300 μ, including stalk, which may be 30 u
broad just above its origin; the tip above the hunch, 32 μ long, the
base 28 to 30 u broad, the apex about 7 μ. Appendage 25 X 10 un.

Described from a single female on Lipeurus longipilus. No. 1563
(Kellogg, No. 128d), California.

This form is so peculiar that I have not hesitated to describe it
from a single well developed female in good condition. There are a
dozen or more perithecia on the specimen in various stages of develop-
ment, the four which are mature suggesting the heads and necks of a
flock of geese. The distal cell of the appendage is somewhat longer
than the basal, tapering from base to apex.

ppt νου.

Proceedings of the American Academy of Arts and Sciences,

Vor. XLVIII. No. 11.— Novemser, 1912.

THE SPACE-TIME MANIFOLD OF RELATIVITY. THE
NON-EUCLIDEAN GEOMETRY OF MECHANICS
AND ELECTROMAGNETICS.

By Epwin B. WILSON AND GILBERT N. LEwIs.

THE SPACE-TIME MANIFOLD OF RELATIVITY.
THE NON-EUCLIDEAN GEOMETRY OF MECHANICS
AND ELECTROMAGNETICS.

By Epwin B. WILSON AND GILBERT N. Lewis.

Introduction.

1. The concept of space has different meanings to different persons
according to their experience in abstract reasoning. On the one hand
is the common space, which for the educated person has been formu-
lated in the three dimensional geometry of Euclid. On the other
hand the mathematician has become accustomed to extend the concept
of space to any manifold of which the properties are completely de-
termined, as in Euclidean geometry, by a system of self-consistent
postulates. Most of these highly ingenious geometries cannot be
expected to be of service in the discussion of physical phenomena.

Until recently the physicist has found the three dimensional space
of Euclid entirely adequate to his needs, and has therefore been in-
clined to attribute to it a certain reality. It is, however, inconsistent
with the philosophic spirit of our time to draw a sharp distinction
between that which is real and that which is convenient,! and it would
be dogmatic to assert that no discoveries of physics might render so
convenient as to be almost imperative the modification or extension
of our present system of geometry. Indeed it seemed to Minkowski
that such a change was already necessitated by the facts which led
to the formulation of the Principle of Relativity.

2. The possibility of associating three dimensional space and one
dimensional time to form a four dimensional manifold has doubtless
occurred to many; but as long as space and time were assumed to be
wholly independent, such a union seemed purely artificial. The idea
of abandoning once for all this assumption of independence, although
fore-shadowed in Lorentz’s use of local time, was first clearly stated by

1 See, for example, H. Poincaré, La Science et |’ Hypothése.

390 PROCEEDINGS OF THE AMERICAN ACADEMY.

Einstein. The theorems of the principle of relativity which correlate
space and time appeared, however, far less bizarre and unnatural
when Minkowski showed that they were merely theorems in a four
dimensional geometry.

Suppose that a student of ordinary space, habituated to the inter-
pretation of geometry with the aid of a definite horizontal plane and
vertical axis, should suddenly discover that all the essential geometri-
cal properties of interest to him could be expressed by reference to a
new plane, inclined to the horizontal, and a new axis inclined to the
vertical. Whereas formerly he had attributed special significance
to heights on the one hand and to horizontal extension on the other,
he would now recognize that these were purely conventional and that
the fundamental properties were those such as distance and angle,
which remain invariant in the change to a new system of reference.

Let us now consider a four dimensional manifold formed by ad-
joining to the familiar ἃ, y, z axes of space a t axis of time. Any
point in this manifold will represent a definite place at a definite time.
Space then appears as a sort of cross section through this manifold,
comprising all points of a given time. For convenience we may
temporarily ignore one of the dimensions of space, say 5, and discuss
the three dimensional manifold of x, y, t. This means that we will
consider only positions and motions in a plane. The locus in time of
a particle which does not change its position in space, that is, of a
particle at rest, will be a straight line parallel to the ¢ axis. Uniform
rectilinear motion of a particle will then be represented by a straight
line inclined to the ἐ axis.

3. If we adopt the view that uniform motion is only relative, we
may with equal right consider the second particle at rest and the first
particle in motion. In this case the locus of the second particle must
be taken as a new time axis. What corresponding change this will
necessitate in our spacial system of reference will depend entirely
upon the kind of geometry that we are led to adopt in order to make
the geometrical invariants of the transformation correspond to the
fundamental physical invariants whose occurrence in mechanics and
electromagnetics has led to the principle of relativity.

It is immediately evident that if uniform motion is to be repre-
sented by straight lines, the statement that all motion is relative shows
that the transformation must be of such a character as to carry
straight lines into straight lines. In other words, the transformation
must be linear. Further we must assume that the origin of our space
and time axes is entirely arbitrary.

WILSON AND LEWIS.— RELATIVITY. 391

The further characteristics of this transformation must be deter-
mined by a study of the important physical invariants. Fundamental
among these invariants is the velocity of light, which by the second
postulate of the principle of relativity must be the same to all observ-
ers. Hence any line in our four dimensional manifold which repre-
sents motion with the velocity of light must bear the same relation
to every set of reference axes. This is a condition which certainly
cannot be fulfilled by any transformation of axes to which we are
accustomed in real Euclidean space. It is indeed a condition sufficient
to determine the properties of that non-Euclidean geometry which we
are to investigate.

Minkowski, in his two papers on relativity,? used two different
methods. In his first and elaborate treatment of the subject he in-
troduced the imaginary unit V— 1 in such a way that the lines which
represent motion with the velocity of light become the imaginary
invariant lines familiar to mathematicians who discuss the real and
imaginary geometry of Euclidean space. In this way, however, the
points of the manifold which represent a particle in position and time
become imaginary; the transformations are imaginary; the whole
method becomes chiefly analytical. In his second, a brief paper,
Minkowski makes use of certain geometrical constructions which
have their simplest interpretation only in a non-Euclidean geometry.

4. It is the purpose of the present work to develop the four dimen-
sional non-Euclidean geometry which is demanded by the principle
of relativity, and to show that the laws of electromagnetics and
mechanics not only can be simply interpreted in this way but also are
for the most part mere theorems in this geometry.

In the first sections we shall develop in some detail the non-Eucli-
dean geometry in two dimensions. For it is only by a thorough
comprehension of this simpler case that it is possible to proceed into
the more difficult domains involving three and four dimensions. This
part of the paper will be continued by a discussion of vectors and the
vector notation that will be employed. At this point it is possible
in a few simple cases to show the applications of the non-Euclidean
geometry to problems in kinematics and mechanics.

The sections devoted to three dimensions will be occupied largely
with numerous analytical developments of the vector algebra, many of
which are directly applicable not only in space of higher dimensions

2 Gesammelte Abhandlungen von Hermann Minkowski, Vol. 2, pp. 352-
404 and pp. 431-444.

392 PROCEEDINGS OF THE AMERICAN ACADEMY.

but also in Euclidean space. We are led further to a consideration
of certain vectors of singular character. The study of the singular
plane leads to the brief consideration of another interesting and im-
portant non-Euclidean plane geometry.

Passing to the general case of four dimensions we shall meet further
new types of vectors, and shall attempt even here to facilitate as far
as is possible the visualization of the geometrical results. We shall
continue further the analytical development, and in particular con-
sider the properties of the differential operator quad. In this con-
nection a very general and important equation for the transformation
of integrals is obtained. The idea of the geometric vector field will
then be introduced, and the properties of these fields will be taken up
in detail.

The subject of electromagnetics and mechanics is prefaced with a
short discussion of the possibility of replacing conceptually continuous
and discontinuous distributions by one another, and we shall point
out that in one important case such a transformation is impossible.
The science of electromagnetics is treated both from the point of view
of the point charge and from that of the continuous distribution.
In both cases it is shown that the field of potential and the field of
force are merely the geometrical fields previously mentioned, except
for a constant multiplier. Particular attention is given to the field
of an accelerated electron,® and in this field we find that the vectors
of singular properties play an important rdle. With the aid of these
vectors the problem of electromagnetic energy is discussed. The
science of mechanics, which is treated in a fragmentary way in some
preceding sections, is now given a more general treatment, and the
conservation laws of momentum, mass and energy are shown to be
special deductions from a single general law stating the constancy of a
certain four dimensional vector, which we have called the vector of
extended momentum. Finally it is pointed out that this last vector
gives rise to geometric vector fields which can be identified with the

3 There seems to be a widespread impression that the principle of relativity
is inadequate to deal with problems involving acceleration. But the essential
idea of relativity can be expressed by the statement that there are certain
vectors in the geometry of four dimensions which are independent of any
arbitrary choice of the axes of space and time. Those problems which involve
acceleration will be shown to possess no greater inherent difficulties than
those that involve only uniform motion. It is, moreover, especially to be
emphasized that the methods which are to be employed in this paper necessi-
tate none of the approximations that are commonly employed in electro-
magnetic theory. Such terms as “quasi-stationary,’’ for example, will not
be used.

WILSON AND LEWIS.— RELATIVITY. 393

fields of gravitational potential and gravitational force. Moreover,
it is shown that these fields are identical in mathematical form with
the electromagnetic fields, and that all the equations of the electro-
magnetic field must be directly applicable to the gravitational.

In an appendix a few rules for the use of Gibbs’s dyadies, which have
occasionally been employed in the text, are stated. And a brief
discussion of some of the mathematical aspects of our plane non-
Euclidean geometry is given.

Tue Non-EvuciipEaN GrEoMEtTRY IN Two DIMENSIONS.
Translation or the Parallel Transformation.

5. In discussing a non-Euclidean geometry various methods of
procedure are available; a set of postulates may be laid down, or
the differential method of Riemann may be followed, or the theory
of groups may be used as by Lie, or (if the geometry falls under the
general projective type, as is here the case) the projective measure
of length and angle may be made the basis. For our present purpose
we need not restrict ourselves to any one of these; but since the first
is familiar to all, we shall employ it as far as convenience permits.
Some of the other methods will, however, be briefly discussed in the
appendix, §§ 64, 65.

With a view to simplicity we shall at first limit the discussion to the
case of a plane. Points and lines will be taken as undefined, and
most of the relations connecting them will be the same as in Euclidean
plane geometry. Thus: *

1°. Through two points one and only one line can be drawn.

2°. Two lines intersect in one and only one point, except that

3°. Through any point not on a given line one and only one
parallel (non-intersecting) line can be drawn.

4°. The line shall be regarded as a continuous array of points in
open order.

6. In regard to congruence or “free mobility” it is important to
proceed more circumspectly than did Euclid. The transformations
of Euclidean geometry may be divided into translations and rotations,
of which the former alone are the same for our geometry. It seems
desirable, therefore, to discuss first and in some detail the postulates

’

4 We make no claim of completeness or independence for these postulates,
which are designed primarily to show the points of similarity or dissimilarity
between our geometry and the Euclidean. A like remark may be made with
respect to proofs of theorems.

394 PROCEEDINGS OF THE AMERICAN ACADEMY.

and propositions relating to this type of transformation, and common
to the two geometries. We therefore postulate for translation:

5°. Any point P can be carried into any point P’, and any two
translations which carry P into P’ are identical.

6°. Any line is carried into a parallel line.

7°. Any line parallel to PP’ remains unchanged.

8°. The succession of two translations is a translation.

These postulates determine the characteristics of a group of geome-
tries of which the two most important are Euclidean geometry and
that non-Euclidean geometry with which we are here concerned.
Another non-Euclidean geometry belonging to this same group will be
discussed briefly in §31. This group excludes such geometries as the
Lobachewskian and the Riemannian in which a parallel to a given
line at a given point is not uniquely defined. We shall first proceed
to develop some of those general theorems which are true in this
whole group of geometries.

I. If two intersecting lines are parallel respectively to two other
intersecting lines, the corresponding angles ° are congruent.

For by translation the points of intersection may be made to coin-
cide, and the lines of the first pair, remaining parallel with the lines
of the other pair (6°), must come into coincidence with them, by
postulate 3°.

II. The opposite sides of a parallelogram are congruent.

For if ABCD is a parallelogram and if A be translated to B, the line
of DC remains unchanged, by 7°, and the line of AD falls along the line
of BC by I. Hence D falls on C by 2°.

Cor. If two points P, P’ are carried by a translation into Q, Q’,
the figure PP’ Q’ Q is a parallelogram.

7. We may now set up a system of measurement along any line
and hence along the whole set of parallel lines. Consider the segment
PP’. By the translation which carries P into (δ΄, the point P’ is
carried into a point P” of the same line. The measure of the separa-
tion of P and P’ we will call the interval ® PP’. And since the segment
PP’ is congruent to the segment P’ P”, the intervals PP’ and P’ P”
are said to be equal. We may thus mark off any number of equal
intervals along the line. We shall assume further the Archimedean
postulate.

5 The word angle here refers to a geometrical figure only, and does not as yet
imply any measure of angle.

6 We use the word interval to avoid all ambiguity. The notion of distance
will be separately considered in Appendix, § 65.

WILSON AND LEWIS.— RELATIVITY. 395

9°, Ifa sufficient number of equal intervals be laid off on a line,
any point of the line may be surpassed.

Now the whole theory of commensurability or incommensurability
of two intervals along the same line or parallel lines may be treated
by the usual methods. Thus the intervals along a line, starting from
any origin upon the line, may be brought into one-to-one correspond-
ence with the series of real numbers. It is, however, to be especially
emphasized that we have not established, and cannot establish by the
translation alone, any comparison between intervals on non-parallel
lines.

III. The diagonals of a parallelogram bisect each other.’

For let (Figure 1) the parallelogram ABCD, of which the diagonals
intersect at 1, be translated into the
position BB’ C’ C (by translating A to
B), in which the diagonals intersect at
Ε΄. Now BE’ is parallel to EC, and EL
to CE’. Hence BE’ which is congruent
to AF, is congruent to EC by II. Con-
sequently 4H is congruent to EC by 8°.

IV. If two triangles have the sides of one respectively parallel
to the sides of the other, and if one side of one is congruent to one side

of the other, then the remaining sides of the
C,4A’ one are respectively congruent to the remain-

ing sides of the other.
For if the two congruent sides are brought
into coincidence by translation, the two tri-
, angles will either coin-
cide throughout, or will
together (Figure 2) form

a parallelogram (II).

; Two triangles with the
sides of one respectively
parallel to the sides of the
other will be called similar.

VY. In two similar triangles the sides of
the one are respectively proportional to the
sides of the other.

For if ABC and A’B’C’ are the triangles, the vertex A’ may be
made to coincide with A by a translation (Figure 3). Suppose, now,

FIGureE 1.

B BD

FIGURE 2.

FIGURE 3.

7 Theorems like this and the preceding and some which are to follow are
proved in elementary geometries by the aid of propositions (on congruence of
triangles) not deducible from translations alone.

396 PROCEEDINGS OF THE AMERICAN ACADEMY.

that AB’ falls along AB, and AC’ along AC. Assume that AC and
AC’ are commensurable. Apply the common measure to the side
AC, and through the points of division draw lines parallel to BC
and to AB. In the small triangles thus formed the parallel sides will
be equal by IV, and therefore the intervals cut off on AB must be
equal by II. In case of incommensurability the method of limits
may be applied.2 The case in which the two triangles fall on opposite
sides of the common vertex may be treated in a similar manner by the
aid of IV.

8. For our future needs, the conception and the measure of area
are fundamental, and it is important to show that this subject may be
satisfactorily treated with the aid of the parallel-transformation
(that is, the translation) alone. Indeed, any arbitrarily chosen unit
intervals along any selected pair of intersecting lines determine a
parallelogram which may be taken as having a unit area. By ruling
the parallelogram into equal parallelograms by lines parallel to its
sides, an arbitrarily small element of area may be obtained. The area
enclosed by any curve may be divided into like elements by similar
rulings, and thus by the method of limits the enclosed area may be
compared with the assumed unit area.’ In particular some simple
propositions on areas will now be deduced.

VI. Any parallelogram with sides parallel to those of the unit
parallelogram has an area equal to the product of the intervals along
two intersecting sides.

8 It may be observed at this point that if two intersecting lines be taken as
axes of reference, if systems of measurement (as yet necessarily independent)
be set up along the two lines with the point of intersection as common origin,
and if to each point P of the plane are assigned coordinates (x, y) equal to the
intercepts cut off from the axes by lines through P parallel to the axes, then
straight lines are represented by linear equations, and conversely. For the
deduction of the equation of a line depends merely upon the properties of
triangles similar in our sense. The transformation from any such set of axis
to any other such set will clearly be linear.

9 If axes be introduced as above, the area of a triangle and the area of any
closed curve are expressed analytically by the usual formulas.

πη |
41a yo 1! and ΤΩΣ = fudy ΞΞ —Lydte,
[az ye 1|

in terms of our assumed unit parallelogram. The theorems on areas could
then be proved analytically, but the elementary geometric demonstrations
seem preferable. It is important to observe further that in a transformation
to new axes, such that

x = ar’ ob by’ 55 ὯΣ y= a's’ 4+ by’ a cs

WILSON AND LEWIS.— RELATIVITY. 397

VII. The diagonal of a parallelogram divides it into two equal
areas.

For if the sides of the parallel- Va
ogram be divided by repeated bi-
section into 2” parts, there will \/
be an equal number of equal τι
parallelograms on each side of pes
the diagonal (Figure 4), and in
the limit the total area of these if
parallelograms approaches the
area of the triangles. Ficure 4.

VIII. If from any point in
the diagonal of a parallelogram lines be drawn parallel to the sides,
the two parallelograms formed on either side of

the diagonal are equal in area (Figure 5).
γιὸς» IX. Two parallelograms between the same
AWW YN / parallel lines and with congruent bases are equal
Figure 5. in area.
Cor. ‘Two triangles having congruent bases on
one line and vertices on a parallel line have equal areas.

Cor. The diagonals divide a parallelogram into four equal triangu-
lar areas.

Proofs may be given by obvious and familiar methods.

X. Of all parallelograms having two sides common to two sides of
a given triangle and a vertex on the third side of the triangle, that one
has the greatest area whose vertex bisects that third side.

For in the figure (Figure 6), where ABC is the triangle and F is the
middle point of the third side, the difference of the two parallelograms
is

HBFE — IBGD = MGFE —IHMD = KMEL— IHMD
= KMEL— KDNL = DMEN.

Propositions IV and VIII are used in the proof.

the value of the area, in terms of the area measured with reference to the new
axes, 15

dx’ dy.’

dxdy = μη ᾿

Ια ὃ
Hence if the measure of area is to be the same, that is, if the unit parallelogram
on the new axes is to have a unit area referred to the old axes, the determinant
of the transformation must be unity. This implies a relation between the
choice of unit intervals on the new axes. Indeed when the unit interval on
one of the new axes has been arbitrarily chosen, the unit interval on the other
is determined. In other words the unit intervals on the new axes must each
vary inversely as the other.

398 PROCEEDINGS OF THE AMERICAN ACADEMY.

As an extension of the idea of similarity for triangles, we may say
that any two polygons which have their corresponding sides parallel

B G F σ

Ficure 6.

triangles ABF, CAE, BCD.

and in proportion are similar. It fol-
lows that if any two corresponding
lines are drawn in the polygons, these
lines must be parallel.

XI. If on two sides of a triangle
similar parallelograms be constructed,
and on the third side a parallelogram
with diagonals parallel to the diagonals
of the other parallelograms, the area
of this parallelogram will be equal to
the difference of the areas of the other
two.

The areas (Figure 7) of the paral-
lelograms on AB, CA, BC are respec-
tively four times the areas of the
If wetake the unit parallelogram with

sides parallel to the diagonals, it will suffice to prove that

FIGurReE 7.

FBX AF = AE X EC— BD X CD,

for each of these areas is twice the area of the corresponding triangle.
In the similar triangles ACE and GCD,

HO CD: vAL DEG:

WILSON AND LEWIS.— RELATIVITY. 399

But by ΠῚ, BD is equal to DG. And writing AF = FB + BD, we
have
EC X BD = CD X FB + CD X BD.

Add to each side the product FB & EC. Then

EC(BD + FB) = CD X BD + FB(CD + EC).
Hence
ECO X:AE—CD X BD = FB X AP.

Non-Euclidean Rotation.

9. The group of parallel geometries determined by Postulates
1°-9°, which, notwithstanding its generality, gives rise, as we have
seen, to some interesting and important theorems, may be subdivided
by adding a set of postulates belonging to a second transformation
which by analogy may be called rotation. It is this set of postu-
lates which will differentiate our non-Euclidean geometry from the
Euclidean.

The difference between our non-Euclidean rotation and the ordi-
nary kind is that in addition to a fixed point, two real lines through
the point remain unchanged. We may postulate for rotation:

10°. Any one point and only that one remains fixed.

This point may be called the center of rotation.

11°. Two lines through this point remain unchanged.

These lines may be called the fixed lines of the rotation.

12°. Any half-line (or ray) from the center, and lying in one of
the angles determined by the fixed lines, may be turned into any other
ray in the same angle, and this uniquely determines the rotation.

13°. The succession of two rotations about the same point is a
rotation.

14°. The result of a rotation about O and a translation from O
to O’ is independent of the order in which the rotation and transla-
tion are carried out.

It follows immediately from 14° that the fixed lines in a rotation
about any point O are parallel to the fixed lines in a rotation about
any other point Θ΄. All lines in the plane may now be divided into
classes in such manner that neither translation nor rotation can
change the classification. Namely,

(a) lines parallel to one of the fixed directions,

(8) lines parallel to the other of the fixed directions,

400 PROCEEDINGS OF THE AMERICAN ACADEMY.

(y) lines which lie in one of the pairs of vertical angles determined
by the fixed directions,

(6) lines which lie in the other pair of vertical angles determined
by the fixed directions.

The lines of fixed direction, namely, the (a)-lines and (§)-lines,
will be called singular lines.

A system of measurement may be set up for angles between rays 19
which issue from a point into one of the angles determined by the
fixed lines through the point. For a succession of rotations may be
used (in the same manner as the succession of translations was used
to establish the measure of interval along a line). Thus if a line
a is carried into a line a’ and at the same time the line a’ is carried
into the line α΄, the angles between a and a’ and between a’ and a”
are congruent and the measures of the angles are said to be equal.
Now as the rotation may be repeated any number of times without
reaching the fixed line, it is possible to find an angle aa“ which shall
be n times the angle aa’. We shall assume the postulate, analogous
to the Archimedean:

15°. If a sufficient number of equal angles be laid off about a
point from any initial ray, any ray of that class may be surpassed.

It thus appears that the angles between any given line and other
lines of the same class may be placed into one-to-one correspondence
with all positive and negative real numbers, just as the intervals
from a point on a line may be thus correlated.!! This constitutes a
very great difference between our geometry and the Euclidean.

It is impossible to show from the preceding statements that any
given figure maintains a constant area during rotation.1? We shall
therefore lay down the additional postulate:

10 The relations of order of all lines of a given class, (y) or (δ), are the same
as those of points on a line, as in 4°.

11 The angle between two singular lines (α) and (8) can obviously not be
measured. Such an angle, and also the angle between any line and a line of
fixed direction, must be regarded as infinite.

12 This matter may readily be discussed analytically. As axes of reference
choose the fixed lines, and let wu, v denote coordinates. As rotation is a linear
transformation, the point P (u, v) and the transformed point P’ (μ΄, v’) are
connected by the equations

μ' =au+bv+e, υ' = du+ev+f.
As the lines u = 0 and νυ = 0 are fixed, these equations reduce to τ΄ = au,
υ' = ev; and as rotation depends on only one parameter, we may write
e = d(a). The succession of two rotations is then expressed by
(u’ = au {ὦ = bu’ ; u"”’ = abu

lv Ξ-- φ(α), Lv” = φ()ν', = $(a)G(b)u,

-
|

WILSON AND LEWIS.— RELATIVITY. 401

105. In rotation an area becomes an equal area.!%

10. We are now prepared to discuss in some detail the general
characteristics of our rotation.
Consider (Figure 8) a series of rota-
tions about ὁ), whereby the point P
assumes the positions P’, P”,....
Let the parallelograms on OP, OP’,
OP”,.... as diagonals and with
sides along the fixed lines be con-
structed. Then by 16° the areas
of these parallelograms are equal,
and in terms of the intervals on
the fixed lines

OA X OB = OA’ X OB’
SOA 6 OR’. Ficure 8.

The point P thus traces a curve which in ordinary geometry would be

with the condition

$(a)b(b) = (ab)

necessitated by 13°. This is a functional equation of which the only (con-
tinuous) solution is φί(α) = α΄. Hence rotation must be of the form

a= au, w= αἴ.

The unit parallelogram on the axes of τὸ and v is hereby transformed into a
parallelogram on these same axes with intervals a and a” along u and v. By
VI the area of the new parallelogram is therefore αὔτ]. If this is to be unity,
r =-—l. The transformation equations for rotation are therefore

oh S01, δ Soy Gp

where a is necessarily positive because points do not change from one side of
the axes to another.

The intrinsic significance of these equations should not be overlooked. A
rotation may be represented as a multiplication of all intervals along one of
the fixed lines by a constant factor and a division of all intervals along the
other fixed line by the same factor. Or, increasing the unit interval along
one fixed line and decreasing it in the same ratio along the other is equivalent
to a rotation. (This process effected along any other axes than the fixed lines
would leave the area unchanged, but would not be a rotation). As the unit
interval along one fixed line cannot be compared either by translation or by
rotation with the unit along the other, and as one of these units is arbitrary,
we have additional evidence that there is no natural zero of angle.

13 Such a postulate is unnecessary in Euclidean geometry owing to the
cada nature of the Euclidean rotation. Postulate 16° could be replaced

y one involving only the notion of symmetry between rotations in opposite
directions.

402 PROCEEDINGS OF THE AMERICAN ACADEMY.
considered a branch of a hyperbola.!* Since, however, this curve is
here generated by the rotation of a line OP about its terminus Q,
we shall call this locus (taken with the other branch Q Q’ Q” sym-
metrically situated with respect to O) the pseudo-circle.

By means of such a rotation we are able to compare intervals upon
any line with intervals upon any other line of the same class. For
the intervals of the congruent radii OP, OP’, OP” will be called equal.

When we consider the fixed lines we observe that the effect of
rotation is to carry the segment OA into OA’ or OA”. It is therefore
evident that segments are congruent by rotation which are incongru-
ent by translation. This source of ambiguity exists only in the case
of singular lines, for in no other case is it possible to compare two
segments both by rotation and by translation. We may remove this
ambiguity at once by stating that intervals along singular lines, al-
though metrically comparable with intervals on other singular lines
of the same class by translation, are
all of zero magnitude when compared
with intervals on any non-singular
line. This will become more evident
later.

Consider next (Figure 9) the inter-
cept AB terminating on the fixed lines
corresponding to a rotation with cen-
ter at O. Let P be the middle point
of the line, and C any other point.
Through C draw a line parallel to OB,
and on this line mark the point P’
such that the area OD P’G equals the
area OF PH. The area OECG is less

FIGURE 9. than each of these by X. Hence

P’ lies on the further side of AB

from Ὁ. But P’ is a point on the pseudo-circle through P concentric

with O, as we have just seen. Since C was any point of AB, it follows

that P’ may be any point of the pseudo-circle. Hence as the line

AB meets the pseudo-circle at P and only at P, it is tangent to the
curve. As a species of converse, we may state the theorem:

14 There is no special significance in the fact that a rectangular hyperbola is
drawn in the figure and that the fixed lines a, 8 are perpendicular in the
Euclidean sense; in subsequent figures the singular lines are often oblique.
From the non-Euclidean viewpoint the question of perpendicularity or
obliquity of the singular lines is of course meaningless.

δ. (neler

WILSON AND LEWIS.— RELATIVITY. 403

XII. The tangent to a pseudo-circle lies between the curve and
its center, and the portion of the tangent intercepted between the
two fixed lines is bisected at the point of tangency.

11. In a pseudo-circle the radius and the tangent at its extremity
are said to be perpendicular. Or in virtue of XII we may say that the
perpendicular from any point O to any non-singular line is the line
from O to the middle point of that segment of the line which is inter-
cepted by the fixed lines through ὦ. The construction of a perpendic-
ular to any line of class (y) or (δ) at a point of the line is equally simple.

By the aid of propositions concerning similar triangles, the follow-
ing theorems concerning perpendiculars are readily proved.

XIII. Ifa line ais perpendicular to a line b, then ὁ is perpendicular
to a.

XIV. Through any point one and only one perpendicular can be
drawn to any line.

XY. All lines perpendicular to the same line are parallel.

XVI. The singular line of one class
which is drawn through the intersection
of any two perpendicular lines will bisect
the segment intercepted by these lines
upon any singular line of the other class
(Figure 10).+°

XVII. The perpendicular to a (y)-line Braun 10.
is a (6)-line, and vice versa.

Intervals along lines of class (6) cannot be compared by congruence
with intervals along lines of the (y) class. We may, therefore, arbi-
trarily define equality of intervals between the two classes. Jf two
mutually perpendicular lines are drawn from any point and terminate
on a singular line, the intervals of these lines will be said to be equal.'®
The consistency of this definition is readily proved.

The definition of perpendicularity is such that if two lines are per-
pendicular they must remain perpendicular after a translation or
rotation. The former case is obvious, and the latter becomes so
when the lines are considered as radius and tangent in a pseudo-circle
generated by the rotation; the more general case in which neither of
the perpendicular lines passes through the center of rotation then
follows with the aid of XV. It is important to observe one peculiar

15 In the figure BO and OC are equal, and AB and AC are perpendicular.
16 In Figure 10, the intervals AC and AB are therefore equal by this
definition.

404 PROCEEDINGS OF THE AMERICAN ACADEMY.

characteristic of our rotation, namely that two perpendicular lines
approach each other and the fixed line between them scissor-wise,
as may be seen, in Figure 11, where OC and
OD become respectively OC’ and OD’, OC”
and OD", ---- The pseudo-circles traced by
OC and OD may be called conjugate pseudo-
circles, since the interval OC equals the
interval OD, the lines CD, C’D’, ----, being
OS CSS ae singular, and bisected by a fixed line.

Since two mutually perpendicular lines ap-
proach, during rotation about their point of
intersection, the same fixed line, we may
extend our definition of perpendicularity by

Figure 11. regarding every singular line as perpendicular

to itself. This extension is also suggested by

the fact that the fixed line may be considered an asymptote of a

pseudo-circle. Special caution must be given against the idea that a

singular line of one class is perpendicular to a singular line in the

other class. The peculiarities of singular lines will become clearer in
the work on vector analysis.

12. A triangle of which two sides are perpendicular will be called
a right triangle, and the third side will be called the hypotenuse. A
parallelogram of which the two adjacent sides are perpendicular and
of equal interval will be called a square. The following theorem is
obvious:

XVIII. One diagonal of every square is a singular line and the
other diagonal is a singular line of the other class.

XIX. Pythagorean Theorem. The area of the square on the
hypotenuse of a right triangle is equal to the difference of the areas of
the squares on the other two sides.

For by XVIII the diagonals of the squares are lines of fixed direction,
and hence parallel each to each. The squares on the two legs are
similar. And the proposition is evidently a special case of XI. (In
Figure 7 if the dotted lines are singular lines, the lines AC and BC
are so drawn as to be approximately perpendicular.)

XX. Any two squares whose sides are of unit interval are equal in
area.

For by suitable translation and rotation one may be brought into
coincidence with the other. The unit of area will henceforth be taken
as the area of a square whose sides are of unit interval. Hence
follows:

WILSON AND LEWIS.— RELATIVITY. 405

Cor. The area of any rectangle is the product of the intervals of
two adjoining sides.

We may therefore obtain from XIX the theorem

XXI. The square of the interval of the hypotenuse of a right
triangle is equal to the difference in the squares of the intervals of the
other two sides.

Cor. The perpendicular from a point to a line has a greater interval
than any other line of the same class drawn from the given point to
the given line.

Having now given a final definition of the measure of area, we may
define the unit of angle. The radius of the pseudo-circle, in advancing
by rotation over equal angles, necessarily sweeps out equal areas
(by 16°). Hence by the familiar argument sectorial areas in any
pseudo-circle are proportional to the angles at the center. The unit
angle will be taken as that angle which, in a pseudo-circle of unit
radius, encloses a sectorial area of one-half the unit area.

Vectors and Vector Algebra.

13. ‘Translation or the parallel-transformation leads at once to
the consideration of vectors. We have shown that when a translation
carries A into B and A’ into B’ the directed segments AB and A’B’
are parallel and congruent (Cor. to 11). Hence a translation may be
represented by a vector, that is, by any directed segment laid of from
any origin and having the same interval and direction as AB. The
succession of two translations is represented by the sum of their
corresponding vectors. The addition and subtraction of vectors and
their multiplication by scalars follows the usual laws (by δὲ 5-7).

If two vectors a and Ὁ are laid off from a common origin, the paral-
lelogram constructed on the vectors is called their outer product axb,
and the magnitude of this product will be taken numerically equal to
the area of the parallelogram.17 We must bear in mind that not this
magnitude (nor yet a vector perpendicular to the plane), but the
parallelogram itself is the outer product. We may, however, repre-
sent the outer product by any other closed figure of equal area, pro-
vided that it is taken with the same sign. The sign attributed to an

17 Our vector notation will be based upon that of Gibbs, and is identical with
that employed by Lewis (Four dimensional Vector Analysis, These Proceedings,
46, 163-181) except in the designation of the inner product which we shall
define asin that paper, but represent by a+b instead of ab; the latter form will
be reserved to denote the dyad. The scalar magnitude of a vector will be
represented by the same letter in italic type.

406 PROCEEDINGS OF THE AMERICAN ACADEMY.

area does not arise from any positive or negative geometric charac-
teristics of the area itself, but from an interpretation or convention
concerning the way in which one area is considered as generated
relative to another, and is required for analytic work. We shall make
the convention that axb and (—a)xb or ax(—b) have opposite signs.

The outer product of a vector by itself or by any parallel vector is
zero, because the parallelogram determined by these vectors has zero
area; thus axa = 0. The associative law for a scalar factor is valid,
because multiplying one side of a parallelogram by a number multi-
plies the area by that number; thus

(na)xb = naxb = ax(nb).
The distributive laws,
ax(b + c) = axb + axe, (a+ b)xc = axc+ bxe,

also hold; for inspection shows that the parallelogram ax(b + Ο) is
equal to axb plus axc. The anti-commutative law,

axb = — bxa,
holds; for
(a + b)x(a + b) = axa+ axb + bxa + bxb = 0.
Hence
axb = — bxa.

14. Thus far we have proceeded by means of the parallel-trans-
formation alone. It is evident that this much of vector algebra is
common to all geometries, including the Euclidean and our non-
Euclidean geometry, in which there is such a parallel-transformation.
The other type of product, the inner product, cannot be defined with-
out some concept of rotation or perpendicularity, or its equivalent.

We shall so define this inner product a:b that it obeys the associa-
tive law for a scalar factor and the distributive and commutative laws,
namely,

(na)-b = na-b =a-(nb),
a:(b + c) = a-b+ ac,
a-b = bea,

and furthermore remains invariant during rotation.

As the fixed lines are fundamental in rotation it is sometimes ex-
pedient to resolve vectors into components along these directions.
Let p and q be definite vectors in the two fixed lines; any vector in

WILSON AND LEWIS.— RELATIVITY. 407

the plane may be written as r = 0 - yq._ By the postulated formal
laws,
rr=2p-ep+ y2q-q + 2zy pq.

We may now note that by rotation a vector along a fixed line is con-
verted into a multiple of that vector. If p becomes np, and the inner
product p-p remains invariant, then p-p = n*p+p; whence it is ob-
vious that p-p = 0. In general: The inner product of any singular
vector by itself is zero, and this suffices to characterize a singular
vector. Hence r-r reduces to

rer = 27ry p-q.

Before proceeding further with the definition of the inner product,
we may observe that the signs of xv and y are determined by that one
of the four angles (made by the fixed lines) in which r lies. According,
then, as x and y have the same sign or different signs, the vector r
belongs to one or the other of the classes (γ) or (δ), and the product
r-r will have one sign or the other. These considerations suffice to
show that if r and r’ are two vectors, and if rer and r’-r’ have the same
sign, the vectors are of the same class, but if rer and r’-r’ are of op-
posite sign, rand r’ are of different classes. We have here a marked
departure from Euclidean geometry, in which the inner product of a
real vector by itself is always positive.

We are now in a position to complete the definition of the inner
product by stating that the product is a scalar, and that the product
of a vector by itself is equal to the square of the interval of the vector,
taken positively if the vector is of class (v), negatively if of class (δ).
This does not imply any dissymmetry between the classes (γ) and (δ),
but is only such a convention as is often made with respect to sign.

The equation rer = 2xy p-q shows that the inner product of any
singular vector and any singular vector of the other class is equal to
one-half the inner product by itself of the diagonal of their parallelo-
gram.

The inner product of any vector and a perpendicular vector is zero.
For by XVI it is evident that if p and q be the components along the
fixed directions of any vector r, so that r= p+ q, then p—q is a
perpendicular vector, and in general any perpendicular vector r’ has
the form n(p — q). Hence

17

r-r = n(p — q)-(p+ q) = n(D-P + 6 — ap — a-d) = 0.

17 The fact that the inner product of a singul wr vector by itself vs anishes
justifies our convention that a singular line is perpendicular to itself.

408 PROCEEDINGS OF THE AMERICAN ACADEMY.

The inner product of any two vectors is equal to the inner product
of either one by the projection of the other along it. For either
vector may be resolved into two vectors one of which is parallel and
the other perpendicular to the other vector. Thus Ὁ may be written
as na + a’, where na is the projection of b on a, and a’ is perpendicu-
lar toa. Therefore

b-a = na-a+ a’-a = nasa,

which was to be proved. Geometrically the only puzzling case is that
in which the vectors are of different classes. Let OA (Figure 12) be
a vector of class (vy) and OB of
class (δ). The projections of
OA on OB and of OB on OA
are respectively OB’ and OA’.
Note that whereas OB’ extends
in the same direction as OB,
the vector OA’ extends along
the opposite direction to OA.
Thus OB’ is a positive multiple
of OB, whereas OA’ is a nega-
tive multiple of OA. But the
inner product of OB by itself is negative, since the vector is of class
(6), while the inner product of OA by itself is positive, since the vector
is of class (y). Hence the inner product of OA and OB has the same
sign, whichever way the projection is taken.

In obtaining the inner product of a singular and a non-singular
vector by projecting one upon the other, it is necessary to project the
singular vector upon the non-singular vector; for it is impossible to
make a perpendicular projection upon a singular vector. In case
both vectors are singular the method of perpendicular projection fails
entirely, and we must use analytical methods (or have recourse to
parallel projection).

15. It will often be convenient to select two mutually perpendicular
lines as axes of reference. We will denote 18 by Κι and k, unit vectors
along such axes, k, being the vector of the (7)-class, and Καὶ, of class (δ).
For these vectors we have the rules of multiplication

Figure 12.

k, Κι = ily ky-ky i | k, ky = ky-k, = 0.

18 We reserve the symbols ky and ks for other unit vectors of class (7) in
space of higher dimensions.

WILSON AND LEWIS.— RELATIVITY, 409

Any two vectors ἃ and b’may be written in the form

a= ak; + ayky, Ὁ = bik; + byky,
and the inner product is then, by the distributive law,

| arb = ab; — αὐι.

In terms of these unit vectors we may also express outer products.
If we write, for brevity, Κὰ = Κιχ Κι, the rules for outer multiplica-

tion are
Κι = —Ky, ki, = Ky = 0.

The outer product of the vectors a and b is therefore
ax) -Ξ (ayb4 == aby) ky.

Since Κις represents a parallelogram of unit area, the question
arises as to why we write k.xk, as ky, and not simply kxk, = 1. The
answer is that the outer product axb possesses a certain dimension-
ality, which, it is true, is not exhibited in a marked degree until we
proceed into a space of higher dimensions, but which renders it un-
desirable to regard the outer product as merely a scalar. We may call
it a pseudo-scalar, and later extend this designation to n-dimensional
figures in a manifold of m dimensions.

Every vector in two dimensional space uniquely determines, except
for sign, another vector, namely, the one equal in interval and per-
pendicular to the first. This vector will be called the complement of
the given vector. To specify this sign, the complement a* of the
vector a may be defined as the inner product of a and the unit pseudo-
scalar k,,, namely, a* = a+Ky, where the laws of this inner product are

ki -kyy = — ky, ky-Kkyy = — kj. .
Thus if a = ak, + ak,, then for the complement
a* = (ayky + agky)* = (αἰκι + agky)+kyy = — agk, — ay ky.

This type of multiplication, as will be seen later, obeys all the general
laws of inner products (§§ 27, 29).

Referred to a set of perpendicular unit vectors, the singular vectors
take the form n(+ k, + k,). The complement of a singular vector is

n(= ky + ky)*=n(+ ky + Κι) Κὶς = n(+ ky - Κι),

that is, the complement of a singular vector is its own negative.

410 PROCEEDINGS OF THE AMERICAN ACADEMY.

We may extend the idea of complements .to scalars and pseudo-
scalars. The complement of the scalar n will be defined as the pseudo-
scalar nk,,; the complement of the pseudo-scalar nk,, will be defined
as the scalar — ἡ. This may be written

(nky)* = nkyeky = — n,

thus establishing the convention kKieki,= —1. It may readily be
shown that, for any two singular vectors p and q of different class,
the outer product is the complement of the inner product, that is,

pxq = (Ῥ αὐ Κι.

In other words the inner and outer products of singular vectors are
numerically equal.

Some Differential Relations.

16. As the inner product r-r of a vector by itself is numerically
equal to the square of the interval of the vector r, the equation of
the unit pseudo-circle of which the radii are all (y)-lines is rer = 1;
and the equation of the conjugate unit pseudo-circle of which the
radii are (6)-lines is rer = —1. As the tangents to a pseudo-circle
are perpendicular to the radu, they must be of opposite class. A
pseudo-circle of which any tangent is a (6)-line (the radii being (y)-
lines) is called a (6)-pseudo-circle; and a pseudo-circle of which
any tangent is a (y)-line (the radii being (6)-lines) is called a (y)-pseudo-
circle. In general if a curve has tangents which are all of the same
class (δ) or (vy), the curve may be designated as a (6)- or a (y)-curve;
the normals to the curve will then be respectively of the opposite
class (y) or (δ). The interval of the are of any such curve will be the
limit of the sum of the intervals of the infinitesimal chords along the
are. We shall not be obliged to consider any curve which is not
altogether of one class as here defined.

As dr is the infinitesimal chord as a vector quantity, the formula
for the scalar arc is

ee i sip de: sae ΟΝ Σὲ bp a Ἐπ ΤΠ

according as the curve is a (γ)- or ἃ (6)-curve.

The sectorial area in a unit pseudo-circle may be regarded as the
sum of infinitesimal right triangles, of which the area is numerically
equal to 4rxdr if r is drawn from the center. The numerical

WILSON AND LEWIS.— RELATIVITY. 411

value of the area is therefore one-half the numerical value of dr, that
is, one-half the infinitesimal interval of are. From our definition of
unit angle (§ 12), it is evident that an angle is equal to the are sub-
tended upon a unit pseudo-circle centered at the vertex of the angle.
This might, in fact, have been made the definition of the measure of
angle. It is evident from these considerations that a rotation turns
all non-singular lines through the same angle.

Angles may be classified according to the classes of their sides. If the
two sides are (y)-lines, the angle will be designated as of class (yy);
if they are (6)-lines, the angle is of class (66). Consideration of angles
(y5), which have one side a (y)-line and the
other a (6)-line, and which cannot be gener-
ated by rotation, need not detain us here. (See
Appendix.)

If any line (Figure 13) through the center
be taken from which to measure angle, posi-
tion upon the unit pseudo-circle may be
expressed parametrically in terms of the
angle as follows. Let the given line be a
line of class (y) (the pseudo-circle then being
of class (6)), and construct the perpendicular Fievre 13.
line of class (δ). These two lines may be
taken respectively as axes of x, and x, with the unit vectors k, and
Κι along them. The equation of the unit pseudo-circle is then

rer = (ak, + agky)-(ayk; + ayky) = αἵ — af = 1.

The differential of angle or arc is in this case

d0=ds= V_dr.dr= V (kidx,+ k,dz:) . (k,d2,+ k,dx,) = Vde2—dx2

Whence, by differentiation of 2? — rf = 1,

[« - [ὦ =) - dats ΕΞ . | dxy hy
Nl ea Va? — 1

and x; = cosh 6, % = sinh, 6;

where θ is the angle between the 2,-axis and the radius vector, and
therefore of the class (yy). If the given line had been of class (δ)
(the pseudo-circle of class (y)), and if the angle ¢ had been of class
(65) measured from the a-axis to the radius vector, the results
would have been

412 PROCEEDINGS OF THE AMERICAN ACADEMY.

x, = sinh @¢, xs = cosh ¢,

with 2°—a? = — 1 as the equation of the pseudo-circle.

If now in general r be the radius of any pseudo-circle, the foregoing
results may readily be generalized, and we obtain the following pair
of equations.

x; = r cosh 6, 2, = rsinh 0, Xs = 2, tanh 6; (1)
x; = r sinh ¢, x4 = r cosh 9g, x; = x, tanh ¢.

In the first case r is a (y)-vector and θ is a (yy)-angle; in the second,
r is a (6)-vector and φ is a (66)-angle. We thus have equations which
express the relations between the hypotenuse and the sides of any
right triangle in terms of one angle. The inclination of the vector r
to the axes k, or k, in the respective cases is the angle

6 = tanh! or oo tanh71 :
11 v4
and the slope of r relative to the axes is the hyperbolic tangent of
the angle, not the trigonometric tangent.
17. Consider next any curve of class (δ). Let

denote scalar arc along the curve, and let r be the radius vector from a
fixed origin to any point of the curve. Then the derivative

ἀντ dey, y divs
Lillian ποτε Bi ΚΕ ΤΣ

ds (2)

is a unit vector tangent to the curve. If this vector makes the angle
¢ with the axis k;, so that the slope of the curve is

ἢ = tanh ὦ = as (3)

the components of the vector are

day eh BC ay v dis Mm ἐν: 1
gs τ sinh Φ = ie: τὶ Ἐπ cosh Φ = Pipers (4)
and Wa aoe (vk, + ky). (5)

V1 — 7

* > ab

WILSON AND LEWIS.— RELATIVITY. 413

If we had chosen a different set of perpendicular axes Κι', ky’, where
k,’ makes an angle Ψ = tanh ''w with k,, so that the inclination of w
to ky’ is φ' = φ — ψ, the new components of w would be

dx’ : Σ : v’
! = sinh φ' = cosh ¢coshy — sinh ¢ sinh y = ————
ds V1 — 0”
ot
Vi — # V1— wv

dics! = cosh’ = cosh ¢ coshy — sinh¢ sinh y = —- :
ds V1 —?
Τ' 1 — vu
τ Vo evil
where 2 ᾿ a
: ary! ; tanh φ — tanh i — al
μ᾿ om τς 1 --- tanh ¢ tanh Ψ πὐ ΠΕ (6)

It will be convenient to have a general equation for the components
of a vector upon one set of axes in terms of its components on another
set. Let Κι, ky be one set of perpendicular unit vectors, and ky’,
k,’ another set. If the angle from Κι to Κι΄ be y, the angle from k,
to Κι΄ is also ψ by ὃ 106. The products

Κι Κι΄ = coshy, k,-k,’= — coshy,
Κι Κι΄ = sinhy, k,’-k, = — sinhy,
follow from (1). To obtain the transformation equations we write
r= ak, + ayky = αἱ Κι + x Κῳ,
and multiply by ky, ky, ky’, ky’;

r-k, = 2; = x; coshy + ay’ sinhy,

—reky = χὰ = 2 sinhy + ay’ coshy, (7)
r-k,’ = 2’ = 2, cosh — ay sinhy,
—r-k, = 2, = — 2x,sinhy + x coshy.

Curvature in our non-Euclidean geometry is defined, as is ordinary
geometry, as the rate of turning of the tangent relative to the are.
As w is a unit tangent, dw is perpendicular to w and in magnitude is
equal to the differential angle through which w turns. Hence

414 PROCEEDINGS OF THE AMERICAN ACADEMY.

se 8)
is the curvature, taken as a vector normal to the curve. Hence
bee a eee ®
In magnitude the curvature is
dv Cx,
APF dx. iy. dx

~~
—
©
τὸ
es
ιν.
ΙΒ.
--
yan 3
ὧν ἐν ©
δ ἢ
i μ᾿
So
| neal |
oe

Relative to axes k,’, k,’, the result is
‘ay k,’ v' ky’ dv’
a la —")? us (1 — ae dx4'
_f d—w)k (v — μὴ ky’ ᾿
Ε —e2vi—w d—v? vli—w

In complete analogy with the circle in Euclidean geometry the
pseudo-circle in our non-Euclidean geometry has a curvature of con-
stant magnitude throughout. The curvature of any other curve may
always be represented as the curvature of the osculating pseudo-circle,
and in magnitude is inversely proportional to the radius of that pseudo-
cirele.

Kinematics in a Single Straight Line.

18. Before proceeding to the discussion of the non-Euclidean geom-
etry of more than two dimensions we may consider some simple but
fundamental problems of physics which may be treated with the aid
of the results which we have already obtained.

The science of kinematics involves a four dimensional manifold,
of which three of the dimensions are those of space, and one that of
time. By neglecting two of the spacial dimensions, in other words
by restricting our considerations to the motion of a particle 15. in a
single straight line, kinematics becomes merely a two dimensional
science. The theorems of kinematics, not in the classical form, but in
the form given to them by the principle of relativity, are simply
theorems in our non-Euclidean geometry.

19 By particle we do not as yet mean a material particle but merely an
identifiable point in motion.

ue lS

WILSON AND LEWIS.— RELATIVITY. 415

The units of distance and time, namely the centimeter and second,
were chosen without reference to each other. Retaining the centi-
meter as the unit of distance, we may take as the unit of time one
which had been frequently suggested as the rational unit long before
the principle of relativity was enunciated, namely, the second divided
by 3 X 10, or the time required by light in free space to travel one
centimeter. The velocity of light then becomes unity.

Let us consider in our geometry two perpendicular lines, and meas-
ure along the (y)-line extension in space, along the (6)-line extension
in time. Then any point in the plane will represent a given position
at a given time. We are considering the motion of a particle along a
specified straight line in space. If x denotes distance along the line
from a chosen origin, then in terms of our previous nomenclature,
we shall take x = αι andt = a; The k,- or f-axis, or any line in the
at-plane parallel to this axis, represents the locus in time of a particle
which does not change its position in space, in other words, of a sta-
tionary particle. Any straight line of the (6)-class making a non-
Euclidean angle Y with k,, represents the locus in space and time of a
particle moving with a constant velocity

dx
Lanse δεν tanh y

A singular line in our plane represents a velocity wu = 1, and is the
locus of a particle moving with the velocity of light.

We have seen that in our plane no pair of perpendicular lines is
better suited to serve as coordinate
axes than any other pair. If then
we consider (Figure 14) two (6)-lines,
marked ¢ and ?’, and the respectively
perpendicular (y)-lines, marked «x
and 2’, and if we regard the first
(6)-line as the locus of a stationary
particle and the second as the locus
of a moving particle, we might
expect to find that we could equally
well regard the second (6)-line as the
locus of a particle at rest and the first as the locus of a moving particle.
And this is, in fact, the first postulate of the principle of relativity.
The one relation between the two lines, which is independent of any
assumption as to which line is the locus of a stationary point, 15

FIGURE 14.

416 PROCEEDINGS OF THE AMERICAN ACADEMY.

the angle y whose hyperbolic tangent is the relative velocity which is
the same by either of the assumptions.

If now we have a third (6)-line t’’ making an angle ¢ with the first
(6)-line, and ¢’ with the second, where ¢’ = ¢—y, and if we call the
relative velocities corresponding to these angles

v = tanh φ, v = tanh@’, u = tanhy,

then it is not true that υ' = v—u, but since ¢’ = ¢—y,

by (6). This is the theorem regarding the addition of velocities ob-
tained by Einstein.?° The true significance of this result cannot be
emphasized too strongly, namely, that the velocity as such can only
be determined after a set of axes have been arbitrarily chosen;
relative velocity, however, has a meaning independent of any co-
ordinate system. Furthermore it is not the relative velocities, but
the non-Euclidean angles, which are their hyperbolic anti-tangents,
which are simply additive. If we were constructing a new system
of kinematics uninfluenced by the historical development of the
science, it might be preferable to make these angles fundamental
rather than the velocities.

Suppose that from a given (6)-line we lay off successively equal
angles, so that each line determines with the preceding line the same
relative velocity, then the angle measured from the given line increases
without limit, but its hyperbolic tangent, which is the velocity relative
to this line, approaches unity, that is, the velocity of light. The
relative velocity, therefore, determined by any two (6)-lines whatever,
is less than the velocity of light. The velocity of light itself appears
the same regardless of the choice of coordinate axes. This is the sec-
ond postulate of the principle of relativity. Indeed if angle, instead
of relative velocity, had been made fundamental, the motion of light,
as compared with all other motions, would have been characterized
by an infinite value of the angle.

19. Let us return to our figure and consider once more the lines
that have been marked ¢, t’, anda, α΄. If we take the ¢-line as the locus
of a stationary particle, then all points along the line x or along any
parallel line are said to be simultaneous, for along any line perpendicu-
lar to the t-axis the value of ἐ is constant. In like manner if we con-

20 Hinstein, Jahrb. d. Radioak, 4, 423.

WILSON AND LEWIS.— RELATIVITY. 417

sider the ?¢’-line as the locus of a particle at rest, then simultaneous
points are those along x’ or along lines parallel to x’. Hence points
which are simultaneous from one point of view, are not simultaneous
from the other. In fact any two points through which a line of class
(y) can be drawn may be regarded as simultaneous by choosing this
(y)-line as the axis a, and the perpendicular line as the axis ἡ. Sim-
ilarly any two points through which a (5)-line can be drawn may be
regarded as having the same spacial position; in other words any point
may be taken as a point at rest.

It thus appears that the measurements of time and space are de-
termined only relative to some selected set of axes. Further to exhibit
this fact, and to determine the relations
which exist between the measures of
time and space when different sets of
axes are chosen, let us consider (Fig-
ure 15) two parallel (6)-lines in our
non-Euclidean plane. These lines
represent the loci of two particles
which have no relative velocity. Let
any set of axes of time and space be
drawn. The constant intervals cut off
by the two parallel (6)-lines from the
x-axis and all lines parallel to this axis
represent the constant distance, as Bicure 15.
measured by these axes, between the
two particles at any time. The constant intervals cut off by the
two parallel (6)-lines on the f-axis and all lines parallel thereto repre-.
sent the constant interval of time as measured by these axes, which
must elapse between the instant when one of the particles has a certain
position (upon the line in which we are considering rectilinear motion
as taking place) and the instant when the other of the particles has
this same position.

One particular choice of axes is especially simple, namely, that
in which the t-axis is parallel to the two (6)-lines, and the z-axis is
perpendicular. Relative to this assumption of axes the particles are
at rest. The distance between them is AB. If another set of axes
is drawn, the particles appear to be in motion, and the distance be-
tween them is taken as A’ B’. If y denotes the angle between the
axes, the projection of A’B’ on AB is equal to AB,

/ /
AB = A’B’ coshy = ἘΞ

V1 — uw?

418 PROCEEDINGS OF THE AMERICAN ACADEMY.

where w is the relative velocity determined by y. Or,
A’'B' = AB sechy = AB V1 — w?.

That is to say, the distance A’B’ between the particles when con-
sidered in motion with the velocity wu is to the distance AB between
the particles when considered at rest as V1 — u2:1. This statement
embodies Lorentz’s theory of the shortening
of distances in the direction of motion.
Consider now (Figure 16) two intersecting
(6)-lines along which equal (unit) intervals OT
and OT" are marked. If OT is taken as the
time-axis, the point 1], obtained by dropping

vg oe from 7’ the perpendicular 7’M to OT, is
as ΝΟ simultaneous with 7’. But the interval OM
Ficure 16. is greater than OT in the ratio 1: V1 — wu

where w= tanhy is the relative velocity
determined by the two lines. Hence a unit time O7” as measured
along OT’ appears greater with reference to OT than the unit OT
itself. This is another statement of Einstein’s theorem that unit time,
measured in a moving system, is longer than unit time measured in
a stationary system.
All of these special thorems follow directly from the general trans-
formation equations (7). We have

x = 2, cosh Ψ — ay sinh y,
vy = —a,sinhy + a2 cosh y.

Now substituting

u/ V1 — wv, cosh y =1/ V1 — w,

u = tanh y, sinh Ψ

1
σι ἘΞΞ SS (αι = U4),

1
4 = — = (a4 — Uni);

Or, replacing a, by ἐ and 2: by x, we have the fundamental transfor-
mation equations of Einstein for the change from stationary to
moving coordinates.

20. Let us next consider instead of a (6)-line any (6)-curve. This
will represent the space-time locus of a particle undergoing accelerated
rectilinear motion. As the distinction between curved and straight

ee

WILSON AND LEWIS.— RELATIVITY. 419

lines is independent of any reference to axes, it follows that accel-
erated motion must remain accelerated motion regardless of the axes
chosen. Moreover, the curvature (§ 17) of a curve is also independent
of any choice of axes. Hence, although it is impossible, as we have
seen, to define absolute velocity (that is, all velocity is relative to
some assumed set of axes), we may define absolute acceleration if we
are willing to define it as the curvature or as any function of the
curvature alone. If, however, we wish to use the ordinary measure
of acceleration, we must consider the projection of the curvature
upon a chosen z-axis, namely,

1 dw dw

= —— - =— -- y2)2
ΓΝ ee Ok ape es ee

Cry
It is evident that curvature of constant magnitude does not mean
uniform acceleration. Indeed if the numerical value of the curvature
is constant the point in the vf-plane must move upon a pseudo-circle.
Since the tangent to this curve approaches, but never reaches, the
asymptotic fixed direction, it is clear that the velocity of the particle
approaches as its limit the velocity of light. For such a motion, the
relation between x and ἐ is easily seen to be

(1 — v*) Be ΤΥ (ee) a pag) ξων;

where /# is the radius of curvature, and ¢, 65 are constants of inte-
gration depending on the choice of origin for x and ἡ.

The interval of are along any (6)-curve is that which was called
by Minkowski the Eigenzeit. This quantity is of course invariant
in any change of axes. Thus

Mechanics of a Material Particle and of Radiant Energy.

21. Hitherto we have not assigned to our moving particles any
distinguishing characteristics. Let us now consider what follows if
we attribute to each particle a mass. It is true, as we shall later see,
that the phenomena which must be discussed in connection with the
dynamics of a material particle, even in the case where that particle
moves only in a straight line, cannot be adequately represented in
our two dimensional diagram. Nevertheless those results which can

420 PROCEEDINGS OF THE AMERICAN ACADEMY.

be discussed are so much more readily visualized in this simple case
that we shall consider a few important theorems before entering upon
the treatment of three and four dimensional manifolds.

The meaning of the mass of a particle, when that mass is determined
by a person at rest relative to the particle, will be taken as understood.
We shall call that value of the mass mp. Let us consider a (6)-curve
which represents the locus in time and space of this material particle,
and at any point of the locus a tangent of unit interval (or unit tan-
gent) w. By multiplying w by the scalar mo, we make a new vector
which we shall call the extended momentum. Τῇ now we choose any
pair of axes x and ft, the slope of the locus with respect to these axes,
that is, the velocity of the particle, we have called v. The momentum
vector may then be written, by (5),

Mov

Mw = ae Κι + 3 ky. (10)

If the t-axis were chosen parallel to the tangent w, the coefficient
of k,, that is, the component of the extended momentum mow along
the time axis, would be simply mo, the stationary mass. If, as we
have assumed, the particle is regarded as moving with the velocity
v, we shall take the component of mow along the t-axis as the mass m.
In other words, the mass of a body appears to increase with its velocity
in the familiar ratio

Mo
m Fae (11)
The component along the a-axis is then mv, the momentum. We
may therefore write the vector of extended momentum as

mw = mok, + mky. (42)
22. From our equation for the curvature we may write
1mow = d 1 d
Ps dmow _ dmv ay a ae ΕΝ (Ξ ΠΝ a ae): (13)
ds ΝῚ Sey?

The vector moe we shall call the-extended force. Since our ordinary
definition of force is time-rate of change of momentum, it is evident
that the z-component of the extended force multiplied by V1 — v? is
ordinary force. That is,

dmv

f= V1— ve me = Tie (14)

WILSON AND LEWIS.— RELATIVITY. 421

By comparison with equation (9), or by substituting for m from (11)
and differentiating, we obtain the results?!

bm ea a ae
dm moo dv dk

— 5 ΞΞ 70 => ---- 10
ἀν (i— 2)! dt ‘ae: a

where dE//dt represents the rate at which energy is acquired by the
particle when acted upon by the force f. Since dE /dt and dm/dt are
equal, we may, except possibly for a constant of integration, write
E=m. This is a special statement which falls under the more
general law, that the mass of a body, in the units which we employ,
is equal to the energy of the body. We may therefore use the terms
mass and energy interchangeably.

The type of motion which, from the viewpoint of the principle of
relativity, corresponds most closely to motion under uniform accelera-
tion in Newtonian mechanics, is motion under a constant force f.
The equation of motion may readily be integrated.

. adm d v a asin
Se MRC τς
v K dx Kt
tA); Fpl πὴ -- ,
v(1 — ἡ) {1 αἱ Ving? EKA Ey
2 2
and («2+ τὴ) — (t—t)? = =

The representative point in the at-plane therefore describes a pseudo-
circle of which the curvature is the constant force acting on the particle
divided by m. The mass of the particle at any time is

i EE 55 ( R)
Sas a 7 aie t — x + στο

which shows that the increase in mass is equal to the product of the
force by the distance traversed, as it should be from the principle of
energy above stated.

23. Let us consider the problem of the impact of two particles A
and B of which the vectors of extended momentum (mW) are respec-

21 See later discussion ($36) of the so-called longitudinal mass.

422 PROCEEDINGS OF THE AMERICAN ACADEMY.

tively a and Ὁ before collision, and a’ and b’ after collision. Several
important laws are subsumed under a law which we may call the law
of conservation of extended momentum, namely,

atb=a'+Dd’. (17)
Assume any set of space-time axes, and write
a= ak, + ask, b = bik, + buku,
a = aki+ ak, b’ = δι ky + δι.
Then the law states that
(a) + δι) Κι + (ας + δὼ) Κα = (ay! + by’) Κι + (αὐ + by’) ky,

or

a + by) = ay + by, (18)
4 -ἰ- by aS Qs + Da’. (19)

Now (by ὃ 21) as and ὃς are the masses of the two particles before
collision, a,’, b,’ the masses after collision, and equation (19) expresses
the law of conservation of mass or energy. The components m, bi,
ay’, δι΄, are the respective momenta (in the ordinary sense), and equa-
tion (18) is the law of conservation of momentum.

To assume that the impact is elastic is equivalent to assuming that
the value of mp for each particle is unchanged by the collision; and
since each value of mp is the magnitude of the corresponding vector
of extended momentum, the assumption may be expressed in the
equations

b= Db’.

The condition that the extended momentum

/
Ἢ ΞΞ ἢ"

* λ », 1s unchanged gives
Ν zo
holly (@t b)s(at b) = (a + b)-(a’ + bY,
Ν ΄
we or a:b = a+b’
“ὦν. by the above relations. Hence it follows
7 ‘ : =
ios Dx (Figure 17) that
. Ν
΄ ἣν
Ry cosh @ = cosh ¢’, or Ὁ Ξ

as is evident from the rules of projection
previously deduced. It is thus seen that
the relative velocity is the same before and after collision, and thereby
a rule which has been found very useful in the discussion of simple

Figure 17.

Le

WILSON AND LEWIS.— RELATIVITY. 423

problems in Newtonian mechanics proves equally applicable in the
new mechanics.

If the impact, instead of being perfectly elastic, were such that the
particles remained together after the collision, the two vectors @ and b
would merely be merged into a single vector ἃ - Ὁ. The sum of the
mo’s would not in this case remain constant, but would be increased
by the heat (or mass) produced by the impact and obtained from the
“kinetic energy” of the relative motion. This is all equivalent to
the simple geometrical theorem that the (5)-diagonal of a parallelo-
gram whose sides are (6)-lines is greater than the sum of the two
sides.

24. The concepts of momentum and energy (mass) are ordinarily
extended from the primitive mechanical phenomena to those involving
so-called radiant energy. We shall see that the ascription of mass
and momentum to light or other radiation is in consonance with the
geometrical representation which we have adopted.

Let us consider a ray of light emitted in a single line for a definite
interval of time. Such a ray alone can be considered in our two di-
mensional system. If the interval of time is very short, so that the
front and the rear of the ray are very near together, we may regard
the ray as a particle of light. The motion of such a light-particle
can only be represented in our geometry by a singular vector, and to
any observer its velocity is unity. Although the interval of any
singular vector is zero as compared with the interval of any (y)- or
(5)-vector, intervals along a given singular vector are, as we have
pointed out, comparable with one another."

Supposing now that a given light-particle is represented by a definite
singular vector, let us see whether such a vector can be regarded as
an extended momentum. If so, its projection on any chosen space-
axis must represent momentum, and its projection on the correspond-
ing time-axis mass or energy. These two projections must, moreover,
be of equal magnitude in this case, since the velocity of light is unity.
It is immediately obvious that this latter condition is fulfilled, since
the vector is singular (δ 11). If ἃ is the vector, then in terms of two
sets of axes

a= mk, + mk, = m ky’ + m ky’.

If then a represents extended momentum, m must represent the mass
of the light to an observer stationary with respect to the first system
of axes, and m’ the mass as it appears to an observer stationary with
respect to the other system.

424 PROCEEDINGS OF THE AMERICAN ACADEMY.
If ¢ is the angle from Κι to k,’ or from k, to k,’, we have from (7)

m' = mcosh ¢ — msinh¢ = m cpa. (20)
where v = tanh ¢ is the relative velocity of the two sets of axes.
But this is in fact the very relation between the energy of a given
particle of light as measured by two different observers whose relative
velocity is v. It is therefore, as far as the energy relations are con-
cerned, proper to consider a as a vector of extended momentum.

The final proof of the desirability of considering the vector a as
extended momentum comes when we consider the interaction of a
light-particle with a particle of the ordinary sort. We shall see that

the law of the constancy of extended momen-

A tum is true, and is only true, when we include

Ξ / the momentum of radiant energy as well as
Ἂς ay. that of so-called material particles.

yy Let the vector a (Figure 18) be the vector

3 due to a light-particle, and Ὁ that due to ἃ

a/\\s, material particle which has the power of absorb-

a ing light. Then if our law of extended mo-

7 -ς mentum applies to ἃ and Ὁ, there will be a
rs single vector after impact equal to a+ Ὁ which
will represent the extended momentum of the
material particle after it has absorbed the light.
Let us choose any set of axes. Then

FIGURE 18.

a= aki+ ak, b = δι Κὶ + by ky,

where ας = a, 15 the mass of the light-particle, and b, is the mass of the
material particle before impact, while a and δι = b, v are the respec-
tive momenta. The momentum after impact is

ay -- by = ας + by v.

Hence the change in momentum of the material particle is equal in
our units to the energy of the light absorbed, which gives at once the
well known formula of Maxwell and Boltzmann for the pressure of
light.

While it is evident, therefore, that such a vector a satisfies fully all
the conditions of an extended momentum, it must as a singular vector
have properties quite distinct from those of a momentum vector
which can be written in the form of mow. Since a singular vector

— ἥδ

WILSON AND LEWIS.— RELATIVITY. 425

has zero magnitude we can ascribe to the light no finite value of mo
or w. In this case, as in the case of inelastic impact between material
particles, the total values of mo does not remain constant, but is larger
after impact. In all cases we obtain the same results from the law
of the constancy of extended momen-
tum as those obtained by the appli-
cation of the ordinary laws for the
conservation of energy, mass, and mo-
mentum, whatever axes be arbitrarily
chosen.

Another simple illustration of these
laws is furnished (Figure 19) in the
case where the material particle does
not absorb the light, but acts as a
perfect reflector, which corresponds
closely to elastic impact between
particles. Here a’ and b’ are the
vectors of the light-particle and the Figure 19:
material particle after impact; and
these vectors are readily shown to be determined either by the condi-
tion that the magnitude of b is equal to the magnitude of b’, that is
that the value of mp for the material particle undergoes no change, or
from the condition that the angle between Ὁ and ἃ - Ὁ is the same
as the angle between b’ and a’+ b’. This latter condition may in
fact be regarded as necessary ἃ priori, since it is the only construction
which can be, in the nature of the case, uniquely determined.

Let us now consider light traveling back and forth in a single line
between two mirrors whose positions are fixed relative to one another.

If the mirrors are very close to one another,

\ we may as before consider the whole system

as concentrated at a point. This gives us
a new kind of particle, an infinitesimal
one-dimensional Hohlrawm. Since how-
ever the energy contained within the par-
ticle is in part moving with the velocity
of light in one direction and in part with
the velocity of light in the other direction,
Ficure 20. we may draw two singular vectors (Figure

20) to represent the extended momenta in

the two directions. Now these vectors added together give a (6)-vector
which will behave in every way like the extended momentum mow of

426 PROCEEDINGS OF THE AMERICAN ACADEMY.

a material particle, and mp represents the mass or energy of the Hohi-
raum as it appears to any observer at rest with respect to it. To such
an observer the amount of energy traveling in one direction appears
equal to that traveling in the opposite direction, and the resultant
momentum is zero. To any observer moving with the velocity ὃ
relative to the particle, the momentum is the difference between the
momenta which he observes in the two directions, and the mass of
the particle is increased in the ratio 1/¥1 —v?. These results are
all evident geometrically, and follow analytically from (20).

THe Non-EvucitipEAN GEOMETRY IN THREE DIMENSIONS.
Geometry, Outer and Inner Products.

25. We shall now consider a three-dimensional space in which the
meaning of points, lines, planes, parallelism, and parallel-transforma-
tion or translation are precisely as in ordinary Euclidean geometry.
In such a space, in addition to directed segments of lines or one-di-
mensional vectors, we have directed portions of planes or two-dimen-
sional vectors. Any two portions of the same or parallel planes
having the same area and the same sign will be considered identical
two-dimensional vectors, briefly designated as 2-vectors. The ordi-
nary one-dimensional vectors may be called 1-vectors for definiteness.
It is evident that the outer product axb of two 1-vectors in space is no
longer a pseudo-scalar but a 2-vector lying in the plane determined
by the two vectors and having a magnitude equal to the area of their
parallelogram.

The addition of two 2-vectors may be accomplished geometrically
in the following way. Take a definite segment of the line of inter-
section of the planes of the 2-vectors. In each plane construct on
this segment as one side parallelograms equal respectively to the given
2-vectors. Complete the parallelepiped of which these two parallelo-
grams are adjacent faces. The diagonal parallelogram of the paral-
lelepiped, passing through the chosen segment, is the vector sum;
the diagonal parallelogram parallel to the chosen segment is the
vector difference.

Let us consider the outer product of a l-vector and a 2-vector,??
axA. Let A be represented as a parallelogram, and a as a vector
through one vertex; the product axA is the parallelepiped thus

22 In general 2-vectors will be designated by Clarendon capitals (except in
the case of the unit coordinate 2-vectors).

WILSON AND LEWIS.— RELATIVITY. 427

determined. This outer product axA, being three-dimensional in a
three-dimensional space, is a pseudo-scalar; and different pseudo-
scalars are distinguished only by magnitude and sign.

If in axA we regard A as itself an outer product bxc, the parallel-
epiped is written as ax(bx¢). This same parallelepiped can be re-
garded, with the possible exception of sign, as (axb)xc. We shall in
fact consider the sign as the same, and write

ax(bxc) = (axb)xe = axbxce,

so that the associative law holds for the three factors a, Ὁ, 6. As
bxe = — exb, we shall write ax(bxc) = — ax(exb), in order that
we may keep the law of association for the scalar factor. By succes-
sive steps we may write

axbxc = — bxaxc = bxexa;

and hence the outer product of a 1-vector and a 2-vector is not anti-
commutative but commutative, namely,

axA = Axa.

All of these statements are valid in any geometry of the group charac-
terized by the parallel transformation.

26. In the three-dimensional non-Euclidean space, rotation about
a fixed point is characterized by the existence of a fixed cone through
the point, corresponding to the fixed lines in our plane geometry.
An element of this cone always remains an element; points within the
cone remain within, and points without remain outside. Besides the
lines which are elements of this cone, or parallel to them, there are
two classes, namely,

(5)-lines through the vertex and lying within the cone, and all lines
parallel to them, :

(y)-lines through the vertex and lying outside the cone, and all lines
parallel to them.

In like manner planes may be separated into classes. Besides the
planes of singular properties which are tangent to the cone along an
element, or planes parallel to these, there are

(5)-planes through the vertex cutting the cone in two elements, and
all planes parallel thereto,

(y)-planes through the vertex and not otherwise cutting the cone,
and all parallel planes. The former set, the (6)-planes, contain (6)-

428 PROCEEDINGS OF THE AMERICAN ACADEMY.

lines and also (y)-lines; the latter set, the (y)-planes, contain only
(y)-lines.

Any plane passed through a given (6)-line cuts the cone in two ele-
ments and is therefore a (6)-plane. The geometry of such a plane is
the non-Euclidean plane geometry above described, and the elements
of the cone are the fixed directions. The-perpendicular in this plane
to the given (6)-line is a (y)-line. The locus of the lines perpendicular
to the given (6)-line in all the planes through the line is a (y)-plane.
This (y)-plane will be called perpendicular to the (6)-line. Such a
plane possesses no elements of the cone, that is, no lines which are
fixed in rotation; hence the geometry of a (y)-plane is ordinary
Euclidean geometry. In the plane any line may be rotated into any
other line, and the locus of the extremity of a given segment issuing
from the center of rotation is a closed curve which is the circle in that
plane. Moreover, the idea of angle, and of perpendicularity between
lines in the (y)-plane, being the same as in ordinary Euclidean geome-
try, need not be further defined.

A plane passed through a (y)-line may cut the cone in two elements
and be a (6)-plane, or may fail to cut the cone and will then be a (y)-
plane.?3 The perpendiculars to a (y)-line will therefore be in part
(5)-lines and in part (y)-lines, and the plane perpendicular to a (7)-
line will therefore be a (6)-plane. Thus a plane perpendicular to a
(5)-line is a (y)-plane, and a plane perpendicular to a (y)-line is a
(6)-plane.

In any three dimensional rotation one line, the axis of rotation,
remains fixed, and points in any plane perpendicular to the axis remain
in that plane. If the axis is a (6)-line, the rotation is Euclidean; if
a (y)-line, non-Euclidean.

When all possible rotations, Euclidean and non-Euclidean, about
axes through a given point are considered, the locus of the termini
of a (y)-vector of fixed interval, and a (6)-vector of equal interval,
issuing from the common center of the rotations, is a surface which
from a completely Euclidean point of view appears to be the two
conjugate hyperboloids of revolution asymptotic to the fixed cone,
but which from our non-Euclidean viewpoint is really analogous to
the sphere. The (6)-lines cuts the two-parted hyperboloid; the (y)-
lines, the one-parted.

27. If we construct at a point three mutually perpendicular axes,
two will be (v)-lines, and one a (6)-line. The unit vectors along these

23 Planes tangent to the cone will be discussed later.

WILSON AND LEWIS.— RELATIVITY. 429

axes will be denoted respectively by Κι, Ko, and ky. The outer products
Κιχκο, Kk, k.xk, will be denoted for brevity by Ky, Κι4, Ko4.
In terms of these arbitrarily chosen axes a l-vector may be repre-

sented as
a= ak, + ak» + a4Ky.

Similarly a 2-vector may be represented by the sum of its projections
on the coordinate planes as

A= Apky + Aki + AosKos.

If we had chosen ky; in place of Kj. as one of our unit coordinate 2-
vectors, we should have written

A= Anko + Avkiy + Asko.

Since A 12 Κιο ΞΞ Ay ko; and Κιο Ξε :- ko, we have A i — Ay.
If we denote by Kjos the outer product k,xk»xk,, then
Kin = — Kye = Kye = — Ky = ky, = — Koi,

by the rules of outer products given above. In three-dimensional
space these products are unit pseudo-scalars.

In terms of their components we may now expand the two types
of outer product which occur in three-dimensional space. In this
expansion we employ the distributive law and the law of association
for scalar factors. Then

axb = (a,b aad αὐ.) kp + (ay, = ash) Ἐπ + (dob, — ας.) ko,
axA = (a)Ao + Ag + ἀμ} ki.

At this point we may discuss the general characteristics of inner and
outer products of vectors of various geometric dimensionalities in an
n-dimensional space. In such a space we have vectors of 0, 1, 2,...,
n-1, n-dimensions, designated as OQ-vectors (or scalars), 1-vectors,
2-vectors, ..., (n—1)-vectors, and n-vectors (or pseudo-scalars). The
outer product of a p-vector and a q-vector is a (p + q)-vector; the
product vanishes if by translation the p-vector and g-vector can be
made to lie in space of less than p + q dimensions. The inner product
of a p-vector and a q-vector, where p = 4, will always be defined as a
(p-q)-vector. Thus whereas the inner product of a l-vector by a
1-vector is a scalar, the inner product of a 1-vector and a 2-vector is
a l-vector.

Both the inner and outer products will obey the distributive law,
and the associative law as far as regards multiplication by a scalar

430 PROCEEDINGS OF THE AMERICAN ACADEMY.

factor. Furthermore the outer product will always obey the associa~-
tive law, and the inner product the commutative law.

28. The inner product of any 1-vector into itself may, by an im-
mediate generalization of the definition in plane geometry (§ 14),
be defined as equal to the square of its interval, taken positively for
(y)-vectors, negatively for (6)-vectors. The inner product of two
1-vectors is equal to the inner product of either one and the projection
of the other upon it. The rules for the unit coordinate vectors are
therefore

Κι -k, = ky: ko = ἽΝ ky-k, — —— ik. k, «ky = Κι ky, = ky +k, he
The product of two vectors

@= mk, + mk, + asky, Ὁ = bk, + doko + bdiky,
is arb = ab; + ab. — aybs.

The inner product aA of a 1-vector and a 2-vector will be a 1-vector
in the plane A and perpendicular to a (that is, perpendicular to the
projection of a on A); its magnitude will be equal to the product of
the magnitude of A and the magnitude of the projection of a on A;

its sign is best determined analytically. If a and b are perpendicular
l-vectors we may make the convention

(axb)bi—= a(b-b), οἴ » (axb)-3\=> μμίλ:5.. (21)
Thence follow the rules for the unit vectors,

ky Ky =a Kp, κι Κα — ἔστ ky, Κι -Kos = 0,

0 Kyo — Κι, το" ἴα a 0, koe Kog ΞΘ - ky,
Κι Κρ ἐπ 0, kyeky4 = — ky, Κι Koy = Ξ 5 kp.
24

Hence
a-A= (ay. 1 τὶ 4A 14) kj, + (— a Aj. — a4Ao4) ky ++ (— aA, — az Aos) Ky.

24 We may show that these rules do give an inner product which in all cases
agrees with the geometric definition above stated.

The condition that a-A lies in the plane A is that the outer product of it
and A shall vanish, that is, (a-A)xA = 0; the condition that it is perpen-
dicular to @ is that the inner product of it and ἃ shall vanish, that is,
(a-A)-a = 0. These two products are

(a*A)xA = [(a2 Aw — ag Ay) 424 + (αι 415 + a4 4.4) Ata
— (μά + a2Ao4) 4.15] King = 0,
(8. Α).ἃ = αι (d2Ajq2 — a4Ay4) — a2 (Aq + a4Ao4) + ag (Arg + α5.4.4) = 0,

as required. It is also necessary to show that the component of a perpendi-
cular to A contributes nothing to the product aA, so that the component in

WILSON AND LEWIS.— RELATIVITY. 431

The inner product of two 2-vectors is a scalar which is equal to the
inner product of either vector by the projection of the other upon it.
The inner product of two perpendicular 2-vectors is zero. The inner
product of a 2-vector by itself is numerically equal to the square of
its magnitude, and is positive in sign if the vector is of class (y),
negative if of class (6). Hence we have as rules of inner multiplication
for 2-vectors

KK» = 1, KyeKiy = Κα = — 1,
Κι Κα = Kyoko = Κι το, = 0,
A-A= A)?” = Ay a Ao;’, A-B= “4.50 otk AysBiy —s 4..}.,.

29. Every 1-vector a, or 2-vector A in a three-dimensional space
uniquely determines, except for sign, another vector (respectively
a 2-vector or 1-vector) perpendicular to it and of equal magnitude.
This vector will be called the complement of the given vector, and
designated as a* or A* respectively. To specify the sign, the comple-
ment may be defined as the inner product of the vector a or A and the
unit 3-vector or pseudo-scalar Kj.4, where the laws of this inner product
are

τὸ

τῷ

Κι Κορ. = Kos, koeKyy = — Ky, kyekioy = — Ky,

Κρ "Κι, = ky, Kysy+Kios = Kp, Koq*Kiog = — ky.
Thus

a* = (ak) + ake + agky) + Ky = — ak, — aokyy + ako,

A* = (Apky + ArKiy + Aoskos) + Kies = — Aodks + Ayko + Akg.

These complements satisfy the condition of perpendicularity pre-
viously derived (footnote 24), and the inner products

at-a* = α(" — a” — a;’, aca = ar+ a? — aZ,

A*-A* = Ao? + Ay? — Ap’, A-A= Aj? — Ai? — Ao?

the plane is alone of importance. We shall do this by deriving the expression
for a vector perpendicular to the plane A. Let

Cc=aki+ake+aky, n= 7 ki + mk. + τὰ ky
be respectively any vector in the plane A and a vector perpendicular to the
plane. Then the products
oa (cyAo4 = c2Ay4 + C4A yo) Kj04 ΕΞ Cen = οι + ΟἿ — ON = 0
vanish. Hence it follows that the condition of perpendicularity for the vectors
n and A is

71. 2. Ns = Ags! -- Aj: -- Aj,

and that n must be some multiple of Agsk; — Ayko — Awky. By the rules,
the inner product of this vector and A vanishes.

432 PROCEEDINGS OF THE AMERICAN ACADEMY.

show that the magnitudes are equal. The reversal of sign is to be
expected from the fact that the complement of a vector (whether 1-
or 2-- of class (vy) is a (6)-vector (whether 2— or 1—), and vice versa.

The use of the term complement in connection with scalars and
pseudo-scalars is sometimes convenient. Since, by the rule of inner
multiplication, we have Kj4*Ky2.4 = —1, the complement of any
pseudo-scalar is a scalar of the same magnitude and of opposite sign.
We may define the complement of a scalar a as the product of the scalar
and the unit pseudo-scalar; thus αὖ = akjy,.

All the special rules for the inner products of unit vectors (and
pseudo-scalars) are comprised in the following general rule, which
will also be applied in space of four dimensions: If either of two unit
vectors has a subscript which the other lacks, the inner product is
zero; in all other cases the inner product may be found by so trans-
posing the subscripts that all the common subscripts occur in each
factor at the end, and in the same order, by then canceling the com-
mon subscripts, and by taking as the product the unit vector which
has the remaining subscripts (in the order in which they stand), pro-
vided that if the subscript 4 has been canceled, the sign is changed.?°
Thus

Κι Ks, = 0, Kjos? Kis = Kuo°Ky = ky, Κι». Κι == ky +k; a aa kp,
Kjos Ky = a Κι», Kisae Kua ayes K314* Κα = Κ:.

80. Hitherto we have given little attention to the singular vectors
of our geometry, namely, the lines which are elements of a singular
cone and the planes which are tangent to a singular cone. We have
seen (ὃ 14) that the inner product of a singular 1-vector by itself is
zero, and have expressed that fact by stating that a singular line is
perpendicular to itself. Analytically expressed, the condition that
a l-vector a shall be singular is that

aca = αι," Ἢ αο -- ας = 0.

25 Instead of regarding the common subscripts as canceled, it is possible to
regard their corresponding unit l-vectors as multiplied by inner multiplica-
tion,— and in this case the change of sign takes care of itself. Thus

Kpgr* Ky ἐπ kp (ky° ky) (Κ, Κι).

Indeed if a, b, ¢ are mutually perpendicular 1-vectors, then all the rules given
above may be expressed in the equations

(axb)+(axb) = (aa) (b-b), (axbxc) - (axbxc) = (8.8) (b-b) (66),
(axb)*b = a(beb), (axbxc)*c = axb (c°c),
(axbxc) + (bxc) = a (bb) (66).

a= ak, + mk, + Va, + a’ky.
The complement of a singular vector is
A= a* = 8." Kjos τε ay Ko, — ky = Va; + a’? Kp.

This 2-vector A must be itself a singular plane vector; for we have
seen that the complement of any (6)-plane is a (y)-line and of any
(y)-plane a (6)-line, and vice versa. The inner product of A by itself
is obviously zero,?® for,

A-A = — αι — a?’ + (a?+ αοὖ) = 0.
Conversely if we consider any 2-vector

A= ΑΚ ΞΕ Ayky a= AosKo4,
such that
A-A= 4." ἘΠῚ Ay? ar 4. = 0,

its complement is a singular line, and it is itself a simgular 2-vector.
The standard form may be taken as

A= + VA24+ AoPKy + Auku + Adan.

The outer product of a singular vector by its complement, whether a
l-vector or a 2-vector, vanishes, as may be seen by multiplying out.
Thus the singular vector and its complement lie in the same plane,
that is, an element of the cone and the tangent plane through that
element are mutually complementary.

When we have to consider the inner product of any singular vector
with any other vector, singular or not, the geometrical method de-
pendent on projection often fails to be applicable; for it is impossible
to project a vector upon a singular vector. We may in such cases
employ the analytical method, which is universally applicable, or
replace the inner product with an outer product by a method intro-
duced in a following section (§ 32).

We have seen that an element of the cone is complementary to the
tangent plane to the cone through that element, that is, the element
is perpendicular to the plane. Hence the element is perpendicular to
every line in the plane (including itself).

26 A singular vector, or vector of zero magnitude, has, like any other vector,
areal geometrical existence and is not to be confused with a zero vector, that
15, ἃ non-existent vector.

434 PROCEEDINGS OF THE AMERICAN ACADEMY.

31. We have seen that rotation in a ()-plane about the perpendicu-
lar (6)-line is Euclidean, whereas rotation in a (6)-plane about the
normal (y)-line is non-Euclidean. In this latter case not only do the
(6)-planes normal to the axis remain fixed during the rotation, but
the two singular planes through the axis and tangent to the cone also
are fixed; for the axis remains fixed and the lines in which the planes
are tangent to the cone are respectively the two fixed lines in the (6)-
plane. As every point in the axis of rotation is fixed, the whole set
of lines parallel to the elements of tangency is fixed. The effect in
the two singular planes of a rotation is therefore to leave one line, the
axis, fixed point for point, to leave a set of lines fixed, and to move
the points on these lines either toward the axis or away from it by
an amount which is proportional to the interval from the point to
the axis.

Since a rotation in a (6)-plane multiplies all intervals along one of
the fixed directions in a certain ratio, and divides all intervals along
the other fixed direction in the same ratio, the effect upon areas in
the two singular planes is to multiply all areas in one of the planes
in that same ratio, and to divide areas in the other in that ratio.
This however is not inconsistent with our condition that areas should
remain invariant; for it is evident that, when compared with areas
in other planes, areas in singular planes are all of zero magnitude.
This is also shown by the fact that the inner product of any singular
vector by itself vanishes. That areas in a singular plane have a zero
magnitude does not prevent our comparing two areas in the same
singular plane or in parallel singular planes, just as the fact that
intervals along singular lines had zero magnitude did not prevent our
comparing intervals along any such line.

A limiting case of rotation occurs when the axis of rotation is itself
an element of the cone, that is, a singular line. Here the infinity of
fixed planes perpendicular to the axis, and the two singular planes
through it, have all coalesced into the one singular plane through this
line and tangent to the cone. In this plane the rotation consists in a
sort of shear. Every point moves along a straight line parallel to the
axis. In this case areas are rotated into areas which are from every
point of view equal. For if a parallelogram whose base is on the axis,
which is fixed point for point, is subjected to this rotation, its base
remains fixed and the parallelogram remains enclosed between the
same two parallel lines (Theorem IX).

The geometry in this plane, depending upon translation and upon
such a rotation as has just been described, is interesting as affording a

WILSON AND LEWIS.— RELATIVITY. 435

third geometry intermediate between the Euclidean and the non-
Euclidean which we have discussed. In Euclidean plane geometry
there is no line fixed in rotation, in our non-Euclidean plane geometry
there are two fixed directions, in this new case there is just one. If we
were to investigate this geometry, we should find one set of (parallel)
singular lines and one set of non-singular lines. Every non-singular
line may be rotated into any other. Angles about any point range
from — οὐ τὸ - © on each side of the singular line through that point.
The interval along any line intercepted between two singular lines is
equal to the interval along any other line thus intercepted. Every
non-singular line is perpendicular to the singular lines, as the singular
line is complementary to the singular plane through it.

Some Algebraic Rules.

32. We shall develop here a number of important relations be-
tween outer products, inner products, and complements which will be
of frequent use later. Many of these relations hold in any number
of dimensions. We shall consider primarily a non-Euclidean space
in which one of a set of mutually perpendicular lines is a (6)-line, the
rest being (y)-lines. But except for occasional differences of sign,
the results are valid in a Euclidean space.

In a space of n dimensions, the complement of a vector of dimension-
ality p is itself of dimensionality n — p. If a is a scalar and aisa
vector of any dimensionality, then from the associative law for scalar
factors, we have

fan — eal Kg = ΜΙ; πα ΞΡ πὶ Ξ ao oa — ae... (24)

Let a, 3, . . . be vectors of the respective dimensionalities p,
icc! Then

Bxa = (— 1)?%axf. (23)

Owing to the availability of the distributive laws it is sufficient to
prove such relations as this for the simpler case where the constituent
vectors a, @ are unit vectors k,..., kj... of dimensionality p, 4.
In the permutation of a and β, there are involved pq simple transposi-
tions of subscripts; for each subscript in Κι... has to be carried
past all the subscripts of k,... Hence there are pg changes of sign.
Hence the outer product is commutative if either of the factors is
even, but is anti-commutative if both factors are odd in dimensiona-
lity.

436 PROCEEDINGS OF THE AMERICAN ACADEMY.

We may next show that
(axf)* = α.β". (24)
Suppose again that a, β are unit vectors k,..., k;.... We have to show

(ko. Ky...) Kye. = Ryn. (pe. Kr.)

where kj... denotes the unit pseudo-sealar. Without changing this
equation, it is possible on both sides to arrange at the end, the sub-
scripts of the pseudo-scalar Κι... in the same order as in the factors
k,..., Κι... Thus we have to show that

(ΧΕ ΘΚ, (Karger ag anee:

But now the products on the right are found by canceling succes-
sively the common subscripts h... and g...; whereas the product
on the left is found by canceling simultaneously the subscripts of
k,...,..- The identity is therefore proved.

As a corollary of the two preceding results we may write the formula

(exo)? τὺ τ ξυ Ξε eB (25)

All these rules are true for any space, Euclidean or non-Euclidean.

The complement of the complement of a vector a is the vector
itself, except for sign. [1 α is of dimensionality p in a space of ἢ
dimensions, the exact relation is

Ci) bee En (26)

The complement of the complement of a vector will therefore be the
negative of the vector except when p (n — p) is odd, that is, when the
dimensionalities of the vector and of the space are respectively odd
and even.?” For the proof, the consideration may be restricted to
the case where a is a unit vector k,.... Then

(a7) ake ik; ekg. =, (Kp. Kage ikea:
ἘΞ (-- 1) PG Ὁ) ΕΠ:
Here again the subscripts in the pseudo-sealar k;... have been re-

arranged so as to bring g... to the end. Then as gq... denotes p
subscripts and j ... denotes n — p, the permutation involves p (n— p)

27 In Euclidean space (a*)* = (— 1)?(—P). Some writers who have identi-
fied vectors with their complements have perhaps overlooked this relation
which would, upon their assumption, make a vector sometimes identical with
its own negative.

ων»

WILSON AND LEWIS.— RELATIVITY. 437

changes of sign. In the final form thus found the subscripts g.. .
and 7... have successively to be canceled. But one of these is
necessarily the subscript 4 (corresponding to the (6)-vector), which
requires a change of sign. Hence

(ae) ee! ome ΞΞ -- (— 1) PP)... ’
and the desired result is proved.
Consider the product a*+8*. We have by (24) either
arbi (ax8) or B*sa* = (0*xa)*. (27)
Now, although αἴθ and §*+a* are equal, the two expansions obtained
are usually different. In fact, as the total dimensionality of an outer

product cannot exceed n, the first formula holds only when p =p
and the second only when g — p. Let us assume q=—p. Then

α".β᾽ = peak = (β' κα)" = (— 1)ρίατῷ (axg)*
ΕΞ (= 1) P(n—9) ἘΠ Ἐ (= 1)¢_ 9a) af. (28)

As a corollary
a*-a* = — area. (29)

The complement of an inner product may likewise be proved to be
(a -G)* — (= 1) Pie») oxo, (30)

where it is assumed that the product αὐ has been so arranged that
the second factor is of dimensionality q greater than the dimension-
ality p of the first. We have furthermore

a*xa =(aea)*; (31)
and also if 9 is a pseudo-scalar
(aeB)* = (— 1)2%?) B¥a = "Bea". (32)

It is important to observe that by means of these rules it is possible
to replace any outer product by an inner product, and vice versa.

33. Weare now able to obtain rules for the expansion of the vari-
ous products in which three vectors occur. The simplest type, and
one which needs no further comment, is

(ax?)xy = αχ(βχγ), (33)

which follows from the associative law.

438 PROCEEDINGS OF THE AMERICAN ACADEMY.

Consider next the product a+(bxc) of three 1-vectors. Here

a-(bxc) = (a-c) Ὁ — (a-b)e. (34)

Perhaps the simplest proof is obtained from the relation 78

= (06) ὁ τ o- (bxe)

C°C c°c

b

which states that a vector is equal to the sum of its components.
By clearing and transposing, and by permuting the letters, we have

c-(bxc) = (c-c) Ὁ — (e-b)c,
b:(bxc) = (b-c) b — (b-b)c.
If now ἃ is any vector perpendicular to Ὁ and 6, we have identically
d-(bxc) = (d-c) Ὁ — (d-b)c = 0.
If these equations be multiplied by 2, y, z and added, we have
(xe + yb + 2d)-(bxe) = [(τὸ + yb + 2d)-c]b — [ἃ + yb + 2d)-ble,

and any vector ἃ may be represented in the form ae + yb + 2d.
From the rules (33), (84) combined with the rules (22)—(32) we may
obtain a number of other reduction formulas by simply taking comple-
ments of both sides of the equation.
Thus
(axb)-C = a-(b-C) = — b-(a-C). (35)

28 With the aid of inner and outer products we may write down expressions
for the components of a 1-vector a along and perpendicular to another 1-vector
b or a 2-vector A. The components of a along Ὁ and perpendicular to Ὁ are

(a:b) b ἢ (axb)-b-

b-b beb

The components of a along A and perpendicular to A are
. (a-A)-A ΓΝ (axA) +A,

A-A A-A

The component of the plane A on the plane B is
(A+B) B
B-B

and a vector in the line of intersection of the two planes is

A*-B or A-B*.

WILSON AND LEWIS.— RELATIVITY. 439

For by (33) and (24),
[(axb)xe]* = [ax(bxc)]*,
(axb)-c* = a-(bxc)* = a-(b-c*).

But since ¢ is any l-vector, its complement C is any 2-vector.
Again,

ax(b-C) = (axC)-b — (a-b)C. (36)
For by (84), (22), and (30),
[a+(bxe)]* = [(a-c¢) b]* — [(a-b) e]*,
(— 1.18 ax(bxe)* = (— 116 (axc*)-b — (a+b) ο",
ax(b-C) = (axC)-b — (a+b) C.

Again,

(pices οἰ: Αὐ (37)
For from (35), (30), and (24),
[C-(axb)]* = [(b-C)-a]*,
(— 1)?8—2) Cx(axb)* — (= 1)16—D (b+C)xa*,

— Cx(bxa)* = — Cx(b-A)=(b-C)xA.
Again
(b-C)-A = — b(C-A) + C:(bxA). (38)

For from (36), (24), (32), (22), and (80),
[(b-C)xa]* = — [b+(Cxa)]* + [C(b-a)]*,
(b-C)-A = — b(Cxa)* + C-(b-a)*,
— b(C-A) + (—1)!@—) C-(bxA).

These rules (33) to (38) involve every possible combination of three
vectors in three dimensional space. Since the formulas which we
have used in deriving them, have the same form in Euclidean space,
the rules will be true in Euclidean space. The particular use of the
complement has implied a three dimensional space, and a similar use
of the complenent in a four dimensional space would obtain analogous
but different formulas; it should be observed, however, that the rules
here obtained (with the exception of (87)) must hold in space of four
dimensions, even when the three vectors in question do not lie wholly
in a three dimensional space. For consider (36) as a typical case.
Let Ὁ be a l-vector which does not lie in the space of a and C; we

440 PROCEEDINGS OF THE AMERICAN ACADEMY.
may write Ὁ = b’ + b”, where b’ is in the space of a and C and b’”
is perpendicular toa and C. Then by (36)
ax(b’-C) = (axC)-b’ — (a-b’) C,
and ax(b’’-C) = (axC)-b” — (a-b”)C

holds identically, since each of its terms vanishes. Hence by addition
(36) is seen also to hold in general.

Some products involving more than three 1-vectors are of frequent
occurrence. By (85) and (94) we may write immediately

ih. ry ee Dee lacc aed)
(axb)+(exd) = (a-c) (b-d) — (Ὁ 0) (a-d) = Ne bed (39)
In a similar manner we may prove
δι ἃ a-e a-f|
(axbxc) + (dxexf) = Wed b-e bf),
σ΄ c-e cf

and
(axb)+(exdxe) = (axb)-(dxe) ¢ + (axb)-(exe) ἃ + (axb)-(exd) e.

These formulas are all valid in space of any dimensions.

The Differentiating Operator VY.

34. In discussing the differential calculus of scalar and vector
functions of position in space, the vector differentiating operator V/ is
fundamental. The definition of this operator may be most simply
obtained as follows. Consider a scalar function F of position in space.
Let dr denote any infinitesimal vector change of position, and let dF
denote the corresponding differential change in F. Then let V be
defined by the equation

dF = dr-V/F.

Now VF is a vector. If dr is a vector in the tangent plane to the
surface F = const., dF is 0, and as dr+\/F then vanishes, the vector
dr and VF are perpendicular. Hence VF is a vector perpendicular
to the surface F = const. Now V F may be a vector of the (6)-
class or of the (y)-class, and the tangent plane is then respectively
a (y)-plane or a (6)-plane.?9

29 In our non-Euclidean geometry VF’ will not be a vector in the line of the
greatest change of F. If dr be written as Ὁ ds, where w is a unit vectorin the

WILSON AND LEWIS.— RELATIVITY. 441

If we select three mutually perpendicular axes Κι, ky, ky, and denote
by 21, 2, 24 the coordinates (intervals) along these axes, then

dF = dx, oF + εχ. oF + dey oF = (dayk; + disks + dxyky)? VF.
02, ΠΕΣ O24

From this V may be determined as

V= I ob ea go — κε σο: (40)

Thus V appears formally as a 1-vector, and may be treated formally
as such.3°

direction of dr and where ds is the interval or magnitude of dr, we may write
dF = dsu-vVF or u-VF = ἐπ,
8

Hence the component of V F along the direction dr is the directional derivative
of F in that direction. Consider now two neighboring surfaces of constant F’.
Suppose first that the (approximately parallel) tangent planes to the surfaces
are of class (7), so that the perpendicular VF is a (4)-vector. Then, in
our geometry, the perpendicular from a point on one surface to a point of the
other is, of all lines of its class, the line of greatest interval ds (§12). The
directional derivative along the normal is therefore numerically a minimum
(instead of a maximum) relative to neighboring directions. In fact, the
derivative along a line of fixed direction would be infinite, because along the
fixed cone ds = 0. Along the (y)-lines the directional derivative varies
between Ὁ and ». Suppose next that the tangent planes are of class (δ), so
that the perpendicular VF is a (y)-line. Then the interval ds along the
perpendicular from a point on one surface to a point on the other is neither a
maximum nor a minimum, but a minimax. For it is less than along any
neighboring direction (of the same class) which with the perpendicular
determines a (y)-plane, but greater than along any neighboring direction
(of the same class) which with the perpendicular determines a (5)-plane.

30 The above definition of VF depends on inner multiplication, and hence
upon the notion of perpendicularity or rotation. It is, however, interesting
to observe that we may define a differential operator y’ dependent upon the
outer product, and hence upon the idea of translation alone. The definition
would then read

axbxcdF = drxv’/F = (adr, + bdx: + ¢dxs)xv’F,
where a, b, ¢ are any three independent vectors, and where αὶ, 22, Ys are co-
ordinates referred to a set of axes along a, Ὁ, 6. Then
= bxe τς, : τ: oa τς ΒΗ axb Ὁ ΕΝ (41)
Now V’ may be regarded as ἃ "Ov ector ope pais in Site same sense as V 18
regarded as a l-vector. To show the relation of τ΄ to Vv, when the ideas
of perpendicularity are assumed, we may take a, Ὁ, ¢ as Κι, Κα, Ky and ἃς as

zy Then
- 6 a] a) fe) 0 \"
= Καὶ -- 4 a πε ὶ | Re St τ k ΛΎΣΙΣ .
ὃ 7 = " 0x2 OX2 δος ; Ons (x Ox, τῇ - OX2 : Ons
Thus V’ is the sheen νον In fact if

(dF)* = drxv’F and dF =dr-VF,
our rule of operation (30) shows that ν΄ = v*.

442 PROCEEDINGS OF THE AMERICAN ACADEMY.

If we consider a field of 1-vectors, that is, a 1-vector function f
of position in space, we are naturally led to enquire what meaning,
if any, should be associated with the formal combinations

ΧΕ and ΧΕ
obtained by operating with the l-vector V. Let
f (αι, 2, v4) = Aiki + foko + fake.

Of Oe , Ofe
02, τ OX» Ἢ Oxy

Of. δῇ Of πὸ ἢ ὁ. δῇ,
ἡὐητς- (2 - ral Eel aa vy το uae - ει: Ox. *) ks

Then
ἊΣ ef —

Of these the first, Vf, is a scalar function of position, and the second,
V ΧΕ, is a 2-vector function of position. They correspond respectively
to the divergence and curl in Euclidean three dimensional space.
The first, V +f, has indeed the same formasusual. And this was to be
expected: for physically or geometrically the idea of divergence
depends on translation alone and not on rotation, and it would also
have appeared analytically evident if we had used in the definition
of divergence the operator Δ ἢ instead of V. The second, V*xf,
differs from the ordinary curl not only in that we have retained it as
a 2-vector (instead of replacing it by the 1-vector, its complement,
as is usually done in Euclidean geometry of three dimensions), but
also in that it represents non-Euclidean rotation in the vector field in
the same sense that the curl represents ordinary rotation.

If F is a scalar function of position, then V F is a 1-vector function.
We may then form

αν πο υ".

Of these the second, VxV/ F, vanishes identically, as may be seen by
its expansions or by regarding it as an outer product in which one
vector is repeated. The first, V+ V F, may be expanded as

fe Oe OLE sooner
and her tere er τι»
δὰ 0..." Ong

and VY’: V corresponds to ee operator in Euclidean seometry.
If fis a 1-vector function, there are four different expressions which
involve the operator V twice, namely

N7 Waa: VeVi V+ Vxé, VxVxe.

WILSON AND LEWIS.— RELATIVITY. 443

Of these the last is a 3-vector function, which clearly vanishes identi-
cally. The first three are 1-vector functions, and are connected by
the relation

ViVx'¥= V(V-f)—VVeE,

as may be seen by expansion or by the application of (34).

Kinematics and Dynamics in a Plane.

35. The three dimensional non-Euclidean geometry which we
have developed is adapted to the discussion of the kinematics and
dynamics of a particle constrained to move in a plane. The two
dimensions of space and the one of time constitute the three dimen-
sions of our manifold. Any (y)-plane in this manifold may be called
space, and extension along the complementary (6)-line may be called
time. As in the simpler case, any (6)-line represents the locus in
time and space of an unaccelerated particle, and any (6)-curve the
locus of an accelerated particle. If we choose an¥ two perpendicular
axes 21, 2 of space, and the perpendicular time axis x4, then if the locus
of any particle is inclined at the non-Euclidean angle ¢ to the chosen
time axis, the particle is said to be in motion with the velocity v
of which the magnitude is » = tanh φ.

For the locus of a particle let

a { Ἢ ay PCM

be the arc measured along the (6)-curve, and let r be the radius vector
from any origin to a point of the curve. Then the derivative of r by
s is the unit tangent w to the curve. We have

dx, day

W= Κι ἢ ἀξ ke = a πὶ
If the velocity vis | v= μάν τ oe,
° dis om γὴν tt
then since iin cosh ¢ = WF ae
we write 3!
1 dx, dato ) v+k,
v=) ky κι) = . 42
Ἧι Ξ (i ΓΝ ΤΣ Ξ na ἢ ( )

31 By a transformation to a new set of axes we may derive at once the ge Hen
form of Einstein’s equation for the addition of velocities.

444 PROCEEDINGS OF THE AMERICAN ACADEMY.

To obtain the vector curvature of the locus we write

dw ἀκ ΑΝ ἂν ν ἘΚ, dv

ds ἀῶ 1—vwvdxy ( --- Yr)? ee

Cc =

or
Att av v+tk, do

iene a a {1 — ee” dt

(43)

If v be written as v = vu, where Ὁ is a unit vector, the resolution of ¢
into three mutually perpendicular components along u, ky, and du
follows immediately:

a yuu ok dv
dt dt * dt
2S aes ar = oh (44)
The magnitude of ¢ is
dv\? ,du du]?
dt "dt dt
ν τ: = 7
τ a—* Go]
(45)

a
2

1 ΝΣ 1 Σ
κῶν alert r= i)

To γδ νὸς νϑλ οἰ οτννς

In case the acceleration is along the line of motion, these expressions
reduce to those previously found; the additional term is due to
the acceleration normal to the line of motion.

36. Mass may now be introduced just as in the simpler case already
discussed, and here likewise we are led to the equation

The extended momentum in this case is also mow, that is,

mw = mv + mk. (46)

We may speak of w as the extended velocity, of ¢ as the extended
acceleration, and of mp¢ as the extended force. It is to be noted that
while ordinary momentum is the space component of extended momen-
tum, ordinary velocity, acceleration, and force are not the space com-

WILSON AND LEWIS.— RELATIVITY. 445

ponents of the corresponding extended vectors. Indeed the space
component of the extended velocity is v/¥1 — vw. The ordinary
force, measured as rate of change of momentum, is

mo — Mov mM

dmv dv dm oT alt *" at
᾿Ξ =m—+v = —; + =, (47
dt dt dt (i .Ὦ (1 —2)3 )

which is the space component of mp¢ multiplied by V1 — υ",
It is evident that in our mechanics the equations

dmv
ee

where a = dv/dt, are not equivalent, and it is the first of these which
we have chosen as fundamental. This makes the mass a definite
scalar property of the system. Those who have used the second of
the equations have been led to the idea of a mass which is different
in different directions, and indeed have introduced as the “longitudi-
nal’’ and the “transverse” mass the coefficients

and fi ΠΝ

Mo Mo

Gist... ae

of the components of acceleration along the path and perpendicular
to it, that is, of the longitudinal and! transverse accelerations, which
are respectively
ait
dt’ dt

The disadvantages of this latter system are obvious.

An interesting case of planar motion is that under a force constant
in magnitude and in direction, say f, = 0, f, = —k. The momen-
tum in the z-direction is constant, that in the y-direction is equal to
its initial value less kt. From these two equations the integration may
be completed. Or, in place of the second, the fact that the increase
in mass (that is, energy) is equal to the work done by the force, may be
used to give a second equation. The trajectory of the particle is
not a parabola, but a curve of the form y + a = —b cosh (ca — d),
resembling a catenary.

The space-time locus of uniform circular motion is a helix

r = a(k, cos nt + ky sin nt) + ky.

446 PROCEEDINGS OF THE AMERICAN ACADEMY.

Then
mv = man(— k,sin nt + 0 cos nt) + my,
lmv ᾿
ἘΝ ΞΞΞ rae = — man*(k cos nt + ke sin nt) = — mn’r,,

where r, is the component of r on the two-dimensional “space.”
The force is directed toward the center, as usual. It may be observed
that if in general the force is central, the moment of momentum is
constant. For if

d d d
ii (ny) =f, To (mv) = 7 ὐπν =" rb):

That the rate of change of moment of momentum is equal to the mo-
ment of the force is therefore a principle which holds in non-Newtonian
as in ordinary mechanics.

Tue Non-EvucLuipEAN GEOMETRY IN Four DIMENSIONS.
Geometry and Vector Algebra.

37. Consider now a space of four dimensions in which the elements
are points, lines, planes, flat 3-spaces or planoids, and which is sub-
ject to the same rules of translation or parallel-transformation as two
or three dimensional space. If a and Ὁ are two 1-vectors, the product
axb is a 2-vector, that is, the parallelogram determined by the
vectors. The parallelograms axb and bxa will be taken as of
opposite sign, but otherwise equal. The equation axb = 0 ex-
presses the condition that a and Ὁ are parallel. If ¢ is any third 1-
vector, not lying in the plane of a and b, the product axbxe,
which is now itself a vector will represent the parallelepiped deter-
mined by the three vectors. The condition axbxe = Ὁ there-
fore states that the three 1-vectors lie ina plane. If now dis a fourth
l1-vector, not lying in the 3-space or planoid determined by a, b, 6,
the product axbxexd will represent the four dimensional parallel
figure determined by the vectors. This product is a pseudo-scalar
of which the magnitude is the four dimensional content of the
parallel figure. The condition axbxexd = 0 shows that the four
vectors lie in some planoid. In all these outer products the sign is’
changed by the interchange of two adjacent factors, as in the case of
lower dimensions. Moreover, the associative law, the distributive
law, and the law of association for scalar factors will also hold, as is
evident from their geometrical interpretation.

WILSON AND LEWIS.— RELATIVITY. 447

Two l-vectors are added in the ordinary way by the parallelogram
law. The same is true of two 2-vectors if they intersect in a line, that
is, if they lie in the same 3-space (ἢ 25). It is, however, clear that in
four dimensional space it is possible to have two parallelograms which
have a common vertex but which do not lie in any planoid, that is,
do not intersect in a line. For two such 2-vectors the construction
previously given for the sum is not applicable, and it is indeed impossi-
ble to replace the sum of the two 2-vectors by a single plane vector.
The sum may, however, be replaced in an infinite variety of ways by
the sum of two other 2-vectors. For if A and B are any two 2-vectors,
and if a and Ὁ be two 1-vectors drawn respectively in the planes of A
and B, then the 2-vector axb = C may be added or subtracted from

A and B so that
A+ B= (A+ C)+ (B—C)= A'+B.

The sum of more than two 2-vectors can, however, always be reduced
to a sum of two. For if three planes in four dimensional space pass
through a point, at least two must intersect in a line. A sum of
2-vectors, which is not reducible to a single uniplanar or simple 2-
vector will be called a biplanar or double 2-vector whenever it is
important to emphasize the difference. Since the analytical treatment
of these two kinds of 2-vectors is not materially different, they will be
designated by the same type of letters (clarendon capitals).

A vector of the type axbxe will be called a3-vector. As two planoids
which have a point in common, intersect in a plane, a geometric
construction for the sum of two 3-vectors may be given in a manner
which is the immediate extension of the rule for 2-vectors in three
dimensional space. The sum of two 3-vectors is always a simple
3-vector.

In respect to rotation and to the classification of lines, planes, and
planoids, our four dimensional geometry will be non-Euclidean in
such a manner as to be the natural extension of the non-Euclidean
geometries of two and three dimensions which have been already
discussed. As in two dimensions there were two fixed lines through a
point, and in three dimensions a fixed cone, so in four dimensions
there will be a fixed conical spread of three dimensions, or hypercone,
which separates lines within the hypercone and called (6)-lines, from
lines outside the hypercone, which are called (y)-lines. Besides the
singular planes which are tangent to the hypercone, there are two
classes of planes, namely, (6)-planes which contain a (6)-line, and (γ)-
planes which contain no (6)-line. Besides the singular planoids which

448 PROCEEDINGS OF THE AMERICAN ACADEMY.

are tangent to the hypercone, there are two classes of planoids, namely,
(6)-planoids which contain a (6)-line, and (y)-planoids which contain
no (6)-line. In the (vy)-planoids the geometry is the ordinary three
dimensional Euclidean geometry; in the (6)-planoids the geometry
is that three dimensional non-Euclidean geometry which we have
discussed at length.

Every (6)-line determines a perpendicular planoid of class (vy), and
every (y)-line determines a perpendicular planoid of class (δ). Thus
if we construct four mutually perpendicular lines, one will be a (6)-line,
and three will be (y)-lines. A plane determined by one pair of these
four mutually perpendicular lines is completely perpendicular to the
plane determined by the other pair, in the sense that every line of
one plane is perpendicular to every line of the other, and the planes
therefore have no line in common. Jn general every plane determines
uniquely a completely perpendicular plane. One of the planes is a
(y)-plane and the other is a (6)-plane.

As in our previous geometries, perpendiculars remain perpendicular
during rotation. If then in a rotation any plane remains fixed, its
completely perpendicular plane will also remain fixed; and a general
rotation may be regarded as the combination of a certain ordinary
Euclidean rotation in a certain (y)-plane, combined with a certain
non-Euclidean rotation in the completely perpendicular (6)-plane.

38. Let ki, ke, ks, Κὰ be four mutually perpendicular unit vectors
of which the last is a (6)-vector. The six coordinate 2-vectors may
then be designated 53 as ky:, Kos, Kgs, Kos, κοι, Kix. There are furthermore
four coordinate unit 3-vectors Ko3i, K3i4, Kiog, Kie3; and a unit pseudo-
scalar Κρ. We may represent 1-vectors, 2-vectors and 3-vectors,
as the sum of their projections on the coordinate axes, coordinate
planes, and coordinate planoids. Thus

ak, + doko + aj3k3 + ας,
A= Ayaky4 == AoiKos He ΑΚ ar Aoskos == Agiksi =F Apkis,
Zl == ΡΝ ὍΝ ΞιΞ Moisksis == Yoko -Ξ ϑ[γ031Κ|53.

a

The outer product of any two vectors is defined geometrically and
expressed analytically in a manner entirely analogous to that of the
simpler cases already discussed. We thus obtain the following equa-
tions for the different types of products.

32 The particular order of subscripts is chosen for convenience only.

WILSON AND LEWIS.— RELATIVITY. 449

axb = -- bxa = (aby — ayb,)Ki4 ΒΕ (anbs — aybo) Koy ΒΒ (agb, — abs) Kg4
+ (a2b3 — ash) ko; ++ (αὶ — ayb3)Ks31 - (aib, — arb) Ky,

axA = (a2 A3x — a3Aoy + a4Ao3) Koss ie (ag3Ai4 — aA + a;A31) Κρ
ΕΙΣ (αι.1:. - a@Ay+ αι 12) Κι» + (a, Ao3 + azA3) + ἀμ.) Kus,

ax = — Ζῖχα = (ales, + a2lsig + asXliex — ayes) Ki2s4,

AxB = (AyBx3 + AuBs: + AsBr2 + AgsBiy + Asi Bo + As2Bas) Kiss.
The outer product of two vectors the sum of whose dimensions is
greater than four vanishes. The outer product of a vector by itself

vanishes except in the case of the biplanar or double 2-vector where
the product becomes

AxA = 2(Aj4Ao ΞΕ Ao4A31 ΞῈ 4:4.) Kj231.

If the biplanar vector be written as A = B+ C, where B and C are
two simple plane vectors, the product may be written

AxA = (B+ C)x(B+ C) = 2BxC.

It thus appears that AxA is twice the four dimensional parallele-
piped constructed upon any pair of planes into which the double
vector may be resolved. The vanishing of the outer product, AxA
= 0), is the necessary and sufficient condition that A be uniplanar.

The general rule for all cases of inner product has been stated (§ 29).
We may tabulate the following cases.

aeb = ab, + abo + ash3 — asda,
a-A = (a2 Ayo — a3A3; — a4A 14) |i (— aAy. + a3Ao3 — a4Ao4) kp
+ (a,A31 — d2Ao3 — a4A34) k3 + (— αι — 2A — α3. 14) Κι,
a- Al = (a3 Asia a αὐϑί.»4) ky + (alos = a3 234) Koy
ΞΞ (ayYlozs Ξ-- a 2314) k34 + (αιϑί 0. = a42lo34) ko;
a (alias — ayrlsi4) ἵκει + (aslo — ἀμί 4) Kip,
A-B = — AyBy — AuBoy — AgsBo, + Avg Bo3 + Agi Bs: + AwBry,
A-A = (— AosQliog + Azalgiy + Aos2ia3) ki (δέ μος — Ags Mos,
+ Agi 223) & Γ (— Aylsis Ξε ΓΌΝΥ + 4.) 153) ks
ΞΕ (Ao3%oss ai Ag lois Ξε Ayo) k,,
A-3B Se ΡΥ = Us Bsis st ΟΝ ΞΕ Wros Bros.

The geometrical interpretation of these inner products follows the
same lines as before. The inner product of a vector into a vector

450 PROCEEDINGS OF THE AMERICAN ACADEMY.

of equal dimensions is a scalar, and is the product of either into the
projection of the other upon it. In the case where a biplanar 2-vector
is projected, or is projected upon, each simple plane has to be treated,
and the results compounded. That this may be done follows at
once from the distributive law. The product of two vectors of dif-
ferent dimensionality is a vector of which the dimension is the differ-
ence of the dimensions of the factors; this vector lies in the factor
of larger dimensions and is perpendicular to the factor of smaller
dimensions. ‘However, the product a:A, if A is biplanar, is com-
pounded of two 1-vectors lying in the two component planes.

The complement of a vector is again defined as its inner product
with the unit pseudo-scalar ky31. ‘The complement of a 1-vector is a
perpendicular 3-vector, and vice-versa; that of a simple 2-vector is
the completely perpendicular 2-vector. We may tabulate the results
for the unit vectors.

Κι = - kos, k.* = — Kgu, k;* = — Kj, k,* = — kps,
ky," = — ky, Κο = — βι, k34* = — Kp,
k3* = Ku, κοΐ = Ku, Κιῦ = Ky,

ko34* a ee ἘΠ ks14* = —k, Κι = — k;, Κι = — ky.

With the aid of complements a unique resolution of a given 2-vector
into two completely perpendicular parts may be accomplished. Sup-
pose the resolution effected as

A= mM-+ aN

where M is a unit vector of class (y) and N one of class (6) so chosen
that MXN is a positive unit pseudo-scalar. Then

A* = —nM + mN,
mA — πὰ n& + mA*
d M = = "--τττ--.-.-.--ὄο
sie m? + nz n m? + n?
nA — mnA* nA + nmA*
Η αν τὸ =i ea
ici: m= ue n ἢ m+ n?
Let p= A-A= m — n’, gq = A-A* = — 2mn.

The quantities m, n may then be expressed in terms of p, 4, that is,
in terms of A-A, Δ. A*. The result is

Pe i a artes al a a a
Vp + ᾧ Ve + ᾧ

WILSON AND LEWIS.— RELATIVITY. 451

The general relationships between products of vectors and _ their
complements have been developed in a previous section for aspace
of any dimensions. It was there shown that (except 37) formulas
(34)-(39) for the expansion of all types of products involving 1-vectors
and 2-vectors would be true in higher dimensions, and this is true
even if the 2-vectors involved happen to be biplanar, because any such
vectors is the sum of two uniplanar vectors and the equations are
linear or bilinear in the vectors. Similar equations may, if occasion
requires, be developed for products involving 3-vectors.

39. We have not yet considered those vectors whose inner products
with themselves are zero. The case of the 1-vector, which is an ele-
ment of the hypercone, need not be treated again in detail. For
such a vector

aca = ay + ly” + a3” == ag? =i (i)

A uniplanar 2-vector such that A+A = 0 satisfies the conditions
AxA = 2 (4...4. εἰν AgsA31 ΞΕ AA 12) Kyo34 = 0,
A-A = — Ai? — Ao? — Az? + 452 + An? + Ax? = 0.

Such a vector is obviously a plane tangent to the hypercone; for it
can be neither a (y)- nor a (6)-plane. The singular plane has the
same properties as in three dimensional space. The element of
tangency may be found as follows. If a is any vector, ἃ" Α is a line
in the plane A, and (a*A)-A is a perpendicular line of the plane. But
the only line which is perpendicular to another line in this peculiar two
dimensional space is the singular line, that is, the element of tangency
with the hypercone. If ky be taken as a, the element may be written
as
(Κ..4}.4 = ky, (Ag143: — AvtA we) + ke (μά. — 4.4.3)

ΞΞ ks (Ao Ao ik A\4A31) =F ky (Ay? ΞΕ 40. ΞΞ 44),
an equation which we shall find serviceable.

The complement of a uniplanar singular 2-vector is itself such a
vector, and it may readily be shown to pass through the same element
of tangency. Indeed through every element of the hypercone is a
whole single infinity of tangent planes which are mutually comple-
mentary In pairs.

If a 2-vector be biplanar, that is, if AxA is not zero, the condition
A-A = 0 is satisfied when, if the vector be resolved into the two
complementary (γ)- and (6)-vectors, these have the same magnitude.
For if

A= mM + oN, A-A = πηι — n’.

Such a vector is singular only in an analytical sense.

452 PROCEEDINGS OF THE AMERICAN ACADEMY.

The complement of a singular 1-vector is a 3-vector which itself
is evidently singular. It is the planoid tangent to the hypercone
through the given element.3? It contains, besides the pencil of singu-
lar planes through the element of tangency, only (y)-planes.

We may take this opportunity of summarizing the properties of
singular vectors in general. The inner product of any singular vector
by itself is 0. Every singular vector is perpendicular to itself and to
every singular vector lying within it. The magnitude of a singular
vector is zero. This does not imply that such a vector is not a
definite geometric object, but only that the interval of a singular
1-vector, the area of a singular 2-vector, and the volume of a singular
3-vector are zero when compared with non-singular intervals, areas,
and volumes.

The visualization of the geometrical properties of a four dimensional
and especially of a non-Euclidean four dimensional geometry is
extremely difficult. It is of course possible to rely wholly on the
analytic relations, and thus avoid the difficulty. But we believe that
it is of the greatest importance to realize that we are dealing with
perfectly definite geometrical objects which are independent of any
arbitrary axes of reference, and that it is therefore advisable to make
every effort toward the visualization. It seems probable that Min-
kowski, although he employed chiefly the analytical point of view
in his great memoir, must himself have largely employed the geo-
metrical method in his thinking.

The Differentiating Operator }.

40. By analogy we may in four dimensions define the operator ©,
called quad, by the equation

“Ξε (48)
When referred to ἃ set of perpendicular axes, quad takes the form

fe} fe) 6 fe}
O= kbs the ths ka (49)

Me
o

and like V7 it may be regarded formally as a 1-vector.

38 The geometry in a singular planoid is analogous to that in a singular plane
(§31). In this3-space there are two classes of lines, singular lines, all of which
are parallel to each other, and non-singular lines, (7)-lines, all of which are
perpendicular to the singular lines. Similarly there are two classes of planes,
singular planes, all of which are parallel to the singular lines, and non-singular
(y)-planes, which are perpendicular to every singular plane. Volumes are
comparable with one another but are all of zero magnitude as compared with
a volume in any non-singular planoid.

WILSON AND LEWIS. — RELATIVITY. 453

We may therefore write the following equations. The result of
applying © to a scalar function F is a 1-vector OF, which might be
called the gradient of F.

oF oF oF
OF = nS Ὁ + iS + Ks, — ky
On: 7. v3 Oxy
The application of © to a 1-vector function f by inner multiplication
is a scalar, which might be called the divergence of f.
Of. 9 U2 ai. On, Of
of = =
9 π ἰἀψ μεν Ὁ τ τ
The application of ©, by outer multiplication, to the 1-vector f is a
2-vector function, which might be called the curl of f.

Ont = (Fe ὀπὴν, + (et Fe) tas + (+P

Oxy 0x4 Ox
87: af) df, as ) (38 δ
ate bs vp 0x3 Kos τε (2 aa Ox, ἴοι Ἂν Ox, ary OX, Ke.

The expression °F is a 1-vector.

_ (Af — fs iu) (ὦ: Of “ἢ
° og (2 ἊΝ 0X3 Ox Κι +r Ox O24 ὡ

Ofsi ὁ [5 δ = (ὦ: ΟΝ at
+ (ge ὅπ ὅθι, ὃ Tae as τὰ

The product *xF is ἃ 3-vector.

_ (Of _ ofes — 22) Of Afss ue
OF i (4 — O23 O24 Koss & a θαι e O24 ὼς
Ofer δίμ — ve) Ofes , fn δ΄ *)
a5 (: Oa. ΤΟΣ Kio + fe τὸ Ox as ὃ. Kis.
We might likewise expand ©-Jf and Oxf.
The rules (30) and (24) for operation with the complement enable
us to write

(O-a)* = — Oxa*, (xa)* = τὰ"

when a is a vector function of any dimensionality in four dimensional

space.
It is important to note in all these equations that while quad

operates as a l-vector, it is not a l-vector in any geometrical sense.

454 PROCEEDINGS OF THE AMERICAN ACADEMY.

Thus we find, for example, that xf is not always a plane passing
through f, and in fact will usually be a biplanar vector. Also ΟΕ is
not necessarily in the plane of F.

We have used the same symbol <> for our differential operator as
was used by Lewis in his discussion of the vector analysis of four
dimensional Euclidean space, and which corresponded to the “lor”
of Minkowski. There seems no danger of confusion, since it will
never be desirable to work simultaneously in Euclidean and non-
Euclidean geometry. Sommerfeld?* has also developed a vector
analysis of essentially Euclidean four dimensional space, and his
notation is an extension of that current in Germany for the three
dimensional case. For the sake of reference we will compare the two
notations, as far as the differential operator is concerned, in the follow-
ing table.

OF ὦ Grad F,
Of w Div f,
Oxf ὦ Rot f,
O:Fo Div F.
Operations involving © twice are of frequent use in a number of

important equations. These may be obtained by rules already given
if } be regarded as a 1-vector.

OXOF) = 0, (50) Oxn(Or€) = 0, (51)
Oil Ei, (52) Ox(OrxF) = 0, (53)
Ca τι (54)

DOD) = OOD AIOE (55)
QPOs DN NOT ΕΟ ΕΣ (56)
CAO) ΞΟ ΚΟΥ. (57)

The important operator ©: or <* has sometimes been called the
D’Alembertian. In the expanded form it is

ὁ: ὁ: 6: ὍΝ 4 ὁ:
ios = Die eyes ;
O23" Ox Oxy

(58)

where V now denotes the Euclidean differentiating operator in the
Κιο5 space.

34 Sommerfeld, Ann. d. Physik [4] 33, 649.
35 Kraft (Bull. Acad. Cracovie A, 1911, p. 538) devotes a paper to the
proof and application of this formula.

WILSON AND LEWIS.— RELATIVITY. 455

41. In the ordinary integral calculus of vectors the theorems due
to Gauss and Stokes play an important réle. In our notation we may
express these laws with great simplicity and generalize them to a
space of any dimensions. Let us consider first the form of these
theorems in the case of two dimensions, beginning with the more
familiar Euclidean case.

Stokes’s theorem states that the line integral of a vector function f
around a closed path is equal to the integral of the curl of f over the
area bounded by the curve. The analytic statement is

J dset = J fascut,

where ds is the vector element of arc, and dS the scalar element of
area. In our notation 35 this becomes

ist = [ [aso

where d§$ is now the 2-vector element of area (a pseudo-sealar) and
Vf is a pseudo-sealar (the complement of curl f, which itself is a
scalar in the two dimensional case). Transforming by (35), we may

also write
Fre ἐὸν eae te

Gauss’s theorem states that the integral of the flux of a vector
through a closed curve is equal to the integral of the divergence of the
vector f over the area bounded by the curve. The analytic statement

1S

‘where f,, is the component of f normal to the curve. In our notation
this becomes

-- [ὦ - [ fasyt= f fastv-t,

or, by taking the complement of both sides,

— [ avet -- [[ὠν-

36 One of the advantages of our system of notation is that if one term in an
equation is a vector of p dimensions, every other term is a vector of p dimen-
sions. This furnishes at once a check on the correctness of any equation.

456 PROCEEDINGS OF THE AMERICAN ACADEMY.

and transforming by (36), where in two dimensions fxd§S vanishes,
we obtain the form

fcc ON oa he «0

Equations (59) and (60) can be combined into the operational

equation ; F
fao=—f favo, (61)

where the operators may be applied to f in either inner or outer
multiplication.

In three dimensions Stokes’s theorem states that the line integral
of a vector around a curve is equal to the surface integral of the normal
component of the curl of the vector over any surface spanning the
curve, with proper regard to sign. The ordinary statement is

fost - [{{{ (curl ἢ),,

which in our notation becomes

ΤΠ f face:

and may be transformed by (35) into

fis-t= ἘΠ (62)

In like manner Gauss’s theorem states that the integral of the flux
of a vector through a closed surface is equal to the integral of the
divergence of the vector over the volume inclosed by the surface.
Thus, if dS is the scalar element of volume,

ff fras= ff faveras:

In our notation, if dS denotes vector element of volume, this
becomes

fuss [J frevse ff fase

which, by transformation by (24) and (82), becomes

[fase = ff fase os)

WILSON AND LEWIS.— RELATIVITY. 457

As an example of a similar formula involving a scalar function f,
we may take the familiar theorem of hydrodynamics that the surface
integral of the pressure is equal to the volume integral of the gradient
of the pressure f. This is usually written as

J sas = [ff sraasaz,

but in our notation becomes

J fas- Jf fes-con - f fas-vv.

42. All these formulas lead us to suspect the existence of a single
operational equation which is valid when applied to scalar functions
and to any vector functions whether with the symbol (+) or (x).
This would have the form

J dono ai (— Def (dain) Ch (64)

where do, is the p-vector element of a closed spread bounding a spread
of p+ 1 dimensions. We may extend this equation to four (or more)
dimensions, and demonstrate its validity as follows.

It will perhaps be sufficient to give the proof of the formula in case
the (p+ 1)-spread is a rectangular parallelepiped with p+ 1 pairs
of opposite faces. For let

do (p41) == K193.. pil da,dxodx3 δἰ Ὁ dts 11.

Then, by the rules for multiplication,

ὯΝ 6
d S = P οὐ τη, « 2 0 y 2 a
ἥν. ἀν τὰ Saat ΟΣ dips οι, oi Ox,
0
dxydxs . . . dp Κι ρει dx δε ᾿

The partial integrations may now be effected upon the right, and leave

J doon> = (—1 fda,
JY (p+1) (p)

if it be remembered that Ko3,p,1, — Kuis,.ps1, - - - are the positive faces
perpendicular to ki, ko,...
It will be evident from this mode of proof that (64) is valid both

458 PROCEEDINGS OF THE AMERICAN ACADEMY.

for Euclidean and for our non-Euclidean geometry. The equation
may be put in another form by the aid of rules previously given.?7

J mate “OS i Beda τς (a: (65)

In four dimensions a large number of special formulas may be
obtained by applying our operational equation to scalars and to
vectors of any denomination with either symbol of multiplication.
As examples we may write the formulas corresponding to Stokes’s
and Gauss’s theorems. Let p = 1 and apply the operator by inner
multiplication to a 1-vector function. Then

[st = — f { @s-o)-t = ff [ as-#).

This is the extended Stokes’s theorem. Again let p = 3 and apply
the operator by outer multiplication to a 1-vector function. Then

{{{{Φ4- -Γ{{{|{.0»«- Ὡ[7 ἘΠ

This is the extended Gauss’s theorem, where d= represents a differ-
ential (pseudo-scalar) element of four dimensional volume.

In these cases also the same equations apply in Euclidean and in
our non-Euclidean space. If, however, we write these two equations
in non-vectorial form, they become in the non-Euclidean case

Jide + fodar oa fsdas = fadvs)

= of: 3 ch ΓΕ: of: Of )
= Ἵ τς pean daodi3 + i Tas dx3dx,

ag (Ξ = ΕῚ αατάχ. -- (ee == ah daydatg

Ox, O25 OX) θα,
Ofs | ont fs ch) Bet
se ( δὲ Ἐ ae) deades — ( πε ΕΒ davde |

37 This equation embraces both of the operational equations given by Gibbs
in δὲ 164-5 of his pamphlet Vector Analysis (1884) reprinted in his Scientific
Papers, 2. In case p + 1 is equal to n, the number of dimensions of space,
then do(p41)* is ascalar and the equation has no meaning unless we adopt the
convention ™xa = ma, where mis a scalar and ἃ any vector. This convention
would lead to no contradiction, and might occasionally be useful.

WILSON AND LEWIS.— RELATIVITY. 459

and

| Υ yi a (fidaed. xg -- fe dusdayd v4 + fadaid xed v4 fid xd xodars)

ὅπ Ὁ ὁ: ἢ
{ΜΕ}: Ox, + oh hyo τ dajdiodagdiry.

The theorems may be used to demonstrate in a vectorial manner
such an equation as (52), O+(:F) = 0. For

Jf ffeocon-- ff fon
τ ff [aso - f fase.

As the final integral extends over the bowndary of the closed three
dimensional spread which bounds the given region of four dimensions,
the final integral vanishes, since the closed spread has no boundary.

Geometric Vector Fields.

43. The idea of a vector field is ordinarily associated with concepts
such as those of force or momentum, which are not wholly geometri-
cal in character; but it is per-
fectly possible to construct ra
vector fields which are purely R n=
geometrical. Thus in ordinary er
geometry we may derive a R} 4
vector field, when a single k 4
point is given, by constructing (δ) “ae
at every other point the vector “ ΄
from that point to the given eS)
point, or that vector multiplied pg =
by any function of the dis- “2 ὟΣ
tance.

In our non-Euclidean four
dimensional space we may as-
sociate with any (6)-curve a vector field derived from that curve in
the following way. At each point of the (6)-curve construct the
forward unit tangent w, and the forward hypercone.3® At each point
Q . these hypercones construct the vector w/R, parallel to the vector

FIGURE 21.

38 Tv hat half of the hypercone lying above the origin, ee ue w Hak
will represent later times than the time of the origin, will be called the forward
hypercone.

460 PROCEEDINGS OF THE AMERICAN ACADEMY.

w at the vertex, and equal in magnitude to the reciprocal of the
interval A along the perpendicular drawn from the point Q to that
tangent produced (Figure 21). On account of analogies which will
soon become apparent we shall call this vector function the extended
vector potential of the given (6)-curve.29 We shall write

Ww
ig = R (66)
We shall next consider the 2-vector field
il il
P= Op = (Opt κίον). (67)

We shall consider the evaluation of xp in two steps. First we shall
assume that the original (6)-curve is a straight line. In this case w
is constant and ©xw = 0. If we arbitrarily take ky along w, we
may write
1 1 Ὁ ἢ 1

Vie νῶν
for it is clear that a displacement parallel to w does not change R.
It is evident that R becomes a radius vector in the 3-space perpendicu-
lar to w. Τῇ ἢ represents a unit vector from the point Q normal to w,
that is, in the direction in which R was measured, then by the well
known formula, VR! = ἢ ΠΣ, Hence

And hence P= Op = ΞΕ (68)

The determination of +p follows in precisely the same way;
in each of the above formulas the symbol of inner multiplication will
replace that of outer multiplication, and we find that

O-p= Ξὺ (69)

for n is perpendicular to w.

Of all the geometrical vector fields which might have been con-
structed from a given (6)-curve, we shall show later that those which
we have just derived are the most fundamental (footnote § 44). The

39 The vector fields produced at a point by two or more (s)-curves may be
regarded as additive. The locus of all possible singular lines 1 drawn (as
in Fig. 21) from (s)-curves to a given point is the backward hypercone of which
that point is the apex.

WILSON AND LEWIS.— RELATIVITY. 461

2-vector xp is a simple plane vector in the plane of the point Q
and of w. The 1-vector p has everywhere the direction of the funda-
mental vector w; if 1 be the singular vector from the vertex of the
cone to the point Q, the scalar product 1+p is constant. In fact

Ww lxw
τ (1-w)*

are the expressions for the fields in terms of 1 and w.

Let us now choose arbitrarily a time-axis ky, and then the perpen-
dicular planoid is our three dimensional space. We may resolve our
l-vector and 2-vector fields as follows.

aie (70)

lew’

p — «τὸ δὰ πον cod _ La ΞΕ κι τ SS
l-w (1; + Usky)+(v + ky) (71)
= — Vv ky
eee ie

where 1, and p, are the space components of land p._ As 1 isa singular
vector, J; is equal to the magnitude of ],.

ἘΠ τῆνος 2) (Is ++ Liks)x(v + ky)
a ame ἐν, ees oa
pee 2s (1 — v) xv ᾳ — υἢ) (eS Lw)xKy,

i. (Ls Ἐς τε 1.. νυ)" (Ly =e 1,-v)8

Of these two planes into which P is now resolved, the first lies in
“space”? and the second passes through the time axis and is perpen-
dicular to “space.”

We shall attempt to show with the aid of a diagram (Figure 22) the
geometrical significance of the various terms which we have employed
in the above formulas. The origin, that is, the vertex of the hyper-
cone, is any chosen point O on the given (6)-line w. A point upon the
forward hypercone is Q, and 1 is the element OQ. The unit vector ἢ
is drawn along QJ from @ towards and perpendicular to the vector
w. The intervals OJ and QJ are equal, and equal to R = —1-w.
The vector p drawn at Q parallel to w and of magnitude 1/R is the
extended vector potential at Q due tow. The 2-vector P lies in the
plane 0/Q, and is equal in magnitude to 1/R?. The arbitrarily cho-
sen time-axis is ky, and on the planoid perpendicular to ky (that is,
on “‘space”’) the vector 1 projects into 1, = O’Q. The intersection
of the line of w with the planoid is G (the point of the line w which is
simultaneous with Q). Similarly O’ is the intersection of ky with the

462 PROCEEDINGS OF THE AMERICAN ACADEMY.

planoid. The line OO’ = I; represents the lapse of time between O
and Θ΄; and this is equal in magnitude to 0’Q or 1,, the space compo-
nent of 1. The interval OG = 1, ¥1 — υ and the interval O’G = lw = 1,v.
The direction w projects into the direction v. Hence as a vector,
O’G is equal to /,v. The quantity 1,-v = O’F may be obtained by

Figure 22.

dropping a perpendicular from G to 0’Q. The interval FQ is then
1, — 1,*v or 1; —1,*v, the expression which occurs in the denomina-
tors. The vector GQ = ris clearly 1, — lv or 1, — lav.

44. We shall now remove the restriction that the (6)-curve which
gives rise to the potential p = w/R = — w/(l-w) is rectilinear, and
consider the general case of any (6)-curve. For the sake of simplic-
ity in this complex problem we shall use dyadic notation (see appen-
dix § 61, ff.). The results, however, might all be obtained by means
of the more elementary geometric and vector methods.

We may write

w

Op= OF = (Opt pOW= — POR Wt ZOw.

Now ΟΝ is defined so as to satisfy the relation dr-Ow = dw. A
displacement (Figure 23) dr = w ds parallel to w, makes a change
dw = cds. A displacement dr along the vector 1 (Figure 24) intro-

WILSON AND LEWIS.— RELATIVITY. 463

duces no change in w, and in like manner a displacement dr in the
plane perpendicular to that of w and 1 does not affect w. Hence we
may write

1 1

w= c= ——le. 73
NS pe R (73)
a 4
n τὰ coe
Ca ae
΄
Pi cs adr=d1
4a ie -
wl” wl Ie,
Ag (8)
ψ ὃν
\ds ds” wx
x
FIGURE 23. FIGuRE 24.
To compute OR = — © (1-w), we may write

O(l-w) = (O)-w+ (Ὁ ν}:}.
Here ὧν is already known. To find ΟἹ observe that dl = dr-©1
is equal to dr when dr is along 1 (Figure 24). Further if dr is elsewhere
in the hypercone, for instance, in the plane perpendicular to that of 1
and w then also dl = dr. But when dr = wds 1s along w the differ-
ential dl vanishes. Hence we may write

1 1
ΦΙΞΙ- τ ἘΞ ῚΈ εν, (74)

where I is the idemfactor. Thus we have

il ]
> (1-w) = (1 { R Iw)-w— le+l,

or, performing the multiplication by w,
OR= —O(1-w) = —wt

From this it follows at once that
1 1

eM 1+ le (76)
= ae (tc + R lw — ww )

i+ le

alt (75)

464 PROCEEDINGS OF THE AMERICAN ACADEMY.

The two expressions xp and +p may now be obtained by inserting
the cross and dot in ©p. Hence

nD R AC e+ ee bw) (77)
1 1 Ξ
Se ey 77) (1-¢ Ἢ a “ew + 1) = 0. (78)
Here also <>+p vanishes, since l-w = — R.

As 1 varies with R, the parts of <p may be separated into one
which varies as {1 and one which varies as 1 2, namely.

P= Oxp = — me (1c ΞΕ εἰς bw) -- i lxw. (79)
This may be brought out most clearly by expressing 1 as
1= R(w—n), (80)

where n is a unit vector from Q perpendicular to w.

1

es ΞΘ p we — xe + π- ὁ mw) + jan xW. (81)
Another manner of expressing P is
1
P= — R 1x(1- (wxe)] — ἣν lxw (82)
or -
P= — Ε (Ixwxce) +1 — — ja kw. (83)

Any of these forms of P shows, what perhaps appears clearest
from (82), that the part of P which varies inversely as R is a singular
plane, through the element 1 and cutting the plane of wxe; for
1x{1- (wxc)] is a plane through 1 and the vector 1+ (Χο) (in wxe), and
the inner product of the plane by itself is readily shown to be zero.

In a similar manner we may calculate ©P, a dyadic with its first
vectors 1-vectors and its second vectors 2-vectors. The differentiation
requires nothing new except ©c. And by the same reasoning applied
to find ΟὟ, it appears that

de ldc

ORs ee TRE (84)

WILSON AND LEWIS.— RELATIVITY. 465

Hence © brings in, as might be expected, the rate of change of
curvature, just as ©w brought in the curvature. We have

Ix .
OP = διῶ) = 0 (-- Fr pg” bw)

2 1+ 1.6 1 1 1 lde
= κ(- w+ R 1) Ιχο — ΠΣ (1 Ss R ὮΝ ΠΕ R [3 R “he
3 1+ 1.6 l Ι ἐς
t+ pi (1 + 150) (— να τ Ι) Pir (c ὭΣ: 5) sii
1-ὄ 1.6 1 Las 1
ue (1 ae μὰν rp ex.

In this expression the product indicated by the cross is always per-
formed first, regardless of the parentheses. If now the cross be
inserted to find xO xp, the result xp = 0 is obtained, as
required by equation (51). Moreover, if the dot be inserted so as to
find +(< xp), the result is also

O-Oxp = 0. (85)

We have, of course, proved this theorem only for points lying off the
given (6)-curve.
We have the mathematical relation (55), namely,

CRD OCD) Ξ τῶν.
But we have seen that <>+p = 0, and therefore
O-OrP = Op = 0. (86)

The existence of this extended Laplacian equation justifies the use
of the term potential *° for p.

40 It isinteresting to enquire what form the potential p might be given other
thanw/Rk. Suppose that p should be independent of the curvature of the (6)-
curve. The only vectors then entering into the determination of p at any
point Q would be w and 1. The only possible form of a 1-vector potential

would therefore be
P= ο( πο - (hl,

where R = —l-w. ‘The expression for Op becomes
Op = 0 (R)( - wx. 1) =% (R) ple

+ f’ (R) [- wt ! 1) +5@) (1 Ἔ ΩΣ

466 PROCEEDINGS OF THE AMERICAN ACADEMY.

ELECTROMAGNETICS AND MECHANICS.

The Continuous and Discontinuous in Physics.

45. It has been customary in physics to regard a fluid as composed
of discrete particles (as in the kinetic theory) or as a continuum (as in
hydrodynamics) according to the nature of the problem under investi-
gation; it has been assumed that even if a fluid were made up of
discrete particles, it could be treated as a continuum for the sake of
convenience in applying the laws of mathematical analysis. For
example we introduce the concept of density which may have no real
exact physical significance, but which by the method of averages
yields apparently correct results. Provided that the particles in a
discontinuous assemblage are sufficiently small, numerous, and regu-
larly distributed, it is assumed that any assemblage of discrete
particles can be replaced without loss of mathematical rigor by a
continuum.

However, when we investigate problems of this character in the
light of our four dimensional geometry, we are led to the striking
conclusion that in some cases it is impossible, except by methods
which are unwarrantably arbitrary, to replace a discontinuous by a
continuous distribution and vice versa. Especially we shall see that
this is the case with radiant energy, a conclusion which 15. particularly

Hence
Op ΞΞ --ἰ Ἰτρ [- (R) + ze ®)| ΞΕ (pcr) ΞΕ 3f(R) )-

If ep is to vanish eek of the curvature of the (s)-curve, then

¢’ (R) nee Rn?) Rf'(R) + 3f(R
The integration of ae equations determines ¢ and f as
A B
Chi R’ ii = R®
where A and B are constants. The expression for ©>xp is
A 1+ 1c 2B
xp pe [το - τας ἢ bw] =a Ixw.

The calculation of -+Oxp = — +p gives
O-Op = 2 Β [Ἐπ +3 ει )

It therefore appears impossible to satisfy <>+p = Oand +>p = ὁ with δὴν
other form of potential, dependent only on 1 and w, than the one chosen.

WILSON AND LEWIS.— RELATIVITY. 467

notable when taken in connection with the recent theories regarding
the constitution of light, embodied in the quantum hypothesis.

Let us for simplicity first consider such cases as arise in our two
dimensional geometry. Consider a material rod of infinitesimal cross
section moving uniformly in its own direction. Suppose now that
we regard this rod as made up of discrete particles. Then in our
geometrical representation each particle will give rise to a vector
of extended momentum mow, and these vectors will all be parallel.
The whole space-time locus of the rod will be a set of parallel (6)-lines.
The rod as a spacial object possessing length has no meaning until a
definite set of space-time axes have been chosen, and this choice is
arbitrary. There is, however, one such choice which is unique, and
that is the selection of the time-axis along w, and the space-axis per-
pendicular thereto. In this system the mass of each particle is its
mo, and the sum of the m’s of any segment of the rod divided by the
length of the segment is the average density. If the particles are
sufficiently numerous, we may regard the rod as continuous and re-
place conceptually the locus of the rod as a set of discrete (6)-lines
by a vector field continuous between the two (6)-lines which mark
the termini of the rod, and represented at each point by a vector
parallel to w and equal in magnitude to the density at that point.
This is the density as it appears to an observer at rest with respect to
the rod, and may be called up. The vector uw has therefore a defi-
nite four dimensional significance. Its projections on any arbitrarily
chosen space and time axes are, however, not respectively the density
of momentum and mass in that system. For

Haw = Ξ- ΕἸ τοῦ a (87)

Vi—?
But μ, the density in this system, is not equal to μη. V1 — v, but

Mo

= (88
1 ---οἴ' (88)

μ

as the units of mass and length both change with a change of axes.
Conversely we may replace a continuous by a discrete distribution.

' Let us consider a continuous vector field f of (6)-lines. Then any
region of this field, embraced between two (6)-lines sufficiently near
together, may be replaced by one or several parallel (6)-vectors, of
which the sum is equal to f multiplied by the length of the line drawn
between and perpendicular to the boundary (6)-lines. We may also

468 PROCEEDINGS OF THE AMERICAN ACADEMY.

use another construction which is essentially identical with this.
Let dr be any vector drawn from one boundary line to the other.
Then (drxf)*f/f is the same vector as the one just obtained. Although
the method of obtaining this vector may seem somewhat artificial,
the vector is, however, a definite vector obtainable from the field
without any choice of axes.

46. These methods fail completely when the vector field is com-
posed of singular vectors. Let us consider instead of a material rod,
a segment of a uniform ray of light. If this
can be represented by a continuous vector
field bounded by two lines representing the
loci of the termini of the segment then all
these vectors must be singular. Let 1 be
(Figure 25) the value of the vector through-
out the field. It is evident that we cannot,
as in the former case, draw any line across

Fiqure 25. the field perpendicular to 1. The second
method likewise fails because it would involve
the magnitude of 1 which is zero. Moreover it can be stated that
there is no method whatever, independent of any choice of axes,
which will enable us to change from this continuous distribution of
the light to a set of light particles. Conversely it is equally true that
given a system of light particles moving in a single ray it is quite
impossible to replace them by means of any continuous distribution,
and this is true no matter how small and numerous and close to-
gether these particles are. This statement regarding singular vectors
will be seen to hold also in space of higher dimensions,*! and is of
fundamental importance.

While it is impossible, therefore, to find continuous and discontinu-
ous distributions of singular vectors which are equivalent to one
another, it is possible to obtain by four dimensional methods out of
a specified region of a singular vector field a single vector or group of
discrete vectors uniquely determined by that vector field but quadratic
instead of linear in the vectors of the field. Consider any portion of
the field bounded by two singular vectors sufficiently near together.
Let 1 be the vector of the field, and then if dr is any vector drawn from —

41 In the case of the peculiar geometry of a singular plane (§ 31), the interval
dr from one singular line to another is independent of the direction of αὐ. It
is therefore possible to replace the field 1 between two boundary lines by the
single vector ldr linear in 1. Thus there are exceptional singular fields in
higher dimensions for which the passage from continuous to discrete and vice
versa may be accomplished.

WILSON AND LEWIS.— RELATIVITY. 469

one boundary to the other (Figure 25), the 2-vector dr«1 is independ-
ent of the way in which dr was drawn and the 1-vector (drxl)*1 is
determined, and is in a certain sense representative of the region of
the field chosen.

It may be of interest to obtain the projection of 1 and (dr«1)*1
upon two sets of axes Κι, ky and k,’, ky’ where the angle from ky, to
Κι' is φ = tanh !v. Let the vector 1 be written as

l= a (κι + κω) — a’ (k,’ + k,’).

Now by the transformation equations (7) we have

a’ = a(coshy — sinhy) = a erst τὴν ΕΝ « = 2!
VI — 2 L+u

Hence the ratio of the components of 1 along the new axes to the
components along the old axes is V1 — v/ V1 +. But (drx1)* is a
member independent of any system of axis. Hence the ratio for
(drx1)* 1 is the same as that for 1.

Now while it is impossible by any four dimensional methods
to redistribute the vector (drxl)*1] as a continuous vector field, it is
always possible after arbitrary axes of space and time have been
chosen to make such a distribution. Thus if between the two bound-
ary lines dr be taken parallel to Κι and dr’ parallel to k’:, then as
before drxl = dr’*1. By taking the complement of both sides and ap-
plying (24), then, since 1 is its own complement, we find αὐ] Ξε σ΄].
But dr-l is equal to adr-k, = adr, and dr’-1=/’dr’. Hence
dr/dr’ = a’/a. Thus the density of the components of the vector
(drx1)*1 in the one case is to the density of the components in the
other case as a” is to a”, equal to (1 — v)/(1+). Thus while we
have seen that the energy and momentum of a light-particle (§ 24)
appear different in the ratio V1 — v/ V1 + » to two observers, if the
energy and momentum are regarded as distributed their densities will
appear different to the two observers in the ratio (1—v)/(1 + 2).

Let us proceed at once to the discussion of similar problems arising
in space of four dimensions. Here also it is possible to pass at will
from a consideration of continuous 1l-vector fields to a consideration
of equivalent discontinuous distributions of 1-vectors in the case of
all non-singular vectors, by an extension of either of the methods
which we have used in two dimensional space. Thus if a region of
the field is cut out by a (hyper-) tube of lines parallel to the vector of
the field, then the original vector multiplied by the volume of inter-

470 PROCEEDINGS OF THE AMERICAN ACADEMY.

section of a perpendicular planoid is a single vector (or the sum of a
group of vectors) which may replace the original field within the tube.
Or if f represents the vector field and d the 3-vector cut off on any
planoid by the tube, then the same result as before may be obtained
by the operation (dSxf)*f /f.

In the case of singular vectors we encounter the same difficulties
as in two dimensions. Let us consider a field of singular 1-vectors 1,
and a portion of this field cut off by a small tube of lines parallel to 1.
A little consideration shows that it is impossible by any means what-
ever to replace this portion of the field by a single equivalent vector
along 1. It is possible, however, as before to obtain a single vector
quadratic in 1 and determined by the given portion of the field. Let
d& be the 3-vector volume cut off on any planoid by the tube. Then
(d§}~1) is independent of the planoid chosen, and (d»1)* 1= dg is
the vector thus determined.

47. Now it is impossible to distribute the vector just obtained
over that portion of the four dimensional spread which has given rise
to it. But there is, nevertheless, in one case another kind of dis-
tribution which is possible and which possesses considerable interest.
In order to introduce the somewhat difficult construction which is
necessary in this case let us investigate first a particular type of
singular vector field in three dimensions. Let ds be a small vector
segment of a (6)-curve. Each point of this segment determines a
forward cone. The field which we wish to consider is such that at
each point the vector 1 is along an element of the cone and of any
interval which is a continuous function of position. This construc-
tion gives a limited field bounded by the two forward cones from the
termini of the segment ds. Let a plane cut across the two cones.
The region of this plane intercepted between the two boundary cones
is the surface lying between two nearly concentric circles. Let dS
be an element of this surface. Now just as before the vector
(d§x1)*1 = dg may be formed and is different for each element dS. The
singular lines drawn from all the points bounding dS to the corre-
sponding points of the segment ds determine a sort of tube of nearly
parallel singular lines. The value of dg for each tube is at each point
independent of the particular position of the plane through that point
whose intersection with the tube is dS. If therefore the whole field
is divided up into an infinite number of such tubes, the infinitesimal
vectors of the second order in 1 obtained for the several tubes are
at each point independent of the plane which was used in constructing
them.

WILSON AND LEWIS.— RELATIVITY. 471

Now it is impossible to redistribute the discrete vectors dg over the
three dimensional field from which they were derived, but it is possible
to replace them by a continuous distribution over a two dimensional
spread in one of the cones. Let us assume that the infinitesimal
tubes are so chosen that the elements of surface dS = dqxdr are
four-sided figures approximately rectangular
and that the outer cone is divided into small
regions lying between the elements of the
cone, a, a’, a’, ... (Figure 26). In each of
these small two dimensional regions we may
place the corresponding vector dg. Now
any two neighboring lines drawn from a to
a’ are of equal interval because they lie in a
singular plane between two singular lines
(see preceding footnote and ὃ 31). The vec-
tor dg/dr is therefore determined at each
point of the cone independent of the direc-
tion of dr. It is a vector representing a Ficure 26.
kind of density and when all the vectors dg -
are similarly treated, it is continuously distributed over the whole
cone.

The vector dg /dr is a function of the interval ds. Let us determine
this relation analytically. Since dS= dqxdr we may write

dg = (dqxdrx1)*1 = [(dqxdr)*+1]1 = 11 dqdr,

where /; is the component of 1 perpendicular to dqxdr; for since dq is
perpendicular to dr, (dqxdr)* is a l-vector perpendicular to dqxdr
and of magnitude dqdr._ We therefore find dg/dr = Ildqg. It remains
to determine dq in terms of ds.

The plane of intersection having been chosen, the two circles are in
general eccentric and the distance de between their centers is the pro-
jection of the segment ds upon their plane (Figure 27). If the normal
to this plane makes an angle with ds whose hyperbolic tangent is ὃ,
then de = rds/ V1 — x. The two segments cut off by the two circles
on de produced are found as follows. Pass a plane through de and ds.

Then AB isreadily shown to be

ds V1 — »/ V1 + », and CD = dsV1 + v/ V1 — 2:

Then the value of dq is readily proved by Euclidean methods to be

472 PROCEEDINGS OF THE AMERICAN ACADEMY.

(1—v cos Φ) ds/ V1 — v2, where ¢ is the angle between dg and AD.
Hence
dg ii 1 — vecos¢

Ap 4 ae, lds. (89)

We have gone through this somewhat complicated calculation for
the three dimensional case because of the greater ease of visualisation

FIGURE 27.

and because the results obtained are applicable without essential
change to four dimensions. Again let ds be a segment of any (6)-
curve each point of which determines a forward hypercone. Let us
consider the four dimensional vector field 1 bounded by the two
limiting forward hypercones, 1 at every point lying along an element
of one of the hypercones whose apex is on ds. Any (y)-planoid will
intersect the limited vector field in a three dimensional volume bounded
by the intersections of the two limiting hypercones with the planoid;
these surfaces of intersection appear in the planoid as two nearly
concentric spherical surfaces.

If as before the vector field is divided into infinitesimal portions, so
that the volume of intersection is divided into the infinitesimal vol-
umes d, each of which is approximately a rectangular parallelepiped,
and one of the surfaces of intersection is thus divided into the infi-
nitesimal portions dS such that dqxd$ = d%, then for each infinitesimal
portion of the field we may at any point obtain as above the vector
dg = (d%»1)*1. Then precisely as in the previous case 52

42 In the peculiar three dimensional geometry of a tangent (singular) planoid
there is one set of parallel singular lines, and every plane in the planoid is

erpendicular to these lines. Every cross-section of a given tube of singular
ΤῊΝ has the same area.

WILSON AND LEWIS.— RELATIVITY. 473

dg = (dqxdSx1)*1 = Ildq dS, and dg/dS = [4] ἀη.

This vector is distributed uniformly over one of the hypercones and is
independent of the particular planoid used in obtaining it. Then also
just as before

dg 1 — veos¢d

το Ξε ἰς ——=— lds (90

dS V1 — yy ; )
where ¢ is the angle between v, which passes through the centers of
the two spheres, and the line, from either center, to the chosen point
upon the surface.

The Field of a Point Charge.

48. Much of recent progress in the science of electricity has been
due to the introduction of the electron theory, in which electricity
is regarded not as a continuum but as an assemblage of discrete
particles. In Lorentz’s development of this theory he has deemed it
necessary, however, to regard the electron itself as distributed over a
minute region of space known as the volume of the electron. This
deprives the theory of some of that simplicity which it would possess
if the charge of an electron could be regarded as in fact concentrated
at a single point. Whether the theory of the point charge can be
brought into accord with observed facts and with the laws of energy
cannot at present be decided. It seems, however, highly desirable
to develop this theory as far as possible. In our application of our
four dimensional geometry to electricity we shall therefore consider
first an electric charge as a collection of discrete charges or electrons,
each of which is concentrated at a single point.

The locus of a point electron in time and space must be a (6)-curve.
If w is a unit tangent to such a curve, then we may consider at every
point the vector ew, where εἰ is the magnitude of the charge, negative
for a negative electron, and positive for a positive electron (if such
there be). It is explicitly assumed that εἰ is a constant. We shall
show that the geometric fields obtained from this vector by the
methods of § 48 give precisely the equations which are of importance
in electromagnetic theory.

The vector w determines at every point of our time-space manifold
the vector p = w/R. Similarly the vector ew determines the vector
field
ew ΕΥ̓͂ ek, (91)

τ εν τὴς ΣΎΝ,

474 PROCEEDINGS OF THE AMERICAN ACADEMY.

The last equality is obtained when any ky, axis has been arbitrarily
chosen. Then v is the velocity of the electron and /,;—1,°v is the
distance FQ in Figure 22, that is, the projection of the distance from
the point of observation to the contemporaneous position of the
electron (if assumed to be moving uniformly) upon the line 1, joining
the “retarded”’ position of the electron to the point of observation.

We may call m the extended electromagnetic vector potential.
Its projections on space and on the time-axis are respectively the
vector potential a and the scalar potential φ,

eV €
"τ ΘΕ στο δ ἐὰν
l —— lev

(92)
precisely in the form first obtained by Liénard.*® From (69) we have
ὃ
Om = (ν a κι}. + ok) = 0.

Hence Vato = 0.

We see therefore that the Liénard potentials are connected by the
same familiar equation as connects the ordinary vector and scalar
potentials. Assuming that vector fields produced by two or more
electrons are additive, these equations are true for the general case.
The 2-vector field produced by an electron, whether in uniform or
accelerated motion, is obtained immediately from (81)—(83).

Mm << — ες ΡΞ -: a [wxc — nxc+ n-c nxw| + <“nxw.
i ra QE}
Or (
€ : € tes € 7 < €
M = — RB Ix[1-(wxe)| — R kw = — RB (Ixwxe)-1 — pw: (94)

The first term in this expression vanishes when the curvature is zero.
The fact that this term is a singular vector has already been pointed
out, and the great importance of this fact in electromagnetic theory
will be pointed out later. In the second term nxw is the unit 2-vector
determined by the line wand the point Q where the field is being dis-
cussed.

49. In case the electron is unaccelerated the equation assumes the
simple form

€

ΝΞ pow. (95)

43 Eclairage électrique, 16, 5 (1898).

WILSON AND LEWIS.— RELATIVITY. 475

This may be expanded according to (72) when an axis of time has been
chosen. Then, noting that lx«v = (1, — lv)xv,

M = —e—]— mv — ε- τ κα, (96)

Where r is the vector r = 1, — lv from the contemporaneous position
of the charge to the point Q in the field, and γ΄ = ἰῷ — 1,-v. The
2-vector M is thus split automatically into two 2-vectors, of which
one passes through the time-axis ky, and the other lies in the planoid
Κις which constitutes ordinary space. These will be designated
respectively by the letters Eand H. Thus

M= H+ E. ᾿ (97)

This separation may in all cases be made whether the field is caused
by one or more electrons in constant or accelerated motion. We shall
thus see that the 2-vector M is precisely the “ Vektor zweiter Art”
which Minkowski introduced to express the electric and magnetic
forces.

Out of H and E spacial 1-vectors h and e may be obtained by the
equations

hi H:-kps, e = E-ky. (98)

Then h is the three-dimensional complement of H, and e the inter-
section of E with three-dimensional space. Evidently

hy = Π5., hy = Hz, hs = Hy,

a= — ἔνι, e = — En, 68 = — Ey.

(99)

Referring now to (96) we see that in the case of a uniformly moving
electron
1—?”

rae rr
r3

Vv
τ “h= -- ae (rxv) Kis, (100)

or Ὁ ΘΞΞ ΠΕ. — Ho.

Noting that (rxv)+kw3 is that which in ordinary vector analysis is
known as the vector product of r and v, we see that these equations
are precisely the equations for the electric and magnetic forces.**

It may seem surprising to one who is not fully convinced of the very
fundamental relationship between the four dimensional geometry of
relativity and the science of mechanics that we should thus be led

44 See Abraham, Theorie der Elektrizitat, 2, p. 88.

476 PROCEEDINGS OF THE AMERICAN ACADEMY.

from simple geometrical premises to conclusions of so purely physical
a character. Of course it is to be noted that while our values of e and
h are identical in mathematical form with equations for electric and
magnetic force, we should need some additional assumptions before
actually identifying these quantities.

50. Our next step will be to show that the values of e and h derived
from the 2-vector xm = M are identical with the expressions for
electric and magnetic force in the general case in which the electron
is no longer restricted to uniform motion. We have from (94)

M = <P = — = (Ikwxe) +] — πε lxw. (101)

Thus, assuming some time-axis, we see from (43) that

wxe = wxv/(1 — 2°).

Then
ie e (Ixwxv) +1 fe eye
Μ — Pn ΕΒ RB lxw (102)
Hence
» ε 1-vlxw + Riv €
el πάσα, igh ieee C08)
M — εΓ 1: τι a 1,xv Se eta
(1 —v ?)? Ὥς ( — υΣ)3
(104)

a Vv (1, = l,v) xk, vag a SF (1, =a lw) xk;
(1 — 2°)? Lo Re (1 — 23

Hence, if again we use r = 1, — lv andr’ = ky —1,-ev = RU — v2) 2,

we have

em Bm <[ etait a]

r
= ‘ 2) (105)
h = Ε΄ Κι = —e[ = si οι sed |. + Kes
If we look at the form in 1, — γ᾽ (104) we observe that
|e ee I 1,xe, E = — exk,. (106)

I

Hence

M = Ε 1, Ὁ Σ a2 ape. (107)
i Ἷ

WILSON AND LEWIS.— RELATIVITY. 477

These are the equations for the field of an accelerated electron
which were obtained by Abraham and Schwarzschild.*° It will be
convenient to divide the field M into that part M’ which is due to
acceleration alone and that M” which is independent of acceleration.
The former, which is the first term in any of the above expressions
for M, (101)—(103), is a singular vector field, and is the only one which
is important at great distances from the electron, for it varies as 1/R
(since 1 varies with 10) whereas M” varies as 1/R?. If we divide the
field M’ into its two parts M’ = E’ + H’, we see here also that

ἘΠῚ - 1 ae ΕΞ ιν (108)
ἄς

and since, in this case, 1,-e’ = 0 (as may be seen by performing the
multiplication) and 1, is perpendicular to e’, we find that Β΄, H’ are
equal in magnitude. Moreover e’, h’ are equal in magnitude and
perpendicular to each other and to 1,. In other words in a radiation
field the electric and magnetic forces are equal in magnitude, perpen-
dicular to each other, and perpendicular to the “direction of propa-
gation.” All these results are geometric consequences of the fact
that the 2-vector M’ is singular.

51. In four dimensional space every singular 2-vector determines
a singular l-vector, namely, a vector pointing outward along the
element of tangency of the 2-vector with a forward hypercone. This
l-vector is the complement of the 2-vector in the tangent planoid.
If I’ is the 1-vector thus determined by the 2-vector M’, then we may
write

Me = tux’.
where Ἃ is any unit vector in the plane of M’, provided the sign of ἃ
be properly chosen.*® In the case of the singular vector M’ which we
have obtained in the previous section we may write, from (94),
. x

re τὶ Μμ[1-(πχο)] = — Ε: abe . ὃ)
where a is the magnitude οὗ 1+(wxe) and therefore the last vector is
a unit vector. Hence we may write at once for the l-vector deter-
mined by M’,

M’ = (109)

l= 1 Ὁ (110)

45 See Abraham, Theorie der Elektrizitiit, 2, p. 95.

46 Owing to the nature of the geometry in a singular plane, the unit vector ἃ
drawn from a given point always terminates on a definite singular line and
thus determines the same 2-vector uxl’ for all values of ἃ. (§ 31)

478 PROCEEDINGS OF THE AMERICAN ACADEMY.

The value of a is, from (80),
a = V{l-(wxe)]-[1-(wxe)] = R V(nxe)-(nxe). (111)

Now the vector 1’, being a singular vector continuously distributed,
can be treated by the method of § 47 to give at any point a discrete
vector of the second order in 1’, namely,*”

de (gesx) )*1 (112)

where d§ is the vector volume cut off on any planoid by an infinitesimal
tube of singular lines parallel to I’. If ds is an infinitesimal portion
of the locus of the electron which gives rise to the fields M’ and I’,
and if we consider the region of the I’ field bounded by the two forward
hypercones from the termini of ds, then all the vectors dg belonging
to this region can be redistributed continuously on one of the hyper-
cones, and just as in § 47 we obtain the vector

dg _ ι 1 — veos¢

τ lds.
Now we may substitute the value of I’ and obtain
dg = ὅς αὐ (dA), (113)
eed edt ls): Wea eer (114)

dS Ἧι Ré V1 = v

Before proceeding further with the second of these equations, let
us obtain dg in another form. We may first show that

dg = (d&xl1’')*1I’ = (dS*-M’)-M’. (115)

For M’ = u«l’ where wu is a unit vector perpendicular to 1. Hence
(d*-M’')-M’ = [d*-(uxl’)]-(uxd’) = [(d*-l) u

— (d*-u)1']-(wd’)

by (34). Applying this rule again and noting that ueu = 1 and

U1 -— ἢ
(d&*-M’)-M’ = — (d*-1) 1,

From this, (115) follows by (24). Now we have written M’ as

/ / / 1 / ,
M - H+ E =; lxe — exk,
4

47 Since l’ involves a and therefore nxe, the vector dg is zero for all points
in the line of ¢, and is a maximum when N is perpendicular to 6.

WILSON AND LEWIS.— RELATIVITY. 479

Now we may choose d§} perpendicular to Κι and with proper sign,
then dS* = k, dS. Hence, performing the multiplication,

dg = [ἡ " es) dS. (116)
4

Now if e’ is interpreted as electric force in a radiation field, then we
are accustomed to regard e’ (= h”) as the density of electromagnetic
energy, and the vector e” 1, //;, where 1, //; is a unit vector perpendicular
to e’ and Β΄, as the Poynting vector. Therefore dg becomes a vector
of extended momentum of which the components are the total energy
and the total momentum in the chosen volume dS. The vector dg is
moreover independent of any choice of axes and is representative at
any point of the tube whose cross section with any chosen space is
the volume ¢§. But the vector dg/dS obtained by combining the
Poynting vector and a vector along the Κι axis representing the
density of energy is by no means independent of the choice of axes.
In fact we may state that no way can be found of representing the
density of energy by a strictly four dimensional vector. Thus we
have a vector of extended momentum for energy-quanta, but not for
energy density — an observation which is not without significance in
view of certain modern theories of light.

52. It is interesting to note that the same energy vector dg may be
obtained from different 2-vectors M’. For any two singular 2-vectors
of the same magnitude and passing through the same element of the
hypercone determine the same vector I’ as above defined. If we
regard any singular 2-vector M’ produced by an accelerated electron
as the extended electromagnetic field of the radiant energy which is
moving out along the space projection of the element 1 with the
velocity of light, then it is evident that, since there is an infinite num-
ber of such 2-vectors to which the element 1 is common, there is
something else necessary to characterize the light besides its energy.
In fact a 1-vector such as I’ or dg upon which the condition is imposed
that it shall be singular has three degrees of freedom; a 2-vector such
as M’ subject to the two conditions that it shall be singular and uni-
planar has four degrees of freedom. It is this additional degree of
freedom in M’ which gives rise to such phenomena as polarisation
which show a dissymmetry of light with respect to the direction of
propagation.

If the vector dg represents radiant energy (moving out along the
hypercone with unity velocity), then the integration of equation (114)
around the whole hypercone should give a vector representing the

480 PROCEEDINGS OF THE AMERICAN ACADEMY.

extended momentum of all the energy emitted by the electron, between
the ends of the segment ds of its locus. We wish to evaluate the

integral
- yr ile 2 atl, "8? ras, (117)

Vv] — υ

This integration may be simplified by the observation that the vector
dg is not only independent of the direction of the planoid which cuts
the boundary of the elementary tube in the surface dS, as has already
been shown in general, but is also in this case independent of the
position of the planoid, for dg/dS varies as 1/R? and dS varies as R?.
The integral therefore is the same for any planoid whatsoever, and we
may therefore choose for simplicity a planoid perpendicular to the
locus ds, and cutting the hypercone in a spherical surface of unit
radius, that is R = 1,= 1. Substituting the value of a from (111)
gives, since v = 0 and1 = R(w—n),

ie io is [- *(nxe)?(w — n) dw,

where dw is a solid angle at the center of the:sphere subtended by dS.
The vector ¢, normal to w, is then along some diameter of the sphere;
and n is directed from the various points of the surface toward the
center. For diametrically opposite points the terms (exn)? n cancel.
We need only integrate the terms (exn)? w. If the diameter deter-
mined by ¢ be taken as polar axis, these terms may be expressed as
c’sin’9w; and the element of surface is sin@d@d¢. The integral is
therefore

fos ΞΞ τ cows. (118)

This integral should be the vector of extended momentum for all
the energy emitted by the electron between the two points considered,
and its projections on any chosen time and space should be the corre-
sponding energy and momentum. If the ky axis is chosen parallel to
ds, that is if the electron is considered momentarily at rest, we obtain
a simple expression; for then w = ky, c? = "Ὁ, and ds = dt. The
momentum altogether is zero, and the energy is

8a

“3 & (We) df. (119)

When some other ky, axis is chosen, such that the electron is assumed

WILSON AND LEWIS.— RELATIVITY. 481

to have the velocity v, the expression becomes more complicated.
Since w = (v + k,)/ V1 — υ" andds = V1 — υ dt, we have from (45),

8 Ξ ἣν PS ae
fis ΕΞ 4 a < 0)" [60 — (vxv)+(vxv)](v + Κι) dt. (120)

The two parts of this expression are precisely in the form obtained
by Heaviside and Abraham *° for the momentum and energy radiated
from an accelerated electron.

53. When a singular vector field such as dg/dS is distributed
continuously over a hypereone and is of such a character that its
magnitude falls off along any element inversely as the square of the
interval of that element measured from the apex (that is, inversely
as 15), or in other words, if it is of such character that the integral
of the vector over the surface of intersection of the hypercone with
any three dimensional spread is constant, then we may call such a field
a simple radiation field. (In three dimensional space the magnitude
would fall off inversely with R, and in two dimensional space would
be constant.) The fact that the integral of dg/dS over the inter-
section of the hypercone with any two parallel planoids is constant
may be regarded as equivalent to the law of conservation of radiant
energy.

While the discussion which we have given of the vector dg is in
complete accord with current theories of electromagnetic energy, there
is another singular 1-vector which is suggested by the geometry and
which may be of importance in case it is necessary to revise our ideas
of radiant energy. This vector also gives a simple radiation field,
in the sense just defined, and is likewise of the second order in M’;
but unlike the vectors dg and dg/dS it is continuously distributed
over a four dimensional field. This is the vector 495 (w+ M’)-M’ = b.
The vector b is along the element of tangency 1 by §39. Indeed if
we take M’ from (93) we have

; jie ἘΞ
b= (w-M’)-M’= >,

εξ

-- πε(θα !. (121)

[c-c — (n-c)?] (w—n)

48 Abraham, Theorie der Elektrizitat, 2, 116.
49 To obtain a vector, of the second degree in M’, out of M’ itself is out of
the question; for the only two prcducts of the seecnd degree in M’ which are
geometrically significant, namely M’+M’ and M’xM’, both vanish, since M’ is
singular and uniplanar. The vector b involves not only M’, the field of the
electron, but also w which expresses the state of motion of the electron itself.

482 PROCEEDINGS OF THE AMERICAN ACADEMY.

If a ky axis has been chosen, Ὁ may be obtained in terms of e’, or of
e’ andh’. For instance with M’ taken from (108),

he (= -- ky 1.xe’ + hve’) lee τὸς Like’

vee Ι, ἢ

When we perform the reductions, remembering that 1,-e’ = 0, we
find simply

e? ( =) { )
ee | | eee, 122
b ae Ἢ Ἴ ΞΡ θὰ (122)
If we use M’ in the form M’ = E’ + H’, we find °°
[i= sayin ile Jlé-hiea wee Gv bh — hey ee v-exh Κι),
ΥἹ --ὐὶ (123)

where e’xh’ has been used to denote the 1-vector (e’xh’)+Ky3, which
is the three dimensional complement of the 2-vector e’xh’. Another

equivalent form is
ΘΕ ee στ aire (124)

V1 == he ls

The coefficient (J; —1,-v)/l:¥1 — & is unity when 2 is negligible
compared with the velocity of light, and therefore in all such cases b
is the sum of two vectors one of which is the Poynting vector and the
other along k; equal in magnitude to the density of energy. Since
the vector b comes so near to being the extended vector of energy
density, the possibility is suggested that the energy of an electro-
magnetic field may not depend solely upon the field itself but to some

50 For rapid calculation a rule for obtaining the three dimensional form of
some products is useful. The most important of these rules is that if

= aK; = bxk, and c=C; τον ciK,,
where a, b are three dimensional vectors, then
cA = Cx + οὖ + (6,50) Κι.
1

Thus we have here

b = (w-M’)-M’ = Brg | + Κι). (h’ekios — e’xky)]- (Ὠ΄ «Kies — e’xks)
-- v*
= ἯΙ zt [vxh’ +e + (vee) ka]- (h’ «kis — e’xk,)
= 7
= as [vxh xh’ +e’xh’+ (v-e’)e’-+ (vxh’-e’+e’+e’)k,],
— vp

which is identical with the form given.

WILSON AND LEWIS.— RELATIVITY. 483

extent upon the velocity of the emitting electron. It is interesting
further to note that by the application of rules already given we may
evaluate +b and show that it vanishes. Hence

0 bs

Ob = V "Ὁ. + at

=, (125)
where b, is the vector which we have just shown to be approximately
equal to the Poynting vector, and δι is approximately equal to the
density of energy. This equation is therefore entirely analogous
to the familiar theorem of Poynting. If we integrate over a three-
dimensional volume,

if Ι ! V “Ὁ. ἀχσια χοάς = -- | | ! bydaydxodxs,
ΕἸ Γ 0 .
} [baa sae [J J dsdedesdrs (126)

Thus the induction of b, through any closed surface is equal to the
rate of loss of by in the enclosed volume.°+

If in the vector field b we cut the hypercone by any planoid, it
will be evident that the integral of bdS over the surface of intersection
will be independent of the position and direction of the planoid; for
the surface dS always lies in a tangent plane and b varies inversely as
R? and hence as dS. The vector bdS bears a simple relation to dg
which we have studied. For dg = (εἰ ἢ. ΝΠ)" ΜΙ’, where d§ is deter-
mined by any planoid. We may therefore choose d perpendicular
to ds, that is, tow. Then d* is wdS and dS = dSds, and since Ὁ by
definition is (w+ M’)-M’, the integral of dg is the product of ds and
the integral of bdS. We might therefore by a consideration of b
alone have obtained the same vector of extended momentum for the
total energy emitted by an electron in the interval ds.

We shall not pursue further the study of this interesting vector b,
but it may be well to point out that the two fields M’ and b cannot
both be additive. For since b is quadratic in M’, we obtain a differ-

or

51 In general if a 1-vector field in four dimensions is of such a character
that its four-dimensional divergence vanishes, we may obtain in three dimen-
sions an equation of the type just found, wherein the surface integral over a
closed surface of the space component of the vector is equal to the negative
time derivative of the integral of the time-component of the vector over the
enclosed volume. Such an equation may be interpreted as a continuity or
conservation equation whenever the space component appears as a velocity
multiplied by the quantity defined by the time-component.

484 PROCEEDINGS OF THE AMERICAN ACADEMY.

ent result when we obtain b from a resultant M (no longer necessarily
a singular vector) and when we add the b’s obtained from the original
M’’s. All the classic ideas of electromagnetic energy assume that
it is the vectors M that are additive at a point.

The Field of Continuous Distributions of Electricity.

54. Since the locus of an electric charge is not a singular line, we
may regard the charge as distributed continuously over a given region
or regions rather than as concentrated at one or more discrete points.
Thus instead of a single vector representing the locus of an electron,
we may consider a vector field. Let a small (6)-tube be parallel to
and comprise 7 electron-loci each of charge «. Then we may replace
these on the one hand by a single vector new, and on the other hand
by a vector field q such that, if dS is the volume of any portion of the
tube cut off by a planoid perpendicular to w,

[«Ξ = new.

Or if d& is the vector volume cut off by any plancid whatever, then as
im S70:

[«5ῳν = new. (127)

If now we write
qd = pow, (128)

po evidently represents the density of electricity as it appears to an
observer stationary with respect to the charge. ΤῸ an observer with
respect to whom the charge appears to be moving with the velocity v
the density appears to be different. For we may write (127) in the

form
ie (d*+q) w;

and if d§ is the volume cut off by the planoid perpendicular to the
chosen time-axis ky, d%* = dSk,; then writing

w= (v+ k,)/V1 — 2,
we have

ΟὟ =~
i} ΞΞ dS = new. (129)
J Vi—Yv

WILSON AND LEWIS.— RELATIVITY. 485

If then p is the density of the moving charge, we must write

Po

δα V1 — ye

(130)
When we compare the two vectors

ew = FS (v+ ki) and pw=p(v+k,)
— νυ"

with the two vectors which we have obtained for a material system

mow = m(v+ k,) and yow= i= (v + k,)
— (iad

we see that they are identical in mathematical form. But the com-
ponents of ew are not quantities which are commonly used in physics,
while the components of pow are
the density of electricity and of
electric current. On the other
hand the components of mow are
the fundamental quantities known
as mass and momentum, while the
components of μοῦ are not com-
monly used. This is probably due
to the fact that the fundamental
conservation law for electricity is
Σε = const., whereas the funda-
mental conservation law for mass
is not 2m = const., but 2m =
const.

55. We may now construct the
potential at a point due to a con-
tinuous distribution of electricity,
directly from (91) and (127).

m = [«5.ῳ’ , (131)

FIGURE 28.

The interpretation of this equation will be evident from an examination
of a diagram which is an immediate extension of the one previously
used in discussing potentials. And we may then show that, when a
particular space and time have been assumed, the components of the

486 PROCEEDINGS OF THE AMERICAN ACADEMY.

vector m on the chosen space and time are the ordinary “retarded”
potentials.

If (Figure 28)5? we draw the backward hypercone from the point at
which the potential m is to be determined, and if this backward hyper-
cone cuts an elementary tube of the field q in the vector volume αἰ,
then F is the perpendicular interval from the point in question to w
or w produced (where w is the direction of q at the point where the
tube cuts the cone). That part of the additive potential vector m
which is due to this particular tube is

dm = ($Sxq)* ἢ = = {S*-q * (132)

Evidently the integration of dm is to be taken over the whole three
dimensional spread produced by the intersection of the backward
hypercone with the whole assemblage of infinitesimal tubes.

Figure 29.

Now if (Figure 29) we construct any planoid through the point in
question, the retarded potentials are calculated as follows. This
planoid, which we may regard as our space, is divided into elements
of volume dS’ (corresponding to dS’ in the figure). We consider the

52 Figure 28 and Figure 29 are drawn and lettered for one dimension lower.

WILSON AND LEWIS.— RELATIVITY. 487

values [p] and [pv] of the density and the current density which were
in the element dS’ at a time previous by the length of time required
for light to pass from dS’ to the point in question. From the four
dimensional point of view this means that we project the element dS’
parallel to the time-axis upon the hypercone, and take as [p] and [pv]
the projections on time and space of the vector q at this point of the
hypercone. We then form the integrals

{2 dS’ and jf dS’, (133)

where r is the distance from dS’ to the point at which the potential
is wanted.

Let us now consider the element dm of our potential. The vector
dS (corresponding to d§ of the figure), being cut out of the hyper-
cone, is a singular 3-vector, and its complement d%* is therefore a
singular l-vector. Hence dS’ is numerically the projection of dS*
upon ky, and it is readily seen that

τ, ἯΙ.

dS’ ἢ
Substituting in (132),

dW ae) SW Wey
dm δ l; R oS ly R
But l-w = — R by (80) and iis equal to /,, that is, to the r in (133).
Hence
ae Ἴ [ev] τ [pl Κι as (134)

If we designate the vector and scalar potentials as a and ¢ respec-
tively, then
m= a+ ku. (135)

We may show as before ° that

C-m—"0 οἵ Vat @ = 0. (136)

We have seen (ὃ 44) that O-©p = 0, or ©?p = 0, and consequently
<*m = 0 in the case of a point electron for all points not upon the

53 A single differentiation under the sign of integration is permissible if Pg
remains finite; but a second differentiation is not permissible, as is well
known in the theory of the potential.

488 PROCEEDINGS OF THE AMERICAN ACADEMY.

locus of the electron. In the case of a continuous distribution of
electricity we have ὅς

'm = — 4πα, (137)
which might be proved directly; but this is unnecessary since it has.
frequently been shown by familiar methods that

'a = —Ampy and νῷ = —Arnp. (138)

Furthermore it is unnecessary to evaluate once more in detail the
2-vector

M = Oum = ὅκα + (Ve + 5? de (139)
For \7xa is the three dimensional complement of what is ordinarily
known as curl a or h, and V¢ + a= —e. Hence
M= H+ E,

where the components of H and E are once more the components of
magnetic and electric force.

56. Whether the 2-vector M of extended electric and magnetic
force be derived from a number of point charges or from a charge
continuously distributed, it is in general a complex or biplanar 2-vec-
tor.°5 The two invariants of M are M-M and M-M* = (MxM)*.
If, after choosing space and time axes, we write

M = hikos Ἔ hoks) == hski2 — ky — Ko, — eka,
Me — €1Ko3 + e@2k31 + ¢3Ki2 + hikys == hyko. = hsksa,

54 The vector 4 πᾷ which we use 15 identical with the vector q used by Lewis,
owing to a different choice of units of electrical quantity.

55 Since it is customary to divide a complex 2-vector into the two completely
perpendicular uniplanar vectors which are uniquely determined, one being a
(y)-vector, the other a (s)-vector, we might expect.that the two lines of inter-
section of the (s)-plane with the hypercone, and their projections upon a
chosen space, might prove important. This is, however, not the case, although
indeed from an analytic point of view the four directions, two of them imagi-
nary, in which the hypercone is cut by the completely perpendicular (6)-
vector and (y)-vector form a set of four independent directions possessing
some advantages over the system ki, kx, ks, ki. In fact four vectors ji, jz,
js, ja can be selected along these directions such that

jiehi =Je°2=Js°js =jaejs=0, jitje=Js°ja=1,
jiehs =jie da =Jo°)s =jo° ju =0.
In terms of such a set of vectors the differential of are is given by the equation
dredr = dx? + dy? + dz — dt? = Adudv + Bdwds.
(See Bateman, Proc. Lond. Math. Soc. [2] 10, 107).

_ Other vectors which might be thought important would be the two lines.
in which the completely perpendicular planes cut the planoid which is taken

(140)

WILSON AND LEWIS.— RELATIVITY. 489

then M-M = /? — e = 2L, where L is known as the Lagrangian fune-
tion, and M-M* = 2e-h. It isnot surprising that the Lagrangian
function should prove to be one of the fundamental invariants, but
it is strange that the other invariant should be a quantity which has
not been regarded as of fundamental importance in electromagnetic
theory.

Since we have obtained our 2-vector from the equation

ΜΞ <>xm,
we may readily evaluate OxM and Ὁ Μο By (51) as ἃ mathematical
identity we have
ὌΝ xe τῇ Ξ 0) (141)
By (55)
OM = O-(Omm) = Of} m) — ©:O)m;

and since we have seen that in general <>:m = 0, and substituting
for +m or Φ τὰ from the preceding section,°® we find

©: Mj= 474. (142)
By (52) as a mathematical identity,
O(O-M) = 0. (143)

By the expansion of these equations we obtain directly the familiar
equations of the electromagnetic field and the continuity equation

as space. Following the method of $38 we may write M as the sum of its
two completely perpendicular parts in the form

(V(M-M) + (M-M*)? + M-M)M + (M-M*)M*
Vv(M-M)? + (M-M*)?

(V(M-M)? + (M-M*)? — M-M)M — (M-M*) M*
V(M-M)* + (M-M"*)

Now the lines in which these two completely perpendicular planes cut the space

ky; may be found by multiplying the planes by k, by inner multiplication.
As kyeM = e and kye-M* = — h, we have for the lines

pate 2e (VL? + (e-h)? — L)e + (e-h)h_
Vi? + (eh? ee

These vectors, however, like those mentioned above, are not found to be im-
portant in electromagnetic theory.
56 cf. equation (85).

M =

bole

+3

1
2 ; 2

490 PROCEEDINGS OF THE AMERICAN ACADEMY.

expressing the conservation of electricity. We may write (141) in the
form Ὁ ΜῈ = 0. Expressing M* as in (140), this equation becomes

ee
Ve ἐπ = 0, |

τ ἢ 1.
Similarly from (142)
— oe
Vxh — apt TOY |

These are the well known field equations. Finally (143) gives the
continuity equation

Op”
Ve(pv) + ape 0.

It cannot be too strongly emphasized that all these equations follow
from the theorems of our four dimensional geometry without any
further assumption than that the geometrical vector potential field
derived from the locus of an electric charge is the extended electro-
magnetic vector potential.

57. We have seen that the singular 2-vector field M’ produced
by an accelerated electron determines a vector dg of four dimensional
significance involving quantities which may be identified with energy
and momentum in the radiation field. A search for similar vectors
due to the field M, which in general is not singular, proves, however,
to be unsuccessful. In the case of radiation we wrote

dg = (d&*-M’)-M’,

or since it is readily shown (see footnote, ὃ 62) that in this case
(d&*+M’)-M’ = (d&*-M’*)-M’* we could have obtained a more sym-
metrical form

dg = 1 (dS*-M’)-M’ + (d*-M’*)-M’*. (144)
In the case of the vector M we may write by analogy
4[(dS*+M)-M + (d&*-M*)-M*], (145)

where d& is the vector volume produced by intersecting a selected
portion of the four dimensional field by a planoid. However, this
cannot be made to give rise to a real vector in a four dimensional
sense, but will only have meaning for the particular planoid chosen.

WILSON AND LEWIS.— RELATIVITY. 491

If we choose a particular ky axis and its perpendicular planoid, then
d%* = dS ky, and the above expression becomes

A {(ky+M)+M + (k,-M*)-M*|dS. (146)

We may perform the operations here indicated upon the expanded
form (140) of M and obtain®”

[exh + 3(e + h?) ky] dS. (147)

Now exh, the complement in three dimensional space of exh, and
4(e? + h*) are the familiar expressions for the Poynting vector and the
density of electromagnetic energy, and the above expression therefore
represents what is ordinarily regarded as the total electromagnetic
momentum and energy in the volume dS.

Now after the axes have been chosen we may perform similar
operations with ki, ky, Κα. Thus

3 (ce M)+M + 3 (Κι ΜΗ) Μ᾿
2 (Ko-M)-M + 3 (κυ ΜῊ) ΜῈ" = Y,ki+ Y,k. + Y.k; — Yiky,
1 (IcgeM)-M + 3 (ks-M*)-M* = Z,ki + Z,k. + Z.ks — Ziku,
3 (k,-M)-M ΞΕ 3 (Ky+ M*)-M* = Tk, + Tyke + Tks + Tik,,

Xe + Xykp FF Xk; me X Ka,

where

Ay = = (οι; — οὐ — e + hy — h? — hs),
Y, -Ξ ᾿ (ο es? ---οὐῷ + hy? — he — hi),
Z.= % (es — οι — e)? + πῇ — hy? — h”),
T; = > (οι + 65 + ὁ + hy? + [5 + hs”),
Xy = Yz= ee. + hh, ete.,
T, = Xi = eh3 — eh, etc.

In these equations X,, etc., are the familiar expressions for the
components of the Maxwell strains; 7, 7, T, are the components
of the Poynting vector; and 7; is that which is ordinarily assumed
to be the density of electromagnetic energy. This procedure is
essentially that of Minkowski. We may reproduce his procedure
exactly with the aid of dyadics. It may readily be shown (see appen-
dix, § 62) that if M is any 2-vector, and I the unit dyadic or idemfactor,
then the dyadics

Φ = (I-M)-(I-M) o* = ([-M*)-(I-M*)

57 For abbreviated methods see a footnote in § 53.

492 PROCEEDINGS OF THE AMERICAN ACADEMY.

are such that

a-® = (a-M)-M δ ἢ = (ἃ ΜΠ). Μ΄,

where ἃ is any 1-νϑοΐου. The expressions which we obtained from M
and Κι, Ky,.. . in the form

3 (Κι M)+-M + 34(k,-M*)-M™%, ete.
might therefore equally well have been written
2 Κι (ᾧ + &*), ete.

It is these latter expressions which Minkowski obtained. The dyadic
4(@ + *) is identical with Minkowski’s matrix S, except in as far
as he used imaginary space, and distinguished between electric force
and displacement and between magnetic force and induction.*®

While, as we see, the use of the dyadic 1 (® + &*) yields no results
which are not also obtainable by the methods of simple vector analysis,
yet to one who is familiar with the dyadic method it frequently affords
a considerable gain in simplicity. Thus for example we may obtain
an important result by considering the expression }<>+(@ + &*),
which may be shown to vanish in free space.o? Now, if VY, be the
three dimensional dyadic of the Maxwell strains, if exh is the Poynting
vector, and if 7; is the density of energy, we have

0= 10-(@+ 6*) = ει — exhk, — kiexch — kik, 7), (148)
or

Wek ae - (exh)=0 and V-exh+ δ T,= 0. (149)

The first is the important equation of Lorentz connecting the force-

58 The form of the dyadic YW = 4 (6 + #*) is
X;kik; + ΧΙ. + X-zkk; — Xikiky
+ Y,k.k, + Yykok, + Y-zk:k; — Yikoky
+ Zk:3ki + Zyk;k. + ZkKsk; — Zikskg
— 7T7ksk, — Tyksk, — ΤΊΚΙΚ: — Tikiky.

59 From (158), with A = M, A’ = M, and from (141) and (142), sincé in
free space q = 0. Where there is electricity the equation would be

0 Ψ = 4rq-M.

WILSON AND LEWIS.— RELATIVITY. 493

due to the Maxwell strains and the rate of change of the Poynting
vector; the second is Poynting’s theorem.®°

Mechanics of a Material System, and Gravitation.

58. The mechanics of a particle which we have treated in restricted
cases in ὃ 21 and §36 can now be completely generalized. If mp is
the mass of a particle, and w the unit tangent to its locus, then

mow = m(v + ky)

is the vector of extended momentum, whose projections on any chosen
space and time are mv, the momentum, and m, the mass or energy.
If we consider any number of such vectors, we may state the laws of
conservation of momentum, mass and energy in a single theorem as
follows. The sum of all the vectors of extended momentum is constant,
that is, the sum of all such vectors cutting any unclosed and continu-
ous three dimensional (y)-spread is independent of the (y)-spread
chosen. This law is, however, true only when we state that wherever
there is energy there is a vector of extended momentum, whether .
or not this energy is associated with that which is ordinarily known as
a material system. Thus in § 51 we have discussed the vector dg
which we have identified with the vector of extended momentum of
radiant electromagnetic energy. A Hohlraum obeys all the laws of
a material system, and must be treated as such. We shall mention
presently another form of radiant energy to which also we must assign
an extended momentum.

Just as the discrete locus of an electric charge was replaced by a
continuously distributed field of density vectors, we might regard a
material system as a continuum. Thus if we have a small (6)-tube
parallel to and comprising one or more (6)-lines of which the resultant
vector is mpW,we may replace this vector by the expression (dxupw)*w,
where d®& is the intersection of the tube with any planoid, and uow
is the vector of the distributed field. If d is taken perpendicular
to w, this reduces to upwdG, and therefore μὺ is the density as it appears
to an observer at rest with respect to the system. It must, however,

60 In case there is electricity present, these equations become respectively

Vows - ΕΞ = 4xp(e + vxh), V -exh + Sf = — 4άπργ 0.

Note that if v is small, the second equation is corrected by the small term

—4rpv-e, whereas the first has the large correction 47p(e + vxh), approxi-
mately 4πρθ.

494 PROCEEDINGS OF THE AMERICAN ACADEMY.

be borne in mind that when the system in question embraces any
energy which is moving with the velocity of light, this method fails
completely. And this is an essential difference between a system of
electric charges and a system of matter or energy. Indeed a consid-
eration of the properties of a Hohlraum shows that it may be unsafe
in any case to assume that a material system is not composed wholly
or in part of energy moving with the velocity of light.

59. In the study of hydrodynamics cases are considered in which
the different portions of the fluid exert forces upon one another, and
these forces may be themselves due to a flow of energy with the
velocity of light. In fact it is only when we consider a fluid devoid of
such mutual forces that we are able to obtain from our continuously
distributed field and the law of extended momentum the known equa-
tion of hydrodynamics. Let us consider a continuously distributed
field divided into infinitesimal tubes in each of which the extended
momentum is now written as (dxu)w)*w. Then our conservation
law leads to the equation

if (dSxuow)*w = const. (150)

Or if we consider a portion of the field composed of a number of
adjoining tubes and cut off by two different planoids, then since none
of the vectors of extended momentum cut the boundary tube the
integral of our vector over the whole three dimensional boundary of
this four dimensional region is merely the integral over the two planoids
namely,

— [ (@S*-now)w =0= — f aS*- (www),

by definition of the dyadic μον. Now by the application of (65)
we may convert this triple integral into a quadruple integral. Thus

if eee) = J d=*)+(uoww) = 0.
Hence
> (uoww) = 0. (151)

If now we set w = (v-+ k))/V1 — & and p=po/(1 — w) by (88),
this gives by expansion®!

[ue (Ὁ + ku) (Ὁ + ΚΩ)] = [O-u (v + ky)] (v + ky)

A τς [μ (Ra, ky) -O](v aE Κρ Ξ 0,
61 Τῇ ab is a dyadic, evidently + (80) = (+a)b + (aeO)b.

WILSON AND LEWIS.— RELATIVITY. 495

or
OV

| ν- *(uv) + of lo Ἐκ +u[ (Vv +o = 0,

Hence the space and time components both vanish, and

I

ὁ
ΨΥ) + 5, = 9, (152)

(WeV)v to = 0. (153)
The first of these two is the continuity equation, the second is the
dynamical equation of hydrodynamics in the present restricted case.®?
The fact that we are thus led not to the general laws of hydrodynamics
but merely to the laws for a comparatively trivial case shows the
inadequacy of any attempt to distribute the vectors of extended mo-
mentum into a continuous field.

Minkowski added to his great memoir on the “ Grundgleichungen
fiir die electromagnetischen Vorgiinge”’ an appendix on mechanics
which seems to have been more hastily written. In this section he
bases his analysis upon two assumptions which must be considered
as fundamentally erroneous. The first of these is that μ = uo/ V1 — 0°;
and the second that Simp is a constant.®* The results should be that
= pwo/(1 — v*) and that Ym is a constant. We have already dis-
cussed (ἢ 23) cases in which mp is not a constant.

60. Every locus of a particle to which belongs the vector mow
gives rise to the geometric vector fields

mop = mw/R and moP = m)xP.

By replacing the constant ε by the constant mp we might proceed
to reproduce identically all of the formulas which we have obtained
for the electromagnetic field. If a suitable unit of mass be cho-
sen, we should then observe that in case axes are so taken that the
panne peo at rest, the Space vector ΤῸ "Κα becomes ome

62 It may well [ε that the ined ation of additional terms sufficient to give
(153) a form as general as that ordinarily used in hydrodynamics would not
require serious modifications in (152). For in ordinary units the pressure of
light is measured by the density of electromagnetic energy, whereas the mass
of the light is its energy divided by the square of the velocity of light. _Com-
pare also the fact that the changes in the equations (149) w hen electricity is
present is small in one case and large in the other.

63 The second of these errors has already been pointed out by Abraham,
Rend. Cire. Mat. di Palermo, 30, 45.

496 PROCEEDINGS OF THE AMERICAN ACADEMY.

in form with gravitational force, and the time component of mop
with gravitational potential. When the particle is not at rest it is
evident that just as in electromagnetics we must add to the scalar
potential a vector potential, and to the (corrected) gravitational force
another force which by analogy we may call gravito-magnetic. In
every other respect, moreover, the two problems must be completely
analogous. Thus an accelerated particle must give rise to a singular
vector field which we should expect to be associated with the flow of
a new form of radiant energy.®*

APPENDIX.
Dyadics.

61. The dyad or formal product of vectors, introduced in 1844
by Grassmann under the name of open product, was given a funda-
mental position in vector analysis by Gibbs. Gibbs also developed
the idea of the dyadic, or sum of dyads, as the most general type of
linear vector operator. The dyadic is useful not only in the treat-
ment of the linear vector transformations or strains, but also as a
mere formal product (or sum of products) which can later be converted
into such determinate products as the outer and inner products of our
analysis. We shall outline very briefly the form taken by the theory
of dyadics in the vector analysis which we employed.®

If a,b, c¢,... are 1-vectors, then the product expressed by the mere
juxtaposition of a and b, namely, ab is called a dyad. The sum of
two or more such dyads is called a dyadic, and any such dyadic in
an n-dimensional space can be reduced to the sum of n dyads. As
the dyad is in part defined by the assumption of the distributive law,
every dyadic in four dimensional space may be expressed as a block
of sixteen terms analogous to a matrix. Such an expansion is of great

64 It should, however, be noted that there is nothing in electromagnetics
corresponding to the vector of extended momentum of energy moving with
the velocity of light. It is, furthermore, to be noted that while the radiation
fields produced by the acceleration of two electrons, whether of the same or
opposite sign, due to their interaction, are cumulative, that produced by the
acceleration of two material particles, due to their gravitational attraction,
must tend to compensate one another. (Cf. the paper of D. L. Webster,
These Proceedings, 47, 569, 1912.) }

65 For further developments we refer to Gibbs’s work as set forth in his
Scientific Papers, 2, in the Gibbs-Wilson text on Vector Analysis, and in
Wilson’s “On the theory of double products and strains in hyperspace,” Trans.
Conn. Acad., 14, 1.

WILSON AND LEWIS.— RELATIVITY. 497

convenience when the individual vectors are expressed in terms of
coordinate vectors. Thus,

αὐκικι + ἀμ Κι. + ay3kiks + ayukik,
+ aykek; + ἀρ 00 + doskok3 + ankek,
+ ἀρ κι + (3. 80 τς ΘΚ 15 + dsaksky
+ aykik; + ἀρ. + (ty3kykKe + ἀμ Κι.

The product of a vector a and a dyad be is expressed and defined

as
a:be = a-(be) = (a-b)e,

It is a l-vector along 6. Similarly ab-c = (ab)-c = a(b-c). The
product of a vector into any dyadic follows from the distributive law.
The product of two dyads is expressed and defined as follows.

ab-cd = (ab)-(cd) = a(b-c)d = (b-c)ad.

It is another dyad. The product of two dyadics then follows from the
distributive law, and is therefore a dyadic.

Since the dyad product is obtained without implying any relation
between the sixteen units k;k;,, it is the most general product and com-
prises within itself the more special products which we have desig-
nated as the inner and outer products and which we may obtain from
it by inserting the special sign of multiplication corresponding to these
products, thus giving respectively a scalar or a 2-vector. Hence
from any dyadic a scalar or a 2-vector may be obtained by converting
each dyad into an inner or outer product. This method was employed
in computing +p and Φ ΧΡ in § 43 and ὃ 44.

A dyadic is said to selfconjugate when for all the coefficients
a;; = aj, and anti-selfconjugate when for all the coefficients a, = — aj.
The latter can have no terms in the main diagonal, and therefore
has but six degrees of freedom, whereas the selfconjugate dyadic has
ten.°® Except for sign the anti-selfeonjugate dyadic not only deter-
mines, but conversely is determined by, a 2-vector of the form

dyky + ay3ki3 + duakiy + (o3Ko3 + A24Ko4 + d34K34,

where dy, . . . are the coefficients of kiko, . . . in the expanded form of
the dyadic. This 2-vector is one half the 2-vector obtained by insert-
ing the sign of outer multiplication in the dyads constituting the dya-
die.

66 Any dyadic may be written as the sum of two dyadics one of which is
selfconjugate, the other anti-selfconjugate.

498 PROCEEDINGS OF THE AMERICAN ACADEMY.

If Φ is any dyadic, then we have seen that ἃ is another 1-vector.
In general 8." is not equal to ®:a. If, however, ® is selfconjugate,
a:b = Φ. 8; and if Φ is anti-selfconjugate ach = —®-a. Hence it

may readily be shown that an anti-selfconjugate dyadic turns a vector:

into a perpendicular vector.
The dyadic which turns a vector into itself is called the idemfactor I.
Thus
a1 515. = a; (154)

for I is selfeonjugate, and when expanded in terms of chosen coordi-.

nate vectors 15,57 in the non-Euclidean geometry which we are dis-
cussing,

ii = kk, τ kok + k;k; = kik.

62. We could now proceed to develop the theory of dyadics in-
volving vectors of any dimensionalities and their products with each
other and with vectors of various dimensionalities. In general
if a, 2, y are vectors of any dimensionalities the dyad @y may be defined
in terms of our inner product by the equation a+ (Gy) = (a*3)y. This.
product is itself a dyad unless a, @ are of the same dimensionality.
Such a discussion, however, would carry us further than is necessary
for our present purpose, and we shall therefore consider chiefly one
case, which has acquired particular importance through the work of
Minkowski.

If r is any 1-vector, and A any 2-vector, then the product

Pra

is a linear vector function of r. It is evident therefore that this
multiplication by A is equivalent to a multiplication by some dyadic
Q. Let us find the relation between this dyadic Q and A.

If Φ is any dyadic (made up of 1-vectors), we may define the prod-
ucts @:A and A-® by first defining the products,
(ab)-A = a(b-A), A-(ab) = (A-a)b,

67 Asa matrix the idemfactor would be written

ἄν Oe sO {]) dee Or oO? Ὁ

D ore | instead of Oe Pyar 0 :
Τὴ | One
10 0 O—1 | (0) ἢ al

and the laws of multiplication of matrices would be modified. It is possible,
however, to keep the ordinary theory of matrices by the introduction of
imaginaries, as Minkowski does.

WILSON AND LEWIS.—.RELATIVITY. 499

and then applying the distributive law. The products A-® and ®-A
are therefore themselves dyadics of the same type as ®. If in place of
Φ we use the idemfactor I, then it is easily shown that

I-A (= — A-T)
is the anti-selfeonjugate dyadic which is determined by the 2-vector A.
Q — I-A = -Ξ Ak ke =~ Ajsk)ks == Aykik,
+ Apkeky — Asskoks — Ankok, (155
+ Arsksk; + Aosk3ke — Asksk, Ὁ

+ Auikski + Aoskike + ἄμ ΚιΚ

If we denote by Q, the 2-vector obtained by inserting the cross in the
dyads of Q, we have Q, = (I-A), = — 2A.

It is this relation between 2-vectors and linear vector functions or
dyadies which enables Minkowski to replace a 2-vector by an anti-
selfconjugate (or alternating) matrix and vice versa.

If 2 and Q’ are the two dyadics obtained from the two 2-vectors
A and A’, we may form the product 2-2’. (This is the product fF of
Minkowski). We can then write

(r-A)-A’ = (r-Q)-Q’ = r-(Q-0’). (156)

We employed (ὃ 57) the selfconjugate dyadic 2-Q = (I-A)+(I+A),
and another dyadic 3 (Q°Q + Q*-Q*), where Q* was defined as
Q* = [-A*, This dyadic corresponds to the matrix S of Min-
kowski,®® and may be regarded as the dyadic representing stress in
four dimensional space.

68 The expression (r*eA)+A’ may be transformed by (38).
(reA)eA’ = — r(A-A’) + Ae(rxA’).

As A-(rxA’) is a 1-vector, the complement of its complement is itself, by (26).
By rules (30) and (24)

[A+ (rxA’)]** = [Ax(rxA’)*]* = [(r-A’*)xA]* = (r-A’*)-A*,
Hence we obtain the important relation
(r-A)-A’ = —r(A-A’)+ (re A’*)-A*.
By introducing dyadics and canceling the vector r, we have

(IeA)+(I-A’) = — (A-A)I + (1.4 .(1.ΑὮ.
Ψ = 3[(1-A)+(I+A’) + (I-A) «(I-A*)],

If we set
we may write

(I-A)-(I-A’) = VY — 3(A-A’)I, (Ie A’*)-(IeA*) = Ψ + 3(A-A’)I.
The dyadic ¥ is precisely the matrix S of Minkowski.

500. PROCEEDINGS OF. THE AMERICAN ACADEMY.

The transformation r’ = r-A, where A is a uniplanar 2-vector, can
be regarded geometrically as an annihilation of that part of r which
is perpendicular to A, and a replacing of the component of rin A by a
perpendicular vector magnified in the ratio of A tol. The transforma-
tion r’ = (r-A)-A therefore annihilates components perpendicular to A,
and reverses components in A, multiplying them further by A-A.
Hence if A is a (v)-plane, the transformation in that plane is rotation
through a straight angle combined with a stretch as A?:1; whereas
if A is a (6)-plane, the transformation is one of stretching only, as
A-A is negative.

In case A is biplanar we may resolve it into its two completely
perpendicular parts, A = B+ C, where B is a (y)-vector and C
a (6)-vector. Then the equation

r’ = (r-A)-A = (r-B)-B + (r-C)-C

holds by virtue of the fact that r-B is perpendicular to C, and r-C
perpendicular to B. Hence the transformation r’ = (r-A)-A consists
of rotation through a straight angle and stretching in the ratio B?:1
for components along B, and of stretching alone in the ratio C?:1
for components along C. ;

The transformation r’ = (r*-A)-A + (r-A*)+A* is now readily seen
to be a stretching of components along B or C in the ratio (B? + C?):1
combined with a reversal of the direction of the components along B.
If this transformation were repeated, the result would be to stretch
all vectors in space in the ratio (B? + C?)?:1. But

(B? + 0°)? = (B? — 0%)? + 4B°C? = (AA)? + (A-A*?.

Hence the square of 3 (Q°Q + Q*-Q*) is 1[(A+A)? + (Δ Δ] 1,
a multiple of the idemfactor. This is the geometric interpretation
of a result obtained analytically by Minkowski.

63. From the definition (48) of the differentiating operator ©,

df = ἀτ- ΟΥ̓,

it follows that the expression ©>f, where f is a 1-vector, is a dyadic.
This definition may frequently be applied directly and with ease to
determining the dyadic ©f, and renders unnecessary the expansion
of ΟΣ in terms of its components. For if the value of df for four
independent displacements dr can be found, the dyadic is thereby
completely determined, and in some cases can immediately be written
down by inspection. This was the method pursued in § 44. The
dyadic itself, however, was not then desired except for the purpose

WILSON AND LEWIS.— RELATIVITY. 501

of deriving the scalar +f and the 2-vector ©»*f, which are functions
of it.

By means of the same defining equation the operator © may be
applied to 2-vector functions of position. The result ©F is then a
dyadie in which the first vectors of the dyads are l-vectors and the
second vectors 2-vectors. If written out in terms of the coordinate
unit vectors, such a dyadic would consist of twenty-four terms, each
of the type k;k;,, 7 #k. By inserting the dot or cross, the 1-vector
©>+F and the 3-vector ©xF are immediately found. In case the 2-
vector F is given as a product fxg of two 1-vectors, the dyadic OF
may be obtained directly by means of the rules of differentiation in
terms of the dyadics Of and Og. For

dr-OF = dF = d (fxg) = dfxg +. dfxdg = fxg — dgxf,
dr-OF = dr-O fxg — dr-Ogxf,
OF = Ofke — Oe.

It was such analysis which was used in ὃ 44. It illustrates strikingly
the great advantage of the symbol © over such symbols as Div, Rot,
Grad, and Div.

If Ψ is a dyadic function of position, the equation dr-OwW = dv
may be used to define ©W, which is a triadic, that is, a sum of formal
products of which each contains three vectors juxtaposed without
any sign of multiplication. By interposing a dot between the first
two of the three vectors in the triads, we find the l-vector ©:W. The
expression <>*W corresponds to what Minkowski calls lor Ψ, where Ψ
is for him a matrix.

We may compute the expression <>W in the case where

= 3[(I-A)-(I-A’) + (I-A™)-(I-A*)]. (157)
First we write
dr-<> [(I-A)-(I-A’)] = d[(I-A)-(I-A’)]
=([d(I-A)|-(I-A’) + (1-A)-d(I-A’).

The second term may be transformed so that the differential comes to
the front. For by the equation found in the previous footnote,

(I-A)+(I-dA’) = — A-dA’I+ (I-dA’*)-(I-A*).
Hence
d{(I-A)-(I-A’)] = — (dA-I)-(I-A’) — (dA™*-])-(I-A*) — dA’- Al.
Now

(dA-1)-(I-A’) = dA-(I-I-A’) = dA-(I-A’).

502 PROCEEDINGS OF THE AMERICAN ACADEMY.

Hence
dr+<>|(I-A)-(I-A’)]
= (dr-A)-(I-A’) — (dr-OA”™)-(1-A*) — dr-OA’- Al.
Hence finally
20OV = — OA-(I-A’) — OA*-(I-A*) — OA’-AI
— ©A”™.(1-A*) — OA-(1-A’) + OA- AT.

If the expression +W is desired, care must be exercised to insert the
dot between the first two vectors of each triad. Hence 89

2O°W = 2©-A)- A’ + 2(O- A) A*— OASA + OA-A,
OW = (©-A)-A’ + (2.4 .4" 4 HOA-A’ — OA’A). (158)

Some Projective Geometry, and Trigonometry.

64. We may discuss very briefly the relations between our non-
Euclidean measure of angle and the projective measure as determined
by logarithms of cross-ratios. Let
us consider Figure 30 first as a
Euclidean and second as a non-
Euclidean diagram. The two fixed
lines a, @ are drawn so that they
are perpendicular from the Eu-
clidean point of view. The initial
line from which angles are meas-
ured is taken as the bisector of
one of the right angles; this line
and its perpendicular through the
origin will be taken as axes of x
and y. The pseudo-circle appears
as a rectangular hyperbola with
the equation 2? — κ᾽ = 1. The angle between the initial line and any
radius in the pseudo-circle in Euclidean measure will be called 6, and
tan@ = y/x. Now in non-Euclidean measure, if this angle be called
¢, we have seen that tanh ¢ = y/x. Hence we have the relation

tan 6 = tanh ¢.

FIGureE 30.

69 The form <>A+(I+A’) may be written as a sum of triads of the type
aA-(ef) or a(A-e)f. Now by (35), as(A*e) = — (a*A)+e. Hence the in-
sertion of a dot in OA: (I- A’) gives — (+A) .(1.4) or — (+A): A’. In
the form ©A-A'l, the dot goes between © and I, since A+A’ is a scalar.
But as I is the idemfactor, we have simply <>A+A’ as the result.

WILSON AND LEWIS.— RELATIVITY. 503

The cross-ratio formed by the four lines, x, 7, a, 8 is

sin Z (8, r) sin Z (a, a)

~ gin Z (r, a) sin Z (3, x)’
where the angles are measured in Euclidean fashion. Hence
π
i 6
sin(T + ) Wer tanie! W/E ὙΠΟ ΟΝ 2

-- ἘΞ ἈΠ ον
(ξ ) 1—tan@ 1—tanh¢
sin aie θ

A=

Or
φ = logy.

Hence the non-Euclidean angle is measured by one-half the log-
arithm of the cross-ratio of four rays. Although the Euclidean
point of view has been adopted for simplicity, the final result, depend-
ing as it does only on the cross-ratio, is projective; it is therefore
independent of the particular assumptions that the rays a and ( are
perpendicular and that the initial line bisects the angle between them.

Consider next a ray γ΄ such that in the Euclidean sense

ad Te) a ( er

(In the non-Euclidean sense r and r’ are perpendicular). In forming
the cross-ratio it is evident that \’ = — ἃ. Hence for the non-Eucli-
dean angle ¢’ between x and 7’

o = zlogh’ = slog(— A) = Φ + flog (— 1).
Hence
d' = d = πὸ:

The angle ¢’ — φ, that is, the angle between two lines perpendicular in
the non-Euclidean sense is therefore = ἐπὶ. This result also is projec-
tive and independent of our special assumptions. It is only natural
that the angle between two lines in different classes should appear as a
complex number, owing to the fact that it is impossible to rotate
one line into the other.

In setting up a projective measure of angle by means of cross-ratios,
it is customary among mathematicians to define the angle as

1
d= ay log X,

504 - PROCEEDINGS OF THE AMERICAN ACADEMY.

where the logarithm of the cross-ratio is divided by 2ὲ instead of by 2
as above. The choice of the divisor 27 is due to the desire to have
the angle real when the fixed lines are conjugate imaginary lines and
to have the total angle about a point equal to 27 as in Euclidean
geometry; this is not, however, in any way suggested by projective
geometry. In our non-Euclidean geometry, where we have taken a
different set of postulates for rotation, the real divisor 2 is more natural.
We have seen that from the point of view of the postulates of trans-
lation or the parallel transformation our geometry and the ordinary
Euclidean geometry fall into one class, while such geometries as the
Lobatchewskian and the Riemannian belong to another class. With
respect to the postulates of rotation, however, the Euclidean and most
of the non-Euclidean geometries which have been studied lie in one
class, to which our geometry does not belong. The methods of pro-
jective geometry are applicable to all these classes. |

If the ray r is perpendicular to the rays γ΄ and r’’, the latter two being
in the same line but oppositely directed, it is evident that we must
choose arbitrarily the sign of the angle = πὶ between r and γ΄; but
we shall assume that if the sign of the angle rr’ has been determined
the sign of the angle rr’ will be the same. Thus the angle r’r’’ is
zero. ‘This means that a pair of intersecting lines determine but one
angle except for sign; thus any angle is identical, except for sign, with
its supplement.

The angle from a line to a second line and the angle from the first
line to the perpendicular to the second will be called complementary.
The complement of a real angle is a complex angle, and vice versa.

65. Hitherto we have chosen to avoid the use of the term distance,
and have used the word interval to represent a positive number
expressing the measure of length. If is a line drawn from the origin,
the interval of r has been defined as Va? — y? or Vy? — a? according
as x is greater than y or y greater than x. This was done to avoid
altogether the use of imaginaries. We might, however, haye defined

distance as
Ἵ = ga? egies

where a is, for example, measured along a (y)-line, y along a perpendic-
ular (6)-line. Then every (y)-line would have a real, and every (6)-
line an imaginary distance. In this case it would be convenient to
consider the distance along any vector AB as the negative of the
distance along BA. The distance along any singular line is zero.

a i ii

WILSON AND LEWIS.— RELATIVITY. 505

The preceding ideas can be used to give new definitions of the inner
and outer products of two vectors. Namely,

δ. Ὁ = distance of a times distance of Ὁ times cosh Z (a, b),
axb = distance of a times distance of b times sinh Z (a, b),

it being understood that the latter quantity is not a scalar but a pseudo-
scalar. If a and Ὁ are vectors of the same class the angles are real,
and the equations are essentially identical with those which have been
previously derived. Ifaand Ὁ are (6)-vectors the distances are purely
imaginary and the product a+b is negative if the vectors issue into the
same “‘quadrant.”’ If a and Ὁ are of different classes, and the angle
between them complex, we may use in place of these complex angles
their complementary real angles by the aid of the familiar formulas
cosh (¢ + 477i) = isinh@, sinh (φ + ἐπι) = φοβῇ φ.

MassacHusetts INSTITUTE OF TECHNOLOGY,
Boston, Mass., May, 1912.

TABLE OF NOTATIONS.

General Symbols.
1-vectors, lower case Clarendons, a, b, 6;...;
their magnitudes, corresponding Italic, a, b, ¢,...;
their components (algebraic magnitudes), ai, a2, ds, a4, ete.;
their (vector) space components, as, Ds, @s,....
Κι, ko, ks, unit coordinate space vectors;
Κι, unit coordinate time vector.
2-vectors, Clarendon capitals, A, B, C,...;
their magnitudes, corresponding Italic, A, B, C,...;
their components, 441), .453,..., Ags; ete.;
ky, k»;,..., Κρ, unit coordinate 2-vectors.
3-vectors, Tudor black capitals, A, JB, C,...;
their magnitudes, corresponding German, Y, 8, Bir
their components, Aoss,..., A123}
ko34,..., Ky23, unit coordinate 3-vectors (the last, “‘space’’).
unit pseudo-scalar, Kio34.
sign of the outer product, small cross, x.
sign of the inner product, heavy dot, 5.
sign of the complement, asterisk, a*, A%*,....
three-dimensional differentiating operator, del, V.
four-dimensional differentiating operator, quad, ©.
dyadics, Greek capitals, #,... (idemfactor, I).

506

PROCEEDINGS OF THE AMERICAN ACADEMY.

Special Symbols (non-vectorial).

a, 8, singular lines (§ 9).

y, spacial lines; ὃ, temporal lines (§ 9, 37).

«, electric charge (ὃ 48).

u, material density (ὃ 45); μὺ, density under no relative motion.
p, electric density (ὃ 54); »,, density under no relative motion.
φ, electric scalar potential (ὃ 48).

m, Mass; Mo, Mass under no relative motion.

t, time (also 24).

u, v, velocities.

2X, y, 2, Space coordinates (also 21, 2, 23).

T, idemfactor.

L, Lagrangian function (§ 56).

R, a perpendicular interval (§ 43).

Epa Symbols (vectorial).

a, (three-dimensional) ordinary vector potential (§ 48).
b, a special four-dimensional “‘radiation field”’ (ὃ 53).
6, extended curvature (ἢ 22, 35).

e, (three-dimensional) electric force (§ 49, 50).

f, (three-dimensional) mechanical force (§ 35).

g, as in dg, special vector of extended momentum (§ 47).
h, (three-dimensional) magnetic force (§ 49, 50).

1, extended light-vector, singular ray (ὃ 43).

m, extended (four-dimensional) vector potential (§ 48, 55).
n, unit normal to (6)-curve (ὃ 43).

Ῥ, geometric potential vector (§ 43).

q, vector of extended electric current density (ὃ 54).

r, four-dimensional radius vector.

S$, asinds, vector element of arc.

v, (three-dimensional) velocity (§ 43).

WwW, unit tangent to (s)-curve.

E, electric 2-vector (§ 49).

H, magnetic 2-vector (§ 49).

M, electromagnetic 2-vector (§ 48).

P, geometric 2-vector field (§ 43).

S, asind§, element of (two-dimensional) surface.

$, as in d§&, element of three-dimensional volume.

x, as in ds, element of four-dimensional volume.

SECTION
1. Introduction

The Non-Euclidean Geometry in Two Dimensions.
5. Translation or the parallel transformation

61.
64.

WILSON AND LEWIS. — RELATIVITY.

TABLE OF CONTENTS.

. Non-Euclidean rotation
. Vectors and vector algebra

Some differential relations

. Kinematics in a single straight line
. Mechanics of a material particle and of radiant energy

The Non-Euclidean Geometry in Three Dimensions.

. Geometry, outer and inner products.
2. Some algebraic rules

. The differentiating operator Vv

. Kinematics and dynamics in a plane

The Non-Euclidean Geometry in Four Dimensions.

. Geometry and vector algebra

The differentiating operator

. Geometric vector fields

Electromagnetics and Mechanics.

. The continuous and discontinuous in physics

The field of a point charge ‘
The field of continuous distributions of electricity |
Mechanics of a material system, and gravitation .

Appendix.

Dyadies
Some projective geometry, and trigonometry
Table of notations

507

PAGE

389

393
399
405
410
414
419

426
435
440
443

446
450
459

466
473
484
493

496
502
505

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Proceedings of the American Academy of Arts and Sciences.

Vou. XLVILI. No. 12.— Novempsnr, 1912.

ON THE EXISTENCE AND PROPERTIES OF THE ETHER.

By D. L. WEBSTER.

ON THE EXISTENCE AND PROPERTIES OF THE ETHER.
By Ὁ. L. WrssTER.
Presented by G. W. Pierce. Received September 12, 1912.

In the science of mechanics of ordinary matter we are accustomed
to regard velocity as essentially relative but acceleration as absolute;
and to say that, if a body is not acted upon in any way by other bodies,
its acceleration is zero, but that, if it is acted upon by any other body,
the accelerations of the two are opposite, and inversely proportional
to their masses. But how can we test this law? and how can we
measure the acceleration? If we measure the velocity relative to the
earth, or to the sun, or to any star, at any two times separated by a
very short interval, how can we be sure that the system of reference
has not been accelerated during the time that has elapsed? And if
it has, on what system is its acceleration measured?

This difficulty is made still more puzzling if we consider two mechan-
ical systems, such as the solar system, exactly similar in every way,
but one of which is removed to a practically infinite distance from all
other matter while the other is subject to the attraction of a tre-
mendous mass, so large and far removed that its gravitational field
is practically uniform, and at absolute zero temperature so that no
radiation would be received from it. These systems would be accel-
erated relatively to each other, but which of them would be acceler-
ated? No observer on either of them could tell by any mechanical
means.

An answer to these questions appears to be given by the electro-
magnetic equations, which assume the especially simple form with
which we are familiar when expressed in terms of the length, mass,
and time units of any one of a certain set of systems, any one of which
appears to be moving relative to any other with a constant velocity,
less than the velocity of light. -These systems may all be assumed
to be unaccelerated, and assuming the impossibility of any system’s
moving relative to one of these with a velocity greater than that of
light, we say that all other systems are accelerated.

δ12 PROCEEDINGS OF THE AMERICAN ACADEMY.

But acceleration means rate of change of velocity, and therefore
absolute acceleration means rate of change of absolute velocity, and,
if there is no such thing as absolute velocity, how can there be such
a thing as rate of change of it? We must, therefore, redefine the
absolute acceleration of any system to mean the acceleration relative
to another system moving in such a way that the simple electromag-
netic equations hold on it, and on which the velocity of the first system
is zero at the instant in question.

Even now, however, there is difficulty, because in place of our set
of systems with the constant relative velocities, for which the equations
hold, we might equally well imagine any other exactly similar set of
systems each of which has a certain given acceleration relative to the
corresponding one of the first set. And, disregarding the rather
arbitrary definition of absolute acceleration given above, it is evident
that, if space had no properties other than those of geometry and time,
any difference between the laws of nature as observed from two of
these relatively accelerated systems would be impossible. But
since the observed laws are simpler in one of the first set than in one
accelerated relative to it, the space must have other properties than
the above mentioned ones; and, because of these properties, it appears
highly probable that there must be some sort of a substance, or me-
dium, filling all space, having no acceleration relative to any of the
systems for which the simple electromagnetic equations hold, not
directly affecting our senses, but having properties which account
for all the laws of the phenomena that are directly observable, includ-
ing the exact mathematical similarity of the expressions for these
laws in terms of quantities measured on any system moving with
uniform velocity, less than that of light, through it. This is the
medium to which we give the name of “ether.”

The Ether.—To obtain any knowledge of the properties of this
medium, that enable it to show the phenomena of electricity, mag-
netism, and gravitation, and to account for the laws of motion of
matter, the principal of relativity, and the permanent existence of
positive and negative electrons in spite of the possibility of collisions
between them, it will be necessary to obtain the simplest possible
form of the set of laws which govern these phenomena.

Since many of the quantities that we deal with are vectors, we shall
find it convenient to use some simple vector analysis, with the follow-
ing notation, that of Gibbs, in which all vectors will be printed in
Clarendon type while scalars are in italic type. The scalar product,

(arb ΞΕ a,b, +azbz),

WEBSTER.— PROPERTIES OF THE ETHER. 513

of any two vectors, a and Ὁ, will be denoted by a+b; while the vector
product,

i (a,b. aT a:b,) te (ab, τὰ" 8,2) ata (arb, = a,b,),

will be denoted by axb, where i, j and k are the unit vectors in the
directions of x, y, and 2 respectively.
The symbol V will be used for the operator,

so that Va = the gradient of scalar a, a vector; V+a = the diver-
gence of vector a, a scalar; and Μ χὰ = the curl of vector a, another
vector.

The symbol “Pot” will be used for the operation of taking the
Newtonian potential of any function, so that

where r is the distance from dz to the point at which we wish to find
Pot a. We may apply the operator Pot to a vector as well as a scalar,
and, in either case, Poisson’s equation tells us that

(V? Pot) = — πὶ

or the application of the operator 7? to the Pot of any function gives
-- 4π times the original function.

It will be found convenient to indicate differentiation with respect
to ct, where ¢ is the velocity of light, by a dot over the letter that
stands for the function. Thus

0a

TIC

For brevity let us assume also, unless otherwise stated, that the func-
tions used in the following work all vanish at infinity and are finite
and continuous throughout space.

Laws of the Ether.—To write out the laws of the ether in the form
that accounts for all the above mentioned phenomena, we must dis-
tinguish between the effects due to positive and negative charges, and,
therefore, it will be convenient to call the density of positive electricity

+
at any point p, (a quantity which is always positive), and that of

514 PROCEEDINGS OF THE AMERICAN ACADEMY.

negative electricity 4 (always negative). The electric forces due to

ἝἜ -
all the positive and all the negative electricity we may call E and E,
and the magnetic forces H and 8, while the velocities of the charges

may be represented in terms of β and B, their ratios εἰ the velocity of

light.
These quantities may be supposed to satisfy the following set of

equations:

(1) V-E =o, 2) V-E =p,

(3) VxH = B+ of, (4) VxH = E+ ρβ,
(5) V-H=0, (6) V-H= 0,
Ge = ae 8). VE =a

which determine the positive forces in terms of the positions and
velocities of the positive charges, and the negative forces in terms
of those of the negative charges. But in addition to these equations
we have the following pair,

(9) E+BH+ K—G(E+BxH) =0
(10) E+6<H+ K=0,

which must hold at every point of every electron, positive or negative,

+ = . .
and in which K and K are forces per unit charge due to the internal
stresses of the electron, while Gis a very small number whose presence
in equation (9) accounts for the phenomena of gravitation.!

i 2

The laws governing the vectors K and K may be deduced from the
fact that the deformation of the electron when its velocity is very
ereat is the same as that of a perfectly flexible and compressible,
ἜΛΆΨῸ conducting shell, with no internal stresses, subject to a
constant external hydrostatic pressure or internal hydrostatic ten-

+ --
910η.2 Therefore, we may assume that K and K are forces such as
would result from such a tension, and that they are transmitted by

1 For further details on this point see D. L. Webster, ‘“‘On an Electromag-
πον ποτε of Gravitation,’ These Proceedings, 47, 14 (1912). The rea-
soning and conclusions are changed but little if we introduce a similar term in
equation (10), and thereby gain in symmetry in our theory.

2 Poincaré, Comptes Rendus, 140, 1504-8

WEBSTER.— PROPERTIES OF THE ETHER. 515

the material of the electron. This tension is, of course, constant
throughout its volume only if all the charge of the electron is on its
surface, otherwise, it increases as we go nearer the centre of the
electron.

Abraham has raised the objection to this theory, that it involves an
instability of the shape of the electron,’ that would soon destroy
all such bodies. But this objection is based on the interpretation of
the above vectors as mechanical forces per unit charge, tending to
accelerate the parts of the electrons involved, and on the idea that a
part of the charge may in some way be displaced from the position in
which all these forces exactly balance. Such displacements would
result in a rapid disruption of the electron, a process in which equa-
tions (9) or (10) could not hold indefinitely. But if we take them as
expressions of a fundamental law, which would be violated by such
a process, we have a reason why this process cannot occur, nor even
start to occur, and the problem of stability of shape of the election is
solved.

To determine the motion of a whole electron from these equations
(9) and (10) we are aided by the fact that the resultant of the internal

+ = +
forces is zero, but we have to remember that the vectors E, E, H, and

H, that occur in these equations, include not only the contributions
from external sources, but internal as well. Therefore, the equations
demand motion with constant velocity when the external forces are
zero, and the resultant of the actions of different parts of the electron
on each other must be zero also. But if the external forces are not
zero, each part of the electron must be accelerated in such a manner
that the resultant of all the forces, radiated or otherwise, from all
other parts, will just balance the resultant of the external forces.
Thus we have a reason for the apparent inertia of every electron, and
of bedies composed of electrons, so that the laws of motion of matter
may be proved to be consequences of the laws of electromagnetic
forces.

SIMPLIFICATION OF THE Laws. HAMILTON’S PRINCIPLE.

We may, however, simplify these laws still further, by remembering
the fact that there is one dynamical principle that applies to all
motions of matter and also to all the phenomena of slow changes
of positions of electric charges and of the positions and magnitudes

3 See Lorentz, Theory of Electrons; Chap. V, 1905.

516 PROCEEDINGS OF THE AMERICAN ACADEMY.

of currents, and expresses the laws of the phenomena perfectly with
no other assumptions than equations (1) —(4). Therefore, it seems
reasonable to suppose that this same one principle may replace equa-
tions (5)—(10), and reduce the number of necessary laws from 10 to 5.

This fundamental principle is Hamilton’s Principle, which says that
for any dynamical system whose kinetic and potential energies are
T and W respectively,

be
ὁ [( — Wat = 0,
uy

where ἦι and f) are any two times, and where the variation from the
actual motion is any variation, consistent with the constraints of the
system, that makes the configurations of the system at the times th;
and (ὁ the same as it is in the actual motion. In the case of the ether,

+ = + -
writing Εἰ for E + E and H for H + G, this principle takes the form,

(11) Pf fiar— ar) — αὐ. ὅπ: ovjan=o,
im CS

where U is the sum of the hydrostatic tensions in the positive and
negative electrons, if any, in which the element dz lies, and which

ἝἜ -
produce the forces K and K, and where two configurations are to be

a Ε
considered the same if, and only if, the vectors E and E are the same
in one as in the other.*

To prove that equations (5)—(6) result from equations (1)—(4) and ©
equation (11) we may write (11) in the form,

te a) Ε
(12) | | x | { (H-H—GH-5H)—(E-sE—GE-sE+5U)} drdt =0,
oe δ
+
and then suppose that 6H, 6E, 6B, and 6U are all zero throughout the
+

interval. Now whatever vector H may be we may split it into a sum

+ +
of two parts, Hs and H;, such that

4 For another form of Hamilton’s Principle, involving different assumptions
see Larmor, ‘‘Aether and Matter,’’ Chapter I.

WEBSTER.— PROPERTIES OF THE ETHER. ont

[ [fra
e or

i} | σε τ ἤν.
J.

and then write
as

But by Green’s Theorem, whatever these parts are, if both vanish at
infinity,

(13) | J | Het =i

In this case Ἐ is completely determined by equation (3), so that, if
+

OE, 3E, and 6U are zero, 6Hsg is zero, therefore

(14) qh Ἵ; if ΣΡ, = 2 / [ ip (Hy- 6H, [ΕἸ ΘΠ) dr
Ὁ ie)
> ὃ Uh i
2] ff αι σῆμα.
CO

+ Ἔ --
But this must be zero whatever 6H, is, therefore Hz is zero, as is H;,
also. Therefore

(5) V-H = 0, (6) V-H=0.
To derive equations (7) and (8) we may introduce vectors I,

and P, defined by the equations,

μι}
μου:

ct ct
(15) I =f> Bd( ct), I= { ppd(c),
0 0
(16) P= πε ἢ, P= | pot(E+D).
4π 4π
From these equations we may infer
(17) Vie —« ι 1),
᾿Ξ ΣΊΡΕ

From equation (3) we know that

(18) V-(E-+ pB) = 0,

518 PROCEEDINGS OF THE AMERICAN ACADEMY.

so that ἐς V-Pot (B+ pb) = VP = 0;
and since, whatever P is,
+ Ξε +
VxVxP = — V?P+ V(V -P),
τ ὦ + + + +
(19) VxVxP = (E+ ρβ) = ΔΗ,
which, combined with (5), gives
(20) xP = H.
(21) Similarly VxP = H.

en (12) now takes the form

(22) f i “ἢ fu { (VxP- 7x6P — GyxP- v-sP)

— 46(E? — GE? Ἐπ = 0!
(23) But
t

2 te
| VxP- Vx6Pdt = ἐν. VxoP. ἘΞ J VxP: V7 xdPdt,

b Ὁ ty
i?

= “VP. Vx6P | ἦν. { Px (7x6P)}+ P- 7x xP] dt.

ree

24)

foo Vx6P dt = = Tf J Jo vari |
-- i i} i: [5. vanaf! aah J J Px(7xsP)- dW&dt,

where S is any wae surface that may recede indefinitely in all
directions from any interior point, and of which dS is an element
considered as a vector in the direction of the exterior normal. If
we now let 6I. = 0, then 6P = 0 at ἡ and fy, and the first term on
the right side of equation (24) drops out, and so does the surface
integral when there is only a finite amount of charge in the universe.

+
Treating P in the same way, we obtain, if

+ =
éI = oI = 0,

WEBSTER.— PROPERTIES OF THE ETHER. ~ 519
(25)
ἐς #
fi (δ. Vx7xdP — ΟΡ. 7x 7x6P) + (E-5E — GE-dE + 5U) }drdt = 0,

h
or, since ov = 0 and

(26) VxVx6oP = — VP = +6E,

when no motions of charges have been varied,

(27) Lf fie 4 E)-6E — G(P + E)-sE} drdt = 0.
ty ora)

ΞΕ
Splitting E into the parts Es and Ez, treating E likewise, and applying
Green’s Theorem as in (14),

ta ee
he {(B +.Es)-dBs — G(P — Es)-6Estdrkt = 0,
ty CO

+s
because 6Ey, and 6E; are zero when no charge motions are varied.

(29) Therefore P a Ey ΞΞ ἢ

(80) and Pleas
(81) or Ey ——— i Pot(E -- 58..
(32) and Es ΞΡ ra Pot(E ΞΕ 8).

Applying \7x to (29) and (30) we have
(7) VxE ——— H, (8) VxE = ay

To derive equations (9) and (10) from equation (11) or (12) let us
suppose that, for a short time during the interval ¢; and ty, an infini-
tesimal positive charge de, occupying a small tube of length dr’ and

+
cross section εἰσ ὃ and lying in the direction of g is displaced in some
other direction through a distance δὲ. To satisfy equation (1) with

are
this variation we may superpose on the actual value of E a straight

5 Any eben of surface may pe ΕΠ ΩΣ as a vector r along its normal,
and when its direction is chosen, the positive direction around its boundary is
that of a right-handed screw rotation.

520 PROCEEDINGS OF THE AMERICAN ACADEMY.

+
tube of the vector 6E connecting the new position of de to the old,

are
the flux of 6E being against the direction of 6r and of magnitude de.
And to satisfy equations (3) and (5) we must also assume a certain

+
variation 6H which is uniquely defined by these equations and the
variations assumed above. We may now assume no variations of the
negative forces, and for the positive forces only the necessary varia-

fe
tion of U and the variations specified above.
With these assumptions (12) becomes

t,
(33) {ff fra = GH) 3H (Εἰ GE) -s8 — 00) ade
t; οΌ
(384) To calculate

JJ fe — GE)-6Edr,

+
we need to integrate only over the tube of 6E defined above, so that,
if de is of infinitesimal size, we may take for the result,

(35) (E — GE) -srde.

To calculate
(36) af it af (H = @H)-sHdr,
οΌ

+ Ἔ
we may consider 6H as the H produced by a current of strength

++
pB+-do flowing around the edge of the parallelogram one side of which
contains the old position of de and the other side the new position,

+
while the remaining sides are the tubes of the vector 6E made neces-
sary by the motion of the parallelogram. We may now evaluate the
integral, splitting the space up into elements of each of which two

+
sides, dS, are surfaces whose normals are in the direction of 6H while
the remaining dimension, ds, is in the same direction. The integral
may now be written

(37) | { (H — GH) -6HdS-ds,
οΟ

WEBSTER.— PROPERTIES OF THE ETHER. 521

(38) or Ἱ | | (H — GH) -dSsH-ds.
e rs e
But since Vo = τ ΠΕ ΕΞ"

the surface integral
(39) | | (H — GH)-ds

is the same over any cap of the parallelogram circuit as over any
other; and since

(40) VxdH = 8E + 4(8),
the line integral
(41) | δ. (8

a
is the same around any line of the vector 6H as on any other. There-
fore the integral (38) is

(42) [fsa = cH) .is |[_f o#t-as |.

Any cap Any line

But by Stokes’ Theorem, the line integral is
++
(43) p Bede,
while the surface integral over the plane cap is,

(44) dr'x(H. — GH)-6r,

so that (36) becomes
ν᾽ ++ +
(45) p B-dedr’x(H — GH)-ér

+ + +s
= pdr’ «σβχ(Η — GH)-6r

(46) ax(H — GH)-érde.

+ +
Substituting — K-érde for 6U, (33) now becomes

te
(47) | [βκ(Ε _ GH) -érde + (E — GE) -érde + K-drde} αἱ = 0}

4

ay PROCEEDINGS OF THE AMERICAN ACADEMY

from which we may infer that

(9) BE pak σα pa) ὃ

Obviously, we may derive equation (10) by an exactly similar process
in which the terms involving G do not enter. And if we wish to use
an infinitesimal charge of some other shape, we may consider it as
divided up into a number of cylinders, not necessarily right cylinders,
such as we used above.®

Meanings of the Laws.— To find out what we can about the
properties of the ether, we may now examine carefully the meanings
of these five laws:

τ Ξ Ο τε
8 = Eon (4) Vx = E+ pp,

(11) Af Lf fae — ὧν. ee οὐ 210 no

The first two of these laws contain no reference whatever to time,
and deal with quantities whose existence is in no way dependent
on motion or change with time. Therefore, we may infer that they
probably express relations between the geometrical configurations of
different parts of the ether, and show the dependence of these geometri-
cal configurations upon the presence in the ether of the peculiar mov-
able spots called charges, whose indestructibility and ability to be
located definitely at different times (specified in equations (3) and
(4), as well as the internal forces, suggest that they are due to the
presence of some substances not present in the rest of the ether but
freely movable through it. Since these substances can be located at

is Ἂς
any time if the vectors E and Εἰ are known at every point, the question
arises whether any more information than the value of these vectors
needs to be given to determine completely the configuration of the
ether. A suggestion of the answer to this question is given by the
fact that in applying Hamilton’s Principle to problems of ordinary
dynamics, the variations must be such as to give the actual configura-

6 To be certain that no equations not derivable from equations (1)-(10)
can be derived from (11) and (1)-(4), we need only to consider the facts that
any possible variation in equation (11) can be made up of variations of the
types treated above, and that the mutual energy of two independent varia-
tions of the first order is an infinitesimal of the second order.

WEBSTER.— PROPERTIES OF THE ETHER. 523

tions exactly at the times ¢; and f2, whereas, in equation (11) they must

+ Σ
be such as to give the actual vectors E and E. Hence, from analogy,
we may say that these vectors are probably sufficient to specify the
configuration of the ether completely.

And if this last statement is true, their time derivatives must be

+ =
sufficient to specify completely, not only the quantities B and B, but

all the motions of the ether; and it seems probable that these motions
- — + + --
at any point are specified by the values of E, Εἰ, p B, and p B at that

ΞῈ --
point, and not by the values of the vectors H and H, which depend on
the values of the other vectors at distant points. This hypothesis

is further strengthened by the fact that the whole theory of the ether
co

might be developed without any use of these vectors, replacing H
wherever it occurs by

εἰς VxPot (E pB), and H by an VxPot (E+ 8),
4π 4π

and therefore without any use of equations (3) and (4), except as
they express the indestructibility of the charges.

Therefore we may consider equations (3) and (4) as merely equations
of continuity and partial definitions of two convenient mathematical
functions fully defined by equations (3) and (4) and (11) all together,
and whose values at any point depend on the motions of the ether at
all points, but not in any way on the motions or configurations at the
point in question only. And thus, although they contain time deriva-
tives and quantities dependent entirely on motion and existing only
when there is motion, they tell us nothing about what is going to
happen at some future time from what is happening now, and there-
fore cannot be considered as laws of motion, but only as mathematical
definitions of convenient functions.

Equation (11), however, in form and substance, is essentially an
equation of motion, from which no information about the geometrical
configurations of the ether can be derived at any time, unless the
configuration and motion at some other time, or the configurations at
two other times, are specified; but without which no information
about the configuration or motion at any time can be derived even
if they are given at any number of other times.

Properties of the Ether. — The first question that arises about
the properties of the ether is, Is its structure continuous or granular?

524 PROCEEDINGS OF THE AMERICAN ACADEMY.

To answer this question definitely seems impossible, but at any rate,
we can say that if it is granular and if these equations are to hold, .the
structure must be exceedingly minute compared to the dimensions
of the electrons. A further suggestion is given by the fact that in the
geometrical equations, (1) and (2), the positive and negative quanti-
ties appear very similar, but seem to be more or less independent
of each other; while in the equation of motion (11), and in the phe-
nomena of vacuum tube discharges, etc., differences between the
actions of the positive and negative quantities appear, that seem to
show that not only are the electrons of the different signs made up
differently, but that the forces are transmitted by more or less inde-
pendent, and slightly different, structures in the medium. As this
condition of affairs seems to be incompatible with the idea of a con-
tinuous medium we are thereby led to the conception of a medium in
which there are probably two similar, but slightly different, interlac-
ing, granular structures, whose grains and distances between them are
inconceivably small, even compared to the electrons.

The question of solid or fluid character of the ether appears easier
to answer; for if it were fluid, that is, if no amount of shear at any
point would change the properties at that point in such a way as to
affect the subsequent motions around it, a transverse wave would be
impossible. And if it were quasi-elastic, with effects analogous to
viscosity, that would enable it to transmit wireless telegraph waves
as well as the shortest known light waves, electrostatic forces around
stationary charges should be due to some effect entirely different
from that which produces those of the wireless wave, so that slow
continued flow of ether might occur without hindrance. But the
changes of electric force near a moving electron may be much more
rapid than those of the wireless wave, and yet there appears to be no
viscous retardation of its motion. Furthermore, the aberration of
light and experiments such as that of H. A. Wilson” on the polariza-
tion of a dielectric cylinder rotating in a magnetic field seem to show
that no flow of ether occurs in moving matter. These considerations
and many others compel us to reject the fluid theory, and to say that
the structures of the ether are solid. But by “solid”? we must not
mean possessed of ordinary solid elasticity, but merely that every
particle is permanently connected to the particles near it by con-
nections that cannot be deformed indefinitely, or even by a finite
amount without affecting the subsequent motion.

74H. A. Wilson. “Electric Effect of Rotating a Dielectric in a Magnetic
Field,” Roy. Soc. Proc., 73, pp. 490-492. June 22, 1904.

WEBSTER.— PROPERTIES OF THE ETHER. 525

As we must not assume ordinary elasticity, so also we must not
assume ordinary inertia of the fundamental particles. For, after all,
Newton's laws of motion, that we observe for ordinary matter, appear
to be only approximations to the laws that result from equation (11),
the more general law of motion. And furthermore, they are by no
means the only ones consistent with the relative nature of time and
space, nor is there any other a priort philosophical reason for assuming
that they are true, while there is good philosophical reason for assum-
ing that Hamilton’s Principle, the mathematical expression of the
perfect efficiency of the fundamental machinery of nature, is at least
plausible. Therefore, whatever motions of the parts of the ether it
may involve, and whether or not it is easy for us, with our Newtonian
mechanical training, to form a mental picture of the dynamics of
these motions, the fundamental law of the dynamics of the ether, or
of any mental picture of it, must be Hamilton’s Principle.

A Model of the Ether. — ΤῸ get a mental picture of the actions
of the ether, we must now make some arbitrary assumptions as to the
nature of the two interlacing structures and the strains in them that

4 _
are represented by the vectors Eand E. For simplicity we may think
of them as nets with cubical meshes with each knot of either net in
the centre of a mesh of the other, wherever the electric vectors are

+
zero. The vector E may be a very minute displacement of one of

these nets from this position, and the vector E the negative of a simi-
lar displacement of the other. If we now suppose the strings of these
nets to be hollow and rigid, and the knots to be hollow boxes, so con-
structed that the displacements of the nets will be those of an incom-
pressible substance, we may suppose an electric charge to be a region
in which the pipes and boxes of one of the nets are filled with a liquid
of high surface tension, that will expand the boxes into which it
flows, and cause a divergence of the displacement of the net. An
electron will then be a region of this sort, in the shape of a hollow sphere
when at rest, of which every dimension, including the thickness, is
very large compared with the meshes of the net. The pipes and boxes
of that net that lie inside this region may be filled with a fluid whose
only properties are adhesion with everything it touches and a constant
hydrostatic tension, independent of its volume. For the connections
between the nets we may assume anything we please.

Equations (1) and (2) are satisfied by this model, which also gives
an interesting interpretation for (8) and (4). For in free ether the

526 PROCEEDINGS OF THE AMERICAN ACADEMY.

Fs
vector H becomes a hydrokinetic flow-function for the motion of the
positive net; and where there is any positive charge it is a flow-func-
tion for the motion of the net plus that of the charge. Similarly the

vector H is the negative of a flow-function of the motion of the nega-
tive net and charges. And in each case, equations (5) and (6) tell
us that it is the solenoidal flow-function that is required.

The equation of motion is, as we expected, one which we have some
difficulty in applying. But if we split it up into equations (5) to
(10), and then combine them properly, we may use in electrical
problems onhy the vectors Εἰ and H, representing the relative displace-
ment of the positive net from the negative, and the flow-function of
the relative motion. And in gravitational problems the vectors E and H
disappear entirely.

Collisions of Electrons.— An interesting application of this model
is to the problem of collisions of electrons, of the same or opposite signs,
as in the case of a cathode particle striking an electron in the metal
it hits. If they are of the same kind they will evidently become
flattened as they come together. But as soon as they are within
about their own length of each other, the side of either of them nearest
the other will be effected not only by the displacement due to the
presence of the other, but also by the displacements radiated from
the other on account of its acceleration. To make the vectors bal-
ance, as required by equations (9) and (10), its acceleration must
therefore be so much greater than that required by the inverse square
law that they can never collide.

In the case of two electrons of different kinds, both are lengthened,
and they come together faster than the inverse square law would
demand. But since they may go right.through each other perfectly
freely, there need not be any of the destructive effects that one might
expect from other theories.

Retarded Potentials.°— In calculating the values of the retarded
potentials due to moving electrons it is found necessary to treat each
electron as if its charge were not the same as when at rest, but changed
in the ratio (1 —8,) 1, where β, is the component of β in the direction
towards the point at which we wish to know the potential. This has
been interpreted by some writers ® as indicating that all electromag-
netic actions are due to some sort of pulsation of the electrons, and are

8 For information about retarded potentials, see Lorentz, ‘‘Theory of
Electrons,’’ Chap. 1.
9 L. de la Rive, Phil. Mag., 18, p. 279.

WEBSTER.— PROPERTIES OF THE ETHER. 527

stronger if the pulsations are more rapid, so that the Doppler effect
is introduced if the charge is moving. But with the model it is
obvious that any such interpretation is unnecessary; for the impor-
tant quantity is not the actual charge of the electron, but the volumie
of the ether in which there was a spreading of the net at such a time
as to affect the point in question at the time in question.

SUMMARY.

Because of the apparently absolute nature of acceleration, as well
as for other reasons, we find it necessary to assume the existence of
the ether, and therefore desirable to learn as much as possible of its
properties. To do this, we first reduce the laws of all its phenomena,
including gravitation and the relativity-principle, to five equations,
and then examine their meanings; and find that two of them are
probably laws of the geometrical configurations of the different parts
of the ether; two more, equations partially defining two convenient
vectors, and stating the indestructibility of electricity; while the
fifth, Hamilton’s Principle, is a law of motion, expressing the per-
fectly efficient cooperation of the different parts of the fundamental
mechanism of the universe.

From these laws we may draw certain conclusions about the
structure and properties of the ether, which are not, however, enough
to enable us to determine exactly what it is. But by a few simple
assumptions, we obtain an imaginable model of its actions. And
since the model is based directly on the electromagnetic laws, it may
be applied, without fear of error, to any electromagnetic problem,
to enable us to obtain a qualitative result without mathematical
analysis.

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Proceedings of the American Academy of Arts and Sciences.

Vor. XLVIII. No. 18. — Novemser, 1912.

CONTRIBUTIONS FROM THE PHANEROGAMIC LABORATORIES
OF HARVARD UNIVERSITY.—Nos. 55-58.

THE HISTORY, COMPARATIVE ANATOMY AND
EVOLUTION OF THE ARAUCARIOXYLON
TYPE.

By Epwarp C. JEFFREY.

CONTRIBUTIONS FROM THE PHANEROGAMIC LABORATORIES
OF HARVARD UNIVERSITY. NO. 55.

THE HISTORY, COMPARATIVE ANATOMY AND EVOLU-
TION OF THE ARAUCARIOXYLON TYPE.

By Epwarp Οὐ. JEFFREY.
Received, September 28, 1912.
Parr I.

Fosstz woods of the Araucarioxylon type are extremely abundant
in the Mesozoic deposits. The only living conifers with wood of
this type are confined to the Eastern tropical region, to Australasia
and to South America and are all included under the two genera
Agathis and Araucaria. As a consequence of their habit, which
differs from that of all living Conifers, except certain of the Podo-
carpineae, and of the organization of their woody tissues, the Arau-
carian Conifers have been most commonly referred to affinities with
the Cordaitales, an important gymnospermous group of the Paleozoic.
As will be shown in connection with the present investigations, the
importance of these features of resemblance has apparently been much
exaggerated. The association with the Cordaitales carries with it
the implication, that the Araucariineae are either the ancestors of
the other existing coniferous tribes, as is quite commonly held, or else
that they constitute a separate line of descent, distinct from the
ancestral stock of the remaining Conifers, as has been maintained in
recent years by Seward and Penhallow. It is obviously a matter of
considerable importance to clear up the affinities of the Araucarian
stock, not only from the standpoint of its particular origin; but on
account of the light thus to be thrown on the vexed subject of evolu-
tionary processes as a whole by reason of the abundant display of the
group during so long a period of geological time. The present writer
has devoted nearly ten years to the procuring of material of Araucarian
Conifers living and extinct and to the developmental, experimental
and comparative anatomical investigation of their various organs and
tissues.

§32 PROCEEDINGS OF THE AMERICAN ACADEMY.

It cannot be too strongly emphasized in connection with the present
work, that general principles in biology are either of universal validity
or of little scientific value, and that they cannot in certain cases be
admitted and in others denied. There can be little doubt moreover
that not a little of the existing reaction against the hypothesis of
evolution, is the result of a failure on the part of biologists to apply
evolutionary principles clearly, consistently and logically to the
elucidation of their investigations, even if only from the standpoint of
a working hypothesis. It seems clear that either there are generally
valid biological principles, as there are commonly accepted principles
in chemistry, physics and the other cognate sciences, or that biology
has either not yet reached the scientific stage of development or has
ceased to exist on the scientific footing. There appears to be no reason
to adopt either of the latter alternatives. Darwin in the prolegomena
to his Origin of Species, emphasized the importance of the data
supplied by development, history, comparative anatomy and geo-
graphical distribution in connection with the study of evolutionary
processes in living beings. Since Darwin’s time experimental methods
have come largely into the foreground and there can be little doubt
that evidence derived from this source, especially when controlled
by an adequate knowledge of the geological history of beings now
living, is of paramount importance. It is proposed in the series of
articles of which this is the first, to discuss the origin, affinities and
evolution of the Araucarian Conifers, so far as appears profitable,
along all the important lines of investigation, indicated above.

It will be convenient here to define the Araucarioxylon type of wood.
In the mature secondary wood of the trunk in the living Araucaria
and Agathis, we find certain peculiarities, which are taken together
unique among living conifers. The tracheids in these two genera
are characterized by the presence of pits, which are closely approxi-
mated and flattened, or where they occur in two or more rows, alter-
nating in their arrangement and polygonal in their form. The wood
of the Araucarian type in respect to its pitting resembles in a marked
degree that of the Cordaitales. The remaining tribes of existing Coni-
fers possess a type of tracheary pitting in which the pores are rarely
or never closely contiguous and when in several rows are opposite and
not alternating. The pits in this type too are often separated by
cellulose bars running transversely across the lignified walls of the
tracheids and imbedded in their substance. These bars of Sanio are
absent in the Araucarian conifers.! They should not be confused

1 Gerry, Eloise, The Distribution of the Bars of Sanio in the Coniferales,
Ann. Botany, 24, p. 231.

JEFFREY.— ARAUCARIOXYLON TYPE. 533

with the trabeculae of Sanio, lignified processes, crossing the lumen
of the tracheids, common to the Gnetales, Coniferales and a few
Angiosperms. Another feature of the Araucarioxylon type is the
usual absence of wood parenchyma and the smooth walled character
of the ray cells. The last two features are less typical than the ones
mentioned above since they are shared to a considerable extent by
the woods of the remaining tribes of Coniferales. The last character
has had recently assigned to it an apparently exaggerated importance.?
Gothan has recently referred woods, which are strikingly Araucarian
in the aggregate of their characteristics, to abietineous affinities on
account of their strongly pitted rays, apparently losing sight of the
fact that pitted rays occur commonly or sporadically in all the tribes
of Conifers. The present article is to be devoted to the historical,
comparative anatomical and experimental study of the rays and wood
parenchyma in the Araucarian Conifers.

Beginning with the historical aspect, Figure a, Plate 1, shows the
character of the pitting in the tracheids in an Araucarian wood of
the Upper Jurassic, to be described in detail on another occasion.
The pits are numerous and in several rows, with the marked alterna
tion, characteristic of the Araucarioxylon type. They are not how-
ever as closely approximated as is the case with the pits in the tracheids
of the adult wood of the living genera Araucaria and Agathis. Figure
b, Plate 1, illustrates the ray structure in the same wood. It is clear
that the cells of the ray, in contact with one another are very strongly
pitted, exactly for example as is commonly the case in the rays of the
Abietineae. On account of the pitting of the rays in woods of this
type from the Upper Jurassic of King Carl’s Land 3 and of the island
of Spitzbergen* Gothan has recently referred them to abietineous
affinities. It is to be pointed out in this connection that Seward has
considered woods of a similar type from the Upper Lias of Yorkshire
in England ® to belong to the Araucarian conifers. Moreover Lignier
more recently has described woods of a similar or nearly similar
horizon, as likewise of Araucarian affinities. About the same time

2 Gothan, Zur Anatomie lebender τι. fossiler Gymnospermen-Hoelzer;
Abh. d. Koenig. Preuss. geolog. Landesanstalt; Neue Folge, Heft 44, Berlin
(1903).

3 Gothan, Fossilen Hoelzer von Koenig Karl’s Land, Kung Svensk. Veten-
skap. Handlingar, Bd. 42, No. 10.

4 Gothan, Fossilen Holzreste von Spitzbergen, Kung. Svensk. Handlingar,
Bd. 45, No. 8.

5 Cat. of Mesozoic Plant, Brit. Museum, Jurassic Flora, Pt. 2, pp. 56, 57,
pls. 6, 7, London (1904).

6 QO. Lignier, Végétaux Fossiles de Normandie, IV. Bois Divers (Ire.
Série), Caen (1907).

534 PROCEEDINGS OF THE AMERICAN ACADEMY.

the present writer described woods of a similar type with a similar
expression of affinities from a horizon, variously estimated from Middle
to Lower Cretaceous, displayed at Kreischerville, Staten Island, N. Y.7
It will be noted that the weight of opinion is against Gothan, in the
matter of the reference of woods Araucarian in other respects, which
have the strongly pitted rays of the Abietineae, to affinities with that
tribe of Conifers, since Professor Seward, Professor Lignier and the
writer agree in retaining them with the Araucariineae. Since a
correct scientific verdict, however, does not depend on majorities, it
will be well to investigate the matter from other standpoints.

A fundamental doctrine of Biology, owing its origin primarily to
the deductive methods of the philosopher rather than to the more
severe inductive procedure of the sciences, but since strongly confirmed
by purely inductive data, is the doctrine of recapitulation. While
it is undoubtedly the case that the seedlings and sporelings of the —
higher plants vouch in the strongest way for the validity of the recapi-
tulation hypothesis, we have on the vegetable side corollaries to that
doctrine, not illustrated as a rule by animals. There are organs of
the plant for example, even more strongly retentive of ancestral
characters than the seedling stem. Perhaps the most conservative
organ is the root, which varies so little in its fundamental organization
throughout the vascular plants, that one formula will represent the
organization of all roots. In the case of the Gymnosperms and other
typically coniferous groups, the axis of the cone has likewise been
found to be strongly retentive of features which have disappeared
entirely in the vegetative stem. Figure c, Plate 1, shows the inner
region of the woody cylinder of the cone of Agathis australis, im trans-
verse section. It is clear that the cells of the wood rays are in contrast
to the typical condition for living Araucarian Conifers, very strongly
thickened and even in this unfavorable plane of section, obviously
pitted. We have in other words a condition present like that found
in certain Jurassic and Lower Cretaceous woods which have been
referred by the majority of paleobotamists, who have specially inves-
tigated them, to Araucarian affinities. Gothan however as pointed
out above, places them on account of their thickened and strongly
pitted ray-cells among the Abietineae. Figure d, Plate 1, shows a
vertical section of one of the rays of the cone of Agathis australis,
from which the contents have been removed in order that the sculpture

7 Araucariopitys, a new genus of Araucarians, Bot. Gaz., 44, 1-15, pls.
27-30, (1907).

JEFFREY.— ARAUCARIOXYLON TYPE. 535

of the cell walls might stand out more clearly. It is obvious from the
pitting of the tracheids seen on the left of the figure, that we have to
do with araucarian wood, since the pits are alternating. The ray
cells very strongly pitted on all their walls, towards the right of the
figure, towards the left thin out and assume the ordinary Araucarian
type. Figure e, Plate 1, shows part of the foregoing very highly
magnified. The nature and abundance of the pits are now very
clearly seen.

Not only does the cone of Agathis australis, clearly show the strongly
pitted rays, which are found in the Jurassic and Lower Cretaceous
woods, referred by the majority of recent investigators, to araucarian.
affinities, but we find that the Mesozoic type of ray may be recalled
by injuries to the root and the seedling stem. Figure f, Plate 1,
illustrates the modification of ray structure which frequently occurs
in the old roots of Agathis australis as the result of injury. The cells
in this case too are much thickened and strongly pitted. The normal
seedling rays of A. australis have not been observed to show pitting
or thickening on their terminal or horizontal walls in any case. The
mature stem rarely shows reversion in ray structure to the earlier
Mesozoic type as a result of injury. Agathis australis merely furnishes
a good illustration of a_condition of affairs in normal and traumatic
anatomy, which so far as it goes, in accordance with accepted bio-
logical principles, vouches for the descent of the existing representa-
tives of the Araucarian stock from ancestors in the Mesozoic, which
possessed rays like those of living as well as extinct representatives
of the Abietineae. Similar facts have been observed in other cases
not only in the genus Agathis but also in Araucaria. It appears un-
necessary to enlarge upon these at the present time.

Attention may now be given advantageously to the question of
wood parenchyma in the Araucariineae. As is well known the Cor-
daitales, from which perhaps the majority of botanists at the present
time directly derive the Araucarian Conifers, were characterized by
the complete absence of wood parenchyma. The living species of
Agathis and Araucaria, manifest this condition likewise in the normal
mature wood of the stem and thus present prima facie evidence of
close affinity with Cordaitales and other ancient Gymnosperms.
Here again we may turn with advantage to the historical evidence
and then to comparative anatomical and experimental data in the
living representatives of the Araucarian stock, Figure a, Plate 2,
shows a longitudinal section of an Araucarian wood from the Raritan
Cretaceous of Kreischerville, Staten Island, N. Y. Certain dark

536 PROCEEDINGS OF THE AMERICAN ACADEMY.

longitudinal stripes are to be noticed particularly to the right of the
center of the figure. These represent resiniferous parenchyma.
Figure d, Plate 2, shows a portion of the last figure more highly magni-
fied, to make clear the transverse partitions separating the resiniferous
elements from one another. Figure 6, Plate 2, shows the same wood
in transverse section, the dark spots indicating the presence of the
resiniferous cells. Figure c, Plate 2, shows a section of the same wood
near the pith, making it clear that we have to do with the stem wood of
an extinct araucarian conifer. The resiniferous elements can be seen
as in the preceding figure scattered throughout the wood. The writer
has had the opportunity of examining a number of araucarian woods
from the Raritan Cretaceous of the Eastern United States and has
found in all true Araucarioxyla an abundance of wood parenchyma.
In this respect they present a marked contrast to the normal stem
wood of the living Agathis and Araucaria, although resembling them
to a striking degree in other respects.

Let us now turn our attention to the conservative organs of the
living genera. Figure ὁ, Plate 2, illustrates the structure of an old
root of Agathis australis, near the center. It is to be observed that
the wood is thickly sown with parenchyma cells. These, it may be
added are most abundant near the center of the root and die out pro-
gressively as the outer annual rings of the older root are reached,
unless recalled by injury, as is noted below. Figure a, Plate 3, shows
a longitudinal section of the same root, making it clear that we have
really to do with resin cells and not merely with tracheids filled with a
resinous or mucilaginous contents such as are not infrequent in coni-
ferous woods of varied affinities. Resin cells are extremely common
in the first formed annual rings of the root in the genus Agathis and
likewise occur to a less degree in the root organs of Araucaria. In
certain species of Agathis, they likewise are found in the first annual
ring of the stem. This condition may be illustrated by A. australis
and A. Bidwillii, which represent as nearly as possible the extremes
of affinity within the genus. Figure b, Plate 3, illustrates the mode
of occurrence of parenchyma in the first year’s growth of A. Bidwillia.
The dark spots are parenchyma cells. Figure c, Plate 3, shows a
longitudinal section of the same species. On the left is seen the
protoxylem and a little to the right of the center, a row of parenchyma-
tous elements, still retaining their protoplasmic contents. Figure d,
Plate 3, shows the same conditions in the first annual ring of A. aus-
tralis. Here the parenchyma tends to occupy the face of the summer
wood, in the first yearly increment, thus resembling the conditions

JEFFREY.— ARAUCARIOXYLON TYPE. 537

found by Gothan in certain araucarian woods from King Carl’s Land
apparently wrongly referred by him to abietineous affinities.® Figure
e, Plate 3, is a longitudinal section of the same species, illustrating
the vertical distribution of the wood parenchyma. Seldom or never
does parenchyma make its appearance in the normal wood of outer
annual rings. At this point it is convenient to record another feature
of interest. Through the kindness of Messrs. Eames and Sinnott,
Sheldon fellows of Harvard University, who have recently spent a
year in the investigation of the coniferous flora of the Australasian
region, the writer has been supplied with seedlings of the genera
Agathis and Araucaria. It was found on investigation that in the
ease of Agathis there was usually no wood parenchyma in the first
annual ring in the seedling until it had reached a considerable size.
In fact it is only in the vigorous branches that bear cones that the
parenchymatous elements appear in any abundance. The recapitu-
lationary phenomena in the case of wood parenchyma are accordingly
delayed until the plant has reached a certain vigor, thus presenting
an exact homologue with the conditions found for example in certain of
the Abietineae, which are normally without resin canals in the wood 9
and in Sequoia gigantea.1° Here the resin canals, so characteristic of
the pine-like Abietineae, occur in the first annual ring of vigorous
vegetative shoots and in a few cases only in the axis of the cone. The
evidence in the case of the genus Sequoia and in the Abieteae, has been
accepted by other investigators who have given special attention to
the Conifers, as a clear indication that both the Abieteae and Sequoia
have come from pine-like ancestors.14 Mr. Thomson’s views in this
respect are particularly significant as his attitude in regard to the
affinity of the Araucarian conifers is diametrically opposed to that of
the present writer. As will be pointed out later, the admission of the
validity of certain general principles in the case of certain coniferous
tribes, logically implies their application to the whole series. We find
then this feature of accord between recapitulationary phenomena in
for example Abies and Sequoia on the one hand and Agathis on the

8 Gothan, Die Fossilen Hoelzer von Koenig Karl’s Land, Kung. Svensk,
Vetenskab. Handlingar, Bd. 42, No. 10.

9 Jeffrey, Comp. Anat. of the Coniferales, No. 2. The Abietineae, Mem.
Boston Soc. Nat. Hist., 6, pp. i-37, pls. 1-7 (1904).

10 Comp. Anat. Coniferales, No. 1, The Genus Sequoia, Mem. Bost. Soc.
Nat. Hist., 5 (1903).

11 Coulter and Chamberlain, Morphology of Gymnosperms, Chicago
(1911), and Thomson, R. B., Megasporophy!] of Saxegothea and Microcachrys,
Bot. Gazette, 47 (1909).

538 PROCEEDINGS OF THE AMERICAN ACADEMY.

other, that the resin canals in the case of the former and the resini-
ferous parenchyma in the case of the latter, do not appear in the first
annual ring of the seedlings but only in the first annual increment of
older and more vigorous axes. In the case of Agathis it is clear from
the fossil data, that we actually have a harking back to ancestral
phenomena, presented in the extinct forms as shown above. In Abies
and Sequoia we can only infer that their ancestors had resin canals
in accordance with accepted principles of biological science. It seems
clear also in both types of illustration, that we have in the case of
the living representatives, to do with reduction phenomena. The
fact that Abies and Sequoia on the one hand and Agathis on the other
hand are degenerate descendants of stocks once more vigorous and
richly endowed, doubtless furnishes the explanation of why the recapi-
tulationary phenomena in connection with the first annual ring make
their appearance not in the seedling; but only after the plant has
attained the reproductive age.

Figure f, Plate 3, illustrates the conditions found in connection with
the parenchyma of a wounded root of Agathis australis. It is to be
noticed that most of the parenchymatous cells are thick-walled and in
some instances strongly pitted. This figure is to be compared with
Figure c, Plate 1, which shows the normal condition of the cone axis.
Here both the rays and parenchyma are thick-walled on the side nearer
the pith. In the case of A. australis the adult stem, when injured,
in contrast to the root does not form thick-walled wood parenchyma
but only thin walled elements. That this is the case is demonstrated
by Figures a and b, Plate 4, which show the injured stem wood of
A. australis in transverse and longitudinal section. Thin-walled
parenchyma can be seen in each case.

Figures ὁ and d, Plate 4, show the transverse and longitudinal views
of the heart wood of A. australis, illustrating the presence of resinous
exudations in the tracheids of the wood immediately adjacent to the
rays. In the longitudinal view the relation of the exudation to the
ray cells is particularly well seen. Penhallow has compared these
transverse septa, resulting from substances poured out by the ray
cells into the tracheids with the trabeculae of Sanio. They have in
reality of course nothing to do with these structures.!* Lignier has
described the thickening up of the tracheids adjacent to the rays in
certain Araucarian woods from the French Jurassic. It seems entirely
probable that he has mistaken resin filled tracheids for thick-walled

12 Penhallow, North American Gymnosperms, Boston (1907), pp. 53-58.

a

JEFFREY.— ARAUCARIOXYLON TYPE. 539

ones, as a result of the bad condition of preservation of his material. 18
Figures e and f, Plate 4, make this probability practically a certainty,
Figure e illustrates the transverse view of Araucarioylon nove-
boracense from the Raritan Cretaceous of Staten Island.4 The
tracheids in contact with the rays are apparently distinguished by
their very thick walls. Figure f, which represents a longitudinal view
of the same piece of lignite, makes it clear that the apparently thick
walled tracheids are in reality only tracheids more or less occupied
by a plugging exudation from the rays.

Although a general statement as to the inferences to be drawn from
the series of articles, of which this is the first, will appropriately appear
in connection with the last of the series, it is apposite and necessary
to point out the particular conclusions to be derived from the observa-
tions recorded here. It is clear that there are certain definite struc-
tural relations between the Araucarian woods now in existence and
those no longer living. In general the structural features of the
Mesozoic Araucarioxyla are strongly retained in the cone axis, and
the root of living species. They are less strongly retained in the vege-
tative stem. In the case of the latter, ancestral features may reappear
in the first annual ring of axes of unusual vigor or as a result of injury.
Injuries to the root result in the recall of more ancient features than
those which can traumatically be recalled in the stem. Further it is
clear that the comparative developmental and experimental study of
living Araucarian conifers is of the greatest value and significance in
connection with the accurate diagnosis of fossil forms. A comparison
of living with extinct forms, so far as the points considered in this
article are involved, shows that certain Mesozoic woods, which have
been referred by Seward, Lignier and the present writer to the Arau-
cariineae, in reality have that systematic affinity and are not as has
been recently suggested by Gothan, the woods of Abietineous Conifers.

CONCLUSIONS.

1. The ancestors of Araucaria and Agathis were characterized by
the possession of wood parenchyma.

2. They likewise had strongly pitted rays.

3. The possession of these two features is quite inconsistent with
their derivation from Cordaitean ancestry.

13 Op. cit., pl. 17.
14 Hollick and Jeffrey, Cret. Coniferous Remains, Staten Island, Mem. N. Y.
Bot. Garden, 3, pl. 21.

540 PROCEEDINGS OF THE AMERICAN ACADEMY.

4. Certain woods from the Jurassic and Lower Cretaceous, pos-
sessing at once araucarian pitting, of the tracheids, abundantly devel-
oped wood parenchyma and strongly pitted medullary rays are in
reality aruacarian in their affinities and not abietineous as has recently
been asserted by Gothan on the insufficient basis of their ray structure.

5. The characteristic features of Mesozoic araucarian woods are
retained to a large degree in the wood of cone axis, root and first
annual ring of vigorous branches of living representatives of the Arau-
cariineae.

6. They may be recalled by experimental means particularly in
the root and the seedling stem.

Fig. a.
Fig. b.

Fig. c.

Fig. d.

Fig. e.
Fig. f.

PLATE 1.

Radial view of an undescribed wood from the Lias of Yorkshire,
England, showing the Araucarian type of pitting. Χ 100.

Radial view of the wood of the same showing pitted character of the
medullary ray Χ 100.

Transverse section of the wood of the cone-axis of Agathis australis,
showing the strong normal pitting of the ray cells near the pith.
x 100.

Radial section of the same showing character of the tracheids and
the ray cells. Χ 100.

Part of the same. Χ 300.

Injured wood of the root of the same in transverse section, showing
the thick-walled, strongly pitted ray cells formed traumatically.
Χ 100.

PLATE 1

« JEFFREY-ARAUCARIOXYLON TYPE.

XLVIII

Proc. AMER. ACAD. ARTS AND SCIENCES VOL.

PLATE 2.

Fig. a. Radial view of the wood of Araucarioxylon noveboracense. δζ 50.
Fig. δ. Transverse section of the same. X 40.

Fig. c. Transverse section of the same near the pith. Χ 40.

Fig. d. Long radial section of the same. X 100.

Fig. e. Transverse section of the wood of the root of Agathis australis. X 40.

PLATE 2

JEFFREY-ARAUCARIOXYLON TYPE.

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Fig. a.
Fig. b.

Fig. 6.
Fig. ἃ.

Figs e.
Fig. f.

PLATE 3.

Radial section of the same. Χ 40.

Transverse section through first annual ring of stem of Agathis
Bidwillii, showing resin cells. Χ 40.

Longitudinal section of the same. X 40.

Transverse section of old stem of Agathis australis, showing first
annual ring. Χ 60.

Radial section of the same. X 60.

Transverse section of root wood of Agathis, showing both pitted and
thin walled parenchyma. Χ 100.

JEFFREY-ARAUCARIOXYLON TYPE. PLATE 3

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Proc. AMER. ACAD. ARTS AND SCIENCES VOL. XLVIII

Fig. a.
Fig. b.
Fig. 6.
Fig. d.
Fig. e.

Fig. f.

PLATE 4.

Wounded wood of the stem of Agathis australis in transverse section,
showing the return of the ancestral wood parenchyma as the result
of injury. Χ 100.

The same in radial section. Χ 100.

Wood of Agathis australis (normal) in transverse section, showing
plugging of tracheids in proximity to the rays. 40.

The same in tangential longitudinal section, showing relation of plugs
to the ray cells. Χ 40.

Transverse section of the wood of Araucarioxylon noveboracense, for
comparison with Figurec. Χ 40.

Tangential section of the same for comparison with Figured. Χ 40.

JEFFREY-ARAUCARIOXYLON TYPE. PLATE 4

Proc. AMER. ACAD. ARTS AND SCIENCES VOL. XLVIII

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CONTRIBUTIONS FROM THE PHANEROGAMIC LABORATORIES
OF HARVARD UNIVERSITY. NO. 56.

THE HISTORY, COMPARATIVE ANATOMY AND EVOLU-
TION OF THE ARAUCARIOXYLON TYPE.

By Epwarp C. Jerrrey.

Part II.

In the first article of the present series the structure of the rays and
the parenchyma of woods of Araucarian affinities, was considered.
In the present one the characteristic features of the tracheids and the
nature of the pitting will be particularly discussed. The pitting of the
tracheary elements in the Araucarian Conifers has been considered
by practically all writers as an infallible criterion for the diagnosis
of their woods as fossils. It is unnecessary to enter upon this matter
in detail as the literature on the subject has quite recently been
admirably summarized by Gothan.'® It is universally assumed that
crowded radial pits on the tracheid walls either flattened by mutual
contact, if the pores are uniseriate, or of somewhat polygonal outline
in case the pits are in several rows, indicate Araucarian affinities.
Recently however a tendency to question the universal validity of the
Araucarian type of tracheary pitting as an indication of Araucarian
affinities has made itself felt. On the one hand it has been maintained
that woods with typical Araucarian pitting in reality were referable
to the Abietineae on the assumed more important character of their
ray structure.4® On the other it has been maintained that woods with-
out typical Araucarian pitting in reality belonged, in consideration
of the sum of their characters to the Araucarian Conifers.!7 The

15 Zur Anatomie lebender τι. fossiler Gymnospermen-HoOlzer, Berlin (1905).

16 Gothan, Die Fossilen Hélzer von Konig Karl’s Land, Kung. Svensk.
Handlingar, Bd. 42, and Gothan, Die Fossilen Hoelzreste von Spitzbergen,
Kung. Svensk. Vetenskap Handlingar, Bd. 45.

17 Gerry, Eloise, Distribution of the bars of Sanio in the Conifers. - Ann.
Bot. 24 (1910); Sinnott, E. W., Paracedroxylon, a new type of Araucarian
wood, Rhodora, 11;Jeffrey, E. C., The Affinities of Geinitzia gracillima, Bot.
Gazette, 50.

542 PROCEEDINGS OF THE AMERICAN ACADEMY.

question of the value of Araucarian pitting as an indication of Arau-
carian affinities is all the more important because it likewise has been
made to involve the relationship of the Araucarian Conifers with the
Cordaitales of the Paleozoic, which as regards their pitting strongly
resemble the conditions typical of the wood of the living Agathis and
Araucaria. Still another important question arises in connection
with certain features of organization of the Araucarian tracheid as.
compared with that found in other Conifers. It has been pointed out.
by Miss Gerry 18 that the Araucarian Conifers both living and extinct
are without the horizontal cellulose bands, between the radial bordered
pits, characteristic of all other Conifers. This feature has an added
importance from the fact that a similar feature is likewise character-
istic of the wood of the Cordaitean gymnosperms. It is the purpose
of the present article to deal with these features of the Coniferous
tracheids in regard to their value as indications of tribal relationship:
and evolutional sequence in the Coniferales.

It will be convenient to begin with the subject of Araucarian pitting.
Figure a, Plate 5, shows the crowded alternating arrangement of the
tracheary pores, which is regarded as typically Araucarian. The
illustration is taken from the wood of Araucarioxylon, noveboracense,
from the Raritan Cretaceous of Kreischerville, Staten Island, N. Υ.}9
Figure ὑ, Plate 5, illustrates the arrangement and propinquity of the
radial bordered pits in the first annual ring of the same type of lignite.
The absence of approximation and consequent flattening of the
bordered pits is very apparent. An examination of a considerable
number of true Araucarioxyla from the American Cretaceous has led
the writer to the general conclusion that no matter how typical the
Araucarian arrangement of the pits may be in the mature wood, that
in the first annual ring of the stem one always finds a marked tendency
to the rounded and well spaced pits which are typical of the wood of
the Abietineae and allied Conifers.

Further in connection with recent investigations on woods of the
American and European Mesozoic, numerous instances have been
described, presenting to a greater or less degree Araucarian character-
istics, but with a marked departure from the Araucarian type of pitting
This is notably the case, for example, with the recently established
genus Brachyoylon.?°

An even more striking illustration is supplied by the genus Para-

18 Op. cit. 19 Op. cit.
20 Hollick and Jeffrey, Cretaceous Coniferous Remains from Kreischerville,,
Mem. N. Y., Bot. Garden, No. III.

JEFFREY.— ARAUCARIOXYLON TYPE. 543
cedroxylon recently described by Sinnott.?!_ Perhaps the most con-
spicuous illustrations of this condition are supplied by Araucariopitys 22
and the so called Cedroxylon transiens of Gothan.?3 Here not only
does the pitting depart largely from the Araucarian type, but the wood
is likewise particularized by strongly pitted rays resembling those of
the Abietineae. It is clear from the facts and citations of facts here
assembled, that in the Mesozoic there were woods which either had
the Araucarian type of pitting very imperfectly developed or if well
displayed in the adult wood, not found to be present in the first annual
ring. It may be stated in anticipation of conclusions to be drawn
later, that it follows that Araucarian pitting was not 2 characteristic
of the primitive stock from which the Araucartineae of to-day and their
nearest relatives in the Mesozoic, were derived.

The conditions in the living genera of the Araucariineae as regards
pitting, may now advantageously be considered. Figure c, Plate 5,
shows the appearance of a radial section of the wood in an old seedling
stem of Agathis australis, perhaps the most highly specialized species
of the genus now in existence. The pits are obviously much crowded
and when in a single row strongly flattened, or when multiseriate
somewhat polygonal in shape. Exactly similar conditions are found
in the case of the wood of species of Araucaria, and as a consequence
it is not necessary to illustrate by a figure the wood structure in that
genus. Figure d, Plate 5, shows a radial section of the wood at the
base of the seedling stem of Agathis australis. Here the pits are ob-
viously not crowded or flattened by mutual contact. This condition
is found for several inches above the ground in the seedling stem and
for a great number of annual rings outwards, as many for example as
fifteen. In the main root of the seedling similar conditions are found
to a considerable depth but in the secondary roots, the pitting becomes
typically Araucarian, with the very many rows of pits, characteristic
- of root wood in general. In the seedling stem of Araucaria Bidwillii,
A. imbricata and A. Coolii, very similar conditions were found, to a
less marked degree and lower down in the stem, rather in its hypoco-
tyledonary than its epicotyledonary region. It is an interesting fact
that in the seedling stem of the living genera of the Araucarian Coni-
fers, we find perpetuated the type of pitting charcteristic of Brachy-
oxylon,?* Araucariopitys,?® Paracedroxylon,?® Cedroxylon transiens 2
from various levels of the Mesozoic. Here we have illustrated in a

21 Op. cit. 22 Jeffrey, Bot. Gazette, 44 (1907).
23 Op. cit. 24 Op. cit. 25 Op. cit.
26 Op. cit. 27 Op. cit.

544 PROCEEDINGS OF THE AMERICAN ACADEMY.

remarkable way the validity of the doctrine of recapitulation, in
accordance with which the young individuals of living species may
pass through in their earlier stages of development the condition
found typically in their extinct ancestors of more or less remote
geological time. :

The first annual ring of the living species of Agathis and Araucaria,
unlike the Araucarian woods of the Araucarioxylon type, from the
American Cretaceous, shows only slightly and often sporadically the
departure from Araucarian pitting characteristic of Brachyoxylon, ete.
Not more than two or three tracheids next the protoxylem in the most
favorable cases illustrate this feature. In this respect the existing
woods of the Araucarian type show themselves, as might be ex-
pected, less retentive of ancestral characters than is the case with the
similar woods from the Cretaceous. In the case of the normal type
of Araucarian wood, not only the approximation but also the alterna-
tion of the radial pits of the tracheids are characteristic features.
Figure e, Plate 5, shows under a comparatively low magnification,
the structure of the tracheids adjoining the protoxylem in the cone of
Araucaria Bidwillit. It is easy to make out that the pits in the tra-
cheary elements of the secondary wood nearest the scalariform ele-
ments of the protoxylem, are arranged for the most part in opposite
pairs. Moreover even with the low magnification employed it is
clear that the pits in question are not flattened by mutual, approxi-
mation. In other words we have the conditions present, so far as the
radial pitting is concerned, which are typical of the wood of the Abie-
tineae and other tribes of Conifers. Farther away from the protoxy-
lem the pitting passes into the typical araucarian condition. Figure f,
Plate 5, shows a part of the last more highly magnified. On one side
the tracheids still retain some indications of the spiral and reticulate
sculpture of the protoxylem. On the other tracheids of the secondary
wood have made their appearance. They are characterized, however,
by a distinctly non-Araucarian arrangement of the pits and by other
remarkable and important features. The pits are separated from each
other by appreciable intervals. The most remarkable feature, how-
ever, shown by the tracheids in» this region is the presence of dark
discontinuous stripes crossing the tracheids transversely between the
pits. These dark stripes in the photograph often fork at the ends
and represent cellulose bands in the substance of the tracheid walls.
They are in fact typical bars of Sanio (not to be confused with the
“Balken’ or trabeculae of Sanio, which are a very different thing),
found normally in all the tribes of Conifers except the Araucariineae.

ARAUCARIOXYLON TYPE. 545

JEFFREY.

Before passing to the consideration of the significance of these strue-
tural features of the wood of the cone in Araucaria Bidwillii, it will
be well to examine them more particularly in this species and discover
their occurrence and development in other species of Araucaria as well
as in species of the allied genus Agathis.

Figure a, Plate 6, illustrates the conditions presented in another
photograph of a radial section of the wood in Araucaria Bidwillii.
Here although the magnification is not great the bars of Sanio stand
out with great clearness between the pits, which on the whole tend
more in their arrangement to the typical Araucarian condition of
alternation than in the figures described above. The tracheids are
bounded above and below by wood rays, showing that although
they lie near the primary wood they are typical elements of the second-
ary xylem. Figure ῥ, Plate 6, shows a very highly magnified view of
parts of three tracheids of the secondary wood in proximity to the
primary xylem. Here it is possible to distinguish the bars of Sanio
with great clearness. They are as a rule, invariably in the figure under
discussion, not continuous across the tracheid, but subtend usually
the breadth of a single pit. The forking of the cellulose bars at the ends
can be clearly made out.

Figure c, Plate 6, shows the conditions in the tracheids of the second-
ary wood, adjacent to the primary xylem in Araucaria imbricata, very
highly magnified. On one side of the figure can be seen a spirally
sculptured element of the primary xylem. On the other, one tracheid
in particular shows clear bars of Sanio. In Araucaria imbricata
which, as will be shown later, as a result of the consideration of a
number of lines of evidence is among the least primitive species of the
genus, the tracheids showing well spaced pits and clearly discernible
bars of Sanio are very few in number. <Araucaria Cookii and Arau-
caria Rulei were likewise examined, with results intermediate between
those found in A. Bidwillii and A. imbricata which appear in these as
in other respects to represent the extreme conditions found in the
genus.

For comparison an illustration of the conditions in the mature
secondary wood of Pinus strobus is shown in Figure d, Plate 6.
Here the cellulose bars of Sanio are very distinct between the uni- or
bi-seriate pits. The pits where they are in two rows are opposite,
The occasional forking of the bars at the ends can likewise be made
out. The pits are well spaced and rounded.

Figure e, Plate 6, shows a tracheid wall of Araucaria Bidwillii in
tangential section. That the plane of section is in reality tangential

546 PROCEEDINGS OF THE AMERICAN ACADEMY.

and that the element belongs to the secondary wood is vouched for
by the presence, on the right and left, of cells of the wood rays in
transverse section. The dark transverse sections of the bars of Sanio,
embedded in the substance of the lignified tracheid wall, between the
radial pits, are easily distinguished. Figure f, Plate 6, illustrates the
conditions observable in the ordinary secondary wood of the vegeta-
tive axis. Obviously the pits as seen in profile are here in close contact
and are not separated by bars of Sanio.

The stem of the seedling and the first annual ring of the adult
branches of various species of Araucaria, were examined in the region ~
of the primary xylem for the presence of bars of Sanio. Where any
evidence of their existence was apparent, however, they were ex-
tremely indistinct and ghostly and very evanescent. The same con-
ditions were observed in the root. In accordance with the now
widely accepted dictum of comparative anatomy that the leaf trace is
very apt to perpetuate ancestral conditions, the foliar traces of several
species of Araucaria were investigated, but on account mainly of the
small size of the tracheary elements, it was difficult to make out the
presence of bars of Sanio, with any distinctness, although their
existence in these regions was indicated.

The absence of bars of Sanio in the seedling, where the pits are
often widely separated from one another, is of particular significance,
in view of the statement of Gothan, that their non-existence in Aura-
carian woods is to be explained by the close approximation of the pits.
Obviously such an explanation will not hold in the case of the undoubt-
edly Araucarian wood of Araucarian seedlings.?° It follows that woods
from the Mesozoic which are without typical Araucarian pitting, can
best be diagnosed as to their affinities not on the basis of their radial
pitting or even their ray structure, but by the presence or absence of
bars of Sanio, in well preserved material. Where the bars are present
in the mature wood, we may certainly assume that the wood is not
Araucarian. On the other hand, where the bars of Sanio are dis-
tinetly absent in well preserved Mesozoic woods, it may safely be con-
cluded that they are of Araucarian affinites, no matter what may be
the nature of their radial pitting or that of the cells of their rays.

In conclusion of the descriptive part of the present article, it is
necessary to refer to the pitting and structure of the tracheids in the
living genus Agathis. It has been found here, that even in the cone,
the tracheids very quickly cease to show opposite pitting and the bars

28 Gothan, Die fossilen Holzreste von Spitzbergen, Kung. Svensk. Veten-
skap, Handlingar, Bd. 45.

JEFFREY.— ARAUCARIOXYLON TYPE. 547

of Sanio in all cases are shadowy and difficult to discern, although
they can be made out by the eye of expectancy. Agathis Bidwillii,
material of which was received from the Botanic Garden at Buiten-
zorg, Java, through the kindness of the late Dr. M. Treub, Director,
proved in this respect to be most favorable. Even here, however,
in the most favorable instances, the bars of Sanio are scarcely as well
developed in the wood of the cone, as they are in the least favorable
species of Araucaria, which has been examined and figured in the pres-
ent connection, viz. A. imbricata. It does not seem necessary on that
account to present illustrations of Agathis. A. australis shows bars
of Sanio, less distinctly than any other species examined. No indi-
cation whatever of the existence of bars of Sanio has been found in
the seedling of A. australis, although it has been examined in detail
with considerable care.

Finally attempts were made to discover bars of Sanio in the region
of the primary wood in species of Araucarioxylon. Here on account
of the generally bad state of preservation of the material and also
doubtless on account of the delicate nature of the bars in this region,
even in living representatives of the Araucariineae, the results were
entirely negative. It is well perhaps at this point to indicate the best
method of demonstrating bars of Sanio in the wood of cones of living
species of the Araucarian tribe. Haidenhain’s hematoxylin was
found most useful for bringing out the structure in question; but care
must be taken to have both the hematoxylin solution and the iron
alum solution perfectly fresh. The sections after being subjected
to the action of the iron alum for ten or fifteen minutes are washed
carefully and rapidly in three changes of distilled water. They are
then allowed to remain in fresh distilled water for half an hour or
more. Next they are treated for some time with hematoxylin solu-
tion of one fourth of one per cent strength. In this they remain for
some time, up to half an hour. Unless the solutions are quite fresh
they will become fatally overstained. After a washing or two in
distilled water, the sections are transferred to a very dilute aqueous
solution of safranin and allowed to remain for several hours or over
night. If the process has been successfully carried out, the bars of
Sanio will appear as intense blue transverse bands on the red back-
ground of the lignified cell wall of the tracheid. They are most easily
seen nearer the ends of the tracheary elements, just as is the case in
those coniferous woods where they are abundantly and normally
present in the mature tissue.

It was considered that the appearances described above in connec-

548 PROCEEDINGS OF THE AMERICAN ACADEMY.

tion with the obvious presence of bars of Sanio, might possibly be
common to all secondary woods in the region of the primary xylem.
Sections of the cone axis, the leaf-strands and roots of Cycas and Zamia
were accordingly made and subjected to the same treatment. In no
case was there any indication of the presence of horizontal bands of
cellulose in the tracheids, between the radial bordered pits. Similar
observations were made on the vegetative stem, the leaf strands and
the reproductive axes of Ginkgo. Here as in the case of Cycas and
Zamia, no bars of Sanio were seen in proximity to the primary wood.
In fact in the reproductive axes and in the leaf strands no bars of Sanio
were seen at all. In the vegetative stem, however, they appear late
in the first annual ring, not in close proximity to the primary xylem.
As is well known, Ginkgo resembles the mass of Conifers, in showing
bars of Sanio clearly in its mature wood. Pinus, as probably the most
primitive living representative of the Coniferales was likewise exam-
ined in this connection. Here the conditions closely resemble those
found in Gingko, so far as the vegetative shoots are concerned, for the
bars of Sanio make their appearance late and not in proximity to the
primary wood. In the cone of Pinus strobus, bars of Sanio were not
found at all. It is to be noted in connection with these results, as con-
trasted with those found in the case of the Araucarian Conifers that,
there is clear evidence, so far as may be judged from the structure of
the first annual ring, that Ginkgo and the genus Pinus are directly
connected with the Cordaitean stock, in which bars of Sanio are
absent and the pitting is alternating, while Agathis and Araucaria
have obviously come from ancestors which, in accordance with
accepted principles of comparative anatomy, had opposite pitting and
bars of Sanio in their tracheids.

It seems to be quite clear so far as the particular features of wood
structure, considered in the present article, are concerned, that far
from the absence of bars of Sanio and the presence of alternating
pitting in the woods of the Araucariineae, being an argument for their
direct filiation with the Cordaitales, these features have clearly been
secondarily acquired and the Araucarian stock primitively was
characterized by the bars of Sanio and opposite pitting, which have
been retained in the ligneous structure of all the other living tribes
of the Coniferales. It is also quite clear from the fossil evidence that
the loss of bars of Sanio, in the case of the Araucariineae, as well as
the disappearance of the ancestral opposite pitting, took place at a
period relatively remote. That this general inference is justified
by a number of other equally important facts will be shown in the
later articles.

JEFFREY.— ARAUCARIOXYLON TYPE. 549

SUMMARY.

1. The characteristic pitting of the wood in Agathis and Arau-
caria, the Araucarioxylon type, is not ancestral but more recently
acquired.

2. This conclusion is based on the structure of the first annual ring
of the stem in Mesozoic Araucarioxyla. It is confirmed strongly
by the seedling structure of the living genera and particularly by the
anatomical structure of the wood of their cone axes.

3. The cellulose bars of Sanio, characteristic of the mature wood of
all living genera of the Coniferales, except Agathis and Araucaria, are
clearly present in the secondary tracheids adjacent to the primary
wood of the cone axis in these two genera. They are absent in the
seedling and cannot be clearly discerned in the leaf traces on account
of the small size of the elements.

4. Since bars of Sanio do not occur in similar situations in Cycas
and Ginkgo, it-cannot be assumed that they are a feature of all gymno-
spermous woods in proximity to the primary xylem.

5. Since deviations of a significant nature in the pitting and struc-
ture of the tracheids occur in primitive regions of the Araucarian axes,
which connect them with the remaining tribes of the Coniferales stock,
it follows that so far as these features are concerned, the Araucarian
Conifers are derived from the common coniferous plexus and are not
directly articulated with the Cordaitales.

6. On the basis of comparative studies of the tracheids of the
Araucariineae, they cannot be regarded as primitive representatives
of the Coniferous order.

7. The real affinities of the Araucariineae can best be defined when
all the evidence is considered in the concluding article of this series.

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Fig. e.

Fig. f.

PLATE 5.

Radial section of the wood of Araucariorylon noveboracense. X 200.

Radial section of wood in proximity to the protoxylem in the same.
Χ 200

Radial section of the wood of Agathis australis. > 200.
Radial section of the wood of the seedling of the same. Χ 300.

Radial section of the wood of the cone of Araucaria Bidwillii, in
proximity to the protoxylem. Χ 60.

The same more highly magnified. > 200.

PLATE 5

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PLATE 6.

Radial section of thesame. X 100.

Another of the same. > 500.

Radial section of the xylem of the cone of Araucaria imbricata, in
proximity to the protoxylem. X 500.

Radial section of the wood of Pinus strobus. X 150.

Tangential section of the wood of the cone of Araucaria Bidwillii.
x 500.

Tangential section of the wood of the vegetative stem of the same.
x 300

PLATE 6

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CONTRIBUTIONS FROM THE PHANEROGAMIC LABORATORIES
OF HARVARD UNIVERSITY. NO. 57

THE HISTORY, COMPARATIVE ANATOMY AND EVOLU-
TION OF THE ARAUCARIOXYLON TYPE.

By Epwarp C. JEFFREY.

Part III.

The present article will be devoted to the consideration of resin
canals in the wood of the Araucariineae, living and extinct. Some
time ago the present writer in collaboration with Dr. Arthur Hollick 2°
described the occurrence of resin canals as a result of injury in certain
Araucarian woods from the Raritan Cretaceous of Kreischerville,
Staten Island. Later a more complete study of this phenomenon was
made, which included the consideration of more varied and abundant
material from the Kreischerville deposits, as well as from the strata
of similar age on the island of Martha’s Vineyard and likewise from
the much older Cretaceous Potomac deposits of Virginia. In this con-
nection certain leafy twigs of Cretaceous Conifers were described in
which the wood clearly showed the formation of resin canals as the
result of injury. The twigs in question belonged to the well known
Cretaceous genus Brachyphyllum, and for that reason the Araucarian
type of wood, producing traumatic resin canals as a result of injury
was named Brachyoxylon.*° Still another type of Araucarian wood,
forming traumatic resin canals was described by the present writer
in 1907.5! Here the canals were much more like the traumatic resin-
canals of the Abietineae than has proved to be the case with any other
araucarian woods, showing wound resin canals from the American

29 Cretaceous Coniferous ἘΣ aon Kreischerville, Mem. N. Y. Botanic
Garden, No. III.

30 Jeffrey, E. C., Wound Reactions of Brachyphyllum, Ann. Botany, 20,
pp. 383-394, pls. 27, 28.

Hollick and Jeffrey, Cretaceous Coniferous Remains from Kreischerville,
Mem. N. Y. Bot. Garden, No. III.

31 Araucariopitys, a new genus of Araucarians, Bot. Gazette, 44, pp. 435-444.

ΟΣ PROCEEDINGS OF THE AMERICAN ACADEMY.

Cretaceous. Araucariopitys, not only shows resin canals closely
resembling those of the Abietineae, but likewise has wood rays, with
strongly pitted cells very similar to those found in Abietineous woods.
Previously Seward 52 had described woods of similar organization from
the Lias (Upper Jurassic) of Yorkshire in England, under the appella-
tion Araucarioxylon Lindleyi. 'These woods, which, so far as it is
possible to judge from Professor Seward’s description, belong partly
to the Brachyoxylon and partly to the Araucariopitys type, were
characterized by very well marked Araucarian pitting of the tracheids,
accompanied by quite typical traumatic ligneous resin canals. Con-
temporaneously with the present writer’s article on Araucariopitys,
Gothan published a description of the fossil woods of the Upper Juras-
sic of King Carl’s Land.*? These are characterized by the presence of
Araucarian pitting of the tracheids of the wood, by strongly pitted
rays, resembling those of Abietineous woods, by, for the most part,
terminal wood parenchyma, and often by the presence of traumatic
resin canals. These woods are in general considered by Gothan to be
intermediate between the Araucariineae and Abietineae and to indicate
a derivation of the latter tribe from Araucarian ancestry. The writer
agrees with Professor Seward in considering that the woods in question
are distinctly on the Araucarian side in affinities. He is further of the
opinion, which is apparently not shared by Professor Seward, that the
Araucariineae on the basis of structure of Mesozoic woods are derived
from the Abietineae and not vice versa, as is the opinion of the majority
of competent investigators at the present time. Recently an over-
whelming amount of evidence has been brought to light which appears
to strongly support the present writer’s contentions. More recently
Gothan has published an extensive memoir on the fossil woods of the
island of Spitzbergen, in which he described a number of interesting
woods from the upper Jurassic (or Lower Cretaceous!!) resembling
strongly those of King Carl’s Land and in some instances presenting
a still more striking combination of Abietineous and Araucarian
characters.24 The author in this memoir restates and emphasizes
his opinion that the Abietineae have been derived from Araucarian
ancestors.

Figure a, Plate 7, shows the transverse section of a wounded speci-

32 Cat. Mesozoic Plants. Brit. Museum, Jurassic Plants, 2, pps. 56-59.
London (1904).

33 Kung. Svensk. Vetenskap. Handlingar, 42, No. 10. Berlin (1908).

34 Kung. Svensk. Vetenskap. Handlingar, 45, No. 8. Uppsala u. Stock-
holm (1910) q

JEFFREY.— ARAUCARIOXYLON TYPE. 5538

men of Brachyoxylon. On the left appears the wound parenchyma,
which universally adjoins a wound in woody tissues. To the right
of this appear certain somewhat compressed cavities in the wood,
surrounded by cells filled with dark contents. The cavities in ques-
tion are the traumatic resin canals, which are a feature of the Brachy-
oxylon type. Figure b, Plate 7, from the same specimen shows part
of a row of traumatic resin canals farther away from the same wound.
It is an interesting fact in woods, in which resin canals are either
almost obsolete or may be recalled only by experimental means, that
they occur in nearly continuous tangential rows. This for example
is the case with the resin canals in the woods of species of the genus
Sequoia and with the woods of the genera Abies, Cedrus, Tsuga and
Pseudolarix of the Abieteae, which are admitted by those who have
recently devoted special attention to the comparative anatomy of the
Coniferales, to be descended from ancestors which possessed resin-
canals abundantly and normally in their woods. It follows that the
presence of traumatic resin-canals in close tangential rows in the genus
Brachyoxylon is prima facie evidence that this type has come from an
ancestry which possessed normal ligneous resin canals. This con-
sideration alone enormously complicates the task of those who endeavor
to derive the Abietineae from Araucarian ancestors, for they have to
explain the presence of resin-canals in an obsolete and vestigial con-
dition in forms, which they claim to be the direct ancestors of the
pine-like Abietineae, in which the resin canals are highly developed.
It is searcely necessary to point out that this is a palpable logical con-
tradiction. It is unnecessary to figure the longitudinal view of the
traumatic resin canals in the wood of the Brachyoxylon type of Arau-
carian woods, since this subject has already been sufficiently dealt
with in the articles by the present author cited above. It is well
however to point out at this stage that Brachyoxylon has the type of
ray which is characteristic of living representatives of the Araucarian
stock, namely one in which the cells are without pits and thin walled,
except where they are laterally in contact with the tracheids of the
wood. ‘The pitting in this type is often strikingly Araucarian and at
the same time in many instances the radial pores are widely spaced.
In no case is there any indication of the presence of cellulose bars of
Sanio, although many of the specimens, which have passed under
my notice are in a remarkable condition of preservation, which has
been a matter of comment on the part of all who have examined
them.

Figure c, Plate 7, illustrates part of a transverse section of Arau-

554 PROCEEDINGS OF THE AMERICAN ACADEMY.

cartopitys americana 35 showing a series of traumatic resin canals. The
row nearer the center of the stem is larger and better.developed, while
that farther out is composed of very small canals separated by wider
intervals. As has been pointed out in the article cited above, the
traumatic resin canals in Araucariopitys are more nearly like those
of the Abietineae, than is the case with canals of this type which have
been described in any other American wood of Araucarian affinities.
In Araucariopitys the rays too are distinctly of the Abietineous type,
being composed of thick-walled cells, strongly pitted. The radial
bordered pits of the tracheids however are often arranged in the com-
pressed and sometimes in the alternating manner of the Araucarian
conifers. Moreover there are no bars of Sanio present, although
much of the material on which the genus Araucariopitys has been
founded is in a perfect condition of preservation. Gothan, as has
been indicated in the earlier paragraphs of this article, has described
woods of a similar type from the Jurassic beds of King Carl’s Land
and Spitzbergen. These have traumatic resin-canals, thick-walled
and strongly pitted ray cells. This author does not figure the presence
of bars of Sanio in these woods of the arctic regions, so that it may be
assumed that they are absent as in Araucariopitys, especially as woods
of a similar horizon and identical features of organization, which I
have examined, show no indication whatever of these peculiar struc-
tures, which constitute transverse bands between the radial pits of
the tracheids, in all coniferous except Araucarian woods. Miss
Gerry has investigated the distribution of bars of Sanio in the Coni-
ferales in a comprehensive manner and found them to be absent in all
Araucarian woods, living or extinct, which she examined.3® Before
discussing the conditions found in the Araucariopitys type, it will be
well to consider briefly woods of a similar type from older geological
horizons. It is pertinent before doing this, however, to point out that
the Araucariopitys type, so far as our present knowledge goes, is
rare in the later Mesozoic (7. e., the Cretaceous).

Figure d, Plate 7, shows the presence of two rows of resin canals of
the traumatic type in an Araucarian wood from the Upper Jurassic.
This wood and others of the same type will be described in detail on
another occasion. At the present time only those features, which are
of importance in the present connection, will be dealt with. The
section from which Figure d, Plate 7, was made, shows a distinct wound
cap a few annual rings away from the pith. From this on either side

35 Jeffrey, Bot. Gazette, 44, pps. 435-444.
36 Distribution of Bars of Sanio in the Coniferales, Ann. Bot. 24, pp. 119-124.

JEFFREY.— ARAUCARIOXYLON TYPE. 50

extend rows of wound resin canals. Farther out these disappear
entirely as is wont to be the case in woods, giving rise to canals of
this type, unless the injury is extremely severe. The canals are in
some cases obviously very wide in the tangential plane. This feature
indicates their lateral fusion with one another, a condition quite typi-
cally present-in traumatic resin-canals. The canals are surrounded
by cells filled with very dark contents, which sometimes makes its
way into the lumen of the canal itself. The rays are likewise occupied
by a dense dark hued substance. Figure e, Plate 7, shows the canals
in longitudinal radial section. They are clearly not of equal caliber
throughout as is usually the condition in Pinus, but are constricted
at intervals even in the short portion shown in the figure. This
condition is likewise one, which is characteristic of traumatic resin
canals, although it is also more or less observable in the normal canals
of the wood in the Abietineous genera, Picea, Pseudotsuga and Larix.
To the right and left of the resin canal are medullary rays. The
magnification is not sufficient to show their structure, which will be
figured in detail subsequently. It is enough to state that the rays in
this region of the wood are very strongly pitted, exactly as in Arau-
cariopitys described above. The pitting is Araucarian of the Brachy-
oxylon type, that is the pits are not only flattened or alternating but
also occur in the rounded and well spaced condition characteristic of
the Conifers, other than the Araucarian tribe. Bars of Sanio cannot
be made out in the wood under consideration or in any similar ones
from the same deposits.

It is clear from the foregoing paragraph that there are woods in
the Jurassic, which as regards their features of organization combine
Abietineous and Araucarian characteristics. They have namely the
strongly pitted rays and traumatic resin canals of the Abietineae,
combined with the pitting of the tracheids and the absence of bars
of Sanio which are recognized, by those who have made a special
study of Araucarian woods, as diagnostic of the Araucarian tribe.
There are obviously two possible interpretations of the combination
of characters referred to above. It is agreed by competent investi-
gators that the features under discussion clearly indicate a close
degree of relationship in the Jurassic, between the Abictineous and
Araucarian tribes. The disagreement, however, arises as to whether
the Abietineae have come from the Araucariineae or the opposite
mode of derivation is the correct one. Gothan in the two important
memoirs on the Jurassic woods of King Carl’s Land and Spitzbergen
cited above, takes the view that the transition is from the Araucarian

556 PROCEEDINGS OF THE AMERICAN ACADEMY.

Conifers to the Abietineae and bases his position on the structure of
the rays, which he claims is the most trustworthy diagnostic char-
acter of coniferous woods. That is a view to which the present writer
cannot subscribe, as from an extended comparative, anatomical,
developmental, experimental, and paleobotanical acquaintance with
coniferous woods he is in the position to state that wide variations
of ray structure occur within all the coniferous tribes, and that as a
consequence this feature of the organization of the wood cannot be
successfully employed for the diagnosis of the woods of extinct
conifers. It has been pointed out in the first article of this series,
that even in so highly specialized an Araucarian species as Agathis
australis, rays of the Abietineous type occur normally in the wood
of the cone and may be readily produced traumatically in the wood
of the root. A similar illustration may be cited in «πὸ case of
Sequoia. As is well known the rays in the Sequoiineae are usually
composed of thin walled cells without intercommunicating pits. In
the cones of both the living species of Sequoia, particularly S. gigantea,
the cells of the rays of the woody axis are very strongly pitted, espe-
cially towards the primary wood. Further in this genus strongly pitted
rays appear as the result of injury. It appears quite clear from the
conditions in the case of Agathis australis and Sequoia gigantea, that
ray structure may vary greatly within the same genus and even the
same species and consequently cannot be as an infallible diagnostic
feature. The presence of rays of the Abietineous type consequently
cannot be taken as satisfactory proof that the Jurassic woods under
discussion are in reality Abietineous. This consideration likewise
applies to the presence of traumatic resin canals because if these alone
were a sufficient diagnostic character, we would be compelled to put
the wounded wood and normal cone axes of Sequoia gigantea under
the Abietineae, although the sum of characters of that species by com-
mon consent justify the placing of it in an entirely distinct tribe. Let
us now turn to more constant characters than ray structure or trau-
matic resin-canals, namely the pitting of the tracheids which has
been admitted by all experts, with the sole exception of Dr. Gothan,
as an important Araucarian diagnostic feature. In the Jurassic
woods under discussion the radial pitting of the tracheids is distinctly
of the Araucarian type. Further we have recently had added to the
list of utilizable diagnostic characters of Araucarian woods, the absence
of the cellulose bars of Sanio, as worked out by Miss Gerry.3’ True

37 Op. cit.

JEFFREY.— ARAUCARIOXYLON TYPE. 5B7

Gothan has stated that the absence of bars of Sanio is to be explained
by the close approximation of the radial pits in the tracheids of the
Araucarian tribe. It has been shown however that in the seedling,
cone-axis and leaf trace of the living Araucarian conifers the pitting
is not crowded as is the case in the mature secondary wood of the
trunk and root. This is particularly true of the base of the seedling
stem, where typical Araucarian pitting appears only after many years.
In spite of the free spacing of the pits of the tracheids in the regions
just described bars of Sanio are absent, except in the part of the second-
ary wood of the cone axis, immediately adjoining the primary xylem, as
has been indicated in the second article of the present series. It
follows apparently that Gothan’s explanation of the absence of the
bars of Sanio in Araucarian woods is not the valid one. On the
criteria of the absence of bars of Sanio and presence of Araucarian
radial pitting, the Jurassic woods under discussion are clearly of
Araucarian affinities. Moreover if we admit for the sake of argument
that the Jurassic woods in question are Abietineous, what is to become
of the very numerous woods of the Cretaceous of the Brachyoxylon
type, which have traumatic resin canals but have not normally at
least the strongly pitted rays of the Abietineae? They can scarcely
be included on the basis of Gothan’s view with the Abietineae on
account of their not possessing his sovereign diagnostic, Abietineous
ray structure. Professor Seward has agreed that woods of this type
are “undoubtedly Araucarian”’ and it may be assumed that such is
the case until serious argument to the contrary can be adduced.?®
Gothan in his articles cited above, has to assume that practically all
the coniferous woods of the high arctics are Abietineous in their affini-
ties, thus leaving no woody structures for the numerous Araucarian
conifers, which are known to have flourished in that period. Moreover
if we grant his identification of Jurassic woods with strongly pitted
rays, traumatic resin canals, Araucarian radial pitting and non existent
bars of Sanio, as of Abietineous affinities and indicating a recent deri-
vation of the Abietineae from Araucarian ancestors, what shall we say
of the characteristic Cretaceous woods of the Brachyoxylon type,
which resemble these in every respect except in the absence of the
Abietineous type of ray? If we derive the Araucarian conifers from
the Abietineae no such difficulty arises, because we would expect
on such an hypothesis, to find the Araucariineae progressively less
like the Abietineous stock in later geological time. On the basis of

38 The Araucarieae, Recent and Extinct, Phil. Trans. Roy. Soc. London,
Series B. 198, p. 382.

558 PROCEEDINGS OF THE AMERICAN ACADEMY.

ray structure alone then we find that the woods which as the result of
the consideration of their most reliable diagnostic features are Arauca-
rian, form a logical sequence on the hypothesis of derivation from
the Abietineae, from the earlier to the later Mesozoic (Jurassic and
Cretaceous). The opposite hypothesis, even taking into considera-
tion the ray structure only, apparently involves us in hopeless con-
fusion.

Having considered the known types of fossil Araucarian woods in
regard to the feature of the presence or absence of resin canals, it is
now desirable to inquire whether there is any evidence for the normal
or traumatic occurrence of resin canals in the wood of existing rep-
resentatives of the Araucariineae. In this connection the writer
has had somewhat exceptional opportunities of. securing material.
Through the kindness of the late Director of the Botanic Gardens of
the Dutch Government at Buitenzorg, Java, an abundant supply of
the Malayan representatives of the genus Agathis were secured, in-
cluding all vegetative parts of the plant, together with the very im-
portant cones. Later Dr. Maiden of the Botanic Gardens in Sydney,
N. 5. W. Australia, and Dr. Baker of the Technological Museum,
Sydney, have forwarded abundant material of Australasian and exotic
species of Agathis and Araucaria. The writer is likewise indebted to
his students, Dr. A. J. Eames and Mr. E. W. Sinnott for collections
made in Australia and New Zealand, secured in connection with their
tenure of Sheldon Traveling Fellowships of Harvard University.
The latest contribution to the writer’s stores of valuable material was
supplied through the kindness of the Director of the Royal Garden,
Kew, England, and through the goodness of Mr. L. A. Boodle of the
Jodrell Laboratory, Kew. It should be emphasized here that the
abundant material, which has been secured through the kindness of
many botanists, covers all the anatomically interesting parts of the
two living genera of the Araucariineae and to a remarkable extent
their whole geographical range. Not only has normal material been
available but also that which has through injury or other causes
undergone abnormal development.

It is the writer’s purpose to give an account of the organization of
the cone of the Araucarian conifers, in its systematic and anatomical
aspects in an article distinct from the present series. Only features
of special interest in the present connection will be considered here.
As a preliminary to a description of these features, a general statement
may be made in regard to features of organization of the ovulate stro-
bilus, of importance in the case of this investigation. The writer has

JEFFREY.— ARAUCARIOXYLON TYPE. 559

found, in those species of Araucaria, which have both the upper
and lower systems of fibrovascular bundles present in the cone-scales
of their ovulate strobilus, that the axial region of the cone does not
show certain remarkable features found in the case of those species
in which the upper system of cone-scale bundles has disappeared. In
the latter condition there are apparent medullary resin-canals present
in the pith of the cone axis. In the lower region of the cone these
resin-canals are often surrounded with the tissues of the xylem, which
constitute medullary strands joining with the wood of the cylinder
of the axis, at the points where the supply of the cone-scales is given
off. Without going into the matter here it may be stated that the
medullary strands, containing resin canals in certain species of Arau-
caria and Agathis represent the vanished upper system of cone-scale
bundles. The wooden envelope of the resin-canals disappears in the
upper region of the cone and is best developed in the peduncular region.
In Agathis, only the most primitive species have the medullary vas-
cular strands. In the case of Agathis Bidwillii, resin-canals are found
not only in the wood of the medullary system of bundles but they
likewise not unfrequently make their appearance in the bundles of
the lower cone-scale series, which are alone present in this genus.
This feature is shown in Figure f, Plate 7, which represents a cone-scale
supply in the lower region of the cone, passing out through the wood
of the axis. In the upper region of the scale supply and immersed
in the elements of the primary xylem, is to be seen a dark mass which
represents a resin canal filled with mucilaginous contents, a common
accompaniment of the resinous secretion both in Agathis and Arau-
caria, as well as in the resin passages of extinct representatives of the
Araucarian stock. Mucilage is particularly abundant with the resin
in the canals of Agathis. The peculiar position of the resin canal in
the primary wood, is to be compared with the conditions in living
and extinct pines, where the first formed resin canals are often em-
bedded in the elements of the primary wood. The present writer
has described similar conditions in the case of the vestigial resin-canals
of the cone-axis and cone-scales of the genus Sequoia.*? Interesting
in this connection are likewise the resin canals in the primary wood of
the root in the two subtribes of the Abietineae, the Pineae and the
Abieteae. The occurrence of resin canals in the outgoing vascular
supply of the cone-scales on Agathis Bidwillii is an extremely incon-

39 Jeffrey, Comparative Anatomy of the Coniferales. I. The genus Sequoia,
Mem. Boston Soc. Nat. Hist. 5.

560 PROCEEDINGS OF THE AMERICAN ACADEMY.

stant feature and shows various stages of degeneracy the canal often
for instance being largely or even wholly blocked with tyloses.

The occurrence of resin-canals in the scale bundles in a species of
Agathis is a feature of considerable interest phylogenetically. The
question at once arises whether it is to be regarded as an inchoative
stage in the development of resin canals in the group or a vestigial one.
Its place of origin appears to negative the former hypothesis. We
may in fact compare the occurrence of vestigial resin-canals in the
xylem strands of the peduncle of the cone in Agathis Bidwillii, with
the development of vestigial centripetal wood in the peduncular region
of the cone of certain Cycads, the very interesting and important dis-
covery of Dr. Scott *° or the existence of the same ancestral type of
xylem development in the strobilar organs of Equisetum, long after
it has disappeared in the vegetative axis of the ancient stock from
which that genus has been derived.4+ The resin-canals in question are
also to be regarded as ancestral on account of the wound reactions of
Mesozoic Araucarian woods, which have been discussed above. These
interesting vestigial resin-canals appear in the vascular supply of the
lowermost abortive cone-scales, attached to the peduncle of the cone,
and die out before the cone-seale supply leaves the wood of the pedun-
cular axis. They have as yet been found only in Agathis Bidwillit.
It does not appear at all likely that they will be discovered in other
living species of the genus Agathis. It is probable on other grounds,
that this species is the most primitive now in existence.

It naturally has occurred to the writer to investigate the wound
reactions of the stem and roots of living species of Agathis and Arau-
caria. The results of extensive examinations of wounded material
from the Australasian and East Indian regions have however been
entirely negative. There is reason to suppose however from a series
of investigations carried on with another purpose that traumatic
reactions in the seedlings, particularly the seedlings of Agathis Bid-
willit, may yield more favorable results, since it has been found in
certain instances that seedlings respond much more readily to experi-
ment than does the adult plant. It seems clear that so far as the
mature individuals are concerned, however, that the living representa-
tives of the Araucarian stock have entirely lost their capacity for
producing reversionary wound resin canals, and in this respect as in
other equally important normal features of structure, differ from a

40 Scott, D. H., The Anatomical Characters of the Peduncles of Cycada-
ceae, Ann. Bot. II (1897).
41 Hames, Centripetal Xylem in Equisetum, Ann. Bot. 23, (1909).

JEFFREY.— ARAUCARIOXYLON TYPE. 501

large number of Araucarian forms, which apparently became extinct
with the close of the Mesozoic.

As a consequence of the investigation of the normal and traumatic
occurrence of resin canals in the wood of the Araucariineae, living
and extinct, the conclusion seems clear, that this tribe of conifers
once possessed ligneous resin canals as a normal feature and there is
thus added one more argument for deriving them ancestrally from the
Abietineae and not directly from the Cordaitales, as is commonly held.
This view of the matter is strongly supported by the data described
in the previous article, in connection with the pitting of the tracheids
and the distribution of bars of Sanio. It is likewise confirmed by the
evidence as to the ancestral character of the ray structure in the
Araucarian tribe, which strongly resembled that found in the Abie-
tineae, past and present. The ancestral occurrence of wood paren-
chyma in the Araucarian tribe is likewise a strong argument against
their immediate connection with the Cordaitean forms and indicates
that they in common with the conifers in general, with diffuse wood
parenchyma are of relatively recent origin compared with the Abie-
tineae, which in so many ways show themselves to be a very ancient

group.
SUMMARY.

1. Certain Mesozoic woods from the Jurassic and Cretaceous,
showing traumatic resin canals are of Araucarian affinities.

2. This is shown to be the case by the structure of their tracheids,
both as regards pitting and the absence of cellulose bars of Sanio.

3. Abietineous pitting in the rays of extinct conifers is not in itself
a character of sufficient constancy to serve as a reliable diagnostic
feature, since pitting of this type can readily be produced as the result
of injury and moreover is often normal in the more conservative
parts of living representatives of the Araucariineae.

4. Normal resin canals occur embedded in the primary xylem of
the traces leading to the abortive cone-scales attached to the peduncu-
lar region of the cone of Agathis Bidwillu.

5. This fact taken together with the traumatic phenomena pre-
sented by certain Mesozoic Araucarian woods, supplies an additional
argument for the derivation of the Araucariineae from an Abietineous
ancestry.

‘,

Fig. a.

Fig. ὃ.

PLATE 7.

Transverse section of the wood of Brachyorylon notabile, showing
wound resin canals. Χ 40.

Another section of the same showing traumatic resin canals more
remote from the wound. Χ 40

Transverse section of the wounded stem of Araucariopitys ameri-
cana, showing wound resin canals. Χ 100.

Transverse section of a wood from the English Jurassic, showing
traumatic resin canals. Χ 40.

Longitudinal section of the same. Χ 40.

Tangential section through the wood of the peduncle of the cone of
Agathis Bidwillii, showing the presence of a normal resin canal in
the vascular supply of the cone-seale. Χ 100.

PLATE 7

JEFFREY-ARAUCARIOXYLON TYPE.

paw,

--%9 am, @

XLVIII

ARTS AND SCIENCES VOL.

CONTRIBUTIONS FROM THE PHANEROGAMIC LABORATORIES
OF HARVARD UNIVERSITY. NO. 58.

THE HISTORY, COMPARATIVE ANATOMY AND EVOLU-
TION OF THE ARAUCARIOXYLON TYPE.

By Epwarp C. JEFFREY.

Part IV.

The present article will be devoted to the consideration of the
structure of the pith and the relations of the foliar trace in woods of
the Araucarioxylon type and nearly allied Araucarian lignites. Gothan
in his second memoir on arctic woods, which deals with the fossil
ligneous remains of the island of Spitzbergen, makes the statement
that the Cretaceous fossil, which the present writer has described under
the name Araucariopitys *? and considered on the basis of its general
organization to belong to the Araucarian alliance, cannot be so referred
on account of the abietineous character of its rays and on account of
the sclerotic septa in the pith, a character in his opinion likewise ex-
clusively Abietineous.*? The writer has shown in the first article of the
present series, that the presence of Abietineous rays is by no means
necessarily an indication of Abietineous affinity, especially in the case
of Mesozoic woods. It will be his aim to demonstrate in the present
communication that sclerotic diaphragms in the medullary region are
equally fallacious criteria of Abietineous affinities. Professor Seward
has adduced the persistent leaf trace of the living genera Agathis and
Araucaria and of true Araucarioxyla from the Mesozoic deposits, as
an argument for the antiquity of the Araucariineae and for their
relationship with the extinct Lycopodiales, which he considers like-
wise as characterized by leaf-traces persistent for a long time in the
secondary wood. The writer will attempt to show in the present article
that on generally accepted biological principles the leaf trace was not

42 Jeffrey, Araucariopitys, a new genus of Araucarians, Bot. Gazette 44, pp.
435-444.

43 Gothan, Die Fossilen Holzreste von Spitzbergen, Kung. Svensk. Veten-
skap. Handlingar, Bd. 45, No. 8, Uppsala u. Stockholm (1910).

564 PROCEEDINGS OF THE AMERICAN ACADEMY.

primitively persistent in the Araucarian stock and consequently can-
not be used as an argument for their antiquity or their affinity with
any other group in which the persistence of the foliar strands is a
feature of structure in the wood.

Figure a, Plate 8, illustrates a transverse section of a well preserved
Araucarian trunk from the Raritan Cretaceous of Kreischerville,
Staten Island, N. Y., which has been described by the author under
the name Araucarioxylon noveboracense.** Through the center of the
figure vertically passes the leaf trace. The annual rings are scarcely
curved at all, showing that the stem was one of considerable thickness,
its age in fact being somewhat over fifty years. This persistence of
the leaf trace seems to be a characteristic of all woods of the true
Araucarioxylon type and as has been particularly indicated by Dyer *°
and Seward,*® is likewise a feature of the trunks of the living genera
Agathis and Araucaria. Throughout the wood of the figure may
be seen numerous dark dots, indicating the position of the true resini-
ferous parenchyma, which as has been pointed out in the first article
of this series, seems to have been a constant feature of structure in
the true Araucarioxyla of the Mesozoic, and which interestingly
enough persists as a vestige in the wood of the cone, first annual ring
of vigorous branches and the root of the living genera Agathis and
Araucaria. Woods of the Araucarioxylon type in the stricter sense,
have been described recently by Lignier from the Middle and Upper
Jurassic of France.*”? They are exceedingly common in the Cretaceous
both of Europe and America.

In addition to the true Araucarioxylon type, there exist, particu-
larly in the Cretaceous, woods in which the pitting and general struc-
ture of the tracheids, although unmistakably Araucarian, present
certain features of divergence from those properly included under
the generic appellation Araucarioxylon. These are pitting not in-
variably flattened or alternating and the presence of wound resin
canals in connection with injuries. These woods are further char-
acterized by rays which are frequently of the Abietineous type
after injury. Another interesting feature of these woods is the fact
that the leaf-traces, instead of being persistent as is the case with the
living genera Agathis and Araucaria, endure only for a very short

44 Hollick and Jeffrey, Cretaceous Coniferous Remains from Kreischerville,
Mem. N. Y. Bot. Garden, 3

45 iia a ag of Leaf traces in Araucarieae, Ann. Bot. 15, pp. 547 (1901).

46 Op. cit.

47 Lignier, Végétaux Fossiles de Normandie, IV. Bois Divers, Ire. Série,
Caen (1907).

JEFFREY.— ARAUCARIOXYLON TYPE. 565

time, a few years at most. The writer has discussed and figured
woods of this type in a memoir on the Coniferous remains found at
Kreischerville, Staten Island.*® It is accordingly unnecessary to do
more than call attention to their characteristic features here. It has
been pointed out in the second article of this series that peculiarities
of pitting and other features, found in Mesozoic woods of this type,
to which the writer has given the generic name Brachyoxylon, are
likewise found in the seedling axis and the cone axis of the living genera,
Agathis and Araucaria. In Agathis the Brachyoxylon type of pitting
persists for very many years in the basal region of the seedling. It
has occurred to the writer that since the older less typically Araucarian
mode of pitting persists in the seedlings and cones of the living genera
of the Araucarian conifers, that the evanescent leaf traces, which are
likewise a feature of the Brachyoxylon type of wood as contrasted with
the persistent ones of the Araucarioxylon type, might be found in the
seedling axis of Agathis and Araucaria, in accordance with the general
biological law of recapitulation. An examination of the facts resulted
in a very gratifying realization of this theoretical expectation. Figure
b, Plate 8, shows a tangential section through the epicotyledonary
region of the seedling stem of Agathis australis, material of which was
obtained by Messrs. Eames and Sinnott, Sheldon Traveling Fellows
of Harvard University, ona journey to the Australasian region. In the
center of the figure are seen two leaf traces in transverse section. Of
these one is better developed than the other. The smaller one is
about to disappear. Figure c, Plate 8, shows a section of the same
stem a little farther out. The trace which shows smaller in Figure ῥ,
has now completely disappeared and the persistent one has become
much reduced in size. A serial examination of sections showed that
the leaf trace came off as a single strand from the region of the pro-
toxylem of the stem and after passing out a very short distance divided
into two. The double strand thus produced is of very short duration
and finally disappears in both its divisions in the third or fourth annual
ring. As one passes up the seedling stem, the leaf traces are seen
to become more and more persistent until they reach a condition of
permanency like that characteristic of the older stem. It is clear
from the facts described that the leaf trace of Agathis, so far as A.
australis is concerned at any rate, in the seedling is an evanescent
structure and only becomes permanent later in life. The conditions
are comparable in fact mutatis mutandis, with the conditions found

48 Hollick and Jeffrey, Coniferous Remains of Kreischerville, Mem. N. Y.
Bot. Garden, 3.

566 PROCEEDINGS OF THE AMERICAN ACADEMY.

in the seedling of our only deciduous occidental conifer the larch, for
here in the seedling the leaves are persistent for two or three years and
only gradually become annually deciduous. There can be no doubt
that in the case of the larch we have to do with a tree, which
originally had evergreen leaves, as is the case with the other conifers,
and that its seedling perpetuates that condition. Vice versa in Agathis
we have to do with a coniferous genus, which originally had its leaves
moderately persistent as in conifers in general and that only later did
the extreme condition of persistence of the leaf trace found only
among living conifers in the mature stems and lateral branches of
the genera Agathis and Araucaria, become established. It is to be
emphasized then as a result of the examination of the seedling
anatomy of Agathis that not only the pitting of the older Mesozoic
type Brachyoxylon persists in the seedlings of the living genera but
also the evanescent character of the foliar trace. Seedlings of
Araucaria Bidwillit were examined with similar results, the only
difference being that the leaf traces here are somewhat more per-
sistent in the lower region of the cotyledonary stem than they are in
Agathis. It appears unnecessary to furnish further illustrations,
since the facts seem to be so conclusive and so much in accord with
the natural theoretical expectation.

Having made it clear that both the anatomical conditions found
in the older Mesozoic woods of Araucarian affinities (Brachyoxyla)
and the developmental data supplied by the seedlings of the modern
forms, vouch for the fact that the persistent leaf trace characteristic
of the woody cylinder of the living genera of the Araucariineae and of
woods of a similar type from the Mesozoic, (true Araucarioxyla) is not
an ancestral feature of the stock, and consequently not phylogeneti-
cally important, we may appropriately pass on to the consideration
of the pith in the primitive Araucarian type, in connection with the
affinities of the Araucarian stock.

Figure d, Plate 8, illustrates the structure of the pith in the stems,
the wood of which has been described by the author under the appella-
tion Araucarioxylon noveboracense.*9 At quite regular intervals the
pith is characterized by the presence of lighter bands, which represent
regularly recurring transverse diaphragms of sclerotic tissue. Figure
e, Plate 8, illustrates the same feature in the pith of an undescribed
and different species of Araucarioxylon from the Raritan Cretaceous
of Cliffwood, New Jersey. Sclerotic diaphragms appear at intervals

49 Op. cit.

τ =.

O_O

JEFFREY.— ARAUCARIOXYLON TYPE. 567

in the pith and often occupy a somewhat oblique position. Figure f,
Plate 8, shows a portion of one of these somewhat more highly magni-
fied. The contrast between its organization and that of the ordinary
tissues of the pith can clearly be made out. In the memoir on the
Conifers of Kreischerville, the writer has called attention to the very
frequent occurrence of medullary septa of a sclerotic nature in the
pith of branches not only of the Brachyoxylon type, but also of the
probably still older type, to which the name Araucariopitys has been
applied. It is interesting to consider the organization of the pith
in the two Cretaceous Araucarioxyla described above. They have
the same tendency to form sclerotic diaphragms. Gothan in a recent
memoir on the fossil woods of Spitzbergen 59 has questioned the accu-
racy of the writer’s reference of the genus Araucariopitys to Araucarian
rather than to Abietineous affinities, because he thinks it impossible
that an Araucarian conifer should have the pith structure and ray
structure, which so far as living representatives of the Coniferales are
concerned is more characteristic of the Abietineae than of the Arau-~
cariineae. It is clear that conclusions as to affinities can only be
safely drawn after a full and accurate comparison of Mesozoic and
living forms. Most of the results of structural paleobotany, in the
case of Mesozoic conifers at any rate, are vitiated by a neglect of this
absolutely necessary precaution.

The writer has not observed the presence of true sclerotic diaphragms
in either the seedling stem or the cone-axes of any living Araucarian
species. Isolated stone cells are typical of Araucaria, and sclerotic
nests which never become so extensive as to constitute true dia-
phragms are found in Agathis.

It appears to be definitely established from the data supplied in
the present article that persistent leaf traces cannot in the future be
regarded as an infallible diagnostic of Araucarian woods. It seems
further clear that foliar traces of this type are not a primitive feature
of Araucarian woods, since they are not characteristic of the seedling
structure of living representatives of the Araucariineae, and are not
found, in what we must regard on the basis of a great many concurrent
lines of evidence, as the older Araucarian types, namely Brachyoxyla
and woods of the organization of Araucariopitys. It is moreover ob-
vious that medullary diaphragms are equally characteristic of both
the older Araucariineae and of the Abietineae living and fossil. Their
presence in older Araucarian types, is consequently one more piece

50 Op. cit.

568 PROCEEDINGS OF THE AMERICAN ACADEMY.

of evidence in favor of the derivation of the Araucarian tribe from
Abietineous ancestors.

Having in the present article and those which have preceded it,
considered a number of anatomical features presented by the Arau-
carioxylon type and by the living genera with the same type of wood,
we are in a position to discuss its affinities and evolutionary develop-
ment. It has been pointed out in the first article that there is the
best of evidence, derived from both fossil and living forms, that woods
of the Araucarioxylon type were originally characterized by the pos-
session of strongly pitted rays and abundant wood parenchyma.
These features are quite inconsistent with a direct connection of this
type with the Cordaitean plexus of gymnosperms, since here, we know,
-that the wood was entirely without wood parenchyma and the rays
were composed of cells with unpitted walls. Passing to the next
important item of wood structure, we find that there is every reason
to believe that the older Araucarian conifers were not characterized

“by alternating or compressed pitting. On the contrary the radial
pits were often opposite and moreover were separated from one another,
particularly towards the ends of the tracheids, by cellulose bars im-
bedded transversely in the lignified wall of the tracheids. Bars of
this type do not occur in any Cordaitean woods but are found in the
mature wood of all existing Conifers, except the living Araucartineae.
It follows that on the basis of pitting and the cellulose bars of Sanio,
the Araucarian conifers were derived from the same ancestors as the
remaining coniferous tribes. It is further clear both from a considera-
tion of comparative anatomy and from the organization of the older
woods belonging to the Araucariineae, that the absence of resin canals
is not a primitive feature of Araucarian woods, since the progenitors
of the stock clearly possessed them. The present article appears
moreover to make it clear that persistent leaf traces are not an an-
cestral feature of organization of the Araucarian stock, both the
anatomical conditions found in the older forms and in the seedlings
of the living genera, showing beyond any reasonable doubt, on gen-
erally accepted biological principles, that the leaf strand in the ances-
tors of the Araucarian stock, persisted only for a few years, as is
characteristically the case in all other living conifers.

It is apposite to consider if other facts justify the conclusion reached
in connection with the present investigation, namely that the Arau-
carian stock is distinctly coniferous and is neither the most ancient
tribe of the Coniferales, nor connects them with those ancient Gymno-
sperms, which the majority of competent morphologists regard as

JEFFREY.— ARAUCARIOXYLON TYPE. 569

the ancestors of the coniferous stock, namely the Cordaitales. Taking
first the very important criterion from the standpoint of the systema-
tic arrangement of the Coniferales, the organization of the female
cone, we find little to justify the recent contention of Professor Seward
and his students and of Mr. Thomson, that the ovulate cone of the
Araucarian conifers is of a different morphological order from that
characteristic of the remaining coniferous tribes. It is perfectly
clear that not only in the more primitive species of the living genus
Araucaria but also in the cones of the Mesozoic representatives of the
Araucariineae, described by the present writer either independently
or in collaboration with Dr. Arthur Hollick, that the Araucarian female
cone, like that of the other tribes of conifers was originally composed
of cone-scales with a double system of bundles, independently ema-
nating from the cone axis and of inverse orientation. Consequently
whatever explanation is adopted for the double system of bundles in
one case must be adopted in all. Attempts to read the Araucariineae
out of the conifers must continue so long as the view is adhered to that
they represented the primitive elaboration of the coniferous stock. It
is a noteworthy fact that Professors Penhallow and Seward as well as
Mr. Thomson, who much as they disagree in other matters are in
harmony in regarding the Araucariineae as distinct from other conif-
erous tribes and at the same time as the primitive representatives
of the stock. The recent investgations of Mr. A. J. Eames 51 appear
to make it perfectly clear that whatever explanation is adopted of the
organization of the female strobilus in the Araucariineae, must hold
likewise for all the remaining tribes of Conifers.

If we turn our attention now to the gametophytes, we arrive at
similar conclusions, if our logical processes are based on the established
principles of biological science. Taking first the male gametophyte,
we find a method of germination of the microspore unlike that found
in any other gymnospermous group, which has been inaptly denomi-
nated by Mr. Thomson as ‘protosiphonogamic.’ Certainly we would
not expect to find the primitive type of pollen tube formation in a
group in which the pollen no longer reaches the apex of the ovule,
as it characteristically does in all other known groups of Gymno-
sperms, living and extinct. The peculiar germination of the pollen
of Agathis and Araucaria, on the cone scale and not on the apex of
the young seed is an unmistakable stigma of aberration. The con-
tents of the pollen tube likewise vouch for the highly specialized con-

51 Ann. Bot. Jned.

570 PROCEEDINGS OF THE AMERICAN ACADEMY.

dition of the Araucariineae. Here the two prothallial cells common
to the Abietineae and the equally ancient Ginkgoales become prolifer-
ated into a large number, doubtless in correlation with the extreme
length and meandering course of the fertilizing tube. Moreover
the absence of a stalk cell in connection with the setting off of the body
cell, which gives rise to the two sperm cells, is a clear and outstanding
feature of aberrancy. Mr. Eames in the memoir, already cited, has
shown moreover, that in the organization of the female gametophyte,
the structure of the archegonium, the nature and functions of the
archegonium neck, as well as in the method of penetration of the pollen
tube and the development of the embryo, the Araucarian conifers
manifest not a primitive but an extremely aberrant condition. They
are in fact comparable to a large degree in their systematic position
with the edentate fauna, likewise characteristic of the antarctic region,
Developmental investigations on the zoological side have recently
shown that the edentulous features which have been until the present
time regarded as a primitive feature of this group are in reality marks
of aberrancy, since a more abundant dentition, at first makes its
appearance in the embryo.

Reviewing all the evidence in the light of many recent investigations
both in general morphology and in the morphology of the conifers in
particular, it is clear that it is the anatomical features of the repro-
ductive and vegetative organs, which give us the most reliable criteria
as to the evolution of the coniferous stock and above all in the present
connection, as to the evolution of the Araucarian tribe. The ana-
tomical conditions in the living forms cannot be understood without
careful comparison with the organization of those which are now
extinct. Basing our conclusions on these criteria, the result is reached
that the Araucarioxylon type has been derived from the Pityoxylon
type and as a consequence formerly possessed the opposite pitting,
the bars of Sanio, the strongly pitted rays and the resin canals of the
ancient Abietineous woods. Some of these characters are still to be
observed in primitive regions of the existing Araucariineae, while
others are to be inferred from a consideration of the organization of
Araucarian forms now extinct. It is further clear that the external
form of the reproductive structures and the organization of the
gametophytes supplies as little light, regarded independently from the
anatomical organization of the reproductive and vegetative parts,
for the interpretation of the true course of evolution and affinities
of the ancient but highly aberrant coniferous tribe, the Araucariineae
as is the case with the corresponding structures in the Bennettitean

JEFFREY.— ARAUCARIOXYLON TYPE. 571

tribe among the Cyeadophyta. It is finally clear that morphologists
will find it necessary in the future more and more to adopt certain
general working principles, as in the case for example in the sister
sciences of chemistry and physics. If there prove on trial to be no
generally applicable fundamental principles in morphology, that branch
of biological science cannot be too soon east into the outer darkness,
which prevails outside the scientific view of nature.

GENERAL CONCLUSIONS.

1. The Araucariineae cannot have been derived from the Cordai-
tales since they possessed primitively a number of features which
so far as our knowledge goes, never existed in the Cordaitean stock.

2. The Araucarioxylon type is derived from ancestral forms,
which possessed opposite pitting, bars of Sanio, strongly pitted rays
and horizontal and vertical resin canals.

3. The primitive existence of these features in the ancestral type
from which Araucarioxylon has been derived, show clearly that it has
taken its origin from the Abietineous Pityoxylon type.

4. This conclusion is entirely confirmed by a consideration of the
reproductive structures both sporophytic and gametophytic.

5. Any hypothesis as to the origin of the Coniferales in general
must start with the Abietineae as the most primitive tribe.

6. It is absolutely essential to the progress of plant morphology,
that investigation be carried on in connection with the elucidation of
the general working principles of the biological sciences.

7. The comparative, developmental, paleobotanical and experi-
mental investigation of the Coniferales is likely to throw more light
on the stable and sound general principles of biology, than that of
any other large group of animals or plants, on account of their great
geological age and remarkably continuous and complete display, both
as regards external form and internal structure in the strata of the
earth.

BoTANICAL LABORATORIES OF HARVARD UNIVERSITY,
17th, June, 1912.

Fig. a.

Fig. b.
Fig. 6.
Fig. d.

Fig. e.

Fig. f.

PLATE 8.

-

Transverse section of the wood of Araucarioylon noveboracense,
showing the persistent leaf trace. Χ 15.

Tangential section of the seedling stem of Agathis australis. X 60.
Another of the same further out in the wood. X 60.

Longitudinal section through the pith of a trunk of Araucarioxylon
noveboracense. X 8.

Longitudinal section of an undescribed species of Araucarioxylon
from New Jersey, showing the region of the pith. Χ 15.

Part of the same more highly magnified. Χ 40.

PLATE 8

y-ARAUCARIOXYLON TYPE.

[Ὁ

JEFFR

XLVIII

Proc. AMER. ACAD. ARTS AND SCIENCES VOL.

Proceedings of the American Academy of Arts and Sciences.

Vou. XLVIII. No. 14.—Janvary, 1913.

THE ACTION OF SULPHUR TRIOXIDE ON SILICON
TETRACHLORIDE.

By CHARLES ROBERT SANGER AND EMILE RAYMOND RIEGEL.

THE ACTION OF SULPHUR TRIOXIDE ON SILICON
TETRACHLORIDE.!

By Cuartes Ropert SANGER AND EMILE Raymonp Rieae..}

Presented by ©. L. Jackson, November 13, 1912. Received, October 24, 1912.

THE reaction between sulphur trioxide and carbon tetrachloride
yields phosgene and pyrosulphury] chloride.”

28503 + CCl, = COC], ΒΒ S.05Cle

Since the two elements carbon and silicon resemble each other so
closely, it was reasonable to suppose that a similar reaction might take
place if silicon tetrachloride were substituted for the carbon tetra-
chloride. In order to test this, or to find out what reaction, if any,
took place, this research was undertaken.

The only reference to the subject we can find in the literature is the
following note of Gustavson, quoted in extenso:

_ “Silicon tetrachloride gives with sulphur trioxide pyrosulphuryl
chloride.” ὃ
This information Dammer * enlarges into the following reaction:

4S03 + SiCl, = 28:05Cl: + SiO,

Our investigation showed that on mixing pure melted sulphur tri-
oxide and silicon tetrachloride, there is at first mere solution, but on
standing, a reaction takes place, exceedingly slowly in the cold, but
more rapidly at about 50°, resulting in the formation of a liquid which
when freed by distillation from the unchanged materials boils between
135° and 150° at atmospheric pressure, whereas sulphur trioxide and
silicon tetrachloride boil below 60°. This distillate fumes weakly in

1 This research was suggested by the late Professor C. R. Sanger and most
of the work was done under his direction, until he was prevented by illness
from continuing its supervision, when Professor T. W. Richards took charge
of it. The material was prepared for publication with the aid of Professor
C. L. Jackson after the lamented death of Professor Sanger, who is therefore
in no way responsible for its arrangement or presentation. Iam very grateful
to Professors Richards and Jackson for their respective aid. E.R. R.

The work described in this paper formed part of a thesis presented to the
Faculty of Arts and Sciences of Harvard University for the Degree of Doctor
of Philosophy by Emile Raymond Riegel.

2 If water is present, a certain amount of chlosulphonic acid is formed, very
nearly proportional to the quantity of water. See Sanger and Riegel, These
Proceedings, 47, 673 (1912); Zeit. anorg. Chem., p. 79 (1912).

8 Ber., 1872, 5, 332.

4 Dammer, Inorg. Chem. 1, 667.

576 PROCEEDINGS OF THE AMERICAN ACADEMY.

moist air and reacts violently with water; it contains sulphur,
chlorine, silicon, and oxygen, and the indefiniteness of its boiling point
indicates that it is a mixture. We have not succeeded in isolating the
substances of which it is composed, although we tried every way we
could devise. Nevertheless we are convinced that it is made up of
pyrosulphury] chloride 5260]. and silicon oxychloride Six0Cls, because
all our complete analyses of well-established specimens give percent-
ages corresponding to such a mixture; that is, if the amount of sulphur
found is assumed to be present as pyrosulphuryl chloride, and the
amount of chlorine corresponding to the sulphur in that compound is
calculated, the difference between the total chlorine and this amount
agrees well with the chlorine necessary to form silicon oxychloride with
the silicon found; thus out of 18 analyses, it agrees in 8 cases within
1 percent, in 5 other cases within 2 percent, in one more case within
2.5 percent. The four remaining analyses gave results which did not
agree, but this is satisfactorily explained, for these are analyses of frac-
tions boiling at higher temperatures than the usual one, namely above
150°, indicating the presence of other substances. These analytical re-
sults are confirmed by other observations. A specimen distilled from
a heavy gelatinous residue of silicic acid gave results on analysis differ-
ing by only 1.8 percent on the sulphur, and 4 percent on the chlorine
from pyrosulphuryl chloride, showing that that substance had been
formed; another distilled from a large excess of phosphorus pentoxide,
melted at —40° to —50° and crystallized in radiating crystals like pyro-
sulphuryl chloride which melts at —37°, showing its presence again;
a third, distilled from an excess of sodium chloride gave analytical
results indicating a more impure pyrosulphuryl chloride. It seems
therefore that heating the liquid with a large excess of any solid dis-
poses of most of the silicon oxychloride, but reveals the presence of the
pyrosulphuryl chloride.

The boiling point of the distillate, 135-150°, is what would be ex-
pected of a mixture of pyrosulphury] chloride and silicon oxychloride,
for the former boils at 152.5°-153°, and its boiling-point may be low-
ered 5-10° by a minute amount of water, and the latter boils at 136-
139°. The boiling-point of the mixture is not changed by the addition
of one fifth of its weight of pyrosulphuryl chloride. If a great deal of
water is added to the original distillate a violent reaction attended with
the formation of silicic acid takes place such as would be expected from
silicon oxychloride and a heavy liquid separates at the bottom of the
vessel, dissolving but slowly. This is the behavior of pyrosulphuryl
chloride or of sulphuryl chloride, but the latter is excluded by the

SANGER-RIEGEL.— SULPHUR TRIOXIDE-SILICON CHLORIDE. 577

boiling point of the mixture, hence it must be the former. Chlor-
sulphonic acid, the only other compound of sulphur which might be
expected, and then only in those preparations in which hydrous
sulphur trioxide was used, was found to be absent by a distillation with
salt, when only a very small amount of hydrochloric acid was given off.

It appears from these observations that silicon tetrachloride does
not behave like carbon tetrachloride with sulphur trioxide, the
principal reaction being represented as follows:

2SO3 + 2SiCl, — S.0;Cl. + SOC], (1)
If it did behave like carbon tetrachloride, the reaction would be:
2SO03 + SiCl, = S.OsCl, + SiOCI.

We base our contention that SiOClk, the unknown oxychloride of
silicon which would be analogous to phosgene, and might therefore be
called silico-phosgene, is not formed on the fact that all the properties
of the silicon compound resulting from the reactions point to the oxy-
_ chloride, SixOCle; furthermore, on the analyses, and on our failure to
find the silico-phosgene in the lower boiling fraction, where it would
be expected. The liquid distilled from the reaction mixture below
130° gave on distillation sulphur trioxide vapors, a mixture of sulphur
trioxide and silicon-tetrachloride, an almost pure silicon tetrachloride
which was on several occasions re-distilled and found to boil at 56-58°,
its true boiling point being 57°, and a little of the higher boiling frac-
tion. In the distillation in vacuo, a vessel cooled with liquid air was
added to condense any silico-phosgene, but nothing was found there
beyond silicon tetrachloride and sulphur trioxide. The weights of the
various condensations and residues were always noted; their nature
being established as either unchanged substances, or as the mixture
of oxychloride and pyrosulphury1 chloride, nearly all the material was
accounted for (thus in one case 94%), so that no considerable amount
was left which might have formed the silico-phosgene. In nearly
everyone of the twenty-six preparations made the proportions taken
were those of two molecules of sulphur trioxide to one of silicon tetra-
chloride, favoring the reaction 2503+ 5160], = SiOCl, + S,OsCh;
nevertheless every fact points to the formation of silicon oxychloride,
and none to that of silico-phosgene. That silico-phosgene is unknown
also speaks against the likelihood of its formation in this reaction.

In three cases distillates were obtained which were not very far re-
moved from a mixture of the two products in molecular proportions,
as required by reaction (1), but in most cases there was a decided excess

578 PROCEEDINGS OF THE AMERICAN ACADEMY.

of the pyrosulphury] chloride, especially if the preparation had been
allowed to stand some time, in one case three summer months. This
excess may be formed by the following reaction:

as a considerable amount of silica is deposited during the standing.
It follows from our work that the reaction constructed by Dammer
on Gustavson’s meagre statement

4503 + SiCl, = 25205Cle + SiO»
is incorrect, inasmuch as there is formed at first the oxychloride:
2SO3 + 2516], = S,OsCle + SiOCl,s (1)
and only by a secondary reaction, silica,
SixOCl, + 6SO3 = 258102 + 35205 Cle

By combining the two reactions that given by Dammer is indeed
obtained, but (2) takes place only to a limited extent and always
follows (1). To give Dammer’s equation alone would be misleading;
the two separate equations (1) and (2) must be given and explained.

There is some evidence that the distillate contains a loose compound
of pyrosulphury! chloride, S:0;Cl, and silicon oxychloride, SizOCI.,
formed under the influence of heat. The distillate did not freeze
unaided above —78°, except in a single case, while a mixture of equal
parts of the two substances crystallized easily on cooling and melted
at —40° to —38°. Itis astonishing that this mixture melted at about
the same temperature as its constituents, S,O;Cl, melting at —37°,
SipOCl, at —40°. A mixture of 15.6 grams of S,0;Cl with 5.2 grams
SizOCl¢, which therefore had about the same composition as one of our
distillates crystallizing at — 78°, was divided into two parts, one of which
was heated for 5 minutes in the Bunsen flame; on cooling the two in
the carbon dioxide-alcohol mixture, the portion which had been heated
took 20 times as long to begin to solidify as the unheated one. This
could hardly be accounted for unless the supposition was made that
the two substances had combined under the influence of heat. The
assumption of such a compound does not interfere with the other ob-
servations made, thus the boiling point might remain that of mixed
silicon oxychloride and pyrosulphury] chloride, because the compound
between the two is too weak to exist in the state of vapor, a recombina-
tion, however, taking place as they return to the liquid phase; the
formation by distillation of nearly pure pyrosulphuryl! chloride took
place only when the temperature was raised much higher than usual,

SANGER-RIEGEL.— SULPHUR TRIOXIDE-SILICON CHLORIDE. 579

so that the compound would be decomposed, the silicon oxychloride
disappearing completely as such, leaving the pyrosulphury] chloride;
again the reaction of water on such a compound might well be a de-
composition into the components accompanied by the destruction of
the silicon oxychloride, leaving a part at least of the pyrosulphuryl
chloride to react more slowly, for it is less sensitive to water than the
oxychloride, as shown quantitatively further on. It must be added,
however, that all the distillate which gave distinctly the oily deposit
with water were low in silicon, and contained an excess of pyro-
sulphuryl chloride, so that all of the combined oxychloride and pyro-
sulphuryl chloride might have been destroyed, leaving only the free
pyrosulphuryl chloride to become visible. The assumption of this
compound explains to perfection why the distillates nearing in percent-
age composition an equi-molecular mixture of the two substances did
not crystallize even after seeding with pyrosulphuryl chloride, while
the distillates low in silicon, containing an excess of pyrosulphury]l
chloride, which could exist free, crystallized readily under the same
conditions. Reaction (2) is not affected by this assumption, for it
takes place on standing at room temperature, or at the most at 50°, so
that the loose compound, for which we assume that a temperature of
about 130° is needed, is not formed. Our effort, however, was to
prove reactions (1) and (2) rather than study this subsequent com-
pound.

EXPERIMENTAL PART.

Materials: The commercial sulphur trioxide marked (Ὁ. P. contained
no impurities. In order to obtain a liquid at room temperature it
was melted for some experiments, for others the melted substance was
added to fuming sulphuric acid in the proportions necessary to give
solutions of various strengths which were ascertained by titration or
gravimetrically. The melting was done in a cylindrical copper air
bath built for the purpose, and this was extraordinarily easy with a
fresh sample;° a moderate temperature was required (about 50° in
bath), the melting was rapid, no clots formed in the center, and the
low temperature caused little boiling, hence little pressure, so that the
stopper could be left in place without danger; with an old sample on
the other hand the melting was almost impossible; so much heat was

5 Fresh sulphur trioxide melts at 17.7°; old samples do not melt at all,
but sublime; Knietsch, Ber., 34, 4101 (1901). Compare also Schenck, Lieb.
Ann. 316, 1 (1901); Weber, Ber., 19, 3187 (1886).

580 PROCEEDINGS OF THE AMERICAN ACADEMY.

needed that the small quantity which had melted boiled away before
any more became liquid.

Silicon tetrachloride was prepared by passing dry chlorine over
powdered silicon spread out in a hard glass tube, and heated in a com-
bustion furnace. An adapter at the end of the tube (the latter was
slightly inclined towards the former) fitting into a receiver set in ice,
completed the apparatus. Charges of 50 grams yielded 190 to 225
grams of silicon tetrachloride, that is, 64 to 75 percent of the theo-
retical yield. Special effort to obtain a large yield was never made;
on the contrary economy of time was the only consideration. In
this respect this method is ideal; the apparatus could be set up in a
few minutes, and a preparation carried through in an afternoon.”
The silicon contained iron, which caused the presence of ferric chloride
in the crude product; the latter also contained free chlorine. The
crude product was freed from chlorine by shaking with mercury and
was then distilled. It was kept in glass stoppered bottles under a
dry bell-jar, or the flasks were sealed off. The bottles were left in the
open at first, but the moist air caused a deposit of silica which cemented
the stopper in place, and such a bottle could only be opened by break-
ing it, when it usually exploded. Rubber stoppers were found more
satisfactory, but these hardened in time and also became cemented.
Bottles nearly empty and imperfectly closed to moisture exploded
spontaneously, because of the formation of hydrochloric acid.

Silicon oxychloride was prepared by the method of Troost and
Hautefeuille®, namely, by passing a mixture of chlorine and oxygen
over heated metallic silicon in the same apparatus as the one used for
silicon tetrachloride. The yield was very small; out of 154 grams a

6 Hempel and Haasy state that they used this method, but give no details.
Zeitschr. anorg. Chem., 23, 32 (1900).

7 In our earlier work the silicon tetrachloride was made by passing chlorine
over silicide of copper as done by G. H. Pratt (M. I. T. thesis, 1897, vol. 68;
in the hands of Vigouroux, C. R., 129, 334 (1899), this method did not give
satisfactory results) except that glass retorts were used instead of iron tubes,
but this method was much slower, less convenient, and gave a poor yield.

8 The melting point of silicon tetrachloride is —69° (corr.) It was deter-
mined several times on different samples, by the beaker method (see note 11)
and by complete immersion of the thermometer. W. Becker and J. Meyer
(Zeitschr. anorg. Chem. 48, 251 (1905)) give this point as—89°; they determined
it by winding a thermo-element on the outside of the containing vessel, while
this was suspended in a Dewar tube containing a little liquid air; the junction
was presumably at the bottom of the containing tube. Their material was
exceedingly pure, but the method used in obtaining the melting-point is open
to objection.

9 Bull. Soe. Chim., 35, 360 (1881).

ae

SANGER-RIEGEL.— SULPHUR TRIOXIDE-SILICON CHLORIDE. 581

yield of 5.5 grams of the oxychloride Siz0Cls was obtained, after several
fractionations. The greater part of the crude material was silicon
tetrachloride, besides some 35 grams of the higher oxychlorides. The
method was nevertheless better than that of Friedel and Ladenburg 19,
from which we obtained absolutely no yield. These five grams were
found to crystallize readily, melting at —41° to —38°, corr. by the
beaker method.14

Analyses: Rapid analyses for chlorine and sulphur were made vol-
umetrically. A small bulb containing a known weight was broken in
water; the solution made up to a definite volume and aliquot portions
used. As a rule part of the silica precipitated. The total acidity
was found by titrating against standard potassium hydroxide. The
effect of the silicic acid on the indicator (phenol phthalein) was not
to be considered, as the method was intended merely for following
changes in whole percentages. The chlorine was determined by the
Volhard method, with which the silver silicate does not interfere, for
it is readily decomposed by all strong acids.!*_ The acidity and the
chlorine content were expressed in terms of a normal solution; from
the difference the percentage of sulphur was calculated.

The accurate determinations were made as follows:

Silicon and Sulphur: A bulb containing a known weight was broken
in a freshly prepared solution of sodium hydroxide made from sodium,
and which had been shown to contain no silica, chlorine, or sulphur.
The solution was filtered from the pieces of glass into a platinum dish,
and acidified with sulphate-free hydrochloric acid.4? The analysis

10 Lieb. Ann., 147, 355 (1868); C. R. (1868) 66, 539; also Troost and Haute-
feuille, C. R. (1871) 73, 563; J. prakt. Chem., (2) 4, 304 (1871).

11 A rapid method for obtaining melting-points at low temperatures was
used. A small melting-point tube, as used in organic work, contains the sub-
stance already crystallized by dipping it in liquid air; this is placed in a
beaker containing naphtha which has been cooled by immersion in liquid air
also. By removing the latter, the bath is permitted to warm up until the sub-
stance melts; the temperature is read on a pentane thermometer calibrated
in the same way as it is used. A full description will be found in a previous
article, Proc. Am. Acad., 47, p. 699. It will be called the “beaker”? method.

In addition to this method the ‘‘immersion”’ method, in which the thermo-
meter is placed in the melting substance, after having been standardized for
that use, was employed whenever possible.

12 J. Ὁ. Hawkins, Am. Jour. Sc., 139, 311 (1890).

13 The time during which the alkaline solution was in contact with glass
varied between twelve and twenty-five minutes. In order to show that no
glass was dissolved, the pieces of glass from one of the bulbs were collected,
after the alkaline solution had been removed, and weighed:

Glass recovered 0.7458 gram.
“taken 0.7452 gram.

582 PROCEEDINGS OF THE AMERICAN ACADEMY.

was continued in the customary way, involving in the earlier analyses:
two evaporations with intermediate filtrations, and corrections with
hydrofluoric acid, but these corrections were found to be so small that
the accuracy desired did not justify the work necessitated by them.
Later therefore only one filtration was made, and the hydrofluoric
acid correction left out. In the filtrate from the silica, the sulphur
was determined as barium sulphate.

Chlorine: A bulb containing a known weight was broken in a solu-
‘tion of the sodium hydroxide. The liquid was filtered into a pre-
cipitating flask, and, after adding a drop of phenol phthalein, weakly
acidified with chlorine-free nitric acid; silver chloride was precipitated
from the clear solution, and weighed on a Gooch crucible.

In order to determine how much silica was carried down by the
precipitate, a sample of silicon tetrachloride was treated with sodium
hydrate, and the alkaline solution evaporated in a platinum dish; the
silica was removed, and the chlorine determined. It was found to be
83.3 percent. The same material was then analyzed without remoy-
ing the silica and there was found 83.6 percent of chlorine. Several
other determinations confirmed this result. The amount of inclusion
depends mainly upon the dilution at the moment of precipitation,
and upon the percentage of silicon in the substance. The dilution
was always made considerable, and while silicon tetrachloride contains
16.63 percent of silicon, the material analyzed contained one half to
one fourth as much. Therefore it seemed safe to assume that the
analyses had an accuracy of 3 parts in 1000, or 0.3 percent, which satis-
fied the requirement in this work.

Toe MIXxtTURES.

When sulphur trioxide was added to silicon tetrachloride they
mixed at once forming at 32° a clear colorless liquid, which after being
sealed and standing in the room deposited long white needles like those
of sulphur trioxide from which we inferred little or no reaction had
taken place, but after this liquid had been heated in an air bath to 50°
for 6 hours a reaction took place as shown by the formation of a product
boiling between 135° and 150° at atmospheric pressure, whereas sul-
phur trioxide boils at 46° and silicon tetrachloride at 57°. A con-
siderable deposit of silica also appeared in many of our experiments./*

14 Preliminary experiments tried by Mr. Maurice L. McCarthy led to the
formation of distillates similar to those described later.

SANGER-RIEGEL.— SULPHUR TRIOXIDE-SILICON CHLORIDE. 583

Solid sulphur trioxide did not dissolve in silicon tetrachloride and
liquid mixtures of the trioxide and fuming sulphuric acid containing
8 percent of water or less, did not mix with the tetrachloride, but such
hydrous sulphur trioxide solutions were made to react with it by shak-
ing the two for several hours (53 to 12) at room temperature, or better
still by directing a blast of air warmed to 50°, on the bottle while on
the shaker, when the mixing took place in less than an hour. The
product after distillation could not be distinguished from that obtained
from pure melted sulphur trioxide, except on analysis, when the former
was found to contain roughly 14 percent sulphur, the latter 21 percent,
and on cooling and seeding with pyrosulphuryl chloride, the latter
could be made to crystallize, but not the former. The reason is self-
evident, for in the former cases the water was combined with much of
the sulphur trioxide, reducing its concentration as such; in the latter,
the concentrations remained high, and reaction (2) could take place
to a sufficient extent to raise the amount of pyrosulphury] chloride.
The yield (50 percent in the best case) seemed to be better when no
water had been used in the sulphur trioxide, and when the proportions
were those of two molecules of sulphur trioxide to one of silicon tetra-
chloride; an excess of either reagent diminished the action.

This product was freed from the unaltered reagents by distillation
either at atmospheric or at reduced pressure. Its character and our
attempts to prepare a pure substance from it are best made evident
by the description of two of our most extended experiments.

101 grams of silicon tetrachloride were added to 100 grams of 93.8
percent sulphur trioxide, being 1 molecule of the former to 2 of the
latter, and after shaking 53 hours a pale brown homogeneous liquid
was formed which on standing over night deposited a flocculent pre-
cipitate and became colorless. 145 grams of the supernatant liquid
were distilled at 16 mm. pressure with two condensers inserted between
the receiver and the pump; the first was cooled by solid carbon dioxide
mixed with absolute alcohol, and was destined to collect sulphur
trioxide and silicon tetrachloride; the second was cooled by liquid
air, and could therefore condense hydrochloric acid besides any
material escaping the first tube.1®5 76 grams were collected at 42°
to 70°. The tube at —78° contained 9 grams, the liquid air tube.
19.5 grams. These were silicon tetrachloride and sulphur trioxide
In the subsequent distillations a single condenser cooled by liquid air

15 For description of the kind of tube used in the liquid air, see Sanger and
Riegel, These Proceedings, 47, 697.

584 PROCEEDINGS OF THE AMERICAN ACADEMY.

was used. A hard residue which weighed 32 grams, was left in the
boiling flask.

The 76 grams were distilled again. The material condensed by the
liquid air was 1.7 percent of the weight taken, the residue in the flask
also 1.7 percent. The 72 grams collected were distilled once more;
70.7 grams were obtained. In this third distillation, the more volatile
matter was less than 0.15 percent, the hard residue in flask 0.5 percent.
The material distilled at 49° to 70° with a pressure of 17 mm.; the
highest temperature of the bath was 120°, the time thirty minutes.
The distillations showed that the 76 grams contained no silicon tetra-
chloride, no sulphur trioxide, and no considerable amount of dissolved
or suspended silica; an analysis showed the presence of 17.2% S and
49.3% Cl; the silica was not determined. No crystals could be
formed, but the material congealed at —120°. This behavior sug-
gested impure chlorsulphonic acid; so in order to determine whether it
was present or not, 65 grams of the substance were treated with 40
grams of common salt.!® (22 grams would have been required if all
the sulphur found by analysis had been present as chlorsulphonie acid,
hence the enormous excess would be expected to retain mechanically
a great deal of the liquid). On adding the salt, no bubbling of hydro-
chloric acid gas occurred, as is always the case with chlorsulphonic
acid; a distillation at low pressure gave 43.5 grams of distillate. In
the liquid air condenser there were 3 grams of a liquid which were
undoubtedly uncondensed distillate and hydrochloric acid. The large
distillate, accompanied by the insignificant amount of hydrochloric
acid,” established the absence of chlorsulphonic acid as an essential
part of the liquid. The composition was

5 Si ΟἹ
(1) 16.9% 9.4% 53.3%

not markedly different from that of the liquid before treatment with
salt. Nevertheless in subsequent mixtures a distillation from salt
was frequently performed, in order to remove even the smallest amount
of chlorsulphonic acid that might have been formed.

The 43.5 grams were distilled twice more, at low pressure, in an
effort to obtain a constant boiling-point, but in neither case was the
temperature steady; the best result was the second fraction in the

16 For this method of removing chlorsulphonic acid, see also Sanger and
Riegel, These Proceedings, 47, 689.

17 A portion of this hydrochloric acid was formed by the action of the vapors
on the rubber corks and connections.

Ans

SANGER-RIEGEL.— SULPHUR TRIOXIDE-SILICON CHLORIDE. 585

second distillation, which weighed 23 grams and boiled from 45.8°
to 48.2° at 11-13 mm. This material analyzed gravimetrically con-
tained:

5 Si ΟἹ
(2) 14.63% 10.20% 54.87%
(3) 14.50% 10.18%
1S,0;Cl.
+1Si,0Cl,
12.82% 11.31% 56 .69%

The composition of an equi-molecular mixture of pyrosulphury! chlo-
ride and silicon oxychloride is given above, and it can be seen that the
liquid gives similar figures.

Distilled at atmospheric pressure the temperature rose steadily
and evenly from 141° to 1505, No crystals were obtained on cooling.
To the distillate one fifth of its weight of pyrosulphury] chloride was
added, and it was then distilled again when the temperature readings
were unchanged. On cooling no crystals were formed; the material
congealed as before, below — 100°.

In our second extended experiment 236 grams of silicon tetrachloride
and 221 grams of melted anhydrous sulphur trioxide, that is, one mole-
cule of the former to two of the latter, were heated in the air-bath for
six hours at 50° and deposited 8 percent of a white solid. 205 grams
of the liquid poured off from this solid were distilled at ordinary pres-
sure and gave

90 grams at 37-44°
ΟΥ̓ Agee
Si rie 8 59 AS
BY ΠῚ τ΄ τροαπο:

(Sulphur trioxide boils at 46°, silicon tetrachloride at 57°). The third
fraction and the residue gave on a second distillation 20 grams at 135-
151° and 16 grams at 151-172°; these 20 grams did not crystallize on
cooling, and were therefore distilled again, and separated into four
fractions. The second one only, 6 grams collected at 137-145° (4, δ)
could be made to crystallize at —83°, melting at —50°; the remaining
three fractions were combined and distilled, the distillate being col-
lected in 3 portions, the middle one, 138-143° (8, 9) crystallized spon-
taneously; the lower one, 130-138 (6, 7), on stirring; the upper one,
143-176° (10, 11) only on seeding from the lower one. As none of
these fractions showed any signs of constant boiling-point, the crystal-
lization was studied further. For this purpose each fraction was

586 PROCEEDINGS OF THE AMERICAN ACADEMY.

introduced into a special separator!’, crystallized and the mother
liquor drawn off; the crystals were then allowed to melt, drawn off in
their turn, and analyzed. Only the fraction 138-143° was not sepa-
rated into crystals and mother liquor, because its amount was too
small.

8 Si ΟἹ
(4) 187-145° 21.37% 5.25% 43 68%
(5) 21 .33 5.45 43 .94
(8) — 138-143° 22 .88 4.4 41.65
(9) 41.68
(6) 136-188“ 21.9 4.9 43 .00
(7) 220
(10) 143-174° 22.73 5 .28 39 .74
(11) 22.89 5 .38
(12) Mother liquor 22 .97 5.19 39 .73
(13) οἵ crystals 39 .44

These analyses show that the fractional distillation gives little or
no promise of leading to a pure product as the percentages of sulphur
and silicon in the different fractions differ by 1.1 percent or less,
those of chlorine by 3.56 percent or less Nor is crystallization more
promising since there is essentially no difference in composition be-
tween the crystals (10, 11) and their mother-liquor (12, 13).

Another preparation similar to the last was allowed to stand for
three summer months in a glass stoppered bottle under a bell-jar
whose atmosphere was kept dry by phosphorous pentoxide; during
this time a solid amounting to 23 percent of the total weight was
deposited, and on distillation a fraction of 53 grams or 38 percent
boiling at 136-156° was obtained. This fraction when cooled to —78°
did not crystallize, but on inoculation with a crystal of pyrosulphuryl
chloride it did, so many crystals developing that it became a stiff
paste; this had been done in the separator, and after warming a little,
the mother liquor was drawn off; the process was repeated twice, the
melted crystals serving as starting material each time. After making
an analysis (14) of the final crystals, a portion of the original 53 grams
was taken and the crystallization was repeated, but this time with an
alcohol bath cooled to —65° and —60° instead of —78°, in order to
reduce the supercooling. The material was fractionally crystallized 4

18 Sanger and Riegel, These Proceedings, 47, 710. It consisted essentially
of a glass vessel holding a platinum cone, and connections above and below
so that suction might be applied below or above, all out of contact with moist
air.

SANGER-RIEGEL.— SULPHUR TRIOXIDE-SILICON CHLORIDE. 587

times, with a seed of pyrosulphuryl chloride, the separation taking
place in order at —65°, —60°, —60°, and —60°; the crystals thus
purified weighed 3.5 grams, and their analysis (15, 16) is given
below. The mother liquors were then combined, and a crystalliza-
tion from a silicon oxychloride seed attempted, but it failed, for only
at —78° could crystals be obtained, and at that low temperature,
crystallization was spontaneous; nevertheless, the crystallization was
repeated twice, and the final crystals analyzed (17). The analysis of
the original 53 grams is also given (18).

8 Si Cl
(14) 23.98% 3.7% 40.02%
(15) 24 .28 3°78 39.57
(16) 24 .03 3.85 39 38
(17) 23 .62 4.07 40.08
(18) 23 .26 4.90 41.61

The composition had not changed markedly; (14) has more sulphur
and less silicon than (18) which would point to a concentration of
pyrosulphuryl chloride; the fact that it crystallized at —60° rather
than at —78° also supports this assumption, but at —60° the super-
cooling is still considerable; (15) and (16) differ too little from (14) to
have a meaning, so that neither the analysis nor the crystallization
with pyrosulphury! chloride show that all the pyrosulphuryl chloride
is present as such. The failure of crystallization with silicon oxy-
chloride is reflected in the analysis (17) which hardly differs from (18)
the original material, showing that the silicon oxychloride is not present
free.

The experiments described above show why we did not succeed
in obtaining a pure substance from our product either by fractional
distillation or crystallization; an additional experiment might be
mentioned as having led to the same result. A preparation similar
to the previous one was fractionally distilled 5 times, at atmospheric
pressure, using a dephlegmator, and yielded two fractions boiling over
several degrees:

5 Cl
(26) 145-149° 15.3% 50.6%
(27) 149-157° iy Ae 50.7

But in spite of our failure to isolate the pure substances, our analyses
established the nature of the two compounds of which this mixture is
made up. For this discussion we have collected all the complete
analyses already given and all the others made by us in a table. Of

588 PROCEEDINGS OF THE AMERICAN ACADEMY.

the analyses not already given the product for (19) was made by
heating solid sulphur trioxide and silicon tetrachloride in sealed
tubes at 250°; when the tubes were opened there was no pressure,
showing that no gas was formed by the reaction. A fraction boiling
at 135-157° was purified by distilling it at a pressure of 1.5 mm., anda
product obtained boiling at that pressure at 29.5° to 34°. A prepara-
tion made almost like that of analysis (2) and (3) yielded a lower
fraction analyzed under (20) while a higher fraction which approached
pyrosulphury] chloride in composition and behavior will be discussed
later. Finally three analyses were made of fractions obtained from a
liquid similar to the preceding ones, but which had been treated with
water, in order to destroy if possible one of the constituents; one of
these fractions (21) was submitted to two distillations at low pressure;
another (22) was this preceding product after treatment with salt, .
in order to remove any chlorsulphonic acid which might have been
formed by the action of the water; the third (23) was collected from
the same flask, but after the temperature had been raised from 150°
to 210°, with the pressure still 20 mm., a degree of superheating almost
certain to cause decomposition, since the average boiling-point at such
pressures is below 100°. This action of the study of water will be re-
ferred to further on. ,

The percentages of chlorine marked “calculated” in the table were
obtained by computing the percentage of chlorine which would cor-
respond to the percentage of silicon in each analysis if this were pres-
ent as silicon oxychloride, SigOClg. The amount of chlorine was then
calculated which would be combined with the percentage of sulphur
if this was present as S,O;Cle, and subtracted from the percentage
of chlorine recorded by the analysis and the remainder entered as
“Found” in the table.

From this table it would appear that 13 out of the 18 analyses agree
within 2 percent, of the calculated amount of chlorine in a mixture of
pyrosulphuryl chloride and silicon oxychloride, and one more (18)
within 23 percent; moreover, among these 14, 8 agree within 1 percent.
Of the four which do not agree, all were analyses of fractions boiling
at higher temperatures than the average, 135-150°; thus (10) and (12)
at 143-174°, (22) at 52-110° with a pressure of 20 mm. and (23) over
110° with the same pressure, the oil-bath around the boiling flask being
finally at 210°. These high temperatures indicate that impurities
were present, as products of decomposition, or substances due to the
action of moisture from the air and of organic matter in the shape of
unavoidable rubber stoppers; there would seem to be sufficient ground

SANGER-RIEGEL.— SULPHUR TRIOXIDE-SILICON CHLORIDE. 589

TABLE OF COMPLETE ANALYSES.

Cl Cl

Calculated Found

5.3% |
38 .34
9
49
42
.84

85

---

μὰ

0.:
5.2%
5.
4.
4.
5.
ὃ.
3.
3.
3.
4.
4.
0.
6.
6.
6.
3.

for excluding them, and if this is done, all the complete analyses of the
well-established specimens of the mixture show that it is made up of
pyrosulphury! chloride and silicon oxychloride only. This inference
is confirmed in a number of different ways.

The boiling-point of this fraction 135-150° is what would be expected
for while pyrosulphury] chloride boils at 152.5-153°, the least trace
of moisture causes a considerable portion of it to boil 5° to 10° lower,
and the boiling point of silicon oxychloride is 136-139°.°

The behavior of the distillate with water also is a valuable indica-
tion. When much water was added to it there was a violent reaction
accompanied by the formation of silica, such as silicon oxychloride
gives, and an oily liquid separated and sank to the bottom of the
vessel, where it dissolved very slowly, showing the behavior of pyro-
sulphuryl chloride; dilute sodic hydrate acted in the same way.
As described before, the crystallization could be induced with a com-

590 PROCEEDINGS OF THE AMERICAN ACADEMY.

paratively moderate degree of cooling below its freezing-point by a
crystal of pyrosulphury] chloride in those mixtures which had 5 per-
cent or less of silicon, and the crystals obtained in this way gave an
analysis indicating a concentration of pyrosulphuryl chloride (14)
compared with (18), the mother liquor. Finally several distillates
were obtained under certain conditions stated further on, which were
almost pure pyrosulphuryl chloride; these cannot be used as proof
of its presence because they were obtained at temperatures higher
than usual; but taken in connection with the other agreeing observa-
tions, they help to establish the fact that pyrosulphury] chloride is one
of the two products of the reaction. With pyrosulphuryl chloride
established as one of the products, the table of analyses show beyond
a doubt that the other is silicon oxychloride.

The more regulated action of water on the distillate was next studied
in the effort to destroy one substance and isolate the other. In search-
ing for a neutral diluant it was found that alcohol, acetone, benzol
reacted with the distillate, but carbon tetrachloride, chloroform, and
carbon disulphide did not; chloroform and carbon tetrachloride were
used. 103 grams of chloroform were mixed with 84 grams of the dis-
tillate, the diluted material cooled to —5° and water added drop by
drop. Each drop caused the formation of a white ball which when
pricked, burst with a slight explosion and formation of hydrochloric
acid. The action evidently consisted in the coating of the entering
drop with a silica shell; while on pricking, the unchanged water was
freed and reacted further. 3 grams of water were added, approxi-
mately the amount required to change all the pyrosulphury] chloride
present to chlorsulphonic acid. On transferring the material a sedi-
ment of 6.5 grams (silica) was found. A distillation at low pressure
removed the chloroform and hydrochloric acid; a distillate of 42 grams
was collected, while a semi-solid residue was left in the boiling flask.
A second distillation at low pressure gave 38 grams, free from hydro-
chloric acid. The density at 18° was 1.73 (pyrosulphury! chloride is
1.837 at 20°). An analysis showed the change produced by the water:

5 Si cl
(24) Before treatment with water: 16.7% -- 49.9%
(21) After ες τ᾿ ie, aa el 6.1 43 .4

The figures show that the water attacked mainly the silicon body.
A treatment with salt followed and the distillate from the salt mixture
was collected, under diminished pressure, in two fractions: the lower
one, 9 grams, between 50° and 110°, with oil-bath around the boiling
flask raised to 150°; the second, 4.5 grams, with the bath heated to

SANGER-RIEGEL.— SULPHUR TRIOXIDE-SILICON CHLORIDE. 591

210°, the pressure being 20 mm. throughout. The analyses resulted
as follows:

5 Si ol
(22) 9 grams 19.9% 6.75 % 43.4%
(23) 4.5 grams 24 .2 3.9 35 .2
For comparison, SxO5Cl. 29 .82 -- 32.98

The figures for the 9 grams indicate that no appreciable amount of
chlorsulphonic acid had been removed, hence that the water treatment
destroyed the silicon body, and yielded the sulphur containing body.
That this sulphur body is pyrosulphuryl chloride is indicated by the
figures for the 4.5 grams obtained by heating the salt residue to a
temperature exceeding 200°, while the pressure was kept at 20 mm.

In another preparation in which hydrous sulphur trioxide was used
of such a strength that there was enough water present to form
chlorsulphonie acid instead of pyrosulphuryl chloride according to
- the reaction: 2SO;-+ HO + SiCl, = 2CISO;H + SiOCl,, that acid
was indeed obtained, but the reaction had taken place in a different
way. The water decomposed a portion of the silicon tetrachloride,
forming silica to such an extent that the solid residue in the flask after
distillation was 50 percent by weight of the materials taken, and
hydrochloric acid, which combined with the sulphur trioxide to form
chlorsulphonic acid, a portion of the silicon tetrachloride was recovered
unchanged in the liquid air condenser; all the silicon not accounted for
by it was present in the solid residue.

Three preparations have been observed which approached pyrosul-
phuryl chloride. The most nearly pure was obtained early in our work
by distilling a homogeneous mixture of 115 grams of 94 percent sul-
phur trioxide and 111 grams of silicon tetrachloride (2 molecules to 1)
resulting after 12 hours’ shaking at room temperature. A large
amount of gelatinous silica was filtered off through glass wool, and the
144 grams of filtrate submitted to a distillation at low pressure; the
distillate was collected in four fractions; the analysis of the first one,
boiling at 60° to 100° with a pressure of 70 mm., has been given under
(20) in the table of analyses; the last, boiled at 105°, with the oil-bath
surrounding the flask 240°, and pressure 60 mm., accompanied by
violent foaming, and left a solid residue of 50 grams; its analysis
follows:

5 Si ΟἹ
Found 28% 0.17% 29.4%
S,0;Cls 29 82 an 32 98

The experiment on the action of water on the average distillate
diluted by chloroform has been recorded; there too on heating to 210°

592 PROCEEDINGS OF THE AMERICAN ACADEMY.

with a pressure of 20 mm. and leaving a solid residue mainly sodium
chloride in the flask, a last fraction of 4.5 grams rich in pyrosulphuryl
chloride was obtained, as shown by its analysis (23) and behavior with
water. In the third case 197 grams of a liquid prepared just like the
144 grams above, and not previously distilled, were mixed with the
116 grams of phosphorus pentoxide and distilled at low pressure; only
38 grams could be collected, in three fractions, with the bath sur-
rounding the flask at 220°. On attempting to heat with the free
flame, because the distillate came at the rate of a drop per minute,
the flask exploded. These fractions were tested as to their melting-
point; they all solidified readily in large crystals, radiating from one
point, exactly as pyrosulphury! chloride does; the first and second
melted at near —40°, the third near —50°; pyrosulphuryl chloride
melts at —37°; one of the fractions was tested for silica and contained
none. It would seem as if by distilling from any solid, so that a high
temperature is required, the silicon body is destroyed, while the more
resisting pyrosulphury] chloride can be collected.

That no chlorsulphonic acid was present in our original distillate
was proved by an experiment performed in our first extended study
and already recorded. See page 584.

In an attempt to obtain the ethyl ester of the silicon containing
body,!® the material diluted by carbon tetrachloride was treated with
alcohol and after distilling off the solvent there remained in the boiling
flask a semi-solid mass which was silica and ethyl sulphuric acid.
The experiment was repeated several times, always with the same
result. That the ethyl ester of silicon oxychloride was not obtained
does not show the absence of silicon oxychloride, for such an ester would
hardly be stable in presence of ethyl sulphuric acid and other products
of water on pyrosulphury! chloride.

An examination of the table of complete analyses shows that differ-
ent specimens of the distillate contain the pyrosulphuryl! chloride and
silicon oxychloride in different proportions, three of them show per-
centages approaching those required if the two substances are present
in molecular proportions.

‘ 5 Si Cl
Calculated for S:0s;Cl +. SiOCl, 12.82% 11.31% 56.59%
(2) 14.63 10.20 54.87
(19) 15.14 10.14 53 15
3

(1) 1Geg 9.4 53.

19 Friedel and Ladenburg prepared the ethyl ester of silicon oxychloride
(CoHs)eOSiz; reference 5. Compare Friedel and Crafts, Ann. Chim. phys. 9, 12
(1886); Ladenburg, Lieb. Ann., 173, 144 (1874).

SANGER-RIEGEL.— SULPHUR TRIOXIDE-SILICON CHLORIDE. 593

Besides these, several incomplete analyses show similar proportions:

5 Si ΟἹ
(3) 14.50 10.18 me
(24) 16.7 ἀρᾷ 49.9
(26) 15.3 = 50.6

The results leave much to be desired but certainly indicate that
the two products were formed approximately in the proportions re-
quired by the reaction:

2SO3 + 2SiCl, = S:05Ch, + SixOCle (1)

In the majority of analyses percentages were found indicating a
decided excess of pyrosulphuryl chloride, and a smaller proportion of
silicon oxychloride; the silicon varying from 7.75 to 3.7, instead of
being 11.31; the sulphur varied from 19.6 to 24.28 instead of being
12.82. The formation of more pyrosulphuryl chloride, and the de-
struction of silicon oxychloride is accounted for by the reaction:

An especially large percent of sulphur indicating a great excess of
pyrosulphuryl chloride was obtained from a specimen which had stood
3 summer months undistilled, that is, with the low-boiling portions
containing the excess of sulphur trioxide still unseparated from the
higher boiling portions. It was contained in a glass-stoppered bottle
under a bell-jar whose atmosphere was dried by phosphorus pentoxide.
Comparing this material with a similar one, which had been heated
for 6 hours and had not stood at all, it was found that the higher boiling
fraction had increased on standing from 3 percent to 38 percent, the
solid deposited rising at the same time from 2.3 percent to 23 percent;
in another more favorable case the figures for a similar mixture heated
for 6 hours were 15 percent of higher boiling fraction, and 8 percent
solid. In all three cases two molecules of sulphur trioxide had been
used to each molecule of the silicon tetrachloride. Reaction (1) calls
for equal molecules of the two, while (2) requires six molecules of the
trioxide to each one of the oxychloride already formed, but no more
silicon tetrachloride. This action should be reflected in the lower
boiling fraction in an increase in the proportion of silicon tetrachlo-
ride, evidenced by a higher percentage of chlorine; an analysis showed
that it contained, in the case of the material which stood 3 months,
65.5 percent of chlorine, whereas the original mixture of silicon
tetrachloride and sulphur trioxide contained only 42.95 percent; this
shows that the action is correctly interpreted by reaction (2). It is

594 PROCEEDINGS OF THE AMERICAN ACADEMY.

important to add that once the higher boiling fraction was removed
from the excess of sulphur trioxide, or which is the same, from the:
low-boiling fraction, no solid was deposited.

Most of the mixtures of pyrosulphuryl chloride and silicon oxy--
chloride obtained by us crystallized at various temperatures, the high-
est one being —60°, the lowest —78°; some of them did not crystallize, .
but merely solidified to a vitreous mass, near —120°. Pyrosulphuryl
chloride melts at —37°, silicon oxychloride near —40°. A mixture of
equal parts of the prepared pure substances melted at —40° to —38°,.
but on mixing 15.6 grams of the former with 5.2 grams of the latter, .
and heating half of the mixture on the Bunsen flame, it was found that
the heated portion took twenty times longer to crystallize than the:
unheated one. As stated in the introduction, the only possible expla-
nation is that the two substances form a compound under the influence
of heat. All the mixtures were obtained by means of one or more:
distillations, and submitted to the heat of a flame, and this influence
of heat explains the phenomena of crystallization observed. In the:
mixtures containing approximately one molecule of each substance, ,
the two substances are combined, and not being free, cannot crystallize :
when a seed of either substance is introduced; in the mixtures contain--
ing an excess of pyrosulphury! chloride, the silicon oxychloride is all
combined, but some of the pyrosulphury! chloride remains free, hence
this mixture can crystallize on a seed of pyrosulphuryl chloride, al-
though here again, it will not crystallize on a seed of the oxychloride.

The deposit formed on standing over the summer was placed in a
Gooch crucible, washed twice with silicon tetrachloride, pressing down
the material with a glass rod, and using a suction pump to remove all
the liquid: all as rapidly as possible. The solid was then packed and
sealed in tubes, in which it remained without alteration. This material
appears perfectly dry; it smokes strongly in the air and attracts mois--
ture rapidly. With water it reacts violently; a few bubbles of gas
escape, and a slight yellow color (due to chlorine) develops; the white
particles become transparent, but retain their original shape; no
visible amount of silica separates out from the liquid. The reaction
with dilute sodium hydroxide is the same, but more violent. When
moistened with chloroform the solid becomes translucent and filled
with bubbles. Heated over the flame it evolves white fumes, and
leaves behind a white ash, which no longer reacts with water. The
deposit is not homogeneous; the silicon percentage varied between
6 and 10; the portions which had been formed against the wall of the
flask contained the higher percentage. One sample contained:

SANGER-RIEGEL.— SULPHUR TRIOXIDE-SILICON CHLORIDE. 595

8 Cl Si
26.8% 18.38% 6.2%
The study of this solid suggests that it is silica enclosing much sulphur
trioxide and some silicon oxychloride and pyrosulphuryl chloride.
This silica would have been formed by the equation, which has been
discussed before,

SLOCIs + 6SO3 = 2510. + 35:0;Cl

Our reasons for contending that silico-phosgene is not formed have
been fully stated in the introduction.

SUMMARY,

Melted sulphur trioxide and silicon tetrachloride are miscible; on
standing a long time or on heating 6 to 10 hours to 50° a reaction
takes place:

251ΟΙς + 2503 = SixOClg + S20;Ch;
an excess of sulphur trioxide causes a further reaction:
SiOCle + 6SO3 = 510. + 38,05Cle

The most significant result, as regards the relation of carbon and sili-
con, is the non-formation of silico-phosgene.

We take pleasure in acknowledging a grant from the Cyrus M.
Warren Fund of Harvard University, with which the expense for the
liquid air was met.

CHEMICAL LABORATORY, HarRVARD UNIVERSITY.

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Proceedings of the American Academy of Arts and Sciences.

Vou. XLVIII. No. 15.— January, 1913.

AN ELECTRIC HEATER AND AUTOMATIC THERMOSTAT.

By A. -L. CuLarx.

INVESTIGATIONS ON LigHT aND Herat PUBLISHED WITH AID FROM THE
RumrorpD Funp.

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bP a sh |

AN ELECTRIC HEATER AND AUTOMATIC THERMOSTAT.

By A. L. Cruarkx.

Received October 9, 1912.

In a previous paper! I have described a form of electric heater
and automatic thermostat for control of temperature, capable of a
fair degree of accuracy and possessing a wide range. This has been
improved recently so that the accuracy with which the heater may be
maintained at any given temperature is very much increased. For
the work described in the paper mentioned, it was not necessary to
regulate more closely than 1/10°, but subsequent work developed the
need for a higher degree of accuracy with certainty of operation, and
with no sacrifice of range or capacity. The following is a description
of the improved apparatus. It is given because this form of heater
and thermostat seems to combine accuracy of control, ease of adjust-
ment, wide range and large size of heating spaces as does no other —
at least the writer knows of none.

As mentioned in the previous paper, the device is a modification
of the thermostat used by Griffith? in his work on the Mechanical
Equivalent of Heat. The essential features are as follows: —a
cubical cast-iron box 15 em. on an edge is made with hollow walls and
bottom, the solid parts of the walls being 6 mm. thick, while the
hollow space is of the same thickness. In this way a chamber is
formed in the walls and bottom whose volume is 420 c.c. This is
filled with mercury and forms the bulb of a gigantic thermometer,
the tube of which is outside the apparatus. ‘This cast-iron box with
its enclosed mercury is surrounded by coils of German silver wire, and
placed within a larger box for heating. The air in this space is kept
in constant and rapid motion by a number of fans, so that the en-
tire space is maintained at uniform temperature. This apparatus is
lagged with magnesia and enclosed again in a massive wooden box.
It is perhaps unnecessary to state that the body to be heated is placed
inside the inner cast-iron box, which is provided with windows of
ample size both in front and rear, as are also the enclosing boxes, so
that observation is always possible. The outer windows have covers
that may be closed to investigate effects of radiation. ‘The mercury
space of the inner box is connected by a steel tube with the automatic
part of the apparatus which is shown in Fig. 1.

1 These Proceedings, 41, No. 16, Jan. (1906).
2 Griffiths, Phil. Trans., 184, 361 (1893).

E. is the steel tube from the mercury space of the cast-iron box. A. is a
cylindrical cast-iron chamber or reservoir, opening at the top into the glass
tube B, and closed at the bottom by the stuffing box C, into which the screw
D may be turned. When the temperature is varied the mercury within the
heater expands filling the chamber A and rises eventually into the tube B,
until it reaches the end of a platinum wire. This completes the circuit of a
relay which cuts off the heating current, either entirely or in part. When the
current is cut off, the temperature falls until contact of the relay is broken
at the platinum point, when the heating current is thrown on again. If the
current is properly adjusted and the change in value caused by the action of
the relay be small, the amount through which the temperature rises and falls
may be very small indeed. Obviously the temperature at which the relay
cuts off the current depends on the actual volume of the reservoir A, or in
other words on the position of the screw D. The total capacity of the reser-
voirisabout 18 em. which equals the expansion of the mercury in heater caused
by an elevation in temperature of about 300°. Of course the amount of
current used depends on the temperature at which the work is to be done and
no more than is actually necessary is used.

““

CLARK.— ELECTRIC HEATER AND AUTOMATIC THERMOSTAT. 601

When the proper amount of current is used the regulation near 200°
is within 1 /10° when the entire current is cut off. The adjustment for
this accuracy need not be very carefully made. When a portion only
of the current is cut off and the adjustment be made with sufficient
care the variation in temperature may be made very small. Close
regulation at low temperature is much easier than at higher and there
is less need of careful adjustment; as the temperature is carried
higher regulation becomes more difficult. One source of difficulty in
maintaining constancy of temperature is due to the fact that heat is
conducted along the mercury in the steel tube connecting the mercury
chamber with the reservoir attended by a rise of temperature of the
mercury in the reservoir. This rise in temperature has been obviated
by surrounding the reservoir with a coil of small lead tubing (shown in
Fig. 1) through which a current of cold water is kept circulating.

The table shows the values of the currents necessary to maintain the
heater at different temperatures :-—

Amps. Temp.
1.43-1 .55 67.2
2 .35-2 .45 100.6
2 .88-3 .05 198 .0
4.304 .40 221.0

At 198° with the regulator changing the current from 2.88-3.05 a
thermometer graduated to 1/5° was watched through a microscope and
no motion of the thread was apparent. The regulator worked at
about two-minute intervals. One very serious difficulty which gave
trouble for a long time was with the lubrication of the bearings of the
shafts, driving the fans in the inner box. Ordinary lubricating oils
boil out of the bearings at about 180° and condense on the windows
of the outer box, obscuring the view of the inside of the box. Below
about 180° there is no trouble but above this the distillation of oil
occurs. Various oils were tried with no success because there is always
this distillation at some temperature. Finally the difficulty was over-
come by using paraffin wax which melts at about 50° and does not
distil away enough to cause any trouble. Small pieces are placed
in the ends of the oil tuhes leading to the inner bearings. ‘These are
quickly melted by the heat conducted from within and run down to
the bearings lubricating them very efficiently. The slight jarring of
the whole apparatus causes trembling of the mercury at the relay
contact and no sticking of the mercury to the platinum point has been
noticed. A little aleohol on top of the mercury helps to keep it clean.

Not only is it important that there shall be no unsteadiness of tem-

602 PROCEEDINGS OF THE AMERICAN ACADEMY.

perature but there must be no temperature gradients inside the box,
more particularly vertical gradients. So an investigation of the dis-
tribution of temperature was made. ‘The mercury thermometer was
found to be worthless for this work as it does not show very small
changes readily. Accordingly a platinum resistance thermometer
made by Mr. C. H. Day was used. This is made of about 50 em. of
platinum wire fused on to platinum leads. The resistance wire is
wound on a small mica frame in the form of a cross. The cross was
first made and cemented together with “cementium.” ‘Two slits
were cut in the mica, the platinum wire doubled and the loop in the
end caught in the slit. Then the wire was wound on double in small
cuts in the mica and finally fused to the platinum leads in the oxyhy-
drogen flame. The two thermometer leads together with the com-
pensating leads were thrust through small mica discs, and the whole
placed in a thin walled glass tube. The tube was slightly enlarged
at the top so that it might hang in a hole in a piece of vulcanized fibre.
Flexible cords were then soldered to the platinum leads and finally
a second piece of fibre was fastened to the first by screws holding tube
and leads firmly. The compensating leads are connected in series with
a good resistance box and the two sets are connected to a slide wire
bridge of the circular drum type made by the Leeds and Northrup Co.

A steady current of .007 amps. is allowed to flow through the ther-
mometer so that it is always slightly higher in temperature than its
surroundings, but the amount is very small and is constant. The
thermometer was calibrated by immersing in melted ice, in steam,
and finally in vapor of boiling aniline which had been redistilled
several times. The calibration curve compares very favorably with
those given by Callendar. As the thermometer is used, one small
division on the galvanometer scale corresponds to a change in tempera-
ture of about 1/120° so that the thermometer is easily read to 1/1000°.
The platinum thermometer surpasses the mercury thermometer in
its ability to follow small changes in temperature, and while the scale
of this thermometer in the higher region may be in doubt by as
much as 1/10°, its efficiency is in no way impaired. During the
warming up stages in any experiment, the current for heating is taken
from the 110 volt dynamo circuit, but this is too unsteady for accurate
work. So when the temperature rises near the desired point the 110
volt storage battery circuit is thrown in. For work requiring 1/10°
accuracy the lighting circuit is ordinarily steady enough.

It is extremely doubtful if the readings of most mercury thermom-
eters can be relied upon to 1/100th of a degree when working at
temperatures as high as 2005, The amount of stem exposed, sticking

CLARK.— ELECTRIC HEATER AND AUTOMATIC THERMOSTAT. 603

of mercury, etc., bring its indications under suspicion. With the
platinum thermometer just described, it is possible to follow fluctua-
tions which ought to be visible in the mercury thermometer, but which
are not as a matter of fact. Much interesting and valuable informa-
tion was gained by use of this instrument. It was discovered that the
incandescent lamp behind the box used for illumination caused a rise
in temperature of over 1/10°. A lamp in the room which shone into
the front window affected the temperature of the thermometer no-
ticeably. For work on liquids near the critical point this fact must
not be overlooked. It is essential that the very smallest amount of
light possible be used, particularly when the light shines on a portion
only of the tube, which contains the liquid under experiment. Most
observers have not taken sufficient pains in this matter. Many tests
for constancy of temperature have been made. The following (‘Table
I) may be regarded as typical, and show the possibilities of the ap-
paratus. The first set (Temp. I) was obtained by breaking the entire
current of 3.96 amperes, the second (Temp. II) when the current
varied between 2.62 and 3.90 amperes.

Time in Time in
Minutes Temp. I. Temp. II, Minutes Temp. I. Temp. II.
0 190.194 190.203 154 .210 PAN
3 .194 . 204 16 .215 .199
1 .194 .201 163 .218 .203
1: .202 .198 17 212 .201
2 . 206 .200 174 .208 . 203
24 . 203 .202 18 . 208 . 200
9 200 .208 184 ΤΩ .197
34 190.199 190.204 19 Aly) .197
4 . 202 201 19% .218 .200
4} .207 . 202 20 213 .201
5 .203 . 2038 203 .210 -200
δὲ .201 .202 21 .206 .196
6 . 203 . 200 214 190.209 190.200
64 .205 .199 22 .205 .200
7 .207 .201 22% .207 .198
74 .200 .202 23 .201 . 203
8 200 .201 233 215 202
83 .200 .201 24 .210 .202
9 . 202 .201 244 .197 .203
94 . 205 .202 25 .197 .201
10 . 202 .201 254 . 200 .201
103 . 200 .201 26 . 202 .202
11 .200 .201 263 . 204 .203
113 190.208 190.202 27 190.201 190. 202
12 .210 . 202 27% .206 .200
124 .216 .202 28 .205 .201
13 PAS . 202 28% . 2038 Ade
134 [212 .198 29 .205 .203
14 . 204 . 202 29% . 200 .203
143 . 202 . 202 30 £202 .201

15 .209 .201

604 PROCEEDINGS OF THE AMERICAN ACADEMY.

If the apparatus could be attached to a storage battery on which

there were no other loads, it would be comparatively easy to get -

closer regulation by using a narrower range of current variation.
The battery used in these experiments is liable to have other loads
thrown on at any time. The curves (Fig. 2) show the variations
plotted from the tables.

Temp.

190, 21

190.20

190.19

Temp Ἵ
190.21 ,

ΟὟ, |

nine a Xa

Next the existence of a vertical temperature gradient was examined.
Readings on thermometer were made at different levels and no sure

difference of temperature was observable when the space inside heater -

is empty. When masses of metal or other obstructions were placed
inside, slight differences amounting to one thousandth of a degree
were observed. In experiments like this all the windows in the
apparatus must be covered as radiation causes noticeable differences
in temperature.

The platinum thermometer led to another important discovery.
Even after the automatic controlling apparatus becomes steady it
was found that the temperature of the air inside the heater continues
to rise. This is due to the fact that altogether the wall of the heater
box is about 1.8 cm. thick and while the mean temperature of the
mercury in the wall does not vary, the temperature of the inner part
and the wall adjacent to it is rising while that of the outer part is fall-
ing. This rise may amount to more than .1° and it is a matter of
an hour or so before it disappears. This time has been shortened by
placing a small flat heating coil of fine GS wire along the inner wall
inside. A small current sent through this helps to establish equi-

CLARK.— ELECTRIC HEATER AND AUTOMATIC THERMOSTAT. 605

librium a little more quickly. Considerable judgment must be
exercised in its use however.

Finally the effect of the stirring system was investigated and it
was found that running at normal speed, the fans gave a rise in tem-
perature of about .1° per hour; so that any slight variation in speed
of fans is not important, but great variations may interfere with close
regulation.

The ease with which one temperature after another can be obtained
is one of the features of the apparatus. Other advantages are the
wide range of available temperatures, the precision with which any
given temperature may be reached and maintained, the large volume
of heating chamber, ease of observation and the certainty of operation.
Another advantage in work near the critical point is the small amount
of damage caused by explosion. The windows, which are easily re-
placed, may be blown out but no injury to the essential parts has ever
occurred and explosions have not been infrequent.

QUEEN’s UNIVERSITY,
KINGsTON, ONTARIO.

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Proceedings of the American Academy of Arts and Sciences.

Voz. XLVIII. No. 16.— Marcu, 1913.

CONTRIBUTIONS FROM THE PHANEROGAMIC LABORATORIES
OF HARVARD UNIVERSITY.—No. 59.

CRETACEOUS PITYOXYLA FROM CLIFFWOOD, NEW
JERSEY.

By Ruts Ho.pen.

Wits Four PLATES.

CONTRIBUTIONS FROM THE PHANEROGAMIC LABORATORIES
OF HARVARD UNIVERSITY.—No. 59.

CRETACEOUS PITYOXYLA FROM CLIFFWOOD, NEW
JERSEY.

By στη Ho.wpen.
Presented by E. C. Jeffrey. Received December 1, 1912.

DurING the spring of several successive years, Dr. E. C. Jeffrey
collected a considerable amount of lignite from the Middle Cretaceous
of Cliffwood, New Jersey, which he has since turned over to the writer
for investigation. The material was from two localities,— that from
the yards of the Cliffwood Brick Company, and that from Cliffwood
Beach. The former lot was as a whole badly pyritized and of no
value from a structural standpoint; while the latter was often per-
fectly preserved, revealing all the details of its structure under micro-
scopical examination. The greater part was found to belong to the
genera Cupressinoxylon, Araucarioxylon, and Brachyoxylon, and will
be described later. There were also specimens representing three
types of Pityoxylon; the characteristics and affinities of which it is
the purpose of this paper to discuss.

Pinus protoscleropitys n. sp.

It will be appropriate to begin with the one which most closely
resembles modern forms. Figures a,c, and e, Plate 1, reveal the general
features of the lignite in question. It will be noticed that the tra-
cheides are small and thick walled. 'Thesummer elements are few in
number, but limit a well marked annual ring, as shown in the lower
part of Figure a. Resin ducts such as are characteristic of all Pityoryla
occur in two planes. Figure a includes two vertical canals, and to the
right a horizontal one. It is apparent that both are completely
filled with tyloses,— a condition more clearly seen in Figures ὁ and e.
Surrounding each, there is a jacket of epithelial parenchyma. The
cells composing this jacket are thin walled, heavily pitted, and in
general devoid of contents. Figure d, on the other hand, illustrates
a case where they are filled with a dark, resinous substance. Figure ὃ
gives the topography next the pith,— at a lower magnification. It
will be noticed that, as in the hard pines, there is a double series of

610 PROCEEDINGS OF THE AMERICAN ACADEMY.

resin ducts in the first annual ring, but the inner series in this case lies
in the primary wood. This condition is at variance with that of hard
pines where both are in the secondary wood. The presence of resin
canals in the primary wood is not unparalleled in the coniferous series,
— they occur in the primary wood of the root of all the Abietineae (1),
of the cone axis of Sequoia gigantea (2), and of certain members of the
Araucarineae (3). True medullary canals, such as have been de-
scribed in Pinus succinifera (Goepp) Conw. (4) seem to be entirely
absent. In the succeeding annual rings, the vertical canals are
smaller and less frequent. With the horizontal canals they form a
freely anastomosing system (Figure c).

Figure 6 also shows the character of the pith. Scattered among the
thin walled parenchyma cells there are clusters of very thick-walled
sclerified elements. Such a cluster occurs in the upper part of Figure
b. These show a tendency to be in more or less definite horizontal
bands, but do not form true diaphragms.

The medullary rays are of two sorts,— linear and fusiform. The
latter are frequent, and always embrace a resin canal (at the left of
Figure 6), a leaf trace (Figure f) or both. The linear rays are much
more abundant, as may be seen in any of the illustrations. They are
usually low, and as in living pines, destitute of resinous content. The
walls are thin and heavily pitted. The lateral pits, as shown in
Figures a and ὑ, Plate 2, vary from one to two to each cross field; they
are small, the mouths lenticular on the wall of the ray and circular on
that of the tracheide. Not infrequently there are indications of
fusion where two small pits unite to form one of medium size. At the
extreme lower right of Figure a, and in the upper part of Figure ὃ, such
phenomena are represented. The resulting pore is rarely as large as
in modern pines such as Pinus strobus, though occasionally a single pit
occupies almost the entire cross field, as in the lower left of Figure ὁ.
Both horizontal and end walls are also heavily pitted.

Tn association with this parenchyma, there are longer and lower
cells, always devoid of contents, with bordered pits on lateral, hori-
zontal and end walls. That these are ray tracheides, such sections as
are photographed for Figures ὁ and d, prove beyond question. They
may occur only on one margin of a ray, or on both, as in Figure 6.
Rarely they are interspersed, with parenchyma above and below.
Projecting in from the horizontal walls, there are well marked teeth.
These may be seen in the lower ray tracheide of Figure c, the upper
one of Figure d and better in Figure e. These teeth are doubtless
analogous to similar appearances in hard pines, though less developed

HOLDEN.— CRETACEOUS PITYOXYLA. 611

than is usually the case in the latter. Aside from our specimen, there
are but two instances where ray tracheides have been described in a
fossil,— Pinus scituatensiformis, Bailey (5) and P. succinifera (Goepp.)
Conw. (4). In the former, the walls seem to be smooth like those of
living soft pines, while in the latter, Conwentz figures just such a
sculptured appearance as is presented by the lignite under considera-
tion.

The pitting of the tracheides is entirely confined to the radial wall.
Owing to the small size of the elements, the pores are usually uniseriate.
They are normally circular in outline and scattered; rarely toward
the end of a tracheide, they become closely approximated and flat-
tened by mutual contact. Figure d, Plate 1, represents a typical
condition. In the larger tracheides of the spring wood, the pores are
often diseriate. In such instances they are always opposite and sep-
arated by well marked “bars of Sanio.”’ In the living condition
these bars are formed by the thickening of the cellulose middle lamella,
which in the process of fossilization, rots away, leaving an empty
space. Consequently the bar appears as a white line. A particularly
favorable region is shown in Figure f, Plate 2. Were anything more
needed to demonstrate the Abietineous affinities of our lignite, these
would suffice, since as shown by Miss Gerry (6) these bars of Sanio
are invariably absent in woods of Araucarian affinities.

The short shoots in this fossil are much larger than those in most
living pines, though never showing annual rings as in Ginkgo, Figure c,
Plate 4, represents one of these organs. On careful examination it may
be seen that there is a single row of resin ducts in the wood, and that

“the medulla contains sclerotic nests similar to those of the main axis.
This section was cut at some distance from the pith. Figure d, Plate 4,
shows, at a lower magnification, a section cut considerably nearer the
centre. In the upper part of the photograph the short shoot may be
seen; toward the lower limit, there is a dark spot. Figure f, Plate 1,
represents this spot at a much higher magnification, and demonstrates
its foliar nature. Examination of serial sections has shown that at its
departure from the medulla, each brachyblast is subtended by an
axillating leaf trace, which dies out after a few years, leaving an appar-
ently unaxillated short shoot. A similar condition has been described
by Dr. Jeffrey in the case of Woodworthia, an Araucarian from the
Triassic (7): in Woodworthia, however, these short shoots often branch,
which is never the case in this Pityoxylon. The short shoot of Ginkgo
is always axillated, in this case by a double leaf trace; in Larix also the
short shoots are axillary structures. In the majority of living pines,

612 PROCEEDINGS OF THE AMERICAN ACADEMY.

however, such is not the case. That the primitive condition was for
the brachyblast to be subtended by a leaf trace, is further indicated
by the occasional presence of an axillating strand in the seedling of
certain living pines, —e. g. Pinus strobus, and in the mature wood of
certain others,—e. g. Pinus Jeffreyi. The character of the short
shoot thus presents an interesting example of seedling recapitulation.
The leaf traces of this Pityexylon are not confined to an axillat-
ing position, but are quite numerous near the pith. Their presence
would indicate that the leaves of this conifer were of two sorts,—
those borne directly on the main axis as in the seedling of living
pines, and those on short shoots. Such a condition has been figured
by Fontaine (8) in Leptostrobus, Heer. The foliar strands are jack-
eted by parenchyma, the whole forming a fusiform ray (Figure f).
Not infrequently a resin duct accompanies them in their outward
journey,— a condition comparable to that of the vegetative leaves of
some of the Abietineae, and of the sporophyll traces of some of
the Araucarineae (3).

Having described the salient features in the anatomy of this speci-
men, it remains to consider its affinities. The presence of resin canals
in two planes relegates it at once to the genus Pityorylon, Kraus, and
the short shoots narrow its possibilities to Lariz and Pinus. There
are a number of reasons for excluding the former,— dentate ray
tracheides, thin-walled ray parenchyma, with fusion pits, abundant
tylosed resin canals,— none of which occur in the wood of the larch.
Further Larix has wood parenchyma at the end of the year’s growth
and tangential pits,— both of which are absent here. It seems clear
therefore that our lignite belongs to the genus Pinus. Pines may be
divided into two great groups,— hard and soft. Aside from certain
external criteria,— for the most part unreliable,— the two groups may
be differentiated by the following characters. Hard pines have
sculptured ray tracheides, two or more rows of resin canals in the first
annual ring, sclerified pith (except most of the two-needled varieties)
and lack tangential pitting (except in the first few year’s growth and
the cone axis). Soft pines on the other hand, have smooth walled ray
tracheides, a single row of resin canals in the first annual ring, tangen-
tial pitting, and lack stone cells in the pith. On all four of these fea-
tures, our lignite belongs with the hard pines, and since it is the earliest
known completely differentiated hard pine, we propose for it the name
of Pinus protoscleropitys. In using the generic name Pinus rather
than Pityoxrylon, we are following the example set by Conwentz and
Bailey, since the specimen in question cannot be separated anatom-
ically from living pines.

HOLDEN.— CRETACEOUS PITYOXYLA. 613

It is of interest to compare this type with other fossil pines. The
only ones described up to now with ray tracheides are Pinus scituaten-
siformis, Bailey (5) and P. succinifera, Conw. (4). First let us con-
sider the former, since it is of the same geological age as our specimen.
Both have a sclerified pith, large short shoots, and tyloses in the resin
canals. P. sitwatensiformis differs from the lignite described in this
article in numerous features,— the ray tracheides are smooth walled,
the rays and abundant epithelium of the vertical canals are highly
resinous, the lateral pits of the rays are small and invariably one per
crossfield, the summer tracheides are pitted on their tangential walls,
and the short shoot has no axillating leaf trace. While our specimen
is a typical hard pine, that described by Mr. Bailey unites the char-
acteristics of both groups,— it has the tangential pitting and smooth
ray tracheides of a soft pine, with the sclerified pith of a hard. It
seems to be a more generalized type, perhaps representing an ancestral
condition before the two groups had become sharply separated.

With P. succinifera of the early Tertiary, our lignite has more in
common. Both have sculptured ray tracheides in marginal and inter-
spersed positions; thin-walled, non-resinous ray parenchyma; septate
tracheides around the resin ducts, which are surrounded by thin-walled
heavily pitted epithelium and filled with tyloses. On the other hand,
as opposed to our specimen, P. succinifera has but a single row of resin
ducts in the first annual ring; tangential pits; tyloses in the tra-
cheides; ray cells with sometimes four small piciform pits to each cross-
field, sometimes one large fusion pit; resin canals embedded in the
pith, and no stone cells. Further, ray tracheides in P. succinifera
do not occur normally in the first few years’ growth, while in our form
they are present in the first annual ring.

From this comparison of P. protoscleropitys with other similar
Pityoxyla it is evident that the former represents a higher and more
specialized type than either of the others. It has all the features of a
living hard pine, while the others present different combinations of the
features of both hard and soft. The occurrence of a completely differ-
entiated hard pine as far back as the Middle Cretaceous substantiates
the conclusion reached by Jeffrey (9) from a study of the leaves that
the two groups had already become separate by the Middle Creta-
ceous. Zeiller’s description of cones of both groups from the Jurassic
renders it probable that the separation goes back to that epoch. An
interesting corollary to the presence of such a modern type of wood in
the Cretaceous is afforded by the modern character of the leaves of
Upper Cretaceous pines described by Stopes and Kershaw (10).

614 PROCEEDINGS OF THE AMERICAN ACADEMY.

These facts indicate that the Abietineae are a much older group geo-
logically than is usually supposed. It is further evident that such
forms as these must be the ancestors of living pmes, and that such
forms as Pinus scituatensiformis and P. succinifera,— of the same or
later geological age, yet less specialized,— are off the main line of
development.

Before leaving this specimen, it is convenient to consider the light
it throws on the origin of ray tracheides. Jeffrey and Chrysler (11)
concluded that ray tracheides were evolved during the early Tertiary,
basing their conclusions on the following developmental and palaeobo-
tanical evidence. Ray tracheides are absent from the cone axis of
most modern pines, and poorly developed in the seedling; they are
absent in Pinites Ruffordi, Seward (12) (Wealden), Pityorylon staten-
sense and P. scituatense (Middle Cretaceous) and do not appear for
several years’ growth in Pinus succinifera (Early Oligocene or Late
Eocene). The discovery of ray tracheides in P. scituatensiformis
(Middle Cretaceous) led Mr. Bailey to the conclusion that these
structures came in during the Middle Cretaceous. In that species
they do not appear at all in the first ten to fifteen years’ growth and
thereafter are but poorly developed. Their occurrence, though rare,
in the first annual ring of P. protoscleropitys (Middle Cretaceous)
and their abundance later, seems to indicate that they are a more
ancient feature than has been assumed by any of the above cited
investigators. It is probable that they were developed in the Lower
Cretaceous if not in the Jurassic.

As regards the origin of ray tracheides, the final word remains to
be said. There are two theories which have been advanced to explain
the question. Thompson (13) has suggested that tracheary ray cells
are derived from vertical tracheides, which by progressive shortening,
have taken on a horizontal position. Stages in such a process he found
in Pinus resinosa and P. strobus. As Bailey pointed out there are two
objections to this theory,— if these phenomena are recapitualtionary
or reversionary, in the first place, why are they more evident in these
highly specialized varieties than in such primitive ones as the Nut
and Foxtail pines? And, in the second, why are they completely
absent in fossil forms? Mr. Bailey was unable to find any trace of
such an origin in P. scituatensiformis, and I have been unable to find
any in P. protoscleropitys. Since there is no confirmatory evidence in
the case of the primitive living forms, or the two oldest known fossil
forms, it seems improbable that Mr. Thompson’s interpretation is
correct.

HOLDEN.— CRETACEOUS PITYOXYLA. 615

On the other hand, Penhallow (14) has suggested that they have
been formed from ray parenchyma by a thickening of the cell wall.
As Bailey points out, the evolutionary sequence has been from thick-
to thin-walled parenchyma, not vice versa,—a consideration which
immediately invalidates this hypothesis.

Pityoxylon foliosum n. sp.

The next specimen to be considered is much less like modern forms
than that just described. Figures a and b, Plate 3, represent at
different magnifications cross sections of the wood. As may be seen in
Figure δ, the annual rings are very broad and well marked,— the first
occurring near the lower limit of the field. Another appears a little
below the centre of Figure a. There are many concentric arcs extend-
ing half way or more around the stem, caused by some external
pressure in the process of fossilization. One such is shown in the
upper part of Figure a. That it is not a true growth ring is proven
by the fact that it does not completely encircle the medulla, and that
the tracheides composing it are not pitted on the tangential wall,—
an invariable characteristic of the summer tracheides of the lignite
in question.

Resin ducts are very numerous, extending in two planes,— vertical
and horizontal. The vertical canals are surrounded by clusters of
highly resinous epithelial parenchyma. Not infrequently a single
mass contains three or even four tangentially grouped canals, which
as may be seen from longitudinal sections, intercommunicate. The
epithelium is moderately thick-walled, and densely perforated by
simple pits. The horizontal canals are also numerous, as shown by
Figure e. Together with the vertical canals they form a freely anasto-
mosing system of resin passages throughout the wood. Both hori-
zontal and vertical canals, especially the latter, are almost invariably
filled with thick-walled tyloses. At the extreme right of Figure ὁ the
proximity of the canals to the pith may with difficulty be ascertained.
Figure d, a radial longitudinal section, shows the relation more clearly.
In fact the canals are often so near to the medulla that in transverse
section they appear to be embedded init. A more careful examination
however, reveals the presence of a jacket of metaxylem elements
around the duct. This occurrence of canals in the primary wood is
unknown in the main axis of living pines, but is similar to that of
Pinus protoscleropitys.

Toward the right of Figure δ, a vascular strand may be seen to pass

616 PROCEEDINGS OF THE AMERICAN ACADEMY.

off from the medulla; Figure e shows one of these leaf traces in cross
section. Such leaf traces are quite abundant in this specimen, but in
the limited amount of material available, there was a complete ab-
sence of short shoots,— a remarkable condition for an obvious Pity-
oxylon. The trace appears to be always single, like those of the
fascicular leaves of all living pines, at the point of departure from the
pith. Further, like those traces the xylem is entirely centrifugal.
Not infrequently a resin canal accompanies the strand in its outward
passage, rarely two.

The rays are of two sorts,— linear and fusiform. The latter are
very numerous; they consist of parenchymatous elements embracing a
resin duct, a foliar trace, or both. The character of the linear rays
may be inferred from the photomicrographs. They are low and highly
resinous; the walls are comparatively thin and heavily pitted. The
lateral pits are usually one to each cross field, rarely two: they are
piciform, with an elliptical opening on the side of the ray and a circu-
lar one on that of the tracheide. Unlike living pines, all the cells
composing the ray are parenchymatous, although those on the margin
are often quite different from the others, being irregular in shape and
destitute of resinous content. Figure ¢ shows several instances of
this condition. At first sight they appear to be ray tracheides, but
the unbordered character of the pits negatives that possibility.

The tracheides are uniformly small and thick-walled. The pits on
the radial wall are uniseriate and scattered; in places, indications of
the so called “bars of Sanio”’ could be distinguished, but as a rule the
indifferent state of preservation obscures this feature. In the majority
of cases, the pits are confined to the radial walls, but those tracheides
laid down at the end of the year’s growth, have pores also on the tan-
gential wall. As is well known, this is characteristic of all the Abie-
tineae except hard pines.

The characteristics of the pith are evident from Figures b and d.
There are two sorts of elements,— thin-walled parenchyma and thick-
walled sclerenchyma, the latter standing out as black masses in the
photographs. They show a general tendency toward arrangement in
horizontal bands, which are not, however, sufficiently localized to
form diaphragms.

It remains now to consider the affinities of this lignite. The pres-
ence of resin ducts in both horizontal and vertical planes affiliate it
with the genus Pityorylon, Kraus. Like all previously described
Cretaceous Pityoxyla (with the exception of Pinus scituatensiformis
and possibly Pinus Nathorsti Conw. (15), about which however it is

HOLDEN.— CRETACEOUS PITYOXYLA. 617

impossible to tell, owing to imperfect preservation), the rays are
devoid of tracheides, and bear out the conclusion of Jeffrey (11) that
the majority of pines of this horizon had not yet acquired them. The
affinities of this specimen must, therefore, lie with one of the four
Abietineous genera normally possessing resin canals,— Pinus, Picea,
Larix and Pseudotsuga. Both the last two have well marked wood
parenchyma at the end of the year’s growth. Since this feature is
lacking in our fossil, it cannot be related to them. Between Pinus and
Picea, there is little occasion for hesitation. The abundant, tylosed
resin canals, complete absence of spiral thickenings, thin-walled
parenchyma forming the epithelium of the canals and the cells of the
medullary rays, clearly indicate its connection with Pinus. Another
criterion for distinguishing the wood of Pinus and Picea is the wound
reaction. As pointed out by Jeffrey (1) dense tangential series of resin
canals are an invariable concomitant of injury in the case of Picea.
One fragment of the lignite under consideration had a large wound
cap. This was carefully examined, but no trace of traumatic canals
found. That the capacity for such a reversion had been acquired as
early as the Cretaceous, is proved by the presence of a traumatic series
in Pinites Ruffordi (12) from the Wealden of England. If our fossil
were related to Picea, as severe a wound as it had received would have
unquestionably stimulated this characteristic reaction. Against this
proposed affiliation with Pinus, may be brought forward the absence
of short shoots. Fontaine (8) however, has described from the Po-
tomac certain coniferous remains with both fascicular leaves on lat-
eral and terminal short shoots, and also primary leaves, borne directly
on the main axis, which are spirally arranged like those of seedling
pines. In view of the small amount of available material, it is en-
tirely possible that our specimen really possessed typical short shoot
organs. Jeffrey (9) has suggested that Prepinus may belong with this
Leptostrobus of Fontaine’s. If such is the case, the lignite under
discussion may be referred to Prepinus. Its characteristics are, in-
deed, extremely like those of the wood of the brachyblast of P. state-
nensis. Both have sclerified nests in the pith, resin canals in two
planes, highly resinous rays with piciform lateral pitting and tan-
gential pitting of the tracheides. On the other hand, there are certain
important differences. Modern pines may be divided into the two
classes,— hard and soft. Disregarding the differences in ray trache-
ides, the characteristics of the two are,— first, hard pines have a
double, soft,— a single, leaf trace (in both, however the trace leaves
the wood of the brachyblast as one and divides in the cortex); second,

618 PROCEEDINGS OF THE AMERICAN ACADEMY.

hard pines have two or more rows of resin canals in the first annual
ring,— soft but one; third, hard pines (except most of the two needled
varieties) have stone cells in the pith,— soft have none; fourth, hard
pines have not, soft have, tangential pitting of the summer tracheides.
Our lignite, then, is nearer the hard than the soft pines, having more
than a single row of canals in the first annual ring, and stone cells, but
it has also the tangential pitting of a soft pine. On the other hand,
Prepinus statenensis has the sclerified pith of a hard pine, with the
single leaf trace of a soft. Moreover, it has tangential pitting, and
but one row of resin canals. It must be borne in mind, however,
that we have to do with a brachyblast, and that the second row of
resin ducts may be omitted for lack of space. This condition of
affairs would be analogous to that of many living hard pines, where,
as Pinus rigida, there may be but one row of canals in the short shoot,
and sometimes none at all in the first annual ring of the seedling.
The fact that the leaf trace of Prepinus statenensis is mesarch,
whereas that of our specimen is endark, need not militate against
this suggested relationship. In the first place, we have a record
of only the fascicular leaves of Prepinus, and of only the primary
leaves of this lignite: — there are no grounds for assuming that they
must have been alike in this respect. [ἢ the second place, it is entirely
possible that the strand, though endark in the wood, might acquire
mesarch structure in the cortex, or even in the blade of the leaf. An
analogous condition is true in the case of the Cycads. Any connec-
tion between our specimen and Prepinus viticetensis (16) is less likely,
because even though the latter has two rows of resin canals, it lacks
the highly characteristic medullary stone cells. The identification of
this lignite with the wood of Prepinus, or with either Leptostrobus, Heer
or the somewhat similar Pinites Solmsi (17) of Seward,— both of
which are known only superficially,— must remain very problematical.

Its relation to other Pztyoryla should next be considered. As re-
gards other lignites from Cliffwood, it differs from Pinus protosclero-
pitys in the absence of ray tracheides; and from Pityoxylon hollicke
Knowlton (18) in that the latter has ‘ punctations contiguous,’ ‘ thick-
walled ray cells,’ and often two series of pits. Thickness is, of course
a relative term, and more material of our specimen might show diseri-
ate pitting. However, Knowlton states that the structure is ‘too
obscure for accurate description,’ so further comparison is impossible.
The lignite in question differs from Pinoxylon dacotense, Knowlton, in
that the latter has only vertical canals, and from Pityoxylon statenense
in that the latter has no stone cells in the pith. Further, it can-

HOLDEN.— CRETACEOUS PITYOXYLA. 619

not be identified with Pinites Ruffordi which has tyloses in the trache-
ides and teeth in the ray parenchyma. One character absolutely puts
P. Ruffordi out of the question,— it contains traumatic resin ducts,—
which as pointed out above, were not present here. It cannot be
placed with Pinus Nathorsti (15), which had thick-walled, unpitted
parenchyma around the resin canals and lacked tangential pitting,
or with Protopiceorylon antiquius Gothan (19). That species had
thick-walled ray parenchyma, thick-walled epithelium around the
resin canals, three to four pits to each crossfield on the lateral walls of
the rays, and lacked tangential pitting,— features diametrically op-
posed to those of our fossil. Accordingly, our specimen cannot be
identified with any previously described. In view of the fact that the
leaves were borne on the main axis exclusively, rather than on short
shoots, it may appropriately be called Pityoxylon foliosum. The only
other forms with such leaves are Pinus protoscleropitys and Prepinus.
With the former it cannot be identified because that form had such
abundant short shoots that it would be impossible to miss them, and
further it had ray tracheides. As suggested above, it may very proba-
bly be the wood of Prepinus.

Pityoxylon anomalum n. sp.

The third type of Pityoxylon differs from either of those previously
described, though similar to P. foliosum. Figure f, Plate 3, shows the
general topography of the stem. The annual rings are narrow and
indistinct. Resin ducts are present, extending in two planes, but as
is evident from a comparison of Figures b and e, Plate 3,— equally
enlarged — they are much less frequent in this specimen than in the
former. A further difference is that there is but one row in the first
annual ring; this row occurs in the primary wood. Figure a, Plate 4,
shows the character of the ducts. They are surrounded by a large
mass of epithelium, which is completely filled with resin. This
feature is best brought out in the longitudinal sections (Figures ), f,
and 4). The cells of this jacket are fairly thin-walled, and very heavily
pitted, which doubtless accounts for the abundant tyloses, which are
very thick-walled. As a rule there is but a single canal in each cluster
of parenchyma,— rarely there are two.

The tracheides are badly collapsed, and the lumen usually com-
pletely obliterated. At times, however, in the better preserved
regions, the characteristics of the pitting may be made out. In the
lower part of Figure g, for example, a single row of pores may be ob-

620 PROCEEDINGS OF THE AMERICAN ACADEMY.

served. This is universally the case,— the tracheides being too narrow
to accommodate a double series; in no case was the preservation suffi-
ciently good to make out the bars of Sanio. Tangential pitting also
is present, rather infrequently, on the face of the summer wood.

The rays are of two sorts,— linear and fusiform. Their highly
resinous condition obscures the pitting, which in favorable localities is
seen to be piciform. The pores are one to each crossfield, circular on
the wall of the tracheide, and elliptical on that of the ray. Inno case
was there evidence of pit fusion.

The section photographed for Figure f, Plate 3, was cut at the region
of the exit of a brachyblast. Figure e, Plate 4, shows its structure in
cross section. The enlargement is the same as that of Figure c, which
represents Pinus protoscleropitys. In the case of both, the short
shoots are much larger than those of living pines, and in the medulla
of each, there are aggregations of sclerified tissue similar to that of the
main axis.

The affinities of this specimen are rather difficult to determine.
The presence of short shoots and the absence of wood parenchyma
relegate it definitely to Pinus. Further it is impossible to go, for it
has the characteristics of neither a hard nor a soft pine exclusively ,—
the presence of tangential pitting and single row of resin canals excludes
the former, and the presence of stone cells excludes the latter. As
regards other fossil forms, its affinities are equally indefinite: It lacks
the ray tracheides of Pinus scituatensiformis, P. succinifera or P.
protosclerapitys, and the tracheary tyloses and toothed ray parenchyma
of Pinites Ruffordi; unlike Protopiceoxylon antiquius and Pinus
Nathorsti, there is tangential pitting. On the other hand, Pityoxylon
statenense has no sclerenchyma in the pith, and P. foliosum has
abundant leaf traces. Granted that Prepinus really belongs with
Leptostrobus this cannot be the wood of Prepinus, because it has no
primary leaves. In other characteristics, its general resemblance to
Prepinus is quite striking. The woods look alike,— both have stone
cells in the pith, resinous rays, piciform ray pitting,— further both
have numerous small crystals,—a feature of neither of the other
specimens.

In view of these apparent points of difference from other forms, it is
suggested that this fossil be called Pityoxylon anomalum.

i,

bo

HOLDEN.— CRETACEOUS PITYOXYLA. 621

SUMMARY.

The Pityoxyla of Cliffwood, New Jersey, include the following
previously undescribed varieties:

(1) Pinus protoscleropitys,— probably the earliest form with all
the characters of a modern hard pine, yet retaining certain
ancestral features, as the association of primary and fascicular
leaves, the latter borne on brachyblasts subtended by a foliar
trace.

(2) Pityoxylon foliosum,— possibly the wood of Prepinus, with all
its leaves borne directly on the main axis, and presenting mingled
characteristics now confined exclusively to either hard or soft
pines.

(3) Pityoxylon anomalum,— with ligneous features extremely like
those of Prepinus, yet with all its leaves borne on short shoots.
The absence of tangential pitting in the first described Pity-
oxylon, and its presence in the other two, confirm the conclusions
of Jeffrey and Chrysler that tangential pitting is a primitive
feature now lost in the more highly specialized hard pines.

The absence of evidence confirming thé origin of ray tracheides
from vertical tracheides of the wood, renders it unlikely that this
hypothesis is correct.

The occurrence of a completely differentiated hard pine as far.
back as the Middle Cretaceous is an argument for the great
geological antiquity of the pines as such.

In conclusion, I wish to thank Professor E. C. Jeffrey for all the

material used in this investigation, for an opportunity to examine
sections of Prepinus, and for his helpful advice throughout the
course of the work. To Professor I. W. Bailey, I am indebted for
opportunity to study sections of Pinus scituatensiformis, and to Mr.
E. W. Sinnott for sections of various living pines.

622 PROCEEDINGS OF THE AMERICAN ACADEMY.

LITERATURE.

Jefirey, E. C.
(1) The Comparative Anatomy and Phylogeny of the Coni-
ferales. Part 2. The Abietineae. Mem. Boston soc.
nat. hist. ΜΟΪ ἢ, no: 1.
Jefirey, E. C.
(2) The Comparative Anatomy and Phylogeny of the Coniferales.
Part 1. The Genus Sequoia. Mem. Boston soc. nat. hist.,
vol, 5; no. 5.
Jeffrey, E. C.
(3) The Araucariorylon Type. Proc. Amer. Acad. Arts and
Sciences, vol. 48, no. 13.
Conwentz, H.
(4) Monog. d. Balt. Bernsteinbaume. Danzig, 1890.
Bailey, I. W.
(5) Cretaceous Pityorylon with Marginal Tracheides. Annals
of Botany, vol. XXV, no. xeviii, April, 1911.
Gerry, E.
(6) Bars of Sanio in Coniferales. Annals of Botany, vol. xxiv,
no. 93, Jan., 1910.
Jefirey, E. C.
(7) A new Araucarian Genus from the Triassic. Proc. Boston
soc. nat. hist. vol. 34, no. 9, p. 325-332, pls. 31, 32.
Fontaine,
(8) The Potomac or Younger Mesozoic Flora, Monog. U. S.
Geol. Survey, xv.
Jefirey, E. C.
(9) Structure of the Leaf in Cretaceous Pines. Annals of
Botany, vol. XXII, no. LXX XVI, April, 1908.
Stopes, M. C. and Kershaw, E. M.
(10) Anatomy of Cretaceous Pine Leaves. Annals of Botany,
vol. XXIX, no. 94, April, 1910.
Jeffrey, Εἰ. C. and Chrysler, M. A.
(11) Cretaceous Pityoxryla. Bot. Gaz., vol. XLII, July, 1906,
ὌΡ 1-1Ὁ:
Seward, A. C.
(12) New Species Conifer, Pinites Ruffordi, from English Wealden
Formation. Jour. Linn. Soe. vol. 32, p. 417.
Thompson, W. P. .
(13) The Origin of Ray Tracheides in Conifers. Bot. Gaz., vol.
50, no. 2, Aug., 1910, pp. 101-106.

HOLDEN.— CRETACEOUS PITYOXYLA. 623

Penhallow, D. P.
(14) Manual of North American Gymnosperms, Boston, 1907.
Conwentz, H.
(15) Untersuchungen u. foss. Hoelz. Schwedens, Konig. Svenska
Vet. Ak. Handl. Bd. 24, no. 13, 1892.
Jeffrey, E. C.
(16) A New Prepinus from Martha’s Vineyard, Proc. Boston
Soc. Nat. Hist. vol. 34, no. 10, p. 333-338, pl. 32.
Seward, A. C.
(17) Fossil Plants of the Wealden, pt. 2. British Museum Cata-
logs.
Hollick, A.
(18) Cretaceous Marls of Cliffwood, New Jersey.
Gothan, W.
(19) Die fossile Hoelzreste von Spitzbergen. Kongl. Svenska
Vet. Ak. Handl. Bd. 45, no. 8.

aa eee “See

Shoo ὩΣ 5. τσὶ Εἰ

DESCRIPTION OF PLATES.

PLATE 1.

Pinus protoscleropitys, transverse section of wood. Χ 40.
Same, transverse section near pith. Χ 15.

Same, radial section. Χ 40.

Same. Χ 80.

Same, tangential section of wood. 40.

Same, showing leaf trace. Χ 60.

PLATE 2.

Same, radial section, showing ray pitting. Χ 150.
Same. Χ 500.

Same, showing ray tracheides. Χ 150.

Same. xX 500.

Same, showing teeth in tracheide. X 500.

Same, showing radial pitting of tracheide. x 600.

PLATE 3.

Pityoxylon foliosum, transverse section of wood. 40.
Same, transverse section at pith. Χ 12.

Same, radial section of wood. Χ 40.

Same, radial section at pith. Χ 12.

Same, tangential section of wood. Χ 40.

Pityoxylon anomalum, transverse section at pith. Χ 12.

PLATE 4.

Same, transverse section of wood. Χ 40.
Same, tangential section of wood. Χ 40.

Pinus protoscleropitys, tangential section including short shoot. Χ 15.
. Same, including leaf trace and short shoot, cut nearer pith. 12.
Pityoxylon anomalum, tangential section, including short shoot. Χ 15.
Same, radial section of wood. Χ 40.

Same. Χ 80.

Pirate 1.

Hovtoen. — Cretaceous Pityoxyta.

XLV

—Vot.

Proc. Amer. Acav. Arts AND SCIENCES.

HOLDEN-CRETACEOUS PITYOXYLA. PLATE 2

ἑ
-

Ἵ,. Ὥς, ὁ

6 if

Proc. AMER. ACAD, ARTS AND SCIENCES VOL XLVIII

wri ae
Sie). 4
nt T

5. 0 ἱ "
ἐν a ry A "

ἣν ir ie tee

fy oh ΘΗ SPER

Ριατε 3.

— Cretaceous Pityoxyta.

HoLpen.

XLVIII.

—VoL.

AND SCIENCES.

Acap. Arts

. AMER

Proc

Hovtven. —Cretaceous Pityoxyta. Pate 4

Proc. Amer. Acao. Arts ano Sciences. —Vor. XLVII!.

; Proceedings of the American Academy of Arts and Sciences.
᾽
νοι. XLVIII. No. 17.— Marcu, 1913

ON THE SCALAR FUNCTIONS OF HYPER COMPLEX
NUMBERS.

SECOND PAPER.

By Henry Taser.

Pet Ce νυ ναι at ΠῚ: My
SVAN ΝΥ ee

ΓΤ ΡῈ

ΗΝ τ

’ ΓΝ

ON THE SCALAR FUNCTIONS OF HYPER COMPLEX
NUMBERS.

SECOND PAPER.

By Henry Taser.

δ 1.

In this paper I shall denote by yz, for 2, 7, k = 1, 2,...m, the
constants of multiplication of a given non-nilpotent hyper complex
number system (¢j, é2,..@m).1 We then have

τὴ
(1) δι 6) = Di Ὑγκε (4,7 = 1,2, ... πὶ).
k=1
In These Proceedings, vol. 41 (1905), p. 59, I have shown that there
are two functions of the coefficients of any number

(2) Α - αὐοι - ας et... + dnem

of the system (61, @,... @m) constituting generalizations of the scalar
function of quaternions, to which they reduce, becoming identical
when m = 4, and, at the same time, the system (¢1, 65, 65, 64) is equiva-
lent to the system constituted by the four units of quaternions. These
functions, in designation the first and second scalar of A, are defined
as follows:

1 m m
(3) ae yO Uva,
4 Ξε τ.
1 γῆ τη
(4) Sel = DS aya
LS AS ET

and conform to theorem I given below. In this paper I shall employ
these functions to establish a simple criterion for the existence of an

m
1A number A =)» aje of any hyper complex system (δι, é2, ... @m) is

i=1
idempotent if A? = A #0; A is nilpotent, if A ~ 0 but AP = 0 for some positive
integer p 1. A system is nilpotent, if it contains no idempotent number;
otherwise, non-nilpotent. Every number of a nilpotent system is nilpotent.
See B. Peirce, Am. Journ. Maths., 4, 113, (1881); ef. H. E. Hawkes, Trans.
Am. Math. Soc., 3, 321 (1902).

628 PROCEEDINGS OF THE AMERICAN ACADEMY.

invariant nilpotent sub system of (e, ¢,...€m), and a method of
determining the maximum invariant nilpotent sub system, if any
exist.2. These results are embodied in theorem IT.

Theorem I. Let yj, for 2, 7, k = 1, 2,...m, be the constants of
multiplication of any given hyper complex number system (61, 2, ... €m)-
Let

A= Me - dae + ... + dnem

be any number of the system; and let

Sie = τῇ

: i=1 j=1
SA=—)o ΟΣ ΤΟΙΣ:
Then both 81.4. and S.A are invariant to any linear transformation of
the system: that is, of

é; ἘΞ τ δ᾽ | T7262 A a Pat Tamm CR Bes oni)

the determinant of transformation not being zero, and if

™
Cie p= pe yen ay = eee
k—
and
A=Mat met... + dnem = We: + deco t ... τΈ αἴθ
then
il m γι
S,A = — UY τῇ,
0. j=1 j=l
1 ™ 7
SA = — >) Qi ὩΣ
ἼΩΝ τ: 5
ὌΞΞῚ ἼΞΞῚ
2A sub system δὲ, Bs, ...By of any hyper complex number system
(€1, 65, ... €m) is said to be invariant if the product in either order of each
number of (é1, €, ...€m) and each number of (Bi, Bo, ... By) belongs to the

sub system, for which the necessary and sufficient conditions are

δὲ Bj = gj Bi + o'r, Ba +... + pi Bp,

Bye; = στῇ Bi + 9.2) Bo oF ee 9’ ij Bp

(Gi Se OR ἢ ΞΞΕΕ ΘΟ ὴς-

An invariant sub system (Bi, Bs, ... Bp) is an invariant nilpotent sub system
if its units by themselves constitute a nilpotent system; and in that case
is a maximum invariant nilpotent sub system if it contains every invariant
nilpotent sub system of (e1, 65, ... @m)-

TABER.— SCALAR FUNCTIONS OF HYPER COMPLEX NUMBERS. 629

If p is any scalar, and

a bye, +- be es + eee + bn em

any second number of the system, we have

SipA = pS, A, δορά = pS.A,
S,(A = B) = S,A = 5.8, S.(A = B) = S.A = SOB,
S,:4B = S, BA, S,AB = SBA.

If «is a modulus of the system,

Sie = 1 = Soe.
If A is nilpotent,

δὶ AP = 0, Sp» AP — 0,
for every positive integer p; and conversely, af either
S14°=0 GH 1, 2, ..- mM)

or
See πῆ Gor - ἢν:

Ais nilpotent. Moreover, A is nilpotent if

8S, Ae, = Sj: Ae = nate = Spee τὺ
or
3.2.4. δι = SxAe = τς Ὁ ΞΞ Nolen ἢ.

If A is idempotent, there are m S,A > 0 linearly independent numbers
of the system satisfying the equation

AX = X,

in terms of which every number of the system satisfying this equation can
be expressed linearly, also mS2A > 0 linearly independent numbers
satisfying the equation

XA =X,

in terms of which every solution of this equation can be expressed
linearly.8

Let
(5) X = 216, + meat... + Amem

3 See paper by the author cited above, pp. 61, 69, and 70, also Trans. Am.
Math. Soc., 5, 522, (1904).

630 PROCEEDINGS OF THE AMERICAN ACADEMY.
and let the number system (ει, é...¢,) contain at least one number
satisfying the system of equations

(6) SX e; = αι δὴ ee; τς 2. δ᾽ €2e; + eae -- Um 81 Cm Oy = 0
Re 77)

The resultant of this system being the determinant

(7) ἍΤ ΞΞ sree, Site, --- Sim ΕἸ | :
|
S11 65, 1 6065, ΠΣ S1 Cm 2 |
S1€1 ms δὲ €2€m, Simm

we then have A; = 0. Let X = B be any solution of equations (6).
Then, by theorem I, B is nilpotent. Moreover, for any number A of
(61, €2)...€m), both BA and AB are also solutions of equations (6).
For, for any number

Y = Wer yee a eee at Un
of (€1, €2, ... 6,1)» We now have
S,B Y = yi Be + y2S1 B es + Sat) -- Ym 51 Bem = 0;
in particular,
δι (BA-e;) = δὲ (B- Ae) = 0,
Si (A B-e;) = Sy (A- Be;) = δ᾽ (Be;- A) = Si (B-e;A) = 0
(ue ΤῊΝ
Since both BA and 4B are solutions of equations (6), they are both
nilpotent.
Further, since, for 1 Sim, Be; is nilpotent, it follows from

theorem I that δ. Β 6; = 0, and thus any solution B of the system of
equations (6) is also a solution of the system of equations

(8) 8. X e; => αι So 6, e; 4- Xe So θα; + bie, + Lm Sem ; ἘΞ

Oe i152, Me. HON
of which the resultant is
(9) As = 39 61 61» So 65 61, πὸ ὁ So Cm ΘΙ "
So €1 65, So 65 €2, acc So Cm θὰ

So €1 Cm) So Ca@m - .. Som Cm |

TABER.— SCALAR FUNCTIONS OF HYPER COMPLEX NUMBERS. 631

By theorem I every solution of equations (8) is nilpotent. Let B’
be any solution of this system of equations. Precisely as above,
we may show that B’ is nilpotent, and that both B’A and AB’
are also solutions of these equations for any number A of the system
(€, 65, ... €m); and, therefore, both B’A and A B’ are nilpotent. Since,
in particular, for 1 <i < m, B’e, is nilpotent, it follows from theorem I
that B’ is a solution of the system of equations (6).

Let now the nullity * of the determinant A; be m’, where 0<m’<m.
There is then a set of just m’ linearly independent numbers,
B,, Βα... Byr of the system (6ι, @...€m) satisfying equations (6);
therefore, just m’ linearly independent numbers satisfying equations
(8), whence it follows that the nullity of A: is m’. For 1Sj Sm’,
the product of B; in either order with any number A of the system is
a solution of equations (6) and, therefore, both B;A and AB; are
expressible linearly in terms of By, By ... By,; otherwise, there is a
set of more than m’ linearly independent solutions of equations (6)
which is contrary to supposition. Moreover, since

Si (9: By + p2Be + ... + Pa’ Bu’) οἱ
= p1 1 Bye; + p28; Boe; + ... + Pm 1 Bye; = 0
ΞΟ ΩΣ
every number linear in the B’s is a solution of equations (6), and is,
therefore, nilpotent. Whence it follows that By, B....B, constitute
an invariant nilpotent sub system of (οι, ¢2. . .€m)-

Further, the sub system (Βι, By... By) contains every invariant
nilpotent sub system of (δι, ¢ ... @m), and is therefore the maximum
invariant nilpotent sub system of the latter. For, let (Ci, C2... Cp)
be any invariant nilpotent sub systetn of (οι, ¢ ...@m). Simce every
number of this sub system is nilpotent, in particular,

SiC; = 0 = t, Ὁ
Moreover, since
C3e; = gC + σα + ... + Ijin Cp
G1 te 7 = Lene Ds
we have
SiC,¢; = Iii S,C, + 9ji2 δὲ. 7 oe ee Jip S1 Cp = 0
fare a” oan eee. © 8):

4 The nullity of a matrix or determinant of order m is m’ if every (γ΄ — 1)th
: : : i : :
minor (minor of order m — m’ + 1) is zero but not every m’th minor (minor
a KS : : "
of order m — m'). Nullity of order m’ is equivalent to rank (Rang) πὶ —m’.

632 PROCEEDINGS OF THE AMERICAN ACADEMY.

and thus each of the C’s is a solution of equations (6). Therefore,
each of the C’s is inexpressible linearly in terms of B,, Bo... By.

Let
(10) 88; = bye: + bees + ... + Dimem (gees eee

We may take the b’s to be rational functions with respect to the
domain R(1) of the constituents of A; (or of As) which are integral
quadratic functions, rational with respect to R (1), of the constants
of multiplication of the number system (ει, @...@m). ΠῚ this number
system belongs to the domain R’, that is, if its constants of multiplica-
tion lie in the domain R’, the b’s may be so chosen as to lie in this do-
main. We may take the B’s as m’ new units of the number system.

Thus let
(11) bine ee = B; (j a i 9): se m’),

and let e's, e’2 ... €’m-m’ be any m-m’ numbers of (ει, 65... 6,4) which

constitute with the B’s a set of m linearly independent numbers. By
what has just been said the coefficients of the transformation

(12) é; --Ξ ἼΣΟΙ = T7202 Sane ΞΕ Tim €m ( = i 2, ες- m)

of the number system can be taken rational in any domain to which
the number system belongs.

If the number system is transformed by the preceding substitution
(12), and if we put

(13) A’ = | Sye';e’;

then, since
™ m

Sieie;= 2 DV tataSioneg, G7 = 1, 2,...m)
h=1 k=1

we have
(14) AY = T*Aj.

where 7᾽ is the determinant of the substitution. Similarly, if
(15) A’, = | So θ΄ 6’) | 3
| (aah = Ὁ πὴ |
we have
(16) Al, = TAs,

Therefore, the equations A; = 0, A, = 0 are invariant to any trans-
formation of the units of the system.

oy

TABER.— SCALAR FUNCTIONS OF HYPER COMPLEX NUMBERS. 633

Let now Δι ¥ 0, in which case As τέ 0, and there is no number of the
system satisfying equations (6), or equations (8); and, therefore, the
system contains no invariant nilpotent sub system. In this case,
therefore, if

S,Ae; = 8, Be; ἴιξευ ea

we have A = B; otherwise, A — B τέ 0 is a solution of equations (6).
Similarly, if
δ. 4.6; = S.Be; (ee! a)
then 4 = B.
We have now the following theorem.

Theorem II. Let (ει, 65... .€m) be any non-nilpolent hyper complex
number system; let
X = xe, + met... + anem
and let
Ai = | Siege;

᾽ A, =
@,7 = 1, 2, ....m)

So eC; 6;

Ce ΞΞ a)
be the resultants, respectively, of the two systems of equations
(a) 8, Xe; = x2Siere; + mSiee; + ... + amSieme; = 0

Gi τ πὴ
and

(B) 8. X e; = αι 8. 61 e; + X So 2 e; - χες + Lin S2 me; ΞΞΝ
C= ΙΕ τ
Then, if the number system is transformed by the substitution
e; = tne. + Tee +... + Timem ΞΕ ἮΝ
and τ
ΔΊ = Sie’;e'; | ᾽ Δ', ΞΞ

GQ, ΞΞΙ Ὁ, 0}

we have
Mas ΠΡ Ay, AY = as,

where T is the determinant of the substitution. Further, the condition,
necessary and sufficient, that the number system shall contain no invariant
nilpotent sub system ts that A, τέ 0, or Ao # 0. In this case, if either

634 PROCEEDINGS OF THE AMERICAN ACADEMY.

S,Ae; = S, Be; (Cn pee ee)
or
S.A e; = So Be; (a = 1; 2, oes m),

we have A = B. If Ay = 0, then Ay = 0, and conversely; moreover,
the nullity of Δι is equal to the nullity of As. Every number of the
system satisfying equations (a) is a solution of equations (8), and con-
versely. If B is any solution of equations (a) (or of equations (@)), then,
for any number A of the system (e1, e2 ...€m), both BA and A B are
solutions of these equations. If the nullity of Δι is m’, there is a set
of just m’ linearly independent solutions of equations (a) (or equations
(8) ); and any such set of m’ numbers of (e1, €, ... ὁ) constitute an
invariant nilpotent sub system containing every invariant nilpotent sub
system of (€1, 65, ... €m):

Let the system (e;, ¢, ... @m) contain a nilpotent sub system
ΟἿ such that

p
Crar= > gC (ΞΞ ΤΡ ee, J ἘΣ
h=1

For 1 <j <p, we then have, by theorem I,

»
το — Weasel ΞΟ eam.
h=1
therefore, A; = 0, and thus (¢,, @, ...é€m) contains an invariant
nilpotent sub system to which the sub system (Ci, C2, : .. Cp) belongs.
Similarly, we may show that, if the system (δι, ¢, ...@m) contains a

nilpotent sub system (Cj, Co, ... Cy) such that
p
EC p= iO ΣΝ (oy Dis) sik Der ΤῸΝ.
h=1

it then contains an invariant nilpotent sub system which includes
the sub system (Ci, Co, ... C;).

If (e1, 65, ... €m) contains a sub system (Cj, Co, ... C,) such that
Siti = SiC =e ge --3 SiC, = 0
or
SoC; = SoC a δρεανΞΞ S.C, >= 0,

this sub system is nilpotent, since then, by theorem J, every number of
the sub system is nilpotent. Thus, if

C= mCi + σού: + arate

TABER.— SCALAR FUNCTIONS OF HYPER COMPLEX NUMBERS. 635

is any number of the sub system, we have

Ct = gC, + ge 0} + ... + gpC);

therefore,

S108 = gM δ᾽ Οἱ + go δὲς + ... + σρί 510 = 0,

for any positive integer gq.

§ 2.
For any given number
™m™
A=} aa
s=1
of the non-nilpotent system (¢1, 60), - - - @m) there is a linear relation
between A, A®, ... A”; therefore, a smallest positive integer

uw m+ 1 for which A, 42, ... A“ are linearly related, and thus for
which we have

{17} Q(A) = A* + pp A* t+... + p,1d = 0,

where the p’s are functions of the a’s. Let pi, po, ..- ρ» respec-
tively of multiplicity μι», μο, .-- μη, be the distinct non-zero roots, if
any, of (ρ) = 0; when we have

(18) Ω (p) = pho (p — ρι)βι (ρ — po)h2 ... (ρ — p,)ke,

where ky 2 1. Further, let

(19) W (p) = ρ(ρ — px) (ρ — po) ... (ρ — py).

Let now

P
f(4)= 2 aA"
h=1
be any polynomial in A. If f(A) = 0, then p 2 μ and f (p) contains
Q(p); otherwise, there is a linear relation between A, A2, ... 45 1,
which is contrary to supposition. Wherefore, if f(A) is nilpotent,
f (e) contains W (p). Conversely, if f (9) contains W (p), f (A) is nil-
potent; and, if f(p) contain Q (p), then f(A) = 0.

Let A be non-nilpotent. Corresponding respectively to the r 2 1
distinct non-zero roots of 2 (p) = 0, are r linearly independent num-
bers lh, Io, ... I,, linear in powers of A, which are severally idempo-
tent and mutually nilfactorial: thus we have

Oe tak ΞΟ ΞΕ To = 0 ΞΕ hs eae

636 PROCEEDINGS OF THE AMERICAN ACADEMY.

If, for 1S ur,

a (ρ — pu) — (o— pu) fo
u) a
(21) He =e eo
ww.) — {0 — pu) — (oo — pu)hu\ ho
φυί )(ρ) ΞΞΞ ( τ G. τ ρω) δὰ )

@=1,2,...u—1,u-+ 1, ... 7);
and

(22) fu(o) = bo (p) di™ (p) .... bua™ (p) dur (p) ... br (p),

we may write
(23) i ἢ (A) Gir re

I shall denote by r the greatest value of r for any number A of the
system. Then r is the greatest number of idempotent numbers, mu-
tually nilfactorial, contained in the system (¢1, 60, --- €m). For, if
possible, let the system contain p > r numbers Ky, Ko, ... Καὶ satis-
fying the conditions

K?, = K, #0, K,K, = 0
a ee ens 725. = τὴ)

The K’s are then linearly independent. If now
A ΞΞΞ AL, + ok a knit -Ἔ ΧΕ,

where the λ᾿ 5 are any p distinct scalars other than zero, the equation
Q(p) = 0 has p > 7 distinct non-zero roots, which is contrary to
supposition.

Let A be non-nilpotent and, for any positive integer p, let

(24) N) = Dp (A) = A? = Σὲ ρΐμ Time

5 For then, in the first place, ἔμ (0) contains p as a factor; therefore, fy, (A)
is linear in powers of A. Moreover, for 1<uX7r, fy (p) ‘does not contain
Q(p), whereas (fu(P))?— fu(P) does contain Q(p); and, therefore, eases 0;
1 —I,=0. Further, for any two distinct integers wu and v from 1 tor,
fu(P) fy (P) contains Q (p); and, therefore, /,/, = 0. By the aid of the above

two equations, we may show that J, Is, ... I, , are linearly independent. Thus, if
J =e); + cro + SAS + 6,1], = (().
then, for W Sh SS 77 Olly S Iopdl Ik = Ws

and, therefore, c, = 0.

TABER.— SCALAR FUNCTIONS OF HYPER COMPLEX NUMBERS. 637

in which case NV“) is nilpotent, since
3
Dp (p) = p? — 9 pu? fu (p)
u=1

contains W (p): therefore, by theorem I,

r r
δὶ Α͂Ρ = Σὰ pu? δὶ Τὰ Ἔ S,N® Νὰ pu? δι1,,
u=1 u=1

(25) : :
S,AP 7 Σ pu? Soly ΕΒ" Ss N) = ὟΣ Pu? Sol.
u=1

u=1

If possible, let
S, A? = 51.411 ae S,A?*-1 = 0
for some positive integer p. By (25), we then have

pe?" Siti a p2?** Si Is oa eae + pe Si; = 0
(h = 0)1; 23. ..0r — 1):

and since, by theorem I, neither 8, i, S,lo, ... nor S;J, is zero, it fol-
lows that

Big ee uml

pitiencd peeaet

which is impossible, since by supposition the p’s are distinct and other
than zero. A fortiore, we cannot have

S, A? = S, A? a S, Apt = 0

for any positive integer p. Similarly, we may show that we cannot
have Ξ
Sy AP = So AP*t ΞΘ 7 .-- Sy AP = 0

for any positive integer p if A is non-nilpotent.
We have now the following theorem.

Theorem III. Let (61, 69, ... €m) be any given non-nilpotent number
system; and let r be the maximum number of idempotent numbers,
mutually nilfactorial contained in the system. Then, if for any number

A = aye, + dgé2 + ... + Omem

638 PROCEEDINGS OF THE AMERICAN ACADEMY.

of the system, we have, for some positive integer p,

SA 0) ne "0; 1, ΕΝ
or

Sar? Oe h 0, 1,5) ogee,

A is nilpotent. Conversely, if A is nilpotent, these equations are all
satisfied for any positive integer p.®

With respect to the idempotent numbers hi, Io, ...J,, linear in
powers of any non-nilpotent number A, the number system may be
regularized as follows. Let Τρ denote the aggregate of numbers

— > he — Σ els aie Σ Σ Ted;
u=1

2 Ξ 1 ἢ Ξῖ

ἴον ὁ = 1,2, ...m. For any assigned integer wu from 1 to 7, let Ty,
and Τὼ denote, respectively, the aggregates

—) hel, and el,— Yo hel
=1

v=1
for? = 1, 2, ... m; and, for. any assigned pair of integers u, v from
1 tor, let Γι denote the aggregate of numbers [,,e;I, for 7 = 1, 2, ... m.

Further, for τὲ and v any two integers from o to 7, let my denote the
greatest number of linearly independent numbers of the aggregate T,,;
and, if m,, ~ 0, let Jun, for h = 1, 2, ... my, denote any system of
m,, linearly independent numbers of T',,. We then have, by (20),
(26) Dh = J uks = agin Lo; Ey J ub’o = J uivo J onal ΞΞ J oh’
(ri MeO A 1 Vi πο le ae Wags, — eee Mae
(27) Lyd uno =0= Jubal y

ἤν ἡ τ ἢ ΞΡ my, we — 1, or a Se

We may now show that the J’s are linearly ἘΠ For, if

r ™pq Mpo
J= Σ᾿ Σ Σ᾿ φριεύρια + 3 ΣΣ Iphod pho
p=1 g=1 h=1 pi
Ut Mop moo
at oy Σ Yohp J onp τὶς ᾽Σ Joho oho = 0,
p=1 h=1 h=1

6 Cf. paper by the author in the Trans. Am. Math. Soc., 5, 545, note.

TABER.— SCALAR FUNCTIONS OF HYPER COMPLEX NUMBERS. 639

then, for any pair of integers u, v from 1 tor,

muv

& GQuvdus = I,J I, =

h=1

and, since by supposition Ju, Ju, ete., are linearly independent, we
have
(aN ΓΞ τ Ok, 2a... Mus)

Whence it follows that

r Myo r Mop Moo
J= > 3 Ypho J pho = Σ Σ Johpe Join + Σ aloe — = 0;
p=1 h=1 p=1 h=1

and, therefore, for 1 Su Sr,

muo Mou
Σ GJuhod uko = I,J = 0, Σ GJohud ohu = JI, = 0.
h=1 h=1
From these equations we derive
Gage Oy Whe ae Dy er re. Bia)
Johu =0 Cs COs OR a ea nee se
Thus, ultimately, we have
moo
a :¥ Yoho J oho = 0;
h=1

whence follows

Joho = 0 (h = 1 2, eee Moo)
Since

(28) οἱ ΞΞ > Σ Led

u=1 v=1

== > (he: — ¥ Tues) ἘΣ itu 2 Το δὲ 1)

u=1 a=) = v=1

+ (ὁ; --ἸΣ ΠΩΣ ahtE Σ 1,911,
u=1

u=1 v=1
a eee

it follows that each unit of (ει, e, ... @m), and thus that any number
of this system, can be expressed linearly in terms of numbers in the
(r + 1)? aggregates T',, (u,v = 0, 1,2, ... τ), and, theretore, linearly

640 PROCEEDINGS OF THE AMERICAN ACADEMY,

in terms of the J’s. Whence it follows that we may take the J’s as
new units, and the number system thus transformed is regularized
with respect to the idempotent numbers hi, Js, ... I,.7

Since, for 1 Su <1, I, belongs to wu, we may put

(29) I, ἘΠῚ ὙΠ ον (u ΞΞ iy 2} asl 7).

If now B’ is any number of the system (61, ¢, ... θη) satisfying the
equation I, B’ = B’, then, by (26) and (27),

a Muy
1) -Ξ 3 ἣΣ Beate anys
7—O0 ἧΞΞῚ
similarly, if B’I, = B”, we have
ro My
BY = Ds Wa Pe
v=0 h=1

Therefore, by theorem I,

mS,I, = Σ Murs
(30)

mSoly = Dy Morus
=O (=A τ
Let (wu, v), for u, v any two integers from 0 to r denote a number of
the aggregate [,,. From (26) and (27), it then follows that the non-
vanishing products of numbers in the several aggregates are given by
the following equations:

(31) (u,v) (v, w) = (u, w)

(1; 10,700 ΞΞ ἢ:
and we further have
(32) (u,v) (v',w) =0
(u, 2, 0’, w = 0,1,2,... 7; o' Ξ »).8

7 When the number system is thus transformed each of the new units is
in one or other of Peirce’s four “groups” or aggregates with respect to each
of the r idempotent numbers J), J2, ... J;. Thus, if uw is any integer from
1 to r and v, τὸ any two integers from Ὁ to r other than τι, then the units
Juhyu (1 “ λι S mw), Juhw (A ΕΞ hy = Muy), συμ (1 Shy S My), and
Jin w (A Shy Sk mM) are respectively in the first, second, third, and fourth
groups with respect to /,. See B. Peirce, loc. cit., p. 109.

We have now

8 Cf. B. Peirce, loc. cit., p. 111.

>

TABER.— SCALAR FUNCTIONS OF HYPER COMPLEX NUMBERS 641

Therefore, if in the square array,

ἘΠῚ Γυ, sae Ts, ΓΟ

Ts, Τὼ, Tor, ΤῸ

Tn, Ty, Tyr, Tyo
Ὕ

To, To, τον I Ors Too

we strike out any p rows or any p columns, the units of the aggregates

in the resulting array constitute a sub system of (6), 65, ...@m). In

particular, for Our, the units of I, constitute a sub system.

Since, by (32), (ει, v) is nilpotent if τὸ ¥ v, we have

(33) Si(u,v) = 0, S2(u, v) = 0 (i, 110; 1, te et),
Let now A be so chosen that r = r, where, as above, r is the greatest

value of r for any number A of the system. The units of Ip) then

constitute a nilpotent sub system; and, since every number of a
nilpotent system or sub system is nilpotent, we now have

(34) Si (0, 0) = 0, S,(00) = 0.
For, otherwise, if Τρ contains an idempotent number Jp, we have
fyi = OF = ΠΣ cee =—ial nec ee)
by (27); and thus the number system (e1, é2 ... @m) contains r+ 1
idempotent numbers mutually nilfactoria!, which is impossible, as

shown above p. 19. Moreover, for 147, there is now but one
p

idempotent number in the aggregate Τὼ For, if possible, let Ty,
Muy

contain a second idempotent number I’, = ΣΣ caJuiy other than Jy,
h=1

in which case we have I’,? = I’,; let

M=1,-l'y
when we have, by (20) and (26),
ere el ΞΡ T=
rl, =, —1') =0= — ΩΤ, = Ll’
and, by (32),
i ee ey 0ST, = I ipa, 1, λ( δ» ὡ.
9 Cf. B. Peirce, loc. cit., p. 112.

642 PROCEEDINGS OF THE AMERICAN ACADEMY.

Wherefore, there are then at least r + 1 idempotent numbers mutually
nilfactorial, namely, I’,, /’’,, and J, for» = 1,2,...uw—1l,u+1, r
which is impossible.

The number system when regularized with respect to r idempotent
numbers, so that Γρὺ contains no idempotent number, and each of the
aggregates Ty, M2, ... T';; but a single idempotent number, is said to
be completely regularized.

For 1 Sur, we may now take the m,, — 1 units other than J,
of the aggregate or system I, so that they shall all be nilpotent; in
which case they constitute by themselves a nilpotent sub system,
every number of which is, therefore, nilpotent.!° 1 shall assume that

in each of the aggregates T,,, (wu = 1,2, ... 1) the units have been so
chosen.
et ᾿
7 Muy
(36) ANS 7a DL LD aut Tuto.

u=0 v=0 h=1

By equations (29), (30), (33), and (34), and by what has just been
stated, we now have

(36) S,A = Σ AumyyuS1 ye
u= =
ie a Σ Gumyyu Murs
u=1 v=0
(37) S.A = Σ᾽ um Sel

ὡς: ὯΝ Σ Gumyyu Mou.

u=1 1=0

᾿ nel say that the two idempotent units J, and I, (1 Su Sr,

1 Ξυξϑη,υ τέ wu) are connected if there are two numbers (uw, 0)" and
(0, uy! such that

Si ἴω, v)’ (v, wu)’ 4 0;
otherwise, not connected. If I, and J, are not connected, then

δι (u, v) (v, μὴ = 0

10 This theorem is due to B. Peirce, loc. cit., p. 118. His proof is defective.
The first proof, I believe, of the theorem without the aid of the theory of
groups was given by me in the Transactions American Mathematical Society,
δ, p. 547, by employing the generalized scalar function.

TABER,— SCALAR FUNCTIONS OF HYPER COMPLEX NUMBERS. 643
for any two numbers (u,v) of Ty, and (v,u) of Ty Let (u, 2)’,
(v, u)’ be any two numbers of Ty, Γιὰ respectively. Then
(u, v)’ (2, u)’ = pl, - N,

by (31), where N, is linear in the nilpotent units of I’, and is, there-
fore, either zero or nilpotent, and thus Δ," = 0 for some positive
integer p. Furthermore,

Si(u, v)! (0, u)! = pSil,.1

If now I, and J, are connected, then, for a proper choice of (wu, 9)»
(υ, u)’, we have S,(u, v)’ (v, τ)" σέ 0, in which case p ¥ 0: therefore,
we may put

(v, u)" > ni (2, u)’ (p? Iu + ΩΝ + ΠΣ + pN,P + N.?),

when we have

/ ur ii Y — i =
(u, 7) (υ, u)” = pea (Plu —Ny)(p? Iu t+ p? Nut ... + ΡΝ τ N.?)
= -- (p? I, == Ney = I,;

and since

[(v, μι)" (u, 9}1} = (υ, u)!”. (u, 9) (υ, u)!”. (u, 0)!
= (υ, u)” I, (u, 0)" = (υ, u)” (u, 2)’,
it follows that
(v, u)” (u, v)’ = 1,

otherwise, there is more than one idempotent unit in T,,, which is
contrary to supposition. Wherefore, if I, and I, are connected, there
are two numbers (u, v)’ and (v, u)’, of ΤΊ and Τὼ respectively, such that

(24, 9) (0, 4)” == Ty, (2, u)’ (u, v)’ = ἢ:
and conversely, since in this case
Si (u, v)’ (v, w)’ = Sil, + 0.

If I, and I, are connected, and I, and I, are also connected, then I,
and I, are connected, where u, v, w are any three distinct integers from

11 Further, Se (u, v)’ (v, wu)’ = pSoly;
therefore, if S; (u, v)’ (v, uw)’ σέ 0, then δ (u, v)’ (v, uw)’ # 0, and conversely.

644 PROCEEDINGS OF THE AMERICAN ACADEMY.

1 to r. For, in this case there are two pairs of numbers, namely,
(u, v)’, (v, uw)’ and (v, w)’, (w, v)’ such that

(u, v)’ (v, wu)’ = I, (0, u)’ (u,v) = 1,
(v, 40) (w, 9)" = Ts (w, v)’ (x, w)’ == 1.
Therefore, if
(u, w)’ = (ὦ, 0)" , w)’, (w, wu)’ = (w, 0)’ (, u)’,

we have, by (26),

(u, 10)" (ων, u)’ = (u, υ)΄. (υ, w)’ (w, 0)’. (a, μι)"
ἘΞ (u, v)’ ΝΕ (v, u)’ = (u, v)' (2, ὯΝ = Loe

(w, u)’ (u, w)’ = (w, 0)’. (v, u)’ (u, υ)΄. (a, w)’
= (ω, 2)" I, (υ, w)’ = (w, v)' (2, w)! = Ty.

For u, v any two distinct integers from 1 to r, let J, and I, be con-
nected. Thus let

(u, v)’ (, u)’ =I, (v, u)’ (u, v)’ ΞΞ ic

Let k = m,, — 1; and let the nilpotent units of T,,, be denoted by
NV, N,, ....N,. Then (u, v)’ and the products N,-(u, 2)’,
for h = 1,2, ...k, are numbers of the aggregate I’, linearly inde-
pendent. For, if

k
90. (u, νυ)" -ἘΠΣ gnNu™ - (ὦ, v)’ = 0,
h=1
then

ry k k
σοι Se eB gh NM a [συ ἡ (u, v)' AP Σ σι! Ny ¥ (u, v)'| (2, τ) ΞΞ 0
(sal h=1

which is impossible, unless the g’s are all zero. Therefore,
My 2k + 1 = my.

Moreover, there is no number in the aggregate I’, linearly indepen-
dent of these k + 1 numbers of this aggregate. For, if (wu, v) is any
number of this aggregate, since (wv) (v, wu)’ belongs to the aggregate
Ti, we have

k
(u, v) (v, u)’ = elu t Y oo Nu”;
hea

TABER.— SCALAR FUNCTIONS OF HYPER COMPLEX NUMBERS. 645

and, therefore,

(u, v) = (ω, 0) I, = (4 v)+(v, u)’ (ει, v)’
= (mlut Y co Nu™) (u, 0)’

h=1
k
GO (u,v)’ — Σ Ch Ny (u, υ)΄.
h=1

Whence it follows that m,, cannot exceed my, = k - 1; and, there-
fore, Mmyy = My, Similarly, we may show next that (v, uw)’ and the
product (x, wu)’ V,, for h = 1,2, ...k, are linearly independent,
and that in terms of these numbers every number of the aggregate
T,, can be expressed linearly. Finally, that J, and the k& products
(v, u)’ N,™ (u, v)’, for h = 1,2, ...k, are linearly independent, and
that in terms of these numbers every number of the aggregate I’,, can
be expressed linearly. Therefore, in particular, 1 I, and I, are con-
nected,

Nyy = Myy = My = My.

For 1 Sim and u,v any two integers from 0 to 7, let (u, v);
denote the component of e; in Γὼ- We then have

(38) Ce ΣΡ ne Ge DA δ
p=0 q=0
Whence, from (32), we derive

I

LX FE Siu, ἴα):

p=0 q=0

(39) δ᾽ (u, τ) δ;

COD
q=0

= Σ Sila, φ) (u,v) = Si (v, u)i (u,v) = Si (u, 0) (2, wi
q=0
(ω, υ = 0, ee en 2. τὸ 3 2}.

We may now show first that if, for ΟΞ ur, the aggregate Tp,

contains any unit, that is, if m,) > 0, the number system (¢1, €2, . . .ém)
contains an invariant nilpotent sub system. For, let (u, 0) #0,
and let

(0, u);(u, 0) 3 (0, 0); ( = 1,2, ... m);

646 PROCEEDINGS OF THE AMERICAN ACADEMY.

when, by (34) and (39), we have

S;(u, 0) 6; = Si(u, 0) (0, u);
= δὲ (0, τ); (u, 0) = δὲ (0, 0); = 0
C= ere ae

and thus (u, 0) satisfies equations (6). Similarly, if m,, > 0(1 Sun),

we may show that (ὁ:, 65, ... 6,8) contains an invariant nilpotent sub .
system.

Again, if Ty,(1 Sur) contains more than one unit, that is, if
My, > 1, the system (e, e2, .. . μι) contains an invariant nilpotent sub

system. For, in this case, there is a nilpotent number (u, uw) of Ty,
whose product with any number of this aggregate is, therefore, nil-
potent;!? and thus (wu) (u, u); for i = 1,2, ...m, is nilpotent:
therefore,

Si(u, we;= Si (u,u) (ua w);,=0 (= 1,2; ... mM);

and thus (u, 1) is a solution of equations (6). If, for τὸ, υ any two
distinct integers from 1 tor, I, and I, are connected, and either I,
or I',, contains more than one unit; that is, if either m,, > 1 or
My, > 1, the system (e1, €2, ... €m) contains a nilpotent sub system.
For then, by the theorem p. 645, we have m,, > 1. Further, if 7, and
I, are not connected, and either Τὼ or I’, contains one or more
units, that is, if m,, > 0 or m,, > 0, the number system contains an
invariant nilpotent sub system. For let (uw, v) ¥ 0: in this case, by
the theorem given, p. 642, we have

Si (u, v) (υ, wu); = 0 (Gi Ante Ὁ:
therefore,

Si(u, v)e; = Si(u, v) (v, u); = ὃ (ie Me eee ane

and thus (u,v) satisfies equations (6). Finally, if 7, and J, are not
connected and m,, > 0, (δι, €2, ... @m) contains an invariant nilpotent
sub system.

12 Namely, when my, > 1, any number (wu, w) linear in the nilpotent units
of Ty, is such anumber. For since J, is a modulus of the system ['yy, these
nilpotent units constitute an invariant nilpotent sub system of ['yy. Where-
fore, the products of (uw, w) and any number of [',, belongs to this nilpotent
sub system, and is, therefore, nilpotent.

TABER.— SCALAR FUNCTIONS OF HYPER COMPLEX NUMBERS, 647

I shall now assume that the number system (ει, δι, ... @m) contains
no invariant nilpotent sub system, in which case, by what has just
been proved, we have

(40) et — ier Mi (ef) Ie ee)

that is, no number of the system is contained in Το nor in either of the
aggregates I’,,, I, for wu = 1,2, ...r. Further,

(41) ee CR Rep Ἦν

that is, J, is the only unit in [,,, for 1 Sur. Finally, for wu and »

any two distinct integers from 1 to r, if I, and I υ are connected,
Myy = My, = 1;
whereas, if ἢ and J, are not connected,
Myy = My, = (ἢ:
In the present case, the number system contains a modulus, viz.,

(42) 6 = Ie ase als

since, for u, v any two integers from 1 to r, if Τὰν contains a unit J,1,,
we have

ED ay = Ju = Jur
by (26) and (27).

It is, with the present assumption, convenient to modify our nota-
tion to indicate the connection which may exist between certain of
the idempotent numbers, J;, 19, ... [;. Le shall, therefore, suppose
these numbers arranged in v adevegdtes, 1Ξ yr, containing respec-

tively μι, μὴ» ....m, of the IJ’s, where Σ My Ξε 1, any two idem-
p=1

potent numbers in the same aggregate being connected, but no
pair of idempotent numbers in different aggregates being connected;
and, for 1 < pS», I shall denote by 1,” (uw = 1, 2, ... u,) the idem-
potent See in the p™ aggregate. The 7° agerepates of numbers,
formerly denoted by I, for u, v = 1, 2, ... 7, into, one or other of
which the units fall when the system is regularized as above and
Sopa no invariant nilpotent sub system, will now be denoted by

Buss (pq) for p,q= 1,2, ... v, and for u= 1, 2, δ oi Dek B= Uy 2, ».. sees

648 PROCEEDINGS OF THE AMERICAN ACADEMY.

and the number of linearly independent numbers in T,,,%” will be
denoted by m,,.°°13. By what is shown above we now have

(44) Th PA. AG”, ye eo 9 ιν Da)

(45) m,?? = 0

(pig il 251.0 tgne=ep; a = ἃ, Qype tigi Dy 2 ΠΣ
For 1S pS» and wu and ὃ any two distinct integers from 1 to pp,
we may now, in harmony with the preceding notation, denote the single
unit of Py?” by Ji”; and if, further, we denote by Jin” the idem-
potent unit I, of T,,'””), we shall have as the multiplication table
of the system

(46) Fur Tru” = purw Taw, FAO Ts ©) 1g
(pr 1, 2) . 2.05 Ue s We 1S: es ee
(47) Juv? Pare = 0

(py, q'= 1, 2, isa V3 QF DPD; U0 — AZ, 3 fps μ΄, υ',ΞΞ 1,2, 5 nah)

by (31), (32), and (44), where pyuy = Pu» = 1. For 15 pS», and for
u, Ὁ any two integers from 1 to yp, it follows from (44) that

Pur? Sida? = Si Fug? Tn’? € 0,
and thus pum” τέ 0, otherwise J,” = I, and J,” = I, are not
connected; and, since
(pueu”)? Fun”) = (pueu Fu)? = (Fur Feu?))?
Ξε Ἵ PAs) or es) Ded = Pru”? Jagd Ὁ) 7 (Ὁ)
ΞΞ pei ig Od i= pr ρα Iai 0,
we have ρων) = pu. Further, for 1 < τ 3 uy,
Pin” Pau den = Dag) dau Ian) = eu das Calne
= Te dun daw = Pru OT 9 OT wy
= Pru d ww” τ ἢ):

and, therefore, ρων) #0.

13 Thus, whereas, formerly [’,, denoted the aggregate of numbers J, e; J,
for i = 1, 2,...m, of which my were linearly independent, Ty‘? is now the
aggregate of numbers /,(?) e;J, for ὁ = 1, 2,... m, of which my?” are
linearly independent.

14 Therefore,

v Hp Ep v

Σ my?) =D LD LD My?) = > My.
lv=1 p=lu=11=1 p=

TABER.— SCALAR FUNCTIONS OF HYPER COMPLEX NUMBERS. 649

Let
> ) 1 i) (p
(48) Ju” = TP Jur? iv ?)
Plu Pl
Ὁ aed Deeg ap ety Vi sb, δ... δὴ.
Then
1 Vora” pin?) =
(49) Jus) =| a (Dp) June? Jy) Sie (Pp) : Tu)
Pulv Pulv

(ΞΡ τ Py Uy OS 8 1p ΘΝ τυ pip)

by (46); and, therefore, we may take the J’s as new units. We now
have

(50) Jus Jw? = l

V ora pr . pu” pro”

Jy) ΟΣ I?) 7 Ὁ)

1 ἘΣ
ΞΞ sete ἢ ΞΞΞΞΞΞΞΞ Jy” oS, Loy=- J wos
Pra pwr”
Ν᾽ wT re) = : FiOS +S Sw) = 0
V pra”) pr?) piv prwi Ὁ)
(p ΞΟ es wp oye, we" 1,2)... pips 0 9);
- = 1
(51) Ju Sve = 2 Ὁ)... + Fy Sty =0

Vora™ pin?) pri pri
Cg Spas LE Sy te = Lee ae a es eo)

For1S Pp Sy, the units J, for τι, » = 1, 2, ... μῳ constitute a quad-
rate of order μρ; and, therefore, in the present case, the number sys-
tem is constituted by v mutually nilfactorial quadrates.'® For the
modulus ε of the system we now have

v Kp ν μῃ bes
(52) CA Σ yz [,?) = Σ Σ Fun?)
p=1 u=1 p=1 u=l1

15 For
Fu) Typ) «7. (Ὁ) yy?) = Sy) Sy") Jy?) Siw = Py J?) Sur Tyo
= Pin?) Jin) Jy).
16 A quadrate is a hyper complex number system with m = 7m units
€uy (U, Vv = 1, 2, ... m) which can be so chosen that
Ἐπ μου ΞΞ ἘΠ ΠΟ ἘΠΕ iy ἴω, τ ΞΘ τ τὰ ὃ πε:
B. Peirce, Am. Journ. Maths., 4, 217.

650 PROCEEDINGS OF THE AMERICAN ACADEMY.

By (80), (33), (40), (44), and (45), we now have

a gh) | Mp
(53) m S; EY => 3D Ds Myy PD = OE Myy??) = Mp
q=1 v=1 v=1
Hp v Hg ἄν
ἘΞ Σ Myf?) = y: Σ γι ’Ῥ) = Mm So 5 PE)
v=1 q=1 ὉΞ1

Girt, 2)... pp ae a ee)

(54) Si Juv” = 0, Sod uv — 0
GENE 2. ν ΞΞΙ ΟΣ pe a
™m
And since, for any number 4 = Σ᾽ aje;, we may now put
i=1

v Hp Hp

(55) A= ¥ EE Psi,

gl wad ei
we have

v Lp

Lp in
(56) δὶ A = >. Σ ΝΣ; Cu”) δὶ J a?

p=1 u=1 v=1

v Lp Lp

πὶ Σ oF Σ Cys) So Tus ΞΞ ΝΣ

p=1 u=1 v=
Therefore, in particular,
(57) 16:6; = Soeze; Gi, FS TD Oy

and thus we have A; = A, also in the case now considered, when the
system (1, @, ... €m) contains no invariant nilpotent sub system and
neither A; nor A, 15 zero.

From the conditions, necessary and sufficient, that the m* constants
Viz (1, J, & = 1, 2, ... m) shall constitute the constants of multiplica-
tion of a hyper complex number system in m units, viz.,

(58) Σ verve = ΣΣ venvin
a Et
(G9; ht=1,2,... m),

TABER.— SCALAR FUNCTIONS OF HYPER COMPLEX NUMBERS. 651

we derive
(59) m™A; = | mSi(e¢;)
45.9 = 1; 2; <<< 'm)

ΣΑΣ ΚΎΝΑ Vink

DaLk Vijk Vkhh |
(37 = 1, 2, ....m)

nope

= | Yin,» --- Yilmy ..- Vimly --+ Yimm |
Gee a Te)

Villy +++ Yjmiy +++ Yjimy +++ Yjimm
(7 = 1, 2, ... m)

᾽

(60) πηι Δ. = | γηυδεϑ) 6; |
ΣΉ aay oom)

= ᾿ Dale Vjik Vrkh | = | Dale Vigk Veh
| (1,2) = toi m) (Ἢ 7 -Ξ ΠΡ ἢν)
a Yijly +--+ Ymjly +++ Yijmy +++ Ymjm

Vil, sae Yiims “ὦ ὦ VM s)= 30s Ymim |
aids lane (7)

OT = he eae γη)

A number system containing no invariant sub system is termed by
Cartan a simple system (systeme simple), and he shows that such a
system is what is here termed a quadrate. A non-simple system
containing no invariant nilpotent sub system Carten terms sem-
simple.17 Such a system is constituted by nilfactorial quadrates of
which the invariant sub systems are any p(1 Sp < νὴ) of these quad-
rates. By what is shown above it appears that A; σέ 0 or A, ~ 0
is the condition necessary and sufficient that a number system shall
be either simple or semi-simple. We have, therefore, the following
theorem:

Theorem IV. Let οι, 65, ... €m be the units of any hyper complex
number system, and let
Ar = | Siege; , Ao = | Soee;
1@j=1,2,... 7) | {πὴ = 1,2,... 1) |
Then Ay = Ay. If Δι ¥ 0, the number system contains a modulus and

is either simple or semi-simple, that is, is constituted by v 21 mutually
nilfactorial quadrates; and, conversely, in this case, Ay = Ag γέ 0.

17 Comptes Rendus, 124, 1218 (1897).

652 PROCEEDINGS OF THE AMERICAN ACADEMY.

§ 3. ‘

It has been shown by C. 5. Peirce that any given hyper complex
number system (¢1, €:, ... @m) is a sub system of a quadrate of order n,
where the greatest value nm need assume is m+ 1. This is, of course
equivalent to the theorem that any given number system can be
represented by a matrix whose order need not exceed m + 1.18

Let now (θι, 69, ... €m) be any given number system; let
Cy (uy v = 1,2, ... mn) be the units of the quadrate of which
(e1, €2, ... €m) 18 a sub system, when we have
(61) EuvErw = Euws EwvEv'w = O

(4, 2, wo = 12h me Hw
and let
γι n

(62) CS Σ Me Oise (i = |, ἊΣ ᾿ς γι).

u=1 v=1
The units 61, 65, ... μι may then be regarded as represented, respec-
tively, by the m linearly independent matrices Fy, Fo, ... E,, where
E,, for ὃ = τ, 2, ... m, is defined by the system of equations,

(63) (ξι΄, &, ot OC En’) ἘΞ ( On, Oy, te bin ὕξι, ζω, te ἘΠῚ
6, Bx, sta Boy

| On, Ano, tee Onn |

m
and any number «= Σ᾽ aye; of (1, 65, ... θαι) by the matrix of the
cw
linear substitution
(64)
m m m 7 :
(&', £5’, te 24) = ( by VO, >: XO, oR ὃΣ ri Oin™ ὕξι, fo, τον ἘΠῚ
| ¢=1 i=1 i=1
m m ™
oy iO, >, 2:00, ΠΝ αν Ὁ
i=1 i=1 s=1
™m γι γι
3 XiOni™, 3 Li One™, see +E LOnn™
ἘΞ [=i i=1

18 Loc. cit., p. 221; also These Proceedings, 10, 392 (1875). In certain
cases, as shown by Peirce, we may take ἡ < m; in other cases, n must be
greater than m. See § 4.

TABER.— SCALAR FUNCTIONS OF HYPER COMPLEX NUMBERS. 653

For any number of the quadrate e,,(u, v= 1, 2, ... ἢ) the two
scalar functions with respect to this number system defined in theorem I
are equal as shown in ἢ 2; and, therefore, but a single symbol is re-

quired for these functions. I shall denote by S A the two equal scalar
functions of any number

γι nm
᾿ Qy1, Ayo, ... Ain |
(65) 2 -- 2 3 Cur Euv =
u=1 v=1 Moi, Ago, ... Aen |
Qni, Ana, ... Ann

of the quadrate; and, by theorem I, we then have

ral 1 wal
(66) S €w = δ Seu O (2.0 = 1 2.2. mea 4), 19
and, therefore,

(67) SA = ose ΞΞ 3 » Auyuy-

I shall denote simply by 1 the modulus of the quadrate, and p1, for
any scalar p, simply by p. We have

nm
(68) {eas See
u=1
cm n n
Any number 4 = Σ Σ᾽ awew of the quadrate satisfies an equation
Oh ὑξξϊ
(69) φ(4) = (A — p1)(A — pp) ... (A — pn) = 0,
where the p’s are scalars; and we have
(70) φίρ) =|p—an, —ap,... — an | = (p — ρι)(ρ --- Pp») =
= (ig Ρ -- -- 74 -.. (ρ — pn).
— Gn, An2, Pp — Gnn |

19 For te tae of ΠΕ. ΣΡ ΞΕΡΕΝι Pe X of the Pane

satisfying the equation ey, X = X is n, since every such number is linearly
expressible in €y1, ἐμῶν - - - €un, and each of these numbers satisfies this equa-

tion. Therefore, by theorem I, n2Si,€un =n. Similarly, the number of
linearly independent numbers X of the quadrate satisfying the equation
X€y, = X is also n; and, therefore, n? 2S2€y, =n. Since, for v σέ τι, ἐὰν is nil-

potent, Si ἔων = So€yp = =0 WFu). ᾽
20 Cayley: Philosophical Transactions, p. 800 (1858).

654 PROCEEDINGS OF THE AMERICAN ACADEMY.

The polynomial ¢(p) is termed the “characteristic function” of A,
and ¢(p) = 0 the “characteristic equation” of A. Since, by (67),
nS A is the sum of the constituents in the principal diagonal of the
matrix representing A, it follows that n SAis equal to the sum of the
roots of the characteristic equation of A,

If A is idempotent, the roots of its characteristic equation are 0 and
1. Wherefore, if A is idempotent, n SAis equal to the multiplicity of
the root 1 of the characteristic equation of A.

In conformity with the notation employed in § 2, let

(71) Ω (4) ΞΞ Ae + p, Aets 2 pA = 0

be the syzygy of lowest order in powers of A. Then ρφ (p) contains
Q(p). Whence it follows that » is the maximum number of distinct
non-zero roots of the equation | Q(p) = 0. Therefore, by theorem IIT,

and what was proved p. 636, A is nilpotent if, for some positive integer p,
8 Atte ig oh S01, 2, ΚΕ μα

Conversely, by theorem I, if A is nilpotent, these equations are satisfied
for any positive integer p.

n
For the scalar functions defined in ὃ 1 of any number A= Σ᾽ ae;
i=1
of the system (¢, 62, ... @m) I shall write S,A and S.A as in ὃ 1 and
§ 2. The symbol S also is significant when prefixed to any letter de-
noting a number of the system (ει, @, ... @m), since any such number
belongs to the quadrate éyw (u,v, = 1,2,...n). We have, by (62)
and (67),

γι
(72) Se; : ΣῈ Buu a= Be ee Pe Oc nm);
| u=1

and, therefore

(73) SA = Στ ἧς Σ A: Duy.
ἜΞΞῚ ΦΞΞῚ πἰΞε]
Let now

(74) X= vs YQ = Ὁ Σ Σ χιθι λιν;

i=1 t=1 u=1 v=1

a

TABER.— SCALAR FUNCTIONS OF HYPER COMPLEX NUMBERS. 655

and let the number system (¢, ὦ, ... @m) contain at least one number
satisfying the system of equations
(75) SXe; = xmSeet wSee;+ ... + amSemex = 0
Ce BOs. on).
= es * |
(76) v= Se,é1, See, ἌΓ S@me1 9
Se, eo, S 2 65, hee S €mes |
pees? oi ee βίου |
(> δ ΘΙ SepGa) <2 OW emen |

we, therefore, now have VY = 0, Let X = B be any number of

(1, €2, ... @m) satisfying equations (75). Then B is_ nilpotent;

moreover, the product, in either order, of B and any number
m

A= YL aye, of the system (¢, 62, ... &m) is also a solution of equa-
k=1
tions (75). For, for any number

Y= yer + yo: .. oF Ym em
of the system (¢1, 65, ... @m), we now have
SBY = mSBe, + 2S Bes Ἔ ... Ἑ Ym 5 Bem = 0:

wherefore, ia particular,
SB*=SBBM=0 (h=1,2,...n—-1),
and thus, by the theorem given on p. 654, B is nilpotent; further,
S(BA-¢;) = S(B- Ae) = 0,
S(AB-e,) = S(e;-AB) = S(eA-B) = S(B-e,A) = 0
(GS 1, ΣΝ.
Since both B A and A B are solutions of equations (75), it follows
by what has just been proved that both B A and A B are nilpotent.
In particular, for 1 Si Sm, Be; is nilpotent; and, therefore, by

theorem I, δι 86; = 0. Whence it follows that B is a solution of the
system of equations

(77) S, Xe; —— aie Sie; ες; -- ve ΝΣ + aye + Um δὶ θῃᾳ ei = 0

(t- ΞΞΕΙ τ΄ τὴ:

656 PROCEEDINGS OF THE AMERICAN ACADEMY.

Wherefore, we now have

Ay = As = 0.21
m
Conversely, if B= ) bye, is any solution of equations (77),
k=1

Be; { <j ™m) is by theorem II then also a solution of these equa-
tions, and thus Be;, by theorem I, is nilpotent: therefore, by the
theorem of p. 654, S Be; = 0 for 2 = 1,2, ... m; that is, B is a solu-
tion of equations (75). Let the nullity of VY be m’, where 1 Sm’ Em.
There is then a set of just m’ linearly independent numbers
B,, Bo, ... By of the system (e, ¢2, ... @m) satisfying equations (75);
therefore, just m’ linearly independent numbers of this system satis-
fying equations (77): whence it follows that the nullity of Δι is m’.
And since each of the B’s satisfies equations (77) it follows, from

theorem IT, that B,, Bo, ... By constitute an invariant nilpotent sub
system of (6). ¢, ...@m) contaiming every invariant nilpotent sub
system of (1, €2, ... €m)-

Let now V +0. In'this case, if, for any two numbers
m 7
AS > Aj Ci, B = > bie;
i=1 s=1

of δι» €2, -- €m), we have
SAe; = SBe; (0 ΞΞ νος ΠΩΣ

then A = B; otherwise, there is a number A — B ¥ 0 of the system
satisfying equations (77). In this case, A; #0 and the number
system (01, ¢2, ... @m) contains a nodulus but no invariant nilpotent
sub system.

Let now the number system (¢1, 2, ... ὁπ) be transformed by the

substitution
(78) δ; Ξε ma t+ tee + ...+Timém ἰδ = 1,2, ..: m);
and jet
(79) Y=" Sens
πὴ
Then, since

m ™m™
το ον ld ππ των ¢
Seie;= ) Σ maSae ἀξ me),
h=1 k=1

21 See p. 630.

TABER.— SCALAR FUNCTIONS OF HYPER COMPLEX NUMBERS. 657

we have

(80) Ὄ Ξ Ie

where Τ is the determinant of the transformation. Therefore, the
equation V7 = 0 is invariant to any transformation of the units of the

system (¢; 65, ... €m).
We have now the following theorem:

Theorem V. Let (οι, 2, ... €m) be any given number system consti-
tuting a sub system of the quadrate εἰν (u,v = 1,2, ... u): thus let

n on
Θὲ ΞΞ ἣν by GisGus (a = ΠΣ 2, Pat m).

u=1 v=1

For any given number

of the quadrate, let

when, for any given number

m mn ἢ
8. -Ξ} iD yey = _ 3 ῪΣ αι Ou Eur

t=1 t=1 u=1 r=1

of the system (€1, €2, ... €m), we have

= ya ag
SX ao > Σ iO uy.
” j=1u=1
Let
i See;
[7 Ξ 1
denote the resultant of the system of equations

™
SXe= Σ᾿ aSge = 0. (¢= 1, 25... m).

j=1

658 PROCEEDINGS OF THE AMERICAN ACADEMY.

Then, if the number system be transformed by the substitution

Gf = τιθι + Tee t+ ... + Timm (i= 1,2, πος ΠΡ).

and τ a
V easier s ,
G39 = 1.2
we have
Vv = does
where T 1s the determinant of the substitution. If V7 τέ 0, the system
(€1, 65, ... €m) contains a modulus but no invariant nilpotent sub system;

and, in this case, if for any two numbers

m m
il 3 Qj Ci, B= > be;
i=1 i=1
of the system we have

SAe; = SBe, (=e 2). am),
then A= B. If VY =Oand m' (0 < πι' £m) is the nullity of Ν᾽, the

system (61, €, ...€m) contains a maximum invariant nilpotent sub
system with m’ units constituted by any m’ linearly independent solutions
of the equations SXe;=0 (i= 1,2, ...m).

In precisely the same way we may now prove the following theorem
of which the preceding theorem is a special case:

Theorem VI. Let (¢1, 65, .. . €m) be any given hyper complex number

system constituting a sub system of the number system εἰ, €, ... €n
whose constants of multiplication are Yu» for u,v, w = 1,2, ...n, 80
that

Ey ey = Σ Varnes
and let
n
= Poder τ ἢ

n

For any number A = ΣΣ ayey of the system (ει, ε5, ... €n), let
u=1

S,4 = ue Σ date: ee A= in Σ Σ uYours

Le res u=1 v=1

TABER.— SCALAR FUNCTIONS OF HYPER COMPLEX NUMBERS. 6959

in which case, for any number

75 7 γι
A=} αἵϑι Ξ > Σ abe,
i=1

s=1 u=1
of the system (1, 65, ... €m), we have
ΕΝ 1 ™m n n =
S,A = yD Σ Σ A Din Yur»
nm t=1 ὩΞΞῚ v=]
al l m mn n nr,
S,A = ΡΣ Σ: Le QO iuYvuv-
Lh es
m
Finally, let X = Y xe, and let
i=1
V= Sieie; ᾿ V2= 8.616;
1 Te aM Git Teed τς at)

be, respectively, the resultants of the systems of equations
(a) 8. Xe; = Spee; + aSiee+ ... + amSiene: = 0
(an A τς τὰν;
(8) SoXe = x1 Sy e,¢; + ayS.e6 + ... + amSreme: = 0
(=a best oe on)

Then, of the number system (e, 2, ... €m) is transformed by the substi-
tution

Θ᾽ = τῇσι + ταῦ Γ΄... + Timem
rc, We ae ἸῺΝ
and if
V1= | Sieiej eee = | 8.616}
| (7 = 1,2, ... m) | (i,j = 1,2, ... m)
we have
Wien” Wig V'2= I?Vo,
where T is the determinant of the substitution. If V1 #0, in which case
Yo #0, and conversely, the system (οι, 2, ... €m) contains a modulus,

but no invariant nilpotent sub system; and in this case, if for any two
numbers

m ™
A=) wei, B= ΣΣ bie;
rae ἘΞ]

660 PROCEEDINGS OF THE AMERICAN ACADEMY.

of this system, we have

S, Ae; = S, Be; (2 = 1,2, Lede),
or

S.Ae, = SoBe; (Gi Ae Oe ΠΝ

then A= B. If the nullity of V1 is m’ (0 < m! Sm), in which case
Vi = 0, the nullity of V2 ts m’, and conversely; and the system
(οι, €2, ... Cm) then contains a maximum invariant nilpotent sub system
constituted by any m’ linearly independent numbers of (e1, 2, ... €m)
satisfying equations (a), or equations (3), every solution of equate Ty (a)
being a solution of equations (3), and conversely.

§ 4.

Let (€, €, ... €m) be any given number system; let e,,, for
u,v = 1,2, ...n, constitute a quadrate of which (ἐι, @, ... @m)-is a
sub system; and let

n

(81) Gt a ease capt ΞΡ eee

co

The units of the system (6ι, 60, ...@m) are then represented, respec-
tively, or may be identified, respectively, with the m linearly inde-
pendent matrices defined by equations (63).

The number system (61, ¢’2, ... e’m) reciprocal to (¢, 85, ... &m)
is then also a sub system of the quadrate: that is,

- “ἢ n

(82) 6; = Σ Σ Nur Eup (2 = 1, oe δὴν m)
uw=1 g=1

for a proper choice of the y’s. For the m numbers ¢’y, 6.5, ... e’m of
the quadrate defined by equations (82) may be identified, respecte
with the m matrices E’;, E's, ... Ε΄» where E’;, for 1 [i Sm, is
defined by the equations
(83) Εἰ, &1, & bi) = ( ma, m2), tee min {&, € ξυ τον En) j

nor), noo), ... nent!

nn, nm, “ets nan
(= ΤΟΥ ΤῊΣ

TABER.— SCALAR FUNCTIONS OF HYPER COMPLEX NUMBERS. 661

and, therefore, if we put

(84) Ma — Oy (| ΞΞῚ 2... ὅν; ἀνὰ ΞΞῚ, 9: ἫΝ

we then have

(85) = tr BS ξ΄ πὴ):

whence it follows that 27, 1΄5, ... E’, are linearly independent, and
(86) BE’; = tr. Εν tr. Ej = tr. (E;E;)

™m γῆ ™m
Ξε ἐγ. (Σ Ὑμὲ Εμ) = ΣΣ vietr. Ex = Σ vin’,
k=1 k=1 k=1
(Os a= 1/257, 2m):
that is to say, the numbers e’), e's, ... em of the quadrate are then

linearly independent, and

™m
(87) ees = Yo vee (7 = 1,2, 220m).
Ral

We may take n = m, and, at the same time, put

(88) Bur =" YVivuy Nur = YViue (i, uU, ὃ = i 2, She m),
unless, for αἱ, d2, ... Gm not all zero, we have, simultaneously,
m ™m™
(89) oy αἱ Vivu = oy 04 Duy = 0,
i=1 aa!

(ao — 152, een),

in which case, neither the m matrices Ej, 15, ... Em of order m repre-
senting, respectively, 61» 65, ... @mnor the m matrices E’;, E's, ... E’m
representing, respectively, e’1, e’2, ... é’m, are linearly independent.?%

22 I here follow Cayley in denoting by tr. M the transverse (or conjugate) of
any given matrix M. Loc. cit., p. 31.

23 If n = m and Oy = Yin, for ὃ. u,v = 1,2, ... m, the constituent of
E; Ej in the uth row and vth column is

πὶ r m m m |
Σ Buw™ θων => Yiwu Ύ)νω = > Vijw You = > Vijw Ous™
w=1 w=1 w=1 w=1

by (54); and, therefore,

662 PROCEEDINGS OF THE AMERICAN ACADEMY.

γι

In this case, there is some number A = )) α;ε; τέ 0 of the system
i=1
γι
(€1, δ, --.- 66) such that A X = Ὁ for any number X = JD. a;e; of
i=1

this system; since we should then have

m
AX = DL Git; Vignes
k=

γι
Σ
7! 1
m m
» (LD av) ze, = 0.
k=1 {{ξιὶ

Conversely, if d = Σ aje; #0 and AX = O for every number X of

‘=1
(€1, €2, . . . €m), equations (89) are satisfied for at least one system of
values a, d2, ... Gm not all zero, and we cannot assign to the @’s, nor

to the 7’s, the values given by equations (88). In this case, we have
S, Ae; = 0 = 8, Ae; (ea UR 0) 5

and, therefore,
Ay = Ao == 0.

It is to be noted that equations (89) are the conditions, necessary
and sufficient, that the reciprocal system shall contain a number

γι
= Σ᾽ aje’; τέ 0 such that X’ A’ = 0 for any number X’ = Σ ze’;
i=1 =
of this system.
Further, we may take n = m and put

(90) Bug => Yuiry Nu ΞΞΞ fori (i; U, v= if ὍΣ coe m),
unless for δι, bs, ... b,, not all zero, we have
m m
(91) DS δ᾽ Yuiv TF > bi bu = 0
t=1 s=1
Geel, 2. πὴ:

in which case FE, 9, ... E, are not linearly independent, nor are

TABER.— SCALAR FUNCTIONS OF HYPER COMPLEX NUMBERS. 663

E’;, E's, ... E’, linearly independent.?* In this case, there is some

m

number B = Σ᾽ dye; 4 0 of (6), 65, ... δ) such that XB = Ο for

i=1 :
γι
every number Δ = ΣΣ 2;e; of this system; and there is also ἃ number
i=l

m

B’ = Σ᾽ Dye’; τέ 0 of the reciprocal system such that B’X’ = 0
i=1

for every number X’ of the reciprocal system. Conversely, if there is

m
some number B = ) be; ¥ 0 of (e, 85, ... €m) such that XB = 0
i=1

™m
for every number X of this system (or if, for B’ = dye’; τέ 0 and
i=1
for any number X’ of the reciprocal system, we have B’ X’ = 0) equa-
tions (91) are satisfied for some system of values by, bo, ...5, not all
zero, and we cannot assign to the 6’s, nor to the 7’s, the values given
by equations (90). When equations (91) are satisfied,

Si: Be, = 0 =S.Be; (=. 2, δή»
and, therefore,
A; = As = 0. ;
When the system (¢), @, ... @m) contains a modulus it is not possible

to satisfy equations (89) nor equations (91).
We may distinguish three cases. First, the given number system

γι
(€1, @, ... €m) may contain both a number A = Σ᾿ α;6; ~ 0 and
i i=1
a number B = ) be; #0 such that 4X = 0, XB = 0 for every
face,
number X = Σ᾽ z;e; of the system, in which case the system does
t=1

not contain a modulus and A; = A, = 0. In this ease it is not possible
to assign to the 6’s the values given by either equations (S88) or (90),
nor to assign to the y’s the values given by either of these equations.
Nevertheless, it may be possible in this case to put n = m, provided
m > 2, but not otherwise. Thus let m = 3, and let

ey = δι, 6165 = 0, 103 = 68,

ὯΔ 1Γ n = m and Oy, = Yui for 1, u,v = 1,2, ... m, it follows from (54)
τη
that ΗΕ: ΕἸ => YijwEw. Cf. note 23.

w=1

664 PROCEEDINGS OF THE AMERICAN ACADEMY,

2.61 = €2€2 = G2@3 = 0, 6301 = €3@2 = 6303 = 0:
if
A = aoe. + ages ΚΖ 0, ΠΡ ΞΘ ΟΣ
we have

Ae Ξ se e;B = 0 (ἡ ΞΞ 153 959}
and we may now put 2 = m = τὸν and
61. = ἘΠῚ; 85. — Ἐ58. €3 = Εἴ3-

On the other hand, let m = 2 and let (6ι, eg) contain a number A ¥ 0
such that
A Qj = A eo = 0.

In this case, we may, without loss of generality, put 21 = οι, when we
have
ey” το 0, eo = 0.

Ὅν ΞΞ bee τ (a = ds 2),

Boy, Ang)

If now

we then have, since e;? = 0,

{τ “ἢ =o ᾿ 4 a,

84%), Aa9 1) 0,0
where k τέ 0 and the determinant of the matrix τῷ is not zero; and,.
therefore, since οι = 0, .

at ay = ὦ & 4 wl,
θοι(2, θυ.) 0, 0

where, without loss of generality, we may put a = 1, β = 0, giving

2

γι = 41, eo = 65.

This system, however, contains no number B σέ 0 for which

Cl B = €9 B —— 0.
Second, the number system (e1, ¢, ...@m) may contain either a
number A ¥ 0 such that Ae; = 0 for i = 1, 2, ... m, or a number

Β ¥ 0 such that e;B = 0 for i = 1,2, ... m, but notboth. In this
case, we may put n = m and assign to the 6’s and 7’s either the values
given by equations (90) or equations (88) respectively.

Third, the system (ει, 65, ...€m) may contain ‘neither a number
A ~ 0 such that Ae; = Ὁ for 7 = 1, 2, ... m nor a number B Ξε 0
such that e;B = 0 for i = 1, 2, ... m, for which a sufficient, but not

TABER.— SCALAR FUNCTIONS OF HYPER COMPLEX NUMBERS. 665

necessary condition, is the existence of a modulus, and, a fortiori,
that A; + 0. In this case, we may put n = m and assign to the 6’s
the values given by equations (88), and to the n’s the values given by
equations (90). We then have

m ~ mm
A= 2S ae; = i δῷ Σ Qi Vivu Eury
i=1 t=1 w=1_v=1
(92) |
m m m m
ig = Σ ae’; = YX = pe GY viu Eur;
ἘΝ wat Gal ea
and, therefore,
ql m γι —
S,A = πε Ὲ ΝΣ: αἰ ται = SA,
m een.
(93)
1 γι γι ==
S.A = 1B Σ αἰΎιωι = ὍΣΣ
ἢ 1 u=1

On the other hand, if we assign to the 6’s the values given by (90) and
to the y’s the values given by (88), which is now possible, we shall have

m mmm
= Σ, QE = a ὃ: Σ GY uir €xry
t=

Sal ἸΙΞΞῚΝ 2:5 Ὁ

(94)
m m γι ™m™
A’ = Me aje'; = sy 2 Σ, Οἱ Ὕϊιυ Eur;
Ὁ ΞΞῚ ἘΞΞῚ 12:35: 053}
whence follows
1 m m ae
1.4 = — Fe. 7 GViua = SA’,
NY na Ἐξ
fs i=1 u=1
(95)
1 75 γι γι:
4 Ξ- -Σ Σ aivuin = SA.
ἣν ΤῊΣ
— 3 5, ᾿
When either the representation of the number system (οι @, . .. @p»)
p « m

and its reciprocal system given by equations (88) or by equations (90)
fails, and indeed in any case, we may proceed as follows. Let n =
m-+ 1, and let

(96 a) Bur Vivi Onsite” -Ξ Oi ΤῸ = 0
(Ὁ, 16,0) ee eae MD
(96 b) Ou msi = 0, 6; maa ΞΞ ‘1,

(2, th ΞΕ 1 eee ΞΕ):

666 PROCEEDINGS OF THE AMERICAN ACADEMY.

moreover, let

(97 a) Nu = Yriu Nm+1,0 = ἢ = 0
ἡ 0.4L eee
(97 b) Numa = 0 iyi = 1
(a = ΟΣ Ὁ ee
The m matrices ἔπι, Es, ... E,, which we thus obtain have the same
multiplication table as the units of the system (¢1, é, ...@m) and

are, moreover, linearly independent. For, if

Ey + ὦ 5 + rec + Cm Em = 0,

then

™
Drea = 0 πα τι us, mi a)s
rad

and, therefore, in particular
71 “᾿
YS Gia 0 | Cpe oe et)
j=1

Further, the m matrices determined by the above values of the 7’s
are also linearly independent and have the same multiplication table

as the system (e’1, 6'., ... €’m) reciprocal to (6), 65, ... €m). We now
have
m m m m
A= Σ aye; = Σ Aj Ox Σ σι Cus + Ci m+)
t=1 t=1 i
(98)
m ™m 77. m
A' = = ie = pa αὶ ΟΣ Σ; Yoiu εὐ + Gani):
i=1 t=1 ya

and, therefore,

S,A = ty x Gi Viuu = τ -- S A,
4#=1 u=1 τ
(99)
; m+t+il1s=,,
Ss ve - ἸῺΣ Σ Yuin = - SA
7)}
7=1 u=1

We may also proceed as follows. Let n = m-+ 1, and let

(100 a) A) = Yuiry Bae = θαι, ἀπ Ὁ = 0
5 (ΠΥ = img A. op ΝΣ

TABER.— SCALAR FUNCTIONS OF HYPER COMPLEX NUMBERS. 667

(1005) θη (Ὁ =0, Omari = 1
4,0 =. 1,2, 0m os ἢ"
moreover, let

(101 a) nu) = Yiuvy Qua” = Mmm = 0
iW, Oe DD. 5. My
(101 b) qm”) = 0, nmi, = 1
(o— 1,2, ... ἡ 0 55 i).
The m matrices 121, 2, ... EH, thus obtained are linearly independent,
as are also the m matrices 2’), E's, ... Εἰ αὶ and the former have the
same multiplication table as the units of the system (¢1, @, ... @m)>

while the latter have the same multiplication table as the units of
the reciprocal system. We now have

m m m m
A= oy aye; = > u( dy Yuiv€us τῖ- “ἢ
{τ--1 ΞΟ ΤΙ 1 3} 55

(102)

m m m m
A’ = } aie; = ¥ a(Z DX Yiuvéuw + emis)
i=1

t= ὮΞΞῚ 55}

and, therefore,

aoe m+1—,,
διά = ἘΞ > Σ Yiu = ian ee ἢ
ἘΞΞῚ ἸῺΞΞ
(103) Ὁ
mt ks eS me
S,A = πὶ Σ Σ γὼ" τ a SA.

The fundamental properties of the scalar functions given in theorem I
are more readily proved for the special case in which the number
system is a quadrate than in the general case. What precedes in this
section indicates how the properties of these functions may be made to
depend upon the properties of the single scalar function of a quadrate.

Ciark UNIVERSITY,
Worcester, Mass.

A
γι * ie i ie
7) Ὺ ἡ Ἢ frie ;
ἣν» eg 6 oS

i! wae?

ins

ΔΑ Π ΠῚ crm ἡ Pen | a rater > 9) ull ait
2 7 ¢ havi iif Le Litt sp) ll ; 7) | “ ἤδγι iyi 4 i vale ik ΝΑ
᾿ i al ies ἰ ἢ is} ων “4 4 ΠῚ a. Ι ᾿Ὶ μ:ΠΠ ry ἢ Σ
" ἰσ stint ay wa st t sdb alii?
᾿ς = Ni ὦ want ἊΝ
a! ῇ ᾿
-" 7. i
(: |
vay \ i, 7
* ' ᾿
᾿ \ 2 Ἷ = ᾿ ᾽ν
: ΠΟΥΛῪ Ὁ
' i |
i St; ip 5 Η
ῇ Ἰ} a
᾿ ᾿ ; ; j A :
; ae he
" γι
; ~
| τ
? , ae
> Wi ἘΦ
᾿ , ale \
ἐ 4) (i
i
@
͵
‘

Proceedings of the American Academy of Arts and Sciences.

Vor. XLVIII. No. 18.—Aprm, 1913.

PRELIMINARY STUDY OF THE SALINITY OF SEA-
WATER IN THE BERMUDAS.

By ΚΈΝΝΕΤΗ L. Mark.

PRELIMINARY STUDY OF THE SALINITY OF SEA-WATER
IN THE BERMUDAS.!

By Kenneto L. Mark.
Presented by E. L. Mark, January 8, 1913. Received February 3, 1913.

The objects of this investigation of the salinity and of the tempera-
ture of the waters in and about the Bermudas were the collection of
data which would supplement those recorded for other parts of the
Atlantic Ocean, especially by the ‘‘ Conseil Permanent International
pour L’Exploration de la Mer,” and the study of the relation of the
salinity to the depth below the surface, to the depth of the sea, and
to the locality. A knowledge of these relations was desired as a part
of the basis for studies on the distribution of oceanic organisms at the
Bermudas.

For these purposes, therefore. samples of water were collected at
various places and depths and the temperature of the water was noted
in each case. The salinity of these samples was determined by the
method used by the “Conseil International.” This consists of the
complete precipitation of the halides of the sea-water by the requisite
amount of a standard solution of silver nitrate. The salinity and
density of the samples are then calculated from the analytical results
by the aid of the Hydrographical Tables of Knudsen.

Procedure.

The water was collected in a Buchanan?-Nansen® stop-cock water-
bottle, as modified by Dr. H. B. Bigelow,’ which allows the free
passage of water through it during its descent, but can be made to
enclose a sample of water at any desired depth. The water was
immediately transferred through a brass cock to glass bottles. Care
was taken to allow as little evaporation as possible during this trans-
fer. The glass bottles were provided with porcelain stoppers with
rubber rings, held on by wire, like the old-fashioned beer-bottle stop-

1 Contributions from the Bermuda Biological Station for Research. No. 25.

2 Challenger Report, Narrative, Vol. I, Part 1, p. 112-117.

3 The Norwegian Sea, its Physical Oceanography based cupen the Norwegian
Researches 1900-1904, by B. Helland-Hansen and F. Nansen. Christiania
1909, in a on Norwegian Fishery and Marine- Pe enications, Vol. II,
1909. No. 2, 55.

4 Dr. Bigelow’ s modification consists chiefly in the substitution of a messen-
ger for the propeller used by Nansen, and will be described in a forthcoming
report to be published in the Bull. Mus. Comp. Zoél., Cambridge Mass.

672 PROCEEDINGS OF THE AMERICAN ACADEMY.

pers. They were the so called “citrate of magnesia” bottles made
by the Whitall, Tatum Co. The water was often stored in these
bottles for several days before analyzing it.

The temperature of the water was determined by a Negretti and
Zambra deep-sea thermometer, which was attached to the cable
carrying the water bottle and directly beneath it. This thermometer
had previously been compared with a thermometer standardized by
the Deutsche Physikalische Technische Reichsanstalt.

The volumes of sea-water taken for analysis and the volumes of
silver nitrate solution required to react with them were measured in a
Knudsen pipette and a Knudsen burette respectively; both were made
by R. Goetze, Leipzig. The former is an ordinary pipette of about
25 ec. 6. capacity, provided with a three-way cock at the top. This
arrangement allows the liquid to pass beyond the cock when the
pipette is being filled; but upon turning the cock so that the body of
the pipette is in connection with the air through its third opening, the
pipette empties itself and the excess of liquid remains behind. Thus
an exact filling is always attained. The Knudsen burette also has a
three-way cock at the top, which is used in the same way. [{ is filled
through a side tube entering at the bottom. The lower part is grad-
uated in terms of the standard used in Knudsen’s Tables.° The
volume between the smallest graduation marks is about .05 ο. c. and
the total capacity of the burette is about 42 c.c. The burette used in
this investigation was carefully standardized and the graduations were
found to be equal within the limit of accuracy of the readings.

A silver nitrate solution, containing about 42 grams of the salt per
liter, was prepared and stored in a large bottle of brown glass. This
bottle, which was placed on a shelf several feet above the table, was
provided with a two-hole stopper, through one hole of which a glass
tubule extended from the bottom of the bottle to the inlet tube at the
bottom of the Knudsen burette. The other hole of the stopper was
kept closed except during the filling of the bottle.

The solution was standardized as follows. A tube of standard
sea-water, obtained from the “ Conseil International” at Copenhagen,
was opened and the Knudsen pipette was immediately filled from it.
The water was run from the pipette into a beaker, allowing one minute
for drainage, and three drops of a one percent sodium chromate
solution were added as indicator. Silver nitrate solution was then

5 Knudsen, Martin: Hydrographical Tables ete. Copenhagen, G. E. Ὁ.
Gad, and London, Williams & Norgate. 1901. v + 63 pp.

MARK.— SALINITY OF SEA-WATER IN THE BERMUDAS. 673

run in from the burette, at first rapidly, but at the end drop by drop,
until a faint reddish tinge in the precipitate was permanent for thirty
seconds. This was taken as the end point. The difference between
the volume of silver nitrate used, as expressed in burette divisions,
and the figure accompanying the standard sample was the value “a”
of the Knudsen tables. Obviously this method of standardization
shows only the strength of the solution as compared with the standard
upon which the Knudsen tables are based; but since the analyses
also are expressed in terms of this standard, no further knowledge of
the concentration is required.

A secondary standard sea-water was prepared by diluting ordinary
sea-water till approximately the same volume of silver nitrate was
required to react with it as was required to react with the original
standard. The exact ratio of these standards was determined with
great care, since the secondary standard was the one constantly used
during the investigation. At the end of the work, however, the silver
nitrate was again compared with the original standard and was found
to be unchanged.

In making a series of analyses, the silver nitrate solution was each
day titrated against the standard water, as just described. The
various samples of water were then titrated in an exactly similar way,
and finally the solution was again compared with the standard. The
temperature of the room was noted during the progress of the work,
but in no case did it vary enough to require any correction of the
results. All determinations were made in duplicate.

Accuracy.

Since the method of analysis consists of comparing the amount of
silver nitrate solution necessary to react with a definite amount of
sea-water with that necessary to react with the same amount of sea-
water of known composition, no standardization of the pipette used
for measuring the water was necessary. The amount delivered by
the pipette was constant, as the time allowed for drainage was always
the same.

The determination of the capacity of the burette in absolute units
was not required. Only the relation of the divisions to each other had
to be known, and these were found to be equal within the limit of
accuracy to which the volume could be read. These readings could
be relied upon to one one-hundredth of a unit. As the total volume
of solution used in a determination was about twenty units, the

Pal { | TF
a i i ΒΝ

* [do FI P
5|0"

5 £013) 12
μι το LJ

6451
ie
ΕἸΣ

{ ot
:

Map οἱ 8S. W. third of the Bermuda Islands.
N. B. The latitude and longtitude of this and following maps is that of the British

1s of are less on the chart of the Hydro-

Ordinance Survey published in 1902.
The latitude of all places is about 18 seconc

graphic Office.

MARK.— SALINITY OF SEA-WATER IN THE BERMUDAS. 675

proportional error was thus one in two thousand. This measurement
limited the reliability of the whole analysis, which was thus trust-
worthy to five hundredths of one percent.

Corrections for change of temperature are unnecessary when the
standardization and analyses are carried out under conditions suffi-
ciently similar. As the limit of accuracy of reading the burette was
one in two thousand, this allowed a variation in temperature of 8° C.,
which was a greater change than ever took place.

That no other sources of incidental error existed was shown by the
facts that duplicate analyses always agreed to one part in two thou-
sand or better, and that comparisons between the silver nitrate solu-
tion and the standard water always showed the same ratio to exist.

Table of Results.

Locality ; Depth

| Latitude | Longitude| below | of bot-
Name | N. W.

| surface | tom

32° 64° fm.
Brackish Pond Flats 2110" 4720“ 1
Between No.2&Cobbler’sCut) 19,45“ 4800“ 7
Great Sound Sta. 1 | 1010" 49'40” 6
“ ae “ 1
1710” | 5100" 83
“107 "20" 34
17 10 50 20 Surface
15'40” Dito
15/05” 50'05” | Surface
U see | Ofe " 10
19/46 38'30” | Surface |
10.444“ 38/10” 18
19'50” 40/20" 6
anne | an 6
20'05 41/13 Surface
19/36” 3730” 50 ca. 2
1944“ 3810“ 20 =} ca.
1800“ 9010“ τ | ca.
147) οὐκρη Sur ace |
1914 42/56 d 10. |
1947“ 42/30” er

Little

Off Nonsuch Jd.

“ “ “ “

TR

Pe
2
3
3
2
1
a.

Castle Harbor Sta.

Off Nonsuch Id. Sta.
uw De “ “
Harrington Sd. Sta.

“

ΠῚ

bE οὐ μι el

1914: 49567" | Surface

“μ'

The positions were usually determined by sighting conspicuous
objects on shore.

The “depth below surface” and the “depth of bottom’ were
measured directly on the iron cable which carried the bottle. For the
positions marked with an asterisk the depth of the bottom was not de-
termined, but is that marked on the chart of the ‘‘ Bermuda Islands’? —
issued by the Hydrographic Office, Washington, D. C., and corrected

ae:

1
ὯΝ
3
rt | |
RaSh:
ΩΤ ἷ

τ
τ
Β
-
E
el
ia
ay
Ri
a
cs

]
ἼΙ
PEE |
as

-“

a: bs
~ “a>
ὃ A (a

No eae! FE

coe

S|

|

+++

ἀπ ΠΗ. 1) 5 4 β 2
| An’ fees
{4 os a ee

Map of N. E. third of Bermuda Islands

1 ΡΉΓΑ 2
iT Pee |
166,40] 1 eee
1

MARK.— SALINITY OF SEA-WATER IN THE BERMUDAS. 677

to 1900 —for the position indicated. The temperature and salinity
were determined as described in the preceding pages.

Samples numbers 10, 20 and 22 were taken after heavy rains and
therefore do not indicate the normal condition of the water. Samples
numbers 24 and 25 were collected by E. L. Mark and were brought to
Cambridge, where they were analyzed.

The pipette and burette used in Cambridge were not the ones used
in Bermuda. The silver nitrate solution also was different and it was
standardized against a different sample of Danish water. The agree-
ment in the analytical results of samples 21 and 25, which were thus
determined absolutely independently, serves to increase confidence
in the reliability of all the analyses.

Discussion of Results.

The salinity of the water of the open ocean in the vicinity of Ber-
muda is undoubtedly that of the samples obtained off Nonsuch Island,
namely 36.43 grams of salt per 1000 grams of sea-water. These
samples were all collected outside the reefs, in positions exposed to
the unbroken swell of the ocean from the south. In taking an average
of the results, however, No. 19 has been omitted, as that sample was
collected under unfavorable conditions. The depth below the surface,
even down to 100 fathoms, appears to make no difference in salinity,
except after recent rainfall.

The water of the shallow enclosed bays was found to increase in
salinity with remoteness from the open ocean. This becomes particu-
larly noticeable by comparing samples 2, 3, 4 and 9, where the suc-
cessive samples were collected farther and farther within the shelter
of the reefs and islands. The samples taken in Castle Harbor, also,
were in good agreement with predictions based upon the connection
of that bay with the ocean. The salinity of the water from the
bottom of Harrington Sound, on the contrary, was surprisingly small,
as compared with that of other enclosed bodies of water. It was found
to be nearly the same as that of the open ocean, although the inlets to
this sound are so narrow that the tide rises only about one fourth as
much as it does outside.

Summary.

Data concerning the salinity and temperature of sea-water in the
Bermudas are presented. These indicate that the salinity is inde-
pendent of depth even down to 100 fathoms, but increases considerably
as the water becomes more and more enclosed.

= EE ee

‘foaming souvurpsig oy} jo deur oy} Wody poonpod

‘spurysy vpnuntog 901 10 dey

Proceedings of the American Academy of Arts and Sciences.

Vou. XLVIII. No. 19— May, 1913.

ON CERTAIN FRAGMENTS OF THE PRE-SOCRATICS:

CRITICAL NOTES AND ELUCIDATIONS.

By Wiiuram ArtHurR HEIDEL,

ProressorR OF GREEK IN WESLEYAN UNIVERSITY.

a εἰ Rive an ae Ley
Wen ΡΥ eae ea ἀν νον

4
‘ j ru ν ᾿ ‘6

ON CERTAIN FRAGMENTS OF THE PRE-SOCRATICS :
CRITICAL NOTES AND ELUCIDATIONS.

By WiturAmM ArtTHUR HEIDEL.

Presented April 9. Received February 28, 1913.

Tue collection of notes here presented owes its origin to a request
for suggestions from Professor Hermann Diels when he was engaged
in revising Die Fragmente der Vorsokratiker for the third edition, since
published (1912). In response to his courteous invitation I sent,
together with a list of errors noted in the second edition, a number of
proposals for the emendation of texts and the interpretation of doubt-
ful passages. Had I then had the requisite leisure it would have been
my duty to explain and defend my suggestions; since that was im-
possible, the notes then submitted were in effect mere marginalia, to
notice which as fully as Professor Diels has done required uncommon
courtesy. To be permitted to contribute even in a small measure to
so excellent an instrument of scholarship is an honor not lightly to
be esteemed. The renewal of certain suggestions previously made
but not accepted by Professor Diels is due solely to the desire to enable
him and other scholars to judge of their merits when the case for them
is properly presented; others, in the correctness of which I still have
confidence, are here left unnoticed because, as referred to in the third
edition, they are already recorded and bear on their face such creden-
tials as are necessary for a proper estimate of their claims. But I here
present for the first time a considerable number of proposed readings
and interpretations, the importance of which, if approved by the
judgment of competent scholars, must be at once apparent to the
historian of Greek thought. If it were customary to dedicate such
studies, I should’ dedicate these notes to my honored teacher and
friend, Professor Diels, to whom I owe more for instruction and
inspiration during a quarter of a century than I can hope to repay.
In the following pages reference is made to chapter, page, and line

682 PROCEEDINGS OF THE AMERICAN ACADEMY.

of his second edition (V?), because the pages of this edition are noted
also in the margin of the third (V*).

c. 2. Anaximander.

V? 12, 28. Plin. N. H. 2. 31. Obliquitatem eius [se. zodiaci]
intellexisse, hoe est rerum foris aperuisse, Anaximander Milesius
traditur primus.

Perhaps the full significance of the clause ‘hoc. ..aperuisse,’ what-
ever the source of the sentiment, is hardly appreciated. The Delphin
edition refers to Plin. N. H. 35. 36 ‘artis foris apertas ab Apollodoro
Zeuxis intravit’; but that is not a real parallel. For such we turn
rather to Lucret. 1, 66 sq.

Graius homo [se. Epicurus] .
apm ee eo magis acrem
irritat animi virtutem, effringere ut arta
naturae primus portarum claustra cupiret.
ergo vivida vis animi pervicit, et extra
processit longe flammantia moenia mundi
atque omne immensum peragravit mente animoque,
unde refert nobis victor quid possit oriri
quid nequeat, finita potestas denique cuique
quanam sit ratione atque alte terminus haerens.

The same conception recurs Lucret. 3, 14 sq.

nam simul ac ratio tua coepit vociferari
naturam rerum, divina mente coorta,
diffugiunt animi terrores, moenia mundi
discedunt, totum video per inane geri res.

For these passages I would refer the reader to my essay, Die Be-
kehrung wm klassischen Altertum, mit besonderer Beriicksichtigung des
Lucretius, Zeitschrift fiir Religionspsychologie, Bd. III, Heft 11, p.
13 sq. Heinze’s parallels to Lucret. 3, 14 sq. ought to have made
clear to him that there is here an allusion to the ecstatic ἐποπτεία of
the mysteries evoked, as I pointed out, by the pronouncement of the
ἱερὸς λόγος (ratio. ..divina mente coorta), coming as the climax of the
rites of initiation, when the mystae catch a visioh and seize the
significance of the world (ἐποπτεύειν δὲ καὶ περινοεῖν τήν τε φύσιν καὶ
τὰ πράγματα), according to Clem. Alex. Strom. ὅ. 11. Miiller on Lucil.
30, 1 compared Lucret. 1, 66 sq., and the editors of Lucretius have

HEIDEL.— ON FRAGMENTS OF THE PRE-SOCRATICS. 683

copied the reference, although the resemblance is altogether superficial
and without significance. Recently Professor Reid, Lueretiana, Har-
vard Studies in Class. Philology, Vol. 22, p. 2, has once more drawn
attention to Sen. Dial. 8. 5. 6, Cogitatio nostra caeli munimenta per-
rumpit nec contenta est id, quod ostenditur, scire: illud, inquit, seru-
tor, quod ultra mundum iacet, utrumne profunda vastitas sit an et hoc
ipsum terminis suis cludatur, ete. I doubt, however, the correctness
of his statement that Seneca was here imitating Lucretius. It seems
to me more probable that both authors are reproducing with some
freedom the thought of an earlier, perhaps Stoic, writer, who may have
been Posidonius. Be that as it may, the thought common to Lucre-
tius, Seneca, and Pliny (and I may add, Bishop Dionysius, ap. Euseb.
P. E. 14. 27. 8) is that a great revelation has come, rending as it were
the curtain or outer confines of the world and permitting a glimpse
into the utmost secrets of nature. Such a revelation, according to
Pliny, ensued upon the discovery of the obliquity of the ecliptic; and
a study of early Greek cosmology clearly demonstrates the capital
importance attached to it. To some aspects of this question I drew
attention in my article, The Ain in Anaximenes and Anaximander,
Class. Philol., Vol. 1, p. 279 sq. Very much more remains to be said,
but I shall have to reserve the matter for a future occasion.

V? 13,2. ‘Avatiwavépos ... ἀρχήν τε καὶ στοιχεῖον εἴρηκε τῶν ὄντων
τὸ ἄπειρον.

For the meaning of ἀρχή Diels refers in V* to the preliminary
statement in my Περὶ Φύσεως, Proceed. of Amer. Acad. of Arts and Sc.,
Vol. 45, p. 79, n. 3. The subject has now received a fuller treatment
in my essay On Anaximander, Class. Philol., Vol. 8 (1912), p. 212 sq.
To the statement there given, though much might be said by way of
enlargement and confirmation, | think it unnecessary to add anything,
except to say that the results of my investigations dovetail admirably
into certain other observations recently made by different scholars.
I refer among others to the views of Otto Gilbert as to the original
meaning of the ‘elements’ set forth in his Griech. Religionsphilosophie,
1911, which reached me at the same time with the off-prints of my
essay; and to Mr. Cornford’s conception of Μοῖρα as developed in
From Religion to Philosophy, 1912. Unfortunately both these authors
accept the Peripatetic tradition regarding the meaning of Anaxi-
mander’s ἀρχή; consequently their observations remain fruitless
when they proceed to interpret the early history of Greek philosophy.

684 PROCEEDINGS OF THE AMERICAN ACADEMY.

V? 13, 7. διδόναι yap αὐτὰ δίκην καὶ τίσιν ἀλλήλοις τῆς ἀδικίας κατὰ
τὴν τοῦ χρόνου τάξιν.

In his note on this passage (V* 15, 28) Diels repeats his former
explanation, “ἀλλήλοις: dativus commodi: das Untergehende dem
Uberlebenden und dieses wieder untergehend dem kiinftig Entsteh-
enden. Vel. Eur. Chrysipp. fr. 839, 19. This interpretation, which
is that now currently accepted, rests obviously on the assumption
that the preceding sentence in Simplicius, ἐξ ὧν δὲ ἡ γένεσίς ἐστι
τοῖς οὖσι, Kal τὴν φθορὰν eis ταῦτα γίνεσθαι κατὰ TO χρεών, preserves
the authentic words of Anaximander and that, in consequence, it is
individual things or objects (τὰ ὄντα) that mutually exact and pay the
penalty for injustice done to one another. On that view Diels’s elab-
oration of the implications of ἀλλήλοις is both obvious and necessary.
I believe, however, that in my essay On Anaximander, p. 233 sq., I
showed conclusively (1) that it is not individual objects but the
contraries, hot and cold, that encroach on one another and _ suffer
periodic punishment inflicted by each on the other (wherefore ἀλλήλοις
is here to be interpreted as a strict reciprocal and not as Diels pro-
poses), and (2) that when this mutual κόλασις is said to recur κατὰ
τὴν τοῦ χρόνου τάξιν, reference is had to the seasonal excess of the hot
in summer and of the cold in winter. The strict limitations of space
imposed upon my essay led to the exclusion of many things which I
reluctantly omitted, and did not admit of a full statement of my views.
I propose, therefore, here to add a few points which may serve to
explain and confirm them. Zeller insists that for Anaximander one
pair of contraries only, the hot and the cold, existed, at least as prima-
rily proceeding from the ἄπειρον; this would rule out the moist and
the dry, which are mentioned with the first pair by Simplicius, as due
to Aristotle. This may be true, but it is not necessarily so; for the
Empedoclean and Hippocratic group of four contraries is too well
attested, and if, as seems certain, Anaximander had in mind the sea-
sonal changes it is hard to conceive of him as overlooking the differ-
ences in drought and moisture which Simplicius mentions with those
of heat and cold. <A passage strikingly illustrating and interpreting
that of Simplicius is found in Philo, ‘De Anim. Saerif. Idon. II. 242
Mang. ἡ δὲ εἰς μέλη τοῦ ζῴου διανομὴ δηλοῖ, ἤτοι ws ἕν τὰ πάντα ἢ ὅτι ἐξ
ἑνός τε καὶ εἰς ἕν" ὅπερ οἱ μὲν κόρον καὶ χρησμοσύνην ἐκάλεσαν, οἱ δ᾽
ἐκπύρωσιν καὶ διακόσμησιν " ἐκπύρωσιν μὲν κατὰ τὴν τοῦ θεοῦ δυναστείαν
τῶν ἄλλων ἐπικρατήσαντος, διακόσμησιν δὲ κατὰ τὴν τῶν τεττά-
ρων στοιχείων ἰσονομίαν, ἣν ἀντιδιδόασιν ἀλλήλοις. Philo

————_—>>— α ΑΝ

HEIDEL.— ON FRAGMENTS OF THE PRE-SOCRATICS. 685

is of course far from thinking of Anaximander and has in mind
Heraclitus and the Stoics only; but we know that the conception of
Heraclitus was older than the fifth century, being traceable to Ale-
maeon, a contemporary of Anaximander. The ἰσονομία τῶν δυνάμεων
(Alemaeon, fr. 4), as the condition of health, and the émuparea and
πλεονεξία of the several constituents of the human body as the cause
of disease, are fixed factors of practically the whole medical tradition
of Greece. We may therefore confidently affirm that the ἰσονομία
«τῶν στοιχείων or rather ray ἐναντιοτήτων." ἣν ἀντιδιδόασιν ἀλλήλοις,
which Philo attributes to Heraclitus and the Stoics, applies with equal
propriety to Anaximander, and explains his meaning. These different
factors, correlated also with the seasonal changes, are mentioned by
Plato, Legg. 906 C, φαμὲν δ᾽ εἶναί που τὸ νῦν ὀνομαζόμενον ἁμάρτημα,
τὴν πλεονεξίαν, ἐν μὲν σαρκίνοις σώμασιν νόσημα καλούμενον, ἐν δὲ ὥραις
ἐτῶν καὶ ἐνιαυτοῖς λοιμόν, ἐν δὲ πόλεσιν καὶ πολιτείαις τοῦτο αὐτό, ῥήματι
μετεσχηματισμένον, ἀδικίαν. The connection, here hardly more than
suggested, is clearly noted by Plato, Symp. 188 A, ἐπεὶ καὶ ἡ τῶν
ὡρῶν τοῦ ἐνιαυτοῦ σύστασις μεστή ἐστιν ἀμφοτέρων τούτων, Kal ἐπειδὰν
μὲν πρὸς ἄλληλα τοῦ κοσμίου τύχῃ ἔρωτος ἃ νυνδὴ ἔγὼ ἔλεγον, τά τε θερμὰ
καὶ τὰ ψυχρὰ καὶ ξηρὰ καὶ ὑγρά, καὶ ἁρμονίαν καὶ κρᾶσιν λάβῃ σώφρονα,
ἥκει φέροντα εὐετηρίαν τε καὶ ὑγίειαν ἀνθρώποις καὶ τοῖς ἄλλοις ζῴοις τε
καὶ φυτοῖς, καὶ οὐδὲν ἠδίκησεν " ὅταν δὲ ὁ μετὰ τῆς ὕβρεως "Epws ἔγκρατέ-
στερος περὶ τὰς τοῦ ἐνιαυτοῦ ὥρας γένηται, διέφθειρέν τε πολλὰ καὶ
ἠδίκησεν. On this passage ep. Hirzel, Themis, Dike und Verwandtes,
p- 220 sq. The medical doctrine expounded by Eryximachus in the
Symposium, although perhaps slightly colored with Heraclitean
thought, is that of the Hippocratic treatises, notably of Περὶ φύσιος
ἀνθρώπου, from which we may quote one passage, c 7 (6.48 L.), κατὰ
φύσιν yap αὐτέῳ ταῦτά ἐστι μάλιστα τοῦ ἐνιαυτοῦ . . . ἔχει μὲν οὖν ταῦτα
πάντα αἰεὶ τὸ σῶμα τοῦ ἀνθρώπου, ὑπὸ δὲ τῆς περιισταμένης ὥρης ποτὲ
μὲν πλείω γίνεται αὐτὰ ἑωυτῶν, ποτὲ δὲ ἐλάσσω, ἕκαστα κατὰ μέρος [= ἐν
μέρει] καὶ κατὰ φύσιν (sc. τοῦ ἐνιαυτοῦ] ... ἰσχύει δὲ ἐν τῷ ἐνιαυτῷ τοτὲ
μὲν ὁ χειμὼν μάλιστα, τοτὲ δὲ τὸ ἦρ, τοτὲ δὲ τὸ θέρος, τοτὲ δὲ τὸ φθινό-
Twpov* οὕτω δὲ καὶ ἐν τῷ ἀνθρώπῳ τοτὲ μὲν τὸ φλέγμα ἰσχύει, τοτὲ δὲ τὸ
αἷμα, τοτὲ δὲ ἡ χολή, πρῶτον μὲν ἡ ξανθή, ἔπειτα δ᾽ ἡ μέλαινα καλεομένη.
Not to repeat what I have elsewhere said in regard to the doctrines
of Heraclitus and Empedocles, I refer the reader to my essay Qualitative
Change in Pre-Socratic Philosophy, Archiv fiir Gesch. der Philos.,
Vol. 19. pp. 360 sq. and 365. Since the ἀδικία and the δίκη καὶ τίσις
of Anaximander refer not to the origin and destruction of individual
objects but to the successive encroachment of the elemental opposites

686 PROCEEDINGS OF THE AMERICAN ACADEMY.

one on another in the seasonal changes of the year, it follows that the
words of Anaximander cannot be used to support the interpretation
of his ἄπειρον-ἀρχή as a metaphysical world-ground in which the sin
of individual existence is punished by the reabsorption of the concrete
objects of experience. For this see On Anaximander, p. 225, n. 3, and
my review of James Adam, The Vitality of Platonism and Other Essays,
Amer. Journ. of Philol., Vol. 33 (1912), p. 93 sq.

V? 13, 34. [Plut.] Strom. 2, φησὶ δὲ τὸ ἐκ τοῦ ἀιδίου “γόνιμον θερμοῦ
τε καὶ ψυχροῦ κατὰ τὴν γένεσιν τοῦδε τοῦ κόσμου ἀποκριθῆναι καί τινα
ἐκ τούτου φλογὸς σφαῖραν περιφυῆναι τῷ περὶ τὴν γῆν ἀέρι ὡς τῷ
δένδρῳ φλοιόν. ἧστινος ἀπορραγείσης καὶ εἴς τινας ἀποκλεισθείσης
κύκλους ὑποστῆναι τὸν ἥλιον καὶ τὴν σελήνην καὶ τοὺς ἀστέρας.

The words τὸ... ψυχροῦ have been much discussed and variously
interpreted. Zeller, I* 220, n. 1, pronounces the text corrupt and
suggests φησὶ δ᾽ ἐκ τοῦ ἀιδίου τὸ γόνιμον θερμόν τε καὶ ψυχρόν, rejecting
Neuhiauser’s obviously correct proposal to take the genitives θερμοῦ
and ψυχροῦ as depending on γόνιμον. Burnet, Marly Greek Philo-
sophy*, p. 66, retaining the traditional text, renders, “Something
capable of begetting hot and cold was separated off from the eternal.”
If we were dealing with a poet we might take such liberties, but we
may safely dismiss the interpretation as impossible for prose. Diels
gives no definite indication of his understanding of the words, but
claims γόνιμον as possibly belonging to Anaximander, certainly to
Theophrastus, referring in support of his contention to Porphyr. De
Abstin. 2.5. The text of Porphyry, however, throws no light on ours,
and there is good reason to doubt whether we may attribute the word
to Theophrastus. In all probability we are dealing with a Stoic
source, however related to Theophrastus; for γόνιμον seems to be
a congener to the λόγος σπερματικός of the Stoics. Cp. Mare. Aurel.
9.1.4, λέγω δὲ τὸ χρῆσθαι τούτοις ἐπίσης THY κοινὴν φύσιν ἀντὶ τοῦ συμ-
βαίνειν ἐπίσης κατὰ τὸ ἑξῆς τοῖς γινομένοις καὶ ἐπιγινομένοις ὁρμῇ τινι
ἀρχαίᾳ τῆς προνοίας, καθ᾽ ἣν ἀπό τινος ἀρχῆς ὥρμησεν ἐπὶ τήνδε τὴν
διακόσμησιν, συλλαβοῦσά τινας λόγους τῶν ἐσομένων καὶ δυνάμεις γονίμους
ἀφορίσασα ὑποστάσεὠών τε καὶ μεταβολῶν καὶ διαδοχῶν τοιούτων. It
seems fairly certain that τὸ... γόνιμον θερμοῦ τε καὶ ψυχροῦ is the
Stoic ἄποιος ὕλη which contains δυνάμει the hot and the cold of the
cosmos. We thus find masked in Stoic phraseology the φύσις ἀόριστος
of Theophrastus. This γόνιμον θερμοῦ τε καὶ ψυχροῦ is, at least in
extent, not identical with the ἄπειρον itself, but was “separated off”
from it at the origin of our cosmos. It must, therefore, be that por-

HEIDEL.— ON FRAGMENTS OF THE PRE-SOCRATICS. 6S7

tion of the ἄπειρον-ἀρχή which gave rise to the present world. Tan-
nery, Zeller, Burnet, and others regard ἐκ τοῦ ἀιδίου as referring to the
ἄπειρον, thinking perhaps of certain passages referring to Xenophanes,
Melissus, and Anaxagoras; but Zeller at least perceived that this was
not to be accepted without considerable violence to the text. 1 main-
tain the correctness of my suggestion, On Anaximander, p. 229, n. 2,
that we are to supply ἀπὸ τοῦ ἀπείρου with ἀποκριθῆναι, whether it
ever stood in the text or not, and that the phrase ἐκ τοῦ ἀιδίου, which
stands just where it belongs, means “from eternity.” We are familiar
with és ἀίδιον, “forever,’’ and Marc. Aurel. 2. 14; 4. 21; 10. 5 thrice
uses ἐξ ἀιδίου in that sense, and numerous other instances might be
cited. It happens that I cannot point to another instance of ἐκ τοῦ
ἀιδίου, but the analogy of parallel expressions occurring with and
without the article would render it not at all surprising if such should
be found in late authors. The expression under consideration may be
taken with confidence to mean “ The eternal substratum capable by
dynamic evolution of producing hot and cold.”

The remainder of this interesting passage also deserves renewed
consideration. It speaks of a ‘sphere of flame,’ and this appears to be
generally accepted as establishing the sphericity of Anaximander’s
cosmos. Diels has not, to my knowledge, expressed himself in un-
mistakable terms; but his description of the φλογὸς σφαῖρα as a “ Wa-
berlohe”’ would be best taken as applicable to a circle. A conclusion
so opposed to the apparent meaning of the word σφαῖρα will surprise
no one who is familiar with the general ambiguity of words in Greek
meaning ‘round’ and the uncritical habit among later authors of
attributing Eudoxian notions to earlier cosmologists and astronomers,
provided that the remainder of the statement points to a circle rather
than a sphere. I have no intention of discussing here the whole
subject, which would require a connected examination of all the data
of early Greek cosmology, but propose to confine my attention to this
one passage. It is pertinent, however, to remark that on other
grounds I have elsewhere found reasons for doubting the correctness
of the Aristotelian account, which places the earth in Anaximander’s
scheme at the center of asphere; for if Aristotle’s authority is accepted
as final, the interpretation here offered will be ruled out of court
without a hearing. See my essay, The Δίνη in Anaximenes and
Anaximander, Class. Philol., Vol. 1, p. 279 sq., especially p. 281.

Let us then address ourselves to the text: καί τινα ἐκ τούτου φλογὸς
σφαῖραν περιφυῆναι τῷ περὶ THY γῆν ἀέρι ws τῷ δένδρῳ Provdv* ἧστινος
ἀπορραγείσης καὶ εἴς τινας ἀποκλεισθείσης κύκλους ὑποστῆναι τὸν ἥλιον καὶ

688 PROCEEDINGS OF THE AMERICAN ACADEMY.

THY σελήνην Kal τοὺς ἀστέρας. The orthodox view appears to be that
a sphere of flame is somehow exploded and (rather curiously!) reduced
to a succession of circles of flame confined within an envelope of mist;
these circles being those which constitute sun, moon, and stars.
We have come to expect definite analogies and clear ‘Anschauung’
among the early Greek philosophers; and the severe strain which the
current view puts on the imagination would of itself cast suspicion
on it. We might nevertheless feel compelled, however reluctantly,
to accept it, if the details of the account itself pointed to it or were
even consistent with it. It will probably be conceded that — the
term σφαῖρα apart — it is vastly simpler to conceive of a wide annu-
lar mass breaking up into annular parts than to imagine the same
result ensuing from the destruction of a sphere. But as a matter of
fact our text says nothing that may fairly be interpreted as implying
the breaking or exploding of the sphere. The crucial words are
περιφυῆναι and ἀπορραγείσης. Perhaps the real force of neither word
has been appreciated. Here περιφυῆναι means that the “sphere” at
first “snugly fitted” or was “closely attached to” the “air” which
encircles the earth; whereas ἀπορραγείσης states merely that subse-
quently it became detached, as even a superficial attention to the nor-
mal meaning of the terms will convince the reader. The contrast
may be illustrated by Arist. Hist. Animal. 5. 19. 552°3, ταῦτα δὲ χρόνον
MEV τινα κινεῖται προσπεφυκότα, ἔπειτ᾽ ἀπορραγέντα φέρεται κατὰ τὸ ὕδωρ,
αἱ καλούμεναι ἀσκαρίδες. Besides, ἀπορρηγνύναι is not the proper word
to use of the tearing of such an envelope as a sphere of flame; Greek
writers so use ῥηγνύναι, διαρρηγνύναι, and περιρρηγνύναι, especially
the last-mentioned, as might be shown by a long list of examples
derived from Aristotle and other authors. The same general concep-
tion is implied in the simile ws τῷ δένδρῳ φλοιόν. We may not press
similes beyond the immediate point of comparison, which in this
instance is the snugness of the fit; but if one is to press it, it is
obvious that the bark of a tree is annular rather than spherical. It
will hardly serve the interest of the objector to refer to Anaximander’s
notion of the prickly integument of the first animals, V2 17, 18, ἐν
ὑγρῷ γενηθῆναι τὰ πρῶτα ζῷα φλοιοῖς περιεχόμενα ἀκανθώδεσι....
περιρρηγνυμένου τοῦ φλοιοῦ ; for there, as περιρρηγνυμένου sufficiently
shows, the conception is altogether different. It is quite possible, as
later Greek thinkers prove, to conceive of the cosmos and the human
embryo as equally inclosed in a ὑμήν without pressing the comparison
beyond reason. I have noted with some interest another passage in
which the meaning of ἀπορρηγνύναι has been similarly misconceived.

HEIDEL.— ON FRAGMENTS OF THE PRE-SOCRATICS. 6S9

Arist. Hist. Animal. 5.18. 549” 31 sq. the spawning of the octopus
and the development of its young are described. There we read
550° 3, τὰ μὲν οὖν τῶν πολυπόδων μεθ᾽ ἡμέρας μάλιστα πεντήκοντα γίνεται
ἐκ τῶν ἀπορραγέντων πολυπόδια, καὶ ἐξέρπει, ὥσπερ τὰ φαλάγγια, πολλὰ
τὸ πλῆθος. Professor Thompson in his recent translation renders it
thus: “Some fifty days later, the eggs burst and the little polupuses
creep out”’ [italics mine]. In fact there is no reference to the bursting
of the eggs. Aristotle’s meaning is that that which develops into the
individual polyp becomes detached from the vine-like mass which he
has previously described, and that the young crawl forth (not from
the eggs, but) from the hole or vessel in which the spawn was deposited.

To return to the cosmology of Anaximander: the words καὶ εἴς τινας
ἀποκλεισθείσης κύκλους refer not specifically to σφαῖρα but to φλόξ.
The Waberlohe by some means, doubtless identical with that which
detached the envelope of flame from the envelope of “air” was segre-
gated into a number of annular masses, each like the earth inclosed
in an envelope of “air.” This segregation is not specifically mentioned
but must be inferred; and we can guess only at the immediate cause
of it. Now it is fairly certain that Anaximander knew the obliquity
of the ecliptic or, as the early Greeks seem regularly to have called it,
the inclination or dip of the zodiac or ecliptic. Pliny, as we have
seen, attached great significance to its discovery, and so far as we
know all the early Greek philosophers regarded it as an actual dipping
resulting from some cause subsequently to the origin of the cosmos.
Such an event would amply explain the initial break between the
respective envelopes of “air” and flame; what caused the subsequent
disintegration of the circle of flame into separate rings we do not
know and perhaps it were idle further to speculate.

V? 17, 18. Aet. 5.19.4, ᾿Αναξίμανδρος ἐν ὑγρῷ γενηθῆναι τὰ πρῶτα
ζῷα φλοιοῖς περιεχόμενα ἀκανθώδεσι, προβαινούσης δὲ τῆς ἡλικίας
ἀποβαίνειν ἐπὶ τὸ ξηρότερον καὶ περιρρηγνυμένου τοῦ φλοιοῦ ἐπ᾽
ὀλίγον μεταβιῶναι.

In V! 2"4? the word χρόνον was omitted by mistake after ἐπ᾿ ὀλίγον;
his attention having been called to the omission by me, Diels has re-
stored it in V*. Ordinarily a fact of this sort would hardly deserve to
be noted; but since the false reading has found its way into Kranz’s
Wortindex, s. v. μεταβιοῦν, and has been quoted without question by
various writers, as e. g. by Otto Gilbert, Die meteorol. Theorien des qr.
Altertums, p. 332, n. 1, and Kinkel, Gesch. der Philos., I. p. 7*, it calls
for more than a tacit correction. This is the more necessary because

690 PROCEEDINGS OF THE AMERICAN ACADEMY.

the text has been very generally misunderstood and false conclusions
have been drawn from it. It is perhaps unnecessary to recount in
detail this chapter of curious errors. I have no means of knowing
what interpretation Diels now puts on the text; but in the absence
of any indication in his notes it seems reasonable to assume that he
still adheres to the view briefly set forth in the index to his Dozo-
graphi Graeci, 5. v. μεταβιοῦν: “mutare vitam [cf. μεταδιαιτᾶν].᾽ This
may be said to have been the common view of recent interpreters, until
Burnet, Early Greek Philosophy, p. 72 sq., correcting the version
of his first edition, returned to the correct rendering of Brucker,
“ruptoque cortice non multum temporis supervixisse,” which Teich-
miiller with characteristic ignorance of Greek sharply condemned,
Studien zur Gesch. der Begriffe, p. 64, n. Tannery, Pour V’histoire de
la science helléne, pp. 87 and 117, gives in effect two renderings, each
incorrect. The important point to note is that ἡλικία can refer to
nothing but the age of the individual; and that ἐπ᾽ ὀλίγον χρόνον can
have but one meaning, to wit, “for a short time only.” The force
of μεταβιῶναι must, therefore, be determined with reference to these
known quantities of the problem. This once granted, the decision
between the rival claims of vitam mutasse and supervixisse is easy and
certain. To be sure, μετά in composition far more frequently implies
change than it denotes ‘after’; but μεταδειπνεῖν is as well attested as
μεταδιαιτᾶν. However if, as seemed plausible from Diels’s earlier
editions, it were possible to conceive that the correct text was ἐπ᾽
ὀλίγον μεταβιῶναι, one might have inclined to take ἐπ᾽ ὀλίγον in the
sense of “to a small extent,’’ as in Arist. Meteor. 350 28 and Mar-
cellinus, Vita Thucyd. 36, and to interpret μεταβιῶναι as referring to
a change in the mode of life. Another possibility, which I have con-
sidered, would be to take ἐπ᾽ ὀλίγον and μεταβιῶναι in the sense just
indicated and to read χρόνῳ for χρόνον, thus obtaining the sense “ they
changed their mode of life to a small extent in course of time.” This
suggestion was very tempting to one who was prepared to find an
anticipation of Darwinism in Anaximander; but against all these
proposals ἡλικία stands with its inexorable veto. The sort of change
contemplated would require more than one life-time, and ἡλικία limits
the action of μεταβιῶναι to the life-period of the individual. We must
therefore content ourselves with the rendering “As they advanced
toward maturity the first animals proceeded from the wet on to the
drier ground and as their integument burst (and was sloughed off)
they survived but a little while.” Perhaps this interpretation may
be further supported by a comparison of the view thus obtained with

HEIDEL.— ON FRAGMENTS OF THE PRE-SOCRATICS. 691

that of the origin of animal life attributed to Archelaus, V? 324, 18,
περὶ δὲ ζῴων φησίν, ὅτι θερμαινομένης τῆς γῆς TO πρῶτον ἐν τῷ κάτω μέρει,
ὅπου τὸ θερμὸν καὶ τὸ ψυχρὸν ἐμίσγετο, ἀνεφαίνετο τά τε ἄλλα ζῷα πολλὰ
καὶ οἱ ἄνθρωποι, ἅπαντα τὴν αὐτὴν δίαιταν ἔχοντα ἐκ τῆς ἰλύος τρεφόμενα
(ἦν δὲ ὀλιγοχρόνια) " ὕστερον δὲ αὐτοῖς ἡ ἐξ ἀλλήλων γένεσις συνέστη.

c. 3. Anaximenes.

V? 17, 37. οὗτος ἀρχὴν ἀέρα εἶπεν καὶ τὸ ἄπειρον.

In his note in δ᾽ὃ Diels says: ‘“ Missverstiindnis oder Verderbnis
statt καὶ τοῦτον ἄπειρον. This suggestion is plausible, but far from
certain. As I showed in my study of ἀρχή, On Anaximander, various
vestiges of an earlier cosmological, non-metaphysical, sense of that
word survive in Aristotle; it can hardly be thought impossible that
the same should be true of Theophrastus, from whom this statement
of Diogenes ultimately derives. Indeed, as we shall see when we
discuss Diogenes’s account of the cosmology of Leucippus (ep. p. 732,
on VY? 343, 1), there is at least one such vestige, though almost obliter-
ated by the unintelligence of excerptors or copyists. But, leaving
that for the present aside, we are credibly informed that Anaximenes
regarded the outer “air” as boundless, upon which fact Diels relies
for his proposed correction; and we know that Anaximenes held the
doctrine of the cosmic respiration, in accordance with which the
cosmos subsists, as it arises, by receiving its substance from the
encircling ἄπειρον in the form of πνεῦμα or breath. This πνεῦμα comes
from and returns to the ἄπειρον, which is therefore nothing else but an
ἀρχὴ καὶ πηγή, or reservoir, of πνεῦμα. We thus have a complete
parallel, so far as concerns the πνεῦμα-ἀήρ, to the doctrine of the
early Pythagoreans reported by Aristotle. Cp. my Antecedents of
Greek Corpuscular Theories, Ὁ. 139 sq. In V* I. 354, 16 sq. Diels has
corrected the text of Aristotle along the lines I suggested. I cannot,
however, approve of the bracketing of χρόνου, ib. 22, as proposed by

Diels.
V? 18, 30 sq. Hippolytus, Ref. 1.7.

The corrupt state of the text of Hippolytus’s Philosophumena,
especially in the first book, is well known. With the aid of Cedrenus
Diels has been able to set many passages right; yet much remains
to be done. In 1. 7, the chapter devoted to Anaximenes, several
additions or interpolations which ought to be removed: or bracketed

692 PROCEEDINGS OF THE AMERICAN ACADEMY.

still encumber the text, though we cannot determine to whom they
are due. Diels formerly bracketed πυκνότατον (V? 18, 39), but now
contents himself with characterizing it as an inaccuracy of the late
compiler. There are, however, two larger additions which are false
and misleading. V? 18, 31, ἀέρα ἄπειρον ἔφη τὴν ἀρχὴν εἶναι, ἐξ οὗ
τὰ γινόμενα καὶ τὰ γεγονότα καὶ τὰ ἐσόμενα καὶ θεοὺς καὶ
θεῖα γίνεσθαι, τὰ δὲ λοιπὰ ἐκ τῶν τούτου [so Diels, following C:
τούτων ΤΠ] ἀπογόνων. It is obvious that in the statement of Theoph-
rastus the ἀπόγονοι were those of the first generation, and not the
absurd list we here have presented to us. The primary forms of
existence are afterwards mentioned, V? 18, 35-40: the report of
Theophrastus is even better preserved by Cic. Acad. 2. 37. 118 (V? 19,
16), ‘““Anaximenes infinitum aéra, sed ea, quae ex eo orerentur, defi-
nita: gignt autem terram, aquam, ignem, tum ex ls omnia. The
variant readings above noted are probably due to the intrusion of the
impertinent clause, which clearly does not derive from Theophrastus.
Whether Hippolytus or some other made the addition I find it diffi-
cult to decide. A second instance of the same kind occurs V? 18, 35,
κινεῖσθαι δὲ ἀεί: ov yap μεταβάλλειν ὅσα μεταβάλλει, εἰ μὴ κινοῖτο.
This sentence is awkward and intervenes between two parts of the
exposition of the changes to which “air” is subject. What we expect
from Theophrastus is something about the κίνησις ἀίδιος, and doubt-
less he did refer to it here. The clause κινεῖσθαι δὲ ἀεί in all probabil-
ity is sound and derives from him; but the sentence οὐ yap. . .
κινοῖτο introduces a foreign element. Perhaps Hippolytus found it
in his immediate source.

I add here a note on V? 19, 2, where the MSS read ἀνέμους δὲ γεννᾶ-
σθαι, ὅταν ἐκπεπυκνωμένος ὁ ἀὴρ ἀραιωθεὶς φέρηται, and Diels prints
ὅταν ἢ πεπυκνωμένος ὁ ἀὴρ καὶ ὠσθεὶς φέρηται. This reading seems to
me to depart farther than necessary from the MS. text. I would
propose ὅταν ἢ 7. ὁ ἀὴρ ἢ ἀραιωθεὶς φέρηται. Though a greater degree
of rarefaction or condensation would, according to Anaximenes, re-
sult in fire or cloud respectively, it does not appear why he might
not have held that a more moderate change in either direction gave
rise to wind.

c.11. Xenophanes.

V? 34,16. Diog. L.9.19, (φησὶ) τὰ νέφη συνίστασθαι τῆς ad’ ἡλίου
ἀτμίδος ἀναφερομένης καὶ αἰρούσης αὐτὰ εἰς τὸ περιέχον.

Diels still regards this doxography preserved by Diogenes as de-
rived from Theophrastus through the biographical line of tradition.

HEIDEL.— ON FRAGMENTS OF THE PRE-SOCRATICS. 693

The whole account is, as Diels, Dovographi Graeci, p. 168, pointed out,
remarkable for its curious statements. I confess that, if it be really
derived from Theophrastus, it seems to me to have suffered changes
similar in character to those of the doxography of Hippolytus (V? 41,
25 sq.), which owes much of its data to the Pseudo-Aristotelian
treatise De Melisso, Xenophane, Gorgia. But first let us speak of
the passage transcribed above. What Xenophanes taught concerning
the origin of clouds is clearly stated by Aet. 3. 4. 4 (V? 43, 20),’
ἀνελκομένου yap ἐκ τῆς θαλάττης τοῦ ὑγροῦ τὸ γλυκὺ διὰ THY λεπτομέρειαν
διακρινόμενον νέφη τε συνιστάνειν ὁμιχλούμενον καὶ καταστάζειν ὄμβρους
ὑπὸ πιλήσεως καὶ διατμίζειν τὰ πνεύματα. Cp. also ἔν. 80. It is clear
that Theophrastus simply stated the theory of the meteoric process, ac-
cording to which clouds originate from vapors rising under the action
of solar heat and lifting skyward. In the text of Diogenes we readily
note two inaccuracies. We should doubtless read ὑφ᾽ for ad’, since
vapors rising from the sun are sheer nonsense. The other difficulty
is at first more puzzling; for a vapor lifting clouds skyward is non-
sense likewise. The vapor condensed to mist or fog (ὁμιχλούμενον) is
cloud. I therefore suggested to Professor Diels that we bracket αὐτά
and take αἰρούσης in its intransitive sense: he records, but does not
accept, the proposal in his third edition. It is at once clear that this
would remove all difficulties from the passage. Probably Professor
Diels was doubtful about the intransitive use of αἴρω, which the lexica
almost entirely ignore. Of that usage I gave examples in a Note on
Menander, Epitrepontes 103 sq., published in Berl. Philol. Wochenschr.,
1909, No. 16, col. 509 sq. I there cited Plato, Phaedr. 248 A, Arist.
Respir. 475° 8 and 479% 26, Sophocl. Philoct. 1830. To these in-
stances I would now add Sophocl. O. R. 914 and the Schol. to
Sophocl. ad loc. and p. 239, 4; Proclus in Tim, I. 78, 2 Diehl.
Other examples, concerning which there may be some doubt, I now
omit, but may recur to the subject another time. There can be no
question, therefore, that αἴρειν was used intransitively, and in our
passage the change appears to be demanded by the sense. Probably
some one not familiar with the usage added αὐτά in order to supply
an object, but in so doing he gave us nonsense.

In this same paragraph occur the words (V? 34, 18) ὅλον δὲ ὁρᾶν καὶ
ὅλον ἀκούειν, μὴ μέντοι ἀναπνεῖν. I discussed this passage briefly
in Antecedents of Greek Corpuscular Theories, p. 137 sq., pointing out
its agreement with Plato, Tim. 32 C-33C. I ought in justice to say
that the parallel had been previously noted by Tannery, Pour I’ histoire
de la science helléne, p. 121, though the fact had slippedfrom my memory.

694 PROCEEDINGS OF THE AMERICAN ACADEMY.

Since my previous discussion I have come to doubt whether the words
of the Timaeus may be used to support the statement of Diogenes.
About the agreement itself there can be no question. Plato does not,
however, mention Xenophanes, and there is no indication in his text
that what he says is to be taken as a correct statement of his doctrine.
If we were quite sure that the report of Diogenes came materially
unchanged from Theophrastus, the parallel would unquestionably
prove that Xenophanes expressly denied the doctrine of the cosmic
respiration. Tannery would then be justified in holding, as he did,
that the brief notice of Diogenes was a precious document showing
beyond question that Xenophanes was engaged in a sharp polemic
against the Pythagoreans, whose doctrine, amply attested by Aristotle,
he emphatically denied. Tannery’s position would be untenable
except on the assumption that Pythagoras himself proposed the
theory of cosmic respiration: the testimony of: Aristotle, however,
who refers (as always) not to Pythagoras but to the Pythagoreans,
is scarcely adequate to establish it. On the other hand, as has already
been said, the accuracy and integrity of the account of Diogenes is
subject to grave suspicion. The statement with which it opens, that
Xenophanes held the doctrines of the four physical elements (στοιχεῖα)
and of innumerable worlds, cannot be reconciled with other data
unquestionably derived from Theophrastus. Again, the sentence
V2 34, 19, πρῶτός τε ἀπεφήνατο ὅτι πᾶν τὸ γινόμενον φθαρτόν ἐστι, in
which Otto Gilbert, Die meteorol. Theorien des gr. Altertums, p. 98,
n. 1, sees “nur ein ungenauer Ausdruck fiir die Riickbildung der
Elemente in den Urstoft”’ (!), appears to be nothing but an echo of
the anecdote related by Arist. Rhet. 2.23 1399 6 (V235, 21), οἷον
Ξενοφάνης ἔλεγεν ὅτι “᾿ὁμοίως ἀσεβοῦσιν οἱ γενέσθαι φάσκοντες τοὺς θεοὺς
τοῖς ἀποθανεῖν λέγουσιν,᾽᾽ and of De Melisso, Xenophane, Gorgia, 977
14 sq., which latter passage in turn incorporates arguments derived
from Plato. This fact should give us pause, and suggests that
Diogenes’s account of the philosophy of Xenophanes is derived from
a source which, like that of Hippolytus (V? 41, 25 sq.) and Simplicius
(V2 40, 21 sq.), sought to eke out the scanty Theophrastean summary
with information coming from the spurious De Melisso, Xenophane,
Gorgia, and ultimately from the Timaeus and Parmenides of Plato.
I am therefore inclined to believe that the statement of Diogenes,
μὴ μέντοι ἀναπνεῖν, rests solely on the Timaeus, which the compiler
regarded as a trustworthy source for the philosophy of Xenophanes.

I may add a brief note on the word πρῶτος in the sentence just
quoted (V? 34, 19). Diels long ago observed that the claim of

HEIDEL.— ON FRAGMENTS OF THE PRE-SOCRATICS. 695

Xenophanes to be the originator of this doctrine is absurd and opposed
to statements of Aristotle and Theophrastus. How came the claim
to be made? During the sixth and fifth centuries B. C., as we well
know, much interest attached to the inventors of contrivances and
the first propounders of ideas, as was entirely natural in the fine burst
of individualism characteristic of the epoch. We commonly think of
the passionate quest for εὑρήματα during the Alexandrian Age, but
Herodotus (1.25; 1.171; 2.4; 2.24; 2.109; 3.131; 4.42; 4.44) and
the earlier logographers display the same interest. The exaggerations
to which claims of this nature led have been well illustrated by Pro-
fessor J. 5. Reid, Lueretiana, Harvard Studies in Class. Philol.,
Vol. 22 (1911), p. 1 sq. in his note on Lucret. 1, 66 sq. Certain
peculiarities of phrase used in such connections deserve attention.
Thus Herod. 1.25 says, Γλαύκου τοῦ Χίου, ds μοῦνος δὴ πάντων avOpw-
πων σιδήρου κόλλησιν ἐξεῦρε, using μοῦνος, where we might have ex-
pected πρῶτος, to denote the sole original authorship of Glaucus.
When data were collected for the later compilations such turns may
have given rise to errors. [ἢ some such way we may perhaps account
for the embarrassment of Simplicius (V? 18, 19) in regard to Anaxi-
menes: ἐπὶ yap τούτου μόνου Θεόφραστος ... τὴν μάνωσιν εἴρηκε Kal
πύκνωσιν, δῆλον δὲ ὡς καὶ οἱ ἄλλοι τῇ μανότητι καὶ πυκνότητι ἐχρῶντο.
Here Diels formerly accepted Usener’s suggestion of πρώτου for μόνου,
but has latterly with good reason returned to the MS. reading, which
the context requires.

V2 36. De Melisso, Xenophane, Gorgia 977* 18, ταὐτὰ yap ἅπαντα
τοῖς ye loos καὶ ὁμοίως ὑπάρχειν πρὸς ἄλληλα.

Here Diels follows the reading of L, except that he rightly changes
ταῦτα to ταὐτά: R, which is second only to L, gives ἴσοις ἢ ὁμοίοις.
Probably neither reading is correct. Arist. De Gen. et Corr. 1. 7.
323° 5 has πάντα yap ὁμοίως ὑπάρχειν ταὐτὰ τοῖς ὁμοίοις. Both pas-
sages, however, rest upon Plato, Parm. 139 E-140 D, where the
implications of the ὅμοιον and ἀνόμοιον are first considered, then those
of the ἴσον and ἄνισον. In view of this fact I think we should read
τοῖς γε ἴσοις Kal <Opolois> ὁμοίως.

6. 12. Heraclitus.

V? 61, 356. Fr. 1, ὁκοίων ἐγὼ διηγεῦμαι διαιρέων ἕκαστον κατὰ φύσιν
καὶ φράζων ὅκως ἔχει.

These words have been variously interpreted. So far as I am aware

696 PROCEEDINGS OF THE AMERICAN ACADEMY.

everybody has regarded φύσις as meaning “nature” in some one of
its numerous acceptations and ἕκαστον as being the immediate object
of διαιρέων. With respect to neither word, I believe, is the current
opinion correct. The phrase ἕκαστον κατὰ φύσιν, which has been misin-
terpreted in various connections, means “each after its kind.” We
shall have to discuss a similar phrase in Empedocles, fr. 110, 5. The
object of διαιρέων, as of διηγεῦμαι, is contained in ὁκοίων, which ἕκαστον
distributes: “ Making trial of such arguments and facts as I recount,
distinguishing them each after its own kind and declaring the nat-
ure of each.” I have rendered ὅκως ἔχει ambiguously with “nature,”
for the phrase occurs frequently in Hippocrates where the φύσις of
things is to be explained, when nothing but the context, and often
not even that, makes it possible to decide whether φύσις has regard
primarily to the process of growth or to the constitution of the thing
in which the process eventuates. In this fragment the precise impli-
cation of ὅκως ἔχει cannot be determined; below (V? 91, 23) in Epi-
charmus, fr. 4, 6, we shall find an instance of ὡς ἔχει in which the
process is obviously intended. I referred briefly to this question in
my Περὶ Φύσεως, p. 126, n. 180 and p. 127, n. 185, and illustrated the
scientific ideal of dividing and simplifying complex: problems by
distinguishing between classes and individuals, ibid. pp. 123-125.
Perhaps the most noteworthy text is the following, Hippocr. Περὶ
διαίτης ὀξέων, 1 (2.226 L.), ἀτὰρ οὐδὲ περὶ διαίτης of ἀρχαῖοι ξυνέγραψαν
οὐδὲν ἄξιον λόγου, καίτοι μέγα τοῦτο παρῆκαν. τὰς μέντοι πολυτροπίας
τὰς ἐν ἑκάστῃ τῶν νούσων καὶ τὴν πολυσχιδίην αὐτέων οὐκ ἠγνόεον ἔνιοι "
τοὺς δὲ ἀριθμοὺς ἑκάστου τῶν νουσημάτων σάφα φράζειν ἐθέλοντες, οὐκ ὀρθῶς
ἔγραψαν μὴ γὰρ οὐκ εὐαρίθμητον εἴη, εἰ τουτέῳ τις σημανεῖται τὴν τῶν
καμνόντων νοῦσον, τῷ ἕτερον ἑτέρου διαφέρειν τι, καὶ, ἢν μὴ τωὐτὸ νούσημα
δοκέῃ εἶναι, μὴ τωὐτὸ οὔνομα ἔχειν.

V? 65, 10. Fr. 18, ἐὰν μὴ ἔλπηται, ἀνέλπιστον οὐκ ἐξευρήσει, ἀνεξερεύ-
νητον ἐὸν καὶ ἄπορον.

Here, as in fr. 27, Diels and Nestle translate ἔλπομαι with “hope.”
Burnet here renders the word with “expect,” there with “look for,”
in either case correctly. J am not sure, however, that he understands
our fragment as I do. It is well known that ἐλπίς may signify any
degree of expectation ranging from vague surmise to lively hope or
fear. In reading this fragment I am constantly reminded of a story
which Tyndall tells of Faraday, who required to be told precisely
what to look for before observing an experiment which was in prep-
aration. All scientific observation, whether assisted or not assisted by

HEIDEL.— ON FRAGMENTS OF THE PRE-SOCRATICS. 697

carefully controlled experimentation, presupposes an ἐλπίς — surmise
or clearly formulated anticipation — of that which observation will
show. ‘To form such a conception is to exercise the scientific imagina-
tion, and the findings anticipated assume the shape of a theory or an
hypothesis. Early Greek philosophy was so prolific of nothing else
as of hypotheses, and the philosophy of Heraclitus in particular is
nothing but a bold hypothesis, whatever concrete observations may
have led him to propound it. Now, that is precisely what I conceive
our fragment to mean: “ Eacept a man venture a surmise, he will not
discover that which he has not surmised; for it is undiscoverable and
baffling.” Fr. 128, φύσις κρύπτεσθαι φιλεῖ, ‘the processes of nature
are not to be read by him who runs, for the true inwardness of things
does not appear on the surface’, is probably to be understood in the
same sense; for ἁρμονίη ἀφανὴς φανερῆς κρείττων (fr. 54). So, too, fr. 86,
ἀπιστίῃ διαφυγγάνει μὴ γιγνώσκεσθαι, probably refers not to faith in a
dogma or a revelation but to the scientific faith which is the evidence
of things not seen. .

V? 64,1. Fr. 10, συνάψιες ὅλα καὶ οὐχ ὅλα, συμφερόμενον διαφερό-
μενον, συνᾷδον διᾷδον, καὶ ἐκ πάντων ἕν καὶ ἐξ ἑνὸς πάντα.

I do not recall seeing anywhere a reference to the evident reminis-
cence of this fragment in Seneca, De Otio, 5. 6, utrum contraria inter
se elementa sint, an non pugnent, sed per diversa conspirent.

V? 66,13. Fr. 28, doxedvrwy γὰρ ὁ δοκιμώτατος γινώσκει φυλάσσειν."
καὶ μέντοι kal δίκη καταλήψεται ψευδῶν τέκτονας καὶ μάρτυρας, ὁ
᾿Ἐφέσιός φησιν.

The text of this fragment is regarded by all critics as desperate,
and desperate measures have been taken to restore it. I have no
desire to canvass them, but shall offer an interpretation which, with a
minimal alteration, appears to render it intelligible and quite as
defensible as the texts obtained by introducing more radical changes.
First of all, it seems clear that yap is due to Clement, who quotes
the sentence, and must be set aside as not belonging to Heraclitus.
This is the view of Bywater, who omits the word. If that be true,
what is there to hinder our taking δοκεόντων as an imperative? It
wants a subject, but that was doubtless supplied by the context from
which the sentence was obviously wrested. A plausible conjecture is
made possible by the reference in the last clause to the inventors and
supporters of lies, who are clearly contrasted with those who receive

698 PROCEEDINGS OF THE AMERICAN ACADEMY.

the philosopher’s scornful permission to hold an opinion. If δοκεόντων
has that meaning, it is transitive as in Herod. 9. 65, δοκέω δέ, εἴ τι
περὶ τῶν θείων πρηγμάτων δοκέειν δεῖ. Whether we shall read ὃ for ὁ
or assume that 6 was omitted by haplography before ὁ δοκιμώτατος
is difficult to decide; for, as Diels has remarked, Heraclitus is spar-
ing in the use of the article. I incline to insert <6>, or possibly <a>,
the only change I consider necessary in the text. Critics appear to
consider γινώσκει φυλάσσειν impossible or unintelligible. It is well
known, however, that οἶδα and ἐπίσταμαι are used with the infinitive
in the sense of “knowing how”’ to do anything, and in some cases the
nuance given by these verbs is so slight as to be best disregarded
in translating the thought into English. It is difficult to see why
γινώσκω should not be used in the same construction as οἶδα and
ἐπίσταμαι. In fact we have two passages which are calculated to
support the assumption that it was so used. Sophocl. Ant. 1087,

iva
A A be 3 Ul 9 lol
Tov θυμὸν οὗτος ἐς νεωτέρους ἀφῇ
καὶ γνῷ τρέφειν τὴν γλῶσσαν ἡσυχωτέραν.

Eurip. Bacch. 1341,
εἰ δὲ σωφρονεῖν
ἔγνωθ᾽, ὅτ᾽ οὐκ ἠθέλετε, τὸν Διὸς γόνον
εὐδαιμονεῖτ᾽ ἂν σύμμαχον κεκτημένοι.

Goodwin, Greek Moods and Tenses, 915, 3 (6), mentions the first
passage only and takes γιγνώσκω (ἔγνων) in the sense of “learning.”
The ingressive aorist naturally bears this sense; but it does not ex-
clude the same construction with the present, as may be seen by
comparison with ἐπίσταμαι, which shows the same meaning in the
ingressive aorist, Herod. 3. 15, εἰ δὲ καὶ ἠπιστήθη μὴ πολυπραγμονέειν.
This line of argument would perhaps not suffice to justify a conjec-
tural introduction of γινώσκει into the text, but it is an adequate
defense of a MS. reading. We have then to consider the meaning of
φυλάσσειν. Here we are thrown upon the fragment itself as our only
resource, since the verb has a great variety of meanings. There seems
to be a slight clue in the last clause. Diels appears to be right in
assuming that Homer, Hesiod, and the like, are the ψευδῶν τέκτονες
καὶ μάρτυρες. If this conjecture be true, it is not difficult to see that
ψευδῶν τέκτονας characterizes them as inventors of lies, and that
ψευδῶν μάρτυρας can hardly mean those who commit perjury, but
must rather refer to the witness they bear to falsehoods by recording

HEIDEL.— ON FRAGMENTS OF THE PRE-SOCRATICS. 699

them in their verse. In other words, the woe pronounced upon the
poets is for originating and perpetuating false views, whether they
relate to the gods, to the desirability of banishing discord, or what not.
But φυλάσσειν does bear this precise sense of “ perpetuating,” and we
may be justified in accepting it as referring to the παράδοσις of poetical
tradition. I think it probable that 6 δοκιμώτατος refers to Homer as
the coryphaeus of the group of false teachers of the multitude whom
Heraclitus is denouncing, and that the epithet signifies nothing more
than that he is held in the highest esteem, although fr. 57 would per-
haps rather suggest Hesiod. The subject of δοκεόντων, then, is the
uncritical multitude, who live according to the tradition of the fathers
(fr. 74) and may be pardoned for what they do in ignorance, though
woe shall be unto those through whom offence cometh. Accordingly
I should translate the fragment rather freely somewhat after this
manner: “ Ay, let them think as he who is most highly esteemed among
them contrives to report; but verily, judgment shall overtake those who
invent and attest falsehoods.” It is hardly necessary to add that
Heraclitus was not threatening Homer with hell-fire, as Clement
would have us suppose.

V? 68, 11. Fr. 41, ἕν τὸ σοφόν, ἐπίστασθαι γνώμην, ὁτέη ἐκυβέρνησε
πάντα διὰ πάντων.

Here I accept the text, but not the interpretation of Diels, who
renders the fragment thus: “In Einem besteht die Weisheit, die
Vernunft zu erkennen, als welche alles und jedes zu lenken weiss.”
Nestle translates γνώμην with “Geist’’; and Burnet, with “thought.”
In order to arrive at the thought of Heraclitus, it is needful first of all
to note how in a number of his fragments, which are concerned with
his conception of true wisdom, he surcharges with meaning the terms
for knowledge in contradistinction to sense-perception or opinion.
Fr. 17, ob yap φρονέουσι τοιαῦτα πολλοί, ὁκόσοι [50 Diels, V*] ἐγκυρεῦσιν,
οὐδὲ μαθόντες γινώσκουσιν, ἑωυτοῖσι δὲ δοκέουσι, “The majority of man-
kind [this, I think must be the meaning οἱ πολλοί, whether or not with
Bergk we add οἱ], so far as they meet such problems, do not compre-
hend them even when instructed, though they think they do.” Fr. 34,
“They that lack understanding (ἀξύνετοι) hear, but are like unto them
that are deaf.’ Fr. 35, “Men who are lovers of wisdom must have
acquired true knowledge of full many matters” (εὖ μάλα πολλῶν
ἵστορας εἶναι). But Heraclitus is well aware that much instruction
(cp. μαθόντες, fr. 17) does not impart understanding (fr. 40, πολυμαθίη
νόον ἔχειν οὐ διδάσκει: ‘Holodov yap ἂν ἐδίδαξε καὶ Πυθαγόρην αὖτίς τε

700 PROCEEDINGS OF THE AMERICAN ACADEMY.

Ξενοφάνεά τε καὶ Ἑκαταῖον), else would the champions of the new,
self-styled ἱστορίη and Hesiod, their coryphaeus, have got under-
standing. The same pregnancy of meaning as in fr. 17 attaches to
γινώσκειν in fr. 108, to be discussed more at length below, and in fr. 57,
where Heraclitus says that Hesiod, whom men regard as most knowing,
did not really comprehend (οὐκ ἐγίνωσκεν) day and night; for, contrary
to his opinion, they are one. It is thus clearly shown that by under-
standing Heraclitus means a cognitive faculty or act which penetrates
beyond superficial differences and distinctions, present to sense and
uncritical fancy, to an inner core of truth, and is characterized by
the apprehension of a fundamental unity. Again, the same point of
view finds expression in fr. 56, where he likens mankind, readily duped
when it comes to a true understanding of the surface show of things
(ἐξηπάτηνται οἱ ἄνθρωποι πρὸς THY γνῶσιν τῶν φανερῶν), to Homer, who
could not read a foolish riddle propounded to him by gamins. Above,
in discussing fr. 18, I have already touched on fr. 80,ἀπιστίῃ διαφυγγάνει
μὴ γιγνώσκεσθαι, maintaining that Heraclitus meant to imply that the
true meaning of things is missed for want of a confident act of imagi-
native anticipation, whereby that which does not obtrude itself on our
senses 15 brought home to the understanding. It is perhaps not too
fanciful to detect the same distinction between sense and under-
standing, where understanding involves the synthesis of apperception,
in fr. 97, κύνες yap καταβαὔζουσιν ὧν ἂν μὴ γινώσκωσι. Heraclitus
would thus be merely repeating the distinction of Alemaeon, fr. 1°
(V? 103, 25), ἄνθρωπον yap φησι τῶν ἄλλων (sc. ζῴων) διαφέρειν ὅτι
μόνον ξυνίησι, τὰ δ᾽ ἄλλα αἰσθάνεται μέν, οὐ ξυνίησι δέ.

Returning now to fr. 41 after a considerable détowr, we naturally
pause again before the phrase ἐπίστασθαι γνώμην, which is the real
crux. Scholars appear to be fairly unanimous in holding that, whether
it means “ Vernunft,” “Geist,” or “thought,” γνώμην is an accusative
of the external object, being, in fact, the divine entity which rules
the world. Heraclitus ὁ κυκητής does not much encourage fine dis-
tinctions, but to me this interpretation seems to yield a Stoic rather
than a Heraclitean thought. In obvious reminiscence of our frag-
ment and of fr. 32, ἕν τὸ σοφὸν μοῦνον λέγεσθαι οὐκ ἐθέλει καὶ ἐθέλει
Ζηνὸς ὄνομα, Cleanthes, H. in Iov. 30 could say,

dos δὲ κυρῆσαι
γνώμης, ἣ πίσυνος σὺ δίκης μέτα πάντα κυβερνᾷς.

But Cleanthes was clearly writing from a different, and a later,
point of view, for which the οὐκ ἐθέλει of Heraclitus had no real

HEIDEL.— ON FRAGMENTS OF THE PRE-SOCRATICS. 701

significance. Following him and having regard to Antipho Soph. fr. 1
(V2 591, 18, γνώμῃ γινώσκει, and V? 592, 4, γνώμῃ νῶσαι) one might
incline to propose to emend yraunvand read γνώμῃ ἐπίστασθαι in Hera-
clitus. I should regard that, however, as an error; for I hold that
γνώμην is an accusative of the inner object. In other words, ἐπίστα-
σθαι γνώμην is a periphrasis for γινώσκειν. In the time of Heraclitus
ἐπίστασθαι had not yet acquired the technical sense which it later
bore in philosophical prose: in fr. 57, τοῦτον ἐπίστανται πλεῖστα εἰδέναι,
it means to “fancy”; in fr. 19, ἀκοῦσαι οὐκ ἐπιστάμενοι οὐδ᾽ εἰπεῖν, to
“be skillful.’ The latter sense is common from Homer onward, the
former in Herodotus. It is not surprising, therefore, that Heraclitus
should wish to reinforce it with a cognate substantive. A similar turn
recurs in Ion of Chios, fr. 4 (V? 222, 28 sq.),

ὡς ὁ μὲν ἠνορέῃ τε κεκασμένος ἠδὲ Kal αἰδοῖ
καὶ φθίμενος ψυχῇ τερπνὸν ἔχει βίοτον,

εἴπερ Πυθαγόρης ἐτύμως ὁ σοφὸς περὶ πάντων
ἀνθρώπων γνώμας ἤδεε κἀξέμαθεν.

Here Diels, whose emendation, ἤδεε for εἶδε I heartily approve,
renders γνώμας ἤδεε κἀξέμαθεν with “ Einsichten erworben und erforscht
hat.” I believe we have a sort of hysteron proteron, and that Ion
(for, herein differing from Diels, I believe the verses are his) meant
“if Pythagoras was well informed and really knew whereof he spoke.”
This interpretation of Ion’s phrase is proved correct beyond a doubt
by Theognis, 59,

ἀλλήλους δ᾽ ἀπατῶσιν ἐπ᾽ ἀλλήλοισι γελῶντες,
οὔτε κακῶν γνώμας εἰδότες οὔτ᾽ ἀγαθῶν.

The couplet was reproduced with slight modifications by an unintel-
ligent imitator, Theognis 1113,

ἀλλήλους δ᾽ ἀπατῶντες ἐπ᾿ ἀλλήλοισι γελῶσιν,
οὔτ᾽ ἀγαθῶν μνήμην εἰδότες οὔτε κακῶν.

Here we must without doubt adopt Hecker’s emendation γνώμην for
μνήμην. ‘The imitator did not perceive the true significance of the
original, which sought to hold. up to scorn the blissful Edenic ignor-
ance of good and evil characteristic of the new-made lords of Megara,
who but recently, clad in goat-skins, lived like pasturing deer in the
wilds without the city walls, but now in the city light-heartedly hood-
wink one another. Clearly γνώμας εἰδέναι is a mere periphrasis for
εἰδέναι. A similar reinforcement of εἰδέναι occurs in the LXX. account

702 PROCEEDINGS OF THE AMERICAN ACADEMY.

of Eden, Gen, 2. 9, τὸ ξύλον τοῦ εἰδέναι γνωστὸν καλοῦ Kal πονηροῦ,
where, but for the confirmation of the MS. text by Philo Jud. 1. 55,
27, one might be inclined to suspect that γνωστόν was a corruption of
γνῶσιν or γνώμην. If Ion’s phrase reminds us of such Homeric locu-
tions as νοήματα ἤδη (β 121) and μήδεα οἶδε (2 363), we find something
closely analogous to that of Heraclitus in Plato, Apol. 20 E, οὐ yap δὴ
ἔγωγε αὐτὴν (se. τὴν σοφίαν) ἐπίσταμαι. In this last phrase, however,
the comparison with 20 D, κινδυνεύω ταύτην εἶναι σοφός, may suggest
that Plato had in mind the old force of ἐπίστασθαι, “be skillful.’
However, Theognis 564, σοφίην πᾶσαν ἐπιστάμενον, has the same
construction. Cp. ibid. 1157. If, then, we so interpret ἐπίστασθαι
γνώμην, we cannot take the relative ὁτέη so closely with γνώμην as the
ordinary view requires. I should rather say that 67éy was roughly
equivalent to ἥ ye, quippe quae, as ὅστις in fr. 57 means ut pote qui,
and render the fragment somewhat as follows: “One thing only is
wisdom: to get Understanding: she it is that pervades all things and
governs all.”

V? 69, 2. Fr. 48, τῷ οὖν τόξῳ ὄνομα βίος, ἔργον δὲ θάνατος.

Diels, Die Anfénge der Philologie bei den Griechen, Neue Jahrbiicher,
xxv (1910), I. Abteilung, p. 3, says, “Der Gleichklang der Worte
βιός (Pfeil) und Bios (Leben) war ihm ein iusseres Zeichen fiir seine
Lehre, dass die Gegensiitze Leben and Tod im Grunde eins seien.”
Zeller I, 640, n. 2, expresses himself in much the same way. I have
no desire to controvert this interpretation, so far as it goes; but it
seems to me that the words of Heraclitus imply much more. In V*
Diels properly refers to Hippocrates, Hep! τροφῆς, 2 (V? 86, 1 sq.), τροφὴ
οὐ τροφή, HY μὴ δύνηται, οὐ τροφὴ τροφή, ἢν οἷόν TE ἢ TpEhELY* οὔνομα τροφή,
ἔργον δὲ οὐχί" ἔργον τροφή, οὔνομα δὲ οὐχί. With this passage of un-
doubtedly Heraclitean origin we should take fr. 37, sues caeno, cohor-
tales aves pulvere vel cinere lavari; for the thought apparently is
that mud and dust are not ὀνόματι water, but are ἔργῳ identical
withit. Fr. 13, δεῖ yap τὸν χαρίεντα μήτε ῥυπᾶν μήτε αὐχμεῖν μήτε βορβόρῳ.
χαίρειν καθ᾽ 'Πράκλειτον, where βορβόρῳ χαίρειν alone seems to belong
to Heraclitus, may conceivably have reference to the same problem,
the philosopher meaning to imply that we should call things and men
by names conformable to their ἔργον: by their fruits ye shall know
them! Plotinus ἔπη. 1. 6. 6, ἔστι yap δή, ὡς ὁ παλαιὸς λόγος, Kal ἡ
σωφροσύνη καὶ ἡ ἀνδρεία καὶ πᾶσα ἀρετὴ κάθαρσις καὶ ἡ φρόνησις αὐτή" διὸ
καὶ αἱ τελεταὶ ὀρθῶς αἰνίττονται τὸν μὴ κεκαθαρμένον καὶ εἰς [an év?] δου
κείσεσθαι ἐν βορβόρῳ, ὅτι τὸ μὴ καθαρὸν βορβόρῳ διὰ κάκην φίλον" οἷα δὴ

gg EEE EE

HEIDEL.— ON FRAGMENTS OF THE PRE-SOCRATICS. 703

καὶ bes, οὐ καθαραὶ τὸ σῶμα, χαίρουσι τῷ τοιούτῳ, Obviously glancing at fr.
13, suggests the possibility that Heraclitus used the words in connec-
tion with a discussion of the mysteries, with the intent of which he
seems to have been satisfied, while he denounced their forms. Thus,
fr. 5, καθαίρονται δ᾽ ἄλλως αἵματι μιαινόμενοι οἷον εἴ τις πηλὸν ἐμβὰς
πηλῷ ἀπονίζοιτο, we find a context in which he may have distin-
guished between the form and the substance, the ὄνομα and the
ἔργον. Bethat asit may, there is abundant evidence that Heraclitus
had grasped the fruitful principle that the true nature of a thing is
to be understood in relation to its function or ἔργον. We are familiar
enough with his interest in etymologies, which reveals the desire to
detect the true meaning of objects in the derivation of their names;
but the study of homonyms, which our fragment reveals, almost
necessarily involved a corresponding attention to synonyms, in which
words of very different origin and etymology are shown to have a
common meaning. The test of identity or difference of meaning
Heraclitus found in the ἔργον of the thing. Plato, in a passage clearly
under the influence of Heraclitus, Crat. 394 A sq., develops this two-
fold principle, which underlies the study of homonyms and synonyms,
referring to the law of uniformity in nature, in accordance with which
like begets like, and concludes therefrom that, as the physician recog-
nizes drugs by their physiological action (δύναμις = ἔργον), not allowing
himself to be deceived by their several disguises, so the philosopher
must apply the same name to parent and offspring, or at any rate he
must learn to detect the identity of concepts by whatever names they
may go. Plato is obviously developing ideas derived from Heraclitus,
partly such as are expressed in the fragments above cited, partly
those of fr. 67, which we shall presently discuss more at length. In
Tim. 50 A-51 B Plato combines in a highly suggestive way Heracli-
tean and Eleatic concepts, very much as he develops the law of
uniformity, mentioned in the Cratylus, into the principle of interac-
tion (ποιεῖν καὶ πάσχειν) in Gorg. 476 B sq. In the living tissue of so
vital a tradition as Greek philosophy presents we expect to find con-
tinuous developments of this kind. What is more difficult is the task
of discriminating the stages marked by the individuals who contributed
to the total result. In regard to the particular question with which
we are now concerned, it is clear that Heraclitus and the Heracliteans
laid the foundations for the Socratic procedure of definition by noting
the essential importance of the ἔργον in determining the meaning of
a concept. It was Socrates, however, who elaborated the method of
definition on the basis of dialectic, thus in turn laying the foundations
of the science of logic.

704 PROCEEDINGS OF THE AMERICAN ACADEMY.

V? 69, 10. Fr. 50, Ἡράκλειτος μὲν οὖν «ἕν» φησιν εἶναι τὸ πᾶν
διαίρετον ἀδιαίρετον, γενητὸν ἀγένητον, θνητὸν ἀθάνατον, λόγον αἰῶνα,
πατέρα υἱόν, θεὸν δίκαιον" οὐκ ἐμοῦ, ἀλλὰ τοῦ λόγου ἀκούσαντας ὁμο-
λογεῖν σοφόν ἐστιν ἕν πάντα εἶναι ὁ ἩἫ ράκλειτός φησι.

It is agreed that the authentic words of Heraclitus begin with οὐκ
ἐμοῦ: what precedes we owe to Hippolytus, who obviously modeled
his introductory statement on fr. 67. The comparison of the two
passages shows that Bergk’s «ἕν», which Diels adopts, is unneces-
sary. The predicates of τὸ πᾶν are, as one sees at a glance, arranged
in contrasted pairs. In the fourth pair, λόγος is of course the intelli-
gible principle, virtually the κόσμος νοητός, opposed to αἰών which is
the κόσμος αἰσθητός. The next pair, πατέρα υἱόν, is of course of Chris-
tian origin. Apparently the last, θεὸν δίκαιον, has puzzled Professor
Diels; for he now (V*) proposes to insert [ἄδικον] after δίκαιον. I
long ago saw that this pair was suggested to Hippolytus or his source
by Plato, Crat. 412 C-413 D, but had taken for granted that this
was a matter of common knowledge and not worthy of special notice,
until Diels’s note undeceived me. I observe that Otto Gilbert, Griech.
Religionsphilosophie, p. 62, n. 1, also noticed the connection. He there
proposes a different interpretation of αἰών, but his suggestion I take
to be too clearly mistaken to require refutation. In reference to θεὸν
δίκαιον, it ought to be said that Hippolytus possibly wrote διαϊόν (=
ἥλιον), and that δίκαιον may be due to the copyist; but there is no
sufficient justification for making a change in the text. Diels is
probably right in adopting Miller’s εἶναι for the εἰδέναι of Par.; but
εἰδέναι may possibly have been originally a gloss on ὁμολογεῖν; for if
ὁμολογεῖν is sound it must be interpreted here, as in fr. 51, with
reference to Heraclitean etymology, as “sharing in the (a) common

λόγος.

V? 71,15. Fr. 67, ὁ θεὸς ἡμέρη εὐφρόνη, χειμὼν θέρος, πόλεμος εἰρήνη,
κόρος λιμός (τἀναντία ἅπαντα" οὗτος ὁ Vos), ἀλλοιοῦται δὲ
ὅκωσπερ «πῦρ», ὁπόταν συμμιγῇ θυώμασιν, ὀνομάζεται καθ᾽ ἡδονὴν
ἑκάστου.

This is the text of Diels. I hope to make it clear that it is not
correct, and to show also what Heraclitus wrote and what he meant.
In order to understand and reconstruct this fragment we must com-
pare two passages from Plato, in which he obviously alludes to it.
Crat. 394 A, οὐκοῦν καὶ περὶ βασιλέως ὁ αὐτὸς λόγος ; ἔσται Yap ποτε ἐκ
βασιλέως βασιλεύς, καὶ ἐξ ἀγαθοῦ ἀγαθός, καὶ ἐκ καλοῦ καλός, καὶ τἄλλα

HEIDEL.— ON FRAGMENTS OF THE PRE-SOCRATICS. 705

πάντα οὕτως, ἐξ ἑκάστου γένους ἕτερον τοιοῦτον ἔκγονον, ἐὰν μὴ τέρας
γένηται" κλητέον δὴ ταὐτὰ ὀνόματα. ποικίλλειν δὲ ἔξεστι ταῖς
συλλαβαῖς, ὥστε δόξαι ἂν τῷ ἰδιωτικῶς ἔχοντι ἕτερα εἶναι
ἀλλήλων τὰ αὐτὰ ὄντα: ὥσπερ ἡμῖν τὰ τῶν ἰατρῶν φάρμακα
χρώμασιν καὶ ὀσμαῖς πεποικιλμένα ἄλλα φαίνεται τὰ αὐτὰ
ὄντα, τῷ δέγε ἰατρῷ, ἅτε τὴν δύναμιν τῶν φαρμάκων σκο-
πουμένῳ, τὰ αὐτὰ φαίνεται, καὶ οὐκ ἐκπλήττεται ὑπὸ τῶν
προσόντων. οὕτω δὲ ἴσως καὶ ὁ ἐπιστάμενος περὶ ὀνομάτων τὴν δύναμιν
αὐτῶν σκοπεῖ, καὶ οὐκ ἐκπλήττεται εἴ τι πρόσκειται γράμμα ἢ μετάκειται
ἢ ἀφήρηται, ἢ καὶ ἐν ἄλλοις παντάπασιν γὙρἀμμασίν ἐστιν ἡ τοῦ ὀνόματος
δύναμις. ὥσπερ ὃ νυνδὴ ἐλέγομεν, ““᾿Αστυάναξ᾽᾽ τε καὶ “"Exrwp”’ οὐδὲν
τῶν αὐτῶν γραμμάτων ἔχει πλὴν τοῦ ταῦ, GAN’ ὅμως ταὐτὸν σημαίνει.
καὶ ““᾿᾿Αρχέπολίς᾽᾽ γε τῶν μὲν γραμμάτων τί ἐπικοινωνεῖ; δηλοῖ δὲ ὅμως
τὸ αὐτό" καὶ ἄλλα πολλά ἐστιν ἃ οὐδὲν ἀλλ᾽ ἢ βασιλέα σημαίνει" καὶ
ἄλλα γε αὖ στρατηγόν, οἷον “ἾΑΎις καὶ “Πολέμαρχος καὶ “᾿Εὐπόλε-
μος. καὶ ἰατρικά γε ἕτερα, “᾿Ἰατροκλῆς καὶ ““᾿Ακεσίμβροτος᾽᾽ " καὶ ἕτερα
ἂν ἴσως συχνὰ εὕροιμεν ταῖς μὲν συλλαβαῖς καὶ τοῖς γράμμασι διαφω-
νοῦντα, τῇ δὲ δυνάμει ταὐτὸν φθεγγόμενα. The general con-
nection of this passage with the Heraclitean doctrine of the ἔργον
was noted above in the discussion of fr. 48. The δύναμις or specific
physiological action of the drug is compared to the δύναμις of a word,
its “force” or meaning. The identity of meaning in words that are
different (διαφωνοῦντα, τἀναντία ἅπαντα), and the methods employed
to produce variation (ποικίλλειν, addovodrar), —these are the themes
common to Heraclitus and Plato. We naturally think of Heraclitus,
fr. 15, ὡυτὸς δὲ ᾿Αἰδης καὶ Διόνυσος, and fr. 57, ὅστις ἡμέρην Kal εὐφρόνην
οὐκ ἔγίνωσκεν" ἔστι γὰρ ἕν. The second passage from Plato, to which
I referred above, is Tim. 49 sq., where the relation of the elements
to the δεξαμενῆ or the ἐκμαγεῖον is under discussion. It will suffice
for our purpose to quote a sentence from 50 E, διὸ καὶ πάντων ἐκτὸς
εἰδῶν εἶναι χρεὼν TO τὰ πάντα ἐκδεξόμενον ἐν αὑτῷ γένη, καθάπερ περὶ τὰ
ἀλείμματα ὁπόσα εὐήδη τέχνῃ μηχανῶνται πρῶτον τοῦτ᾽ αὐτὸ ὑπάρχον,
ποιοῦσιν ὅτι μάλιστα ἀὠδη τὰ δεξόμενα ὑγρὰ τὰς ὀσμάς" ὅσοι τε ἔν τισιν
τῶν μαλακῶν σχήματα ἀπομάττειν ἐπιχειροῦσι, τὸ παράπαν σχῆμα οὐδὲν
ἔνδηλον ὑπάρχειν ἐῶσι, προομαλύναντες δὲ ὅτι λειότατον ἀπεργάζονται.
Plato here employs two comparisons to illustrate the relation of the
substratum to the elemental forms, borrowing one from the manu-
facture of unguents, the other from the art of moulding figures in a
matrix. The first of these is obviously similar to that above quoted
from the Cratylus, and was repeated by Lucret. 2, 847 sq.

706 PROCEEDINGS OF THE AMERICAN ACADEMY.

sicut amaracini blandum stactaeque liquorem

et nardi florem, nectar qui naribus halat,

cum facere instituas, cum primis quaerere par est,
quoad licet ac possis reperire, inolentis olivi
naturam, nullam quae mittat naribus auram,
quam minime ut possit miatos in corpore odores
concoctosque suo contractans perdere viro,
propter eandem rem debent primordia rerum
non adhibere suum gignundis rebus odorem, etc.

Heeding the suggestions afforded by these passages from Plato and
Lucretius, which seem to me clearly to reproduce, however freely,
the thought of Heraclitus in our fragment, it should be possible with
considerable certainty to restore the text and to determine its meaning.
It is obvious that in the Cratylus Plato slightly changed the figure,
substituting drugs for unguents, because of the advantage of thus
being able to appeal to the expert knowledge of the physician. He
may have been influenced also by certain Heraclitean elements in
the medical literature, such as we find in Hippocrates Περὶ διαίτης
and Περὶ τροφῆς. At all events, it is clear that «πῦρ», which Diels
has adopted from the conjecture of Dr. Thomas Davidson, and <ofvos>,
which Bergk proposed, are alike inadmissible. The latter part of the
fragment and the use of θύωμα, which Hesychius defines with μύρον
and ἄρωμα, point clearly to the conclusion that Heraclitus, as we
should infer from Plato and Lucretius, referred to an unguent. The
instances of θύωμα (Herod. 2. 86; Lucian, De Dea ὅντα, 8 and 46)
refer to unguents. If one or the other of the passages in Lucian
should be doubtful, there can be no question in regard to Hippocr.
Τυναικείων B, 209 (8, 404 L.), ἑψεῖν τὰ θυώματα ἃ és TO μύρον ἐμβάλλεται,
with which compare ibid. 202 (8, 386 L.) and 206 (8, 398 L.) In the
making of unguents (see Bliimner, Technologie und Terminologie der
Gewerbe und Kiinste?, 1., 359 sq.), the neutral base, as well as the
product resulting from the union of aromatic substances with it, was
called μύρον or ἔλαιον. The finished product bore a variety of names
determined by the volatile ingredients. Theophrastus, Περὲ ὀσμῶν,
gives ample information, from which we may quote a few sentences.
V. 25, πρὸς ἕκαστον δὲ τῶν μύρων ἐμβάλλουσι τὰ πρόσφορα τῶν ἀρωμά-
των, οἷον εἰς μὲν τὴν κύπρον καρδάμωμον, ἀσπάλαθον ἀναφυράσαντες
τῷ εὐώδει. VI. 27, ἅπαντα δὲ συντίθενται τὰ μύρα τὰ μὲν ἀπ᾽ ἀνθῶν
τὰ δὲ ἀπὸ φύλλων τὰ δὲ ἀπὸ κλωνὸς τὰ δ᾽ ἀπὸ ῥίζης τὰ δ᾽ ἀπὸ ξύλων
τὰ δ᾽ ἀπὸ καρποῦ τὰ δ᾽ ἀπὸ δακρύων. μικτὰ δὲ πάνθ᾽ ὡς εἰπεῖν. In inten-

ee ee —————eeeeeEeEeEeEeEeEeEee_ le

a ato —— So ᾳονυ

HEIDEL.— ON FRAGMENTS OF THE PRE-SOCRATICS. 707

tion, therefore, the conjecture of Bernays, συμμιγῇ <Obmpa> θυώμασι,
was better than either of those which we noticed above; but Diels is
right in assuming that the desiderated word is to be supplied after
ὅκωσπερ. The only point in favor of «πῦρ!» is that its omission can
so easily be explained; but with almost equal ease we can account for
the loss of «μύρον», which is obviously required by the sense and by
the Platonic and Lucretian parallels.

But we must now return to the earlier part of the fragment. The
words τἀναντία ἅπαντα" οὗτος ὁ νοῦς have been a stumbling-block.
Bywater and Diels bracket them, since they can make nothing of
them. Mullach accomplished the same result by making two frag-
ments instead of one, and omitting the troublesome words. But a
reference to the passage from the Cratylus should prove beyond
question that they belong just where they stand; only one slight
change is required, viz, ὡυτὸς for οὗτος, as Bergk perceived. He says,
Kleine Philol. Schriften, II. 86, n. 4, “Ceterum etiam verba illa
τἀναντία ἅπαντα, οὗτος ὁ νοῦς non interpretis, sed ipsius Heracliti esse
existimo, quae ita videntur corrigenda: ὁ θεὸς... κόρος, τἀναντία
ἅπαντα" φῳὑτὸς νόος" ἀλλοιοῦται δέ, ὅκωσπερ οἶνος KTA.”’ Unfortunately
Bergk did not interpret his proposed text; but judging by his pune-
tuation and the absence of any remark about the force of νόος, I
venture to suggest that what he had in mind was something like this:
“Gott ist... Uberfluss und Hunger, mit einem Worte, alle Gegen-
siitze. Es ist derselbe Geist,” usw. If this suggestion does him
justice, it will be seen that he did not really anticipate my proposal
except in regard to the change of οὗτος into ωὑτός; and working with
the text of Diels, who did not even record the proposal, I did not
come upon his emendation until I had reached the same conclusion
independently and by a different route. As a matter of fact, it was
the passage from the Cratylus which disclosed the connection of
ideas and led me to the obviously correct text and interpretation;
for I saw at once that νοῦς had no reference whatever to θεός and
did not mean “Geist,’’ but, as in Herod. 7. 162, οὗτος δὲ ὁ νόος τοῦ
ῥήματος, signified “sense” or “meaning.” But, this point once cleared
up, it followed at once that we must read ὡυτός for οὗτος, and that
τἀναντία ἅπαντα did not merely add a generalization to sum up the
bill of particulars which precedes. In short, τἀναντία ἅπαντα is the
plural form of τοὐναντίον ἅπαν, which occurs, Plato, Polit. 310 D, as a
variant for the more usual phrase πᾶν τοὐναντίον; cp. Xen. Mem.
3. 12. 4 and (for the adverbial force of πᾶς or ἅπας) Plato. Protag.
317 B.

708 PROCEEDINGS OF THE AMERICAN ACADEMY.

Restoring to Heraclitus what rightfully belongs to him, we should
therefore write the fragment thus: ὁ θεὸς ἡμέρη εὐφρόνη, χειμὼν θέρος,
πόλεμος εἰρήνη, κόρος λιμός" τἀναντία ἅπαντα, ὡυτὸς ὁ νοῦς" ἀλλοιοῦται δὲ
ὅκωσπερ «μύρον;», ὁπόταν συμμιγῇ θυώμασιν, ὀνομάζεται καθ᾽ ἡδονὴν ἑκά-
στου. “God is day and night, winter and summer, war and peace, satiety
and hunger,— opposites quite, but the sense is the same; he changes,
however, just as the neutral base employed in making unguents, when it
as mixed with volatile essences, receives a name in accordance with the odor
of each.”

In regard to the philosophical interpretation of the fragment, which
thus assumes a rank of capital importance for the thought of Heracli-
tus, it is hardly necessary to say more at present, than that we must
henceforth build upon the foundations laid by Plato, Tim. 48 E-52 C.
Plato and Lucretius prove that the same thought lay at the core of the
atomic theory, and it is evident that Heraclitus here touched one of
the basic conceptions of metaphysics in so far as it is concerned with
the relation of the One and the Many. We are therefore called upon
to consider the questions which crowd upon us with sobriety and
careful discrimination, unless we are to efface the mile-stones that
mark the progress of speculation. Such an inquiry is, however, too
far-reaching to admit of discussion in this connection.

V? 72,18. Fr. 71, μεμνῆσθαι δὲ καὶ τοῦ ἐπιλανθανομένου ἣ ἡ ὁδὸς ἄγει.

The meaning, apparently missed by some scholars, is made clear
by fr. 117, οὐκ ἐπαΐων ὅκῃ βαίνει. He forgets whither he is going.

V? 73, 14. Fr. 77, ψυχῇσι . . . τέρψιν ἢ θάνατον ὑγρῇσι γενέσθαι.

It seems very probable that we are here dealing, if one may so
express it, with a conflate text; that is to say, two utterances of
Heraclitus, otherwise essentially identical, but differing in this, that
one related to τέρψις, the other to θάνατος, appear to have been merged
in one. Either statement, taken by itself, is entirely intelligible;
but it is improbable that Heraclitus combined them in the manner of
this ‘fragment.’

νὴ 73, 19. Fr. 78, ἦθος γὰρ ἀνθρώπειον μὲν οὐκ ἔχει γνώμας, θεῖον
δὲ ἔχει.

The word ἦθος is difficult and improbable. I suspect that we should
write ἔθνος; cp. Eurip. Orest. 976,

HEIDEL.— ON FRAGMENTS OF THE PRE-SOCRATICS. 709

δι φῇ , ea ,
iw ἰώ, πανδάκρυτ᾽ ἐφαμέρων
ἔθνη πολύπονα.

The iambic movement of the fragment is obvious, and the position of
μέν appears somewhat forced. One is tempted to write the sentence
as verse,

ἔθνος μὲν ἀνθρώπειον οὐ γνώμας EXEL,

θεῖον δ᾽ ἔχει.

This may, of course, be nothing more than the work of chance; but
the entire cast of the sentence suggests that we are dealing with verse
converted into prose. Now we know that there were those who
versified the philosophy of Heraclitus. One of their number, Scythi-
nus, a writer of the fourth century, is known by name; and one of the
fragments of Scythinus (fr. 2, V? 86, 22 sq.) has come down to us
reconverted into prose, which Wilamowitz has again rendered in
verse. I do not suggest, though it is possible, that we have before us
another reconverted version of Heraclitus by Scythinus; for the cases
of Cleanthes, whose Stoic verses are in part little more than para-
phrases of Heraclitus, and of ‘Epicharmus,’ among whose fragments
there are some which reproduce the thought of Heraclitus as others
do that of Plato, caution us to avoid hasty conclusions. Neverthe-
less, I incline to think that fr. 78 is in fact a thinly disguised prose
rendering of a verse original; for there are at least two other ‘frag-
ments’ of Heraclitus (80. and 100) whose form suggests a versified
original. As it is best to discuss them separately, I will add only
that one of them, like fr. 78, is quoted by Origen Against Celsus. Τί
my suggestion be approved by scholars, an interesting question
arises, to wit, how accurately the versifier, if he was actually trying
to reproduce the thought of Heraclitus, as Celsus or his source sup-
posed, succeeded in rendering it. In the case of fr. 78, it is a nice
question whether Heraclitus would have said what is here imputed
to him. Origen seems to be clearly right in interpreting γνώμας with
σοφία; but Heraclitus, whose doctrine of τὸ σοφόν we considered above
in the note on fr. 41, although unsparing in his denunciation of the
stupidity of the crowd, clearly believed that he had attained to
wisdom. We naturally think of him as declaring with the Hebrew
prophet that he alone was left.

We may note that fr. 78 seems to have served as a model for the
spurious fragment of Epicharmus, 57,7, which Diels (V2 99, 4) writes
thus:

οὐ yap ἄνθρωπος τέχναν Tw’ εὗρεν, ὁ δὲ θεὸς τοπάν.

710 PROCEEDINGS OF THE AMERICAN ACADEMY.

In the same way Epicharmus, fr. 64 (V? 100, 5 sq.), likewise spurious,

εἰμὶ νεκρός " νεκρὸς δὲ κόπρος, γῆ δ᾽ ἡ κόπρος ἐστίν"
εἰ δ᾽ ἡ γῆ θεός ἐστ᾽, οὐ νεκρός, ἀλλὰ θεός,

glances at Heraclitus, fr. 96, νέκυες γὰρ κοπρίων ἐκβλητότεροι, and also at
the anecdotes relative to the manner of his death, V? 54, 29 sq., and
to the anecdote about the oven, where also there were gods (V? 58,
36 sq.). It seems altogether likely that the case of Heraclitus is in
this a close parallel to that of Pythagoras, that myth soon began to
weave legends about his name, and that forgeries sprang up which were
supported by other forgeries. For the relation of the late Pytha-
goreans to Heraclitus, see Norden, Agnostos Theos, p. 345, n. 1. The
examples given above and to be discussed presently make it extremely
probable that some of these were written in verse and current as
adespota, becoming in time attached to various names, such as Epi-
charmus. Others went under the name of Heraclitus, and it is
probably to them that the Vita in Suidas refers (V2 56, 46), ἔγραψε
πολλὰ ποιητικῶς.

V? 73, 23. Fr. 80, εἰδέναι δὲ χρὴ τὸν πόλεμον ἐόντα ξυνόν, Kal δίκην
ἔριν, καὶ γινόμενα πάντα κατ᾽ ἔριν καὶ χρεώμενα.

This fragment has been discussed times innumerable, more particu-
larly with reference to the last word, which is conceded to be im-
possible. If the sentence be regarded as an authentic prose fragment
of Heraclitus, we probably cannot do better than accept Schuster’s
conjecture, καταχρεώμενα for χρεώμενα, and take it as complementary to
γινόμενα. Diels, however, has rightly refused to admit into his text
any of the numerous substitutes proposed for χρεώμενα. First of all
it should be noted that καὶ γινόμενα πάντα κατ᾽ ἔριν does not look so
much hike an utterance of Heraclitus as like an attempt to summarize
details; this impression is confirmed by fr. 8, Arist. Eth. Nic. 1155? 4,
Ἡράκλειτος τὸ τ τ ξοῦν συμφέρον καὶ ἐκ τῶν διαφερόντων καλλίστην ἁρμο-
νίαν καὶ πάντα κατ᾽ ἔριν γίνεσθαι, which is itself quite obviously not a
verbatim quotation but a summary. Long ago I was struck by the
similarity in thought between καὶ δίκην ἔριν, καὶ γινόμενα πάντα κατ᾽
ἔριν and Cleanthes, H. in Iov. 36,

δὸς δὲ κυρῆσαι γνώμης, ἣ πίσυνος σὺ δίκης μέτα πάντα κυβερνᾷς,

and in a letter to Professor Diels I ἔρως instead of χρεώμενα to
read χρεὼν μέτα, after Eurip. Herc. F. 2

HEIDEL.~— ON FRAGMENTS OF THE PRE-SOCRATICS. 711

εἴθ᾽ “Hpas ὕπο
κέντροις δαμασθεὶς εἴτε τοῦ χρεὼν μέτα.

He replied that the anastrophe of μέτα was impossible ἴῃ prose.
This is of course true, as I well knew, assuming that we are dealing
with real prose. At that time, having nothing more definite than the
vague impression that the diction and movement of certain fragments
of Heraclitus were distinctly poetic, and the statement in the Vita of
Suidas, which I then interpreted as referring in a general way to
poetic diction, I dropped the matter, though 1 still felt that χρεὼν μέτα
was probably the true reading. Recently Dr. Bruno Jordan, Archiv
fiir Gesch. der Philos., 24 (1911), p, 480, has independently made the
same suggestion. In view of the probability that in this ‘fragment,’
as in fr. 78, we have a versified version of Heraclitus reconverted into
prose, I regard my emendation as all but certain. I do not think it
feasible to recover the verse original throughout, because, as I indi-
cated above, καὶ γινόμενα πάντα Kar’ ἔριν appears to be a summarizing
formula; but it is easy to pick out parts of the sentence which fall
almost without change into iambic verse:

> , \ Ul
εἰδέναι δὲ χρή
‘ , ” /
τὸν πόλεμον ὄντα ξυνόν. .. . ..
πεν oe fe Καὶ OLR DE pLy
<rTovU> χρεὼν μέτα.

It must be said that the text of the fragment is not absolutely certain,
as the Mss. of Origen Against Celsus read εἰ δὲ χρή and δίκην ἐρεῖν;
but the emendations adopted by Diels and reproduced above are so
obvious that we may with confidence make his text the basis of our
study. Regarded in the light of the poetic tags which have just been
noted, we have again a close parallel to the prose paraphrase of
Scythinus, fr. 2; but I hazard no guess as to the author of the versi-
fied version.

V? 76,12. Fr. 100, ὥρας ai πάντα φέρουσι.

This fragment is preserved by Plutarch, who again alludes to it.
The movement is clearly dactylic, and one may suspect that it formed
part of an hexameter, though its brevity forbids dogmatic conclusions.
In view of the experiments of Cleanthes it is not improbable that there
were versions of certain Heraclitean sayings in heroic verse. It is, of
course, possible that this fragment owes its rhythmical or metrical
form to chance or to unconscious poetical influences not unnatural

712 PROCEEDINGS OF THE AMERICAN ACADEMY.

in the early stages of prose when verse was still the prevailing medium
of artistic expression. This is perhaps the most probable explanation
of the hexameter ending of fr. 5, θεοὺς οὐδ᾽ Hpwas οἵτινές εἰσι, which I
noted long ago and find referred to Homeric influence by Norden,
Agnostos Theos, p.88,n.1. Dactylic movement, due to epic models,
is much more easily thus accounted for than iambic or trochaic, such
as have been noted above in fragments 78 and 80. Of the latter sort
there is perhaps another example in fr. 120, quoted by Strabo, ἠοῦς
καὶ ἑσπέρας τέρματα ἡ ἄρκτος Kal ἀντίον THs ἄρκτου οὖρος αἰθρίου Διός.
The general trochaic or iambic rhythm is at once apparent, and the
close at least is faultless and strikingly suggestive of a trochaic verse.
See infra, p. 714 sq. One may recast it into trochaics quite as easily
as Wilamowitz did the second fragment of Scythinus, —

ἠοῦς [possibly ἕω δὲ] χἀσπέρας
τέρματ᾽ ἄρκτος κἀντί᾽ ἄρκτου οὖρος αἰθρίου Διός.

V? ΤΊ, 11. Fr. 108, ὁκόσων λόγους ἤκουσα, οὐδεὶς ἀφικνεῖται ἐς τοῦτο,
ὥστε γινώσκειν ὅτι σοφόν ἐστι πάντων κεχωρισμένον.

This fragment has been much discussed; ep. Schuster, pp. 42, 44;
Zeller, I. 629, n. 1. Gomperz proposed to bracket ὅτι σοφόν κτὰ. as an
interpolation. All those who retain the words regard them as an
object clause, whatever interpretation they may put upon it. Diels
identifies (τὸ) σοφόν with God, and understands the fragment as de-
claring the divine transcendence. This view has naturally provoked
vigorous protests; for it is: incompatible with all that we otherwise
know of the thought of Heraclitus. I think λόγους is here used as
Heraclitus uses λόγος of his own philosophic message or gospel: it
refers to the Weltanschauungen of the great teachers and_philoso-
phers; for ἤκουσα does not necessarily refer to actual hearing of the
person who sets forth his views, but includes the reading (by himself
or by a slave) of written records. The pregnant force of γινώσκειν was
sufficiently explained above in the discussion of fr. 41. Heraclitus,
then, says: “Of all those whose message regarding the nature of things
at has been my fortune to learn about, not one has attained to the point
of true knowledge.’ So much seems to be clear frofm a survey of the
conception of knowledge which he is continually proclaiming. But,
once we seize the import of his use of γινώσκειν, it is equally clear that
ὅτι is not “that”; it is causal, and the obvious conclusion to his
sentence follows: “for wisdom is far removed from all” (“men” or
“of them’’). One may illustrate this use of κεχωρισμένον by a pas-

HEIDEL.— ON FRAGMENTS OF THE PRE-SOCRATICS. 718

-sage from Cleanthes quoted by Sext. Empir. 9. 90, ὥστε ob τέλειον
ζῷον ὁ ἄνθρωπος, ἀτελὲς δὲ Kal πολὺ κεχωρισμένον τοῦ Tedeiov. The
questionable fragment of Philolaus, quoted by Diels, and the quotation
from Philostratus ap. Euseb. P. E. 4. 13, ἑνί re ὄντι καὶ κεχωρισμένῳ
πάντων, made by Norden, Agnostos Theos, 39, n. 3, afford but weak
support for so unlikely a theory as that of Diels. In printing the
fragment, I should place a colon between γινώσκειν and ὅτι. The sen-
tence thus furnishes a new illustration of the difficulty, noted by
Aristotle, of phrasing Heraclitus. Diels mentions, but does not adopt,
my interpretation in δ,

V? 77,19. Fr. 112, σωφρονεῖν ἀρετὴ μεγίστη, καὶ σοφίη ἀληθέα λέγειν
καὶ ποιεῖν κατὰ φύσιν ἐπαΐοντας.

The Mss. here, as in fr. 116, show σωφρονεῖν. Diels here substitutes
τὸ φρονεῖν, there φρονεῖν, in order to adapt the diction to that of He-
raclitus. He renders: “Das Denken ist der grésste Vorzug, und die
Weisheit besteht darin, die Wahrheit zu sagen und nach der Natur zu
handeln, auf sie hinhérend.” Besides changing σωφρονεῖν to τὸ φρονεῖν,
he gives a forced rendering of ἀρετή and ἐπαΐοντας which serves to
-conceal the obvious Stoic character of the saying. Again, there is no
other instance of σοφίη in the supposedly genuine fragments of
Heraclitus, who seems to have used (τὸ) σοφόν instead: it does recur
in fr. 129, which Diels reckons doubtful or spurious but others accept
as genuine. Yet, granting that it is genuine, σοφίη there means some-
thing very different: it is, like πολυμαθείη and xaxorexvin, a term
of reproach. One who reads the sentence without bias will readily
admit that ἀρετὴ means an ethical virtue. As for ἀληθέα λέγειν, one
may perhaps defend it by citing the denunciation of the ψευδῶν τέκτονας
kal μάρτυρας in fr. 28; but it is doubtful whether so obviously an
ethical virtue would have counted as a mark of σοφίη in the days
of Heraclitus. In opposition to this it may be said that ᾿Αλήθεια was
the ideal of the Greek philosophers from the beginning. True; but it
was objective Truth which they sought, and not the virtue of truth-
fulness. The juxtaposition of ἀληθέα λέγειν and ποιεῖν κατὰ φύσιν
does not suggest a reference to abstract or objective truth. Finally,
ποιεῖν κατὰ φύσιν ἐπαΐοντας bears all the marks of Stoic doctrine; for
it is hardly defensible to render ἐπαΐοντας with “auf sie hinhérend.”’
The word has here, as in fr. 117, οὐκ ἐπαΐων ὅκῃ βαίνει, the sense which
it regularly bears in Plato, to wit, “knowing”; ep. Xen. Mem. 1. 1. 9,
δαιμονᾶν δὲ Kal τοὺς μαντευομένους ἃ τοῖς ἀνθρώποις οἱ θεοὶ μαθοῦσι
διακρίνειν. The words then clearly mean “to act in accordance with

714 PROCEEDINGS OF THE AMERICAN ACADEMY.

nature consciously and with full knowledge.” This thought is, however,
in substance and in form entirely Stoic, corresponding in the ethical
sphere to the injunction to submit willingly to Fate, in the religious
sphere, as expressed in Cleanthes’s lines to Fate. One may, of course,
discover the germs of this view in genuine fragments of Heraclitus;
but Diels’s alterations in the text and his interpretation do not meet
the reasonable objections long since urged by others to the genuine-
ness of this fragment.

V? 78, 8. Fr. 116, ἀνθρώποισι πᾶσι μέτεστι γινώσκειν ἑωυτοὺς καὶ
σωφρονεῖν.

This fragment, like the preceding, is derived from Stobaeus, and
like it, too, has been by many regarded as spurious. As I have al-
ready stated, Diels writes φρονεῖν for σωφρονεῖν, in order to meet an
obvious criticism. This procedure would be justifiable, however, only
if the passage as a whole created a presumption in favor of Heracli-
tean authorship, which is supported solely by the lemma of Stobaeus.
In fact all indications point to the period after Socrates. Whoever
‘attributed the saying to Heraclitus doubtless did so in view of fr. 101,
ἐδιζησάμην ἐμεωυτόν, but the interpretation of the Delphic γνῶθι σαυτόν
as an injunction to recognize one’s limitations and to occupy oneself
with that which lies within one’s proper scope and power,— this is,
so far as we know, Socratic: he who would claim it for Heraclitus
must assume the burden of proof. But no unbiased reader of our
fragment will doubt that γινώσκειν ἑωυτοὺς καὶ σωφρονεῖν was intended
to express that precise thought. I cannot justify the changing of
σωφρονεῖν to φρονεῖν, and cannot accept the fragment as genuine.
Bywater was clearly right in marking both 112 and 116 as doubtful.
Since they come to us from Stobaeus, who quotes them under widely
different heads, it is plain that their assignment to Socrates is not
due to a mere mistake in the lemmata of his text, but the error
must be charged to his sources.

V? 78, 16. Fr. 120, ἠοῦς καὶ ἑσπέρας τέρματα ἡ ἄρκτος Kal ἀντίον τῆς
ἄρκτου οὖρος αἰθρίου Διός.

In γ5 Diels briefly notes my interpretation οἱ οὖρος αἰθρίου Διός as
“wind of heaven,” which was proposed in my review of his Herakleitos
von Ephesos?, in Class. Philol., 5. p. 247; but he appears still to prefer
his own suggestion that Heraclitus referred to Mt. Olympus. As I
regard my proposal as almost certainly right, I offer here a few addi-

HEIDEL.— ON FRAGMENTS OF THE PRE-SOCRATICS. 715

tional observations to supplement my former statement, which exi-
gencies of space then compelled me to omit. For the meaning of
οὖρος, “wind,” I would refer to Schmidt’s Synonymik. See also
Bonitz, Index Aristotelicus, s. v. ἄρκτος. It was common to say
καὶ πρὸς ἄρκτον Kal πρὸς νότον. The phrases employed by Herodotus
in speaking of the cardinal points are especially interesting; I have
made a complete list of them, and they seem to me to be decisive.
I will refer, however, to but a few by way of illustration: 1. 148,
πρὸς ἄρκτον τετραμμένος . . . πρὸς ζέφυρον ἄνεμον ; 2. 8, φέρον am’ ἄρκτου
πρὸς μεσεμβρίης τε καὶ νότου; 3. 102, πρὸς ἄρκτου τε καὶ βορέου ἀνέμου.
Cp. Hesiod, Theog. 378-82.

Though I do not accept the suggestion of Diels that the οὖρος Διός
is Mt. Olympus, I will refer to a passage which might possibly be
used to support it, to wit, Hippocr. Ilepi ἑβδομάδων, 48 (9. 462 L.),
Definitio autem superiorum partium et inferiorum corporis umbilicus.
It would be interesting to know the Greek text: perhaps Helmreich
or some other ransacker of medical manuscripts may yet recover
it! It occurs in a part of the treatise much discussed of late; see
Roscher, Uber Alter, Ursprung und Bedeutung der hippokr. Schrift
von der Siebenzahl, p. 37, n. 67, who of course, in relating this to his
“Weltkarte,” refers to the ὄμφαλος γῆς or θαλάττης, and believes that
the writer had in mind (not Delphi, but) Delos or Teos. Mt. Olympus
might well serve as a landmark to divide the “upper” or northern
parts of the earth from the “lower” or southern; but it does not
seem so suitable fora zero meridian. I doubt, moreover, whether Hera-
clitus had any “Greenwich” in mind: what he seems to have meant
is merely this, that “east”? and “west” are relative terms and are
delimited by a north and south line drawn through any point that
may bein question. Various special meridians, useful to the geog-
rapher and mariner, were recognized at a comparatively early date,
as may be seen from Herodotus; but a zero meridian, so far as I
know, was not thought of before the time of the Alexandrian geogra-
phers. For the suggestion of a possible verse original for the fragment,
see above onfr. 100. This would readily account for the use of οὖρος
in the sense of wind.

V? 80, 10. Fr. 128, δαιμόνων ἀγάλμασιν εὔχονται οὐκ ἀκούουσιν, ὥσπερ
ἀκούοιεν, οὐκ ἀποδιδοῦσιν, ὥσπερ οὐκ ἀπαιτοῖεν.

In regard to the text of this spurious fragment I agree with Diels,
except that I would set a colon after ἀκούοιεν; from his interpreta-
tion I dissent, because it seems to me obviously at fault. In some

g

716 PROCEEDINGS OF THE AMERICAN ACADEMY.

unaccountable way he appears to have overlooked my note in Class.
Philol. 5. p. 247, for he renders the text thus: “Sie beten zu den Gét-
terbildern, die nicht héren, als ob sie Gehér hatten, die nichts zuriick-
geben, wie sie ja auch nichts fordern kénnten,” The saying is a close
parallel to fr. 127, likewise spurious, in that it charges men with in-
consistency in their dealings with the gods. Hence οὐκ ἀποδιδοῦσιν
(= ἀποδιδόασιν; not the partic.!) answers to εὔχονται as ὥσπερ οὐκ ἀπαι-
τοῖεν answers to ὥσπερ ἀκούοιεν, and the meaning, as I said in my
former note, is: “ They make vows to the images of the gods, that hear
not, as if they heard; they pay not their vows, as if they (the gods)
required it not.” Everyone can supply the necessary classical examples
for εὔχονται, ἀποδιδοῦσιν, and ἀπαιτοῖεν. I will quote one from the
LXX., Deuter. 23. 21, ἐὰν δὲ εὔχῃ εὐχὴν κυρίῳ τῷ θεῷ cov, οὐ χρονιεῖς
ἀποδοῦναι αὐτήν, ὅτι ἐκζητῶν ἐκζητήσει κύριος ὁ θεός σου, καὶ ἔσται ἐν σοὶ
ἁμαρτία.

|Hippocrates.|

V? 81, 36—82, 16. For this passage, see my Antecedents of Greek
Corpuscular Theories, Harvard Studies in Class. Philol., 22 (1911),
p. 148 sq. It is to this article, and not to “Class. Philol. 22.
158,” that Diels should have referred V* 106, 16, note.

c.13. Epicharmus.
ΝΟ, 23. ΗΠ. ἢ,

τὸ δὲ σοφὸν ἁ φύσις τόδ᾽ οἶδεν ὡς ἔχει
μόνα" πεπαίδευται yap αὐταύτας ὕπο.

Diels renders, “ Doch wie sich’s mit dieser Weisheit verhiilt, das.
weiss die Natur allein. Denn sie hat’s ganz von selbst gelernt.”
It is, perhaps, a matter of no great consequence, but I believe his.
translation rests on a misconception of τὸ σοφὸν τόδε and ws ἔχει. As
to the former, it has little in common with (τὸ) σοφόν of Heraclitus,
but, like the familiar phrase οὐδὲν ποικίλον οὐδὲ σοφόν, denotes some-
thing recondite or cunningly devised. In regard to ws ἔχει, 1 remarked
above, in my note on Heraclitus, fr. 1, that it here refers to the process
of becoming, “how it comes about.” The words of the fragment
mean, “Nature alone knows the secret of this cunning device, or
the way in which this mysterious result is brought about.’ This use
of ws ἔχει and related phrases appears to have escaped many scholars.
Possibly it baffled the copyists also in certain instances. Thus Xen.
Mem. 1. 1. 11, οὐδὲ yap περὶ τῆς τῶν πάντων φύσεως, ἧπερ τῶν ἄλλων

ᾷ

HEIDEL.— ON FRAGMENTS OF THE PRE-SOCRATICS. i

οἱ πλεῖστοι, διελέγετο σκοπῶν, ὅπως ὁ καλούμενος ὑπὸ τῶν σοφιστῶν
κόσμος ἔχει, καὶ τίσιν ἀνάγκαις ἕκαστα γίνεται τῶν οὐρανίων κτλ. Here
the Mss. are divided between ἔχει and ἔφυ, and the editors find it dif-
ficult to decide. I believe that ἔχει, which has the better credentials,
is the true reading, though one may question whether the unfamiliar
force of ἔχει or the similarity of sound led to the substitution of ἔφυ.
As I pointed out in my study Περὶ Φύσεως, the same duplicity as
appears in the force of ws ἔχει occurs also in the use of φύσις, which
predominantly signifies that which a thing is, but, pursuant to a
constant habit of the human mind, is most frequently and naturally
defined by recounting the story of its birth.

c. 18. Parmenides.

V? 105, 34. Diog. L. 9. 22, γένεσιν ἀνθρώπων ἐξ ἡλίου πρῶτον γενέ-
σθαι: αὐτὸν δὲ ὑπάρχειν τὸ θερμὸν καὶ τὸ ψυχρόν, ἐξ ὧν τὰ
πάντα συνεστάναι.

Various proposals have been made for the emendatéon of ἡλίου, of
which ἰλύος is the most probable. It is obvious, however, that ἐξ
ἡλίου, or whatever we may substitute for it, was not intended to
denote the elemental constituents of man, since they are expressly
mentioned later in the sentence. If the writer had in mind merely
the source of the force which led to the origin of man, ἐξ ἡλίου,
however singular, may be allowed to stand. But Diels is quite right
in regarding αὐτὸν as corrupt. The language of Aristotle and his
commentators suggests the obvious correction, αὐτοῖς δ᾽ ἐνυπάρχειν,
referring to the στοιχεῖα ἐνυπάρχοντα.

115,110; Fr. 1) 28,
χρεὼ δέ σε πάντα πυθέσθαι
ἠμὲν ᾿Αληθείης εὐκυκλέος ἀτρεμὲς ἦτορ
ἠδὲ βροτῶν δόξας, ταῖς οὐκ ἔνι πίστις ἀληθής.

Something depends upon the precise meaning of πίστις ἀληθής; for it
must to a considerable extent determine our conception of the attitude
of Parmenides toward the βροτῶν δόξαι, which seem to have occu-
pied his thought in much the larger part of his philosophical poem.
The phrase recurs, fr. 8, 26 sq.,

αὐτὰρ ἀκίνητον μεγάλων ἐν πείρασι δεσμῶν
ἔστιν ἄναρχον ἄπαυστον, ἐπεὶ γένεσις καὶ ὄλεθρος
τῆλε μάλ᾽ ἐπλάχθησαν, ἀπῶσε δὲ πίστις ἀληθής.

718 PROCEEDINGS OF THE AMERICAN ACADEMY.

Diels renders it with “ verliissliche Wahrheit” and “wahre Uberzeu-
gung”’; Burnet and Nestle do not vary the phrase but give “true
belief” and ‘‘des Wahren Gewissheit” in both cases. Two other
passages of the poem ought to be compared, to wit, fr. 8, 12,

> [4 + Mes 3 1 sf > i 4 , 3 /
οὐδὲ ToT’ ἐκ μὴ ἐόντος ἐφήσει πίστιος ἰσχύς
γίγνεσθαί τι παρ᾽ αὐτό,

and fr. 8, 17,
οὐ yap ἀληθής
ἔστιν ὁδός.

In the passage last mentioned ἀληθὴς ὁδός is clearly equivalent to
᾿Αληθείης ὁδός, as in fr. 4, 4 we have Πειθοῦς ἐστι κέλευθος. So in
Sophocl. O. R. 500,

ἀνδρῶν δ᾽ ὅτι μάντις πλέον ἢ ᾿γὼ φέρεται,
κρίσις οὐκ ἔστιν ἀληθής,

where the meaning obviously is that “there is no proving the truth
: 5 : :

of the contention that a seer outstrips me.” This use of κρίσις calls

to mind the fact that Parmenides employs the same word, fr. 8, 15,

ἡ δὲ κρίσις περὶ τούτων ἐν τῷδ᾽ ἔστιν"
ἔστιν ἢ οὐκ ἔστιν" κέκριται δ᾽ οὖν, ὥσπερ ἀνάγκη,
τὴν μὲν ἐὰν ἀνόητον ἀνώνυμον (οὐ yap ἀληθής
ἔστιν ὁδός), τὴν δ᾽ ὥστε πέλειν καὶ ἐτήτυμον εἶναι.

Here the context appears to me to furnish the clue to the meaning of
πίστις; for Parmenides clearly has in mind an action at law in which
the issue is sharply drawn and judgment is rendered. So fr. 8, 27 sq.
the πίστις ἀληθῆς sends γένεσις and ὄλεθρος into banishment. The
juxtaposition of κρίσις and πίστις shows that πίστις means such evi-
dence or proof as may be adduced in court, a meaning which the
word quite regularly bore in legal argumentation. Aristotle, the logi-
cian, feeling that forensic oratory employed the enthymeme rather
than the syllogism, and that in consequence its deductions were
less cogent, continued to use πίστις for rhetorical proof in contradis-
tinction to ἀπόδειξις, the stricter proof of logic or science. Thus πίστις
is for him πειθοῦς κέλευθος, the method proper to a procedure which,
like the plea of the rhetor, has for its object the establishment of the
εἰκός. In much the same way the σήματα of Parmenides, fr. 8, 2,
are the σημεῖα of forensic argumentation, which Aristotle in like
manner and for the same reason distinguished from the more certain

HEIDEL.— ON FRAGMENTS OF THE PRE-SOCRATICS. 719

τεκμήρια. Thus we see that the dialectic of Parmenides, which
eventuated in the Aristotelian logic, employed the forms and termi-
nology of forensic rhetoric, though with an evident effort to reduce
argumentation to the exactitude of demonstration; and πίστις ἀληθής is
just this demonstration of truth. When, therefore, Parmenides objects
to the βροτῶν δόξαι, it is because they do not carry the force of logical
or dialectic evidence, or that such evidence is against them.

ΜΠ 110, 19. Fe. 1,37,
Ld wie ‘ eon
μόνος δ᾽ ἔτι θυμὸς ὁδοῖο
λείπεται.

W118; 35: Brae
μοῦνος δ᾽ ἔτι μῦθος ὁδοῖο
λείπεται, ὡς ἔστιν.

It appears to be geherally conceded that θυμός and μῦθος are cor-
ruptions of oneand the same word; θυμός, at any rate, is unintelligible.
Of the numerous emendations proposed Platt’s οἶμος is doubtless the
best, though Diels seems to prefer ῥυμός; but ῥυμός does not so well
explain the corruption as ofuos. I am about to propose a correction,
which seems to me all but certain. The stress on μόνος and λείπεται
suggests that we are reduced to a way that barely remains. Similarly
Plato, Symp. 184 B, μία δὲ λείπεται τῷ ἡμετέρῳ νόμῳ ὁδός, reinforced by
184 E, μοναχοῦ ἐνταῦθα... ἄλλοθι δὲ οὐδαμοῦ, like the Aristotelian
dictum, τὸ ἁμαρτάνειν πολλαχῶς ἔστι, τὸ κατορθοῦν μοναχῶς, calls to
mind the Gospel saying, στενὴ ἡ πύλη καὶ τεθλιμμένη ἡ ὁδὸς ἡ ἀπάγουσα
εἰς τὴν ζωήν. I take it for granted that Parmenides regarded and
characterized the way of Truth as a strait and narrow path, just as,
fr. 6, 2 sq., he obviously thinks of the way of Error as broad, since
“mortals, knowing nought, stagger (πλάττονται) along it with un-
steady minds.” I can think of nothing so suitable for his purpose,
or so likely to give rise to the corruptions θυμός and μῦθος, as the
word ἰσθμός. Plato, Tim. 69 E, uses it of the human neck, Emped.
fr. 100, 19, of the narrow orifice of the clepsydra, and Hom., σ 300,
uses ἔσθμιον of anecklace. The Homeric scholiast says that the throat
is called ἰσθμός, ἀπὸ τοῦ εἰσιέναι τὴν τροφὴν δι᾿ αὐτοῦ. The correspond-
ing use of αὐχήν (Herod. 7. 223) and of fauces in Latin in speaking
of a narrow defile or ‘isthmus’ is sufficiently well known. Now it
happens that in Emped. fr. 100, 19, ic@ués has become corrupted in
a part of the MS. tradition, and in Sophocl., fr. 145,

720 PROCEEDINGS OF THE AMERICAN ACADEMY.

ε A ial

a δὲ μνᾶστις
θνατοῖς εὐποτμότατα μελέων
᾽ , “ ‘ > t
ἀνέχουσα βίου βραχὺν ἰσθμόν,

where ἰσθμός refers to “the narrow span of life,” modern scholars
have ignorantly sought to substitute something else. Nauck here
proposed οἶμον, as Platt does for Parmenides. But the MS. reading
is confirmed by Aelian, V. H. 2. 41, ὅτε αὐτῷ τὸ ἐκ Βουτοῦς μαντεῖον
ἀφίκετο προλέγον τὴν τοῦ βίου στενοχωρίαν, and by Cicero’s use of
angustiae temporis.

I should therefore read ἰσθμὸς ὁδοῖο in both fragments. Lest
anyone be disturbed by the hiatus between ἔτι and ἰσθμός, I remark
that we find another instance of it in fr. 4, 6,

\ U / “ wv 3 ,
τὴν δή τοι φράζω παναπευθέα ἔμμεν ἀταρπόν,

in each case in the bucolic diaeresis. Diels, Parmenides Lehrgedicht,
p. 67, in his note on the latter passage, well says: “Der Hiat in der
bukolischen Diiirese nicht anzutasten!’’ Indeed, the collision of
words ending and beginning with the same vowel was even regarded
by ancient grammarians as peculiarly justifiable. See Christ, Metrik
der Griechen and Romer’, p. 41, §55, and the remarks of ancient
grammarians on Hom. Od. ἃ 595, Verg. Georg. 1, 281, and Hor. C.
1. 28, 24. Herwerden, Lexicon Gr. Suppletorium, p. 400, suggests
that ἰσθμός may have had the digamma, referring to Pindar, Isth.
1. 10, 32 and Bacchyl. 2, 7 Blass., but continues, “Sed fortasse hiatus
nominum propriorum licentiae tribuendus. Cf. O. Schroeder, Prol.
Pind. 11. p. 14 et p. 17. Nee sane digamma habere potuit, si des-
scendit a verbo ἰέναι. Ido not believe it had the digamma.

V? 117, 7. Fr. 5, τὸ yap αὐτὸ νοεῖν ἐστίν τε καὶ εἶναι.

The construction of this sentence has occasioned difficulties. It is
obvious, however, that it is identical in meaning with fr. 8, 34, to be
discussed below. I think we have here a case of brachylogy, and that
we must supply νοεῖν before εἶναι from the preceding νοεῖν. “ For
it 7s one and the same thing to think and to think that it is.” See
the examples cited by Kiihner-Gerth, II. p. 565, ὃ 597, h. Burnet,
Early Greek Philosophy’, p. 198, notes 1 and 3, propounds syntactical
doctrines and puzzles which one ought in kindness to ignore. Any
good grammar will supply abundant examples of the substantive
use of the infinitive, with or without the article, earlier than the date
of Parmenides. For Greek lyric poets, see Smyth, Greek Melic Poets,

HEIDEL.— ON FRAGMENTS OF THE PRE-SOCRATICS. 721

note on Aleman, fr. XII. For the articular infinitive in general,
consult the articles of Professor Gildersleeve in Amer. Journ. of

Philol.
Vv? 17,14. Fro 6. Tf.

χρὴ TO λέγειν TE νοεῖν τ᾽ ἐὸν ἔμμεναι " ἔστι yap εἶναι,
μηδὲν δ᾽ οὐκ ἔστιν.

The view of Diels and Burnet, which takes ἔστι and ἔστιν as
equivalent to ἔξεστι, appears to me to be unsatisfactory; for the
sentence thus becomes weak and out of character. Parmenides says:
“For existence exists, and nought vs ποί. The absence of the article
with εἶναι and μηδὲν makes no difference. In regard to the first sen-
tence, we must, perhaps, acquiesce in the view of Diels, who regards
τό as the epic pronoun, and renders: “Dies ist nétig zu sagen und
zu denken, das nur das Seiende existiert”; but this use of τό would be
unique in Parmenides, in whom we expect the articular infinitive.
It is possible that he meant “Speech and thought must be real’; for,
though we do not otherwise find the recognition of the corporeal
existence of thought and speech clearly expressed before the Stoics
and Epicureans, it is by no means certain that Parmenides would not
be called upon to defend his ‘materialistic’ doctrines by asserting the
corporeality of thought and speech, since he expressly concerned
himself with predication, fr. 8, 35 sq.

ΜΗ 1. hr. 628,
ois TO πέλειν TE Kal οὐκ εἶναι ταὐτὸν νενόμισται
κοὐ ταὐτόν.

Burnet, Early Greek Philosophy’, p. 198, n. 3, tortures this passage
in order to eliminate the articular infinitives and the solecism τὸ...
οὐκ εἶναι; but his interpretation is impossible, and, as we have seen,
his reluctance to admit the articular infinitive is indefensible. As
to τὸ... οὐκ εἶναι, others before him have found in it a rock of offence;
but the responsibility rests with Parmenides. If he could say, οὕτως
ἢ πάμπαν πελέναι χρεών ἐστι ἢ οὐχί (fr. 8, 11) alongside ἡ δ᾽ ὡς οὐκ
ἔστιν τε καὶ ὡς χρεών ἐστι μὴ εἶναι (fr. 4, 5) it is difficult to see why
he should not have said τὸ οὐκ εἶναι instead of τὸ μὴ εἶναι.

V? 119, 6. Fr.8, 9,
τί δ᾽ ἄν μιν Kal χρέος ὦρσεν
ὕστερον ἢ πρόσθεν, τοῦ μηδενὸς ἀρξάμενον, φῦν.

(22 PROCEEDINGS OF THE AMERICAN ACADEMY.

Diels renders ὕστερον ἢ πρόσθεν with “friiher oder spiter”; Burnet,
correctly I believe, with “later rather than sooner”; for I regard the
phrase as a sort of comparatio compendiaria. 'The question was
repeated and amplified by later philosophers; cp. Lucret. 5, 165-180;
Cic. N. D. 1. 9. 21; V? 305, 16 sq.; Diels, Dox. Gr., p. 301, 2, kai ove
κατὰ TO πρῶτον μακάριός ἐστιν ὁ θεός, TO γὰρ ἐλλεῖπον εἰς εὐδαιμονίαν οὐ
μακάριον, οὔτε κατὰ τὸ δεύτερον: μηδὲν γὰρ ἐλλείπων κεναῖς ἔμελλεν
ἐπιχειρεῖν πράξεσιν. In the last passage I think we should clearly
read καιναῖς for κεναῖς; cp. Lucret. 5, 168 sq.,

Quidve novi potuit tanto post ante quietos

inlicere ut cuperent vitam mutare priorem?

nam gaudere novis rebus debere videtur

cui veteres obsunt; sed cui ni! accidit aegri
tempore in anteacto, cum pulchre degeret aevum,
quid potuit novitatis amorem accendere tali?

I may add that Parmenides, fr. 8, 7, πῇ πόθεν αὐξηθέν, and 8, 32 sq.,

oe ᾽ 3 , A | 5" UJ >
οὕνεκεν οὐκ ἀτελεύτητον τὸ ἐὸν θέμις εἶναι"
ἔστι γὰρ οὐκ ἐπιδευές, ἐὸν δ᾽ ἂν παντὸς ἐδεῖτο,

is expanded by Plato, Tim. 32 C-34 A, with an obvious addition 33 A,
which is apparently drawn from the Atomists. Cp. V°343, 4sq., and
my Antecedents of Greek Corpuscular Theories, Harvard Studies in
Class. Philol., 22 (1910), p. 139. See also the discussion above
(p. 693 sq.) of V? 34, 18.

V? 120,13. Fr. 8, 34, ταὐτὸν δ᾽ ἐστὶ νοεῖν τε καὶ οὕνεκεν ἐστι νόημα.

So far as I am aware, all interpreters of Parmenides have taken
οὕνεκεν in the sense of “that for the sake of which.” This is, of
course, quite possible; but we thus obtain no satisfactory sense unless
we are to adopt the Neo-Platonic conceptions which obviously sug-
gested the accepted rendering. Probably no student of ancient
philosophy who has learned the rudiments of historical interpretation
would go so far afield. Only the natural obsession that we must take
our cue from the ancients, whose incapacity in this regard should no
longer be a secret, can account for the failure of some one to make the
obvious suggestion that we take οὕνεκεν as ὅτι, and read ἔστι; for it
seems clear that Parmenides meant, “ Thinking and the thought that
the object of thought exists, are one and the same.’ Wiihner-Gerth, IT.
p. 356, and the lexicons give the examples for this use of οὕνεκα; for

HEIDEL.— ON FRAGMENTS OF THE PRE-SOCRATICS. 723

the dependence of a substantive clause on a verbal substantive,
Stahl, Arit.-histor. Syntax des gr. Verbums der klass. Zeit, p. 546, § 2,
gives abundant examples, to which a careful reader will be able to
add largely in a week. The parallelism of infinitive and substantive
is no closer than Mimnermus, 2, 10,

αὐτίκα τεθνάμεναι βέλτιον ἢ βίοτος.

If the inverted order of words should cause any one to hesitate, let
him recall Xenophanes, fr. 34, 2,

Kal ἅσσα λέγω περὶ πάντων,

and Sophocl. O. R. 500 sq., quoted above, p. 718, on fr. 1, 28 sq.
I regard this construction as of especial importance, because the
frank equivalence of the infinitive with the substantive would seem
to render for all time impossible the strange acrobatic feats performed
by Burnet in his endeavor’to eliminate the substantival infinitive,
with or without the article, from the text of Parmenides.

c.19. Zeno.

V? 133, 8. Fr. 1, καὶ περὶ rod προὔχοντος ὁ αὐτὸς λόγος. Kal yap
ἐκεῖνο ἕξει μέγεθος καὶ προέξει αὐτοῦ τι. ὅμοιον δὴ τοῦτο ἅπαξ τε
εἰπεῖν καὶ ἀεὶ λέγειν. οὐδὲν γὰρ αὐτοῦ τοιοῦτον ἔσχατον ἔσται οὔτε
ἕτερον πρὸς ἕτερον οὐκ ἔσται. οὕτως εἰ πολλά ἐστιν, ἀνάγκη αὐτὰ
μικρά τε εἶναι καὶ μεγάλα μικρὰ μὲν ὥστε μὴ ἔχειν μέγεθος, μεγάλα
δὲ ὥστε ἄπειρα εἶναι.

The question discussed in the portion of the fragment here repro-
duced concerns the second alternative, μεγάλα δὲ ὥστε ἄπειρα εἶναι.
There is some difference of opinion among scholars regarding the
precise conception of τὸ προὔχον. For some years I have been accus-
tomed to think of the προὔχον ἔσχατον of Zeno as the extremum quodque
cacumen of Lucretius 1, 599; or, more exactly, I have held and still
hold that the Epicurean doctrine of the partes minimae, of which the
definition of the extremum cacumen is a part, owed its origin in part
to this argument of Zeno’s. The discussion of the partes minimae by
Giussani had never satisfied me; the view of Pascal, Studii Critici
sul Poema di Lucrezio (1903), p. 49 sq., seemed to me essentially
sound (see Amer. Journ. of Philol., 24, p. 332). He drew attention
to Aristotle’s arguments (De Anim. 400" 13 sq., De Gen. et Corr.
326° 1 sq., Phys. 2408 sq.) to prove that the ἀμερές cannot have

724 PROCEEDINGS OF THE AMERICAN ACADEMY.

motion, or at most can have motion κατὰ συμβεβηκός only, which
would be fatal to the older Atomism. Pascal himself did not see that
Aristotle (and MXG. 977° 11 sq.) derived his arguments from Plato,
Parm. 198 BC. With these we must clearly associate the questions
touching the rotation of a circle or a sphere, Arist. Phys. 2405 29 sq.,
265» 7; Simpl. Phys. 1022; [Arist.] Qu. Mech. ec. 1; Plotin. Ennead.
2.2.1. But Plato clearly had in mind positions taken by the younger
Eleatics, which he was developing. What these were in detail I am
unable to say; but the argument of Zeno which we are considering
seems to me to present the same problem from another angle; if the
criticisms of Plato and Aristotle, applied to the atom, as an ἀμερές,
rendered motion, which the Atomists regarded as inherent in it,
apparently impossible, the criticism of Zeno made it necessary that
there should be a limit to the number and the divisibility of the parts
of which a revised atomism might concede that it was composed.
In fr. 1, therefore, I regard αὐτοῦ in προέξει αὐτοῦ τι as a partitive
genitive, and accept the emendation of Gomperz, ὥστε ἕτερον πρὸ ἑτέρου
for οὔτε ἕτερον πρὸς ἕτερον. As I conceive the matter, Zeno does not
think of a cacumen as being added; but, since every extended part is
susceptible of division, that which we regard as the προὔχον must
always have an outer and an inner half, and so by the division ad
infinitum of the προὔχον itself there is crowded between it and the
next inward ‘unit’ an infinitude of parts which, from Zeno’s point of
view, must in effect advance the’ zpovxov or cacumen outward ad
infinitum. Consequently things become μεγάλα ὥστε ἄπειρα εἶναι.

c. 20. Melissus.

V? 145,10. Fr. 7. 3, ἀλλ᾽ οὐδὲ μετακοσμηθῆναι ἀνυστόν " ὁ yap κό-
σμος ὁ πρόσθεν ἐὼν οὐκ ἀπόλλυται οὔτε ὁ μὴ ἐὼν γίνεται. ὅτε δὲ μήτε
προσγίνεται μηδὲν μήτε ἀπόλλυται μήτε ἑτεροιοῦται, πῶς ἂν μετα-
κοσμηθὲν τῶν ἐόντων εἴη; εἰ μὲν γάρ τι ἔγίνετο ἑτεροῖον, ἤδη ἂν
καὶ μετατκοσμηθείη.

A careful reading of this passage will convince any scholar that there
is something wrong with it. The difficulty, however, lies entirely in
the clause πῶς... εἴη, where the MSS. read μετακοσμηθέντων ἐόντων
τι ἧ. Mullach and Ritter-Preller present the same text as Diels,
except that they read τὶ εἴη. Diels renders the clause thus: “wie
sollte es nach der Umgestaltung noch zu dem Seienden ziihlen?”’
Burnet, apparently accepting the text of Mullach and Ritter-Preller,

HEIDEL.— ON FRAGMENTS OF THE PRE-SOCRATICS. 725
translates “how can any real thing have had its order changed?”
I do not believe this rendering, which agrees with that of Mullach, is
possible, for I know of no such periphrastic form as μετακοσμηθὲν εἴη
(ἀπαρνηθείς, Plato, Soph. 217 C, is aor. pass. in form only); that of
Diels, on the other hand, though clearly necessary if one adopts his
text, does not yield the thought required in the context. I incline to
think that τι and ἢ are marginal corrections which have been misread
and misplaced, and that we should read πῶς ἂν μετακοσμηθείη τι τῶν
ἐόντων; “ How should anything real sutfer change of order?”

V? 149, 1. Fr. 9, εἰ μὲν οὖν εἴη, det αὐτὸ ἕν εἶναι" ἕν δὲ ὃν αὐτὸ
σῶμα μὴ ἔχειν. εἰ δὲ Exot πάχος, ἔχοι ἂν μόρια, καὶ οὐκέτι ἕν εἴη.

Although Simplicius twice so quotes Melissus, and we cannot
therefore doubt that his text so read, I cannot believe that Melissus
wrote σῶμα μὴ ἔχειν. That the Neo-Platonists understood him as
holding that the existent is incorporeal is of course well known, but
is insufficient warrant for attributing the doctrine to him. Zeller
and Burnet seek to obviate the difficulty by referring the fragment,
not to the Eleatic One, but to the Pythagorean Unit. Against this
view there are two objections which appear to me to be fatal to it:
first, we should have to suppose that Simplicius, who read this passage
in its context, did not grasp its import, which must have been fairly
clear; second, even if Simplicius should have erred in this respect,
the argument of Melissus must have been applicable to the Eleatic
One, and so Simplicius would be substantially right in quoting the
words in order to prove that the Eleatic One was incorporeal. This
very conception of Eleatic doctrine, however, would sufficiently
account for a corruption of the text, such as reading ἔχειν for εἶναι.
That is what I conceive to have occurred. Melissus, understanding
σῶμα as an ἄθροισμα of parts which, because divisible ad infinitum,
must be tridimensional or “have thickness,” says that a true Unit
(whether Eleatic or Pythagorean) cannot be conceived as a σῶμα or
ἄθροισμα. See Amer. Journ. of Philol., Vol. 28, p. 79. At the begin-
ning of the same clause the MS. tradition clearly points to the read-
ing ἕν δ᾽ ἐὸν rather than ἕν δὲ ὃν. This correction, which I had noted
several years ago, has now been made by Diels in V’*.

c. 21. Empedocles.

V? 203, 13 sq. Arist. De Anima 1. 2. 404° 8 sq., asserts that Em-
pedocles regarded the soul (ψυχή) as compounded of all the elements,

726 PROCEEDINGS OF THE AMERICAN ACADEMY.

and quotes fr. 109 to prove it. So far as I can recall, all scholars
have been content to accept this deduction of Aristotle, although
the words quoted offer not the slightest confirmation of it and the
doctrine thus ascribed to Empedocles is diametrically opposed to his
conception of ψυχή in matters of religion. This conflict has been
often noted, but no one seems to have seen that the solution of the
difficulty lies in the simple fact that Empedocles did not connect
these functions with the ψυχή, which he, like many other early
Greeks, thought of as the entity only which escapes from man at the
moment of death and survives the body. Fr. 110, 10,

πάντα yap ἴσθι φρόνησιν ἔχειν Kal νώματος αἶσαν,

shows what language Empedocles used: everything has φρόνησις and
νόημα, but not ψυχή. See my remarks in Amer. Journ. of Philol.,
33, p. 94 sq., and Journ. of Philos., Psychol. and Scient. Methods,
1033p: ΤῸ"

V7? 20334:) τ 110;
3 A ͵ 9 3 lal e A , 39 ͵

εἰ γὰρ κέν of ἀδινῇσιν ὑπὸ πραπίδεσσιν ἐρείσας
εὐμενέως καθαρῇσιν ἐποπτεύσῃς μελέτῃσιν,
ταῦτά τέ σοι μάλα πάντα δι᾽ αἰῶνος παρέσονται,
ἄλλα τε πόλλ᾽ ἀπὸ τῶνδ᾽ ἐκτήσεαι" αὐτὰ γὰρ αὔξει
ταῦτ᾽ εἰς ἦθος ἕκαστον, ὅπῃ φύσις ἐστὶν ἑκάστῳ.
εἰ δὲ σὺ γ᾽ ἀλλοίων ἐπορέξεαι, οἷα κατ᾽ ἄνδρας

, \ Ud .“ 3 3 , ,
μυρία δειλὰ πέλονται ἅ τ᾿ ἀμβλύνουσι μερίμνας,
ἢ σ᾽ ἄφαρ ἐκλείψουσι περιπλομένοιο χρόνοιο

lal ’ lal , ͵ 3 \ it e uJ
σφῶν αὐτῶν ποθέοντα φίλην ἐπὶ γένναν ἱκέσθαι *
10 πάντα γὰρ ἴσθι φρόνησιν ἔχειν καὶ νώματος αἶσαν.

σι

The text of this fragment as given by Hippolytus is extremely
corrupt; but I accept the text given by Diels everywhere except in
verses 4 and 5. Here the MSS. read αὔξει and ἔθος: Diels retains the
former and adopts Miller’s suggestion of ἦθος for the latter. This
text I think is clearly wrong, as the difficulties experienced by Diels
in rendering the passage ought to convince any reader. But v. 8 sq.
seem to me to show what we require; for they obviously contain the
converse of the statement which the poet made in the sentence we
are considering. J am convinced that Empedocles wrote ἄξει, not
αὔξει; with regard to ἔθος, one may hesitate before deciding between the
claims of ἔθνος and ἦθος. In favor of ἔθνος one may quote Hippocr.
Περὶ τόπων τῶν κατὰ ἄνθρωπον, 1 (6, 278 L.), τοῦτο δ᾽ ὁποῖον ἄν τι πάθῃ,

— — ae

HEIDEL.— ON FRAGMENTS OF THE PRE-SOCRATICS 727

TO σμικρότατον ἐπαναφέρει πρὸς THY ὁμοεθνίην ἕκαστον πρὸς τὴν ἑωυτοῦ, ἤν
τε κακὸν ἤν τε ἀγαθὸν ἢ " καὶ διὰ ταῦτα καὶ ἀλγέει καὶ ἥδεται ὑπὸ ἔθνεος τοῦ
σμικροτάτου τὸ σῶμα, ὅτι ἐν τῷ σμικροτάτῳ πάντ᾽ ἔνι τὰ μέρεα, καὶ ταῦτα
ἐπαναφέρουσιν ἐς τὰ σφῶν αὐτῶν ἕκαστα, καὶ ἐξαγγέλλουσι πάντα. Other
passages which may be compared are the following. Hippocr. Περὶ
φύσιος ἀνθρώπου, 3 (6, 388 L.), καὶ πάλιν ye ἀνάγκη ἀποχωρέειν és τὴν
ἑωυτοῦ φύσιν ἕκαστον, τελευτῶντος τοῦ σώματος τοῦ ἀνθρώπου, τό τε ὑγρὸν
πρὸς τὸ ὑγρὸν καὶ τὸ ξηρὸν πρὸς τὸ ξηρὸν καὶ τὸ θερμὸν πρὸς τὸ θερμὸν καὶ
τὸ ψυχρὸν πρὸς τὸ ψυχρόν. τοιαύτη δὲ καὶ τῶν ζῴων ἐστὶν ἡ φύσις καὶ τῶν
ἄλλων πάντων " γίνεταί τε ὁμοίως πάντα καὶ τελευτᾷ ὁμοίως πάντα " ξυνί-
σταταί τε γὰρ αὐτέων ἡ φύσις ἀπὸ τουτέων τῶν προειρημένων πάντων, καὶ
τελευτᾷ κατὰ τὰ εἰρημένα ἐς τωὐτὸ ὅθεν περ ξυνέστη ἕκαστον, ἐνταῦθα οὖν
καὶ ἀπεχώρησεν. ἹΠερὶ φύσιος παιδίου 17 (7, 496 L.), ἡ δὲ σὰρξ αὐξο-
μένη ὑπὸ τοῦ πνεύματος ἀρθροῦται, καὶ ἔρχεται ἐν αὐτέῃ ἕκαστον τὸ ὅμοιον
ὡς τὸ ὅμοιον,. τὸ πυκνὸν ὡς τὸ πυκνόν, τὸ ἀραιὸν ὡς τὸ ἀραιόν, τὸ ὑγρὸν ὡς
τὸ ὑγρόν - καὶ ἕκαστον ἔρχεται ἐς χώρην ἰδίην κατὰ τὸ ξυγγενές, ad’ οὗ
καὶ eyevero. Plato, Tim. 63 E, ἡ πρὸς τὸ συγγενὲς ὁδός. Ibid. 90 A,
πρὸς τὴν ἐν οὐρανῷ συγγένειαν. Herod. 4. 147, ἀποπλεύσεσθαι ἐς τοὺς
συγγενέας. Plotin. Ennead. 4. 3. 24, εἰς τὸν προσήκοντα αὐτῷ τόπον.
Hermias, Irris. 7 (V? 19, 14), εἰς δὲ τὴν αὑτοῦ φύσιν ἐπανιὼν anp. Me-
nand. Epitrep. 105,
εἰς δὲ τὴν αὑτοῦ φύσιν
ἄρας ἐλείθερόν τι τολμήσει ποεῖν.

Lucret. 2, 1112,

nam sua cuique locis ex omnibus omnia plagis
corpora distribuuntur et ad sua saecla recedunt.

These examples sufficiently prove that one can draw no inference from
els which would serve to decide the respective claims of ἦθος and ἔθνος;
besides, the epic use of εἰς with reference to persons as well as places
(Il. 7, 312; 15, 402; Od. 14, 126 sq.), which would obtain in Empedo-
cles, leaves the question open. The poet means to say that Pausanias,
to whom he addresses his poem as Lucretius addressed his to Mem-
mius, if he gives heed to the instruction of his master, will find that it
will lead him into all truth, since each truth will seek its fellows, each
after its own kind; but if he deserts the living truth, it will in turn
desert him, each truth, as before, longing to join its kindred. There
are two passages in which Lucretius has plainly derived inspiration
and suggestion from these words of Empedocles.

728 PROCEEDINGS OF THE AMERICAN ACADEMY.

1,400 Multaque praeterea tibi possum commemorando
argumenta fidem dictis corradere nostris.
verum animo satis haec vestigia parva sagaci
sunt per quae possis cognoscere cetera tute.
namque canes ut montivagae persaepe ferarum

405 naribus inveniunt intectas fronde quietes,
cum semel institerunt vestigia certa vial,
sic alid ex alio per te tute ipse videre
talibus in rebus poteris caecasque latebras
insinuare omnis et verum protrahere inde.

1, 1114 Haec sei pernosces parva perductus opella

namque alid ex alio clarescet nec tibi caeca
nox iter eripiet quin ultima naturai
pervideas: ita res accendent lumina rebus.

After 1, 1114, with Munro, I assume a lacuna; for it appears obvious
that the sentence is incomplete. But in the absence of more certain
indications I refrain from speculating as to what and how much may
have perished in the breach. Yet perductus, which is clearly right
and ought not to be changed to perdoctus, and iter, like the words of
Empedocles, suggest guidance on the way of truth: it is possible that
Lucretius may have taken a hint, as 2, 75 sq., from ancient relay
torch races, in which one runner handed over his torch or ignited that
of his team-mate, to illustrate the way in which a truth once known
flashes light far along paths hitherto shrouded in night. In 1, 400 sq.
Lucretius cleverly adapts a conception to his own uses. As he did
not accept the doctrine of the ubiquity of intelligence in nature,
which underlies the thought of Empedocles, he was obliged to intro-
duce a simile in lieu of the bold personification of facts and truths
which renders memorable the passage of his predecessor. We natur-
ally ask whether there was anything in his model to suggest the
particular simile which he chose. Now, it must be confessed that
there is a possible point of contact, if Empedocles wrote ἦθος rather
than ἔθνος; for in that case ἦθος would certainly not mean “charac-
ter” or “heart,” as has been supposed, but “haunts” or “lair,”
according to a usage familiar in Greek. In that event we should
have to think of facts or truths as having, like mountain-ranging
beasts, their lairs where they hide their young and to which they
themselves return and guide the man who follows them. If Empedo-
cles used the word ἦθος, one might see in v. 4, ἄλλα τε πόλλ᾽ ἀπὸ τῶνδ᾽

HEIDEL.— ON FRAGMENTS OF THE PRE-SOCRATICS. 729

ἐκτήσεαι, a reference to τόκος, usury; for, as one may perceive by
Aeschin. 8. 35, δανείσματα οὐκ ὀλίγα, ad’ ὧν ἐκεῖνος τόκους ἐλάμβανε, the
phraseology suggests it. Ancient writers, however, were fully aware
of the metaphor, which was still alive, and played on the word,
as Ar. Thesmoph. 842 sq., Plato, Repub. 555 E, Arist. Pol. 1. 10. 1258»
5 sq... This metaphor would well lead up to that of ἦθος, as the lair
of wild beasts. From this too, it would be easy to explain the figure
of Lucretius, who substitutes mountain-ranging hounds tracking the
beasts to their lairs (quietes, 1, 405, and caecas latebras, 408). Indeed,
it is possible that Empedocles may have used the simile of the hound
in this very connection, fr. 101,

κέρματα Onpelwy μελέων μυκτῆρσιν ἐρευνῶν
«ὀσμᾶθ᾽» ὅσσ᾽ ἀπέλειπε ποδῶν ἁπαλῇ περὶ ποίῃ.

But the context in which the fragment is quoted by our ancient
authorities, as well as Lucret. 4, 680 sq., suggest rather that Empedocles
was there illustrating his doctrine of universal ἀπορροιαί. I find it
difficult, therefore, to decide between the claims of ἔθνος and ἦθος; but
incline on the whole to favor the former because of v. 9,

ποθέοντα φίλην ἐπὶ γένναν ἱκέσθαι.

I may add that Mr. Cornford, From Religion to Philosophy, p. 64,
makes an interesting suggestion in regard to Emped. fr. 17, 28,

τιμῆς δ᾽ ἄλλης ἄλλο μέδει, παρὰ δ᾽ ἦθος ἑκάστῳ,

where he renders rapa .. . ἑκάστῳ, ‘each has its wonted range.’ See
ibid., p. 34.

Now that the general sense of Emped. fr. 110 is clear, there can
be no doubt about the meaning of v. 5, ὅπῃ φύσις ἐστὶν ἑκάστῳ. It is
prout cuique natura est, “each after its kind.”

Ὁ. 32. Philolaus.
V? 239, 381. Fr. 1, ἁ φύσις δ᾽ ἐν τῷ κόσμῳ.

In V3 Diels adopts certain suggestions made in my Notes on Philo-
laus, Amer. Journ. of Philol., 28, p. 79, to which he refers, but rightly
retains δ᾽ ἐν τῷ κόσμῳ instead of δὲ τῶ κόσμω, which I formerly pro-
posed; but in sense τῷ κόσμω was more nearly right than his rendering
“bei der Weltordnung.”’ In the notes he now cites parallels, which
I furnished, for φύσις ἐν τῷ κόσμῳ. They sufficiently explain the

730 PROCEEDINGS OF THE AMERICAN ACADEMY.

phrase and fix its meaning. I will now add another, Plotin. Ennead.
3. 8. 1, παίζοντες δὴ τὴν πρώτην πρὶν ἐπιχειρεῖν σπουδάζειν εἰ λέγοιμεν
πάντα θεωρίας ἐφίεσθαι καὶ εἰς τέλος τοῦτο βλέπειν, οὐ μόνον ἔλλογα ἀλλὰ
καὶ ἄλλογα ζῷα καὶ τὴν ἐν τοῖς φυτοῖς φύσιν καὶ τὴν ταῦτα γεν-
νῶσαν γῆν κτλ. Thus ἡ ἐν τῷ κόσμῳ φύσις = ἡ τοῦ κόσμου φύσις. In
Plotinus there is probably a suggestion of the common, universal
φύσις as manifesting itself in plant-life; but all these passages alike
prove that the phrase does not mean “bei der Weltordnung.”

V? 240, 5. Fr. 2, δηλοῖ δὲ καὶ τὰ ἐν τοῖς ἔργοις.

Since Diels has now (V?) adopted my interpretation of these words,
I might allow the matter to rest there; but the observation that this
and similar phrases have been unduly pressed in other contexts leads
me to illustrate it further. Nestle, in Philol., 67, 544, writing as it
seems in ignorance both of Newbold’s article and of mine, arrived at
substantially the same conclusion with myself. It would carry us
too far afield to consider in detail the passages which I have studied;
hence I will give a list of those only which serve to illustrate Greek
usage. It will be seen that ἐν τοῖς ἔργοις and ἐπὶ τῶν ἔργων are gen-
erally used when appeal is made to facts of common observation or
knowledge, as opposed to theory, argument, or unsupported statement.
As a matter of fact, these references are usually so general that they
amount to nothing but the bald assertion that observation or knowl-
edge confirms or contradicts the proposition in question. In very
few cases which 1 have noted does the context suffice to enable one
to specify the particular facts to which the writer affects to appeal:
many passages are open to different interpretations and competent
scholars find it difficult to agree about them. They are therefore
especially valuable for our purposes. See Plato, Protag. 352 A, Soph.
234 E, Gorg. 461 D, Repub. 396 A, 599 B, Phaedo 110 A, Tim. 19 E,
Legg. 679 D, Axiochus 369 A; Xenoph. Hiero 9.3; Bonitz, Index Arist.
286? 27 sq., 40 sq.; Bywater, on Arist. Poet. 14555 17. Cp. Arist. De
Gen. Animal. 3. 11. 762° 15, οὐθὲν yap ἐκ παντὸς γίνεται, καθάπερ οὐδ᾽ ἐν
τοῖς ὑπὸ τῆς τέχνης δημιουργουμένοις. Meteor. 4. 3. 381° 10, καὶ οὐδὲν
διαφέρει ἐν ὀργάνοις τεχνικοῖς ἢ φυσικοῖς, ἐὰν γίγνηται" διὰ τὴν αὐτὴν γὰρ
αἰτίαν πάντα ἔσται. Such general references to the similarity of prod-
ucts of art and of nature abound in certain works of the Corpus
Hippocrateum. See also Hippocr. Περὶ φυσέων, 5 (where, after stating
his theory, the writer says), περὶ μὲν οὖν ὅλου τοῦ πρήγματος ἀρκεῖ μοι
ταῦτα μετὰ δὲ ταῦτα πρὸς αὐτὰ τὰ ἔργα τῷ αὐτῷ λόγῳ πορευθεὶς ἐπιδείξω

HEIDEL.— ON FRAGMENTS OF THE PRE-SOCRATICS. 731

τὰ νοσήματα τούτου ἔκγονα πάντα ἐόντα. In this instance the particular
“facts”? to which he appeals are mentioned. It is interesting to hear
his conclusion, ο. 15, ὑπεσχόμην δὲ τῶν νούσων τὸ αἴτιον φράσειν " ἐπέ-
δειξα δὲ τὸ πνεῦμα καὶ ἐν τοῖς ὅλοις πρήγμασι δυναστεῦον καὶ ἐν τοῖς σώμασι
τῶν ζῴων - ἤγαγον δὲ τὸν λόγον ἐπὶ τὰ γνώριμα τῶν ἀρρωστημάτων, ἐν οἷς
ἀληθὴς ἡ ὑπόσχεσις (ν. 1. ὑπόθεαις) ἐφάνη " εἰ γὰρ περὶ πάντων τῶν ἀρρω-
στημάτων λέγοιμι, μακρότερος μὲν ὁ λόγος ἂν γένοιτο, ἀτρεκέστερος δὲ
οὐδαμῶς οὐδὲ πιστότερος. :

V? 241,12. Fr. 6, ἰσοταγῆ.

Diels has now adopted my emendation ἰσοταγῆ for MS. ἰσοταχῆ.
When I proposed it, I ventured the suggestion relying on the analogy
of ὁμοταγής, not knowing that icoray7s itself was attested. I now
observe, however, that Sophocles, Greek Lexicon, s. v. cites it from
Nicom. 51.

c. 46. Anaxagoras.

V? 319,19. Fr. 13, καὶ ἐπεὶ ἤρξατο ὁ νοῦς κινεῖν, ἀπὸ τοῦ κινουμένου
παντὸς ἀπεκρίνετο, καὶ ὅσον ἐκίνησεν ὁ νοῦς, πᾶν τοῦτο διεκρίθη "
- κινουμένων δὲ καὶ διακρινομένων ἡ περιχώρησις πολλῷ μᾶλλον ἐποίει
διακρίνεσθαι.

It seems to me clear that 6 νοῦς is the subject of ἀπεκρίνετο in the
second clause. “After the νοῦς gave the initial. impulse to the
motion of the world, it began to withdraw from all that was set in
motion; and all that to which the movement initiated by the νοῦς
extended, was segregated. As this motion and segregation con-
tinued, the revolution greatly increased the segregation.” The νοῦς
gives the first impulse only, then withdraws to its condition of isola-
tion; the revolution, once started, of itself accelerates and its effects
in the segregation of like to like in the πάντα ὁμοῦ increase. Cp.
ἡ περιχώρησις αὐτή, fr. 12, V? 319, 4 sq.

c. 51. Diogenes of Apollonia.

V? 334, 2. Fr. 1, λόγου παντὸς ἀρχόμενον δοκεῖ μοι χρεὼν εἶναι τὴν
ἀρχὴν ἀναμφισβήτητον παρέχεσθαι.

With this statement compare Hippocr. Περὶ σαρκῶν, 1 (8. 584 L.),
᾿γὼ τὰ μέχρι τοῦ λόγου τούτου κοινῇσι γνώμῃσι χρέομαι ἑτέρων TE τῶν
ἔμπροσθεν, ἀτὰρ καὶ ἐμεωυτοῦ - ἀναγκαίως γὰρ ἔχει κοινὴν ἀρχὴν ὑποθέσθαι

ΤΩ PROCEEDINGS OF THE AMERICAN ACADEMY.

τῇσι γνώμῃσι βουλόμενον ξυνθεῖναι τὸν λόγον τόνδε περὶ τῆς τέχνης τῆς
ἰητρικῆς. Περὶ τέχνης, 4 (0. 6 1,.), ἐστὶ μὲν οὖν μοι ἀρχὴ τοῦ λόγου, ἣ
καὶ ὁμολογηθήσεται παρὰ πᾶσιν. ἹΠερὶ τόπων τῶν κατὰ ἄνθρωπον, 2 (6.
278 L.), φύσις τοῦ σώματος, ἀρχὴ τοῦ ἐν ἰητρικῇ λόγου. Ion of Chios,
fr. 1 (V? 222, 1 sq.), ἀρχὴ δὲ μοι τοῦ λόγου: πάντα τρία καὶ οὐδὲν πλέον
ἢ ἔλασσον τούτων τῶν τριῶν : ἑνὸς ἑκάστου ἀρετὴ τρίας" σύνεσις καὶ
κράτος καὶ τὐχη.

c. 54. Leucippus.

V? 343, 1. τὸ μὲν πᾶν ἄπειρόν φησιν, ὡς προείρηται" τούτου δὲ τὸ
\ mn > \ \ “ a \ ar , >
μὲν πλῆρες εἶναι, TO δὲ κενόν, <A> καὶ στοιχεῖά φησι, κόσμους TE EK
τούτων ἀπείρους εἶναι καὶ διαλύεσθαι εἰς ταῦτα.

For some time I have felt that there was some confusion and
corruption in the text, and that the last sentence must refer to the
rise of the worlds out of the ἄπειρον and their return into it at dissolu-
tion. The well-known difficulties of the text of Diogenes alone
deterred me from proposing a change. Now Diels, apparently from
the MSS., restores ἐκ τούτου for ἐκ τούτων. That is obviously the
correct reading, whatever its source; but with it should of course go.
the complementary reading εἰς τοῦτο for eis ταῦτα. The preceding
sentence, however, has likewise suffered. The ἄπειρον is clearly
conceived as the Aristotelian ἀρχὴ καὶ στοιχεῖον by the interpolator
or epitomator who supplied the clause <a@> καὶ στοιχεῖά φησι; for to
his mind the words τούτου τὸ μέν πλῆρες, τὸ δὲ κενόν do not suggest
spatial regions of the extended ἄπειρον, but ontological γένη of the
metaphysical ἀρχή. His addition was absurdly misplaced, as were
many in the text of Diogenes; but once there, it corrupted the
following sentence. See above, p. 691, on V? 17, 37.

V? 344, 14. Arist. De Gen. et Corr. 1. 8. 324° 35, ὁδῷ δὲ μάλιστα

\ \ , iz \ I , yy. \ ,
καὶ περὶ πάντων ἑνὶ λόγῳ διωρίκασι Λεύκιππος καὶ Δημόκριτος.

The meaning of the phrase ἑνὲ λόγῳ has here been strangely
misconceived. Prantl renders it “in einer Begriindung”; Zeller,
1» 847, n. 1, “aus den gleichen Principien”; Déring, Gesch. der gr.
Philos., 1. 238, “die von einem Princip ausgehende Lésung”’; Burnet,
Early Greek Philosophy’, 385, “on the same theory.” I have failed
to find this passage noted in Kranz’s Wortindex, but in a similar one
(V2 83, 8, ἑνὶ δὲ λόγῳ πάντα κτὰ.), omitting to quote πάντα, he gives
the meaning of λόγος as “ Vernunft” (2 II. 2, 357, 30)! Similarly

HEIDEL.— ON FRAGMENTS OF THE PRE-SOCRATICS. 733

Burnet, in his note on Plato, Phaedo 65 D, gives a false emphasis
and in effect a false interpretation, because he overlooks, what is
obvious, that in the phrase καὶ τῶν ἄλλων ἑνὲ λόγῳ ἁπάντων, the
phrase évi λόγῳ is to be taken as emphasizing ἁπάντων; and Capps,
on Menander, Epitrep. 197 sq.

KATAMEVO,
αὔριον ὅτῳ βούλεσθ᾽ ἐπιτρέπειν Evi λόγῳ
ἕτοιμος,

wrongly takes évi λόγῳ with ἕτοιμος instead of ὅτῳ βούλεσθ᾽. Curios-
ity, awakened by the false points made by scholars in connection
with the Aristotelian passage we are considering, led me to make
a collection of cases of évi λόγῳ, which grew to considerable propor-
tions. I will not print a list here, since such collections possess no
value in my sight except as an examination of the context serves to
determine the sense of the locution in question. Suffice it to say that
in almost every instance the immediate context contained a compre-
hensive or universal expression, such as πᾶν, οὐδέν, μυρία, ete. But
ἑνὶ λόγῳ does not stand alone, for there is a considerable number of
phrases similarly used; of these I give a few which should serve to
illustrate the construction. Aeschyl. P. V. 46, ὡς ἁπλῷ λόγῳ...
οὐδὲν; ibid. 505, βραχεῖ δὲ μύθῳ πάντα συλλήβδην wade; ibid. 975, ἁπλῷ
λόγῳ πάντας ἐχθαίρω θεούς; Herod. 2. 24, ὡς μέν νυν ἐν ἐλαχίστῳ δηλῶ-
σαι, πᾶν εἴρηται; ibid. 225, ὡς δὲ ἐν πλέονι λόγῳ δηλῶσαι, ὧδε ἔχει;
ibid. 2. 37, μυρίας ὡς εἰπεῖν λόγῳ; ibid. 3. 6, ἕν κεράμιον οἰνηρὸν ἀριθμῷ
κεινὸν οὐκ ἔστι ὡς λόγῳ εἰπεῖν ἰδέσθαι; ibid. 3. 82, évi δὲ ἔπεϊ πάντα
συλλαβόντα εἰπεῖν; Plato Apol. 22 B, ὡς ἔπος εἰπεῖν ὀλίγου αὐτῶν ἅπαν-
τας; Xenoph. Mem. 4. 3. 7, ὡς γὰρ συνελόντι εἰπεῖν, οὐδέν kTA.; Amphis,
fr. 30, 7 Kock, ἅπαντες ἀνδροφόνοι yap εἰσιν ἑνὶ λόγῳ Adverbs like
ἔμβαχυ are similarly employed. After reciting this list of passages I
think we may be sure that in the passage we are considering Aristotle
merely meant to say that the procedure of Leucippus and Democritus
was not only exceedingly methodical (ὁδῷ μάλιστα), but also com-
prehensive (περὶ πάντων évi λόγῳ). Possibly those who have been
reading something more into Aristotle’s words might receive some
comfort from Hippocr. Περὶ ἑπταμήνου, 3 (7. 488 L.), χρῶνται δὲ πᾶσαι
ἑνὶ λόγῳ περὶ τουτέου: φασὶ yap κτλ. But the context shows that
ἑνὶ λόγῳ means “one formula of expression.”’ Even if one should
insist on taking Aristotle’s words as a parallel to this, it would greatly
affect the traditional interpretations of the passage.

734 PROCEFDINGS OF THE AMERICAN ACADEMY.

V? 344, 21. Arist. De Gen. et Corr. 1. 8. 325° 25, ὁμολογήσας δὲ
ταῦτα μὲν τοῖς φαινομένοις, τοῖς δὲ TO ἕν κατασκευάζουσιν Ws οὐκ ἂν
κίνησιν οὖσαν ἄνευ κενοῦ, τό τε κενὸν μὴ ὃν καὶ τοῦ ὄντος οἰθὲν μὴ ὄν
φησιν εἶναι. τὸ γὰρ κυρίως ὃν παμπλῆρες ὄν.

I cannot understand how scholars have been so long content to
retain this text, which yields no sense and so clearly suggests the true
reading. With it we must compare other passages in which the same
matter is under consideration. Arist. Met. 1. 4. 985> 4 (V2 343, 44),
Λεύκιππος δὲ καὶ 6 ἑταῖρος αὐτοῦ Δημόκριτος στοιχεῖα μὲν TO πλῆρες Kal
τὸ κενὸν εἶναί φασι, λέγοντες τὸ μὲν ὃν τὸ δὲ μὴ ὄν, τούτων δὲ τὸ μὲν
πλῆρες καὶ στερεὸν τὸ ὄν, τὸ δὲ κενὸν καὶ μανὸν τὸ μὴ ὄν (διὰ καὶ
οὐθὲν μᾶλλον τὸ ὄν τοῦ μὴ ὄντος εἶναί φασιν, ὅτε οὐδὲ τὸ
κενὸν «ἔλαττον Diels> τοῦ σὠματο»), αἴτια δὲ τῶν ὄντων ταῦτα
ὡς ὕλην. Whether Diels was right in proposing to insert ἔλαττον we
shall have presently to inquire. Simpl. Phys. 28, 11 (3 545, 5), ἔτι
δὲ οὐδὲν μᾶλλον τὸ ὃν ἢ TO μὴ ὃν ὑπάρχειν, Kal αἴτια ὁμοίως
εἶναι τοῖς γινομένοις ἄμφω. τὴν μὲν γὰρ τῶν ἀτόμων οὐσίαν ναστὴν καὶ
πλήρη ὑποθέμενος ὃν ἔλεγεν εἶναι καὶ ἐν τῷ κενῷ φέρεσθαι, ὅπερ μὴ ὃν
ἐκάλει καὶ οὐκ ἔλαττον τοῦ ὄντος εἶναί φησι. We are familiar
with the pun which Democritus employed to enforce this point of
doctrine, fr. 156 (73 418,11), μὴ μᾶλλον τὸ δὲν ἢ τὸ μηδὲν εἶναι.
It seems to me obvious that in the passage under consideration μὴ ὄν
is a corruption by itacism for μεῖόν. Indeed, I am inclined to think
that the pun τό τε κενὸν μὴ ὃν καὶ τοῦ ὄντος οὐθὲν μεῖον derives from
the same fertile brain as μὴ μᾶλλον τὸ δὲν ἢ τὸ μηδέν, and that we have
thus found another fragment of Democritus partially converted into
the Attic dialect. If this be conceded, it seems more probable that
we should supply μεῖον than ἔλαττον (with Diels) in Met. 985° 9.
Aristotle used the word, Eth. Nic. 5. 1. 1129” 8, δοκεῖ καὶ τὸ μεῖον
κακὸν ἀγαθόν πως εἶναι, Where the true reading, corrupted in the MSS.,
had to be recovered from the commentaries and versions. Cp.
Aeschyl. P. V. 508, ὡς ἐγὼ εὔελπίς εἰμι τῶνδέ σ᾽ ἐκ δεσμῶν ἔτι | λυθέντα
μηδὲν μεῖον ἰσχύσειν Διός; Xenoph. Ages. 6. 8, τρόπαια μὴν ᾿Αγεσιλάου
οὐχ ὅσα ἐστήσατο ἀλλ᾽ ὅσα ἐστρατεύσατο δίκαιον νομίζειν. μεῖον μὲν γὰρ
οὐδὲν ἐκράτει κτὰ.; Herondas 3, 59, ἕξει γὰρ οὐδὲν μεῖον; ibid. 15, 2, ὃς
δ᾽ ἔχει μεῖον τούτου TL.

MIppDLETOWN, ΟΟΝΝ.
ΕῈΒ. 25, 1918.

Proceedings of the American Academy of Arts and Sciences.

Vou. XLVIII. No. 20.— May, 1913.

CONTRIBUTIONS FROM THE ZOOLOGICAL LABORATORY OF
THE MUSEUM OF COMPARATIVE ZOOLOGY AT HARVARD
COLLEGE.— No. 236.

THE STRUCTURE OF THE GORGONIAN CORAL PSEUDO-
PLEXAURA CRASSA WRIGHT AND STUDER.

By WayLanp M. CHESTER.

CONTRIBUTIONS FROM THE ZOOLOGICAL LABORATORY OF
THE MUSEUM OF COMPARATIVE ZOOLOGY AT HARVARD
COLLEGE. — No. 236.

THE STRUCTURE OF THE GORGONIAN CORAL
PSEUDOPLEXAURA CRASSA WRIGHT
AND STUDER.!
By WayLanp M. CuHeEstTER.

Presented by E. L. Mark, March 12, 1913. Received April 5, 1913.

CONTENTS.
Introduction . . . . . . 7387 | Dorsal mesenterial filaments 759
ΒΕ ΟΠΗΝ τ ee 40) Growth 20s ΣΙ τ. 760
General structure . . . . 740 | Musclesandnerves . . . . 760
Ectoderm .... . - - 747 | Skeleton and axis epithelium. 762
ΜΙ ΕΕΟΡΊΟΘΗΝ, Shi. ὅτ & 751.} Summary. cork Le we 4A F68
ROBE ς νον. 75 ΕΒῚ ΘΙ ΟΡ ADDY ear oot wd Ure AO
Structures concerned in nutri- Explanation of plates . . . 773

ST OQ a ὦ eer 0.
INTRODUCTION.

PSEUDOPLEXAURA CRASSA is found on the reefs of Florida, of the
West Indies, and of the Bermuda Islands. It is very abundant in
the shallow water of the inner reefs of Bermuda, and is there one of
the two or three very common sea whips; but it is found in the deeper
waters of the outer reefs as well. The range in depth, to include the
greater number of colonies, is from a position near the surface at low
water to seven or eight meters.

Ellis and Solander (1786) described this colony under the name of
Gorgonia crassa. K6lliker (1872) placed under the name of Plexaura
branched, sea-rod forms in which the polyps completely retract into a
comparatively thick coenenchyma, in which club-shaped and spiny
spindle-shaped spicules appear. The different species were divided
into two groups: Plexaura durae and Plexaura molles. Hargitt
and Rogers (:01, p. 285) follow Verrill (65, p. 34) in describing this
form as Plexaura crassa. Wright and Studer (’89, p. 141-143), from
observations of Bermuda specimens, created for this species a new

1 Contributions from the Bermuda Biological Station for Research. No. 27.

738 PROCEEDINGS OF THE AMERICAN ACADEMY.

genus, Pseudoplexaura. The new genus is characterized by them as
follows: “axis horny, with a central calcareous portion, the outer
layer of coenenchyme is soft and when dry friable; the inner layer
contains a number of light purple or violet coloured irregularly stellate
spicules or spindles with few rays.” It is to be distinguished from
Plexaura, in addition, by the following features, among others: colony
feebly branched, older portions of horny axis solid, younger portions
with calcareous particles in the center; polyps placed close together
in an irregular spiral, completely retractile tentacles without spicules
or having a circlet of them at their base; spicules mostly spiny spin-
dles, with numerous pink stellate forms and a few club-shaped with
attenuated foliaceous expansions.

The important characters of the colony are: the relative smallness
of the spicules; spicules in the outer cortex, and irregularly stellate
forms in the inner cortex; the massing of the latter to such an extent
as to make the inner cortex firmer when dried, while the outer is
friable; the absence of spicules in the tentacles and polyps; the
sluggish but complete retraction of the polyps within the cortex; and
the smooth cortex surface without projecting calyces in the contracted
or dried colony. The polyps are numerous. When they are com-
pletely expanded the tentacles of adjacent polyps overlap, and the
coenenchyme is hidden. Each tentacle has ten to twelve pairs of
pinnae.

Of the three groups of aleyonarian corals,— Aleyonacea, Pennatu-
lacea and Gorgonacea,— only representatives of the first and second
have had their minute structure studied recently; the Gorgonacea,
to which Pseudoplexaura belongs, have received little attention except
from von Koch (’87) in his very important but early comparative
study. Studies on the Aleyonacea have been relatively numerous.
Von Koch (’827) described briefly the structure of Clavularia and
other aleyonacean forms. Bourne (95) described Heliopora coerulea
and later made a very complete study of the origin and structure of
its skeleton (99). Ashworth (99) studied the minute structure of
Xenia Hicksonii Ash. and Heteroxenia elizabethae Koll. He found
gland cells in the stomodaeum and correlated their presence there
with the absence of the ventral and lateral mesenterial filaments.
Hickson (95) has given a detailed account of the cell structure of
Aleyonium digitatum, and Pratt (:05) has described the digesting
and mesogloea cells in several members of the Aleyonidae. She
found a relatively large number of granular gland cells in the stomo-
daeum of feeding colonies and very few or none in starved ones. She

CHESTER— STRUCTURE OF PSEUDOPLEXAURA CRASSA. 739

held the mesogloeal network of cells to be neuro-phagocytic in func-
tion. By feeding with colored material, she proved the ingestion and
the carriage of such material by the amoeboid movements of the
mesogloeal cells. Kassianow (:08) reviewed the literature for the .
muscle and nerve systems in Alcyonaria digitatum, studied these
systems and described in detail the cells of the ectoderm, endoderm
and mesogloea with reference to them. He denied a nervous function
for the neuro-mesogloeal cells of Pratt.

Among the Pennatulacea, studies have been made by Korotneff (81)
and by Bujor (:01) on Veretillum. They described the cells of the
ectoderm and endoderm carefully.

The only complete study of the cell structure of representatives
of the grup Gorgonacea is by von Koch (87), who made a compara-
tive study of the structure and minute anatomy of the forms found in
the Bay of Naples, giving most attention to Unicella (Gorgonia)
‘avolinil.

Wilson (84) studied the mesenterial filaments of a number of
species representing the three groups. He described the difference
in structure of the ventral and dorsal mesenterial filaments and the
origin of each from different germ layers.

Bourne (99), in a paper giving the result of his study of the origin
of the skeleton in Anthozoa, describes the origin and minute struc-
ture of the alcyonarian spicule and the structure of the massive
skeleton of the aleyonarian Heliopora. He further studied the struc-
ture and origin of “holdfasts,” or desmocytes, in Heliopora, as well
as in madreporarian forms.

Woodland (:05) reviewed the literature on the origin of the alcyon-
arian spicule and made a very complete study of it for Aleyonium.
The names of von Koch (18, 82°), Studer (’87, :06), and Alfred
Schneider (:05) are important in the history of researches on the
origin of the horny skeleton. Kinoshita (:10) has seen the origin of
axis epithelium in young forms of Anthoplexaura and has confirmed
von Koch’s account of its ectodermal origin in the young form.

The study of this gorgonian coral (Pseudoplexaura crassa) was
pursued during the summers of 1909 and 1910 at the Bermuda Bio-
logical Station for Research, and during the winter of 1909-1910 at
the Zodlogical Laboratory of Harvard University. I wish to express
my great indebtedness to Dr. E. L. Mark, the Director of these
Laboratories for guidance and generous assistance.

740 PROCEEDINGS OF THE AMERICAN ACADEMY.

METHops.

Small colonies were kept alive in large aquaria of running water
for a short time. Small tips, 5 to 10 cm. long, were easily kept in
smaller dishes of running water, if care was taken to keep them
upright. Both Bouin’s fluid and a five per cent formalin were suc-
cessfully used as fixing agents. The fixing fluids were taken in some
instances to the reefs and large tips or other pieces cut off from the
colony and quickly transferred to the fluid; upon returning to the
laboratory these were cut into small pieces. Both neutral formalin
and Vom Rath’s picric-osmic-acetic-platinic chloride fluid were used
for nerve fixation. Corrosive sublimate and Wilson’s fluid were
both used, but did not give any better results than the formalin or
Bouin’s fluid. Decalcification was effected by 1% acetic acid in
absolute alcohol. Maceration by Hertwig’s method gave good
results. Delafield’s haematoxylin and iron-alum haematoxylin could
be used with decalcified material. Many sections of the soft tips
were made without decalcification; but in these the haematoxylin
overstained the spicules and the axial skeleton, obscuring the neigh- ὁ
boring cells. By far the best general stain for these was Mallory’s
phospho-tungstic haematoxylin, which stained well after formalin
and better after Bouin’s fluid. This has the advantage that, while it
does not obscure the spicules, it differentiates other structures.

GENERAL STRUCTURE.

A colony of Pseudoplexaura crassa presents a loosely divided group
of long branches on a short stem; or the short stem may have short
branches which divide and divide again, terminating in long whips.
A drawing of a very young colony (Fig. A) illustrates the character
of the branching. The short basal shaft spreads out on the coral
rock or on old coral masses, secreting a skeleton that becomes very
firmly attached to its substratum. The whips, which rise in many
planes, are cylindrical, long and flexible, and taper somewhat gradu-
ally to the tips, which, however, end bluntly, or even with a slight
enlargement. The brownish polyps stand at right angles to the
branches (Plate 1, Fig. 1), closely crowded against one another, except
at the tips of the branches, where the coenenchyma can often be seen
even when all the polyps are expanded. Because the polyps when

CHESTER.— STRUCTURE OF PSEUDOPLEXAURA CRASSA. 741

expanded stand at right angles to the branches, and are crowded, the
colony in this condition looks like a miniature leafless shrub with
unusually thick branches; because the tip is often bare of polyps
or these are there contracted, the colony when seen at a distance
below the surface may resemble very superficially a huge compound

Bn 35
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a

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Fig. A. Young colony of Pseudoplexaura crassa, showing method of
branching and the calycle openings in the coenenchyma.

tube sponge. But Figure A, although it shows the character of the
branching, does not show the great number of branches, or whips,
that occur in largerforms. As found on the Bermuda reefs, the species
varies greatly in size. A small colony stood 90 cm. high, its terminal
60 branches spreading over a circle 60 ecm. in diameter. Another

742 PROCEEDINGS OF THE AMERICAN ACADEMY.

colony was 110 em. high with 250 terminal branches. A third meas-
ured 200 em. in height and had 300 terminal branches. These three,
taken from one place, are representative of the forms inside the outer
reefs. On the outer reefs, forms 225 cm. high have been found. In
the first colony (90 cm. high) the diameters of the stems were measured.
Half way between the ground and the tips, with the polyps fully
expanded, the branches were 4 cm. in diameter; at the base, 5 cm.,
and near the tip, a little more than 3 cm. After the polyps were fully
contracted, the measurements were 1.5 cm. for the base, and .5 em.
for the tip.

A transverse section of a branch, or whip (Plate 1, Fig. 1), shows
the structure. In common with that of the branches of Gorgonacea
generally, there are recognizable three zones: a central axis of skeletal
material (az.), a fleshy enveloping layer,— the coenenchyma,— and a
zone of polyps. The polyps can completely retract into spaces in
the coenenchyma, whereupon two zones only are evident. The horny
axis is very hard at the base but quite soft at the tip of the branches
and, except at the basal end, is very flexible. To the naked eye, it is
composed of two parts, a central, soft marrow, light in color (white
in the figure), and an outer, harder, brown or black tubular shaft or
cortex. The marrow has nearly the same thickness in all parts of the
colony.?_ While its diameter is sometimes slightly smaller at the tip,
it is not always so. Its variations are not wholly dependent on age,
for it is slightly larger or smaller in parts of the stem and these parts
occur irregularly. It is composed of a number of chambers filled with
loosely branching threads (compare Plate 4, Fig. 58), and having walls
of horny material, the chambers being generally arranged one above
the other (Plate 4, Fig. 57, med. ax.). The loosely branching threads
in the chambers are not shown in this figure, but are seen in the small
chamber of the axis-cortex shown in Figure 58. The walls of the
medullary chambers are very thin. Those of the axis-cortex chambers
are very thia at the tip of a branch, while at the base they are very
thick and hard. This is due to the fact that while the marrow cham-
bers are laid down axially (i. e., at the end of the axis) in the branch,
the cortex grows radially. The latter is composed of smaller cham-
bers, which in longitudinal sections appear crescent shaped (Fig. 57,
ctx. ax.). Not only is the cavity smaller, but the walls are thicker
than those of the marrow. ‘The first crescents laid down are adjacent
to the marrow and very short, but as the axis-cortex increases in

2 This cortex of the axis will be called axis-cortex to distinguish it from
the more superficial coenenchymal cortex.

CHESTER— STRUCTURE OF PSEUDOPLEXAURA CRASSA. 743

thickness, the outer ones are very long and have much thicker walls
and thinner cavities. To the naked eye this gives the appearance
of a solid cortex.

Where a branch is formed there is a break between the marrow of
the branch and that of the stem (Plate 4, Fig. 61), and the axis-cortex
forms a thick knee-like union at the stem for strength. At the base
of the colony the axis-cortex is spread upon the substratum and the
marrow is lacking. Many of the Bermuda colonies that were located
on the shallow reefs, where the tips were exposed at the lowest tides,
had lost the fleshy envelope of the tips of the branches for the distance
of a few centimeters, the horny axis being here covered by diatoms.
The fleshy coenenchyma was growing loosely around the old axis and
taking the shape of the original branch. In such regenerated tips no
new marrow was formed. In a few instances the old axis had been
completely covered, but the coenosare had not grown enough beyond
the axis to give evidence of the presence or absence of a marrow distal
to the old dead axis.

The coenenchyma is composed of two regions, an inner, exhibiting
longitudinal canals, and an outer, containing the calycles or polyp-
chambers. The longitudinal-canal region is characterized by a number
of large canals running parallel to the axis (Plate 1, Fig. 1, can. lg.),
and by the presence of purple, irregularly stellate spicules (Fig. B,
5-7) loosely massed in groups (spc.’). The spicules are represented
diagrammatically in the left half of Figure 1, to show their positions.
The longitudinal canals are less numerous at the tips of the branches —
where there may be eight to ten — than they are at the bases, where
twenty or more may be found. The diminution in number from the
base to the tips is due to the running together of two adjacent canals
or to the abrupt ending of one or more. Some of them run continu-
ously from the basal half of the stem into the lower (abaxial) face of a
branch. On the axial face of the branch they may be continuous
with those of the stem, or the canal may begin abruptly in the branch
without such connection. At the tips and on the branches the
longitudinal canals connect with one another and with the polyp
‘avities by smaller canals (can.). At the base of the colony they run
out radially and end blindly, or are connected with one another or
with polyps by the smaller canals. At the tips the purple spicules
are loosely arranged in two concentric cylinders separated from each
other by the zone of canals. Where the branches are older, however,
the inner cylinder breaks up into small groups, which lie between the
axis and two adjacent canals (Fig. 1, spe.’); here the spicules interlock

744 PROCEEDINGS OF THE AMERICAN ACADEMY.

in a close mass. The diagrammatic nature of Figure 1 does not per-
mit one to show the closeness of the interlocking of these spicules.

The outer region of the coenenchyma is a thick zone with polyp
chambers (cam. pyp.), into which the polyps can completely retract.
These chambers communicate with each other by a greatly branched
system of small canals (can.). These canals are represented in only
one half of Figure 1 (Plate 1). The actual canals are much more
numerous and are more complexly branched than the diagram shows.
Between the chambers white spindle-shaped and spiny spicules
(Fig. B, 1-4), longer than the purple ones of the inner region, are
found (spe.). Some of the deeper of these may be purple. Indeed
there is considerable variation in both color and form of the spicules
of different colonies and even of the same colony. These spicules
have been described and figured by Wright and Studer (89), by Har-
gitt and Rogers (:01) and by Verrill (:07). Figure B gives the rela-
tive proportions in size, as well as the differences in shape for the
spicules of both the inner and outer regions of the coenenchyma.
Figure B, 5-7, presents spicules of different shapes found near the long
canals, where they are often locked together. In Figure B, 1, 2,
are seen long white forms from the outer part, and in Figure B, 3, 4,
spicules from the deeper part of that region.

The polyp-zone consists of the exposed part of the polyps or antho-
codia (Fig. 1, a-y). These when expanded are cylindrical. The
mouth is oval and the eight tentacles of the crown stand at right
angles to the column. ‘The tentacles are conical, relatively long when
fully expanded, and carry ten to twelve pairs of conical pinnae, ar-
ranged in two longitudinal lines, one on either side. No spicules are
found in the polyps.

The anthocodia are brown and, when expanded, give the colony
its prevailing color, which is caused by the presence of the Zooxan-
thellae (Plate 2, Figs. 20, 21, σου.) that crowd the endoderm cells and
give a lighter or darker brown color in accordance with the degree
of the animal’s contraction. A little magnification shows that each
disk is white and also that along the eight longitudinal lines corre-
sponding to the union of the mesenteries with the body wall the color
is white. The white appearance in both cases is due to the absence
of these algae. The color of the coenenchyma between the anthocodia
is distinctly white because of the absence of Zooxanthellae near the
surface and the presence of white spicules.

The wall of the column of the anthocodium (Plate 1, Fig. 1, 6)
merges into that of the somewhat larger chamber in the coenenchyma

CHESTER.— STRUCTURE OF PSEUDOPLEXAURA CRASSA. 745

and its endodermal epithelium is continuous with that of the chamber.
The stomodaeum (Fig. 1, 7, stmd.) is long, reaching when the polyp is
expanded, nearly if not quite to the level of the surface of the coe-
nenchyma; it is broadest in the dorso-ventral plane and has at its
ventral angle a prominent siphonoglyph (Fig. 2, sipy.), which is not

Bk 6

Fig. B. Calcareous spicules: 90. 1-4, white spicules of outer cortex
region; 5-7, purple spicules from the region of the longitudinal canals.

visible on the disk, but reaches nearly to the deep end of the stomo-
daeum. The structure is that usually found in the siphonoglyph of
Aleyonaria. A transverse section through the stomodaeum is shown
in Figure 2. The siphonoglyph is always ventral, and the longitudi-
nal muscles of the eight mesenteries, as is usual in Aleyonaria, are
located on the ventral sides of the mesenteries. Figure 3 shows a

746 PROCEEDINGS OF THE AMERICAN ACADEMY.

section made below the level of the first cut and near the level of the
lower end of the stomodaeum — but still through the anthocodium —
very close to the coenenchyma. The mesenterial filaments are cut in
this section. - The filaments belonging to the six ventral and lateral
mesenteries are very short (never more than two millimeters long,
and usually less than one), and appear as very slight thickenings of
the edge of each mesentery. The filaments of the two dorsal mesen-
teries are seen to be deeply grooved; they are very long and pass
with the mesentery from the stomodaeum to the very base of the
chamber, being much convoluted at their lower ends. The section
shown in Figure 4 is cut through the lowest part of the polyp cavity.
The ventral and lateral mesenteries here have no filaments, but the
dorsal filaments, cut across several times, show their grooved condi-
tion. In the lower region of the polyp chamber are also many ova,
or else (the colonies being dioecious) masses of sperm mother cells
covered by the endoderm. The ova are attached singly to the sides
of the six ventral and lateral mesenteries. The eggs in July were
large, but there was no evidence of fertilized eggs or of matured sperm.

Phases in the retraction of the polyp have been described by Wright
and Studer (89) and appear to be similar to those of Aleyonium
(Hickson, ’95). When the colonies were transferred from the condi-
tions of the sea to those of the laboratory, it was seldom that they
remained as fully expanded as at first. The polyps were appreciably
shorter, but they had the shape and character described (Plate 1,
Fig. 1, a). Sometimes the mouth was open and observation showed
a slight current of water passing into the stomodaeum; at other times,
or in other parts of the colony, the mouth was tightly closed. Some-
times the tentacles and pinnae were contracted to form eight short
cones at the top of a column comparatively well expanded, the mouth
being either open or closed. Α circular constriction of a narrow region
then appeared just below the disk, while the remaining part of the
body bulged like a flask (Fig. 1, y). A slow withdrawal of the polyp
then occurred, evidently by means of the longitudinal muscles of the
mesenteries, together with a slow inturning of the tentacles, until the
disk and tentacles were at the level of the calycle. These now drew
within and the oval or ovate calycle opening became visible (Fig. 1, 6).
Sometimes in this method of contraction, the tentacles were first
rolled toward the mouth, giving the disk and tentacles the appearance
of a circle with eight indented radii (Fig. 1, β). The column was then
contracted into the polyp cavity of the coenenchyma, as already out-
lined. But this method of contraction is not the invariable rule.

CHESTER.— STRUCTURE OF PSEUDOPLEXAURA CRASSA. 747

Sometimes, although the tentacles are contracted, the mouth remains
open and the column is brought down nearly to the level of the coe-
nenchyma, where it remains for a long time, the current of water to
and from the stomodaeum evidently not being checked (Fig. 1, €).
Probably the coenenchyma is also capable of slight contraction and
expansion, due principally to the action of the muscles of the mesen-
teries. When the tip of a branch is cut off, the coenosare, with the
polyps near the line of the cut, becomes appreciably of smaller diam-
eter, thus partially covering the cut surface; and the same result is
seen in the regenerating branches on the reefs, where the polyps have
been turned from their radial position and are held in such a way as to
lessen the area of the cut surface.

EcropERM.

The ectoderm of the polyp wall in the expanded condition is more
than one cell thick, showing an epithelial and a subepithelial part
(Plate 2, Figs. 8, 18). In the epithelial part, the cover cells (οἰ. teg.)
are conical, with a round or polygonal external surface as a base and
with the opposite end, as apex, extending into the mesogloea as a
process. In the expanded state of the polyp many of the cells are
peltate or mushroom shaped, since they have the appearance of an
external plate supported by a rapidly narrowing stem. This stem
soon takes a thread-like character and may be branched (Figs. 9, 11).
The outer surface is often convex, like a mushroom, but it may be
indented, so that the section of it is cusp like (Fig. 18, cl. teg.). In the
expanded condition of the polyp, the plate-like surface covers a
relatively large area and the process becomes shorter; in the con-
tracted condition, the cells approach a columnar shape, though the
process is still thread-like at the mesogloeal end (Fig. 20, cl. teg.).
The protoplasm is finely granular and sometimes large granules also
occur (Figs. 10, 11). Although sometimes without vacuoles, these
cells usually contain many small ones. The nuclei are large and
granular and are situated in the outer half of the cells or near the point
of the cusp. Among the covers cells are found nettle-cells or thread-
cells with their nematocysts (Fig. 18, nm’cys.) and sense cells (cl. sns.).

The nematoeysts are of two kinds. The larger and more numerous
ones (Plate 2, Fig. 18 and Plate 4, Figs. 43-46) occur in batteries of
six to ten, but they may be found in much larger numbers. The cyst
is sharply outlined and is an elongated oval with a length three times

748 PROCEEDINGS OF THE AMERICAN ACADEMY.

its greatest width. Its length varies from 10 to 14 micra when
unexploded. Around the cyst is a thin layer of granular protoplasm
containing the flattened nucleus of the cell at the region of the greatest
width of the cyst. The nucleus stains deeply with basic stains,
the chromatin being abundant and granular. There is no trace of a
enidocil or of a cytoplasmic process projecting from the free surface
of the cell. After staining in Mallory’s phospho-tungstic acid hae-
matoxylin or methylen blue a thick thread may be distinguished within
the cyst, though not easily. It passes in a zigzag line from its attach-
ment for a third of the length of the cyst and fills the remaining two
thirds of the cyst in a tight coil (Fig. 44). When exploded the thread
is quite thick and short and without barbs. Nematocysts of the
second type (Fig. 47) are not found so abundantly. They are ovate
and much smaller than those of the first type. The length is 5 to ὃ
micra. The nucleus is at the broad end of the enclosing cell. The
thread with four or five spirals is sharply outlined even without
stains. Exploded, it is long and slender, without barbs.

Sense cells (Plate 2, Figs. 8, 13, cl. sms.) occur among the cover
cells, but are readily found only in the nematocyst batteries, where
their bristle tips can be seen in favorable sections and where their
nuclei reveal them by the size, which is smaller than that of the cover-
cell nucleus. The sense cell is narrow and spindle-shaped with a
long process extending into the mesogloea. Its protoplasm is slightly
more evenly granular than that of the cover cells, though not greatly
different from it; but its nucleus is small and round and can be readily
distinguished from the larger nucleus of the cover cells. The bristle
point is exposed between the cover cells, or between these and the
nematocyst cells.

The subepithelial part of the ectoderm is made up of interstitial
cells, globular cells with granules, nematocyst cells, and ganglion
cells. It is not a sharply defined layer, since the cover cells and the
sense-cell processes pass through it. The interstitial cells (Plate 2,
Figs. 18, 20, cl. in.) are globular or have a central body with branching
processes. In fact, the cells, or some of them, may change their
shape in an amoeboid manner. The cytoplasm is similar to that of
the cover cells; the nucleus may be smaller, though it varies greatly
in size. The granular cells are filled with comparatively large granules
and stain sharply with eosin. They have the appearance of the
granular cells found in the mesogloea of the coenenchyma. Besides
cells containing fully formed nematocysts, there are some which show
stages in the formation of the nematocysts (Fig. 18, cl. nm’cys.).

CHESTER.— STRUCTURE OF PSEUDOPLEXAURA CRASSA. 749

Other cells, lying close to the mesogloea with processes parallel to it,
are interpreted as ganglion cells (Fig. 20, cl. gn.). The difficulty with
this interpretation is due to the presence in the adjoining mesogloea
of the mesogloeal cells, which sometimes resemble the supposed
ganglion cells in shape. In preserved material, the fibers of these
ganglion cells sometimes possess many minute varicosities. The cyto-
plasm is more evenly and closely granular than in surrounding cells.

The ectoderm of the tentacles (Plate 2, Fig. 5) and pinnules (Fig.
6) is relatively thicker than that of the polyp wall, but shows the same
superficial and deep layers. It also differs from that of the body wall
in the smaller number of the large kind of nematocysts and in the
presence of muscle cells in the ectoderm of the oral face of tentacle
and pinnule. The deep end of the muscle cell (Figs. 16, 17) is elon-
gated into a process which is perpendicular to the axis of the body
of the cell, and runs lengthwise of the tentacle or pinnule. Each
process contains in its axis a single highly refractive contractile fiber,
or myoneme. The nucleus is small and finely granular. Usually
the cell body is flattened in the plane of the muscle fiber; but the
flattening may be at right angles to that plane. It is only occasion-
ally that these muscle cells reach to the surface of the ectoderm and
thus present the typical condition of an epithelio-muscle cell. Since
all the muscle fibers run lengthwise of the tentacle, a transverse section
of the tentacle (Fig. 7) shows, adjacent to the mesogloea of the oral
surface and the sides, a very definite row of dots — the cut ends of
muscle fibers. In sections dyed in Mallory’s stain these fibers, being
deeply colored, appear as dark dots, or, if cut somewhat obliquely,
as short lines. In the partially contracted condition of the tentacle
the dots no longer occupy a plane surface, for the originally plane
surface is so folded that the line of dots is very sinuous, and even
forms in some regions a series of pinnate figures.

The ectoderm of the polyp wall passes gradually into that of the
coenenchyma, where, between the polyps, the cover cells (Plate 3,
Figs. 23, 24) are very long and conical, but never show the indented
peltate shape seen in the ectoderm of the polyps. The ectoderm of
the coenenchyma shows a thicker subepithelial region, which gradually
merges with the mesogloea. As a rule, the interstitial cells are so
numerous in the thick mesogloea and the mesogloeal elements are so
near the long cover cells that it is hard to find a boundary between
the two layers. The nematocysts of the larger kind are arranged in
very large and numerous batteries; those of the smaller kind occur
individually and are very few. Both kinds of nematocysts have the

750 PROCEEDINGS OF THE AMERICAN ACADEMY.

same structure as those of the polyp wall. Sense cells, like those in
the body wall and tentacles, are found in the batteries and increase
in number with the increase in the number of cysts in the batteries.

Some of the ectoderm cells of the coenosare between the polyps
contain a prominent, highly refractive, homogenous fiber (Plate 3,
Figs. 24, 26, fbr. sst.), beginning near the nucleus and extending to the
base of the cell, which is implanted in the mesogloea. The nature of
these fibers is not perfectly certain, but it is probable that they are
the same as the “Stiitzfasern” described by K. C. Schneider (:02,
p. 622) for Anemonia; however, I have never seen evidence of their
fibrilation, such as Schneider has shown to exist in the case of typical
“Stiitzzellen.” Figure 26 shows the distribution of these Stiitz-
fasern in the coenenchyma and their relation to the grooves which
occur in these regions.

The ectoderm of the disk is, in its content and cell structure, like
that of the oral face of the tentacle. When the disk is fully expanded,
the stomodaeal epithelium reaches over on to the disk. The siphono-
glyph and the dorso-lateral regions of the stomodaeum are both
characterized by extremely long columnar ciliated cells. The siphono-
glyph (Plate 3, Fig. 32) has neither gland cells nor nematocysts, both
of which are abundant in the other regions of the stomodaeum (Figs.
30, 81). The columnar cells of the siphonoglyph are long and of small
caliber; each has a single strong cilium, or flagellum, which is longer
than the cell. The cytoplasm is finely and rather densely granular,
and each oval or elongated nucleus has one or two prominent nucleoli
and a small number of chromatin granules. The nuclei occupy dif-
ferent levels in adjacent cells and are so situated that collectively they
form a definite layer. Four layers, then, are recognizable in the ecto-
derm of the siphonoglyph (Fig. 32): (1) subnuclear, composed of
the bases of the columnar cells, between which may be found occasional
nutrition cells (cl. nut.) and ganglion cells, (2) the nuclear layer, (3) the
layer between the nuclei and the basal granules of the cilia, (4) the
cilia layer, a wide border characterized by the long and prominent
basal granules. No ectodermal muscle cells are found in this region.

In the dorso-lateral portion of the stomodaeum (Plate 3, Figs. 30,
31) four types of cells occur abundantly, supporting cells (cl. sst.),
mucus cells (cl. muc.), granular gland cells (cl. grn.), and the small
nematocyst cells (cl. nm’cys.’). The same four layers as in the siphono-
glyph are found, but the nuclear zone is much wider, and. the cell
bases do not always terminate so sharply against the mesogloea.
The cilia are short. The supporting cells (cl. sst. and Fig. 39, Plate 4)

CHESTER.— STRUCTURE OF PSEUDOPLEXAURA CRASSA. 751

are columnar, finely granular, with very small vacuoles, and with a
short cilium that has a prominent, inverted cone shaped basal granule.
The nuclei vary from oval to globular, but are more often oval, stain
lightly, and have one or two prominent nucleoli. The mucus cells
(Figs. 30, 37, cl. mue.) are columnar or flask like, not always reaching
the full depth of the layer, sometimes staining evenly with eosin, at
other times showing a loose network of protoplasm. This network
stains deeply with muci-carmine. The nucleus is in the basal end,
is globular or nearly so, and stains deeply. The granular digesting
cells (cl. grn.) are very numerous in some colonies, few in others, and
particularly few in starved colonies. They also are columnar or flask
shaped with a small round nucleus, that stains lightly, near the middle
of the cell. Large granules, staining deeply with haematoxylin, some-
times partly, sometimes completely fill the cytoplasm. Nematocyst
cells of the smaller type (Fig. 31, cl. nm’cys.’) are abundant between
the columnar cells in the cilia layer, but the cysts are smaller than
those at the surface of the body. They are here nearly globular with
a deeply staining nucleus at the lower end. The border, or cilia,
region of the supporting cells (Fig. 39) sometimes shows the presence
of variously shaped, but very small, digestive or nutritive granules.
Below the nuclear layer and between the supporting cells are found
many globular cells (Fig. 30, cl. gl.!), containing large granules that
do not stain with haematoxylin. In a few cases these cells have shown
karyokinetic figures. I interpret them to be young stages of gland
cells and think they are the same as those described by Kassianow
(:08). Ganglion cells are found not far from the mesogloea, but they
are very few.

The dorsal filaments and the axis epithelium are described later
in this paper.

MESOGLOFA.

The mesogloea is very thin in the body wall of the polyp and in
the tentacles, as well as in the stomodaeum and mesenteries. The
boundary between it and the ectoderm or endoderm is sharply marked
wherever muscle fibers are found; where there are no muscle fibers
the division is not clear. In the pinnules (Plate 2, Fig. 6) evidence
of mesogloea is seldom found, and even in the tentacle (Fig. 5) cells
are not often seen imbedded in it. In the stomodaeum the layer is
made out with difficulty, but it is thicker than in the tentacles. In
the mesenteries (Plate 3, Fig. 33) it is very evident, though thin,

ἼΟΣ PROCEEDINGS OF THE AMERICAN ACADEMY.

being sharply outlined in regions where there are muscles; but only
occasionally, and then in the thicker parts of the layer, are there any
included cells. A thin layer of it is also found between the endoderm
of the mesenteries and the egg or the sphere of sperm mother cells.
In the body wall, particularly at the base of the polyp (Fig. 19), it is
thicker and here a few included cells appear. These cells (οἱ. ms’gl.)
are smaller than the ectodermal cells and have a correspondingly
small nucleus; they have several elongated, more or less branched
processes. Cells in the coenosare (Fig. 28, οἷ. ms’gl.) which I inter-
pret to be the same as these are very numerous and show plate-like
expansions of the terminal branches, which have been described by
Kassianow (:08, p. 525) for Aleyonium. The mesogloea layer in the
coenosare is very thick (Fig. 22); here the newer mesogloea, that
which is near the ectoderm, is less dense than the portion which occu-
pies the deeper layers. Sections stained in either eosin or Mallory’s
phospho-tungstic haematoxylin show well the differences between
these regions. The ectoderm cells of the coenosare are very long and
the interstitial cells at their bases very numerous. The latter have
the appearance of being pushed away from the ectoderm as growth
proceeds, and they arrange themselves, or are arranged, in masses or
cords (Figs. 22, 28, el.cd.), in which the individual cells are often
only loosely associated. The interstitial cells (Fig. 24, cl. in.) which
are still near the ectoderm, are globular or irregularly branched, but
otherwise they are not different in appearance from the ectoderm cells
of the coenosarc or of the polyp wall and tentacle; but they, together
with the deeper and more specialized cells constituting the cords
(Fig. 22), reach down even to the axis epithelium. A transverse
section of such a cord is given in Figure 29; other sections are shown
in Figures 27 and 28. In these cords some of the cells (cl. in.) are like
the interstitial cells near the ectoderm. Others (cl. grn.’) contain few
or many granules, which vary in size and staining capacity, but always
stain, either slightly or heavily, in haematoxylin or in eosin. The
granules vary in size in different cells. In other respects these cells
resemble interstitial cells. Some of the cells at the edges of the cord
are partially surrounded by the jelly of the coenosare, and these are
appreciably smaller and more elongated than the others. The loosely
arranged cells of the cord show no extra-cellular matter except at the
edges of the cord. Where such matter is evident, the characteristic
finely granular mesogloea cells (οἱ. ms’gl.) are to be found with
their greatly elongated processes and terminal branchings.

I believe the cells enumerated below constitute a genetic series:

CHESTER.— STRUCTURE OF PSEUDOPLEXAURA CRASSA. 7588

(1) the interstitial cells (cl. in.), or some of them; (2) the loosely ar-
ranged cells (cl. grn’.) with few granules, and those with larger granules;
(3) the cells on the outside of the cords, which are either partially or
wholly surrounded by secreted matter; and (4) the smaller mesogloea
cells (cl. ms’gl.); because the interstitial cells and the series of loosely
arranged cord cells are continuous with each other. The cells of each
series may change their shape by amoeboid movements, as sectioned
living material has shown me. Any of the cells, except the meso-
gloeal cells, may have granules. The cytoplasm and the nuclei of all
these cells are alike, except in regard to the size and shape of the
cell and nucleus and the presence of granules. But it would not be
correct to argue from this series of cells found in the coenosare that
the mesogloea is of exclusively ectodermal origin. The bases of the
ectoderm cells seem active in the formation of mesogloea in all parts
of the colony and there is evidence of the secretion of the same sub-
stance by cells associated with the axis epithelium in the axis region.
The evidence drawn from Pseudoplexaura does not exclude the
probability that the endoderm is also active in the formation of
mesogloea in the tentacle, polyp wall, and particularly in the mesen-
teries. The small cells at the end of my series of four given above
occur in most abundance where the jelly layer of the coenenchyma is.
most dense; they simply represent, it seems to me, the ultimate con-
dition of cells whose usefulness may not be limited to the formation
of mesogloea, but which in all of the earlier stages have been more or
less active in the formation of such substance.

But not all of the mesogloeal cells belong in this series, nor are all
those in the cords secreting cells. Some of the interstitial cells develop
nematocysts and some are spicule-forming cells. Those forming
nematocysts are very abundant in the coenosare, and not only are
stages in the development of the cyst found, but cysts (nm’cys.)
as large and as fully formed as any near the surface are very abundant,
not only among the interstitial cells near the ectoderm, but also in the
cell cords and in the deep parts of the coenenchyma. These, I
believe, have been carried in from the ectoderm by the rapid growth
of the outer layer and by the amoeboid action of the cells around them.

In growing regions at the tip of the branches some of the interstitial
cells, pushed deeper by growth, secrete the spicules, probably during
special periods. The formation of the spicules is not different from
that described by von Koch (’87), Bourne (99), or Woodland (:05).
The more or less rounded spicule-cell first shows a small calcareous
mass (Plate 3, Fig. 23, spc.), which increases in size with the division

754 PROCEEDINGS OF THE AMERICAN ACADEMY.

of the cell and takes on a characteristic shape (Figs. 25, 28). Several
nuclei are to be found in the cytoplasm enveloping most of the spicules,
thus showing that the spicule-cell usually divides more than once.
Figure 25 shows the arrangement of the organic matter of the spicule
after decalcification; this is similar to the condition described by
Bourne.

Certain of the cells in the mesogloea (Plate 4, Figs. 48-51) show
ovoid or globular bodies similar to those described by Bourne (99)
and Woodland (:05) as possibly stages in nematocyst formation.
Rounded nutritive cells also occur, sometimes few, but in the coeno-
sare of some colonies very abundantly. They are also found occasion-
ally scattered among the ectoderm cells of the outer edge and also
among endoderm cells, where they probably originate. They stain
more deeply with eosin than the surrounding cells.

ENDODERM.

The endoderm lines the coelenteric side of the stomodaeum, the
disk, the polyp wall, the mesenteries and all the canals. It is composed
of three types of cells; supporting, mucus, and granular gland cells.
Muscle cells are found in some parts. The cell characters are similar
in the endodermal lining of the anthocodia (Plate 2, Fig. 20), the
polyp chamber (Plate 4, Fig. 56) and the connecting canals (not
including the long nutritive canals). The supporting cells are narrow
and columnar, in contact with each other proximally and distally.
Tn partially contracted individuals (Fig. 20) the supporting cells and
the less numerous gland and mucus cells appear crowded into close
contact; but in slightly expanded individuals (Figs. 55, 56) after
fixation frequent spaces occur separating individual cells except at
their two ends. The cytoplasm is coarsely vacuolated. A large
nucleus is found somewhere in the basal two thirds of the cell. The
cells are sometimes crowded with Zooxanthellae (zoa), which are
usually very numerous in and near the polyps, but are not so abundant
in the deeper canals. Three, four, or more of these algae are common
in the sections of each cell in the tentacles, polyp wall or outer
coenosare. Each endoderm cell has a single weak cilium inplanted
in its free end, and at its attached end a myoneme, which runs
circularly in the wall of the anthocodia and polyp chamber, and
generally so in the canals. Mucus glands are abundant (cl. muc.);
they appear as columnar cells with the cytoplasm in the form of a

CHESTER.— STRUCTURE OF PSEUDOPLEXAURA CRASSA. 755

large-meshed reticulum that stains deeply with muci-carmine, and
each has a darkly staining nucleus. There are occasionally found
also gland cells (Fig. 55, cl. grn.) similar in character to the granular
gland cells of the stomodaeum. ‘The feeble staining of the nucleus
and the presence of large granules in the cytoplasm show the likeness.
The cells may be shorter or even spherical They are not limited to
particular regions, but are scattered throughout the endoderm of the
polyp wall, the canals and the mesenteries.

The endoderm of the polyp wall (Figs. 20, 55) has longer cells and
stronger myonemes than that of the polyp chamber or canals. How-
ever, in the pinnules and in the tentacles, except at their very bases,
the myonemes and the granular gland cells are lacking (Figs. 5, 6);
otherwise the layer is here like that of the body wall. |

The epithelial cells and the muscle elements of the endoderm of the
mesenteries (Plate 3, Fig. 33) are specialized, at least in certain
regions. On the so-called ventral surface of the mesentery the longi-
tudinal myonemes belong to cells that are entirely below the free
surface of the epithelium. These muscle cells are long and spindle-
shaped (Plate 4, Fig. 38), with a small amount of cytoplasm envelop-
ing the fiber (myoneme) and most abundant around the elongated
nucleus. The cells are very numerous and the fibers are so arranged
that in the cross section of the mesentery they form wavy rows of
black dots adjacent to the ventral side of the mesogloea (Fig. 33,
my nm.). Other muscle fibers, that run radially on the mesentery,
are found in both layers of the endoderm and their cells are epithelio-
muscular, though in some cases the cell body may be slightly sunk
below the surface. Where the endodermal epithelium covers the
genital cells, the epithelial cells are shorter and bear no muscle
fibers.

The endoderm of the longitudinal canals (Plate 4, Fig. 59) has very
long cells as compared with that of the other canals; they are, however,
of the same type, viz. supporting cells; they are slender, columnar,
vacuolated, and slightly separated from one another except at their
proximal and distal ends. No muscle cells, or myonemes, are found
in this endoderm.

As compared with corresponding structures in other alcyonarians, it
may be said, in brief, that the ectoderm of Pseudoplexaura is like that
of the other members of this group described by previous authors, in
having an epithelial and a subepithelial layer; in the shape and charac-
ter of its cover cells it is like Aleyonium (Hickson, ’95, Kassianow,

756 PROCEEDINGS OF THE AMERICAN ACADEMY.

:08), and is not greatly different in its cell characters from Xenia
(Ashworth, ’99) or Veretillum (Buvor, :01). The nematocysts of the
larger kind are about the size of those of Clavularia (von Koch, ’82?),
and are generally slightly larger than those of Xenia or Aleyonium.
Those of the smaller kind seem significantly numerous in the stomo-
daeum. Sense cells like those of Aleyonium (Kassianow, :08) are
associated with the nettle batteries; but the number of the batteries
in the coenosare and at the base of the polyps appears to be greater
than in Xenia or Aleyonium, and the fewness of the nematocysts on
the tentacles and pinnules seems unusual. Evidently the surface of
the coenosare between the polyps is an important region for the work
that the large nematocysts do. The polyp often contracts to the level
of the coenosare with the mouth still open and the tentacles still
spread, and I have seen food particles passed along from the coenosare
to the mouth by the tentacles. The nematocysts of the smaller sort
are more evenly distributed on the outside of the colony, but they are
very few. I failed to find glaad cells on the outer surface, except per-
haps in the coenosare. Von Koch (87) does not include them in his
list of ectoderm cells for Gorgonacea, but they are present in repre-
sentatives of the two other aleyonarian groups. It seems hardly
probable that the slime which is given off by Pseudoplexaura when it
is handled has come from the mucus cells of the endoderm. The
fibers of certain of the ectoderm cells of the coenosare (Plate 3, Fig. 24)
are, as has already (p. 750) been suggested, possibly supporting
fibers, such as K. C. Schneider (:02, p. 622, Fig. 510) has de-
scribed for Anthozoa and other invertebrates, and figured for a sea
anemone.

The mesogloea of the colony is very thin except in the coenosare
region; but here is thicker than that of the forms heretofore described,
except the Gorgonacea.

The endoderm is similar to that of Aleyonium, and shows no signi-
ficant features, except the absence of muscle fibers in the longitudinal
canals. Menneking (:05), from the study of Stachodes and other
forms, reached the conclusion that the longitudinal canals have origi-
nated as inter-mesenterial chambers of a terminal polyp. The
absence of muscles in the walls of the longitudinal canals of Pseudo-
plexaura, in contrast with their presence in the mesenteries, to-
gether with the fact that the canals are sometimes traced to solenia
without polyps, suggests that in this form the longitudinal canals
have not originated in this way. Kinoshita (:10) did not succeed
in finding muscle fibers in the endoderm of the longitudinal canals

CHESTER.— STRUCTURE OF PSEUDOPLEXAURA CRASSA. 757

of the developing colonies of Anthoplexaura, but in the growing
part he found solenia, which were sometimes continuations of the
longitudinal canals. The structure of adult Pseudoplexaura supports
the conclusion of Kinoshita, that the longitudinal canals have not
always developed from inter-mesenterial chambers.

STRUCTURES CONCERNED IN NUTRITION.

Though I often experimented with small portions of a colony in the
laboratory, I saw very little feeding. Plankton was given, but I saw
none of it stunned, and only the smaller less active organisms, such as
sea-urchin eggs, were swallowed. Sea-urchin eggs and small pieces
of the flesh of fish were placed near the polyps and were often taken
into the stomodaeum. Sometimes a polyp kept large pieces of sea-
urchin ovary against its mouth for a long time. Usually the whole
colony was quite fully expanded, except when it had been vigorously
treated. On the reefs colonies with all the polyps contracted were
very seldom seen. In the laboratory I could not find any difference
in the condition of a colony at night and in the daytime in this respect.
Individual expanded polyps may have the peristome closed, or polyps
that are contracted so that the tentacles are spread out on the coeno-
sare may show it open; but there seems to be no special time for feed-
ing. I think the food is undoubtedly from the plankton, and parti-
cularly the smaller and more sluggish forms.

The nettle cells of the smaller kind (Plate 2, Fig. 31, el. nm’cys.’;
Plate 4, Fig. 47) are very abundant in the ectoderm of the stomo-
daeum, while less numerous on the tentacles. Those of the larger
kind (Plate 2, Fig. 26, cl. nm’cys.; Plate 4, Figs. 43-46) are most
abundant in the coenosare between the polyps and are seldom
found in the tentacles. When sea-urchin eggs are scattered with
a pipette over the tip of a branch whose polyps are expanded, they
fall slowly, and do not seem to be stopped by tentacle or polyp,
but collect in the grooves of the coenosare. Associated with the falling
of sluggish material on the coenosarc, adjacent individual polyps often
contract down to the level of the coenosare with the tentacles still
partly spread and the mouth widely open. In such cases the eggs
are often drawn into the current of the siphonoglyph. The support-
ing cells of the stomodaeum have at times small irregular granules
at the distalend. These may be zymogen granules or, more probably,

395 PROCEEDINGS OF THE AMERICAN ACADEMY.

products of metabolism destined for other than enzyme use. Food
material may be taken into these cells, and even algae have been found
in them in a partially digested condition. Some of the food, then, is
probably digested here, both in an intra-cellular and extra-cellular
fashion. After the remaining food passes the stomodaeum it is in
contact with the six ventral mesenterial filaments. These (Plate 4,
Fig. 64) are very short thickenings of the margins of the six mesen-
teries, and occupy a position immediately below the stomodaeum.
They are less than two millimeters long and in preserved material
may be less than one. They begin at the deep end of the stomodaeum,
but their gland cells may be found on the mesenteries a little above
this. The cross section shows that this thickened margin is nearly
cylindrical. The cells are mostly gland cells that are not different
from the granular cells of the stomodaeum. A few supporting cells
occur among the others and these may contain food matter. There
are no nettle cells.

Until 1899, the stomodaeum was considered as merely a passage
for the food, the mesenterial filaments being regarded as the only
digestive organs. Wilson (84) described the filaments of eleven
genera from the three groups of Aleyonaria and concluded that the
six lateral and ventral filaments are derived from endoderm and that
the two dorsal ones are from ectoderm. The former contain gland
cells and sometimes nettle cells, and are digestive in function; while
the latter have two kinds of cells, are ciliated and are used for the pro-
duction of currents. In 1899 Ashworth found mucous gland cells
in the stomodaeum of Xenia, and correlated their presence with the
absence of the ventral filaments. Miss Pratt (:05), by a very thorough
and complete study of the feeding, in which she employed colored food,
found that food was ingested, not only by the cells of the stomodaeum
and filaments, but also by the mesogloeal cells. But no ingulfing of
food was observed in the cells containing the granules. Gland cells
were abundantly present in the stomodaeum of many members of the
Aleyonaria, but the granular cells were met with in starved individuals
only. Pseudoplexaura agrees with the forms studied by Pratt in the
presence of gland cells in the stomodaeum and the abundance of the
granular cells in the tips of individuals starved in filtered sea water.
In Miss Pratt’s experiments particles of fish artificially colored were
also engulfed by stomodaeum cells, by the network of interstitial cells
in the polyp wall, and by the mesogloeal cells near the outer surface
of the coenosare. Both the stomodaeum and the ventral filaments,
then, are digestive structures; while the granular gland cells, which

CHESTER.— STRUCTURE OF PSEUDOPLEXAURA CRASSA. 759

are quite abundantly scattered in the endoderm of the coelentera,
including the canals and the mesenteries, may considerably aid in
extra-cellular digestion.

DorsaL MESENTERIAL FILAMENTS.

These filaments differ in origin, structure, and use from the ventral
and lateral filaments. As a whole, the filament is a long, deeply
grooved ribbon or cord, attached to the margin of the corresponding
mesentery, and reaches from the stomodaeum to the depths of the
polyp cavity; if there is a large basal canal connecting polyps with one
another, it may even be continued into such canals. In cross section
(Plate 4, Figs. 62, 63) the filament is much thicker than the mesentery
and is deeply notched at its free margin. Consequently, in cross
sections the mesogloea has the form of the letter Y. The epithelial
cells occupying the space between the arms of the Y are of two kinds.
The outer ones (cl. fil.), those nearer the ends of the arms of the 0,
are the more numerous and are similar to the supporting cells of the
stomodaeum. They are columnar, of small diameter and so closely
packed that their nuclei are arranged in several rows. Each cell has
a very strong cilium, and these cilia are so long that those of one side
of the groove touch or cross those of the opposite side. The remain-
ing cells, those occupying the base of the filament groove (cl. fil.c.),
are few but larger, having broad bases and tapering slender necks.
Their cell boundaries usually cannot be demonstrated. Near the
base of each cell is a large, lightly staining nucleus. They possess no
cilia. The cytoplasm is sometimes evenly granular, but often shows
large vacuoles that stain with muci-carmine. The mucus, which they
evidently have secreted, may sometimes be found between the cilia
of the other cells.

Wilson (84) has described in detail these dorsal filaments for other
aleyonarians. But neither in his eleven genera, nor in the figures of
Alcyonium by Hickson (95), nor of Xenia by Ashworth (’99), are the
cells represented to be as large and prominent as they are in Pseudo-
plexaura. I did not observe the effect of the presence of mucus in
this groove, save that sometimes very minute particles, presumably
of food, may be found in it; the mucus is probably for the purpose of
catching material entering the polyp from another polyp or from the
long canals. Portions of colonies kept for some days in the dark or
in weak light lost their Zooxanthellae. The polyps of these portions

760 PROCEEDINGS OF THE AMERICAN ACADEMY.

of colonies are then translucent and the direction of the currents pro-
duced by the cilia can be detected. The current formed by the cilia
of the filaments flows from the base of the polyp to the stomodaeum,
while that of the siphonoglyph is in the opposite direction.

GROWTH.

Growth being both terminal and radial, the polyps may increase
in either direction. The tips formed in summer are of two types.
One type shows no polyps on the terminal two or three millimeters
of the branch, which is crowded with purple spicules. In only a very
few instances were polyps formed at the tip of the stem in this type in
any other position than the radial one. They were usually large and
of the same size. This is not an area of reproduction of polyps at
this time. The other type of stem shows a tip denuded of polyps fora
relatively long region, one half to one or more centimeters. The
coenosare wall of this tip is smooth and many of the polyps nearest
to the denuded region are small. Under the surface of this tip is
found an extensive network of canals. Very small polyps are also
often found in the coenosare at other regions than that of the tip.
Young polyps, then, may be found in the growing stem in all parts
of the colony.

Muscies AND NERVES.

The arrangement of muscles into systems is not markedly different
from that described for Aleyonium by Kassianow (:08). The systems
are: (1) The tentacle and disk system. This is ectodermal. The
muscle fibers (Plate 2, Fig. 5, my’nm.) run longitudinally on the
pinnules (Fig. 6) and on the tentacles (Figs. 5, 7) and are continued
on the disk toward the mouth, but the lateral strands of each of the
eight bands bend outward to be inserted in the mesogloea of the
mesentery. The median strand on the oral side of the tentacle is
continued to the mouth, but these muscles are fewer than in Aleyo-
nium. The aboral surface of the tentacle, as is shown by a transverse
section (Fig. 7; compare Fig. 21), bears no muscles, and muscles are
lacking on a very small portion of the aboral surface of the pinnules
(Fig. 6). (2) The polyp-wall system embraces muscles that are endo-
dermal and are arranged circularly (Fig. 20). They are strongest
where the polyp wall and tentacles meet, and they may pass a slight

CHESTER.— STRUCTURE OF PSEUDOPLEXAURA CRASSA. 761

distance on to the base of the tentacles. In the small canals (as in
Fig. 56, my’nm.) they are generally circular. (3) The stomodaeum
system. Endodermal muscles are feebly developed in the stomo-
daeum, where they run circularly (Plate 3, Fig. 30). ΑἹ the oral end,
and to a less extent at the coelenteric end, they are larger and more
numerous, but hardly enough so to be termed sphincters. (4) The
mesentery system. ‘These are, of course, endodermal. The longitu-
dinal muscles, on the ventral side of the mesogloea (Fig. 33. Com-
pare Plate 1, Figs. 24), are independent of the epithelium. The
folding of the mesogloea, which in cross sections appears branched,
is such as to accommodate a large number of fibers without a cor-
responding increase in the width of the mesenteries. ‘Transverse
muscles are found on both sides of the mesentery (Fig. 33); they are
comparatively few and are arranged in a single sheet, 1. e., without
foldings.

Physiologically the muscles may be divided into, first, the longi-
tudinal muscles of the ectoderm of the tentacle and disk and the
strong longitudinal endodermal muscles of the mesenteries; secondly,
the circular endodermal muscles of the polyp wall and canals together
with the transverse muscles of the mesenteries.

The nerves can hardly be said to be arranged in a system, as they
surely are in colonies of more active alcyonarians. Sense cells are
found, particularly in connection with the nettle batteries, and gang-
lion cells are scattered in the deeper layer of the ectoderm of both
column and stomodaeum. But there is no conspicuous nerve layer,
such as that found by Kassianow (:08) in Aleyonium.

The weakness of the nerve layer accords with the slowness of the
polyps in contracting. These do not respond to touch as quickly as
many other related forms living near them, such, for example, as
Euniceopsis, Plexaura and Gorgonia. The tentacles show no response
to a single light touch, but a sharp touch, or one repeated, gives a
reaction, which is always toward the mouth, as is to be expected from
the fact that the muscles are limited to the oral side. The response
of one tentacle, however, is accompanied by a response of the other
seven. The disk and column respond to touch, and the column
responds more quickly and vigorously near its base than elsewhere.
But the coenosare between the polyps is the most sensitive part of
the colony to touch. When this region is stimulated, the adjacent
polyps respond by a slow contraction toward the level of the coeno-
sarc; the response, however, is more certain than when the column
is touched. There seems to be no nerve system connecting polyps

762 PROCEEDINGS OF THE AMERICAN ACADEMY.

with one another, since touching one does not result in a response
from another. One can draw a pencil across a branch and get a con-
traction of the polyps only in that line, if he does not shake the branch.
When a branch is shaken, all polyps begin to contract, although very
slowly. I saw no reactions that would indicate taste as contrasted
with touch. Food particles on the coenosare cause the contraction
of the polyps near it, the mouth and tentacles remaining expanded;
but clean filter paper does the same. Neither in the field nor in the
laboratory did I find muscular response to light. The polyps were
expanded night and-day alike. In the laboratory, away from the
sunlight they lost the Zooxanthellae and became white after a week’s.
time.

SKELETON AND Axis EPITHELIUM.

The structure of the axis skeleton has already been described under
General Structure (p. 742). I find the axis epithelium (Plate 4, Figs. 54,
58, (e’th. ax.) always present and made up of two types of cells, the
secreting cells and the holding cells, or desmocytes. The secreting
cells are long and cylindrical or prismatic. Of the two ends, the one
directed toward the skeletal axis may be designated as axis-end and
the other as mesogloea-end; the former is flat, the latter tapers and
is more or less rounded (Fig. 54). The large feebly staining nucleus
is nearly in the middle, but typically somewhat closer to the axis-end
of the cell. The cytoplasm is vacuolated at the mesogloea-end, but
near the axis it is finely granular. This type of axis cell is always
found at the tip of a branch, where the horny rim of the axis chambers
is very thin; and I interpret this as a place of most active secretion.
In any region of the colony, except at the very tip, some of the epi-
thelial cells — sometimes only one, sometimes a comparatively large
area of them—are modified into desmocytes (Plate 4, Fig. 41, dsm’cy.).
These cells are broader than the secreting cells at the axis-end, and
relatively shorter. At the axis-end they show a prominent border
of striations perpendicular to the surface. These striations are due
to slender rod-like differentiations of the cell, which seem to be the
means by which the cells hold firmly to the axis, even when, in sections
cut either free hand or after imbedding, the other cells are detached.
Where the outline of the cell is complete (dsm’cy.), a nucleus like that
of the secreting cells is present. Often, however, the cell has united
with the mesogloea so that the boundary between the two is gone,
and then the nucleus may have disappeared (dsm’cy’.). The axis-face

CHESTER.— STRUCTURE OF PSEUDOPLEXAURA CRASSA. 763

of the cell (Figs. 41, 60) is usually flat, but may be coneave (Fig. 58)
or convex (Fig. 42). The desmocytes arise, or at least attain their
differentiation, in the secreting epithelial layer. Cells in contact with
the axis (Figs. 41, 58, dsm’cy.), that apparently are at first not differ-
ent from the secreting cells, broaden their axis-end, pushing other
cells away from the axis. To such a cell a mesogloeal process, prob-
ably secreted largely by adjacent epithelial cells, becomes applied,
so that the cell then appears to be simply a prolongation of the meso-
gloea. The nucleus of the cell persists for a long time, but often it
degenerates. Meantime the differentiation of the broad end of the
cell shows it to be a desmocyte. Secretion on the part of the sur-
rounding cells may continue around these desmocytes. Figure 42
shows that in this case much of the secreted layer of the axis was
formed after the differentiation of the desmocyte and while it was still
functioning as a hold fast. Figure 52 (dsm’cy’.), compared with
Figure 42, shows evidence that the axial portion of the desmocyte
may lose its connection with the mesogloea owing to the constriction
of its neck by the formation of the horny secretion. It is in this way
that some of the smaller chambers of the axis-cortex are formed.
When this has taken place, other desmocytes appear in the same
region peripheral to it.

In places where a great many desmocytes have been formed (Plate
4, Figs. 58, 60), the secreting cells are pushed back from the secreting
surface in disarray. The displacement is perhaps a necessary result
of the broadening of the ends of the desmocytes. At a later time, per-
haps in response to the same stimulus that causes the beginning of a
new skeletal chamber in places where desmocytes do not occur, such
displaced secreting cells rearrange themselves preparatory to the
secretion of a new lamella, leaving a lenticular space between them-
selves and the previously secreted portions of the axis. Later still,
some sort of stimulus may then cause other desmocytes to appear
among these secreting cells, probably as the result of the differentia-
tion of a part of their own number. I consider these holding cells
to be homologous to those seen by Fowler in a madreporarian coral
and to those whose origin was described by Bourne (99) for the mad-
reporarians and for Heliopora, an alecyonarian with a calcareous
skeleton; but I find no reference to similar cells for any other alcyo-
narian, except that possibly A. Schneider (:05, p. 128) found them;
but if so, he evidently thought them artifacts. 1 have found them in
all the colonies of Pseudoplexaura studied, and I have also seen them
in the species of Euniceopsis and Gorgonia which are associated with

764 PROCEEDINGS OF THE AMERICAN ACADEMY.

them on the Bermuda reefs. In Pseudoplexaura the stimulus for the
change from the secreting cell to the desmocyte must be irregular;
it is not associated with any particular position of the polyps or with
any structure that would give a regular pull or strain, since the cells.
occur sometimes in broad patches and sometimes singly; the latter
are completely united with the mesogloea and are therefore fully
formed. They remind strongly of the desmocytes described for the
madreporarians by Bourne (’99), but there is no trace of the membrane
which Bourne found between cell and axis. In their origin they also
differ from those described by Bourne for Heliopora, where the stimu-
lus for the striations occurred before the cells were in contact with the
axis, to which they became adjacent secondarily; for in Pseudoplex-
aura the first trace of the striations is in cells already touching the
axis. It should be noticed that in the present paper the desmocytes.
have been shown clinging to a horny skeleton, whereas previous
researches have shown them only in connection with calcareous skele-
tons. Probably further study will show desmocytes present in a
large number of alcyonarian forms.

The origin of the horny skeleton of the Gorgonacea has been the sub-
ject of much controversy, with which the names of von Koch, Studer,
and A. Schneider have been prominently associated. A. Schneider
(:05) has reviewed the literature carefully, and has shown that Ehren-
berg, Dana, Milne-Edwards et Haime, and von Koch have main-
tained an ectodermal origin; while Lacaze-Duthiers, Kélliker, Studer,
and Heider have not found the ectoderm involved. The arguments.
against the ectodermal origin, as summed up by Schneider and
strengthened by his researches, have to do with (1) the presence of
calcareous spicules within the horny skeleton, (2) the character of the
union between the axis and its branches, (3) the existence of extra-
axial horny masses in the cortex independent of epithelium, (4) the
increase in size of the adult axis, (5) the embryonic origin of the
skeleton.

Kolliker (’65, pp. 163-167) argued in part as follows: since the axis
skeleton in certain forms (Mopsea) is composed exclusively of fused
calcareous spicules, and since these spicules are not produced by epi-
thelium, the skeleton is not an epithelial product. Studer (’87)
and A. Schneider (:05) found numerous calcareous spicules in the axis,
and thought the axis made up principally of them. I have found no
evidence of such spicules in the axis of Pseudoplexaura, though I have
found one or two instances of cellular matter that I conceive to have
been included in the axis owing to the rearrangement of the secreting

CHESTER.— STRUCTURE OF PSEUDOPLEXAURA CRASSA. 765

cells of the axis epithelium over a mass of desmocytes, and I can
account for the possible enclosure of spicules in an axis in the same
abnormal manner.

A. Schneider found that in Eunicella the axis of the branch (Nebe-
naxis) is at first separated from that of the stem, with which, however,
it is later united. It is difficult to see how such an axis can be ex-
plained as the result of the secreting activity of an ectodermal epi-
thelium, except in cases in which the branch is secondarily united
(by anastomosis) to a stem, as in fan corals; but Eunicella does not
usually have such a secondary union of branch and stem. Perhaps,
however, the conditions in Eunicella are not essentially different from
those which are met with in Pseudoplexaura, where I find that a sharp
demarcation line between the axis of the branch and that of the stem
also occurs (Plate 4, Fig. 61); here it is due to the fact that all branches
of the axis are adventitious in respect to the marrow. At the region
of branching, the marrow of the stem-axis is separated from that of
the branch by the secreted cortex of the stem-axis. The walls of the
marrow chambers in the branch were therefore formed after the axis-
cortex of the main stem possessed an appreciable thickness (Fig. 61,
ctx. αα.). But the existence of a stem-cortex between the marrow
chambers of the stem and those of the branch is not inconsistent with
an ectodermal origin of the epithelium secreting the axis of the branch,
because axis-cortex is formed in the same manner as axis-marrow. In
both cases the horny matter is laid down in the form of walls of
chambers; and these differ only in the size and shape of the cavity
and in the thickness of the wall. The chambers of the axis-cortex are
smaller than those of the marrow, nevertheless they vary greatly
among themselves in size (Fig. 57, ctv. av.). It is assumable that, after
some of these axis-cortex chambers of the stem had been formed
(Fig. 61, ctx. ax.), other chambers with the characteristically thinner
walls and larger cavities of the marrow, may have arisen at the place
where a branch was about to be produced. The walls of these cham-
bers would, then, be secreted by the same epithelium that recently
had been building smaller chambers as an axis-cortex of the stem.
The epithelial patch at the distal end of the axis of the branch would
be composed of cells which had changed somewhat the character of
their secretions, so that henceforth they would produce the larger
thin-walled chambers characteristic of the marrow, whereas the
remaining cells (at first situated in the periphery of this terminal
patch) would continue to produce the smaller chambers, with thicker
walls, such as they had been producing as axis-cortex of the stem;
but now as the axis-cortex of the branch.

766 PROCEEDINGS OF THE AMERICAN ACADEMY.

In no part of the axis of a stem or branch has the marrow grown in
opposite directions, part distally, part proximally, for the walls of the
chambers are always convex toward one end of the stem or branch —
the distal end (Plate 4, Figs. 57, 61). The marrow must therefore
have grown from the base of the branch toward the tip, just as it does
in the stem from base toward tip, and not, as maintained by some
writers, in the form of a separately established axis which grows in
two directions: partly toward the tip and partly toward the stem to
which, in their view, it is destined to be attached secondarily.

This type of axis — with the axis-cortex interposed between the
marrow chambers of stem and branch —is the natural one for all
axes except such as may have been formed by the dichotomous branch-
ing of a main stem. Such branches may possibly occur, but my
dissections have not shown any. Occasionally, in colonies that had
attained a height of ninety or more centimeters, the beginning of a
branch was found on some of the whips. These, as short as five milli-
meters, had a soft axis that was continuous with the main axis and
was formed of the characteristic marrow (Figs. 57, 61, med. ax.) and a
very thin cortex. The marrow chambers were separated from those
of the main stem by the cortex region of the stem-axis and, as has
already been stated, were convex toward the free end of the branch,
as in the main branch they were convex toward its freeend. Although
the earliest stage in the formation of the axis of a branch has not been
seen in Pseudoplexaura, I am convinced that the axis skeleton of the
whole colony in this species is not produced by a coalescence of sepa-
rately established axes.

Pseudoplexaura gives no evidence on the third of Schneider’s points,
for no horny substance has been found in the coenenchyma. But the
real issue between the two theories of ectodermal or non-ectodermal
origin hinges on the results of observation as to the origin of the axis
and as to the method of its subsequent growth; whether it is an epi-
thelial secretion, as argued by von Koch (’78, ’87), or results from a
massing of mesogloeal material which is to be resorbed and replaced
either by horny substance or horn and lime. Von Koch has described
(87) a larval stage of Eunicella a week old and has shown sections
having the ectoderm continuous with the axis epithelium. His results
have recently been confirmed by Kinoshita (:10) in embryos of Antho-
plexaura. Kinoshita not only found the ectoderm of the pedal disk
continuous with the axis epithelium, but he also has described and
figured (Fig. 3-5) the beginning of the axis as a secretion product
of the thickened ectoderm of the pedal disk; however, this primitive

CHESTER.— STRUCTURE OF PSEUDOPLEXAURA CRASSA. 767

axis (a single case) did not by its upward growth push before it the
floor of the digestive cavity of the primary polyp, but rather grew
upward in the wall of the column at one side, so that the primary
polyp had the appearance of being a lateral outgrowth from the axis.
From this he concludes that the stem of the colony in Anthoplexaura
apparently does not belong to the primary polyp, but to the coenosare
(at its base), just as in Pseudaxonia.

The existence of a secreting epithelium in the adult of Pseudo-
plexaura cannot be doubted. The axis-secreting cells are large, and
this cell layer, which is evident, can be traced in free-hand sections
from the tip of the axis to the spreading base near the substratum.
I always find an unbroken axis epithelium around the tip. This
seems to me to be irreconcilable with the method of growth outlined
by Studer, and represented by the sections shown in A. Schneider’s
paper. For Studer’s theory demands a mass of spicules at the tip,
as well as in other places, perhaps,— spicules which are later to be
resorbed. These spicules must of course develop in the mesogloea,
and for their incorporation into the axis would require a break in the
epithelium around the tip; but such a break I have not seen in Pseu-
doplexaura. There is often a massing of spicules at the tip outside
of this epithelium, but there is no trace of their inclusion in the axis,
nor of their conversion into it. The spicules are here pushed aside
by the growth of the axis and remain as spicules in the mesogloea.
A. Schneider holds that the axis epithelium as figured by von Koch,
with which the epithelium of my figures is undoubtedly homologous,
is the endodermal lining of the digestive cavity of the axial polyp,
into which the axis has been pushed, and that the longitudinal canals
are mesenterial chambers. But so far as regards Pseudoplexaura,
the cells of the axis epithelium are not like endoderm cells. Moreover,
the longitudinal canals vary considerably in numbers in Pseudoplex-
aura tips, being eight or more; besides, as Kinoshita found for Antho-
plexaura, they have no muscles and sometimes end in solenia.

Pseudoplexaura, then, affords no evidence of spicules included in
the axial skeleton; a secreting axis epithelium is present, the cells of
which are unlike those of the endoderm in their arrangement and
structure. Even when pushed aside by the spreading of the desmo-
cytes, they are not easily to be mistaken for endoderm cells. Kino-
shita’s evidence in the embryos of Anthoplexaura is a strong support
for the ectoderm theory. The results from the study of the adult of
Pseudoplexaura are not in themselves complete evidence, but so far as
they go speak strongly for the ectodermal origin of the horny axis,
as indicated by von Koch.

768 PROCEEDINGS OF THE AMERICAN ACADEMY.

SUMMARY.

Pseudoplexaura crassa, an alcyonarian of the group Gorgonacea,
shows the character of Gorgonacea so far as regards the regions
recognizable in cross sections of the branches; the branches have a
central horny axis, a thick coenenchyma and an outer zone of polyps.
The horny axis shows a marrow composed of large chambers arranged
end to end, and a peripheral layer of smaller less regularly shaped
ones arranged side by side and irregularly overlapping one another.
The coenenchyma has, not far from the axis, a region of large longi-
tudinal canals. These are sometimes prolonged at their tips into
solenia. The polyps are long, and have ten to twelve pairs of pinnae
on each of their tentacles. They are crowded, so that when expanded
they hide the coenenchyma. Groups of small, crowded, irregularly
stellate, purple spicules occupy the deeper parts of the coenenchyma,
and larger, spiny and spindle-shaped, usually white spicules are in its
outer part. No spicules are found in the polyps.

The ectoderm has the usual cover cells, nematocysts, sense cells,
and interstitial, ganglion, and muscle cells. Small nematocysts are
found in the ectoderm of the polyp’s column, tentacles and stomo-
daeum. Large ones in considerable numbers are grouped into bat-
teries in the coenosare. Ganglion cells are very few, and muscle cells
are found on the oral side of the tentacles and disk only. In the
ectoderm of the coenosare between the polyps some of the ectoderm
cells have each a prominent supporting fiber, which runs from near
the nucleus perpendicularly to the mesogloea.

The mesogloea is thin, except in the coenosarce regions, where it is
very thick. Cords of cells like the interstitial cells of the ectoderm
can be traced from the ectoderm to the deeper layers of the mesogloea.
In these cords there are partly formed and fully formed nematocysts,
spicule cells, and cells having an irregular shape and either containing
granules or destitute of them. These irregularly shaped cells form a
transition to the jelly-secreting cells, which are small and have many
long branches. Large spicules are produced by characteristic secret-
ing cells with large granules and one to many nuclei. Spheroidal
nutrition cells occur in many colonies, but these are found in both
ectoderm and endoderm; they probably originate in the endoderm
of the canals which form a network through the mesogloea.

The endoderm cells are of characteristic form, being united with
each other at the proximal and distal ends, but, in fixed material,

CHESTER.— STRUCTURE OF PSEUDOPLEXAURA CRASSA. 769

separate elsewhere. In the tentacles, in the polyp wall and in many
canals they contain large numbers of the alga Zooxanthella. Except
in the tentacles and the longitudinal canals, they have myonemes
running circularly. Unicellular mucus glands and granular cells, that
are probably digestive in function, are numerous. The cells of the
longitudinal canals differ from other endodermal cells in being much
longer and in having no trace of myonemes.

Digestion is accomplished by cells of the stomodaeum, by the six
ventral and lateral mesenterial filaments, and by scattered gland cells
in the walls of the polyp cavity and the canals. The stomodaeum has,
beside its supporting cells, mucus and granular gland cells. The
mesenterial filaments, except the dorsal pair, are very short and their
epithelium is composed of granular gland cells oaly, which give some
evidence of intracellular digestion. I found no special feeding time
and no regular alternation of contraction and expansion of polyps.
Slow-moving organisms, which serve as food, are often transferred
from the surface of the coenosare between the polyps, where large
nettle cells abound, to the mouth of a polyp that independently con-
tracted to the level of the coenosare with its mouth open. The two
dorsal mesenterial filaments are very long and sinuous and their cell
structure is peculiarly significant. The sides of the groove are lined
by cells with strong cilia. The central cells, however, show the char-
acter of mucus cells and produce a mucous secretion.

The muscle system is similar to that of Aleyonium. The colony
is characterized by the weakness of its responses and by the fewness
of its nerve elements. The response to touch is not quick, and the
coenosare between the polyps is more sensitive than the polyps them-
selves.

The axis skeleton is surrounded by an epithelium consisting of
elongated secreting cells, and in places, of desmocytes, or holding cells,
these being shorter and wider, and exhibiting striations at the axial
end. These cells become connected with the mesogloea secondarily.
They may become isolated as the result of being completely enveloped
in the secretion of horny material by the secreting cells. The desmo-
cytes have already been described for Heliopora and for the madre-
porarians. The evidence in Pseudoplexaura favors an ectodermal
origin of the axis skeleton.

770 PROCEEDINGS OF THE AMERICAN ACADEMY.

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Krukenberg, C. F. W.

817. Die nervésen Leitungsbahnen in dem Polypar der Alcyoniden.
Vergl.-physiol. Studien, Reihe II. Abt. 4, Theil 1, pp. 59-
76, Taf. 1. Heidelberg.

Menneking, F.

05. Ueber die Anordnung der Schuppen und das Kanalsystem bei
Stachodes ambigua (Stud.), Caligorgia flabellum (Ehrbg.),
Calyptrophora Agassizii (Stud.), Amphilaphis abietina
(Stud.) und Thouarella variabilis (Stud.). Arch. f. Naturg.,
Jahrg. 71, Bd. 1, pp. 245-266, Taf. 8, 9.

Pratt, Edith M.

05. The Digestive Organs of the Alcyonaria and their Relation
to the Mesogloeal Cell Plexus. Quart. Jour. Micr. Sci.,
vol. 49, pp. 327-362, pl. 20-22.

Schneider, A.

05. Das Aschenskelet der Gorgoniden. Arch. f. Naturg., Jahrg.

71, Bd. 1, pp. 105-134, Taf. 5, 6.
Schneider, K. C.

02. Lehrbuch der vergleichenden Histologie der Tiere. Jena.

G. Fischer, xiv + 988 p., 691 Fig.

772 PROCEEDINGS OF THE AMERICAN ACADEMY.

Studer, T. ,

87. Versuch eines Systemes der Alcyonaria. Arch. f. Naturg.,

Jahrg. 53, Bd. 1, pp. 1-74, Taf. 1.
Studer, T.

06. Ueber die morphologische Bedeutung der Achse der Gor-
gonacea. Verh. allgem. schweiz. naturf. Ges., Versam.
88, pp. 52, 53.

Verrill, A. E.

’65. List of the Polyps and Corals sent by the Museum of Com-
parative Zodlogy to other Institutions in Exchange, with
Annotations. Bull. Mus. Comp. Zodl., vol. 1, no. 3, pp.

29-70.
Verrill, A. E.

07. The Bermuda Islands, Part 5, An Account of the Coral
Reefs. Trans. Conn. Acad. Sci., vol. 12, pp. 204-348,
pl. 28-40. (Alcyonaria, pp. 296-317.)

Wilson, E. B.

784. The mesenterial Filaments of the Aleyonaria. Mitth. Zool.

Sta. Neapel, Bd. 5, pp. 1-27, pl. 1, 2.
Woodland, W.

05. Studies in Spicule Formation. II.— Spicule Formation in
Aleyonium digitatum; with Remarks on the Histology.
Quart. Jour. Micr. Sci., vol. 49, pp. 283-304, pl. 16, 17.

Wright, E. P., and Studer, T.

’89. Report on the Alcyonaria collected by H. M.S. Challenger
during the Years 1873 to 1876. Report on the Scientific
Results of the Exploring Voyage of H. M.S. Challenger,
Zool., vol. 31, Ixxii + 314 p., 48 pl.

CHESTER.— STRUCTURE OF PSEUDOPLEXAURA CRASSA. 773

ax.
cam. pyp.

εἰ. nm’ cys.
el. nm’cys.’
el. nut.

cl. sns.

el. spe.

cl. sst.

cl. teg.

Clr. α.
dsm cy.
dsm’ cy’.
ec’drm.
en'drm.
e’th. ax.

ms’enr. v.
ms’ gl.
mynm.
nm cys.
nm’ cys’.
or.

ov.

sipy.
Spe.
spe’.
stmd.
200.

EXPLANATION OF PLATES.

ABBREVIATIONS.

axis.

polyp chamber.

canal,

longitudinal or nutritive canal.
cords of cells in mesogloea.

ciliated cells of the mesenterial filament.
central cells of mesenterial filament.
gland cell.

incipient gland cell of stomodaeum.
ganglion cell.

granular digesting cell.

granular cell of mesogloea.
interstitial cell.

mesogloeal cell.

mucus cell.

nematocyst cell, large kind.
nematocyst cell, small kind.
nutrition cell.

sense cell.

spicule-producing cell.

supporting cell.

cover cell.

cortex of axis skeleton.

desmocyte.

desmocyte, showing union with mesogloea.
ectoderm.

endoderm.

axis epithelium.

supporting fiber.

dorsal mesenterial filament.

ventral (or lateral) mesenterial filament.
marrow of axis skeleton.

dorsal mesentery.

ventral mesentery.

mesogloea.

myoneme.

large kind of nematocyst.

small kind of nematocyst.

oral.

ovum.
siphonoglyph.

spicule.

spicule of outer coenenchyma,
stomodaeum.

zooxanthella.

FIGURES.

All drawings, except Figures 1 and 61, were carefully outlined with a camera

lucida, and the details filled in afterwards.

The magnification (except in

Figures 1 and 61) is 675 diameters, unless otherwise indicated in the descrip-
tion of the Figure.

Fig. 1.

PLATE 1.

Diagram of a transverse section through a branch of a colony, show-

ing polyps in various stages of retraction.

Fig. 2.

Transverse section of a polyp through the stomodaeum. X 15.

a, expanded polyp, oral aspect

a’,expanded polyp, seen from the side

8, expanded polyp with inrolled tentacles

y, polyp partially retracted

δ, polyp completely retracted ,

e, polyp with column retracted, but with expanded tentacles and
with open mouth

n, polyp in longitudinal section

Fig. 8. Transverse section of a polyp just below the stomodaeum. Χ 15.
Fig. 4. Transverse section of a polyp through the lower polyp cavity.

x 15.

ἐς

CHESTER~PSEUDOPLEXAURA

W.M.C. del.

Proc. Amer. Acao. Arts and Sciences. — Vor. XLVIII.

PLATE |

Fig. 5.
Fig. 6.
Fig. 7.
muscles.
Fig. 8.

PLATE 2.

Longitudinal section from the oral wall of a tentacle.
Transverse section of pinnule. Χ 600.
Transverse section of a tentacle, showing the arrangement of the

x 85.
Longitudinal section of ectoderm of polyp wall.

Figs. 9-12. Isolated ectoderm cells of polyp wall, drawn from maceration

preparations.
Figs. 13-17. Ectoderm cells of tentacle isolated by maceration.

Fig. 13.

Two cover cells and a sense cell.

Figs. 14, 15. Interstitial cells.
Figs. 16, 17. Muscle cells of the ectoderm.

Fig. 18.
expansion.

Fig. 19.

Fig. 20.
Fig. 21.

Longitudinal section of the ectoderm of polyp wall, in state of

Section of ectoderm of the body wall of a polyp near the coenosare.
Longitudinal section of polyp wall, partly contracted. Χ 600.
Longitudinal section of tentacle wall, aboral side. Χ 600.

a
_ CHESTER- ΒΞ ἸΒΟΚΕΕΜΑΜΗᾺ PLATE 2

‘el.teg. cl.in, my’ nm. “zor. 90 ms'gl. οἹ
WMC, del.

Proc. Amer. Acao. Arts ano Sciences. — Vor. XLVIII.

Pee ES Pgh a8 ea Veet RGR en a
ree Sele tS I Le CNN SINR

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τ Ν ᾿ aw 7
Υ ἦν

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PLATE 8.

Fig. 22. Section through the coenosare to show cords of interstitial
cells. X 67.

Fig. 23. Section of epidermis of coenosare.

Fig. 24. Ectoderm of coenosarc in the region shown in Figure 26.

Fig. 25. Section of decalcified spicule, showing spicule-producing cells.

Fig. 26. Outline of portion of coenosare between polyps, to show the
distribution of supporting fibers and of nettle batteries. Χ 67.

Fig. 27. Section to show mesogloea. ‘

Fig. 28. Section showing mesogloea cells. Χ 400.

Fig. 29. Section of ‘‘a cord” in mesogloea of coenosarce.

Fig. 30. Longitudinal section of epithelium (ectodermal) lining the stomo-
daeum and of mesogloea.

Fig. 31. Longitudinal section of the wall of stomodaeum, showing both
ectoderm and mesogloea.

Fig. 32. Transverse section of a part of siphonoglyph.

Fig. 33. Transverse section of a portion of a mesentery.

CHESTER-PSE UDOPLEXAURA PLATE 3
ec'drm. & ΩΝ

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ΚΝ

br.sst.-\ x 7 lf
fb t τ //

\ /
Ν
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Proc. Amer. Acao. Arts ano Sciences—Vor. XLVIII.

wt
. - ᾿
,
.
&
a ὼ =
» Mm ct
Β fon
“
4
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r
* ἁ
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— . rey
i .
> & ϊ 2 ᾿ Υ
͵ ἕν
-
δ 2 {
᾿
5
) 1 ὃν
‘ 4
᾿ a
r
’ ὶ
, -
‘4 . ἔ 1 i
i ri
‘ i ve tit
ϑ ' ἢ: ‘
a 1 rae: Ι
ἊΝ i
᾿ . :
sora
’ 3 4
ἢ 5 4
᾿ 5
> ota i
’ ' Ἑ -
2
’ , 7
Py P es Ae _
me ’
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.

PLATE 4.

Figs. 34-37. Cells isolated by maceration.

Fig. 34. Gland cell of endoderm.

Figs. 35, 36. Supporting cells of endoderm.

Fig. 37. Mucus cell of stomodaeum.

Fig. 38. Muscle cells of mesentery.

Fig. 39. Supporting cell of stomodaeum.

Fig. 40. Granular gland cell of stomodaeum.

Figs. 41, 42. Axis epithelium, with desmocytes.

Fig. 43. Large kind of nematocyst cell, partly exploded.

Fig. 44. Large kind of nematocyst cell, unexploded.

Figs. 45, 46. Large kind of nematocyst cell exploded.

Fig. 47. Small kind of nematocyst cell.

Figs. 48-51. Interstitial cells containing ovoid bodies.

Fig. 52. Desmocyte enveloped in horny matter.

Fig. 53. Face view of the striated ends of six desmocytes.

Fig. 54. Secreting cells of axis epithelium.

Fig. 55. Longitudinal section of endoderm of polyp wall in the region of
the column.

Fig. 56. Longitudinal section of endoderm of a polyp chamber.

Fig. 57. Longitudinal section of the axial skeleton, near the tip of a branch.

Fig. 58. Section of a portion of axis with its axis epithelium and desmo-

Fig. 59. Longitudinal section through the endoderm of a longitudinal

Fig. 60. Epithelium of axial skeleton, with desmocytes.

Fig.61. Diagram of a longitudinal section of the axial skeleton to show the
nature of the skeleton in the region of a branch.

Fig. 62, 63. Cross sections of two dorsal mesenterial filaments.

Fig. 64. Cross section of a ventral mesenterial filament.

aie? 7
τ΄ CHESTER-PSE UDOPLEXAUR A PLATE 4
aa
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CF ΕῚ UT: ᾿ παῖ
τ | “\@x te
] ' Ν
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Proc. Amer. Acao. Arts ano Sciences. — Vor. XLVIII.

ae

i

᾿

Proceedings of the American Academy of Arts and Sciences.

Vou. XLVIII. No. 21.—SEptTemser, 1913.

RECORDS OF MEETINGS, 1912-13.
OFFICERS AND COMMITTEES FOR 1913-14.

LIST OF THE FELLOWS AND FOREIGN HONORARY
MEMBERS.

BIOGRAPHICAL NOTICES.
Ropert Amory. By R. H. Fitz.
ΑΒΒΟΤῚ LAWRENCE Rotcu. By R. DEC. Warp.

CHARLES RosBert SANGER. By C. L. Jackson.
STATUTES AND STANDING VOTES.
RUMFORD PREMIUM.

INDEX.

(TirLE PAGE AND TABLE OF CONTENTS.)

RECORDS OF MEETINGS.

One thousand and sixteenth Meeting.
OcToBER 9, 1912.— Stated MEETING.

The Academy met at its House.

The PRESIDENT in the Chair.

There were twenty-five Fellows and two guests present.

The following letters were received: — from G. ἢ. Agassiz, 5. E.
Baldwin, L. A. Bauer, W. H. Bixby, P. W. Bridgman, Εἰ. W. Brown,
H. L. Chapman, G. H. Chase, R. H. Chittendon, D. F. Comstock,
W. H. Dall, A. L. Day, Frederic Dodge, Wilberforce Eames, A. W.
Evans, Irving Fisher, Desmond FitzGerald, Simon Flexner, G. W.
Goethals, L. J. Henderson, H. L. Higginson, M. A. DeW. Howe,
E. P. Joslin, A. L. Kroeber, Waldemar Lindgren, L. 5. Marks,
S. P. Mulliken, Hanns Oertel, G. H. Palmer, ἢ. 5. Peabody, C. P.
Putnam, A. P. Rugg, W. B. Scott, M. deKay Thompson, J. E.
Thayer, W. J. Tucker, Williston Walker, S. B. Wolbach, F. S.
Woods, J. H. Wright, accepting Fellowship; from Svante Arr-
henius, J. A. A. J. Jusserand, Augusto Rhigi, H. A. Lorentz,
accepting Foreign Honorary Membership; from Louis Cabot,
John Fritz, R. B. Richardson resigning Fellowship; from the
President and Trustees of the Rice Institute, inviting delegates
to the opening of the Institute on October 10, 11 and 12; from
the American Antiquarian Society, giving the order of exercises
at its centennial celebration to be held October 15 and 16, 1912;
from the Académie des Sciences, Lettres et Arts de Bordeaux,
inviting delegates to its centenary celebration, November 11 and 12,
1912; from the Secretary of the Société de Pathologie Comparée,
inviting delegates to the first International Congress of Compara-
tive Pathology, to be held October 17—23, 1912 at Paris; from the

778 PROCEEDINGS OF THE AMERICAN ACADEMY.

Director of Congresses of the Panama-Pacific International Ex-
position, suggesting attendance at the Exposition; a notice of
the death of Eduard Strasburger, from his family.

The following deaths were announced by the chair: — William
Watson Goodwin, Fellow in Class III., Section 2, and President
of the Academy from May, 1903 to May, 1908; Jean Leon Géréme,
Foreign Honorary Member in Class III., Section 4 (died in 1904) ;
Lewis Boss, Fellow in Class I., Section 1; Eduard Strasburger,
Foreign Honorary Member in Class II., Section 2, Jules Henri
Poincaré, Foreign Honorary Member in Class I., Section 1.

The President appointed Mr. Henry H. Edes as delegate to
the celebration of the American Antiquarian Society. He also
appointed Professor G. L. Goodale to represent the Academy at
Amherst.

The following communication was given:—

Dr. Edwin H. Hall. A Brief Account of the Recent Royal

Society Celebration.

Cne thousand and seventeenth Meeting.
NovEMBER 13, 1912.

The Academy met at its House.

The PRESIDENT in the chair.

There were thirty Fellows present.

The following letters were read: — from Franz Boas, accepting
Fellowship; from the Secretary of the British Academy, inviting
the Academy to send a delegate to the third International Congress
of Historical Studies to be held in London, April 3-9, 1913; from
the President of the Accademia Reale delle Scienze di Torino,
giving the conditions of the Avogadro prize; from the Secretary
of the Iron and Steel Institute, giving the conditions of the Andrew
Carnegie Research Scholarship.

The following deaths were announced by the chair: — Arthur
Tracy Cabot, Class I., Section 4; Oliver Clinton Wendell, Class L.,
Section 1; Horace Howard Furness, Class III., Section 4.

The Corresponding Secretary announced that the Council had
granted the use of the Academy Building to the Thursday Even-

RECORDS OF MEETINGS. 779

ing Club for December 5, 1912; to The Colonial Society of Massa-
chusetts for its regular meetings until further notice; to the M. P.
Club (Mathematical-Physical Club) for its regular meetings, the
third Monday of the month, until further notice.

The following letter was read:

ACADEMY OF ARTS AND SCIENCES,
Boston, Mass.

CHARLES R. Cross, Chairman Rumford Committee.

Dear Sir:— Among the bequests in the Will of the late Mrs. Griffith,
the second clause and seventh article is as follows:— “ΤῸ the Academy
of Arts and Sciences of Boston all the Rumford mementos, correspond-
ence and papers of the Count Rumford and of his daughter the Coun-
tess of Rumford, to be examined and culled by my cousin Baldwin
Coolidge, viz: The Count’s Study Clock, Coat of Arms, Silver Knife,
Fork and Spoon, Seal, Cameo Brooch, Diamond and Topaz Ring,
given him by the King of Bavaria, Portrait of the Count painted by
the Countess, the Countess’ Seal, Portrait of Lady Palmerston,
daughter of the first Lord Melbourne, and widow of Earl Cowper,
mounted as a Brooch, a small Mother-of-Pearl and Sapphire miniature
Opera Glass, a green woolen hearth rug with “C. B.” in yellow woven
on it, and a small pair of Silver Sugar Tongs, both of which belonged
to Sir Charles Blagden.”

In accordance with the above I write to say that the Executors are
now ready to carry out the above provisions in the Will on receiving a
notice of their acceptance.

Awaiting your reply I remain,

Yours truly,

Loammi F. BaLpwin,

for the Executors and Trustees.
BALDWIN CoOoOLIDGE, EXECUTOR IN CHARGE OF BEQUEST.
410a Boylston Street, Boston, Mass.

On the recommendation of the Rumford Committee, it was

Voted, That the Academy accept the Rumford mementos men-
tioned in the letter, and that the Executors be notified.

On the recommendation of the Council, a committee consisting

780 PROCEEDINGS OF THE AMERICAN ACADEMY.

of Henry H. Edes and Robert DeC. Ward, was appointed to con-
sider the amendment of the Statutes in such a way as to add to
the Council, ex officio, the Chairman of the House Committee and
such other Chairmen of Standing Committees as it may seem
desirable to have as members of the Council.

The following communications were given: —

Biographical notice of Professor Abbott Lawrence Rotch. By
R. DeC. Ward.

The Geographic Origin of Life in Newfoundland and the Mag-
dalen Islands. By M. L. Fernald.

The following papers were presented by title: —

“On the Scalar Functions of Hyper Complex Numbers.”
Second Paper. By Henry Taber.

“Thermodynamic Properties of Twelve Liquids between 20°
and 80° and up.to 12000 kgm. per Cm.” By P. W. Bridgman.

“The Action of Sulphur Trioxide on Silicon Tetrachloride.” By
C. R. Sanger and E. R. Riegel. Presented by C. L. Jackson.

One thousand and eighteenth Meeting.

DECEMBER 11, 1912.

The meeting was held at the House of the Academy.

The PRESIDENT in the chair.

There were Twenty-eight Fellows and guests present.

The following letters were read: — from Elihu Root, accepting
Fellowship; from Richard Olney, declining Fellowship; from the
Secretary of the ninth International Congress of Zoédlogy, to
be held at Monaco, March 25-30, 1913, inviting delegates; from
the Secretary of The Colonial Society, thanking the Academy for
the offer of its building for the meetings of the Society.

The President called attention to Count Rumford’s study clock
just received as a bequest from Mrs. Griffith.

The following death was announced by the chair: — Sir George
Howard Darwin, Foreign Honorary Member in Class I., Section 1.

The following communication was given: —

“Dana’s Contribution to Darwin’s Theory of Coral Reefs,”’
by Professor W. M. Davis. This was followed by discussion.

RECORDS OF MEETINGS. 781

Dr. W. S. Bigelow showed for Professor Percival Lowell, a
miniature earth or globe, suspended between the two poles of a
horse-shoe magnet, which revolved when a lighted candle was
placed near it, illustrating the theory of the German scientist,
Albert Lotz, that magnetic forces, in conjunction with the sun’s
heat cause the earth to revolve.

One thousand and nineteenth Meeting.

JANUARY 8, 1913.— StatED MEETING.

The meeting was held at the House of the Academy.

VicE-PRESIDENT Walcott in the chair.

There were thirty-three Fellows present.

The following letters were read: — from Lady Darwin announc-
ing the death of her husband, Sir George Darwin; from the family
of Jules Henri Poincaré, announcing his death; from C. 5. Hastings
accepting Fellowship.

On the recommendation of the Council, it was

Voted, To appropriate from the income of the General Fund:
— for House expenses, seven hundred ($700) dollars; for further
protection of the Library from fire risk, seven hundred and seventy
($770) dollars.

It was also

Voted, To appropriate from the income of the General Fund,
one hundred and fifty ($150) dollars for the use of the Treasurer’s
office.

The following report of the Committee on the amendment of
the Statutes was read and accepted: —

The Committee to whom was referred the Amendment of the
Statutes proposed by Dr. Tyler at the November meeting recom-
mend its adoption in the following form: —

The third paragraph of Article I, of Chapter IV is hereby amended
by inserting after the word “‘named”’ the words ‘“‘ and the Chairman
of the House Committee, ea officio,” so as to read: —

The Councillors, with the other officers previously named and the

782 PROCEEDINGS OF THE AMERICAN ACADEMY.

Chairman of the House Committee, ex officio, shall constitute. the
Council.
Respectfully submitted,
Henry H. EDEs,
Rospert DEC. Warp,

Committee.
Boston, 8 January, 1913. :
It was
Voted, To amend the Statutes in accordance with the above
report.

The following gentlemen were elected Fellows of the Academy :—

In Class I., Section 1 (Mathematics and Astronomy) :—

George Cary Comstock, of Madison; Edwin Brant Frost, of
Williams Bay.

In Class I., Section 2 (Physics) :—

Ernest Fox Nichols, of Hanover; Robert Williams Wood, of
Baltimore.

In Class I., Section 3 (Chemistry) : —

Wilder Dwight Bancroft, of Ithaca; Bertram Borden Boltwood,
of New Haven.

In Class I., Section 4 (Technology and Engineering) : —

John Ripley Freeman, of Providence; Alfred Noble, of New
York.

In Class IT., Section 3 (Zoélogy and Physiology): —

Leland Ossian Howard, of Washington; Charles Atwood

Kofoid, of Berkeley; William Emerson Ritter, of Berkeley.

In Class II., Section 4 (Medicine and Surgery) : —

David Linn Edsall, of Boston.

In Class III., Section 1 (Theology, Philosophy and Jurispru-
dence) : —

Ezra Ripley Thayer, of Boston.

In Class III., Section 3 (Political Economy and History) : —

William Milligan Sloane, of New York; Thomas Franklin
Waters, of Ipswich.

In Class III., Section 4 (Literature and the Fine Arts): —

Okakura Kakuzo, of Boston.

The following gentlemen were elected Foreign Honorary Mem-
bers: —

RECORDS OF MEETINGS. 783

In Class IT., Section 4 (Medicine and Surgery) : —

Adam Politzer, of Vienna.

In Class III., Section 2 (Philology and Archaeology): —

Eduard Seler, of Berlin.

The following communications were given: —

“The Study of Infantile Paralysis in Massachusetts by the State
Board of Health.”” By Dr. R. W. Lovett.

“Entomological Studies in connection with Epidemics of Polio-
myelitis.” By Mr. C. T. Brues.

“Experimental Evidence of the Transmission of Infantile
Paralysis.” By Dr. M. J. Rosenau.

The following papers were presented by title: —

“Preliminary Study of the Salinity of Sea-water in the Ber-
mudas.” By Κι L. Mark. Presented by Εἰ. L. Mark.

“Cretaceous Pityoxyla from Cliffwood, New Jersey.” By

Ruth Holden. Presented by Εἰ. C. Jeffrey.

One thousand and twentieth Meeting.
FEBRUARY 12, 1913.

The meeting was held at the House of the Academy.

The PRESIDENT in the chair.

There were ninety-eight gentlemen present: — sixty-eight Fel-
lows and thirty guests.

The following death was announced by the chair: —

Francis Blake, Fellow in Class I., Section 2, and Treasurer of
the Academy from 1899 to 1905.

Professor C. R. Cross, Chairman of the Rumford Committee,
stated the grounds on which the Rumford Medal was to be awarded
to Mr. Frederic Eugene Ives.

The President then presented the medals to Mr. Ives.

Mr. Ives on receiving the medals, spoke of the encouragement he
felt in the recognition of the value of his work by the Academy and
gave an account of his long work in Color Photography, of his
struggles and of his successes.

The following papers were presented by title: —

“The Maximum Value of the Magnetization Vector in Iron.”’
By B. O. Peirce.

784 PROCEEDINGS OF THE AMERICAN ACADEMY.

“Buddhaghosa’s Treatise entitled The Way of Salvation, an
Analysis of the second Part, on Concentration.” By C. R.
Lanman.

After the meeting the following exhibits were shown in the read-
ing room: —

F. E. Ives: Specimens of work in color photography, and
apparatus for color measurement.

S. I. Bailey: Stellar photographs, showing examples of variable
stars having a more rapid rate of variation than any hitherto
known.

Outram Bangs (invited by H. B. Bigelow): Birds from the Altai
Mountains, collected in the summer of 1912 by Prof. Theodore
Lyman, and presented by him to the Museum of Comparative
Zoology.

P. W. Bridgman: Specimens of metals illustrating ruptures
under pressures up to 30,000 atmospheres.

Henry H. Edes: Mementos of Count Rumford, recently be-
queathed to the Academy by Mrs. C. B. Griffith.

L. J. Johnson: Photographs of bent beams, showing novel
results of recent experiments.

Alfred C. Lane: Thin sections of igneous rocks, showing varia-
tions of grain.

W. C. Lane: Two unique fragments of a book in an otherwise
unknown South American language, lately found in the Harvard
College Library.

D. C. Lyon: One of the books of Nebuchadnezzar, King of
Babylon, recording his building operations in that city about
600 B.C,

G. W. Pierce: The talking arc, reproducing speech transmitted
by telephone.

W. T. Sedgwick: Frozen Kansas eggs now two and one-half
years old, Chinese and other eggs, and some egg products.

J. E. Wolff: Specimens of a stony meteorite which fell in Arizona
last summer.

RECORDS OF MEETINGS. 785

One thousand and twenty-first Meeting.
FEBRUARY 24, 1913.— SpecIAL MEETING.

A special meeting of the Academy was held at its House, at half
past eight o'clock, Ρ. M. in honor of Professor Henri Bergson, of
the Collége de France.

Professor Barrett Wendell spoke of the Collége de France as an
exponent of the catholicity of the intellectual life; and presented
the greetings of the Academy to the distinguished visitor.

Professor Bergson in his address of acknowledgment spoke of the
pleasure in meeting a body of scholars and outlined his views of
the true function of philosophy.

After the conclusion of Professor Bergson’s address a reception
was held in the Reading-room. There were present about two
hundred Fellows and guests, including ladies.

One thousand and Twenty-second Meeting.

Marcu 12, 1913.— Statep MEETING.

The meeting was held at the House of the Academy.

The PRESIDENT in the chair.

There were twenty-four Fellows and four guests present.

The following letters were read: —from E. B. Frost, W. ἢ).
Bancroft, E. R. Thayer, L. O. Howard, D. L. Edsall, Εἰ. F. Nichols,
R. W. Wood, J. R. Freeman, Okakura-Kakuzo, G. C. Comstock,
B. B. Boltwood, Alfred Noble, C. A. Kofoid, W. E. Ritter, and
T. F. Waters, accepting Fellowship; from Eduard Seler, accepting
Foreign Honorary Membership; from John A. Aiken, declining
Fellowship; from the Committee of the International Geological
Congress, inviting delegates to its 12th session.

The following deaths were announced by the chair: —

John William Mallet, Fellow in Class I., Section 3; Henry
Leland Chapman, Fellow in Class III., Section 4.

On the recommendation of the Council, the following appropria-
tions were made for the ensuing year: —

from the General Fund, $5475. to be used as follows: —

786 PROCEEDINGS OF THE AMERICAN ACADEMY.

for House expenses $1700.
for Library expenses 1800.
for Books, periodicals and binding 1200.
for Expenses of Meetings 200.
for Treasurer’s Office 175.
for General Expenses 400.

from the Publication Fund, $2500. to be used for publication.
from the Rumford Fund, $1800, to be used as follows:

for research $1000.
for periodicals, books and binding 200.
for publication 600.

and to be used at the discretion of the Committee, the balance of
available income for the year.

from the Warren Fund, $500. for the Committee.

An appropriation of $800. was made from the Publication Fund
for publication during the present year.

A proposed amendment to Chapter XJ., Article 4, of the Statutes.
was referred to a Committee consisting of H. H. Edes and J. H.
Beale.

The President appointed the Committee on Nominations,
consisting of the following Fellows: —

Dro ke Piz;
Pror. G. F. Swain,
Mr. H. H. Epes.
It was
Voted, ΤῸ suspend, for the next election, the rule adopted
February 8, 1911, restricting the rate of increase of Massachusetts
membership of the Academy.
The following letter was presented to the Academy by the
Council.

AMERICAN ACADEMY OF ARTS AND SCIENCES,
Boston, Massachusetts.
February 4, 1913.
To THE HONORABLE THE SENATE AND House oF REPRESENTATIVES
OF THE UNITED STATES.
The American Academy of Arts and Sciences having learned that a
society calling itself the American Academy of Arts and Letters is

RECORDS OF MEETINGS. 787

seeking an incorporation in the House of Representatives and the
Senate, desires to enter a protest against the use of the words, American
Academy of Arts. The American Academy of Arts and Sciences has
been known for more than one hundred and twenty-five years as the
American Academy. It has always had a Section of Letters. Benja-
min Franklin, George Washington, the Adamses, Winthrop and many
other distinguished men have been members: today it includes literary
men as well as men in Arts and Science. It fulfils the same purposes
as the contemplated Academy, and the taking of the essential part
of its name will lead to great confusion in correspondence and in all
matters relating to the conduct of a learned Academy.

JOHN TROWBRIDGE, President,

CHARLES P. Bownpircu, T7'reasurer,

Henry P. Watcort, Vice-President.

It was remarked that, as the Congress to which this letter was
addressed had expired without completing the incorporation of
the Academy in question, formal action by the Academy on this
letter was unnecessary. It was, however,

Voted, That, if similar occasion shall arise, the officers be
instructed to address a similar protest to the proper quarter.

The following paper was presented by title: —

“The Structure of the Gorgonian Coral Pseudo-plexaura crassa
Wright and Studer.” By W. M. Chester. Presented by E. L.
Mark.

The following communication was given: —

“Doctrine of Protection to young Indnstries, as illustrated by
the growth of the American Silk Manufacture.” By Professor F.
W. Taussig.

Remarks on the subject were made by Howell Cheney, Esq., of
South Manchester, Conn.

One thousand and twenty-third Meeting.

APRIL 9, 1913.

The Academy met at the Harvard Medical School.

The PRESENT in the chair.

On motion of Dr. Bradford the reading of the records of the last
meeting was dispensed with.

788 PROCEEDINGS OF THE AMERICAN ACADEMY.

A card from the Carnegie Institution of Washington, announcing
the death of Dr. John Shaw Billings, Fellow in Class II., Section 4,
was presented by the Corresponding Secretary.

Professor R. P. Strong gave an illustrated lecture on the recent
Manchurian Epidemic of Pneumonic Plague.

At the conclusion of this paper, remarks were made by Mr. H.
L. Higginson as follows: —

Ladies and Gentlemen:

Dr. Strong has told us a deeply interesting tale, and now I will tell
you one thing which he cannot tell. He has described his work done
under the most difficult circumstances, but has not mentioned the
dangers accompanying this work.

Dr. Strong and his colleague went alone to Manchuria, lived in a
very dirty town, and fought the terrible disease which threatened
their own lives, through infection or through a possible scratch, and
also ran constant risk of death at the hands of the Chinese, who hate
all work with dead bodies. Dr. Strong and Dr. Teague worked with-
out the usual conveniences of hospitals or the ordinary comforts of life,
saved many patients from death, and discovered the means of combat-
ing with success this terrible epidemic. It was the work of a hero,
and nothing less. One can understand the courage of the fireman as
he runs up a ladder to save a woman and her children, or of the soldier
in the desperate attack on the enemy. In each case these men have
the habit, and perform their work cheered on by the brilliancy of the
deed; they do not stop to consider such risks. But in cool blood,
through many weeks and under such conditions, to study this fell
disease and treat the multitude of patients was a noble act, and we
thank Dr. Strong and his colleagues with all our hearts. It was
heroism of the highest kind.

Professor F. B. Mallory gave an account of the Pathological
Lesion in Whooping Cough and the Relation of the Whooping
Cough Bacillus to the Lesion. (Illustrated by lantern slides.)

The following paper was presented by title: —

“On Certain Fragments of the Pre-Socratics: Critical Notes
and Elucidations.” By W. A. Heidel.

On motion of Professor Webster, it was

Voted, That the thanks of the Academy be given to the mem-
bers of the Faculty of the Medical School who arranged the exhi-

RECORDS OF MEETINGS. 789

bitions and have made possible this most interesting and instruc-
tive meeting.

One thousand and twenty-fourth Meeting.
AprRIL 23, 1913.

The meeting was held at the House of the Academy.

The PRrEsIDENT in the Chair.

There were fifteen Fellows, with guests present.

Dr. Percival Lowell gave the following paper: —

“The Origin of the Planets.”’

This was followed by extended discussion on the part of Fellows
of the Academy.

One thousand and twenty-fifth Meeting.
May 14, 1913.— AnnuaAL MEETING.

The Academy met at its House.

The PREsIDENT in the chair.

There were fifty-one Fellows present.

The following letters were read: — from the Reale Accademia
delle Scienze, Bologna, giving the conditions of Elia De Cyon
prize; from the Institut International de Physique Solvay, Bru-
xelles, enclosing the Statutes of the Institute.

The annual report of the Council was read: —

REPORT OF THE COUNCIL.

Since the last report of the Council, there have been reported
the deaths of nine Fellows: — William Watson Goodwin, Lewis
Boss, Arthur Tracy Cabot, Oliver Clinton Wendell, Horace
Howard Furness, Francis Blake, John William Mallet, Henry
Leland Chapman and John Shaw Billings; and of four Foreign
Honorary members: — Jean Léon Géréme, Eduard Strasburger,
Sir George Howard Darwin, and Jules Henri Poincaré.

Three Fellows have resigned: — Louis Cabot, John Fritz and
R. B. Richardson.

Sixty-one Fellows have been elected, of which number two have

790 PROCEEDINGS OF THE AMERICAN ACADEMY.

declined Fellowship and one has not replied to his notice of election
and six Foreign Honorary Members, of which number one has not

yet accepted.

The roll now includes 336 Fellows and 54 Foreign Honorary

Members.

The annual report of the Treasurer was read, of which the

following is an abstract: —

GENERAL FUND.

Receipts.
Balanee; April 771912) 2 2. πι' 2,035 .38
Investments seen cs Sete e 2,319 .82
ASSESSIMEIILSHECEME Sets ss eee 2,360 .00
MANNERS so, Jy Coe τ" 560 .00
SUMGriCSMNe Ge es eee 165 .00
Expenditures.
Expenses of Library « - - - + = - $2,800.92
Expense of House . .--- +: > 2,139 .36
Expense of Meetings . ..-..: - 184 .07
Treasurer . . Sian Baits tly 178 .00
General Expenses a ἔτος ΝΥΝ τον. aor ΟΝ
ΝΗ ρον οΕοέΨσροΕὁΕι«ιὁ.ὁᾳοου ο΄ 127 .75
ΠΑ ΠΟΙ ts, ΠΕ hs enh Gane fae 628 .43
Sundries. ἐν αν {ἀν aye 226 .96
Interest on στ ΠΡ αν νον Ἀν 43 .20
Income transferred to Principal. .'. . 191 .84
Charged to cancel premium on Bond . . 45 .00
Balance, April 1, 1913 .
RumrorD Funp.
Receipts.

Balance, April 1,1912*'. 2. Sea” 8575»
Investments . . . UPS s Sa eee 3,070 .35
Sale of Pubheations «. ὁ ἢν ee Donte

$7,440 .20

$6,923 .04
57 16

7,440 .20

$4,492 .02

RECORDS OF MEETINGS.

Expenditures.

Research .... ree ate) ΙΒ
Books, periodicals and ἜΡΘΗ 21). .0]
Publication ΤΥ Pe See 555406
ΜΕ SO te ae ae a 400 .00
BUMOTIES -. ἢ: "ee 1.00
Income transferred ἰὸ Poca ae 197.71
Balance, April 1, 1913
C. M. Warren Funp.
Receipts.
alanee, April 1: 1012 eS 4 ΠΥ $377 .34
τ ΒΘ ΕΓ ΟΠ Θ᾿ our i ak oe ee eee 745 .84
Expenditures.
LCESIE® ΤΠ νυ,» εἴν. ρρν ρον Pa $290 .00
πὸ} rent, part... -,. Clas wee 4 00
Interest on Bonds, ΠΕΣ ce RE rot ale 61.11
Income transferred to principal . . . . 31.03
Balance, April 1, 1913
PUBLICATION Funp.
Receipts.

Bamvceraped. 1902) ah yk eS $715 .35
Appleton Fund investments . . . . . 842 .06
Centennial Fund investments . . . - 2,432 .84.
pale OLE ubleamons. |S). 2. Le 560 .35

791

$1,123 .18

$386 .14
737 04

$1,123 .18

792 PROCEEDINGS OF THE AMERICAN ACADEMY.

Expenditures.
Pablications + 4). t® 44 Baeaiee cy, “Sewbieoe
Sundries :/Movyingy 1 eee -:.-: 15 .20
ὙΠ Jen ewes es) os ee 12.50
Interest on Bonds, bought .... . 49 δῦ
Income transferred to Principal. . . . 138 .78 $3,483 .56
Balance April 1, 1913 _ A eS be 1,067 .04

$4,550 .06
May 14, 1913.

The following reports were also presented:

REPORT OF THE LIBRARY COMMITTEE.

During the past year the books on Arts and Sciences, the Periodicals
and Society Publications, the books on Mathematics and those on
Astronomy — these forming the first four of our 32 classes — have
been transferred from the stack to the fourth floor of the main build-
ing. The space released in the stack has been utilized by rearranging
the books of the remaining 28 classes. It is estimated that the avail-
able shelf-room will suffice for fifteen years’ growth at the present
rate.

The question of protection against fire has given the committee
serious concern, in view of the close proximity of our stack to the backs
of the Boylston Street buildings.

The best remedy was believed to be the substitution of wired glass
in the east wall of the stack, and this change has been made at an
expense of $757.

Pressure of other work has prevented any progress in the important
task of filling gaps in our serial publications. The arrangement of
the unbound pamphlets is nearly completed. The folios have been
transferred temporarily to the broader shelves of the entrance hall.

A complete set of the Academy publications has been placed in the
reading-room, together with the International Catalogue of Scientific
Literature.

87 books have been borrowed from the library during the year by
19 persons, including 16 Fellows and 4 libraries. All but one book
has been returned for examination, or satisfactorily accounted for.

RECORDS OF MEETINGS. 793

The number of bound volumes on the shelves at the time of the
last report was 32,068. 647 volumes have been added during the
past year, making the number now on the shelves, 32,715. This
includes 527 received by gift and exchange, 84 purchased by the
General Fund, and 36 by the Rumford Fund.

603 volumes have been bound, and 150 have been stamped and
plated during the financial year, May 1, 1912 to April 1, 1913, ata
cost of $835.45.

The expenses charged to the library for the eleven months ending
April 1 are:

Miscellaneous (including $108.75 for cataloguing) . . . $775.18
Binding
Gevcthanteer 9 on ee ἀπ 989
Rumford Fund joi Mls bray ch lan sD as ἢ 98 .10
Purchase of periodicals and books
Pearcueena es oe ee, ee ree, OL ERB SS
inert 2 ere ΠΡ ΡΟ Pa i

The committee begs to remind members of the desirability that
copies of their own published works be donated to the library. The
value of the library would be greatly increased by a general response
to this invitation.

It is the desire of the committee to increase the use of the library
by making its resources better known. Suggestions and coéperation
in this direction from members of the Academy will be most welcome.

H. W. Tyuer, Librarian.

May 14, 1913.

REPORT OF THE RUMFORD COMMITTEE.

During the present year grants have been made in aid of researches
as follows :—
June 5, 1912, to Professor Norton A. Kent of Boston Univer-
sity, for the purchase of a lens to be used in his investigation on
the “Effect of the Magnetic Field on the Spectra of Gases,
nent τ α΄ 0 S875
To Professor Frederick A. Saunders of Syracuse University,
for his research, “Spectroscopic Studies in the Ultra-violet

Region” ΠΥ ee a τ GP ey be ες 00
October 9, 1912, to Mr. William O. Sawtelle of Harvard
University, in aid of his research on the “Spectra of the Light

from the Spark in an Oscillatory Discharge” . . . . «© . = 250

794. PROCEEDINGS OF THE AMERICAN ACADEMY.

The Committee voted to transfer to Professor Edward L.
Nichols of Cornell University the unexpended balance of the
appropriation ($100) made to Professor Willard J. Fisher in
1908 for his research on the “ Viscosity of Gases,” together with
the apparatus used by him, as Professor Fisher is not likely to be
able to continue the research.

November 13, 1912, to G. W. Ritchey of Pasadena, for the
construction of a reflecting telescope employing mirrors with
new forms" of curvese sy 2... 2) <4. eee

November 13, 1912, as modified May 14, 1913, to Professor
Edward L. Nichols of Cornell University, in aid of the research
of Mr. W. P. Roop on the “ Effect of Temperature on the Mag-
netic Susceptibility of Gases... 250

May 14, 1913, to Frederick G. ε΄ es i the ΤΡ ἐδ
Institute of Technology, to be used for the payment of assis-
tants in the computation of thermodynamic tables for ammonia 300

It was also voted at this meeting, in accordance with the
desire of the Council of the Academy, that an appropriation of
$100 be made to Professor Theodore W. Richards to be used in
aid of the ee al of the Annual International Table of Con-

Stants’ tle US Cae
The ΤΠ τίν papers ae as τ in volute 48 of the
Proceedings of the Academy with aid from the Rumford Fund since
the last annual meeting.
No. 1. “On the Ultra Violet Component in Artificial Light.” By
Louis Bell.

No. 5. “A Study with the Echelon Spectroscope of Certain Lines
in the Spectra of the Zine Arc and Spark at Atmospheric
Pressure.”” By Norton A. Kent.

No. 9. “Thermodynamic Properties of Liquid Water to 80° and
12000 kgm.” By Perey W. Bridgman.

No. 15. “An Electric Heater and Automatic Thermostat.” By
Arthur L. Clark.

The Committee has also prepared and caused to be printed a pam-
phlet Supplement to the publication entitled “The Rumford Fund”
published in 1905, which contains the record of the awards of the
Premium and of researches and papers aided from the Fund to the
close of the year of the Academy ending May 8, 1912, together with
some other matters of permanent interest.

The necessary photographs or other fac-simile copies of the inscrip-

RECORDS OF MEETINGS. 795

tions upon all the earlier Rumford Medals having been secured,
replicas of the medals will be made shortly.

Reports of progress in their several researches have been received
from the following persons: P. W. Bridgman, W. W. Campbell,
A. L. Clark, D. F. Comstock, H. C. Hayes, L. R. Ingersoll, N. A. Kent,
F. E. Kester, G. N. Lewis, C. E. Mendenhall, E. F. Nichols, E. L.
Nichols, J. A. Parkhurst, T. W. Richards, G. W. Ritchey, M. A.
Rosanoff, F. A. Saunders, W. O. Sawtelle, M. deK. Thompson, Εἰ W.
Very, R. W. Wood.

At the meeting of November 13, 1912, the Committee voted to
recommend to the Academy the acceptance of the bequest of the late
Mrs. Griffith described in a letter of Loammi F. Baldwin, Esq., repre-
senting her executors and trustees, dated October 8, 1912.

At the meeting of February 12, 1913, it was unanimously voted
for the first time and at the meeting of March 12, 1913 for the second
time to recommend to the Academy that the Rumford Premium be
awarded to Professor Joel Stebbins of the University of Illinois for his
development of the selenium photometer and its application to astro-
nomical problems.

Cuas. R. Cross, Chairman.
May 14, 1913.

ReEporT OF THE C. M. WARREN COMMITTEE.

The C. M. Warren Committee begs to report that one grant has
been made during the year of $140 to Professor Arthur B. Lamb of
Harvard University, for work on the rhodiumamines. It now has
at its disposal for the current year an unexpended balance of $860.
During the year Professor H. G. Byers has published two papers on
the passivity of iron, the work on this subject having been carried on
in part through the grants from the Warren Fund. Reports of pro-
gress have been received from Dr. Gilpin and Professor Lamb and Dr.
Washburn.

The Committee has in preparation a circular regarding the purposes
of the Warren Fund which it is hoped will occasion renewed interest
in the opportunities which it affords for the support of research.

H. P. ΤΑΊ ΒΟΥ, Chairman.
May 14, 1913.

796 PROCEEDINGS OF THE AMERICAN ACADEMY.

REPORT OF THE PUBLICATION COMMITTEE.

Between April 1, 1912, and April 1, 1913, there were published one
number of Volume XLVII (No. 22) and seventeen numbers of Volume
XLVIII of the Proceedings. There were also published two obituary
notices. The total publication for this period amounted to 771 pages.
The expense of publishing three of these numbers and a part of a
fourth number has been assumed by the Rumford Committee.

There was available for the use of the Publication Committee an
unexpended balance from last year of $428.70, an appropriation of
$2500, and an additional appropriation of $800, and an amount of
~ $560.35 from the sales of publications — in all, $4289.05 from the
Publication fund and sales. Bills against this appropriation to the
amount of $3267.53 have been approved by the Chairman. This
leaves an unexpended balance of $1021.52.

Bills aggregating $555.05, incurred in publishing papers on light
and heat, have been referred to the Rumford Committee for payment
in accordance with their authorization.

G. W. Pierce, Chairman.
May 14, 1913.

ReEporT OF THE House CoMMITTEE.

The House Committee submits the following Report for the year
1912-1913: The Committee had at its disposal a balance of $108.54
from last year. The appropriations by the Academy for the past
year have been $2240, making a total of $2348.54 for the use of the
Committee. Of this sum, $2348.32 has been expended. These
expenditures include approximately $500 which may properly be
regarded as unusual expenditures incidental to the establishment of
the Academy in its new house. The larger of the latter items are
those for window screens, the electric lamp bulbs for the entire
building, the installation of a telephone and electrically operated lock
on the front doors, alterations in the electric lighting of the stack and
stack rooms, additional shelving and cupboards, a residual payment
of rental at 711 Boylston St., and the cost of moving. While certain
additions to equipment, and some repairs, will necessarily be made
every year, the amount of expenditures for equipment should be
materially less than during the past year.

The Academy has held seven regular and two special meetings in
the building since May, 1912. The small rooms have also been used
for eight Council and ten committee meetings.

RECORDS OF MEETINGS. 797

The Council has authorized the use of the building by the Thursday
Evening Club, and for a meeting of teachers of geology on one oceasion,
and by The Colonial Society and the Mathematical and Physical Club
for their regular meetings. The Colonial Society has held four
meetings in the late afternoon and the ‘“M. P. Club” three meetings
in the evening. Both of these organizations have made payments,
determined by the Treasurer, sufficient to reimburse the Academy for
the cost of light, heat and attendance.

The present janitor, who with his wife occupies the janitor’s apart-
ment in the building, is the third employed during the year. He is,
at present, rendering excellent service.

The experience of the year has shown that the Academy building is,
in most respects, well adapted to meet the needs of the Academy.
The provisions for the use of the lantern in the meeting-room are not
as satisfactory as could be desired, especially with respect to the use
of the sereen, which is rather unsightly in appearance, suggestive of an
emergency rather than a permanent arrangement. The Committee
expects to provide a better equipment as soon as the necessary ex-
penditures seems to be warranted and the best device can be selected.

With a desire to avoid unnecessary duplication of effort, the House
Committee has taken over the charge of the simple collations served
after the evening meetings of the Academy, which are provided from
funds under the charge of the Committee on Meetings. The House
Committee has not undertaken, and would prefer not to undertake,
to provide for the more elaborate collations necessary on special occa-
sions.

The building has been open during the year from ὃ A. M. to 5 P. M.
except on Saturdays, when it has been closed at 1 p.m. No sugges-
tions have been received from Fellows of the Academy regarding
more acceptable hours, but such suggestions would be welcomed.

The Committee desires to express its sense of obligation to the
Assistant Librarian, Mrs. Holden, for her constant codperation with
the work of the Committee and her care of details for which it
would otherwise have been very difficult to provide. Mr. Charles
Wilder has also codperated most helpfully with the work of the
Committee.

H. P. Tarsot, Chairman.
May 14, 1913.

On the recommendation of the Rumford Committee, it was
Voted, To award the Rumford Premium to Professor Joel

798 PROCEEDINGS OF THE AMERICAN ACADEMY.

Stebbins, of the University of Illinois, for his development of the
selenium photometer and its application to astronomical problems.

The following report of the Committee on the Amendment of
the Statutes was read and accepted: —

Boston, Mass., 14 May, 1913.

The undersigned, a Committee to which was referred an amendment
to the Statutes offered at the Stated Meeting in March, has attended
to the duty assigned to it, and begs leave to report as follows:

Your Committee recommends that there be added to Article 4 of
Chapter XI., at the end, the words “The Council, in its discretion,
by a duly recorded vote, may delegate its authority in this regard to
one or more of its members.”

If the amendment is adopted by the Academy, the Article will
then read as follows:

“Article 4. No report of any paper presented at a meeting of the
Academy shall be published by any Fellow without the consent of the
author; and no report shall in any case be published by any Fellow
in a newspaper as an account of the proceedings of the Academy with-
out the previous consent and approval of the Council. The Council,
in its discretion, by a duly recorded vote, may delegate its authority
in this regard to one or more of its members.”

Respectfully submitted,
Henry H. Epss,
JosEPH H. BEALE,
Committee.

On the recommendation of the Committee, it was

Voted, To amend the Statutes in accordance with the recom-
mendation contained in the foregoing report. |

On motion of the Treasurer, it was

Voted, 'To appropriate from the income of the General Fund,
the sum of $112., to pay for accident insurance for 1912-13, and
1913-14.

On motion of the Treasurer, it was

Voted, That the Annual Assessment be ten (10) dollars.

The Council reported that in accordance with the provisions of
Article 1 of Chapter IX of the Statutes, the Reverend Dr. Timothy
Dwight, a Fellow in Class III., Section 2, and the Reverend Drs.
William Wallace Fenn, Edward Caldwell Moore, George Herbert
Palmer, James Hardy Ropes, William Jewett Tucker and Williston

RECORDS OF MEETINGS. 799

Walker, Fellows in Class III, Section 4, had been transferred to
Class III., Section 1.

A marble bust of Dr. Jacob Bigelow and an inkstand used by
him were presented to the Academy by his grandson, Dr. William
Sturgis Bigelow.

The President in receiving the gifts for the Academy made the
following remarks: —

“Dr. Jacob Bigelow was President of this Academy from 1846
to 1863, and was the eighth in a distinguished line of Presidents —
James Bewdoin, John Adams, Edward A. Holyoke, John Quincy
Adams, Nathaniel Bowditch, James Jackson, and John Pickering.
Dr. Bigelow was an eminent writer on botanical and medical
subjects; and his great services to science and to the community
are set forth in volume 14 of the Proceedings of the Academy. He
was greatly interested in technological education and was the first
to advocate the foundation of an Institute of Technology in Boston.
Dr. Bigelow was also Rumford Professor in Harvard University;
and it seems very fitting that the Academy should receive these
remembrances of him at this meeting, when the Rumford medals
are to be conferred.”

In moving the thanks of the Academy, Professor A. G. Webster
hoped that similar gifts in honor of distinguished members would
be received.

It was

Voted, That the thanks of the Academy be given to Dr. W.
S. Bigelow for his valuable gifts.

The Rumford Medal which had been awarded to Professor
James M. Crafts, was presented to him in his absence through
Professor Charles R. Cross.

The following draft of certain sections in the tariff act, was sent
to the Academy by Francis E. Hamilton of 32 Broadway, New
York. It was presented to the Council and was referred to a
Committee of one — Professor F. W. Taussig.

SUBSTITUTE FOR SECTIONS 517-—519-650-714-715.

Books, maps, music, engravings, photographs, etchings, bound or
unbound, and charts, which shall have been printed more than twenty

800 PROCEEDINGS OF THE AMERICAN ACADEMY.

years at the date of importation, and all hydropgraphic charts, and
publications issued for their subscribers or exchanges, by scientific
and literary associations or academies, or publications of individuals
for gratuitous private circulation, and public documents issued by
foreign governments; ALSO, books, maps, music, photographs,
etchings, lithographic prints, and charts specially imported not more
than two copies in any one invoice, in good faith for the use and by
order of any society or institution incorporated or established solely
for religious, philosophical, educational, scientific, or literary purposes,
or for the encouragement of the fine arts, or for the use and by order
of any college, academy, school, or seminary of learning in the United
States, or any State or Public Library; ALSO, philosophical and
scientific apparatus, utensils, instruments, and preparations including
bottles and boxes containing the same, specially imported in good faith
for the use and by order of any society or institution incorporated
or established solely for religious, philosophical, educational, scientific,
or literary purposes, or for the encouragement of the fine arts, or for
the use and by order of any college, academy, school, or seminary of
learning in the United States, or any State or Public Library; ALSO,
works of art, drawings, engravings, photographic pictures, and_philo-
sophical and scientific apparatus, for use temporarily for exhibition
and in illustration, promotion and encouragement of art, science, or
industry in the United States; ALSO, works of art, collections in illus-
tration of the progress of the arts, sciences, or manufactures, photo-
graphs, works in terra cotta, parian, pottery, or porcelain, antiquities
and artistic copies thereof in metal or other material, imported in
good faith for exhibition at a fixed place by any State or by any Society
or institution established for the encouragement of the arts, science,
or education, or for a municipal corporation, and all like articles im-
ported'in good faith by any society or association, or for a municipal
corporation, for the purpose of erecting a public monument. Any
and all of the above imported in good faith only for the purposes
mentioned and not for sale, shall be admitted free of duty upon oath
from an authorized officer of the society, institution, college, academy,
school, seminary of learning, corporation, association, and without
bond, under regulations to be prescribed by the Secretary of the
Treasury: PROVIDED, that the privileges of this and the preceding
section shall not be allowed to associations or corporations engaged
in or connected with business of a private or commercial character.

EEE

RECORDS OF MEETINGS. SO1

The following report was given by Professor Taussig.

The draft submitted to the Academy by Francis E. Hamilton of
New York of certain sections in the tariff act relating to the free im-
portation of books, scientific apparatus and works of art, is, in the
main, a consolidation of scattered sections as they now stand in the
tariff act of 1909. The only changes of substance are in the direction
of making more liberal certain provisions concerning the importation
of works of art, and the like, for temporary exhibition. These are to
be brought in without requirement of a bond, and without requirement
that they shall be in charge of professional artists or lecturers. I see
no reason why the Academy should not allow its name to be used
in favor of the proposed rearrangement, and recommend that it allow
the use of its name.

F. W. Tavusste.
May 14, 1913.

It was then
Voted, to reeommend the proposition made by Mr. Hamilton.

The annual election resulted in the choice of the following

officers and commitees: —

JoHN TROWBRIDGE, President.

Exumiu THomson, Vice-President for Class I.

Henry P. Watcort, Vice-President for Class IT.

A. LAWRENCE LOWELL, Vice-President for Class IIT.

Epwin H. Hau, Corresponding Secretary.

Wituiam Watson, Recording Secretary.

CHARLES P. Bowpircnu, Treasurer.

Harry W. Tyter, Librarian.

Councillors for Four Years.
DersmMonp FirzGERALp, of Class I.
JOHN CoLLins WARREN, of Class. II.
GeorGE L. KITTREDGE, of Class III.
Finance Committee.
JoHN TROWBRIDGE, GARDINER M. LANE,
JoHN CoLiins WARREN.

802 PROCEEDINGS OF THE AMERICAN ACADEMY.

Rumford Committee.

Cuar_es R. Cross, Erasmus D. Leavitt,
Epwarp Οὐ. PICKERING, Evisu THoMsoN,
Artuur G. WEBSTER, Louis BELL,

ArTHUR A. NOYES.

C. M. Warren Committee.

Henry Po Taner WALTER L. JENNINGS,
CHARLES L. JACKSON, Grecory P. BAxtTEr,
Artuur A. NOYES, James F. Norris,

WILLIAM H. WALKER.

Publication Committee.

GrorcE W. Pierce, of Class I.
Water B. Cannon, of Class II.
ALBERT A. Howarp, of Class III.

Library Committee.
Harry W. Ty Ler,
Harry M. Goopwin, of Class I.

SaMuEL Hensuaw, of Class II.
ταν ὦ. Lane, of Class III.

House Committee.
Henry P. Ta por, Louis DERR,
Hammonp V. HAYEs.

Committee on Meetings.

THE PRESIDENT, Tue RECORDING SECRETARY,
Wiituam M. Davis, WALLACE C. SABINE,

ARTHUR FAIRBANKS.

Auditing Committee.

Exiot C. CLARKE, WorTHINGTON C. Forp.

RECORDS OF MEETINGS. S03

The following gentlemen were elected Fellows of the Academy ,—
a printed list of nominees having been sent to all Voting Fellows
with the notice of the April meeting, in accordance with Chapter
III., Article 3 of the Statutes: —

In Class I., Section 1 (Mathematics and Astronomy) : —

George David Birkhoff, of Cambridge; Julian Lowell Coolidge,
of Cambridge; Edward Vermilye Huntington, of Cambridge.

In Class I., Section 2 (Physics) : —

Henry Crew, of Evanston, Ill.; Norton Adams Kent, of Cam-
bridge.

In Class I., Section 3 (Chemistry) : —

Arthur Dehon Little, of Brookline; William Albert Noyes, of
Urbana, IIl.

In Class I., Section 4 (Technology and Engineering) : —

Harold Pender, of Boston.

In Class IT., Section 4 (Medicine and Surgery) : —

Henry Asbury Christian, of Boston; Frank Burr Mallory, of
Brookline; Edward Hall Nichols, of Boston.

In Class IIT., Section 1 (Theology, Philosophy and Jurispru-
dence) : —

Frederick Perry Fish, of Brookline; William Lawrence, of
Boston; Henry Newton Sheldon, of Boston; Moorfield Storey,
of Boston.

In Class III., Section 2 (Philology and Archaeology) : —

Charles Hall Grandgent, of Cambridge; Charles Burton
Gulick, of Cambridge; Hans Carl Gunther von Jagemann, of
Cambridge; James Richard Jewett, of Cambridge; Edward
Kennard Rand, of Cambridge.

In Class III., Section 3 (Political Economy and History): —

Charles Jesse Bullock, of Cambridge; Davis Rich Dewey, of
Cambridge; Edwin Francis Gay, of Cambridge; Albert Bushnell
Hart, of Cambridge; Charles Homer Haskins, of Cambridge;
William Bennett Munro of Cambridge.

In Class III., Section 4 (Literature and the Fine Arts): —

George Whitefield Chadwick, of Boston; Samuel McChord
Crothers, of Cambridge; Franklin Bowditch Dexter, of New Haven,
Conn.; Arthur Foote, of Brookline; Daniel Chester French, of

804 PROCEEDINGS OF THE AMERICAN ACADEMY.

Cambridge; Robert Grant, of Boston; John Torrey Morse, Jr.,
of Boston; Bela Lyon Pratt, of Boston; George Edward Wood-
berry, of Beverly.

The following communication was given: —

Dr. Theodore Lyman. “A Journey in the Highlands of Siberia.’”

The following papers were presented by title: —

“Passivity of Iron under Boiler Conditions.” By H. G. Byers
and F. T. Vores. Presented by H. P. Talbot.

“Relation between the Magnetic Field and the Passive State of
Iron.”” By H. G. Byers and 8. C. Langdon. Presented by H. P.
Talbot.

Contributions from the Gray Herbarium. New Series XLI.
I. A Redisposition of the Species heretofore referred to Lepto-
syne. II. A Revision of Encelia and some Related Genera.
By 5. F. Blake.

Contributions from the Gray Herbarium. New Series XLII.
I: A Key to the Genera of the Compositae Eupatoricae. By
B. L. Robinson. II: Revisions of Alomia, Ageratum, Cteno-
pappus and Oxylobus. By B. L. Robinson. III: Some new
Combinations required by the International Rules. By C. A.
Weatherby. IV: On the Graminae collected by Professor
Morton C. Peck, in British Honduras, 1905-1907. By F. F.
Hubbard. V: Diagnoses and Transfers among the Spermato-
phytes. By B. L. Robinson.

BIOGRAPHICAL. NOTICES.

ROBERT AMORY.

Ropert Amory A. M., M. D., was born in Boston, May 3, 1842,
and died in Nahant, Aug. 27, 1910. He was graduated from Harvard
College in 1863 and from the Harvard Medical School in 1866. After
the medical degree was conferred he continued his studies for a year
in Europe and while in Paris became especially interested in the
experimental study of the action of drugs.

He began the practice of medicine in Brookline and soon opened a
small laboratory for experimental research in the stable adjoining
his residence in Longwood. He then interested a number of medical
students in physiological investigations, especially with reference to
the action of medicines. Dr. Edward H. Clarke, professor of materia
medica in the Harvard Medical School encouraged his undertaking
and recommended his appointment to a lectureship on the physio-
logical action of drugs. Dr. Amory later opened a larger and more
convenient laboratory in La Grange St., Boston, for the use of his
students and for the benefit of those physicians who were interested
in experimental methods of biological study. A centre thus was
established for advanced students of medical problems and the labo-
ratory became the meeting place of the Boston Society of Medical
Sciences of which Dr. Amory was one of the founders. During this
early period of his career were published his researches on hydrocyanic
acid, caffein and thein, absinth, the bromide of potassium and am-
monium and on nitrous oxide. In connection with Dr. 5. G. Webber
he published a paper on veratrum viride and veratria, and, with
Dr. E. H. Clarke, a monograph on the physiological and therapeutical
action of the bromide of potassium and the bromide of ammonium.

His reputation as a scientific investigator along physiological lines
thus being established he was appointed in 1872 lecturer on physiology
at the Medical School of Maine and in the following year was made
professor of physiology in that institution. At this time he translated
the lectures in physiology given by Professor Kiiss of the university

800 ROBERT AMORY

of Strasbourg. He also accepted the editorship of the section on
poisons in the third edition of the Medical Jurisprudence of Wharton
and Stillé. In connection with Professor E. S. Wood, and later with
Dr. R. L. Emerson he edited the chapters on poisons in the subse-
quent editions of this treatise.

He was elected a Fellow of the American Academy of Arts and
Sciences in 1871 and in 1875 presented a communication on photo-
graphs of the solar spectrum which he had made with the assistance
of Mr. J. G. Hubbard who then was working in his laboratory. Com-
munications also were presented by him on the action of dry, silver
bromide collodion to light rays of different frangibility and on the
theory of absorption bands in relation to photography and chemistry.

In 1874 he resigned his professorship and devoted his time largely
to medical practice and to such laboratory studies as his various
obligations would permit. He was appointed the medical examiner
of his district, held various positions in the medical staff of the Massa-
chusetts Volunteer Militia and in 1880 was President of the National
Decennial Convention for the Revision of the United States Pharma-
copoeia. During this period he contributed a paper on the haema-
tinie properties of dialyzed iron, with Dr. G. K. Sabine made a study
of an epidemic of typhoid fever in Brookline and, in 1886, published
a treatise on Electrolysis and its therapeutical and surgical use.

For a number of years he had been in the habit of spending his
summers in Bar Harbor, Me., where he also practised medicine. Then
having become interested in the telephone he was persuaded to with-
draw from medical practice and to devote himself to commercial affairs.
He identified himself with telephone, electricity and gas, and became
President and Manager of the Brookline Gas Company, from which
he retired in 1898.

Dr. Amory, while engaged in scientific pursuits, was an earnest,
diligent worker, with high ideals. He gave liberally of his time,
the freedom of his laboratory and apparatus for the encouragement
of others. He was a pioneer in the introduction into this country
of the study of the physiological action of drugs by experiments on
animals and apart from his individual researches thus contributed
to the advancement of exact knowledge.

Beers:

ABBOTT LAWRENCE ROTCH. 807

ABBOT LAWRENCE ROTCH.

Aspotr LAWRENCE ἨΌΤΟῊ was born in Boston, January 6, 1861,
the son of Benjamin Smith and Anna Bigelow (Lawrence) Rotch.
He was graduated from the Massachusetts Institute of Technology
(S.B.) in 1884. In 1891 Harvard recognized the importance of the
work which he had already accomplished by bestowing upon him the
honorary degree of A.M. From 1888 to 1891, and again from 1902 to
1906, he held the appointment of assistant in meteorology at Harvard,
a position which involved no teaching and in which no salary was
paid. In 1906 he was appointed professor of meteorology, an honor
which he prized very highly, and which gave him the position on the
teaching staff of the university to which he was in every way fully
entitled. He was the first professor of meteorology who has occupied
that position at Harvard, and he served in this professorship without
pay. Inthe year 1908-09, at the request of the department of geology
and geography, he generously put the splendid instrumental equip-
ment and library of Blue Hill Observatory at the service of the uni-
versity, by offering a research course (“Geology 20f”) to students
who were competent to carry on investigations in advanced meteorol-
ogy. This action on the part of Professor Rotch gave Harvard a
position wholly unique among the universities of the United States.
It brought about a close affiliation, for purposes of instruction and of
research, between the university and one of the best-equipped meteoro-
logical observatories in the world. To his work as instructor Professor
Rotch gladly gave of his time and of his means. He fully realized
the unusual advantages which he was thus enabled to offer those stu-
dents who were devoting themselves to the science of meteorology,
and the experience of the men who had the privilege of his advice
and help in the work at Blue Hill shows clearly how much they profited
by this opportunity. Only a short time before his death he had
expressed the wish to bring about a still closer connection, for purposes
of instruction, between the university and Blue Hill Observatory.
He thus showed his appreciation of the importance of the new field
of work which he had undertaken.

While thus planning still further usefulness for his observatory;
in the midst of a life singularly active; with an ever-widening sphere
of scientific influence and a constantly increasing importance of his
contributions to meteorology, Professor Rotch died suddenly in Boston
on April 7, 1912, in the fifty-second year of his age. His wife, who was

808 ABBOTT LAWRENCE ROTCH.

Miss Margaret Randolph Anderson, of Savannah, oe ., and three
children survive him.

Professor Rotch early developed that absorbing interest in meteorol-
ogy which caused him to devote his life to the advancement of that
science. Possessed of large means, he preferred to work persistently,
and not infrequently to undergo discomfort and hardship in his chosen
field of research, rather than to live a life of ease. Realizing the need
of an institution which could be devoted to the collection of meteoro-
logical observations, and to meteorological research, free from any
entanglements, he established, in 1885, Blue Hill Observatory. This
was first occupied by Mr. Rotch and his observer, Mr. W. P. Gerrish,
on February 1, 1885. This observatory he not only equipped and
maintained until his death, but he made provision in his will for havy-
ing the work there carried on without a break. Blue Hill Observatory
is to-day one of the few private meteorological observatories in the
world, and there is not one which is better equipped. In fact, it is
probably safe to say that there is no private scientific establishment
which is better known for the high standard of its work. The Blue
Hill Observatory was, with the exception of the municipal meteoro-
logical station in New York, the first in this country to be equipped
with self-recording instruments, and it is to-day one of the compara-
tively few in the world where nearly every meteorological element is
continuously recorded. Beginning with 1886, hourly values have been
printed. Professor Rotch took a splendid pride in his observatory,
and in its equipment, and his library, to which he devoted constant
care, was one of the most complete and valuable in the world.

Professor Rotch early realized that the advance of meteorology
must come through a study of the free air, and with keen and prophetic
judgment he planned and carried out the remarkable series of investi-
gations which have made Blue Hill so famous. He secured assistants
who were well fitted to carry out the researches which he planned and
supervised. He thus showed his ability to judge the value of men,
as well as his capacity to organize the work for them todo. Mr. H. H.
Clayton became a member of the Observatory staff in 1886, and served
as observer and meteorologist, with some interruptions, for twenty-
three years. His work brought distinction to himself and to the ob-
servatory. Mr.S. P. Fergusson joined the staff in 1887, and remained
there until 1910. Many new instruments were devised by him, and
perfected with care and success. Mr. A. E. Sweetland died after eight
years of service and was succeeded, in 1903, by Mr. L. A. Wells, who
is now observer-in-charge. Year after year the Blue Hill publications

ABBOTT LAWRENCE ROTCH. SO9

have contained results of far-reaching importance. It is not an exag-
geration to say that much of the recent rapid advance of meteorological
science is due to the pioneer work which was done at Blue Hill.

Under an arrangement entered into between Blue Hill Observatory
and the Astronomical Observatory of Harvard College, Professor
Rotch was, for nearly twenty-five years, closely associated with the
latter institution. All of the observations made at Blue Hill were
published in the Annals of the Harvard Observatory, and fill eight
quarto volumes. The international form of publication, and metric
units, were first used in the United States in the publications of the
Blue Hill Observatory.

It was one of Professor Rotch’s most striking characteristics that he
never neglected any opportunity which might help him to keep his
observatory not only abreast of the times but ahead of the times.
He thought nothing of the time and the expense of taking a trip to
Europe in order to attend some scientific meeting, meteorological or
aeronautical, if he believed, as he most firmly did, that he might by so
doing gain inspiration and new ideas. Few scientific men are so
regular in their attendance at congresses and meetings; few contribute
so much that is new, or gain as much inspiration as he did at such
gatherings. It was not the blind following of the dictates of his New
England conscience that prompted him to be so regular in his meetings
with his scientific colleagues. His motive was a higher one than that.
It was his absorbing desire to advance his science by every means
within his power. An English colleague (Dr. H. R. Mill) has written
of him that he was “the most widely travelled and best-known of
meteorologists. It would be hard to name a meteorological observa-
tory or institution in any country which he had not visited, or a meteor-
ologist with whom he was not on terms of personal friendship... .
He was not only a name but a friend to all his colleagues in the meteoro-
logical world.” The list of scientific bodies of which he was a member
was a long one, but every one of them gained much from his member-
ship and from his presence at its meetings. He was regular in his
attendance; always ready to contribute papers; always modest in
his estimate of the importance of his own work; always generous in
his appreciation of the work of others; always ready with a word of
sympathy, or encouragement, or fellowship.

The productivity of Blue Hill Observatory has been remarkable,
especially when it is remembered that this activity was the result of
the support and inspiration of one man. The study of cloud heights,
velocities, movements, and methods of formation, at Blue Hill, was one

810 ABBOTT LAWRENCE ROTCH.

of the most complete investigations of the kind ever undertaken. The
first series of measurements in America of the height and velocity of
clouds, by trigonometrical and other methods, was made at Blue
Hill in 1890-91. These measurements were repeated in 1896-97,
as a part of an international system.

It was at Blue Hill that the modern methods of sounding the air by
means of self-recording instruments lifted by kites were first developed
and effectively put into practise (1894), methods which have now been
adopted by meteorological services and scientific expeditions in all
parts of the world. The use of cellular kites flown with steel wire and
controlled by a power windlass originated at Blue Hill. Grants for
carrying on this kite work were obtained from the Hodgkins Fund.
The success of this exploration of the free air at Blue Hillled, more than
anything else, to the establishment of the Observatoire de la Météoro-
logie dynamique at Trappes, under the direction of M. Léon Teisserene
de Bort, and of the Aeronautisches Observatorium of the Royal Meteoro-
logical Institute, near Berlin, under Professor Richard Assmann.

It was Rotch who, in 1901, during a voyage across the Atlantic,
first obtained meteorological observations by means of kites flown
from the deck of a moving steamer, thus indicating the feasibility of a
new way of securing information concerning the conditions of the
free air over oceans and lakes. It was Rotch who, in 1904, secured
the first meteorological observations by means of sounding balloons
from heights of 5 to 10 miles over the American continent, and who,
in 1909, made the first trigonometrical measurements of the flight of
pilot balloons in the United States. In 1905-06 he joined his col-
league, Teisserenc de Bort, in fitting out and taking part in an expe-
dition to explore the tropical atmosphere over the Atlantic Ocean by
means of kites and pilot balloons, an undertaking which resulted in
the collection of important data regarding the temperatures and
movements of the upper air, and especially concerning the existence
of the anti-trades. But Rotch was not content with merely sending
up kites and balloons. His enthusiasm in the study of the free air,
and his desire to visit the mountain observatories of the world, led
him to become a mountain climber of no mean ability. He ascended
to the summit of Mont Blanc at least five times, and in South
America and elsewhere he himself made meteorological observations
at considerable altitudes on mountains, and carefully observed the
physiological effects of the diminished pressure. He also took part
in several balloon ascents, taking important observations during
these trips, notably on that of October 24, 1891, starting from Berlin,

ABBOTT LAWRENCE ROTCH. S11

when he earried out a series of comparisons between the sling ther-
mometer and Assmann’s aspiration thermometer. He was a member
of more than one solar eclipse expedition. His studies of eclipse
meteorology are among the most complete which have been made.
Among his many contributions to the advancement of meteorology
must also be mentioned his invention of an instrument for determining
the true direction and velocity of the wind at sea.

Professor Rotch was naturally intensely interested in the recent
rapid development of aeronautics. His earlier training at the Massa-
chusetts Institute of Technology, and his untiring zeal in the explora-
tion of the upper air, combined to give him this interest. He turned
his attention largely in that direction of late years. It was character-
istic of him that, not content with the mere collection of data, and with
investigations of theoretical interest, he always strove to make these
results of practical use. Thus, soon after the establishment of his
observatory, the issue of local weather forecasts was begun, and one of
the last things which he published (in association with Mr. A. H.
Palmer) was a set of “Charts of the Atmosphere for Aeronauts and
Aviators” (1911), a pioneer work, embodying many of the results
of observations made at Blue Hill in a practical form for the use of air-
men.

Professor Rotch originally suggested the issue of a cyclostyle weather
map, and himself paid the expenses of the first publication of such maps,
which was on May 1, 1886, at the Boston office of the United States
Signal Service, Sergt. O. B. Cole, who was then in charge of the station,
cooperating in the undertaking. This was the first printing of a synop-
tic chart outside of the Central Office at Washington, and the Signal
Service soon extended this method of issuing maps to several of its
other stations. The local weather predictions were first made at
Blue Hill on July 1, 1886. Their superiority over the Washington
predictions made by the Signal Service was soon apparent, and in
February, 1887 (American Meteorological Journal), Professor Rotch
suggested that the United States Signal Service “discontinue its
Washington predictions by having the district indications made at
the chief station of each district by a competent person and from
the data of the synoptic charts.” This plan was soon thereafter
adopted by the Signal Service at Boston, and was later generally
extended over the country.

Forecasts made at Blue Hill were first published in the Boston
Evening Transcript from January 4, 1887, until March 7, 1887. From
May 2, 1887, until April 30, 1888, and from January 1, 1889, until

812 ABBOTT LAWRENCE ROTCH.

October 16, 1891, the Blue Hill forecasts were given to the Associated
Press and published in the papers of Boston and neighboring cities.
Since October 16, 1891, forecasts have been signaled by flags from Blue
Hill, and since July 9, 1911, local forecasts have been displayed at
the Observatory gate daily.

Professor Rotch’s list of published papers and books comprises 183
titles. These cover a wide range of subjects, by no means strictly
confined to meteorology, and show most emphatically how varied were
their author’s interests; how extended was his reading; how alert
and progressive he was in all he undertook. These 183 titles in them-
selves furnish a satisfactory outline of the development of meteoro-
logical science during the past 25 years. In addition to the “Charts
of the Atmosphere” just referred to, he published two other books,
“Sounding the Ocean of Air,” (1900) and “The Conquest of the
Air” (1909).

Professor Rotch gave his support freely to a large number of scien-
tific societies and undertakings. He was one of the pioneer and most
enthusiastic members of the New England Meteorological Society.
He was, for more than ten years (1886-96), one of the associate editors
and one of the mainstays of the American Meteorological Journal,
which did a unique work for American meteorology.

He was elected a Fellow of the American Academy of Arts and .
Sciences March 14, 1888, and served as Librarian from May 10, 1899,
until his death. He was a member of the Astronomical and Astro-
physical Society of America; a member and trustee of the Boston
Society of Natural History; a member of the American Philosophical
Society, of the Physical Society of London, of the International Solar
Commission, of the International Commission for Scientific Aero-
nautics, of the International Meteorological Committee; fellow and
later Honorary Member of the Royal Meteorological Society (London) ;
member of the Société Météorologique de France, of the Deutsche
Meteorologische Gesellschaft, of the Oesterreichische Gesellschaft
fiir Meteorologie, corresponding member of the Deutscher Verein
fiir Férderung der Luftschiffahrt, and member of many other societies.

_ He was lecturer at the Lowell Institute, in Boston, in 1891, and again
in 1898. He was a member of the International Jury of Awards at
the Paris Exposition (1889), and was then made a Chevalier of the
Legion of Honor. He received the Prussian Orders of the Crown
(1902) and Red Eagle (1905) of the Third Class in recognition of his
services in advancing the knowledge of the atmosphere. Further
evidence of the high regard in which his scientific work was held abroad

CHARLES ROBERT SANGER. 813

was his selection, by the French ministry of public instruction, as
exchange professor at the Sorbonne for the year 1912-13. The official
letter announcing this selection arrived in this country within a very
few days after Professor Rotch’s death.

He was a pioneer in a new science; an investigator, whose name is
known wherever meteorological work is done; a loyal teacher who
served without salary; a generous benefactor, who left to the uni-
versity an enduring monument of his enthusiasm and untiring devo-
tion to the science which he himself did so much to advance. His
life and labor have been an inspiration to his scientific colleagues
everywhere, but especially to those who were most closely associated
with him in the work of his observatory, and in the department of the
university of whose staff he was a valued member.

Rosert Dre Ὁ. Warp.

CHARLES ROBERT SANGER

THE most important achievement of Charles Robert Sanger grew
out of an incident, which occurs in the life of almost every young
chemist. While he was Assistant in Chemistry at Harvard College,
Professor H. B. Hill was consulted by a literary colleague in regard
to a number of cases of obscure poisoning in his family. At first he
suggested that they might be due to carbonic oxide from the furnace
and referred the question for investigation to Sanger, who found
however that the air of the house was free from carbonic oxide, and
therefore turned his attention to the other surroundings of the family,
when it appeared the wall papers were heavily charged with arsenic,
and, after these had been removed, the unpleasant symptoms gradu-
ally disappeared. In this way Sanger’s attention was called to the
relation of arsenic to common life, but instead of contenting himself
with the study of this particular case, as most men would have done,
he took up the general subject, made this field of research especially
his own, and produced in it his most important additions to the science.

In attacking the subject he determined, with characteristic love
of truth, to place it on a secure experimental foundation by looking
for arsenic in the excreta of people suffering from the disorders com-
monly attributed to poison from wall papers. Before doing this how-

814 CHARLES ROBERT SANGER.

ever it was necessary to improve the methods of testing for arsenic,
so that the quantity of poison could be detected with accuracy, even
when it was present in very minute amounts. Owing to its frequent
use in criminal cases very delicate tests for arsenic had been already
worked out, but these showed only its presence or absence, not how
much existed in the object tested; for further development therefore
Sanger adopted the best of these — the Berzelius-Marsh test— in
which the arsenic was detected by a stain (mirror) on a capillary tube;
and his improvement consisted in producing all mirrors under identical
conditions, when by comparing that from the object under examina-
tion with a set made from known weights of arsenic the quantity
could be determined with surprising accuracy. Armed with this
delicate quantitative method he studied the amount of arsenic in the
excreta of persons living in arsenical surroundings, and found that
this depended on the amount of exposure to the wall papers, curtains,
carpets, or other sources of the poison. In one case even the quantity
of arsenic obtained from one patient was half as great as that obtained
from another exposed to the same conditions twice as long each day.
Further, when the sources of the poison were removed, the arsenic
gradually disappeared from the excreta at the same rate as the morbid
symptoms vanished.

He was now ready to take part in the battle raging between the
two camps, into which chemists at that time were divided, one main-
taining that the connection between the morbid disturbances and an
arsenical environment was proved, the other with equal vigor asserting
that it was not. The frequent discussions of the question up to this
time had consisted of a lively fusillade of assumptions and theories
from both sides, which like a sham fight with blank cartridges had little
result except noise. Sanger’s thoroughly established facts therefore,
thrown into this wordy warfare like a volley of shot, swept opposition
from the field and converted to his views all, not too prejudiced to be
open to conviction.

This establishment of the connection between these obscure diseases
and arsenic was a service of great importance to the world as well as
to chemistry, since it gave the physician a means of secure diagnosis
and a certain cure for them; and further his results were used in an
important study of the general relation between nervous disorders
and chronic poisoning with small quantities of various agents.

It will be of interest next to consider how he had been fitted for this
triumph by inheritance and training. His taste for study came

directly from a line of scholarly ancestors, graduates of Harvard

CHARLES ROBERT SANGER. 815

College — his great grandfather Zedekiah Sanger, minister at Dux-
bury and South Bridgewater, Ralph Sanger his grandfather, the last
town minister of Dover, so eminent that he was remembered last
year by a celebration of the one hundredth anniversary of his ordina-
tion, and in the generation immediately preceding him from his father
George Partridge Sanger who was judge of the court of common pleas
and later United States District Attorney for Massachusetts, and from
an aunt, who kept a successful girls’ school in Boston, so that on this
side he inherited with these scholarly instincts a love of truth and the
judicial faculty for weighing evidence. On the other hand he undoubt-
edly owed his accuracy, his executive ability, his power of discipline,
and the neat orderliness so characteristic of him to the family of
Portsmouth sea captains from which he was descended through his
mother, Elizabeth Sherburne (Thompson) Sanger; while from both
sides he drew that faithfulness, which was his most prominent char-
acteristic.

It was to be expected from this family history that he should choose
the life of a student, but it is strange that he turned to chemistry rather
than to some branch of literary work. Perhaps the practical ability
inherited from his mother’s ancestors gave this direction to his energies.
However this may be, the call of science to him was irresistible, and
even when he entered Harvard College, his taste for chemistry was
strongly developed. I remember well the marked impression he pro-
duced on me in his first chemical recitation, and throughout his course
he was an eminent student in that subject, which occupied a large
part of his time.

On graduating in 1881 he began the higher study of chemistry, and
for the first time came into intimate relations with Professor H. B.
Hill, who was to have such a determining influence on his life; for,
although he passed the second year after his graduation (1882-1883)
in Europe studying at Munich, and at Bonn, where Professor An-
schiitz, struck by his ability, devoted special attention to him, and
thus became an important factor in his higher education, Hill was his
chemical father. During four of the five years, when he was growing
into a chemist, he shared Professor Hill’s private laboratory, working
the entire day in his company, and part of the time in the even closer
intercourse of a common research. Upon Hill therefore he modelled
his methods of research, and views of chemistry, and this was the
easier, since the two men naturally resembled each other as closely
as father and son in aims, mental habits, and ideals. This warm and
beautiful friendship was broken only by the death of the older man.

816 CHARLES ROBERT SANGER.

His work for the Ph. D. consisted of an investigation of substituted
pyromucic acids, but the research on arsenic, already described, soon
removed him from this field of pure organic chemistry cultivated so
successfully by his master. Continuing study in his chosen line,
after he had proved the reality of arsenical poisoning from wall papers,
he attacked a puzzling mystery, which had baffled all attempts to
penetrate it, but with this he proved less fortunate. The symptoms
of wall paper poison are divided into two classes, one consisting of
irritations of the mucous membrane obviously produced by arsenical
dust, the other appearing in far reaching disturbances of the nervous
system. Disorders of this latter class have been observed, when
poisonous dust was nearly excluded, since the arsenic was contained
in a glazed paper, or even, when its formation was impossible, because
the arsenical paper was covered by one or more free from arsenic, so
that in these cases the poisoning could have been due only to a gas;
but here was the mystery —all attempts to detect an arsenical gas had
failed (with two exceptions) whether in rooms with poisonous wall
papers, or in mixtures of arsenic with organic matter, which should be
even more efficient. During the earlier theoretical stage of the dis-
cussion those contending against the arsenical source of the nervous
disorders were fond of arguing, that if arsenical they could be due to a
gas only, as this gas could not be detected, it did not exist, and there-
fore the symptoms were not caused by arsenic. I think this is a fair
statement of this argument, which in spite of its want of logic carried
much weight, until Sanger destroyed it, by his discovery of arsenic
in the excreta. But, although he proved in this way the existence of
an arsenical gas, the puzzle still remained, as to what the gas was,
how it was formed, and why it escaped detection. To the study of this
problem he devoted a great deal of time, but, as he followed the
methods of his predecessors, he was no more successful than they,
and in spite of the most careful work did not succeed in detecting
a trace of an arsenical gas. The truth was a new line of attack was
needed, and this came from cryptogamic botany instead of chemistry,
when Gosio announced his discovery that an evil-smelling gas con-
taining arsenic was given off by three sorts of moulds growing in
contact with arsenic and organic matter. Sanger at once repeated
Gosio’s experiments with the only one of these moulds accessible to
him (mucor mucedo), but without success. Later however with a
specimen of the most efficient sort (penicillium brevicaule) sent him
by Gosio he succeeded in confirming the Italian’s results. This
important confirmation of the efficiency of moulds in the production

CHARLES ROBERT SANGER. Siz

of an arsenical gas was his last contribution to the study of poisoning
from wall papers, because he felt obliged to retire from the field in
order not to interfere with Gosio. This was certainly unfortunate,
since his earlier work justifies the conviction that he would have
solved this problem also, if he had not been compelled to relinquish
the study of it. As it is, the mystery remains; Biginelli has found,
it is true, that the gas formed by the moulds is an arsine, a substance
related to the alkaloids and therefore probably more poisonous than
most other compounds of arsenic, but it has not been shown how this,
or any other gas can be formed from wall papers, which only in excep-
tional cases are in situations moist enough to favor the growth of
moulds.

When in this way Sanger was shut out from the practical side of
this investigation, he turned his attention to the purely chemical side
of the work, extending his analytical method to the quantitative
determination of antimony; and later applying this system of deter-
mining the amounts of arsenic, or antimony to the method of Guth-
zeit, which in his hands became the most accurate and delicate method
known for such work, and even displaced his own earlier Berzelius-
Marsh process, admirable as that was. I think he considered this
the best piece of work that he did, but I must give the preference to
his work on arsenical poisoning from wall papers on account of its
great practical importance, and because in this connection he worked
out the general principle at the bottom of all these methods.

Two important papers, which occupied the last years of his life,
belong to a different line of work. His object here was to prepare the
silicon compound corresponding to phosgene, a well known derivative
of carbon; but a reaction, which should have led to it in view of the
strong resemblance between these elements, gave different products,
the identification of which, simple as it seems at first sight, required
an unusual amount of ingenuity, chemical insight, and skill in manipu-
lation. This research brought out the entirely unexpected fact, that
our knowledge of pyrosulphurylchloride and chlorsulphonic acid —
two compounds supposed to be thoroughly established — rested on an
inadequate experimental foundation, and in the first of these papers
accordingly he placed them on a secure basis with his usual faithful
accuracy. The skill in devising apparatus, and overcoming obstacles
shown in these papers adds to our regret, that he was not spared to
carry on other researches in this somewhat neglected field of inorganic
preparations.

Among the work he left unfinished was a much needed method for

SIS CHARLES ROBERT SANGER.

the quantitative determination of small amounts of fluorine, a beauti-
ful application of the general principle, that had proved so useful
in his work on arsenic. It is hoped that this (and some other papers)
can be brought into a state fit for publication, and, although shortly
before his death he told me it was far from ready, I feel sure that even
then it had been tested as carefully, as most chemists think necessary
for their work; and this leads me to speak of Sanger’s most marked
characteristic, admirable in itself, but developed to such an extent,
that it reduced the amount of his work very materially. This was an
accuracy and care truly phenomenal. Most chemists are satisfied,
when they have followed the work of their students closely, and tested
it at certain commanding points. A few think it necessary to repeat

all the work of their students, of these Hill was one, and in this single

respect I must feel his influence was unfortunate, as his precept and
example developed this side of Sanger’s character to such an excess,
that he was never willing to publish, until he had repeated the work
of his students not once but many times. This is the principal reason
why the list of his papers is short, and does no justice to the amount
of work he did, or to his chemical ability; but on the other hand the
wonderful accuracy of every published statement of his gives his work
unusual authority. Other reasons for the comparatively small
number of his papers are, that much of his time was taken up by
work in industrial chemistry, which could not be published, and still
more the almost over-faithful performance of his duties as teacher and
Director of the Laboratory. In this last capacity he was always
ready to sacrifice at the expense of his own investigations unlimited
time for the purpose of advancing the researches of his colleagues by
providing special apparatus, or material for them.

Apart from his chemical work Sanger’s life, like those of most scien-
tific men, was barren in striking events. He was born in Boston,
August 31, 1860, but early in his boyhood his father moved to Cam-
bridge, where he was fitted for college at the High School. He soon
became an important member of the Class of 1881 at Harvard, partly
because of his prominence in the societies, and as a member of his
class nine, still more because his warm affectionate nature endeared
him to his classmates, and enriched him with many lasting friendships.
In his senior year he was elected Class Secretary — the important
permanent officer of the class — and he met the duties of this office
with the same enthusiasm he showed in his chemical work, while his
characteristic methodical thoroughness and devotion made his work
a model for all class secretaries.

— ......

CHARLES ROBERT SANGER. $19

His first year after graduation was passed in study for the degree
of Master of Arts with Professor Hill, to whom he returned after his
year (1882-1883) in Europe. He took his degree of Doctor of Phil-
osophy in 1884, after which he served as Assistant in Chemistry in
Harvard College, until in 1886 he was appointed Professor of Chem-
istry at the United States Naval Academy at Annapolis, a post for
which he was especially fitted by nature, or perhaps rather by inheri-
tance. In 1892 he accepted the better position of Eliot Professor of
Chemistry at the Washington University of St. Louis.

In 1899 Professor Hill found the duties of Director of the Chemical
Laboratory of Harvard College so exacting, that he was forced to
give up the large elective in qualitative analysis (Chemistry 3) which
he had taught for many years. We considered this course, as devel-
oped by him, our most precious treasure, since it trained men in ob-
servation and inductive reasoning better than any other known to us,
but on the other hand, if improperly taught, it would sink to a mechani-
cal routine worthless for educational purposes. It became therefore
a matter of grave anxiety with us to find a successor for Professor Hill
in this course, who should be able to carry it on worthily; and after a
careful search of the whole field we decided that Sanger was by far
the best man, and accordingly he was called to Harvard University
as Assistant Professor of Chemistry in 1899; and in keeping the work
in qualitative analysis on its previous high level he more than justified
our faith in him.

As a teacher he was somewhat austere; all his students were ex-
pected to live fully up to his own standard, and he always retained
some touch of the naval discipline. In particular research with him
was no easy matter — the same accuracy, the same thoroughness, the
same limitless patience, that he showed in his own work, he demanded
of his students, but, as they saw he required nothing from them, which
he did not exact from himself in even greater measure, they worked
with enthusiasm, and felt for him an affection perhaps even deeper
and stronger, than would have been inspired by an easier teacher.

An additienal reason for his appointment at Cambridge had been
that he was excellently fitted to act as director of the laboratory,
should this become necessary. The death of Professor Hill in 1903
brought this necessity only too soon, and led to his appointment as
Director, and promotion to a full professorship. I have already
dwelt on the self-sacrificing devotion shown by him in this position.
In all other respects too he proved an ideal choice, wise, and prudent
in planning the work, methodical, thorough, and efficient in doing it.

820 CHARLES ROBERT SANGER.

At first it was hoped that he would take charge of the teaching of
industrial chemistry in Harvard University; and in 1902 he went
abroad for the summer semestre to fit himself better for this work.
There he studied at Dresden with Professor Hempel, but with little
result beyond a very pleasant and long continued friendship, for it
was found that the great labor involved in the directorship rendered
it impossible for anyone to give more than a single course in addition,
and in his case this could be no other than qualitative analysis. He
was not convinced of this impossibility however, until for several years
he had made a gallant effort to carry the industrial chemistry on ‘his
already overburdened shoulders.

His uncommon administrative ability made him very useful on
committees, especially in the Administrative Board of the Lawrence
Scientific School, of which he was one of the pillars, but this also
robbed him of much time, which would otherwise have been devoted
to research.

The care and thoroughness shown in his work appeared also in his
amusements, and made him an unusually skilful photographer and
successful gardener.

On December 21, 1886 he married Almira Starkweather Horswell,
who died January 6, 1905, leaving three children, Mary (married to
H. A. Bellows), Eleanor Sherburne and Richard. On May 2, 1910
he married Eleanor Whitney Davis, the daughter of Andrew Me
Farland Davis, who survives him.

He was a member of the German Chemical Society, the Society
for Chemical Industry, and the American Chemical Society (Vice-
president of the New England Section 1902-1903). He was elected
a fellow of our Academy, January 14, 1891; served on the C. M.
Warren Committee from 1904, until his death; and was Chairman
of the Publication Committee, that is editor of the Proceedings, from
1909 to 1910. His service in this last capacity showed his usual effi-
ciency. Its short duration was due to the fact that he was already
stricken with the disease, which led to his death, in fact the most
prominent symptom of this was his nervous eagerness to add new
undertakings to the load which already weighed him down, for in
addition to our Proceedings he took sole charge of raising money fora
new laboratory at Cambridge, and, when the American Chemical
Society met in Boston and Cambridge in 1909, he was most active
in arranging for its reception, and organized an interesting exhibit
of the chemical activities of Harvard College. This was the finishing
touch however, and at the end of that academic year he was so com-

CHARLES ROBERT SANGER. $21

pletely broken down that he was obliged to give up his regular work.
Then followed a weary chase after health. A journey to Europe
that summer did no good, nor was he more fortunate in the next winter
spent on leave of absence, or in the following summer. In the autumn
of 1911, although no better, he took up his teaching again, for his
physicians decided that, if work were forbidden, the longing for it
would do him more harm than the work itself. Accordingly he began
to lecture in spite of agonizing attacks of pain, giving us the spectacle
of duty triumphing over suffering, as before it had led him to disregard
his own ease and advantage; but this heroism was in vain, the attacks
grew more frequent, until in the middle of the year lecturing became
impossible; but even then, as before, he filled up every cranny of his
life with work on his papers feeling that rest was impossible, while
anything remained undone, until death found him working at his
post on February 25, 1912. The faithfulness, which had moulded
every action of his life, reached a fitting climax in the heroic devotion
to duty to its close.

ΘΙ. JAGKSoN.

Chemical Papers of C. R. Sanger.

Ueber die Einwirkung von salpetrigsauren Kali auf die Muco-
bromsdure. With Henry B. Hill. Ber. d. deutsch. chem. Gesell.,
15, 1906 (1882).

Brompyromucie Acids. With Henry B. Hill. Proc. Amer. Acad.,
21, 135 (1884).

Ueber substituirte Brenzschleimséuren. With Henry B. Hill.
Ann. Chem. Pharm., 232, 48. (1885).

The Quantitative Determination of Arsenic by the Berzelius-Marsh
Process, especially as applied to the Analysis of Wall Papers and
Fabrics. Proc. Amer. Acad., 26, 24 (1891). Amer. Chem. Journ.,
13, 431 (1891).

The Chemical Analysis of three Guns at the U. 5. Naval Academy
captured in Corea by Rear Admiral John Rodgers, U. S. N. Proce.
U.S. Naval Institute, 19, 53 (1892).

On the Formation of volatile Compounds of Arsenic from Arsenical
Wall Papers. Proc. Amer. Acad., 29, 112 (1894).

On Chronic Arsenical Poisoning from Wall Papers and Fabrics.
Ibid., 29, 148 (1894).

822 CHARLES ROBERT SANGER.

The Determination of Small Amounts of Antimony by the Berze-
lius-Marsh Process. With James Andrew Gibson. Jbid., 42. 717
(1907).

The Quantitative Determination of Arsenic by the Guthzeit Method.
With Otis Fisher Black. Jbid., 48, 295, (1907).

The Determination of Arsenic in Urine. With Otis Fisher Black.
Ibid., 43, 325 (1907).

The Quantitative Determination of Antimony by the Guthzeit
Method. With Emile Raymond Riegel. Jbid., 45, 19 (1909).

Pyrosulphuryl Chloride and Chlorsulphonic Acid. With Emile
Raymond Riegel. Jbid., 47, 671 (1912).

The Action of Sulphur Trioxide on Silicon Tetrachloride. With
Emile Raymond Riegel. Jbid., 48, 573 (1913).

Other Publications of C. R. Sanger. "

Logarithms of Numbers and Chemical Factors. Edited. Cambridge,
Mass. The editor, 1881; 5th Edition revised, Harvard University
Publication Office, 1901.

Laboratory Experiments in General Chemistry. St. Louis, Mo.,
The Author, 1896.

A Short Course of Experiments in General Chemistry with Notes
on Qualitative Analysis. St. Louis, Mo., The Author, 1896.

Notes in “ Chemistry 3” (qualitative analysis). Harvard University
Publication Office, 1901; 2nd edition. Jbid., 1903.

Henry Barker Hill, Memoir. Harv. Grad. Mag., 12, 43 (1903).

i ΘὍΝο =

American Academy of Arts and Sciences

OFFICERS AND COMMITTEES FOR 1913-14.
PRESIDENT.
Joun TROWBRIDGE.
VICE-PRESIDENTS.
Class I. Class II. Class III.
Evisu THomson, Henry P. Watcort, A. LAWRENCE LOWELL.
CORRESPONDING SECRETARY.
Epwin H. Hat.
RECCRDING SECRETARY.
Wiuuram WATSON.
TREASURER.
Cuartes P. Bowonrrcu.
LIBRARIAN.
Harry W. Tyter.
COUNCILLORS.

Class I. Class II. Class III.
Rosert W. WILSON. ReGinatp A. Daty, JoserH H. Bratz,
Terms expire 1914.

ARTHUR G. WEBSTER, Merritt L. FERNALD, GeorGcE F. Moore,
Terms expire 1915.

James F. Norris, GerorGE H. ParkKErR, FraNK W. Tavussic,
Terms expire 1916.

DesmMonp FirzGerRaLD, JOHN CoLurns WARREN, George L. KrrrrepGe.
Terms expire 1917.

COMMITTEE OF FINANCE.
JoHN TROWBRIDGE, GARDINER M. LANE, JOHN COLLINS WARREN,

RUMFORD COMMITTEE.

CuHarLEs R. Cross, Chairnam,
Erasmus D. Leavirt, Epwarp C. PIcKERING, Louris BELL,
ARTHUR G. WEBSTER, Ev.tnu THOMSON, ArtTHuR A. Noyes.

σι M. WARREN COMMITTEE.

Henry P. Tarsot, Chairman,
Wa tter L. JENNINGS, CuHarLEs L. JACKSON, Grecory P. Baxter,
ARTHUR A. NOYEs, James F. Norris, Wiui1am H. WALKER.

COMMITTEE OF PUBLICATION.
GrorGE W. Pierce, of Class I, Chairman,
Wa ter B. Cannon, of Class II, ALBERT A. Howarp, of Class III.
COMMITTEE ON THE LIBRARY.

Harry W. Tyier, Chairman,
Harry M. Goopwin, of Class I, SamuEL HensHaw, of Class II,
Wiiiam C. Lane, of Class III.

AUDITING COMMITTEE. 7
Euiot C. CLARKE, WoRTHINGTON C. Forp.
HOUSE COMMITTEE.

Louis Derr, Henry P. Tatsot, Chairman, Hammonp V. Haygs.

COMMITTEE ON MEETINGS.
THE PRESIDENT,
5 THE RecorDING SECRETARY,
Wituram M. Davis, WaLuace C. SaBINne, ARTHUR FAIRBANKS.

LIST
OF THE
FELLOWS AND FOREIGN HONORARY MEMBERS.

(Corrected to July 1, 1913.)

FELLOWS.— 366.

(Number limited to six hundred.)
Crass I.— Mathematical and Physical Sciences.— 148.

Section I.— Mathematics and Astronomy.— 34.

George Russell Agassiz
Solon Irving Bailey

Edward Emerson Barnard
George David Birkhoff .
Ernest William Brown .
Sherburne Wesley Burnham .
William Elwood Byerly

William Wallace Campbell . .

Seth Carlo Chandler .
Julian Lowell Coolidge
George Cary Comstock .
Fabian Franklin .

Edwin Brant Frost
George William Hill
Edward Singleton Holden

Edward Vermilye Huntington .

Percival Lowell

Emory McClintock

Joel Hastings Metcalf
Eliakim Hastings Moore
Edward Charles Pickering

Boston

; ; : . Cambridge

Williams Bay, Wis.
ὃ Cambridge

. New Haven, Ct.
Williams Bay, Wis.
Cambridge

Mt. ΠῚ σαὶ Cal.

Wellesley Hills
Cambridge
Madison, Wis.
New York

Williams Bay, Wis:

West Nyack, N. Y.
West Point, N. Y.
Cambridge

Boston

New York
Winchester

Chicago, Il.
Cambridge

826

William Henry Pickering .

Charles Lane Poor .
Arthur Searle . :
George Mary Searle
Vesto Melvin Slipher

John Nelson Stockwell . .

William Edward Story
Henry Taber .

Harry Walter Tyler . .
Robert Wheeler Willson
Edwin Bidwell Wilson

Frederick Shenstone Woods .

Paul Sebastian Yendell .

Section II.— Physics.— 44.

Joseph Sweetman Ames
Carl Barus oe
Louis Agricola Bauer
Alexander Graham Bell
Louis Bell’. .
Clarence John Blake
Percy Williams Bridgman
George Ashley Campbell

Harry Ellsworth Clifford .

Daniel Frost Comstock .
Henry Crew 2-2). .
Charles Robert Gere
Harvey Nathaniel Davis
Arthur Louis Day

Louis Derr . .
Alexander W ates Duff
Arthur Woolsey Ewell
Harry Manley Goodwin
George Ellery Hale
Edwin Herbert Hall

Hammond Vinton Hayes .

William Leslie Hooper
William White Jacques .
Norton Adams Kent
Frank Arthur Laws
Henry Lefavour .

FELLOWS.

Cambridge
New York

. . Cambridge
Berkeley, Cal.
Flagstaff, Ariz.
. Cleveland, O.
Worcester
Worcester
Boston
Cambridge
Cambridge
Newton
Dorchester

Baltimore, Md.
. Providence
Washington
Washington
Boston

Boston
Cambridge
New York
Newton
Boston
Evanston, Ill.
Brookline
Cambridge

j ‘Washington, DEG

Brookline
Worcester
Worcester
Brookline
Pasadena, Cal.
Cambridge
Cambridge
Somerville
Boston
Cambridge
Boston
Boston

FELLOWS.

Theodore Lyman ᾿ .
Richard Cockburn Riawelnirin é
Thomas Corwin Mendenhall
Albert Abraham Michelson .
Harry Wheeler Morse
Edward Leamington Nichols
Ernest Fox Nichols

Charles Ladd Norton
Benjamin Osgood Peirce
George Washington Pierce
Michael Idvorsky Pupin
Wallace Clement Sabine

John Stone Stone we
Maurice deKay Thompson
Elihu Thomson

John Trowbridge.

Arthur Gordon Webster
Robert Williams Wood .

Section III.— Chemistry.— 35.

Wilder Dwight Bancroft
Gregory Paul Baxter .
Bertram Borden Boltwood
William Crowell Bray
Russel Henry Chittenden .
Arthur Messinger Comey .
James Mason Crafts .
Charles William Eliot
Henry Fay ;
Frank Austin Gaoch .
Lawrence Joseph Henderson
Eugene Waldemar Hilgard
Charles Loring Jackson
Walter Louis Jennings
Gilbert Newton Lewis
Arthur Dehon Little.
Charles Frederic Mabery
Forris Jewett Moore .
George Dunning Moore
Edward Williams Morley .

Samuel Parsons Mulliken .

827

Brookline
Boston
Ravenna, O.
Chicago, Ill.
Cambridge
Ithaca, N. Y.
Hanover, N. H.
Boston
Cambridge
Cambridge
New York
Boston

Boston

Boston
Swampscott
Cambridge

: Worcester
ΒΑ ας Μα.

. Ithaca, N. Y.

: Cambridge
. New Haven, Ct.
. . Berkeley, Cal.

. New Haven, Ct.
Chester, Pa.

. Boston
Cambridge

. . Boston

oo Hav en, Ct.
Cambridge
Berkeley, Cal.
Cambridge

. . Worcester
Berkeley, Cal.
Brookline

. Cleveland, O.
Boston

W orcester

an West δ σι.

. Boston

$28

Charles Edward Munroe . .

John Ulric Nef
James Flack Norris

Arthur Amos Noyes .
William Albert Noyes

Ira Remsen . .

Robert Hallowell Richer te
Theodore William Richards .
Stephen Paschall Sharples
Francis Humphreys Storer
Henry Paul Talbot.
William Hultz Walker

Willis Rodney Whitney
Charles Hallet Wing .

FELLOWS.

es . 2. ae, Wieishmetons es
Chicago, Ill.
. Boston

. . Boston

<= sel Σ πιὰ Ill.

Baltimore, Md.

. Jamaica Plain

Cambridge

Cambridge

. Boston

Newton

anf Boston

: ἜΝ τι ΝΣ

. Boston

Secrion IV.— Technology and Engineering— 30.

Henry Larcom Abbot
Comfort Avery Adams .
William Herbert Bixby .
Alfred Edgar Burton . .
Eliot Channing Clarke .
Desmond FitzGerald .

John Ripley Freeman.
George Washington Goe thals
Ira Nelson Hollis
Frederick Remsen Hutton
Dugald Caleb Jackson
Lewis Jerome Johnson
Arthur Edwin Kennelly
Gaetano Lanza
Erasmus Darwin Leav itt ‘
William Roscoe Livermore
Lionel Simeon Marks
Hiram Francis Mills .
Alfred Noble

Cecil Hobart Peabocy
Harold Pender
Andrew Howland Ru ἘΠ
Albert Sauveur

Peter Schwamb

Henry Lloyd Smyth .

ot AS. 5 RS ΚΣ Ἦν Cambridge
τ Cambridge
Washington, D. C.
ae . Boston

. Boston

. Brookline
Providence, R. I.

. Culebra, Canal Zone
Cambridge

New York

. Boston
Cambridge
Cambridge
Philadelphia, Pa.
Cambridge

. Boston
Cambridge

. Lowell

New York

. Lrookline

Boston

. Plymouth
Cambridge
Arlington
Cambridge

FELLOWS.

Frederic Pike Stearns
Charles Proteus Steinmetz
George Fillmore Swain .
William Watson .
Robert Simpson Woodw ard .

829

Boston

Schenectady, Tas act

Cambridge
. Boston

Washington: Dit

Crass 11.-- Natural and Physiological Sciences.— 107.

Section I.— Geology, Mineralogy. and Physics of the Globe.— 28.

Cleveland Abbe .

Thomas Chrowder C Rarer alge
Henry Helm Clayton
Herdman Fitzgerald Cleland
William Otis Crosby . .
Reginald Aldworth Daly
Edward Salisbury Dana
Walter Gould Davis

William Morris Davis
Benjamin Kendall Emerson .
Grove Karl Gilbert. ;
Oliver Whipple Huntington .
Robert Tracy Jackson
Thomas Augustus Jaggar .
Douglas Wilson Johnson
Alfred Church Lane
Waldemar Lindgren

Charles Palache . .

John Elliott Pillsbury
Raphael Pumpelly

William Berryman Scott
Hervey Woodburn Shimer
Charles Richard Van Hise.
Charles Doolittle Walcott
Robert DeCourcy Ward
Charles Hyde Warren

John Eliot Wolff

Jay Backus Woodworth.

Section II.— Botany.— 21.

Oakes Ames ἊΨ
Liberty Hyde Bailey .

Washington, D. C.
Chicago, IIl.
Canton
Williamstown
Jamaica Plain
Cambridge

. New Haven, Ct.

. Cordova, Arg.
Cambridge
Amherst

Ww ἐπ ππ πο DAG:

Newport, R. I.
ate Cambridge
. Honolulu, H. I.

Cambridge
Cambridge

- Boston
Gambr idge

W: ashington, D. C.

Newport, R. I.
Princeton, N. J.
a)... . Boston
Sitadisom Wis.
Washington, D.C.
Cambridge
Auburndale
Cambridge
Cambridge

. North Easton
ithaca, N. Y.

§30 FELLOWS.

Douglas'Houghton Campbell ........ Stanford Univ., Cal.
Frank sinpley-Collins © i242 1.0.2.1 Sea Malden
Joun!Merlée‘Coulter -. «2 35h 8). ..‘: 2 4 SN ee Chicago
Kdward Murray East...) 20, 82... J. ul ee. ΟΣ Blam
Alexander William Evans’ = 5. . » Jey New Haven, Ct.
William Gilson Farlow ..... . . + Sie. 2 Gaim
Charles Edward Faxon. .... . .. sw... oC) ΡΠ ΠῚ
MenittsLyndonHermaldga. . . . .. . . . . . Cambridge
George Lincoln’ Goodale “2 =. *. 2 ππο- Cambridge
Robert Almernsibarperceeme i. 5)... % ss. ae . New York
ΠΟ ΒΟ Jack! “Sete vie. 2. τ ee Jamiaca Plain
Edward Charles Jeffrey ...... See Cambridge
Winthrop*John Vanleuven Osterhout . ... . . . . Cambridge
Benjamin EmcolnRobmson 2... . =. = » slew’. Cambridge
Charles:;Sprague Sargent > 2... . . 5 2: fi τον, | Brookline
Artie dbhiespaemmonr τ. oo. |. π΄ ee Cambridge
JohnwDonnelieamntlisne 3 τς aks 2. 2-2 πο Ee Baltimore
ΠΟΙ ΠΕ ΙΘΤΣ 6.0 eae Ὁ νον ον Cambridge
Willian ΠΟΙ σαν 20-5} ea Lee eee St Louis, Mo.
Section III.— Zoélogy and Physiology.— 31.
ΕΙΣ ΒΗΘ του js) A Pach τυ New York
Hrancimanospenedict...-% 22 4 3 eRe eee Boston
ἘΠΕ τ θεν ἀπ Bigelow) 22 2. a ἀν . 4, π᾿ Οὐποῦτα
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Miter bradiord Cannon, . 4) 5°02 4.tNke & ie --". Cambridge
Wilhtianreiimest Castles.) 2 8 he Sly . . . Cambridge
Samuel Pessenden Clarke 4.3... ..% 4). 2 Re Williamstown
Wilham’Phomas Couneilman’:. . . . 2) .. ΠΕ τ Boston
Willianiviealey Dall... ogo. « . 1.) 20 4) Washington ere:
Charles Benedict Davenport. . . . . . Cold Spring Harbor, N. Y.
Otto απ Rolinvtee a 24). on. Ge ae . . Brookline
Samuel Henshaw. .... . ει σοι ς Cambridge
Leland’ @ssiam Howard <4 2... . . se Washington, DG:
CharlessAgwood Kofoid 3.7. cee 2)... πὴ Berkeley, Cal.
Resnldinggeme Mall.) ~. m2 2s ea, sek eae Baltimore, Md.
ἘΠ ΘΠ ἀπο Mark... a6 .elseeeeas. cee ee Cambridge
Charles Sedgwick Mianot:...s)-. 5). sae το ea
Silas«WeiraMingelbell | <°" 0" a0 cs, nn meee se Philadelphia, Pa.
Kowardisylvester Morse. <i ..0<..0 Meee ee) τ Salem

Henry Fairfield Osborm.):.. (ee. Fae New York

FELLOWS. 831

Geéorve Howard Parker. ........ . . «te © 4, Cambridge
ΠΕ Ὁ] ΘΙ ΟΠ ΕΠ πο... i) 4 .°. . . Sie SR. Bostan
Plerhnert Wuour Wend) 2G). «ipo. . ἈΠ
Walliam: Pmerson Rittee . 9. 5... ὍΠΕΡ eee ollie, Cal.
Witham. Thompson sedgwick . ......:. 2%...) Bosten
ΠΟ PAVED Go) αι. Ske τ΄. τ΄ . Lancaster
medion Pamory ΟΡ. 2.4 ff eee sw. alt Cer Haven, Ct.
Meme Miorton Wheeler \y 2 cee... vs. «+ a oo eee ΡΌΒΙΟΝ
Mumes rare Vyinite—y Sete se cis) sb ed ee
Barris Hawthorne Wilder . ....... .... . . s, ».Northampton
Edmund, beechner Wilson. ὦ. Πρ ik 8. «we 4 ne a Weg Yom

Secrion IV.— Medicine and Surgery.— 27.

Baweriicklnge bradford... 00. τ We a.) Boston
Men nsanry Christian: 2.) το τὰ ey 2 oo ΒΟΒΙΘΝ
Derpiciebatin asa 3. he bea ta eA . 2 Boston
MarciavGlarence Ernest) ..-: a0. re She ταν. iy amaica Plain
ΕἸ ΕΙΠΕ ΡΘΕ ΕΙΣ ὐπὸ. Ποὺ ede. ios
Simon Flexner. . «Rte se a, ie 2 On, SNe wr orks
William Stewart Halsted * wets wt! 2 eee LBaltimorxe, ‘Midt
ΠΠΡΉ ΠΗ ΤΩ ΠΉΘΟΡΙΗ,. F-test Su.) Se dn. Gd 8 ee es ΝΟ York
lobe roctor JOsmy τ eG a kK . . Boston
MalhanyVWVitisms: Keen. τ. τ. Ὁ π΄ Sew ὦ ΤΥ ΤῊΝ Pay
Heanor Mallory: . . .. 4: 2. . ΟΝ eiBrookline
emmuceonson Mixters ... 2/4. 6 os ss. 22) πῸ Boston
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Sreyviupamlsleness se ie A ee co el ee ΠΟ
Theophil Mitchell ΕΠ ἢ it ἘΣ ae ee a as ὦ ΟΝ ον core
Chaves: Fickenng Putnam... ς΄. .. πον ΒΒ ο οη
Wilhantw Lambert Richardson . .. τοὖἢ οὐ ὸοέυν τ Boston
Mataiwosepe.nosena 2.. ss 6... < i) eee. Boston
EEO Scr 2 ih 2h i ee Teraaica Plain
Per Prnest.pouthard . 0s... .-. os. ΠῚ Boston
Henry bickering’ Waleott . . . . .... .. 42. > Cambridge
ere oars artes eke hy ler νὸς ls Cake . . Boston
Wratarmienmy ΘΙ... . . . . . wu wae. alimore: Md.
Prange Henmyowiltams..7 . ......22 % 8%. . . Boston
PRCOUnrowenaCcn £5... . ὁ τ οὖς Boston
ETO αν νοῦ “΄.. . . τὸν τος Pp milnde Iphia, Pa.

PieeIGHIGn VEMIENt τ". .. 4 τὸν, we Pee i. ἀπ Boston

Crass III.— Moral and Political Sciences.— 116.

Section I.— Theology, Philosophy and Jurisprudence.— 29.

Simeon Eben Baldwin
Joseph Henry Beale

Melville Madison Bigelow

Joseph Hodges Choate .
Frederic Dodge
Timothy Dwight
William Wallace Fenn
Frederick Perry Fish
John Chipman Gray .

Marcus Perrin Knowlton .

William Lawrence
George Vasmer Leverett
Edward Caldwell Moore
Hugo Miinsterberg
George Herbert Palmer
Charles Sanders Peirce .
George Wharton Pepper
Roscoe Pound . ae
Elihu Root .

James Hardy apes
Josiah Royce
Arthur Prentice Roce

Henry Newton Sheldon .

Moorfield Storey .

Ezra Ripley Thayer
William Jewett Tucker .
Williston Walker
Samuel Williston
Woodrow Wilson.

New Haven, Ct.
Cambridge

. Cambridge
New York
Belmont

New Haven, Ct.

Cambridge

. Brookline
Boston
Springfield

. Boston

. Boston
Cambridge
Cambridge

. Cambridge
. Milford, Pa.

Philadelphia, pat

Belmont
New York
Cambridge
Cambridge
Worcester
Boston
Boston

. Boston

“Hanov rer, N. H.

New Haven, Ct.
Belmont

Banestou Nea.

Section II.— Philology and Archeology.— 32.

Franz Boas .

Charles εκ Baw ΤΩΝ ͵

Franklin Carter .
George Henry Chase .
Roland Burrage Dixon .

New York
Jamaica Plain
. Williamstown

Cambridge

Cambridge

FELLOWS.

William Curtis Farabee
Jesse Walter Fewkes

Basil Lanneau Gildersleeve
Charles Hall Grandgent
Charles Burton Gulick
William Arthur Heidel
Albert Andrew Howard
James Richard Jewett
Alfred Louis Kroeber
Charles Rockwell Lanman
Thomas Raynesford Lounsbury
David Gordon Lyon
Clifford Herschel Moore
George Foot Moore

Hanns Oecertel

Charles Pomeroy Parker
Frederick Ward Putnam
Edward Kennard Rand
Edward Robinson

Fred Norris Robinson
Edward Stevens Sheldon
Herbert Weir Smyth .
Franklin Bache Stephenson .
Charles Cutler Torrey
Alfred Marston Tozzer .
Andrew Dickson White
John Williams White

$33

, Cambridge
Wakbineton DAG
. Baltimore, Md.
Cambridge
Cambridge
Middletown, Ct.
Cambridge
Cambridge
Berkeley, Cal.
Cambridge
New Haven, Ct.
Cambridge
Cambridge
Cambridge
New Haven, Ct.
Cambridge
Cambridge
Cambridge
New York
Cambridge
Cambridge
Cambridge
Pittsfield
. New Haven, Ct.
Cambridge
Ithaca, N. Y.

Cambridge

Section III.— Political Economy and History.— 25

Charles Francis Adams .
Henry Adams. .

Charles Jesse Shiba
Thomas Nixon Carver
Edward Channing .
Archibald Cary Coolidge
Andrew McFarland Davis.
Davis Rich Dewey

Ephraim Emerton .

Irving Fisher
Worthington C 1: Ford

Lincoln
"Washington, Dies
‘ambridge
‘ambridge
Sambridge

. Boston
‘ambridge
‘ambridge
Cambridge
New Haven, Ct.

. Boston

ree a ορ

834

Edwin Francis Gay
Abner Cheney Goodell
Arthur Twining Hadley
Henry Cabot Lodge

Abbott Lawrence Lowell . ..

Alfred Thayer Mahan
William Bennett Munro
James Ford Rhodes.

William Mulligan Sloane

Charles Card Smith
Henry Morse Stephens
Frank William Taussig

Frederick Jackson Turner
Thomas Franklin Waters

FELLOWS.

Cambridge
Salem
New Haven, Ct.
. soho) Nahant
Cambridge
New York
. . Cambridge
Boston
New York

Boston
Berkeley, Cal.
Cambridge
. . Cambridge
Ipswich

. . . .

Section LV.— Literature and the Fine Arts.— 30.

James Burrell Angell
Francis Bartlett
Arlo Bates

William Sturgis Bigelow
Le Baron Russell Briggs
George Whitefield Chadwick
Samuel McChord Crothers

Wilberforce Eames
Henry Herbert Edes
Arthur Fairbanks
Arthur Foote
Kuno Francke ;
Daniel Chester French
Robert Grant.

Henry Lee Higginson

Mark Antony DeWolfe Hone
George Lyman Kittredge. . . .
Gardiner Martin Lane .

William Coolidge Lane
Albert Matthews. . .
Okakura-Kakuzo.

Robert Swain Peabody . .

Bela Lyon Pratt . .

Herbert Putnam

Oh a. Oh peg) ed las Vege ΡΜ αν κὸν sa

Cambridge
Boston
Cambridge
New York
Cambridge
Cambridge
Brookline
. . Cambridge
. Stockbridge
hols, oh COS TORE
. Boston

. Boston
Cambridge
. Boston
Cambridge
. Boston

. Boston

. Boston

. Boston

Ww ΤΡ ΗΝ DG:

FELLOWS. 835

Penman Valco Ross... . ... cs... . . τ δ΄. Cambridge
Jobmecmper sargent .);.. .° 9. . . = - ms. » , London, Eng.
Ryamigra ener WERE fo. ee... ey gas wen ee OM
Herbert Langford Warren .......... ... . Cambridge
Barrett Wendell . . . ee. 5 Sy ee Ce

George Edward Waodheny ΡΥ. OR ee Severs

836

Svante August Arrhenius . Stockholm
Arthur Auwers Berlin
Sir David Gill . . London
Felix Klein . Gottingen
Emile Picard . Paris.
Section II.— Physics.— 6.
Oliver Heaviside Torquay
Sir Joseph Larmor . Cambridge
Hendrik Antoon Lorentz . . Leyden
Augusto Righi . . Bologna
John William Strutt, Baron Rayleigh Witham
Sir Joseph John Thomson Cambridge
Section III.— Chemistry.— 4.
Adolf, Ritter von Baeyer . Munich
Emil Fischer. ay Berlin
Wilhelm Ostwald A . Leipsic
Sir Henry Enfield Roscoe . London
Section IV.— Technology and Engineering.— 2.
Heinrich Miiller-Breslau Berlin
William Cawthorne Unwin London

FOREIGN HONORARY MEMBERS.

FOREIGN HONORARY MEMBERS.— 54.

(Number limited to seventy-five).

Crass I.— Mathematical and Physical Sciences.— 17.

Section I.— Mathematics and Astronomy.— 5.

FOREIGN HONORARY MEMBERS.

837

Crass II.— Natural and Physiological Sciences.— 17.

Section I.— Geology, Mineralogy, and Physics of the Globe.— 4.

Sir Archibald Geikie
Julius Hann

Albert Heim.

Sir John Murray

Section II.— Botany.— 3.

Adolf Engler . .
Wilhelm, Pfefier .

Hermann, Graf zu Gomis latabach Ὰ

Section III.— Ζοδίοσῃ and Physiology.— 5.

Ludimar Hermann .

Hugo Kronecker _ . :
Sir Edwin Ray ἔπ Ε
Elie Metchnikoff

Magnus Gustav Retzius

Section IV.— Medicine and Surgery.— 5.

Emil von Behring :

Sir Thomas Lauder Brunton, Bari
Angelo Celli
Sir Victor Alexander Haden Horsley
Adam Politzer

Crass III.— Moral and Political Sciences.—

. Haslemere, Surrey

. Vienna
Zurich
{dinburgh

Berlin
. Leipsie
Strassburg

. K6nigsberg

. Bern

. London

. Paris
Stockholm

. Marburg
London
Rome
London

. Vienna

20.

Section I.— Theology, Philosophy and Jurisprudence.— 4.

Arthur James Balfour
Heinrich Brunner

Albert Venn Dicey . .
Sir Frederick Pollock, Bart

. Prestonkirk

Berlin
. Oxford
London

838 FOREIGN HONORARY MEMBERS.

Section II.— Philology and Archeology.— 8.

Ingram Bywater. προ oy 4 een) ee eonden
Hriednch! Delitzsch . eaeae. 6. 2 τ
Hermann Diels * > 9s: Sees τ 5) ey ert
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Sir Gaston Camille Charles Maspero Soca orig ee ees wee Reet
ΠΣ ΠΕ ἄορ ΠΡ (Geers a «τ erlign

Section [11Π].--- Political Economy and History.— 5.

James-DIVice Vamenta gS RS ΕΝ ΝΥ ΡΤ τ
Adolf Harnack. . . MTL hohe, ae a ee
John Morley, “Hagens ΔΙ τευ πὶ ΕΠ ΤΠ] τ τ onder
sir ‘George Otto Trevelyan; Bart..: .. . +. . «4 ) 2 Londen
Pasquale*Villant 2c )a.06 oe 4 2 Ae ee 2 ee ailorenne

Section LV.— Literature and the Fine Aris.—3.

Georg Brandes. . . . » 2 we 2 eo. Copenharen
Jean Adrien Aubin Tales J Hessen Ue Fre Lil) C84 ee ie Spe rete
fvudyard ‘Kipling: <0!) af) APT ee Poe hy ον ΡΤ

STATUTES AND STANDING VOTES

STATUTES

Adopted November 8, 1911: amended May 8, 1912, January 8, and
May 14, 1913

CHAPTER ri
THE CORPORATE SEAL

ARTICLE 1. The Corporate Seal of the Academy shall be as here

depicted:
~<i1UM_ET
SG RTATE Ss
DEGERTATE FPSO
Sav
NK

MDCCLXXxX.
aL TTOTETTT

ARTICLE 2. The Recording Secretary shall have the custody of the
Corporate Seal.

See Chap. v. art. 3; chap. vi. art. 2.

840 STATUTES OF THE AMERICAN ACADEMY ©

CHAPTER II

FELLOWS AND ForerGN Honorary MEMBERS AND DUES

ArTICLE 1. The Academy consists of Fellows, who are either
citizens or residents of the United States of America, and Foreign
Honorary Members. They are arranged in three Classes, according to
the Arts and Sciences in which they are severally proficient, and each
Class is divided into four Sections, namely:

Cuass I. The Mathematical and Physical Sciences
Section 1. Mathematics and Astronomy
Section 2. Physics
Section 3. Chemistry
Section 4. Technology and Engineering

Cuass II. The Natural and Physiological Sciences
Section 1. Geology, Mineralogy, and Physies of the Globe
Section 2. Botany
Section 9. Zodlogy and Physiology
Section 4. Medicine and Surgery

Cuass III. The Moral and Political Sciences
Section 1. Theology, Philosophy, and Jurisprudence
Section 2. Philology and Archaeology
Section 3. Political Economy and History
Section 4. Literature and the Fine Arts

ARTICLE 2. The number of Fellows shall not exceed Six hundred,
of whom not more than Four hundred shall be residents of Massachu-
setts, nor shall there be more than Two hundred in any one Class.

ArtTIcLE 3. The number of Foreign Honorary Members shall not
exceed Seventy-five. They shall be chosen from among citizens of
foreign countries most eminent for their discoveries and attainments
in any of the Classes above enumerated. There shall not be more
than Twenty-five in any one Class.

ArticLte 4. If any person, after being notified of his election as
Fellow, shall neglect for two months to accept in writing and to pay
his Admission Fee (unless he be at that time absent from the Common-
wealth) his election shall be void; and if any Fellow resident within
fifty miles of Boston shall neglect to pay his Annual Dues for twelve
months after they are due, provided his attention shall have been

OF ARTS AND SCIENCES. S41

called to this Article of the Statutes in the meantime, he shall cease to
be a Fellow; but the Council may suspend the provisions of this
Article for a reasonable time.

With the previous consent of the Council, the Treasurer may dis-
pense (sub silentio) with the payment of the Admission Fee or of the
Annual Dues or both whenever he shall deem it advisable. In the case
of officers of the Army or Navy who are out of the Commonwealth on
duty, payment of the Annual Dues may be waived during such absence
if continued during the whole financial year and if notification of such
expected absence be sent to the Treasurer. Upon similar notification
to the Treasurer, similar exemption may be accorded to Fellows sub-
ject to Annual Dues, who may temporarily remove their residence for
at least two years to a place more than fifty miles from Boston.

If any person elected a Foreign Honorary Member shall neglect for
six months after being notified of his election to accept in writing,
his election shall be void.

See Chap. vii art. 2.

ARTICLE 5. Every Fellow hereafter elected shall pay an Admission
Fee of Ten dollars.

Eyery Fellow resident within fifty miles of Boston shall, and others
may, pay such Annual Dues, not exceeding Fifteen dollars, as shall
be voted by the Academy at each Annual Meeting, when they shall
become due; but any Fellow shall be exempt from the annual pay-
ment if, at any time after his admission, he shall pay into the treas-
ury Two hundred dollars in addition to his previous payments.

All Commutations of the Annual Dues shall be and remain perma-
nently funded, the interest only to be used for current expenses.

Any Fellow not previously subject to Annual Dues who takes up his
residence within fifty miles of Boston, shall pay to the Treasurer within
three months thereafter Annual Dues for the current year, failing which
his Fellowship shall cease; but the Council may suspend the provi-
sions of this Article for a reasonable time.

Only Fellows who pay Annual Dues or have commuted them may
hold office in the Academy or serve on the Standing Committees or
vote at meetings. .

ARTICLE 6. Fellows who pay or have commuted the Annual Dues
and Foreign Honorary Members shall be entitled to receive gratis one
copy of all Publications of the Academy issued after their election.

See Chap. x. art. 2.

842 STATUTES OF THE AMERICAN ACADEMY.

ARTICLE 7. Diplomas signed by the President and the Vice-
President of the Class to which the member belongs, and countersigned
by the Secretaries, shall be given to all the Fellows and Foreign
Honorary Members.

ARTICLE 8. Τῇ, in the opinion of a majority of the entire Council,
any Fellow or Foreign Honorary Member shall have rendered himself
unworthy of a place in the Academy, the Council shall recommend to
the Academy the termination of his membership; and if three fourths
of the Fellows present, out of a total attendance of not less than fifty,
at a Stated Meeting, or at a Special Meeting called for the purpose,
shall adopt this reeommendation, his name shall be stricken from the
Roll.

i See Chap. 1{| 7 chap: vi. art. 15 chap. 1x. art. 1, ΠΣ chap: x. art. 2.

CHAPTER III
ELECTION OF FELLOWS AND ForEIGN Honorary MEMBERS

ARTICLE 1. Elections of Fellows and Foreign Honorary Members
shall be by ballot, and only at the Stated Meetings in January and
May. Three fourths of the ballots cast, and not less than twenty,
must be affirmative to effect an election.

ARTICLE 2. Candidates must be proposed in writing by two
Fellows of the Section for which the proposal is made. These signed
nominations shall be sent to the Corresponding Secretary and shall be
retained by him until the fifteenth of the following October or Febru-
ary, as the case may be, when all nominations then in his hands shall
be immediately sent in printed form to every Fellow having the right
to vote, with the names of the proposers in each case, and with a
request to send to the Corresponding Secretary written comments on
these names not later than the fifth of November or the fifth of March
respectively.

All the signed nominations, with the comments thereon, received up
to the fifth of November or the fifth of March shall be sent at once to
the appropriate Class Committees, which shall report their decisions
to the Council at a special meeting to be called to consider nom-
inations, not later than two days before the meeting of the Academy in
December and April respectively.

ARTICLE 3. All nominations approved by the Council shall be read
to the Academy at a meeting in December or in April, or be sent to the

OF ARTS AND SCIENCES. 843

Fellows in print with the official notice of the meeting, and shall then
be posted in the Hall of the Academy until the balloting.

Not later than two weeks after any nomination is reported to the
Academy, the Corresponding Secretary shall send to every Fellow hav-
ing the right to vote a brief printed account of the nominee.

See Chap. ii.; chap. vi. art. 1; chap. ix. art. 1.

CHAPTER: IV
OFFICERS

ArticLe 1. The Officers of the Academy shall be a President (who
shall be Chairman of the Council), three Vice-Presidents (one from
each Class), a Corresponding Secretary (who shall be Secretary of the
Council), a Recording Secretary, a Treasurer, and a Librarian, all of
whom shall be elected by ballot at the Annual Meeting, and shall hold
their respective offices for one year, and until others are duly chosen
and installed.

There shall be also twelve Councillors, one from each Section of each
Class. At the Annual Meeting in 1912 three Councillors, one from
each Class, shall be elected by ballot to serve for one year, three for
two years, three for three years, and three for four years. At each
subsequent Annual Meeting three Councillors, one from each Class,
shall be elected by ballot to serve for the full term of four years and
until others are duly chosen and installed. The same Fellow shall
not be eligible for two successive terms.

The Councillors, with the other officers previously named, and the
Chairman of the House Committee, ex officio, shall constitute the
Council.

See Chap. x. art. 1.

ArTIcLE 2. If any office shall become vacant during the year, the
vacancy may be filled by the Council in its discretion for the unexpired
term.

ARTICLE 3. At the Stated Meeting in March, the President shall
appoint a Nominating Committee of three Fellows having the right
to vote, one from each Class. This Committee shall prepare a list of
nominees for the several offices to be filled, and for the Standing Com-
mittees, and cause it to be sent to the Recording Secretary not later
than four weeks before the Annual Meeting.

844 STATUTES OF THE AMERICAN ACADEMY

ArticLE 4. Independent nominations for any office, if signed by
at least twenty Fellows having the right to vote, and received by the
Recording Secretary not less than ten days before the Annual Meet-
ing, shall be inserted, together with the list of nominees prepared by
the Nominating Committee, in the call therefor, and shall be mailed
to all the Fellows.

See Chap. vi. art. 2.

ArticLte 5. The Recording Secretary shall prepare for use in
voting at the Annual Meeting a ballot containing the names of all
persons duly nominated for office.

CHAPTER V

THe PRESIDENT

ArtIcLE 1. The President, or in his absence the senior Vice-Presi-
dent present (seniority to be determined by length of continuous
fellowship in the Academy), shall preside at all meetings of the Acad-
emy. In the absence of all these officers, a Chairman of the meeting
shall be chosen by ballot.

ArticLE 2. Unless otherwise ordered, all Committees which are

ae

not elected by ballot shall be appointed by the presiding officer.

Articite 3. Any deed or writing to which the Corporate Seal is to
be affixed, except leases of real estate, shall be executed in the name of
the Academy by the President or, in the event of his death, absence, or
inability, by one of the Vice-Presidents, when thereto duly authorized.

See Chap. ii. art. 7; chap. iv. art. 1, 3; chap. vi. art. 2; chap. vil.
art. 1; chap. ix. art.6; chap. x. art. 1; 2; chap. ΧΙ. art. 1.

CHAPTER Vi
THE SECRETARIES

ArticLe 1. The Corresponding Secretary shall conduct the corre-
spondence of the Academy and of the Council, recording or making an
entry of all letters written in its name, and preserving for the files all
official papers which may be received. At each meeting of the C ouncil
he shall present the communications addressed to the Academy which

OF ARTS AND SCIENCES. 845

have been received since the previous meeting, and at the next meeting
of the Academy he shall present such as the Council may determine.
He shall notify all persons who may be elected Fellows or Foreign
Honorary Members, send to each a copy of the Statutes, and on their
acceptance issue the proper Diploma. He shall also notify all meet-
ings of the Council; and in case of the death, absence, or inability of
the Recording Secretary he shall notify all meetings of the Academy.
Under the direction of the Council, he shall keep a List of the
Fellows and Foreign Honorary Members, arranged in their several
Classes and Sections. It shall be printed annually and issued as of the
first day of July.
See Chap. ii. art. 7; chap. iii. art. 2,3; chap. iv. art. 1; chap. ix. art. 6;
chap. x. art. 1; chap. xi. art. 1.

ArTICLE 2. The Recording Secretary ghall have the custody of the
Charter, Corporate Seal, Archives, Statute-Book, Journals, and all
literary papers belonging to the Academy.

Fellows borrowing such papers or documents shall receipt for them
to their custodian.

The Recording Secretary shall attend the meetings of the Academy
and keep a faithful record of the proceedings with the names of the
Fellows present; and after each meeting is duly opened, he shall read
the record of the preceding meeting.

He shall notify the meetings of the Academy to each Fellow by mail
at least seven days beforehand, and in his discretion may also cause
the meetings to be advertised; he shall apprise Officers and Commit-
tees of their election or appointment, and inform the Treasurer of
appropriations of money voted by the Academy.

He shall post in the Hall a list of the persons nominated for election
into the Academy; and after all elections, he shall insert in the Rec-
ords the names of the Fellows by whom the successful candidates were
nominated.

In the absence of the President and of the Vice-Presidents he shall,
if present, call the meeting to order, and preside until a Chairman is
chosen.

See Chap. i.; chap. ii. art. 7; chap. iv. art. 3, 4, 5; chap. ix. art. 6;
chap. x. art. 1, 2; chap. xi. art. 1, 3.

ARTICLE 3. The Secretaries, with the Chairman of the Committee
of Publication, shall have authority to publish such of the records of
the meetings of the Academy as may seem to them likely to promote
its interests.

846 STATUTES OF THE AMERICAN ACADEMY

CHAPTER VII

THE TREASURER AND THE TREASURY

ΔΈΤΙΟΙΕ 1. The Treasurer shall collect all money due or payable to
the Academy, and all gifts and bequests made to it. He shall pay all
bills due by the Academy, when approved by the proper officers, except
those of the Treasurer’s office, which may be paid without such ap-
proval; in the name of the Academy he shall sign all leases of real
estate; and, with the written consent of a member of the Committee
on Finance, he shall make all transfers of stocks, bonds, and other
securities belonging to the Academy, all of which shall be in his official
custody.

He shall keep a faithful gecount of all receipts and expenditures,
submit his accounts annually to the Auditing Committee, and render
them at the expiration of his term of office, or whenever required to
do so by the Academy or the Council.

He shall keep separate accounts of the income of the Rumford Fund,
and of all other special Funds, and of the appropriation thereof, and
render them annually.

His accounts shall always be open to the inspection of the Council.

ARTICLE 2. He shall report annually to the Council at its March
meeting on the expected income of the various Funds and from all
other sources during the ensuing financial year. He shall also report
the names of all Fellows who may be then delinquent in the payment
of their Annual Dues.

ARTICLE 3. He shall give such security for the trust reposed in him
as the Academy may require.

ARTICLE 4. With the approval of a majority of the Committee on
Finance, he may appoint an Assistant Treasurer to perform his du-
ties, for whose acts, as such assistant, he shall be responsible; or, with
like approval and responsibility, he may employ any Trust Company
doing business in Boston as his agent for the same purpose, the com-
pensation of such Assistant Treasurer or agent to be fixed by the
Committee on Finance and paid from the funds of the Academy.

ArticLte 5. At the Annual Meeting he shall report in print all his
official doings for the preceding year, stating the amount and condition

OF ARTS AND SCIENCES. 847

of all the property of the Academy entrusted to him, and the character
of the investments.

ArticLeE 6. The Financial Year of the Academy shall begin with
the first day of April.

ArtTIcLE 7. No person or committee shall incur any debt or
liability in the name of the Academy, unless in accordance with a
previous vote and appropriation therefor by the Academy or the
Council, or sell or otherwise dispose of any property of the Academy,
except cash or invested funds, without the previous consent and ap-
proval of the Council.

See Chap. ii. art. 4, 5; chap. vi. art. 2; chap. ix. art. 6; chap. x. art.
}, 2; 32 chap. xi. art. 1.

CHAPTER VIII
Tue LIBRARIAN AND THE LIBRARY

ArticLE 1. The Librarian shall have charge of the printed books,
keep a correct catalogue thereof, and provide for their delivery from
the Library.

At the Annual Meeting, as Chairman of the Committee on the Li-
brary, he shall make a Report on its condition.

ARTICLE 2. In conjunction with the Committee on the Library he
shall have authority to expend such sums as may be appropriated by
the Academy for the purchase of books, periodicals, ete., and for de-
fraying other necessary expenses connected with the Library.

ArTICLE 3. All books procured from the income of the Rumford
Fund or of other special Funds shall contain a book-plate expressing
the fact.

ArTICLE 4. Books taken from the Library shall be receipted for to
the Librarian or his assistant.

ArticLe 5. Books shall be returned in good order, regard being had
to necessary wear with good usage. If any book shall be lost or
injured, the Fellow to whom it stands charged shall replace it by a new
volume or by a new set, if it belongs to a set, or pay the current price
thereof to the Librarian, whereupon the remainder of the set, if any,

848 STATUTES OF THE AMERICAN ACADEMY

shall be delivered to the Fellow so paying, unless such remainder be
valuable by reason of association.

ARTICLE 6. All books shall be returned to the Library for examina-
tion at least one week before the Annual Meeting.

ArTICcLE 7. The Librarian shall have the custody of the Publica-
tions of the Academy. With the advice and consent of the President,
he may effect exchanges with other associations.

See Chap. 11. art. 6; chap. x. art. 1, 2.

CHAPTER IX
THE CoUNCIL

ARTICLE 1. The Council shall exercise a discreet supervision over
all nominations and elections to membership, and in general supervise
all the affairs of the Academy not explicitly reserved to the Academy
as a whole or entrusted by it or by the Statutes to standing or special
committees.

It shall consider all nominations duly sent to it by any Class Com-
mittee, and present to the Academy for action such of these nomina-
tions as it may approve by a majority vote of the members present
at a meeting, of whom not less than seven shall have voted in the
affirmative.

With the consent of the Fellow interested, it shall have power to
make transfers between the several Sections of the same Class, report-
ing its action to the Academy.

See Chap. iii. art. 2, 3; chap. x. art. 1.
ARTICLE 2. Seven members shall constitute a quorum.

ARTICLE 8. It shall establish rules and regulations for the transac-
tion of its business, and provide all printed and engraved blanks and
books of record.

ἈΈΤΙΟΙΕ 4. It shall act upon all resignations of officers, and all
resignations and forfeitures of fellowship; and cause the Statutes to
be faithfully executed. |

It shall appoint all agents and subordinates not otherwise provided
for by the Statutes, prescribe their duties, and fix their compensation.

OF ARTS AND SCIENCES. S49

They shall hold their respective positions during the pleasure of the
Council.

ArtTIcLE 5. It may appoint, for terms not exceeding one year, and
prescribe the functions of, such committees of its number, or of the
Fellows of the Academy, as it may deem expedient, to facilitate the
administration of the affairs of the Academy or to promote its interests.

ArticLe 6. At its March meeting it shall receive reports from the
President, the Secretaries, the Treasurer, and the Standing Commit-
tees, on the appropriations severally needed for the ensuing financial
year. At the same meeting the Treasurer shall report on the expected
income of the various Funds and from all other sources during the
same year.

A report from the Council shall be submitted to the Academy, for
action, at the March meeting, recommending the appropriation which
in the opinion of the Council should be made.

On the recommendation of the Council, special appropriations may
be made at any Stated Meeting of the Academy, or at a Special Meet-
ing called for the purpose.

See Chap. x. art. 3.

ArtIcLE 7. After the death of a Fellow or Foreign Honorary Mem-
ber, it shall appoint a member of the Academy to prepare a Memoir for
publication in the Proceedings.

ArtIcLE 8. It shall report at every meeting of the Academy such
business as it may deem advisable to present.

See Chap. ii. art. 4, 5, 8; chap. iv. art. 1, 2; chap. vi. art. 1; chap. vii.
art. 1; ‘chap, x: art. 1, 4.

CHAPTER X
r STANDING COMMITTEES

ARTICLE 1. The Class Committee of each Class shall consist of the
Vice-President, who shall be chairman, and the four Councillors of the
Class, together with such other officer or officers annually elected as
may belong to the Class. It shall consider nominations to Fellowship
in its own Class, and report in writing to the Council such as may
receive at a Class Committee Meeting a majority of the votes cast,
provided at least three shall have been in the affirmative.

See Chap. iii. art. 2.

850 STATUTES OF THE AMERICAN ACADEMY

ArtTIcLE 2. At the Annual Meeting the following Standing Com-
mittees shall be elected by ballot to serve for the ensuing year:

(i) The Committee on Finance, to consist of three Fellows, who,
through the Treasurer, shall have full control and management of the
funds and trusts of the Academy, with the power of investing the funds
and of changing the investments thereof in their discretion.

See Chap. iv. art. 3; chap. vii. art. 1, 4; chap. ix. art. 6.

(ii) The Rumford Committee, to consist of seven Fellows, who shall
report to the Academy on all applications and claims for the
Rumford Premium. It alone shall authorize the purchase of books
publications and apparatus at the charge of the income from the
Rumford Fund, and generally shall see to the proper execution of the
trust.

See Chap. iv. art. 3; chap. ix. art. 6.

(iii) The Cyrus Moors Warren Committee, to consist of seven Fel-
lows, who shall consider all applications for appropriations from the
income of the Cyrus Moors Warren Fund, and generally shall see to
the proper execution of the trust.

See Chap. iv. art. 3; chap. ix. art. 6.

(iv) The Committee of Publications, to consist 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 Proceedings and the Memoirs shall be entrusted.

It shall fix the price at which the Publications shall be sold; but
Fellows may be supplied at half price with volumes which may be
needed to complete their sets, but which they are not entitled to
receive gratis.

Two hundred extra copies of each paper accepted for publication in
the Proceedings or the Memoirs shall be placed at the disposal of the
author without charge.

See Chap. iv. art. 3; chap. vi. art. 1, 3; chap. ix. art. 6.

(v) The Committee on the Library, to consist of the Librarian, ex
officio, as Chairman, and three other Fellows, one from each Class,
who shall examine the Library and make an annual report on its
condition and management.

See Chap. iv. art. 3; chap. viii. art. 1, 2; chap. ix. art. 6.

OF ARTS AND SCIENCES. 851

(vi) The House Committee, to consist of three Fellows, who shall
have charge of all expenses connected with the House, including the
general expenses of the Academy not specifically assigned to the care
of other Committees or Officers.

See Chap. iv. art. 1,3; chap. ix. art. 6.

(vii) The Committee on Meetings, to consist of the President, the
Recording Secretary, and three other Fellows, who shall have
charge of plans for meetings of the Academy.

See Chap. iv. art. 3; chap. ix. art. 6.

(viii) The Auditing Committee, to consist of two Fellows, who shall
audit the accounts of the Treasurer, with power to employ an
expert and to approve his bill.

See Chap. iv. art. 3; chap. vii. art. 1; chap. ix. art. 6.

ARTICLE 3. The Standing Committees shall report annually to the
Council in March on the appropriations severally needed for the ensu-
ing financial year; and all bills incurred on account of these Commit-
tees, within the limits of the several appropriations made by the
Academy, shall be approved by their respective Chairmen.

In the absence of the Chairman of any Committee, bills may be
approved by any member of the Committee whom he shall designate
for the purpose.

See Chap. vii. art. 1, 7; chap. ix. art. 6.

CHAPTER XI
MEETINGS, COMMUNICATIONS, AND AMENDMENTS

ARTICLE 1. There shall be annually four Stated Meetings of the
Academy, namely, on the second Wednesday of January, March, May,
and October. Only at these meetings, or at adjournments thereof
regularly notified, or at Special Meetings called for the purpose, shall
appropriations of money be made, or amendments of the Statutes or
Standing Votes be effected.

The Stated Meeting in May shall be the Annual Meeting of the
Corporation.

Special Meetings shall be called by either of the Secretaries at the
request of the President, of a Vice-President, of the Council, or of ten

852 STATUTES OF THE AMERICAN ACADEMY

Fellows having the right to vote; and notifications thereof shall state
the purpose for which the meeting is called.

A meeting for receiving and discussing literary or scientific com-
munications may be held on the second or the fourth Wednesday,
or both, of each month not appointed for Stated Meetings, excepting
July, August, and September; but no business shall be transacted at
any meeting which may be held on the fourth Wednesday.

ARTICLE 2. Twenty Fellows having the right to vote shall consti-
tute a quorum for the transaction of business at Stated or Special
Meetings. Fifteen Fellows shall be sufficient to constitute a meeting
for literary or scientific communications and discussions.

ARTICLE 3. Upon the request of the presiding officer or the Record-
ing Secretary, any motion or resolution offered at any meeting shall
be submitted in writing.

ARTICLE 4. No report of any paper presented at a meeting of the
Academy shall be published by any Fellow without the consent of the
author; and no report shall in any case be published by any Fellow in
a newspaper as an account of the proceedings of the Academy without
the previous consent and approval of the Council. The Council, in
its discretion, by a duly recorded vote, may delegate its authority in
this regard to one or more of its members.

ARTICLE 5. No Fellow shall introduce a guest at any meeting of
the Academy until after the business has been transacted, and espe-
cially until after nominations to Fellowship have been read and the
result of the balloting for candidates has been declared.

ARTICLE 6. The Academy shall not express its judgment on
literary or scientific memoirs or performances submitted to it, or
included in its Publications.

ARTICLE 7. All proposed Amendments of the Statutes shall be re-
ferred to a committee, and on its report, at a subsequent Stated Meet-
ing or at a Special Meeting called for the purpose, two thirds of the
ballot cast, and not less than twenty, must be affirmative to effect
enactment.

ARTICLE 8. Standing Votes may be passed, amended, or rescinded
at a Stated Meeting, or at a Special Meeting called for the purpose,
by a vote of two thirds of the members present. They may be
suspended by a unanimous vote.

See Chap. ii. art. 5, 8; chap. iii.; chap. iv. art. 3, 4, 5; chap. v. art. 1;
chap. vi. art. 1, 2; chap. 1x. art. 8.

92)
σι
Oo

OF ARTS AND SCIENCES.

STANDING VOTES

1. Communications of which notice has been given to either of the
Secretaries shall take precedence of those not so notified.

2. Fellows may take from the Library six volumes at any one time,
and may retain them for three months, and no longer. Upon special
application, and for adequate reasons assigned, the Librarian may
permit a larger number of volumes, not exceeding twelve, to be drawn
from the Library for a limited period.

3. Works published in numbers, when unbound, shall not be taken
from the Hall of the Academy without the leave of the Librarian.

RUMFORD PREMIUM

In conformity with the terms of the gift of Sir Benjamin Thompson,
Count Rumford, of a certain Fund to the American Academy of Arts
and Sciences, and with a decree of the Supreme Judicial Court of
Massachusetts for carrying into effect the general charitable intent and
purpose of Count Rumford, as expressed in his letter of gift, the Acad-
emy is empowered to make from the income of the Rumford Fund, as
it now exists, at any Annual Meeting, an award of a gold and a silver
medal, being together of the intrinsic value of three hundred dollars,
as a Premium to the author of any important discovery or useful
improvement in light or heat, which shall have been made and pub-
lished by printing, or in any way made known to the public, in any
part of the continent of America, or any of the American Islands;
preference always being given to such discoveries as, in the opinion of
the Academy, shall tend most to promote the good of mankind; and,
if the Academy sees fit, to add to such medals, as a further Premium
for such discovery and improvement, a sum of money not exceeding
three hundred dollars.

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INDEX.

Académie des Sciences, Lettres et
Arts de Bordeaux, centennial
celebration, 777.

Agassiz, Alexander, Biographical no-
tice of, 31.

Agassiz, G. R., accepts Fellowship,
TT

Ageratum, Revision of, 804.

Aiken, J. A., declines Fellowship, 785.

Alomia, Revision of, 804.

Altai mountains, Birds from, 784.
American Antiquarian Society, cen-
tennial celebration of, 777.
Amory, Robert, Biographical notice

of, 805.

Andrew Carnegie Research Scholar-
ship, 778.

Angle, A Theory of Linear Distance
and, 45.

Araucarioxylon Type, The History,
Comparative Anatomy and Evo-
lution of the, 531.

Are, The talking, reproducing speech
transmitted by telephone, 784.

Are and Spark, Zine, Spectra of, 91.

Argentine, New or Critical Laboul-
beniales from the, 155.

Arrhenius, Svante, accepts Foreign
Honorary Membership, 777.

Assessment, Annual, Amount of, 798.

Atmospheric Pressure, A Study with
the Echelon Spectroscope of Cer-
tain Lines in the Spectra of
the Zine Are and Spark at, 91.

Avogadro prize, 778.

Bailey, 8. I., Stellar photographs,
showing examples of variable
stars having a more rapid rate of
variation than any hitherto
known, 784.

Baldwin, L. F., letter from, 779.

Baldwin, 8. E., accepts Fellowship,
dé.

Bancroft, W. D., elected Fellow, 782;
accepts Fellowship, 785.

Bangs, Outram, Birds from the Altai
Mountains, 784.

Bauer, L. A., accepts Fellowship, 777.

Beams, bent, showing novel results of
recent experiments, Photographs
of, 784.

Bell, Louis, On the Ultra Violet Com-
ponent in Artificial Light, 1.
Bergson, Professor Henri, Special

meeting in honor of, 785.

Bermudas, Preliminary Study of the
Salinity of Sea-water in the, 783.

Bigelow, Dr. Jacob, Marble Bust of,
799.

Bigelow, W.S., presents marble bust
of Dr. Jacob Bigelow, 799.

Billings, J. S., death of, 788.

Birds from the Altai Mountains, 784.

Birkhoff, G. D., elected Fellow, 803.

Bixby, W. H.,accepts Fellowship, 777.

Blake, Francis, death of, 783.

Blake, 8. F., a Redisposition of the
Species heretofore referred to
Leptosyne, 804; A Revision of
Encelia and some related Genera,
804.

Boas, Franz, accepts Fellowship, 778.

Boltwood, B. B., elected Fellow, 782;
accepts Fellowship, 785.

Boss, Lewis, death of, 778.

Bowditch, C. P., Report of Treasurer,
790.

Bridgman, P. W., accepts Fellowship,
777; Specimens of metals illus-
trating ruptures under pressures
up to 30,000 atmospheres, 784;
Thermodynamic Properties of
Liquid Water to 80° and 12000
Kgm., 307, 780.

Brown, E. W., accepts Fellowship,
741:

Brues, C. T., Entomological Studies
in connection with Epidemics of
Poliomyelitis, 783.

Buddhaghosa’s Treatise entitled The
Way of Salvation, an Analysis of

856

the Second Part, on Concentra-

tion, 784.

Bulbils, Fungi producing, and Similar
Propagative Bodies, Culture
Studies of, 225.

Bullock, C. J., elected Fellow, 803.

Byers, H. G., and Langdon, S. C.,
Relation between the Magnetic
Field and the Passive State of
Tron, 804.

Byers, H. G.,and Vores, F. T., Passiv-
ity of Iron under Boiler Condi-
tions, 804.

Cabot, A. T., death of, 778.

Cabot, Louis, resigns Fellowship, 777.

Chadwick, G. W., elected Fellow, 803.

Chaetomium, Preliminary Diagnoses
of New Species of, 81.

Chapman, H. L., accepts Fellowship,
777; death of, 785.

Chase, G. H., accepts Fellowship, 777.
Cheney, Howell, Remarks on Ameri-
can Silk Manufacture, 787.
Chester, W. M., The structure of the
Gorgonian Coral Pseudoplexaura
crassa Wright and Studer, 735,

787.

Chittendon, R. H., accepts Fellow-
ship, 777.

Chivers, A. H., Preliminary Diagno-
ses of New Species of Chaeto-
mium, 81.

Christian, H. A., elected Fellow, 803.
Clark, A. L., An Electric Heater and
Automatic Thermostat, 597.
Cliffwood, New Jersey, Cretaceous

Pityoxyla from, 607, 783.

Colonial Society of Massachusetts,
The, 779, letter from, 780.

Color measurement, Apparatus for,
784.

Color photography,
work in, 784.

Committee on amendment of Stat-
utes, report of, 781, 798.

Committees, Standing, elected, 802;
list of, 823.

Comstock, D. F., accepts Fellowship,
Wile

Comstock, G. C., elected Fellow, 782;
accepts Fellowship, 785.

Coolidge, J. L., elected Fellow, 803.

Coral Pseudoplexaura crassa Wright
and Studer, Gorgonian, The
Structure of the, 735, 787.

Specimens of

INDEX.

Coral Reefs, Dana’s Contribution to
Darwin’s Theory of, 780.

Council; Report of, 789.

Crafts, J. M., Rumford Medal pre-
sented to, 799.

Cretaceous Pityoxyla from Cliffwood,
New Jersey, 607.

Crew, Henry, elected Fellow, 803.

Cross, C. R., Report of the Rumford
Committee, 793.

Crothers, 8. M., elected Fellow, 803.

Cryptogamic Laboratories of Har-
vard University, Contributions
from, 81, 155, 225, 363.

Ctenopappus, Revision of, 804.

Culture Studies of Fungi producing
Bulbils and Similar Propagative
Bodies, 225.

Dall, W. H., accepts Fellowship, 777.
Dana’s Contribution to Darwin’s
Theory of Coral Reefs, 780.

Darwin, Sir G. H., death of, 780.
Darwin’s Theory of Coral Reefs,
Dana’s Contribution to, 780.
Davis, W. M., Dana’s Contribution

to Darwin’s Theory of Coral
Reefs, 780.
Day, A. L., accepts Fellowship, 777.
Dewey, D. R., elected Fellow, 803.
Dexter, F. B., elected Fellow, 803.
Diaphragms, The Impedance _ of
_ Telephone Receivers as affected
by the Motion of their, 111.
Distance, Linear, and Angle, A Theo-
ry of, 45. i
Dodge, Frederic, accepts Fellowship,
cee
Dwight, Timothy, transferred from
Class III., Section 2 to Class III.,
Section 1, 798.

Eames, Wilberforce, accepts Fellow-
ship, 777. ;

Echelon Spectroscope, A Study with
the, of Certain Lines in the
Spectra of the Zine Are and
Spark at Atmospheric Pressure,

91.

Edes, H. H., delegate to Am. Anti-
quarian Soc., 778; Mementos
of Count Rumford, recently be-
queathed to the Academy by
Mrs. C. B. Griffith, 784; Report
of Committee on Revision of
Statutes, 781, 798.

INDEX.

Edsall, D. L., elected Fellow, 782;
accepts Fellowship, 785.

Eggs, Frozen Kansas, now two and
one half years old, 784.

Electric Heater and Automatic Ther-
mostat, 597.

Electromagnetics, The non-Euclidean
Geometry of Mechanies and, 387.

Elia De Cyon prize, 789.

Encelia, A Revision of, and some re-
lated Genera, 804.

Entomological studies in connection

with Epidemics of Poliomyelitis,

783.

Ether, The, On the Existence and
Properties of, 509.

Eupatoricae, A Key to the Genera of
the Compositae, 804.

Evans, A. W.,accepts Fellowship, 777.

Fellows deceased, (9) —
J.S. Billings, 788.
Francis Blake, 783.
Lewis Boss, 778.

A. T. Cabot, 778.

H. L. Chapman, 785.
H. H. Furness, 778.
W. W. Goodwin, 778.
J. W. Mallet, 785.

O. C. Wendell, 778.

Fellows elected, (51) —
W. D. Bancroft, 782.
G. D. Birkhoff, 803.
B. B. Boltwood, 782.
C. J. Bullock, 803.

x. W. Chadwick, 803.
H. A. Christian, 803.
G. C. Comstock, 782.
J. L. Coolidge, 803.
Henry Crew, 803.

S. M. Crothers, 803.
D. R. Dewey, 803.
F. B. Dexter, 803.
D. L. Edsall, 782.

F. P. Fish, 803.
Arthur Foote, 803.

J. R. Freeman, 782.
D. C. French, 803.
E. B. Frost, 782.

K. F. Gay, 803.

C. H. Grandgent, 803.
Robert Grant, 804.
C. B. Gulick, 803.
A. B. Hart, 803.

C. H. Haskins, 803.
L. O. Howard, 782.

857

I. V. Huntington, 803.
H. C. (ἃ. von Jagemann, 803.
J. R. Jewett, 803.

N. A. Kent, 803.

C. A. Kofoid, 782.
William Lawrence, 803
ΗΠ. D. Little, 803.

IF. B. Mallory, 803.

J. T. Morse, Jr., 804.
W. B. Munro, 803.

EK. F. Nichols, 782.

EK. H. Nichols, 803.
Alfred Noble, 782.

W. A. Noyes, 803.
Okakura Kakuzo, 782.
Harold Pender, 803.
B. L. Pratt, 804.

EK. Καὶ. Rand, 803.

W. E. Ritter, 782.

H. N. Sheldon, 803.

W. M. Sloane, 782.
Moorfield Storey, 803.
E. R. Thayer, 782.

T. F. Waters, 782.

R. W: Wood, 782.

G. E. Woodberry, 804.

Fellows resigned, (3) —
Louis Cabot, 777.
John Fritz, 777.

R. B. Richardson, 777.

Fellows, List of, 825.

Fenn, W. W., transferred from Class
III., Section 4, to Class III.,
Section 1, 798.

Fernald, M. L., Geographic Origin of
Life in Newfoundland and the
Magdalen Islands, 780.

Fish, F. P., elected Fellow, 803.

Fisher, Irving, accepts Fellowship, 777.

Fitz, R. H., Biographical notice of
Dr. Robert Amory, 805.

FitzGerald, Desmond, accepts Fel-
lowship, 777.

Flexner, Simon, accepts Fellowship,
ΠΩΣ

Foote, Arthur, elected Fellow, 803.

Foreign Honorary Members, de-

ceased (4) ,—
Sir George Howard Darwin, 780.
Jean Léon Géréme, 778.
Jules Henri Poincaré, 778.
Eduard Strasburger, 778.
Foreign Honorary Members, elect-
ed (2),—
Adam Politzer, 783.
Eduard Seler, 783.

858

Foreign Honorary Members, List of,
6

Freeman, J. R., elected-Fellow, 782;
accepts Fellowship, 785.

French, D. C., elected Fellow, 803.

Fritz, John, resigns Fellowship, 777.

Frost, E. B., elected Fellow, 782; ac-
cepts Fellowship, 785.

Fungi producing Bulbils and Similar
Propagative Bodies, Culture
Studies of, 225.

Furness, H. H., death of, 778.

Gay, E. F., elected Fellow, 803.

General Fund, 790; Appropriations
from the Income of, 781,785, 798.

Geometry, The non-Euclidean, of
Mechanics and Electromagnet-
ics, 387.

Gérome, J. L., death of, 778.

Goethals, G. W., accepts Fellowship,

Tee

Goodale, G. L., delegate to Amherst,
778.

Goodwin, W. W., death of, 778.

Gorgonian Coral Pseudoplexaura
crassa Wright and Studer, the
Structure of the, 735, 787.

Graminae collected by Professor
Morton C. Peck, in British Hon-
duras, 804.

Grandgent, C. H., elected Fellow, 803.

Grant, Robert, elected Fellow, 804.

Gray Herbarium, Contributions
from, 804.

Griffith, Mrs., C. B. Rumford Gifts
from, 779.

Gulick, C. B., elected Fellow, 803.

Hall, E. H., A Brief Account of the
Recent Royal Society Celebra-
tion, 778.

Hamilton, F. E., draft of sections in
tariff act, 799.

Hart, A. B., elected Fellow, 803.

Harvard College Library, Two uni-
que fragments of a book in an
otherwise unknown South Ameri-
can language, lately found in,784.

Harvard Medical School, Meeting at,
787.

Harvard University. See Crypto-
gamic Laboratory, Gray Her-
barium, Jefferson Physical Labo-
ratory, Phanerogamic Labora-
tory, Zoological Laboratory.

INDEX.

Haskins, C. H., elected Fellow, 803.

Hastings, C. 8., accepts Fellowship,
781.

Heidel, W. A., On Certain Fragments
of the Pre-Socraties: Critical
Notesand Elucidations, 679, 788.

Henderson, L. J., accepts Fellow-
ship, 777.

Higginson, H. L., accepts Fellow-
ship, 777.

Holden, Ruth, Cretaceous Pityoxyla
from Cliffwood, N. J., 607, 783.

Hotson, J. W., Culture Studies of
Fungi producing Bulbils and
similar Propagative Bodies, 225.

House Committee, Report of, 796.

House Expenses, Appropriations for,
781, 786.

Howard, L. O., elected Fellow, 782;
accepts Fellowship, 785.

Howe, M. A. DeW., accepts Fellow-
ship, 777.

Hubbard, F. F., On the Graminae
collected by Professor Morton
C. Peck, in British Hondurus,
1905-1907, 804.

Huntington, E. V., elected Fellow,
803.

Infantile Paralysis, Experimental
Evidence of the Transmission of,
783.

Infantile Paralysis in Massachusetts,
The Study of, by the State
Board of Health, 783.

Institut International de Physique
Solvay, Statutes of, 789.

International Congress of Compara-
tive Pathology (first), 777.

International Congress of Historical
Studies, (third), 778.

International Congress of Zoology,
(ninth), 780.

International Geological
(twelfth), 785.

Iron, The Maximum Value of the
Magnetization Vector in, 783.

Tron, Passivity of, under Boiler Con-
ditions, 804.

Iron, Relation between the Magnetic
Field and the Passive State of,
804.

Ives, F. E., presented with Rumford
Medal, 783; Specimens of work
in color photography, 784; appa-
ratus for color measurement, 784.

Congress

INDEX.

Jackson, C. L., Biographical notice
of C. R. Sanger, 813.

von Jageman, H. C. G., elected Fel-
low, S803.

Jefferson Physical Laboratory, Con-
tributions from, 307.

Jeffrey, E. C., The History, Compara-
tive Anatomy and Evolution of
the Araucarioxylon Type, Parts
1—4, 531.

Jewett, J. R., elected Fellow, 803.

Johnson, L. J., Photographs of bent
beams, showing novel results of
recent experiments, 784.

Joslin, E. P., accepts Fellowship, 777.

Jusserand, J. A. A. J., accepts For-
eign Honorary Membership, 777.

Kennelly, A. E., and Pierce, G. W.,
The Impedance of Telephone
Receivers as affected by the
Motionof their Diaphragms, 111.

Kent, N. A., elected Fellow, 803; A
Study with the Echelon Spectro-
scope of Certain Lines in the
Spectra of the Zine Arcand Spark
at Atmospheric Pressure, 91.

Kofoid, C. A., elected Fellow, 782;
accepts Fellowship, 785.

Kroeber, A. L., accepts Fellowship,
41:

Laboulbeniales, New or Critical, from
the Argentine, 155.

Lane, A. C., Thin sections of igneous
rocks, showing variations of
grain, 784.

Lane, W. C., Two unique fragments
of a book in an otherwise un-
known South American language
lately found in the Harvard Col-
lege Library, 784.

Langdon, ὃ. C. See Byers, H. G.,
and Langdon, S. C.

Language, South American, Two
unique fragments of a book in
an otherwise unknown, lately
found in the Harvard College
Library, 784.

Lanman, C. R., Buddhaghosa’s
Treatise entitled The Way of
Salvation, an Analysis of the
Second Part, on Concentration,
784.

Lawrence, William, elected Fellow,
803.

859

Leptosyne, A Redisposition of the
Species heretofore referred to,
SO4.

Lewis, G. N. See Wilson, E. B., and
Lewis, G. N.

Library, Appropriation for, 781, 786.

Library Committee, Report of, 792.

Light, Artificial, On the Ultra Violet
Component in, 1.

Lindgren, Waldemar, accepts Fellow-
ship, 777.

Linear Distance and Angle, A Theory
of, 45.

Little, E. D., elected Fellow, 803.
Lorentz, H. A., accepts Foreign
Honorary Membership, 777.

Lotz, Albert, Theory of, 751.

Lowell, Percival, Miniature globe,
781; The Origin of the Planets,
789.

Lovett, R. W., The Study of Infantile
Paralysis in Massachusetts by
the State Board of Health, 783.

Lyman, Theodore, A Journey in the
Highlands of Siberia, 804.

Lyon, D. C., One of the books of
Nebuchadnezzar, King of Baby-
lon, recording his building opera-
tions in that city about 600 B.
C., 784.

Magnetic Field, Relation between
the, and the Passive State of
Iron, 804.

Magnetization Vector in Iron, The
Maximum Value of the, 783.

Mallet, J. W., death of, 785.

Mallory, F. B., elected Fellow, 803;
Pathological Lesion in Whoop-
ing Cough and the Relation of
the Whooping Cough Bacillus to
the Lesion, 788.

Mark, K. L., Preliminary Study of
the Salinity of Sea-water in the
Bermudas, 669, 783.

Marks, L. 5., accepts Fellowship,
(beg

Mathematical-Physical Club, 779.

Mechanics and Electromagnetics,
The non-Euclidean Geometry
of 9557:

Metals illustrating ruptures under
pressures up to 30,000 atmos-
pheres, Specimens of, 784.

Meteorite, Specimens of a_ stony,
which fell in Arizona, 784.

860

Moore, C. L. E. See Phillips, H. B.,
and Moore, C. L. E.

Moore, E. C., transferred from Class
III., Section 4, to Class ΤΗΣ,
Section 1, 798.

Morse, J. T., Jr., elected Fellow, 804.

Mulliken, 8. P., accepts Fellowship,
Uk:

Munro, W. B., elected Fellow, 803.

Museum of Comparative Zodlogy
αὖ Harvard College. See Ζοῦ-
logical Laboratory.

Nebuchadnezzar, King of Babylon,
One of the books of, recording
his building operations about
600 B. C., 784.

Nichols, E. F., elected Fellow, 782;
accepts Fellowship, 785.

Nichols, E. H., elected Fellow, 803.

Noble, Alfred, elected Fellow, 782;
accepts Fellowship, 785.

Nominating Committee, appointed,
786.

Noyes, W. A., elected Fellow, 803.

Numbers, Hyper Complex, On the
Sealar Functions of, 625, 780.

Oertel, Hanns, accepts Fellowship,
711.

Officers, elected, 801; List of, 823.

Okakura-Kakuzo, elected Fellow,
782; accepts Fellowship, 785.

Olney, Richard, declines Fellowship,
780.

Oxylobus, Revision of, 804.

Palmer, G. H., accepts Fellowship,
777; transferred from Class III.,
Section 4, to Class III., Section 1,
798.

Panama-Pacific International Expo-
sition, 778.

Peabody, R. 8., accepts Fellowship,
ie

Peck, M. C., Graminae collected by,
in British Honduras, 804.

Peirce, B. O., The Maximum Value
of the Magnetization Vector in
Iron, 783.

Pender, Harold, elected Fellow, 803.

Phanerogamic Laboratories, Contri-
butions from, 531, 607.

Phillips, H. B., and Moore, C. L. E.,
A Theory of Linear Distance and
Angle, 45.

INDEX.

Photography, Color, Specimens of
work in, 783.
Pierce, G. W., Report of Publication
Committee, 796; The talking
are, reproducing speech trans-

mitted by telephone, 784.

Pierce, G. W. See Kennelly, A. E.,
and Pierce, G. W.

Pityoxyla, Cretaceous, from Cliff-
wood, New Jersey, 607, 783.
Pneumonic Plague, The Recent Man-

churian Epidemic of, 788.

Poincaré, J. H., death of, 778.

Poliomyelitis, Entomological Studies
in connection with Epidemics of,
783.

Politzer, Adam, elected Foreign
Honorary Member, 783.

Pratt, B. L., elected Fellow, 804.

Pre-Socratics, On Certain Fragments
of the, 679, 788.

Pressure, Atmospheric, A Study with
the Echelon Spectroscope of
Certain Lines in the Spectra of
the Zine Are and Spark at, 91.

Pseudoplexaura crassa, The Structure
of the Gorgonian Coral, 735, 787.

Publication, Appropriation for, 786.

Publication Committee, Report of,
796.

Publication Fund, 791; Appropria-
tion from the Income of, 786.

Putnam, C. P., accepts Fellowship,
bib

Rand, E. K., elected Fellow, 803.

Receivers, Telephone, The Imped-
ance of, as affected by the Mo-
tion of their Diaphragms, 111.

Records of Meetings, 777.

Relativity, The Space-Time Mani-
fold of, 387.

Rhigi, Augusto, accepts Foreign
Honorary Membership, 777.

Rice Institute, invitation from, 777.

Richardson, R. B., resigns Fellow-
ship, 777.

Rickia and Trenomyces, Preliminary
Descriptions of New Species of,

363.
Riegel, E.R. See Sanger, C. R., and
Riegel, E. R.

Ritter, W. E., elected Fellow, 782;
accepts Fellowship, 785.

Robinson, B. L., Diagnoses and
Transfers among the Sperma-

INDEX,

tophytes, 804; A Key to the
Genera of the Compositae Eu-
patoricae, 804; Revisions of Al-
omia, Ageratum, Ctenopappus
and Oxylobus, S04.

Rocks, Igneous, Thin sections of,
showing variations of grain, 784.

Root, Elihu, accepts Fellowship, 780.

Ropes, J. H., transferred from Class
III., Section 4, to Class III.,
Section 1, 798.

Rosenau, M. J., Experimental Evi-
dence of the Transmission of
Infantile Paralysis, 783.

Roteh, A. L., Biographical notice of,
780, S07.

Rugg, A. P., accepts Fellowship, 777.

Rumford Committee, Report of, 790.

Rumford Fund, 798; Appropriations
from the Income of, 786; Papers
published by aid of, 1, 91, 307,
597.

Rumford Medal; presented to Fred-
eric Eugene Ives, 783; presented
to James M. Crafts, 799.

Rumford mementos, 779, 784.

Rumford Premium, 853; Award of,
797.

Salinity of Sea-water in the Bermudas
Preliminary Study of the, 669,

783.
Sanger, C. R., Biographical notice of,
813.

Sanger. C. R., and Riegel, E. R., The
Action of Sulphur Trioxide on
Silicon Tetrachloride, 573, 780.

Sealar Functions of Hyper Complex
Numbers, 2d paper, 625, 780.

Seott, W. B., accepts Fellowship, 777.

Sea-water in the Bermudas, Prelimi-
nary Study of the Salinity of,
669, 783.

Sedgwick, W. T., Frozen Kansas eggs
now two and one-half years old,
Chinese and other eggs, and
some egg products, 784.

Seler, Eduard, elected Foreign Honor- -

ary Member, 783; accepts For-
eign Honorary Membership, 785.
Sheldon, H. N., elected Fellow, 803.
Siberia, A Journey in the Highlands
‘ of, 804.
Silicon Tetrachloride, The Action of
Sulphur Trioxide on, 573, 780.
Silk Manufacture, 787.

861

Sloane, W. M., elected Fellow, 782.

Space-Time Manifold of Relativity,
387.

Spectra of the Zine Are and Spark at
Atmospheric Pressure, A Study
with the Echelon Spectroscope of
Sertain Lines in the, 91.

Spectroscope, Echelon, A Study with
the, of Certain Lines in the
Spectra of the Zine Are and
Spark at Atmospheric Pressure,
91.

Standing Committees elected, 802;
List of, 823.

Standing Votes, 853.

Statutes, 889, Amendment of, 781,
798.

Report of Committee on Amend-
ment of, 781, 798.

Stebbins, Joel, Rumford Premium
awarded to, 797.

Stellar photographs, showing exam-
ples of variable stars having a
more rapid rate of variation than
any hitherto known, 784.

Storey, Moorfield, elected
803.

Strasburger, Eduard, death of, 778.

Strong, R. P., The Recent Manchu-
rian Epidemic of Pneumonic
Plague, 788.

Sulphur Trioxide, The Action of, on
Silicon Tetrachloride, 573, 780.

Fellow,

Taber, Henry, On the Scalar Func-
tions of Hyper Complex Num-
bers, 2d paper, 625, 780.

Talbot, H. P., Report of C. M.
Warren Committee, 795; Report
of House Committee, 796.

Tariff act, draft of certain sections in,
799.

Taussig, F. W., Doctrine of Protec-
tion to young Industries, as illus-
trated by the growth of the
American Silk Manufacture, 787;
Report on draft of sections of
tariff act, 801.

Telephone Receivers, The Impedance
of, as affected by the Motion of
their Diaphragms, 111.

Thaxter, Roland, New or Critical
Laboulbeniales from the Argen-
tine, 155; Preliminary Descrip-
tions of New Species of Rickia
and Trenomyces, 363.

862

Thayer, E. R., elected Fellow, 782;
accepts Fellowship, 785.

Thayer, J. E., accepts Fellowship,

Rae:

Thermodynamic Properties of Liquid
Water to 80° and 12000 Kem.,
307, 780.

Thermostat, Automatic, An Electric
Heater and, 597.

Thompson, M. de K., accepts Fellow-
ship, 777.

Thursday Evening Club, 778.

Treasurer, Report of, 790.

Trenomyces, Preliminary Descrip-
tions of New Species of Rickia
and, 363.

Tucker, W. J., accepts Fellowship,
777; transferred from Class III.,
Section 4 to Class III., Section 1,
798.

Tyler, H. W., Report of Library Com-
mittee, 792.

Ultra Violet Component in Artificial
Light, 1.

U.S. Senate and House of Represent-
atives, Letter to, 786.

Vores, F. T. ~See Byers, H. G., and
Wores. He at:

Walcott, H. P., Alexander Agassiz,
31

Walker, Williston, accepts Fellow-
ship, 777; transferred from
Class III., Section 4, to Class ITI,
Section 1, 798.

Ward, R. DeC., Biographical notice
of A. L. Rotch, 780; 807.

INDEX.

Warren (C. M.) Committee, Report

of, 795.

Warren (Ὁ. M.) Fund, 791; Appro-
priations from the Income of,786.

Water, Liquid, Thermodynamic
Properties of, to 80° and 12000
Kgm., 307, 780.

Waters, T. F., elected Fellow, 782;
accepts Fellowship, 785.

Weatherby, C. A., Some new Combi-
nations required by the Interna-
tional Rules, 804.

Webster, D. L., On the Existence and
Properties of the Ether, 509.

Wendell, O. C., death of, 778.

Whooping Cough, Pathological Le-
sion in, 788.

Wilson, ΕΣ. B., and Lewis, G. N., The
Space-Time Manifold of Rela-
tivity. The non-Euclidean Ge-
ometry of Mechanics and Elec-
tromagnetics, 387.

Wolbach, 8. B., accepts Fellowship,
ΤΙΣ

Wolf, J. E., Specimens of a stony
meteorite which fell in Arizona
last summer, 784.

Wood, R. W., elected Fellow, 782;
accepts Fellowship, 785.

Woodberry, G. E., elected Fellow,
804. ἢ

Woods, F. S8., accepts Fellowship,

Wright, J. H., accepts Fellowship,

Zoological Laboratory of the Museum
of Comparative Zoédlogy at Har-
vard College, E. L. Mark, Direc-
tor, Contributions from, 735.

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