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KONINKLIJKE AKADEMIE

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= TE AMSTERDAM ==

PROCEEDINGS: OF - THE
SECTION OF SCIENCES

VOLUME XXV
— (Nos. 1—10) —

PUBLISHED BY
“KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN”, AMSTERDAM
MARCH 1923

—>

(Translated from: ,,Verslag van de Gewone Vergaderingen der Wis- en
Natuurkundige Afdeeling” Dl. XXXI).

2 b- 104 264- jot

Proceedings N°.
Mes.
Nos,
NSS,

Nes:

COMLENTS.

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1 and 2
3 and 4
dna 6
7 and 8

9 and 10 .

229

383

G [te
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ON pat

KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM.

PROCEEDINGS

VOLUME XXV

Nes, 1 and 2.

President: Prof. F. A. F. C. WENT.
Secretary: Prof. L. BOLK.

(Translated from: “Verslag van de gewone vergaderingen der Wis- en

Natuurkundige Afdeeling,” Vol. XXXI).

CONTENTS.

P. EHRENFEST and G. BREIT: “A remarkable case of quantization”, p. 2.

G. L. FUNKE: “The influence of hydrogen ion concentration upon the action of the amylase of
Aspergillus niger”. (Communicated by Prof. F. A. F. C. WENT), p. 6.

R. KR4USEL: ,Ueber einen fossilen Baumstamm von Bolang (Java), ein Beitrag zur Kenntnis der

fossilen Flora Niederlandisch-Indiens*. (Communicated by Prof. J. W. MOLL), p.9. (Mit 1 Tafel).

L. BOLK: “On the Significance of the Supra-orbital Ridges in the Primates”, p. 16.

JAN DE VRIES: “Representation of a Bilinear Congruence of Twisted Cubics on a Bilinear Con-
gruence of Rays”, p. 22.

J. M. BIJVOET and A. KARSSEN: “Research by means of Röntgen-Rays on the Structure of the
Crystals of Lithium and some of its Compounds with Light Elements. II. Lithium-Hydride”.
(Communicated by Prof. P. ZEEMAN), p. 27.

J. W. JANZEN and L. K. WOLFF: “Studies about D’HERELLE’s Bacteriophagus”. (Communicated by
Prof. C. EYKMAN), p. 31.

K. LANDSTEINER: “Experiments on Anaphylaxis with Azoproteins”, (Communicated by Prof. C. H. H.
SPRONCK), p. 34.

K. J. FERINGA: “On the Causes of the Emigration of Leukocytes”. (Communicated by Prof. H. J.
HAMBURGER), p. 36.

ROBERT F. GRIGGS: “Observations on the Incandescent Sand Flow of the Valley of ten thousand

smokes”. p. 42.
Erratum, p. 50.

Proceedings Royal Acad. Amsterdam. Vol. XXV.

Physics. — “A remarkable case of quantization.” By Prof. P.
Exrenrest and G, Breit.

(Communicated at the meeting of January 28, 1922).

1. It is possible to indicate simple mechanical systems for which
a formal application of the quantum rules gives well defined and
yed apparently unreasonable stationary motions. Bour’s Principle of
Correspondence’) offers an essentially new viewpoint for the treat-
ment of these cases and will probably contribute to their complete
solution. It will suffice to discuss a special case which is so chosen
as to minimize the mathematical analysis. ®)

2. A rigid electric dipole having a moment of inertia / is free
to rotate in the X, Y plane about its own midpoint.

Let us suppose that by means of a suitable kinematical arrange-
ment the rotating dipole is thrown back elastically as soon as the
angle ~, which the dipole makes with the axis of X, reaches the
boundaries of the interval

<=. ONE Pp Stan AOU Tes, a EEE)
where / is a large, in general an irrational number. Let an angular

velocity w be given to the dipole. Its angular momentum is then
p = lw and it executes a periodic motion with the period

27

During the motion the dipole traverses the interval (1) making
in a period 2f complete revolutions to the right followed by the
same number of revolutions to the left. In the motion the “quast-
periode”

1) N. Bour, Quantum theory of line-spectra I, If Kopenhagen 1918. H. Kramers,
Intensities of spectral lines. Kopenhagen 1919.

2) A case which differs slightly from the one discussed in § 2, namely the case
of a rigid dipole torsionally suspended by an elastic thread of small rigidity one
of us submitted to EinsrerN for consideration as early as 1912 (with reference to
the problem of quantization of H, molecules — P. EHrenrest. Verh. d. D. Phys.
Ges. 15, 451, 1913). It was impossible however to settle the Se here discussed
by the means which were then available.

8

2
Rn ien Alie Er va)
w

becomes noticeable. This period is a 4d f!* part of 7’ and is equal to
the time taken by the dipole to make a complete revolution through
the angle 22. The projection of the moment of the dipole on aline
in the plane X-Y-say on the axis of X depends on the time in the
manner shown on the figure (for the sake of economy the “large
number” f is here taken as being approximately 2).

EA pk Ee ZF

| Á rt

et KN

3. The quantum relation for our system is

firdg = nn ARO, SNARE Ron OE Me a

where the coordinate gq is the angle , p is the corresponding
momentum | w and the integral is taken over a complete perid 7’.
This gives in our case

Sf CARB Ri iy Si beelt lee Heit orks)
or

(6)

If now the restricting boundary of the interval (1) is so chosen
as to make f very large, then the differences between consecutive
values of p (see (6)) (and therefore also between consecutive values
of the energy) are very small.

4. This result appears to be unacceptable. In fact if we pass to
the limit of f= o ie. if the restriction of the boundaries on the
dipole disappears then equation (4) gives certainly

h
AN TE Me ES
for now @ is the period. Here (Equ. (7)) p changes by finite steps
whereas if the previous consideration be applied (Equ. (6)) the steps
become infinitesimal for f— oo. This is the contradiction to be
discussed.

5. Bour’s principle of correspondence offers a new point of view
for the treatment of this case. As before let f be a very large
1*

4

number and suppose that the permissible values of p are truly
given by Equ. (6). We want to know the requirements made by
the principle of correspondence as to the “probability of a transition”
from the state n = n, to the state n = n, (say as the result of absorption
in a field of radition). The Principle of correspondence regards the
probability of the transitions as analogous to the amplitudes of
“corresponding” harmonics in a Fourier series expansion of the
function represented graphically on the figure. This function repre-
sents the dependence on the time of the X or Y component of
the dipole’s moment. The Fourier expansion of the function may
be put into the form

2
X= E Ayo (0) Ce ine Fe
4 1

The harmonics “corresponding” to the transition »,—n, are
given by:
SE LET
From an inspection of the figure or by means of a short calcul-
ation it becomes apparent that for a large value of f the amplitudes
of all the harmonics are small with the exception of those harmonics
whose period is nearly equal to the “quasiperiod” 6 i.e. with the
exception of those for which

EO oe TS ERD

or
EE acl 5 Sal
Therefore if f is large all the transitions have a very small
probability with the exception of those for which very nearly
Ee RAL det on Ks AL
and therefore (in virtue of (6)) |

BAT MS eR 13)
Thana abe . DCN ee . (
which is the same as the interval between consecutive values of p
prescribed by (7) for infinitely large values of /.

Ps Pi ilt

6. If therefore we should take a collection of identical samples
of our system having all the same very large value of f, being all
at rest i.e. in the state p=—O at the time {— 0 and if we should
subject each sample independently to the action of a black body
radiation — then we should find at a later time ¢ that:

A. Out of the very dense succession of the p levels which are

5)

permitted by (6) only those are occupied by an appreciable number
of the systems which nearly coincide with the levels of p given
by (7).

B. The transitions which take place have almost without excep-
h

tion the magnitude a (and not a multiple of it) (See (13)). This is
zt

again in good agreement with the fact that for f= the Fourier
expansion of the a (or y) component contains only the fundamental
and no higher harmonics so that for this case the Principle of
Correspondence allows only the transitions (see (7)) for which
ie, Ee |

7. A question must now be mentioned the precise explanation of
which would be of value. For the discussion of thermal equilibrium
in our complex we must know the “weights” (the a priori proba-
bility) to be ascribed to each p level. For f+ o it would appear
that the same weight should be given to every stop of (6) — in-
dependently of the value of f and independently of the density
with which the levels follow each other. On the other hand for
f= only the levels given by (7) are to have a weight (the same
for all). A closer examination of this case will probably make it
necessary to consider the fact that we are concerned here with a
double limit viz. im t= (the lapse of an infinitely long time for
the establishment of thermal equilibrium) and im f=; our dis-
satisfaction is really based on an unconscious demand that the result
should be independent of the order in which the two limits are
approached.

The junior author of the paper (G. Breit) is Fellow of the National
Research council, United States of America.

The University, Leiden.

Botany. — “The influence of hydrogen ton concentration upon the
action of the amylase of Aspergillus niger”. By G. L. Funke.
(Communicated by Prof. F. A. F. C. Wenz).

(Communicated at the meeting of January 28, 1922).

Aspergillus niger produces large quantities of amylase, part of
which migrates into its nutritive surrounding. In the mean time the
fungus forms acids which cause that medium to have a high hydrogen
ion concentration. As this however seemed not to influence un-
favourably the action of the amylase, the supposition was justified
that the amylase of Aspergillus niger could not have its optimal
action at the same hydrogen ion concentration as the ptyaline which
works best at a nearly neutral or faintly acid reaction (4 and 5).

Therefore I made a preliminary investigation in the way as
has been indicated first by SöreNseN (1). Buffer solutions however
were made according to the methods of Crark and Luss (7).

Generally the same amounts of enzyme solution out of the
nutritive liquid were mixed up with buffer solution and amylum

|

1 Pr 2 3 4 5 6 zi 8

solution 0.16°/,. The hydrogen ion concentration of this mixture
was determined by aid of colorimetric indicators, the rate of
hydrolysis of the amylum by the iodine reaction.

7

Results are. plotted into the annexed curve (I). As can be seen
there is no point of optimal action but a broad optimal zone
extending from a Py of about 3,5 till about 5,5.

Neither the concentration of the amylase, nor the composition of
the nutritive liquid appeared to have influence. The same results
were obtained with amylase extracted from the mycelium.

These results largely confirm the theory of MicHakiis who con-
siders the enzymes as ampholytes (2 and 3). The form of the curve
indeed is nearly identical to the dissociation rest curve of an amphotere
electrolyte. According to his formulas

Ca. EK, and Vr ky
(H) (OH)
in which 9 = 1 — y= dissociation rest
n= rate of dissociation
k= dissociation constant of the acid
B dissociation constant of the base
the points on the ordinate = half of the maximum height of the

curve indicate the logarithms of the dissociation constants of acid
and base on the abscissa. These are to be found at about 2,26 and

6,2. So the dissociation constant of the acid would be =6.3 x 10 7,

that of the base = 2.884 « 10-!2,

1Pu 2 3 4 5 6 7 8

We may consider in the same way curve Il which represents

8

the influence of the hydrogen ion concentration upon the amylase
of malt’).

The dissociation constant of the acid appears to be the same as
for the amylase of Aspergillus, that of the base on the contrary is
bigger ie. = 5.76 X 10-". So as an acid the two amylases are
equally strong, as a base that of the malt is the weakest.

Further investigations on other sorts of. amylase will perhaps
instruct us, if pointing out their differences in this way will be of
any value.

Utrecht, November 1921. Botanical Laboratory.

LITERATURE.

1. SöRENSEN S. P. L., Biochem. Zeitschr. Bd. 21, 1909. Enzymstudien II.

2. MicHAELIS, L., Biochem. Zeitschr. Band 33, 1911. Ueber die Dissoziation der
amphoteren Electrolyte.

3. MICHAELIS L. und DavipsoHn, Biochem. Zeitschr. Band 35, 1911. Die Wir-
kung der H. lonen auf das Invertin.

4. Ringer, W. E, en Triat H. van, Onderzoek. Physiol. lab. der Un. Utrecht.
5e reeks, dl. 14, 1913. Over den invloed van de reactie op de werking van ptyaline.

5. MrcHaArLis L. und Pecusrern, H., Bioch. Zeitschr. Band 59, 1914. Die
Wirkungsbedingungen der Speicheldiastase.

6. Apter, L., Biochem. Zeitschr. Band 77, 1916. Ueber den Einfluss der Was-
serstoffionen auf die Wirksamkeit der Malzdiastase.

7. Crark, W. M. and Luss, H. Am., Journ. of Bact. Vol. IL. 1917. The colori-
metric determination of hydrogen ion concentration and its applications in bacteriology.

1) It might be doubted if the iodine reaction method is accurate enough to get
exact results. I therefore refer to those of ADLER (6) who determined the hydro-
lysis of amylum by means of rotation and reductive power. The numbers he
obtained appear to give a curve nearly identical to mine.

Palaeontology. — ‘Ueber einen fossilen Bauinstamm von Bolang
(Java), ein Beitrag zur Kenntnis der fossilen Flora Nieder-
ländisch-Indiens”. By Dr. R. Krauser. (Communicated by
Prof. J. W. Motz.)

(Communicated at the meeting of January 28, 1922).

In der Sammlung des Mineralogisch-Geologischen Instituts der
Reichsuniversität zu Groningen befindet sich ein äusserlich sehr gut
erhaltenes Stück eines verkieselten Baumstammes von Bolang auf
Java. Der Durchmesser des 23 cm langen Bruchstückes beträgt
19—23 cm. Ueber Fundort u-s.w. gibt folgende Notiz Auskunft:
„Fossiler Baumstamm (batoe sempoer), wie solche in verschiedener
Grösze, bis 2 m lang und mit einem zuweilen 60 em erreichen-
den Durchmesser in Bolang auf Java gefunden werden. Sie kommen
häufig auf der Oberfläche oder im Fluszbette zerstreut vor, finden
sich aber auch in 1—2 m Tiefe im Boden auf dem Kamm eines
Hügelzuges. (Empfangen von Herrn C. BARENDS)”. Angaben über
das geologische Alter der Fundschicht liegen nicht vor.

Der von Herrn Prof. Dr. Bonnema, dem an dieser Stelle zu
danken, mir eine angenehme Pflicht ist, ausgehenden Anregung
zur Untersuchung des Holzes leistete ich um so lieber Folge, als es
wünschenswertes Vergleichsmaterial für eine gleichzeitig durchge-
fiihrte Bearbeitung fossiler Hölzer aus Sumatra bot, über die
an anderer Stelle berichtet wird (KräuvseL 1). Dort ist auch zu
zeigen versucht worden, dasz die Behandlung derartiger Reste
keineswegs nutzlos ist, selbst angesichts der zum Teil noch recht
unvollkommenen Kenntnis vom anatomischen Bau der rezenten,
tropischen Laubbäume. Gerade dieser Umstand verlangt aber eine
möglichst ausführliche Beschreibung der Fossilien. Nur dann ist
eine brauchbare Grundlage für eine etwa später vorzunehmende
kritische Revision gegeben. Aus diesem Grunde wurde die Beschrei-
bung der von Morr und Janssonius (l) in die Literatur eingeführten
Methode angepaszt, soweit dies angesichts des Erhaltungszustandes
der fossilen Hölzer eben möglich war. Das soll auch hier geschehen;
hinsichtlich aller Einzelheiten kann auf die schon genannten Arbeiten
verwiesen werden.

Beschreibung des anatomischen Baues (Topographie) :

Zuwachszonen mit freiem Auge kaum sichtbar, unter dem
Miskroskop an einer deutlichen Anhäufung und damit verbundenen
Gröszenabnahme der Gefäsze kenutlich. Die tangentialen Schichten, die

10

auf dem Querschnitt fiir das blosse Auge Zonengrenzen ähnlich sind,
enthalten zahlreiche, stets von reichlichem Holzparenchym umgebene
Harzgänge und auch Gefäsze, aber fast kein Libriform. Diese
Schichten nicht überall gleich deutlich, stets eine Reihe Harzgänge ent-
benachbarte zuweilen verschmelzen (auf 18 mm

haltend, von denen 2
9 Harzgangreihen, die sich über einen

radialer Erstreckung kommen 5
eroszen Teil des Querschnitts verfolgen lassen). (Textfig. 1, Tafel,
|, 2). Gefasze + gleichmaszig verteilt, zu 8—16 auf dem mm’,

Fig.

BE@

H
‘
®
il

|

Our:
LON
opm O2 ran

ae,

Kro OD.

Fig. 1. Querschnitt.

in der Regel vereinzelt liegend, seltener in Gruppen, dann oft zu
zweien. Sehr oft an beiden oder wenigstens an einer Seite an Mark-
strahlen grenzend, sonst meist von Holzparenchym oder Fasertra-
cheiden umgeben. Diese sehr spärlich, nur an Gefäsze grenzend.
Libriformfasern die Grundmasse des Holzes bildend, + undeut-
lich in radialen Reihen angeordnet.

Kinfaches Holzparenchym die Gefäsze und Harzgänge
umgebend, tangentiale Bander bildend, einige zerstreute Fasern anschei-
nend auch im Libriform eingesprengt; die die Harzgänge umgebenden
Zellen oft in die Breite gezogen, kaum in den Harzgang hineinragend
(diinnwandiger als die anderen). Harzgänge nur in den tangentialen
Bändern zahlreich, ausserhalb derselben nur vereinzelt. Markstrahlen
seitlich von einander getrennt durch 1—10 Libriformfaserreihen, 1—6-,

11

am häufigsten 3—5-schichtig, 3—30 Zellen hoch, die breiteren
nicht immer aus 3 Stockwerken zusammengesetzt, das obere und
untere dann meist eine, seltener bis 4 Zellen hoch, die wie die der
einfachen Markstrahlen aufrecht oder aufrechten ähnlich sind. Die
breiteren Stoekwerke oft von tangential haufig sehr breiten Hüll-
zellen umgeben. Nicht selten stehen mehrere Markstrahlen, nur
durch ein oder zwei Fasern von einander getrennt, übereinander, ver-
schmelzen auch gelegentlich ganz (Tafel, Fig. 3; Textfig. 2). Ihre
Zellen enthalten oft Kristalle.

Fig. 2. Tangentialschnitt.

Beschreibung der Elemente:

Gefäsze: Weite radial 65—275 u, tangential 70—210 u, ellip-
tische, auch Kreiszylinder, Querwände + horizontal (selten sichtbar),
Perforation + unkenntlich (lochförmig?) mit zahlreichen Hoftiipfeln,
wo sie aneinander oder an Fasertracheiden grenzen, Tiipfel polygonal-
rundlich oder elliptisch; die Pori oft elliptisch, schief bis vertikal
gestellt; mit einseitigen Hoftiipfeln und einfachen Tüpfeln, wenn an
Holzparenchym und Markstrahlen grenzend, bäufig mit dünnwan-
digen Thyllen erfüllt.

Fasertracheiden: Nur in der Umgebung der Gefäsze vorhanden,
Tüpfelung wie bei den Gefäszen.

Libriformfasern: Weite radial 8—16 u, tangential 1O—16 u,

12

polygonal mit oft abgerundeten Kanten, oft auch vierseitig. Tiipfel
spaltenformig, seltener auch rundlich. Interzellularräume wurden
nicht beobachtet.

Holzparenchymzellen: Weite radial 10—35 u, tangential 10—
30 u, Lange 40 —200 u, 4—8-seitige Prismen mit abgerundeten Kanten
und vertikaler Achse, die Zellen um die Gefäsze und namentlich
um die Harzgänge oft in die Quere gezogen, mit einfachen Tüpfeln,
wo sie aneinander und an Markstrahlen grenzen, im übrigen vgl.
das bei den Gefäszen bzw. dem Libriform gesagte. Die Tüpfel oft
auf der Radialwand in 1 oder 2 vertikalen Reihen angeordnet.
Interzellularen nicht erkennbar.

Harzgange: Weite radial 30—90 u, tangential 30—80 u, darin
gelegentlich braune Harztropfen.

Markstrahlzellen:

1. Liegende: Weite radial 30 —80 u, tangential 7 —20 u, Lange
10—40 u, polygonale Prismen mit radialer Langsachse und abge-
rundeten Kanten, die tangentiale Wand meist senkrecht stehend,
getüpfelt wie die Parenchymzellen.

2. Aufrechte: Weite radial 30—60 u, tangential 10—20 u, Länge
20 —60 u, mit langsgerichteter Achse, im übrigen wie die liegenden
Zellen. Inhalt fast stets Harz, auszerdem sehr oft in den aufrechten,
aber zerstreut auch in Hiillzellen und liegenden Zellen ein deutlicher,
meist + kleiner Einzelkristall, der in der Regel nur einen Teil des
Zellinneren ausfüllt (Tafel, Fig. 4, 5).

Bestimmung des Holzes:

In der Beschreibung fehlen, gemessen an der „Linnean Method”
von Morr und Janssonius, viele Einzelheiten. Das ist eine Folge der
zum Teil mangelhaften Erhaltung des Fossils. Dennoch ist eine
Bestimmung durchaus möglich. Charakteristische Merkmale sind die
Markstrahlen, das Parenchym und die Harzgänge, die erkennen lassen,
dasz in dem Holz eine Dipterocarpaceenart vorliegt. Solche
waren auch unter dem Djambimaterial ‘Kräuskr 1) häufig; sie sind
als Dipterocarpoxylon Tobleri, Dipterocarpoxylon sp. (? Tobleri) und
Dipterocarpoxylon sp. beschrieben worden. Dazu tritt noch Diptero-
carpoxylon burmense HorpeN, und es konnte schlieszlich gezeigt
werden, dasz auch Grewiorylon Swedenborgii Scnuster sowie Wobur-
nia Scotti Storrs zu Dipterocarpoxylon gestellt werden müssen, von
denen die erste Art Dipterocarpoxylon Tobleri recht nahe steht, aber
höhere Markstrahlen und gefachertes Holzparenchym besitzt.

Sehen wir von Dipterocarpoxylon Scottii aus der unteren Kreide
Englands ab, das wegen seiner anders verteilten Harzgange und der
im übrigen + mangelhaften Erhaltung für den Vergleich mit dem

13

vorliegenden Fossil nicht in Frage kommt, so sind alle diese Holzer
auf Südostasien beschränkt. Mit keinem kann das Holz von Bolang
vereinigt werden. Dipterocarporylon burmense besitzt einreihige
Markstrahlen, Dipterocarpoxylon sp. viel gröszere Gefäsze und häufi-
geres zerstreutes Parenchym, Dupterocarpoxylon Swedenborgi viel
höhere Markstrahlen (bis 80 Zellen hoch) und teilweise gefächertes
Parenchym. Dipterocarpoxylon Toblert schlieszlieh stimmt in allge-
meinen zwar mit unserem Holz gut überein, doch ergeben sich für
dieses folgende Unterschiede: Alle Elemente sind relativ viel kleiner,
das wird vor allem deutlich bei Gefäszen, Harzgängen, Höhe und
Breite der Markstrahlen. Wenn auch diese Verhältnisse innerhalb
einer Art individuellen Schwankungen ausgesetzt sind, so dürften
derartige Unterschiede (die Weite der Harzgänge z. B. bei Dipterocar-
poxylon Tobleri 100—300 u, hier nur 30—90 u), wo es sich doch
unzweitelhaft um altes Stammholz handelt, systematisch bedingt sein.
Namentlich der Tangentialschnitt mit den verhältuismäszig viel
breiteren Markstrahlen bietet ein ganz anderes Bild. Dazu kommt
in den Markstrahlen das häufige Auftreten von Einzelkristallen, die
Dipterocarpoxylon Tobler ebenso wie anscheinend allen anderen
bisher beschriebenen Formen durchaus fehlen. Dass es sich hierbei
nicht um etwaige schlechte Erhaltung handeln kann, ist bereits
betont worden (Krauser 1). Das vorliegende Fossil, dessen Gewebe
viel schlechter erhalten ist als das eines Teiles der Djambihölzer,
zeigt aufs Neue, dass gerade die Kristalle, wenn überhaupt vorhan-
den, auch sehr gut erkennbar bleiben.
Es ist eine neue Form, die als

Dipterocarpoxylon javanense

bezeichnet werden soll.

Mit einer bestimmten lebenden Art kann das Fossil bei dem
derzeitigen Stande der anatomischen Holzuntersuchung kaum identi-
fiziert werden. Es sei auf das an anderer Stelle gesagte (KRAusEL 1)
verwiesen. Auszuschliessen dürfte die Gattung Dipterocarpus selbst
sein, bei der die Markstrahlkristalle nach allen bisherigen Unter-
suchungen fehlen. Sie finden sich dagegen sicher bei Arten von
Hopea und Vatica. Auch Morr und Janssonius (1 1 347 u. f.)
geben sie nur für Hopea fagifolia Miq. und Vatica bancana Scuurr.
an, wo sie aber nur in den aufrechten Markstrahlzellen auftreten.
Jedoch fehlen beiden Zuwachszonen und Vatica bancana auch die
tangentialen Harzgangreihen, wozu noch manche kleinere Unter-
schiede kommen. Nach alledem handelt es sich bei dem Fossil also
vielleicht um eine Hopea-oder Vatica-art. Gerade die Häufigkeit und

14

Verteilung der Harzgänge scheint ja ziemlich groszen Schwankungen
innerhalb der einzelnen Gattungen zu unterliegen.

Die bisher bekannt gewordenen Dipterocarpoxyla sind tertiären
Alters, und dies gilt wohl auch für Dipterocarpoxylon javanense.
Kieselhölzer sind ja im Tertiär des ganzen Gebietes weit verbreitet,
und schon Gorppurt (1) hat solche in seiner Tertiärflora von Java
abgebildet, ohne dasz allerdings seine Bilder eine Bestimmung der
Holzer ermöglichen würden.

Immer wieder zeigt sich also, dasz die Dipterocarpaceen auch im
Tertiär in Südostasien weit verbreitet waren. Wir gehen daher in
der Annahme kaum fehl, dasz sie schon damals eine ähnliche Rolle
wie heute in der Flora des Gebietes gespielt haben, dasz diese also
verhältnismäsig geringe Veränderungen vom Tertiär bis zur Jetztzeit
durchgemacht hat.

Zum Schlusse mögen noch die bisher bekannt gewordenen fossilen
Dipterocarpaceenhölzer in Form einer Tabelle zusammengestellt
werden.

DIPTEROCARPOXYLON Houpen.

a) Markstrahlen ohne Kristalle
b) Markstrahlen mit Kristallen

a) Markstrahlen mehrreihig
b) Markstrahlen einreihig

a) Harzgänge in (+) langen tangen-
tialen Parenchymbändern
b) Harzgänge nur sehr zerstreut

a) Neben den tangentialen Reihen
auch zerstreute Harzgänge

b) Neben den tangentialen Reihen
keine zerstreuten Harzgänge

a) Die tangentialen Harzgangreihen
sehr lang

b. Die tangentialen Harzgangreihen
kiirzer, oft unterbrochen

a) Markstrahlen bis 80 Zellen hoch,
die Einzelzellen bis 140u hoch
(gefächertes Parenchym)

b. Markstrahlen bis 50 Zellen hoch,
die Einzelzellen bis 90u hoch
(einfaches Parenchym)

2
D. javanense
(Tertiär? Bolang, Java).
3
D. burmense
(Tertiär, Burma).

4
D. Scottii
(untere Kreide, England).

3)

DSP.
(Tertiär, Sumatra).

6

D. sp. (Tobleri?)

(Tertiär, Sumatra).

D. Swedenborgii
(Tertiär, Ostindien).

D. Tobleri
(Tertiär, Sumatra).

15

Die Zahl der bisher untersuchten fossilen Hölzer des Gebietes ist
angesichts der Häufigkeit ihres Vorkommens verschwindend gering,
obwohl sie einen wesentlichen Beitrag zur Keuntnis der fossilen
Flora liefern würden.

ABBILDUNGEN.

Textfig. 1. Querschnitt, Uebersichtsbild.

Tafel, Fig. 1. Desgleichen. Markstrahlen, Gefiisze, tangentiale Holzparenchym-
binder mit Harzgängen. °5/,.

Tafel, Fig. 2. Desgleichen. *5/;. :
Tafel, Fig. 3. Tangentialschnitt. Verteilung der Markstrahlen. 25/,.
Textfig. 2. Desgleichen. 5°/,.

Tafel, Fig. 4, 5. Radialschnitt. Aufrechte und liegende Markstrahlzellen, teilweise
darin Harz und Kristalle. 150/,.

LITERATUR VERZEICHNIS.

Goerrert, H. R. (1), Die Tertiärflora der Insel Java. ’s-Gravenhage 1854.

Horpen, R. (1), Fossil Wood from Burma. Rec. Geol. Surv. of India XLVII. 1916.

Krauser, R. (1), Fossile Hölzer aus dem Tertiär von Süd-Sumatra. No. 4 der
„Beiträge zur Geologie und Paläontologie von Sumatra; unter Mitwirkung von
Fachgenossen herausgegeben von Ava. Toprer, Basel”. Verhand. Geol. Mijnbouwk.
Genootsch. Nederl. en Kol. Geol. Ser. V. 1922.

Mou, J. W. und Janssonius, H. H. (1), Mikrographie des Holzes der auf Java
vorkommenden Baumarten I. Leiden. 1906.

Morr, J. W. und Janssonius, H. H (2), The Linnean Method of Describing Ana-
tomical Structures. Rec. Trav. Bot. Néerl. IX. 1912.

SCHUSTER, |. (1), Ueber Nicolien und Nicolien ähnliche Hölzer. Kung. Svensk.
Vetensk. Akad. Hand. XLV. 1910.

Stores, M., (1), Petrifactions of the Earliest European Angiosperms. Phil. Transact.
Roy. Soc. London: B. CCIV. 1913.

Dezember 1921. Frankfurt aM. Geologisch-Paläontol.
Institut d. Uniwersität.

Anatomy. — “On the Significance of the Supra-orbital Ridges in
the Primates.” By Prof. L. Bork.

(Communicated at the meeting of February 25, 1922).

The significance of any morphological feature may be gathered
either from the function it performs, or from its mode of origin.
Of these two methods it is always best to follow the first and to
employ the second only when the first fails or yields unsatisfactory
results. That the first method yields more reliable results is sub-
stantiated by the fact that in the application of this method direct
observations are the basis for our conclusions, which in the other
case are supported at best by more or less plausible reasoning and
speculation about the possible influences and correlation of phenomena.

What I wish to state about the significance of the supra-orbital
ridges in the Primates I have preceded by this contrast between the
two methods of scientific morphological research, since not long ago
the same subject was raised at one of our meetings by our fellow-
member Prof. Dusois, who chiefly adopted the second method. I also
propose to discuss the question of the supra-orbital ridges of the
Primates — about which I pronounced my opinion on a previous
occasion. However, in my discourse I will scrupulously keep within
the bounds of immediate observation.

First of all let us consider the facts. When comparing the human
skull with that of Anthropoids -— to which group I will confine
myself for the time being — we are struck at once by the difference
in contour where the cerebral crane passes into the facial skull.
That this difference is accentuated by the orthognathy of the human
skull as contrasting with the marked prognathy of the Anthropoid
skull, is only of secondary importance for our problem. The Anthro-
poid skull has no external frontal vault, which is the reason why
some consider this skull to be flattened. This belief may be sup-
ported by the comparison of young Anthropoid skulls with those of
adults. In the former the supra orbital ridges are absent, which
makes the skull look much more like that of man. The ridges are
formed as the ape grows up. This development commences shortly
after the complete eruption of the milk set about the time when
the first permanent molar appears. —

17

Now what is the function of these supra-orbital ridges? To find
the answer the researcher should ascertain the part played by these
ridges in the structure of the skull as a whole, and what is their
topographical relation to their immediate surroundings. This may be
done quickest by making a sagittal section that extends along the
axis of the orbit, through the ridge and the adjoining part of the
skull. The image resulting from it is represented for Gorilla in fig. 1.

Fig. 1.

What does this figure teach us? First of all that, properly speaking,
the term supra orbital ridge is not quite fit and that this formation
cannot be compared with the occipital-, and the sagittal ridge also
characterizing the skull of Gorilla. For, in reality, of this so-called
supra-orbital ridge the lateral portions form the roof of the orbits,
while the central part forms the roof of the nasal cavity. If, there-
fore, the supra-orbital ridge should be removed, nearly the whole
content of the orbita would be deprived of the overlying osseous wall
and would consequently come to lie immediately under the skin.

Direct observation of the topographical relation, therefore, leaves
no manner of doubt about the function of the so-called supra-orbital
ridge, it is namely the indispensable osseous wall of the orbita at the
top. It is not a crest like the crista sagittalis and the crista
occipitalis, but it is an indispensable wall of a cavity in the skull.
But if this is a fact the origin of the superorbital ridge must be
closely allied to general growth-phenomena of the skull after the
early childhood of the ape. For we stated that, notwithstanding the
absence of the supra-orbital ridges in the child-ape, still also here

2
Proceedings Royal Acad. Amsterdam. Vol. XXV.

18

the orbita is provided with an osseous roof. It is a fact, indeed,
that in this part of the skuil radical changes have taken place in
the topographical relations. These changes may be summarized as
follows: in the child-anthropoid, and a fortiori in the fetus, the
orbits are situated under the cranial cavity, whereas in the adult they
are for the greater part precerebral. While they are lying under the
cranial cavity the bottom of this cavity makes up the roof for the
orbits, but when the orbitae are shifted precerebral a new roof
is to be formed for an adequate protection of the contents. That we
really have to do here with a displacement of the whole content
of the orbita anteriorly and not with a simple enlargement of the
orbitae, is illustrated by Figs 2 and the folllowing. They represent
casts of the cranial cavity and orbita, in situ.

Fig. 2. Fig. 3.

These casts were made in the following way: Copper wire of
adequate thickness was stuck through the communications between
orbit and cranial cavity; subsequently the orbit and the cranial
cavity were filled with plaster of Paris. Finally the enclosing skeleton
was cautiously removed with a chisel. In this way an exact image
is obtained of the topographical relations between the cranial cavity
and the orbita.

19

Fig. 2A represents a cast of the cranial cavity and orbita of a
young Macacus cynomolgus, Fig. 2B those of an adult specimen,
A dotted line indicates the location of the eye-ball. When comparing
the two figures, the difference between the young and the adult
specimen as to topographical relation of the orbita and consequently
of the eyeball, is quite obvious. In the young specimen the eyeball
is still subecerebral, in the adult it is on the other hand precerebral.

The same holds for Siamanga syndactylus, though in a smaller
degree than for Macacus, as will be seen in Fig. 3A (young animal)
and 3B (adult). Here the anterior displacement of the orbit during
growth is not so considerable as with Macacus, which accounts for

Fig. 4.

Va

20

the fact that in Gibbon the so-called supra orbital ridge is less
developed than in Macacus.

This is the case in a still smaller measure in Orang, as appears
from a comparison between fig. 4A and 4B. Although we distinctly
observe here an anterior shifting of the orbita, it is only slight.
This is why in Orang no supra-orbital ridges have been developed,
but only a general thickening of the frontal bone immediately over
the orbitae.

A comparison of the figures 2, 3,and 4 inter se clearly shows the
causal correlation between the origin of supra-orbital ridges and the
shifting of the orbitae, for the less this shifting, the less strong the
ridges will be.

This appears even more distinctly from a comparison of Fig. 5A
and Fig. 5B.

Fig. 5A shows a cast of cranial cavity and orbita of a one-month-
old child, and Fig. 5B that of an adult man. It will be seen

R. Kräusel: ,,Ueber einen fossilen Baumstamm von Bolang (Java), ein Beitrag zur Kenntnis der
fossilen Flora Niederlandisch-Indiens.”

art's
te

nn
ke aed

Bays

ER Ok On

yf

a

e

Kräusel phot.

Proceedings Royal Acad. Amsterdam Vol. XXV

Heliotype van Leer, Amsterdam

21

that there is no question about a displacement of the orbita, in the
baby as in the adult the orbita is situated subcerebral, which
accounts for the complete absence of supra-orbital ridges in man.

The subcerebral position of the orbitae is a typical feature of the
human skull, by which it is distinguished from all other mammalian
skulls. In this respect the Orang skull is most like that of man.
Parenthetically I call attention to my former pronouncement, quite
in harmony with the fact established here: that all typical human
somatic properties are persisting fetal features.

The Figures 4A and 4B also induce me to say something relative
to the so-called flattening of the skull of Anthropoids. The hypothesis
that the skull of Anthropoids bas been flattened through mechanical
causes, I consider, in principle, erroneous, as it is based only on
deficient observation and inaccurate measurement. As to the latter
it must be considered as a fundamental error when, in devermining
the length-height-index of the skull, the greatest length of the skull
is considered to be the distance between two points lying on the
outside of the skull. According to this method the height of the
skull should be measured from the basion to the superior margin
of the crista sagittalis. For a comparison of the forms of skulls of
allied species measures should be used that cannot be influenced by
a difference in thickness of the cranial bones, or by other adventi-
tious circumstances. Points on the inside of the skulls should be used.

But the hypothesis that the Anthropoid skull is flattened, rests on

deficient observation, as stated above. A flattening of the skull would
necessarily entail a transformation of the cranial cavity. Now when
comparing the relative figures it will be seen that in Macacus the
brains of the adult individual with his large supra-orbital ridges are
not flatter than those of the young individual, in which the ridges
were lacking; it will furthermore be seen that the cranial cavity
of the adult Orang in the frontal region is still as much vaulted as
in the young specimen.
_ The anthropomorphous child has a frontal vault that is visible on
the outside. The absence of this vaulting in the adult skull is not
to be ascribed to a flattening, undergone by the frontal region, but
is due to a shifting of the orbits anteriorly and to their consequent
precerebral situation. From the vaulted front a new roof overlaps
the orbita, and the originally apert frontal vault has thereby be-
come an occult one.

Mathematics. — ‘‘Representation of a Bilinear Congruence of
Twisted Cubics on a Bilinear Congruence of Rays.’ By Prof.
JAN DE VRIES.

(Communicated at the meeting of February 25, 1922).

In a communication entitled: Congruences of Twisted Cubics in
connection with a Cubic Transformation (these Proceedings Vol. XI,
p. 84, 1908) I have shown that the congruence of the twisted
cubics 9* through five points (congruence of Rere) may be converted
by a simple transformation (a; yx = 1,k = 1, 2, 3, 4) into a sheaf of
rays. Now I shall show how a different congruence [o°] likewise
by means of a cubic transformation, may be represented on a
bilinear congruence of rays.

§ 1. The transformation in question arises in the following way.
Three crossing straight lines a,, a,, a, are the axes of involutions
of planes with pairs «x, a’, (k= 1, 2,3); to the point of intersection
P of the planes a@,,a,,¢, the point of intersection P’ of the
corresponding planes a’',, a’, a', is associated.

For a point A, of a,,a, is indefinite; any point of the straight
line ¢,, which is the line of intersection of the planes a’,,a,
corresponding to A,, may be considered as the image of A,. To the
points of the singular straight line a, the rays of a quadratic scroll
(t,,)? having a, and a, as directrices are therefore associated.

Let ¢ be a transversal of a,,a, and a,, S the point of intersection
of the three planes «'; associated to the planes ap = tar. Evidently
S is associated to every point of ¢. The locus of the singular points
S is a twisted cubic o', each point of which is represented by a
ray of the quadratic scroll (¢)? having a,,a, and a, as directrices.

S being especially associated to the points A,, A,, A, where ¢
rests on @,,a,,a,, 6° is the partial intersection of the three scrolls
(laa), (ts,)°, (¢,,)"; these have in pairs a straight line a, in common.

When P describes the straight line r, the pencils (ax) become
projective; also the pencils (@',) become projective and they produce
a twisted cubic @* which is the image of the straight line r. As r

23

cuts two rays of each of the scrolls (t7/)*, 9” has the straight lines az
as chords; it rests in two points on o° because r meets two rays t.

Let us now consider the bilinear congruence of rays [r] which
has two of the straight lines ¢ an directrices. Through the cubical
transformation it is transformed into the congruence [v°] of which
the curves o° pass through two fixed points S, and S, and have
the three fixed straight lines a,,a,,a, as bisecants ‘).

Inversely any congruence [o°] with two base points S,,.S, and
three fixed bisecants az can be represented on a bilinear congruence
[r]. With a view to this we take two transversals ¢,, ¢, of the
straight lines a, and we define the involution of planes through az
by associating the planes (au9,) and (amS,) to the planes (agt,) and
(axt,).

§ 2. The curve 9° degenerates as soon as the ray 7 rests on one
of the singular lines o° or az.

If 7 passes through the point S of o® its image is composed of
the straight line ¢ associated to S, and a conic @’ through S, and S,
cutting a,,a, and a,. The locus of the conics 9’ is the dimonoid
of the fourth order, A‘, which has threefold points in S, and S,,
contains the straight lines a, and has a double torsal straight line
Ten

The image of A‘ is the scroll (7)* with directrices 9°, ¢, and 4,,
where f, and ¢, are threefold, which has the straight lines a, as
double generatrices. This may be verified by combining (#)° with
a curve u?, which is the image of a straight line mm.

If the ray 7 is to rest on a,, it must belong to one of the plane
pencils having the points 5',=a,t, or B",=a,t, as vertex and
belonging to the bilinear congruence of rays (1,1). The former
plane pencil lies in the plane B’, ¢,; the image of this plane is the
scroll (¢,,)? combined with the plane S,a,. For [o°] there is found
from this a pencil of conies which have S, and the intersections of
a, and a, with the plane S,a, ase base points. The fourth base
point is the intersection with the straight line 6',,, which, as a
transversal through S, of a, and a,, is the image of the point B’,.
Here we have therefore a group of degenerate figures each consisting
of the straight line 6',, and a conic of the pencil in question.

1) This congruence has for the first time been investigated by M. StuyvaERT
(Dissertation inaugurale, Gand 1902). A different treatment of the “Congruence of
~ StuyvAERT” is found in the thesis for the doctorate of J. pe Vxres, Utrecht 1917,
where also the literature on bilinear congruences of twisted cubics is mentioned,

24

There ‘are of course five more analogous groups represented by
the plane pencils having their vertices in b",, BB, B',, B,

§ 3. A degeneration into three straight lines is represented by a
ray of (1,1), which cuts the singular lines twice. This is among
others the case with the bisecant d of o* which rests on ¢, and t,
(and differs from a,,a,,a@,). Its image consists of the straight line
d,,=S, S, and the two transversals ¢ and 4’ that rest on d,,,a,, a,
and a, and that are the images of the points were d rests ono’.

The image of the ray B, B", consists of the line of intersection
of the planes a’, and «', corresponding to the planes «,=a, B’,
and a, =a, B', and of the straight lines b',, and 5’, Through com-
bination of the points 5, and Bb", we find in this way siz configu-
rations 9? formed by three straight lines.

The straight line 06',, lies on A‘; together with S, it defines a
plane; the straight line in this plane through S, intersecting a,
forms together with 6',, and the straight line ¢ resting on it a con-
figuration 9°.

There are apparently five analogous configurations ; the congruence
[v?] contains accordingly in all tharteen of those figures, each con-
sisting of three straight lines.

§ 4. The curves of |o9*] resting on a straight line /, are repre-
sented by the straight lines 7 of the (1,1), which cut a curve 4’
that has a,, a,, a, as chords and that meets o* twice. These straight
lines 7» form a scroll of the sixth order, (7)°, with threefold direc-
trices ¢,,¢, and double generatrices az. The straight line r, which
is a chord of 4°, hence a double generatrix of (r)°, bas for image
a curve o,* that meets / twice and which is therefore a double
curve of the image of (7)*. As therefore an arbitrary straight line is
cut twice by only one @*, |e*| is a bilinear congruence.

The image u* of a straight line m has four points on a, in common
with (r)°, for this curve cuts the double straight line a, in two points.
Besides the straight lines a, u° and (r)° have six more points in
common; hence the image of (r)° is a surface of the sixth order,
A’, with three double lines, aj, and the double curve @,°.

If u? passes through a point of the line ¢, (which is threefold on
(r)®, m contains only three points of A® outside the singular lines;
here S, and S, are therefore threefold points.

On A° there lie also the six lines 5 ($ 2) as component parts of
the degenerate figures of which the conics 9? rest on J.

25

§ 5. The transformation used here, gives also the representation
of another congruence [o°|. Let us consider the image of the sheaf
that has J/’ for centre. A ray 7’ through J/’ cuts each of the scrolls
(t°) and (¢j,)* twice and is therefore the image of a curve 9° through
the fixed point M that cuts o° and the lines az twice. This {@*] is
a special case of a congruence described by VeENERONI ').

Through a point there passes one @’* of this congruence. A curve

uw, the image of a straight line m, sends one chord through M/’;
hence m is a chord of one curve g’. Also this [o°] is therefore
bilinear.
If r' intersects the curve 6%, g? consists of a straight line ¢ anda
through M, which intersects o* twice and which rests on a,,a,,
and ¢. The cone 4° projecting 6* out of MM’, has two points of
in common with a u’; there are accordingly seven o° resting
on m. The conics of the degenerate figures in question form there-
fore a surface yw’; on this a,,a,,a, are double lines (each straight
line ¢ defines one point S, hence one ray M'S, and cuts w’ for this
reason besides in az in one more point) and o° is a threefold curve
(¢ meets three generatrices of 4°).

The surface w’ is represented on a plane by the chords of o°;
it is therefore a rational surface and belongs to the group of homa-
loids to which I have drawn attention in a communication of
Vol. XX, p. 419 of these Proceedings.

If 7! rests on a,, 9* degenerates into a straight line ¢,, (the image
of the point a,r) and a o’ of the plane @ corresponding to the
plane a'=M’a,. The conics o° form a pencil with base points M,
the points A, and A, of a, and a,, and the intersection of « with
6°, which point does not lie on a,. Each 0? is connected with a
straight line ¢,, and this rests on a,,a, and o°.

There are accordingly in all four systems of compound figures g°.

The chord of o* passing through M’, is the image of a @’ com-
posed of two straight lines ¢ and the straight line through M/ which
cuts them and which is at the same time a chord of 5*.

The transversal of a, and a, through J/’ is the image of a @
formed by a straight line ¢,,, a straight line ¢,, and their transversal
through M which rests at the same time on a, and a,

The transversal through M’ of a, and o* is the image of a o°
formed by a straight line ¢, a straight line /,, and their transversal
through M which rests at the same time on a, and on 65°.

There are therefore in all seven figures o° consisting of three
straight lines.

1) Rend. Palermo XVI, 209.

ws

3
3

a 8 ©

26 .

The curves 9° resting on a straight line /, are represented by the
generatrices of the cone that projects the curve 4° out of M’. As
this cone is cut by a u? in nine points, the curves 9° intersected
by / form a surface 7°. On this surface a,,a,,a, and o’ are three-
fold lines, because any straight line ¢,; and any line ¢ cuts the
cone (M’, 23) three times and the image of the double generatrix of
this cone is a double curve of 4°. Any curve of [9°] has 8x3
points in common with 4’ on the singular lines; hence M is a
triple point of A’.

Physics. — “Research by means of Röntgen- Rays on the Structure
of the Crystals of Lithium and some of its Compounds with
Light Elements. U. Lithium-Hydride’. By J. M. Bisvorr and
A. Karssen. (Communicated by Prof. P. ZEEMAN).

(Communicated at the meeting of February 25, 1922.)

1. Introduction. The investigation with X-rays on the structure
of lithium-hydride was taken up in connection with the analogy
drawn by Mogrs') between lithium hydride and the heteropolar
alkali halogenides.

2. Röntgenograms. The photographs were made as described in
our preceding paper’). The difficulty presented itself that after the
exposures the hydride-content had been reduced by 15 or 20 percents
of weight. The parasitical lines were eliminated: by comparing
the photographs of samples of decreasing hydride-content (the place
of the LiH-lines appeared to be independent of the degree of decay,
hence no formation of mixed crystals); by photographing a coarse
crystallized, non-rotated sample, appeariug the interference lines of
LiH markedly distinguished by dots of greater intensity; by
checking up ‘the parasitical lines by those of LiOH).

3. Calculation. The table contains for LiH the values of 10°
eae
sin? 3 for the centres of the a-lines. As appears from the occurrence

of a factor 77,5 + 0,5 LiH is regular, and the side of the elementary
cell a=4, 10.10-8 em. From this common factor the number
of particles per elementary cell, » is calculated to be 4.30, with the
aid of the density according to Moers, mol. weight, constant of AvoGaprRo,
and wavelength Crx, (resp. 0,816 ; 7,94; 0,6062 . 10°“ and 2,284 .10-).
This points to n=4, which is in agreement with the supposed
NaCl structure together with the absence of the planes of mixed indices.

1) Moers, Z. f. allg. u. anorg. Chem. 113, 179, (1920).
Nernst, Z. f. Elektrochemie 26, 323 and 493 (1920).
3) Biuvoer and Karssen. These Proceedings Vol. XXIII, p. 1365.

28

Putting n=4 the said common factor determines the density at
0,76 + 0,01"). In absence of all further erystallographical data we
have confined ourselves to the question whether sticking to a NaCl
or ZnS structure an electron grouping could be found, according to
the intensities of the reflections found.

The table gives the observed and calculated intensities. Only those _
factors which bring about an abrupt change in the intensity as
function of A’, have been taken into account, viz. the factor of
the number of planes and the structure factor, in which the influ-
ence of the configuration of the electrons too has been accounted
for. For this were tested some approximative suppositions. We have
considered the possibility that the valency-electron remains near its
mother-nucleus (atomic lattice); that the Li has lost its valency-
electron to the hydrogen (ion lattice)®); that binding of Li and H
takes place by means of rings of electrons revolving round the
connecting line in planes normal to the non intersecting trigonal
axes halfway the Li and H nuclei (binding cireles; passing along a
trigonal axis two-electron-rings may be imagined between Li and
H: molecular lattice, case A; or one-electron-rings between Li and
H as well as between H and Li, case B).

As to the orbits of the electrons it has been assumed: 1. that the
electrons are so near to their nucleus that they may be supposed
to lie in one point (points; reflecting power proportional to the
number of electrons); 2. that the connecting line of nucleus and
electron is of a definite length y, and is equally occuring in all
orientations throughout the part of the crystal that is cooperating
in the interference (spheres; diminishing factor for such an electron
sin 2m ae

a

EE! in which H=W/2h®); and 3. that these connecting

Den

a
lines are in planes normal to the non-intersecting trigonal axes,
all the directions equally occurring in those planes (rings: diminish-

»
ing factor J, (2% ha r) in which J, is the Bessilian-function of
a

the order of magnitude 0 and y the angle between orbit and lattice
plane‘). In the binding cireles also only circular orbits have been

') Impririties have no influence on this value of the densty, as there is no
formation of mixed crystals.

2) Also the less probable case Li-H+ has been considered.

3) Cf. Korkmeyer, These Proc. Vol. XXIII NO. 1, p. 120.

4) Cf. Coster, These Proc. Vol. XXII N°. 6, p. 586.

29

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30

considered, and here too relation of phases has been neglected
(diminishing factor as under 3). *)

The influence of the heat motion, of which nothing is known
for the different electrons, was left out of consideration. The radius
of the comparatively small inner ring of Li has always been taken
equal to Bour’s initial value’); in all the suppositions mentioned
it has been examined what values of the radii of the other orbits
made the caleulated and observed intensity concordant. Finally the
supposition “rings, ou — = + 5/6 times the radius of a two-quanta
ring in a free H -ion” appeared to give the best agreement. As a
specimen some of the calculated intensities are given i.a. those for
Bour’s initial values of go, and in the last column the case
en — = + 0,6a and prij = + 0,05a, which is in agreement with
the observations.

In how far the factors neglected here, as heat motion, and the
occurrence of non-circular orbits, may affect the conclusions drawn
here, must at present be left undecided.

4. Summary. The Röntgenogram of lithium hydride (method
Depyk-SCHERRER) has been taken with Kg, rays. LiH appears to
crystallize regularly with 4 LiH per elementary cell. [Side a=
410.108 cem.|. The density is found to be 0,76 + 0,01. On the
basis taken for the calculation the following assumptions appeared
to be most satisfactory: NaCl-structure with positive Li-ions and
negative H-ions; systems of two-electron rings both round Li- and
H-nuclei with radii resp. + 0,05a and + 0,6a, the planes of which
are normal to non-intersecting trigonal axes.

In conclusion we express our great indebtedness to Prof. Smits
for his valuable help and the great interest he took in our work.

Laboratory of Physical and Inorganic Chemistry.
Amsterdam, February 15, 1922.

1) In Coster’s computation of the binding circles of diamond this has also been
introduced, whereas KoLKMEYER bases his calculations on an undisturbed phase
relation.

*) Bonr, Phil. Mag. (VI) 26 490 (1918).

Bacteriology. — “Studies about p’Hereiin’s Bacteriophagus’. By
J. W. Janzen and L. K. Worrr. (Communicated by Prof.
C. Eyxkman).

(Communicated at the meeting of February 25, 1922).
I. The Bactertophagus in Enteric Fever.

We have succeeded in proving the existence of this bacteriophagus
in the faeces of patients recovering from enteric fever, as has also
been described by p’HeERELLE.

If pb’ HeRELLE’s views are right, it must be possible to influence
the process of enteric fever favourably by administering bacterio-
phagum antityphoideum.

We have tried this in three cases and perhaps we have observed
a somewhat favourable result, but not a striking success. The
explanation hereof might be found in the fact that this bacterio-
phagus did not happen to be adjusted at the bacterium, that caused
the illness of these patients. We have considered it worth while to
examine this systematically.

We have been able to make use of three bacteriophagus specimen,
two of which were from the faeces of patients recovering from
enteric fever, the third from the faeces of a healthy person who
had had enteric fever forty years ago. We have examined the effect
of the bacteriophagi as opposed to 17 typhoid strains, 15 of which
came from the collection of the Laboratory for Hygiene, the two
others from the blood of patients out of which the bacteriophagus
had also been taken. We have steadily examined the clearing up
of the broth, which has turned slightly turbid by typhoid bacilli 6
hours old from agarcultures, the checking of the growth of typhus-
bacilli in broth, and finally the formation of little islands on the
agarplate(plages).

What can be the cause of this difference in behaviour?

It might be supposed that the aninfluenced typhoid strains would
be so called resistent strains.

This would be possible for some strains that are not influenced
by any of the three bacteriophagus strains (3, 8, 20).

But. we also see that the bacteriumstrain which is influenced by
one bacteriophagus is not influenced by the other, and vice versa.

1. Clearing up of the typhoid bacilli distributed in the broth.

„32

TABLE.

2. Checking of the growth of typhoidbacilli.
3. Formation of little islands on the agarplate, on which some of the contents
out of tube I has been smeared.

Bacteriophagus Wi.

|
typhoidstrain | 2 3

+ ft) ++ | t+ | t+

Sm.

Eed nr
id . a

3 kil ES has

8 Je HE ie

9 ernie halle el stem ees
15 = EN enn
19 = BM
20 — = —

23 ttds eee re
24 Fat Aileen
25 an alae ane
26 staat oats tredende
27 — Edle,
29 Sai oldest Parbat
31 = Se ME os eae
32 Saath Cate | ages

Bacteriophagus Wi negative with regard to 1,

i Sm En
9) Re ”

Bacteriophagus Sm.

1

>)

>)

2

+++

ion
Et

4b
jdt

3, 8, 20

Bacteriophagus Re.

2 3

+ |++++
+++ [tt
++ Itt
++ |4+++
H+
44+ |++++

++ |++++]/4+4+44+

Hh td
++ [tt

… W1ij13j16s180 0275 129
„Wi, 3, 8, 20, 28, 24, 27, 29.

Bij agglutination with a highly agglutinating horseserum (Saxonian
serum-works) no difference between the strains could be demonstrated,
they all agglutinated to '/,
So it will be necessary to find or to prepare a bacteriophagus
which also affeets the negative strains.

For the time being we have not succeeded in vitro to adapt the
bacteriophagus to these. So we shall have to wait until a new

33

bacteriophagus is found which fills up this gap, if need be we can
then administer a mixture of the various bacteriophagi.

We have been able to convince ourselves that, with a dose of 10
cM. bacteriophagus per os, the bacteriophagus was already to be
found the next day in the faeces of two typhoid patients who had
not had it before.

p’Here..e has proved that the bacteriophagus is not absorbed by
foreign bacilli on which it has no effect.

Our bacteriophagus however was absorbed by living typhusbacilli
who were not influenced in their growth by our bacteriophagus.

February 1922. Amsterdam, Lab. for Hygiene of the
’ University.

Proceedings Royal Acad. Amsterdam. Vol. XXV.

Bio-Chemistry. — ‘‘Ewperiments on Anaphylaais with Azoproteins’’.
By K. LANDSTEINER. (Communicated by Prof. C. H. H. Spronck.)

(Communicated at the meeting of January 28, 1922).

In previous articles the writer described methods for producing
immune sera, acting upon known chemical groups. These methods
are based upon. the use of antigens, consisting of proteins, which
are chemically combined with substances of simple constitution. *)

As already indicated, the question suggests itself as to whether
anaphylaxis can be produced by these compounds and what is
the action in anaphylaxis (sensitization and shock) and antiana-
phylaxis of each of the two components of the antigen, viz. the
proteins and the simple substances combined with it. The significance
of these problems for the theories of immunity and anaphylaxis and
the knowledge of the condition of hypersensibility produced by
simple substances is evident (ef. Dorr) *).

The experiments presented here*) form part of a series, the car-
rying out of which has been delayed because of external circum-
stances. a at

The guinea pigs were sensitized by means of azoprotein *) prepared
from horse serum and p-arsanilic acid (1 gr. of atoxyl for 100 ce.
of serum).

For the second injection an azoprotein formed by combining fowl
serum and p-arsanilic acid was employed. The use of a number of
other azoproteins was rendered difficult because of their toxicity
when injected intravenously.

Results: It was found to be more difficult to produce the ana-
phylactic state with the substances mentioned above than with the
proteins usually employed, and in the experiments to be described
it was necessary to make three intraperitoneal injections, correspond-

ing to 0.5 to 1.0 cc. of serum each, in order to produce consider-
able effects.

') Zeitschr. f. Immun. 26, p. 258 (1917), Biochem. Zeitschr. 86, p. 343 (1918).
2) Doerr, Schweiz, med. Wochenschr. 1921. No. 41.

5) Details will be given later.

*) 1. c. Bioch. Zeitschr. 86, p. 359.

35

In the case of 14 of the sensitized guinea pigs, the reinjection
was made intravenously, using 1 to 2 cc. of azoprotein*) per
500 gram weight of the animals. 5 animals died within a few
minutes, 3 showed severe, 5 slight manifestations of anaphylactic
shock. Nine control animals showed no symptoms.

Five animals treated in the manner described showed no ana-
phylactie reaction after the intravenous injection of azo-compounds
obtained by combination of tyrosin and. p-arsanilic acid; the injection
of azoprotein (fowl serum —+ p-arsanilic acid) made an hour later
failed to produce shock, As a control experiment, in 3 animals an
azo-compound of metanilic acid and tyrosin was used for the intra-
venous injection. These animals showed anaphylactic symptoms on the
subsequent injection of azoprotein (fowl serum + p-arsanilic acid).

The results obtained demonstrate that guinea pigs previously
injected with an azoprotein: (horse serum + arsanilic acid), show
anaphylactic reactions upon being reinjected with another azoprotein
containing the same group, i.e. fowl serum + arsanilie acid; but
they do not show such symptoms upon being reinjected with a
compound of arsanilic acid and a substance of simple composition,
i.e. tyrosin. The latter substance, on the other hand, seems capable
of desensitizing the animals. |

The Hague. Laboratory of the OR. K. Ziekenhuis”.

1) Prepared as indicated in Biochem. Zeitschr. 86, p. 362.

3*

Physiology. — “On the Causes of the Emigration of Leukocytes’ *)
By K. J. Ferinca. (Communicated by Prof. H. J. HAMBURGER.)

(Communicated at the meeting of February 25, 1922).

Dr. Haan’) has suggested a method by which in a simple manner,
without injuring the laboratory animal, large quantities of poly-
nuclear leukocytes can repeatedly be obtained. He injected into the
abdomen of his animals fluids such as a starch-solution in NaCl 0.9,
and other harmless fluids and thereby obtained invariably a homo-
geneous emigration of polynuclear leukocytes.

My own investigations were performed systematically according
to this method, with a number of liquids in order to demonstrate
a definite chemical cause for the emigration of the leukocytes. I
experimented on rabbits.

For shortness sake I will only summarize the results of these
experiments.

Whatever liquids were injected (electrolytes, non-electrolytes, more
or less physiological fluids such as RinGer’s solution, ultra filtrate
of serum, sterile serum, olive-oil or paraffin) the result was invariably
an exudation with emigration of many leukocytes. The process of
this emigration was the same in all cases. From this 1 concluded
that the emigration is not brought on by a specifically chemotactic
influence exercised by definite substances upon the leukocytes.

However, there was still a factor that had been left out of con-
sideration, viz. the concentration of the hydrogen-ions, which recent
inquiries have proved to play a prominent part in different mani-
festations of life.

I considered it rather interesting to ascertain the proceeding of
the H-ion concentration in the injected liquid at various intervals
after the injection.

We used for this purpose the colorimetric method and applied
phenol-red and cresol-red, recommended by CLARK an Luss’*).

Determinations were made in serum of venous blood and in normal

1) A more detailed communication will appear elsewhere.
3) J. pe HAAN, La. Thesis. Groningen 1920.
3) CLARK and Luss, -Journ. of bact. 2. 7. 109, 191 (1917).

37

abdominal transudate; the pH of serum was slightly less than 7,6
and that of normal abdominal transudate 7,6.

When fluids were injected into the abdominal cavity, a pH of
7,2 invariably occurred in the exudation after a short time (+ */,
hour), no matter whether the injected fluid was acid or alkaline
beforehand. This was the same for all injected substances, also for
strongly buffered fluids, such as serum. Only the interval before a
pH of 7,2 is reached, is somewhat longer. This also applied to oil
and paraffin-injections, the centrifugalized fluid then presented a
pH of 7,2.

It appears, then, that a difference of pH from 0,3 to 0,4 exists
between the blood and the exudation. At the same time it appeared
that emigration of polynuclear leukocytes results from the injection
of the same fluids.

There is now every reason for correlating the constant occurrence
of emigration with this constant phenomenon of the changed pH,
which also always manifests itself, however different the injected fluids
may be.

The question may be asked: in how far this differing H-ion con-
centration may be answerable for the emigration. | have endeavoured
to solve this problem by maintaining artificially in the injected fluid
a pH of 7,6 or a little higher, through the addition of alkali, and
comparing the result obtained with a control-animal, in which the
injected fluid was left to itself. I found from three such experiments
that in the first case no emigration of polynuclear leukocytes ensued,
which, however, revealed itself with the control-animal.

It is evident from these experiments that the degree of acidity is,
indeed, the causative factor of the emigration of the polynuclear
leukocytes; it being the only factor which has altered in the experi-
ments mentioned.

We now have to go into the question in what manner this esta-
blished difference in H-ion concentration with the blood can bring
about the emigration. Presumable potential differences between fluids
with various H-ion concentration are the first to suggest themselves;
such potential difference might well effect a movement of cells in
one direction, in casu an emigration. [ am analogously reminded
here of the well-known cataphoretical phenomena found i.a. by HOBER
and his pupils especially in red blood-corpuscles.

I thought it desirable by following the example of HöBer to
perform cataphoretic experiments with red bloodeorpuseles, with
polynuclear leukocytes and with mononuclear leukocytes of the
rabbit in order to ascertain whether they behaved differently towards

38

the. galvanic current. This appeared not to be the case: all of them
moved towards the anode, their charge was consequently negative.
Through the addition of acid we managed to change their charges:
when the pH was made less than 4.8, they moved towards the
cathode.

In the body, where pH is always greater than 4.8, they will
always be moved by the current towards the anode. This, then,
does not afford an explanation of the various behaviour of the
different kinds of blood-corpuscles in the case of exudation. However,
we need not, on that account, exclude the possibility of the exudation
of the polynuclear leukocytes being caused by a potential difference,
as besides a potential difference other factors come into play, which
may cause or prevent emigration, i.a. the surface-properties with
regard to the capillary wall, and the ameboid mobility. Hence the
passive cataphioresis becomes complicated on account of these surface-
actions. These actions will vary the effect of the cataphoresis in
different cells in «accordance with their composition; even in the
absence of emigration, the cataphoretic effect even on red blood-
corpuscles will reveal itself in the considerable accumulation of
blood-elements in the abdominal vessels.

Now I have tried to demonstrate potential differences between
two fluids differing only in the H-ion concentration. To this end we
made use of a so-called ““úlkette”’. I succeeded in demonstrating with
benzaldehyd and benzylalcohol as oilphase, potential differences between
fluids with a pH of 7.2 and 7.6. When adding lecithin or a mixture
of lecithin and cholesterol to the oilphase, the potential difference
was considerably greater. An addition of cholesterol alone, however
caused the potential difference to disappear altogether.

These experiments have proved it to be very probable, that through
the difference in pH there is also a difference in potential between
the circulating blood and the exudation. Preliminary experiments
justified the same conclusion.

With non-polarisable electrodes we found that under normal con-
ditions the blood is positive (however slightly) relative to the abdomen,
while after the injection of a fluid into the abdomen, a reverse
potential difference manifests. itself. These experiments, however,
will have to be prosecuted further.

Since we have seen that the bloodeorpuscles may be moved by
electromotive forces, we are justified in assuming that under the
influence of the difference in acidity between the blood and the
exudation, which causes a potential difference, the polynuclear
leukocytes are moved towards the exudation. The anomalous be-

39

haviour of the lymphocytes and especially the red blood-corpuscles,
may, as stated above, be ascribed to other surface properties of
these cells.

In conclusion we may state, therefore, that through injection of
any fluid whatever, an increased prolonged acidity can be demonstrated
at the place of injection, which may reasonably be assumed to give
a certain direction to the ameboid movements of the leukocytes, which
reveals itself in the constant occurrence of the emigration of the
polynuclear leukocytes. |
_1 may still add that in no case does the increased acidity exist
longer than 18 hours, after the injection of aqueous fluids, but that
it persists longer. after oil injections; this is the reason why with oil
the ‘emigration lasts longer, as is borne out by all phenomena, i.a.
the changes in the blood-formula, which cannot be gone into. any
further here. Neither can I expatiate here on the cause to which
the increased acid formation itself is due. I can state only that there
is no excessive accumulation of carbonic acid. The only factor we
can take into consideration is a diminution of the normal reserve
of alkali under the influence of the formation of acids other than
carbonic acid.

Now it is of vital importance to know whether our conclusions
regarding the emigration of leukocytes in sterile abscesses and
exudations, also apply in general to every migration of leukocytes
through the body, e.g. to the emigration of leukocytes in exudations
of bacterial origin and to the emigration (normal and pathological)
of the white bloodcorpuscles from the bone-marrow in the blood-
circulation. Concerning the latter we are inclined to believe that
normal supply of the polynuclear cells in the blood from the bone-
marrow is also procured under the influence of a potential difference
between bone-marrow and blood. It may also be possible that, when
that supply from the bone-marrow. proceeds abnormally, as in cases
of leukemia, the relation between the pH in the blood and the
bone-marrow is altered. It also avails to know the reason why, in
the case of fatal infections, the bone-marrow does not react on the
stimulus of inflammation, why no leukocytes are transmitted to the
nidus of the inflammation. |

It may be also that without a potential difference between bone-
marrow. and blood or between blood and the nidus of inflammation,
the emigration of. leukocytes is impossible. It should at the same
time be noted, whether the distribution of lecithin and cholésterol
in the body may, bave influence on the generation of electric currents ;

40

the significance of a proper relation of these substances for various
functions of the body, has latterly been pointed out by several
authors *). Furthermore we have also seen, that cholesterol, added
to an intermediate phase between two fluids with different H-ion
concentration, brought about an isolation which prevented an electric
current. Such an insulator might, therefore, likewise prevent the
occurrence of an electric current in the body.

Thus far I have been able to ascertain whether acidity plays a rôle only with
regard to the abscesses in acute inflammation processes In analogy to what we
have seen in the sterile exudations, it may be expected that in pus or exudations
of inflammatory nature, in which polynuclear leukocytes predominate, there will
be a pH considerably smaller than that of the circulating blood. If only mononuclear
leukocytes occur in the exudations or in the pus, the pH will differ little or not
at all from that of the blood or the blood serum. It may be presumed, therefore,
that in acute suppuration-processes there is in the pus a much lower pH than
that in the serum. In chronic cases of suppuration, especially when there are no
polynuclear leukocytes, the difference in pH with the blood must be much smaller.
Likewise in tuberculous pus, where only mononuclear leukocytes occur, we cannot
expect a great difference in pH with the bloodserum.

The pH of human bloodserum was determined again by the colorimetric method.
Here we met with great obstacles in the yellow colour, which is most often peculiar
to serum and in the occasional excess of fat. In accordance with the values
established by Evans?) with indicators, we found also in the human serum a
pH of + 7.6.

Pus from an acute pleuraempyema was examined. The liquid centrifugalized
from the pus, had a pH of 6.9. The ill-smelling pus contained many streptococci
and beyond mononuclear- many polynuclear leukocytes and remains of them.

Pus from a chronic molar abscess with acute exacerbation had a pH of 7,
beyond mononuclear leukocytes also many polynuclear leukocytes and remains of
them occurred in the pus.

In a case of streptococci-meningites the cerebrospinal fluid had a pH of 7.3
and contained rather many leukocytes, of which 60°/) were mononuclear and 40 °/,
polynuclear. The next day another puncture was made, and the fluid derived from
it, proved to be much more cloudy; the pH was then rather more than 7.2. The
relative number of the various kinds of leucocytes had changed now, the mono-
nuclear cells fetching only 5°/) and the polynuclear as much as 95°/o.

It appears, then, that in these investigations the pH found, agrees
with the presence of polynuclear leukocytes in the pus or in the
exudation.

5 UM MAY.

1. To bring about the emigration of leukocytes from the blood-

1) Cf. c.a. BRINKMAN and van Daw, Studien zur Biochemie des Phosphatide und
Sterine 1—3. Biochem. Zeitschr. bnd. 108, H. 1/3 1920.
2) C. Lovarr Evans, The Journ. of Physiol. 54, p. 167 and 353.

41

circulation, chemotactic properties of definite substances do not come
into play. The process of the emigration is the same, whatever may
be the nature of the substances injected for the purpose of obtaining
the exudation in the abdominal cavity. Neither can any special
significance be attached to fat and lipoids.

2. As for the chemical composition of the obtained exudation, it
appeared that in a short time it becomes about the same as that of
the normal tissue-fluid.

3. The mpected fluid very soon reaches a higher degree of acidity
relative to the blood and the normal tissue fluid; independent of its
being acid or alkaline when injected, a concentration of hydrogen
ions of about pH 7,2 is produced, while the normal reaction of
blood and tissue-fluid is 7,6.

4. This higher acidity must be considered to be answerable for
the emigration, since the emigration stays away, when the acid re-
action is checked.

5. In keeping with this fact also in inflammatory-abscesses, the
reaction of the fluid relative to the blood is distinctly more acid.

6. It is possible to consider the emigration as resulting from the
potential difference arising under the influence of the difference in
concentration of H-ions between the blood and the injected fluid,
in the sense of a cataphoretic action.

7. We call attention to the possibility, that also in other abnormal
accumulations of leukocytes in the body, as in leukemia, corre-
sponding factors play a part.

February 23, 1922.

From the Physiological Laboratory of the
Groningen State- Univ.

Geology. — “Observations on the Incandescent Sand Flow of the
Valley of ten thousand smokes.’ By Koperr F. Griges.
(Columbus, Ohio, U.S.A.)

(Communicated at the meeting of April 29, 1922).

Of the work done by the last expedition (1919) Dr. Escuer has
seen only the popular account in the National Geographic Magazine,
September, 1921, Vol. 40 pp. 219--292. This account, written for
the 725,000 members of the National Geographic Society, was mani-
festly not the proper place for a technical presentation of the detailed
data which the geologist requires as the basis for his conclusions.

A more technical, though only preliminary, account giving more
geological information has been published by Dr. C. N. Fenner,
Petrologist of the cooperating party sent with the expedition by the
Geophysical Laboratory of the Carnegie Institution, in the Journal
of Geology, Vol. 28, pp. 569—606, 1920, under the title “The
Katmai Region, Alaska, and the Great Eruption of 1912.”

A further contribution by E.T. AtLen, Chemist of the Geophysical
party, dealing not directly with the Incandescent Sand Flow but
with the “Chemical Aspects of Volcanism’, appeared in the Journal
of the Franklin Institute, Vol. 193, pp. 29—80, January, 1922.

Further papers giving the scientific results of the Katmai expedi-
tions in more detail are soon to appear in the projected Memoirs
of the National Geographic Society.

Dr. Escnrr believes that the hot sand flow was made possible by the
water of a crater lake which “must have” occupied the top of the
mountain prior to the Eruption of 1912. He is in fact so sure of
such a lake that he even figures it on his diagram.

The first and most obvious fact which renders this explanation
impossible is that Katmai possessed no crater lake prior to the
eruption. On page 43 is reproduced a section of the United States
Coast and Geodetic Survey Chart N°. 8555 showing the condition of
Katmai before the great eruption. It was a three-peaked mass without
any large crater, essentially similar to its near neighbor Mageik, see
map on page 45 also a photograph reproduced in the National
Geographic Magazine, Vol. 31, p. 30, 1917. Both were rounded
domes built up by repeated flows of viscous lava without admixture
of cinders or other fragmental products such as appear in the typical
composite cone,

43

Up till the last eruption the ejecta had consisted entirely of basic-
andesite which had poured out without any explosive accompani-
ments of a major sort. Between the last of these flows and the

Katmai volcano before the eruption

155°
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This map shows that there could have been no crater lake
before the eruption. The site of the present crater (cf. map on
page 45) was occupied by three peaks whose position and
altitude were determined with precision by the United States
Coast and Geodetic Survey, from whose Chart N°. 8555 the

figure is traced.

recent outburst had intervened a pause probably many centuries in
duration and when activity was resumed it differed materially from
what had preceded. The Eruption of 1912 consisted entirely of
fragmental products rather than molten lava. First came the great
outpour of ash and pumice which is the subject of this note. Then
Mt. Katmai blew up in a series of extremely violent explosions
which left behind the present gigantic crater in place of the former
mountain summit. The total quantity of rock that disappeared from

d4

the top of Katmai during the eruption is estimated at 11,000 < 10°
cubic yards (8400 > 10° cubic meters).

Associated with the change in the character of the activity was
an equally great change in the composition of the magma concerned.
The old lavas are dark-colored basic-andesites with a silica content
of about 60 per cent.

But the new magma is a white, acid rhyolite with 75 per cent
of silica.

This change in composition of the magma, while without any
particular bearing on the point at issue here, is of great significance
in interpreting other aspects of the eruption, for it enables us to
gain considerable insight into the processes operation before and
during the explosions.

A second line of proof that the Incandescent Sand Flow could
not have been of the type supposed by Dr. Escuerr is that the slopes
of Katmai show no evidence of such a flow having passed over
them. As Dr. Escner rightly asserts, a lahar erodes in the upper
steep portion of its course. Erosion would have been particularly |
marked if such a flow had passed down the slopes of Katmai, since
they were covered with ice, which would have melted away with
great rapidity before a hot lahar. Yet the slopes down which Dr.
Escner assumes the lahar to have coursed are still clothed by the
glaciers which originally covered them. To be sure, the heads of
these glaciers were blown away in the explosions of the summit of
the mountain and their toes were melted back by the flow of in-
candescent sand across them from Novarupta down the Valley. But
these accidents to the extremities only serve to emphasize the un-
disturbed condition of the middle slopes down which the hypothe-
tical lahar is supposed to have run.

Instead of having flowed down the slopes of Katmai, the mass
clearly moved transversely across the base of the volcano. The high
sand mark, i.e. the edge of the flow, slopes steadily from south to
north across the foot of Katmai. Its altitude at the south edge of
the glaciers is several hundred feet greater than at the north edge,
thus indicating that it flowed north along the foot of Katmai rather
than westward from its heights.

A third circumstance which makes it impossible to assign the
origin of the flow to Katmai volcano is the distribution of its material.
A wore detailed contour map then that published with Dr. EscuEr’s
argument (see page 45) makes it clear that the greater part of any
fluid poured down the western slopes of Katmai would pass through
the East arm of the Valley of Ten Thousand Smokes between Knief

45

Peak and Broken Mountain. A small portion might pass over the
divide at Novarupta and run down between Falling Mountain and
Baked Mountain. But as a matter of fact the quantity of flow material

THE VALLEY OF TEN THOUSAND SMOKES

FROM A SURVEY BY THE KATMAI EXPEDITIONS
OF THE NATIONAL GEOGRAPHIC SOCIETY

ROBERT F GRIGGS, DIRECTOR

SIFEERGULATION AND TOROGRAPHY By C.F MAYNARD
. 2 2

iJ Ed 1

Mt. Katmai and the Valley of Ten Thousand Smokes since the eruption.
Compare Mt. Katmai with the map on page 43. The contours show that it
would be impossible for a liquid flowing under gravity from top of Katmai
volcano to reach the head of Mageik Creek via Katmai Pass.

in the Valley leading away from the base of Katmai appears
markedly less than that in the main arm of the Valley of Ten
Thousand Smokes ten. kilometers across the mountains from Katmai.
No liquid starting from the summit of Katmai and seeking its level
under gravity could possibly reach the summit:of Katmai Pass.

_ It is believed that the map on this page demonstrates this point

46

sufficiently. But it may be added that the relatively small scale map
with contours no closer than 200 feet (60 meters) is much less
convineing than an examination of the ground itself. I venture to
assert that no one who had made field observations would have
suggested the possibility of a flow from Katmai taking the course
outlined by Dr. Escuer. The arrows on his map would make out
that a part of the flow turned out of the direct course and climbed
the 150 meter slope between Falling Mountain and Trident, instead
of continuing in a straight line down the Valley. Not only gravity
but also inertia acting as centrifugal force, would have opposed any
such course. The presence of the flow in the saddle of Katmai Pass
and down the slopes on both sides constitutes inescapable proof that
part of it originated near the divide. A good-sized crater which
may have been one of the points of origin lies in fact near the
summit of the pass.

Any one of these three lines of evidence alone would negative
the possibility of our flow being a lahar of the Klut type. Taken
together they put such a hypothesis entirely out of the question.

But, if the evidence definitely shows that our flow is not ana-
lagous with the hot lahars of Klut, the determination of its real
nature is quite another question.

In our earlier studies, recognizing the evident resemblance of the
terrane to an ordinary mud flow, we sought to interpret it without
assigning a very high temperature to its material — hence the
descriptive name applied, “hot mud flow’. It was recognized from the
first, however, that no ordinary aqueous suspension could ever
convert a whole forest into charcoal. Further study made it more
and more clear that the mass must originally have been very hot.
Charred wood occurs only near the foot of the flow, fifteen kilo-
meters or more from Novarupts. Throughout the main part of the
Valley the vegetation was entirely consumed and its ashes dissipated.
The rock of a whole mountain, named “Baked Mountain”, was
changed from gray-green to brick red — as though subjected to a
high temperature for a prolonged period.

The stiffened tuff left behind after the sand flow had come to
rest differs materially in several respects from the deposits of Klut.
In the first place it was much more viscous while in action. The
average thickness of the Klut lahar is estimated as only 50 centi-
meters. The pictures of destruction in Blitar all show-a relatively’
thin veneer of volcanic debris covering the ground. This terminal
portion moreover was not very hot as is evidenced by numerous
plants with unwithered leaves standing close to the volcanic debris,

47

e.g. a patch of rank herbage beside the railway station at Blitar.
(See this pag.)
In our flow, on the other hand, the average thickness is fifty

Photo from HELMIG & Company.
Volcanic debris from the Lahar of Klut at Blitar about
5 km. above the termimus of the flow. The unburned
buildings and unwithered herbage show that the lahar
could not have been very hot at this point.

times as great, indicating an entirely different sort of fluid. It is
doubtful indeed if the minimum thickness of our flow was as low
as the average thickness at Klut. Few, if any of the deposits lift on
the ground are less than a meter thick. Clear out to the very tip
it retained an excessively high temperature. For a considerable
distance beyond the’ present end of the flow material one finds
stumps of bushes burned off by the heated material that once covered
them but has been eroded away. Outside the limits of the flow
itself moreover all trees were killed for some distance and grass
fires were started well down toward the tip. See pages 48 and 49.

The deposits left behind, while different from the lahar of Klut,
resemble closely those of the “incandescent avalanches” of Pelée
and La Soufrière as deseribed by a number of observers, e.g.
ANDERSON and Frerr *).

This similarity together with the increasing evidence of a high
temperature brought out by further study has convinced us as
detailed by Fenner’) that the tuff filling the Valley of Ten Thousend
Smokes originated as an outpour of red-hot material very much like
the incandescent avalanches that rolled down the slopes of Pelée
and La Soufriere in 1902.

The differences between these and the hot sand flow with which
we are dealing appear in fact to be due to differences in the cir-

“‘1)"Phil:' Frans. Royal Society, A’ vol:'200; p. 492 et seq. 506 ‘et seq.
3) O. p. cit. p. 577.

48

cumstances of extrusion rather than in the character of the ejecta.
Whereas the incandescent avalanches of the West Indian volcanoes
issued from old vents of the central type, observations such as have
been detailed in the case of Katmai exclude as possible source all of
the five old volcanoes adjacent to the Valley of Ten Thousand Smokes.

A section of the sand flow close to the terminus.

Photo by L. G. FoLsom.
The tree, about 30 cm. in diameter, was entirely reduced to

charcoal. The material was much less fluid than the lahar of
Klut, for it did not run out into a thin sheet as there, but
remained relatively massive close to the extremity. (The sand
is covered by stratified ash from Katmai and by outwash of
the stream which later cut the section).

49

The configuration and practically continuous course of the high
sand mark entirely around the Valley basin seem to leave no escape

The edge of the incandescent sand flow of the
Valley of Ten Thousand Smokes.

. Photo by P. H. HAGELBARGER.

The picture was taken about the same distance, circa 5 km.
above the terminus, as the one of Klut. Contrast the total de-
struction here with the uninjured trees at Blitar. On the original
surface where revealed by erosion may be seen the stumps of
trees burned off just above the ground.

from the conclusion that the material originated within the confines
of the Valley itself, that the vents from which it issued were located
within the limits of the high sand mark. Since vents in this situation
would be choked by their own products unless vigorously explosive *)
we need not be surprised if the points of issue are not certainly
identifiable.

The distribution of the flow, sloping as it does both ways across
two divides, shows that it could not have come from any single
vent. A number of considerations suggest that many vents, rather
than a few, were probably concerned. The character and distribution
of the present fumaroles in the Valley, together with some other
circumstances, likewise make it appear more probable that the ori-
fices were fundamentally fissures, not centralized vents on the model
of the ordinary volcano.

The nature of the vents from which the incandescent material

1) Since the type of material composing the tuff is strictly confined to the
Valley basin, not a particle of it being found on the adjacent mountain slopes, it
is clear that the magma must have issued comparatively quietly, albeit the material
is now thoroughly fragmented, indicating a degree of inflation comparable with
the magma of Katmai which exploded with great violence.

50

issued may, however, remain largely a matter of opinion, but their
location within the Valley is, it is believed, definitely established.

In conclusion, may I express my appreciation of the helpful spirit
in which Dr. Escuer has attempted to assist in the solution of what
is admittedly a very perplexing question? I shall hope, moreover,
that the necessity which L have been under of showing that his
thesis does not accord with the facts will not discourage further
discussion of the remarkable phenomena of the Eruption of Katmai.
For it is my belief that here is presented a unique opportunity to
gain an understanding of the phenomena of volcanism; that there
are problems here which, in their ultimate solution, will require
the codperation of many minds approaching them from many differ-
ent angles.

ERRATUM.

In Prof. PrKELHARING'S communication: “On the Movement of
Pepsine, a.s.o.” (Proceedings Vol. XXIV, p. 269) to read p. 272,
2ed Tine from the top 1 mgr. instead of 0,1 mgr.

cd Aigab inane” VERE PARP E NEL Lash “ae
. POPE: AMSTERDAM: he

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shat aye feed.
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i eae yn. Epa ay brahma eo Renee Aga do PS OE
hi ; Wak fj. ik Kael: tee Mi beat Phys! vat has yi wars in Migutan”, gah Jk
POHL jn PRAAG 1 WOK tnt! $
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pauadndenn GP he “ny ela. iede ot kia Opyarios oat en Re
ete Oo hes ou Maagt bard. prada” 4 Aon Pidi pe pale vn: Wen ;

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KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM.

Pai Cee LIN GS

VOLUME XXV
Nes, 3 and 4.

President: Prof. F. A. F. C. WENT.
Secretary: Prof. L. BOLK.

(Transiated from: “Verslag van de gewone vergaderingen der Wis- en

Natuurkundige Afdeeling,” Vol. XXXI).

CONTENTS.

H. J. VAN VEEN: “Axes of Rotation of Quadratic Surfaces through 4 Given Points”. (Communicated
by Prof. JAN DE VRIES), p. 52.

H. J. VAN VEEN: “Axes of Rotation and Planes of Symmetry of Quadratic Surfaces of Revolution
through 5, 6 and 7 Given Points”. (Communicated by Prof. JAN DE VRIES), p. 61.

P. ZEEMAN and H. W. J. Dik: “A Connection between the Spectra of lonized Potassium and Argon”.
(First Communication), p. 67.

J. W. N. LE HEUX: “Explanation of some Interference-Curves of Uni-axial and Bi-axial Crystals by
Superposition of Elleptic Pencils’. (Third paper). (Communicated by Prof. HENDRIK DE VRIES),
p. 81. (with one plate).

J. W. JANZEN and L K. WOLFF: “Studies on the bacteriophagus of D'HERELLE”, II (Communicated
by: Prof. C. EYKMAN), p. 87.

G. HERTZ: “On the Mean Free Path of Slow Electrons in Neon and Argon”, (Communicated by
by Prof. P. EHRENFEST), p. 90.

G. J. VAN OORDT: “On the morphology of the testis of Rana fusca Rosel’”. (Communicated by Prof.
J. BOEKE), p. 99.

G. SCHAAKE: “A New Method for the Solution of the Problem of the Characteristics in the
Enumerative Geometry”. (Communicated by Prof. HENDRIK DE VRIES), p. 113.

W. H. KEESOM and J. DE SMEDT: “On the diffraction of Röntgen-rays in liquids”. (Communicated
by Prof. H. KAMERLINGH ONNES), p. 118. (With one plate.)

N. H. KOLKMEIJER: “The crystal structure of germanium”. (Communicated by Prof. H.KAMERLINGH
ONNES), p. 125.

R. J. WOLVIUS: “An Objective Method for determining the Co-agulation-time of Blood”. (Communi-
cated by Prof. A. A. HIJMANS VAN DEN BERGH), p. 127.

°F. J. J. BUYTENDIJK: “A contribution to the physiology of the electrical organ of Torpedo”
(Communicated by Prof. G. VAN RIJNBERK), p. 131.
RUDOLPH J. HAMBURGER: “On the Significance of Calcium- and Potassium-ions for the artificial

Oedema and for the lumen of the bloodvessels”. (Communicated by Prof. H. J. HAMBURGER),
p. 145.

Erratum, p. 150.

Proceedings Royal Acad. Amsterdam. Vol. X XV.

Mathematics. — “Aves of Rotation of Quadratic Surfaces through
4 Given Points’. By H. J. van VpeN. (Communicated by
Prof. JaN pe Vriks).

(Communicated at the meeting of March 25, 1922).

§ 1. If we assume three points in space, any straight line 7 may
be considered as the axis of rotation of a quadratic surface of revo-
lution through these points. For the eircles which the three points
describe during the revolution vound /, cut a plane through 7 in
six points. These lie apparently on a conic &? which has / as axis
of symmetry. Revolution of 4? round / gives a quadratic surface of
revolution (in what follows to be indicated by O07), which has / as
axis of rotation (briefly axis) and which passes through the 3 given
points.

As a rule an 0? is defined by its axis and three points; if,
however, during the revolution round 7 two (or three) of the given
points describe the same circle, there exists a pencil (net) of O's
that have 7 for axis and pass through the 3 points.

An (* is always defined by 3 circles with the same axis, provided
these circles do not all lie in the same plane.

§ 2. The axes of the O?’s through 4 given points A;(@@=1...4)
form a complex of rayes I’, which will be investigated in what
follows. By O? we shall understand a quadratic surface touching
the sphere-circle y° twice; the line p joining the points of contact,
will be called chord of contact; the conjugated polar line of
p — defined as the locus of the points the polar planes of which
pass through p — is the avis of OU. Asa rule this locus is a straight
line p’ passing through the pole P of p relative to y°; if p’ is
indefinite only the straight line (or lines) conjugated to p and passing
through P will be considered as axis.

As special quadratic surfaces which according to the aforesaid
must be considered as 0%, I mention: a parabolical cylinder with
a plane pencil of axes in the plane Voo at infinity and a pair of
parallel planes with a sheaf of // axes.

53

§ 3. Assume an arbitrary plane a and in it a point P. If Q is
the point at infinity of a straight line of the plane pencil (Pm), PQ
can only be the axis of an O* touching y? in its points of inter-
section with the polar line q of Q relative to y°, but at the same
time the polar plane of P relative to the same 0’, must pass through q.

The 0”’s through A; touching y? at its points of intersection with
q, form a pencil; if Q moves along the straight line at infinity 7
of zm, q revolves round the pole A of 7 relative to y°. We get in
this way oo? 0’’s cutting V, in a system of oo* conics Xk? touching
y’ at its intersections with a ray of the plane pencil round R.

Now I represent the space of the conics of V,, on a five dimen-
sional point-space &, by considering the coefficients of the equation
of a &* as the homogeneous coordinates of a point in R,; to a
conic &* and to a linear system of ook conics (k’)x of Voy there
correspond a point and a linear space R, of R, and inversely.

The double straight lines of a (47), of Vg envelop a conic; two
of those double lines pass through A, hence the image of all double
lines through & has 2 points in common with an arbitrary R,; it
is a conic &,*. To y° there corresponds a point P and to the pencils
touching y? in its points of intersection with rays of the plane pencil
round Â, there correspond the generatrices of the cone K that has
P as vertex and 4,’ as directrix.

All the quadratic surfaces through A; relative to which P and
one of the straight lines g are harmonically conjugated, form a
linear system of oo* individuals, an (0*),; this cuts Vg in a (£°), to
which there corresponds an Zi, in A, Considering the quadratic
surfaces through A; relative to which P and # and P and Vo
are conjugated, it appears that the #,’s corresponding to all the
straight lines g, pass through an FR, and lie in an &,. These R,'s
cut the space &, in which K lies, in a plane pencil the rays of
which by means of the straight lines q are projectively associated
to the generatrices of A. It happens three times that the associated
elements coincide, hence there exist three 0?’s through A; that have
a straight line g as chord of contact and the polar plane of P
relative to such an 0? passes through g. To a plane pencil (P, 2)
there belong therefore three rays of IT or:

the complex U of the axes of rotation of the quadratic surfaces
of revolution through 4 given points is of the order 3, the complex
cones are of the order three, the complea curves of the cluss three.

§ 4. Algebraically the order of I” may be found by determining
e.g. the complex cone of an arbitrary point. With a view to this I
4*

54

take this point as the origin of a rectangular system of coordinates.
The equation of an arbitrary quadratic surface of revolution is:

(ey) =e? Hy? + 2? + a (aw +by+c2)?-+2Ax+2 By+2C2+4+ D=0.

The axis of revolution is defined by the equations:

Of Ob uae
de = dy =
a b c

or
ann mil ne Pre n Aan

a Tj b Dae

‘and passes through O if
Ain Bino O ie
ao WO mer 4
Consequently only the axes of the surfaces
vty? + 2? Hatan + by + cz)? + lar + by + cz) + y= 0
pass through O.
We only consider O's through the four given points (a, yi, zi),
hence:
vit - yi + 27 + a(axi + byi + cz)? + 28 (ax; + by; + cz i) + y=;
elimination of «, 2 and y gives:
et + ye Hei (ams + by; + cz)? ae; + by; + ez; 1|=0
As a,b,c are the direction cosines of an axis through O, they
are proportional to the coordinates of an arbitrary point of such a
straight line. Consequently the equation of the complex cone of O
becomes :
lat Hy? +27 (wa, + yyi ez) vai t+ yyi + 22; 1/=0.
In a similar way an equation may be derived defining the rays
of FP in an arbitrary plane.

§ 5. If the origin of a rectangular system is placed at the centre
of the sphere through 4: the equation of the complex of rays in
line coordinates may be written:

| 0 Pa Ps Pe
dE ROER
2x a, Vs z
PP ty % 2
Psi, Tio Be
where P; = pv: + py: + py:

55

§ 6. All the straight lines through the centre J/ of the sphere B
passing through the points Ai, are rays of I. Likewise all the straight
lines perpendicular to a side plane of the tetrahedron 7’ that has
Ai as angular points; for they are axes of the O? consisting of that
plane and a parallel plane through the 4" angular point. Further
any line perpendicular to 2 subtending sides of 7’ belongs to 1; they
are the axes of the OQ? consisting of the pair of parallel planes
through these 2 sides, hence:

the complex T' has 8 cardinal points: M, the points D; at infinity
of the normals to the side planes and the points at infinity H; of
the normals to the subtending sides of T.

§ 7. If the points A; revolve round a straight line J, lying in
a perpendicular bisector plane of a side of 7’, 2 of the points Ai
describe the same circle; from this follows that / belongs to TI, or:

the six perpendicular bisector planes of the sides of T are cardinal

planes of T.
I shall now show, that all the straight lines of V_ are double

0

rays of I.

§ 8. The axes corresponding to an arbitrary point P of V belong
to a pencil (07); they are the straight lines p’ conjugated to the
polar line p of P relative to y°. The centres of the individuals of
the pencil lie on the polar line p of P relative to y° (they belong
to the parabolical cylinder of the pencil) and on a conic passing
through P and M and intersecting p. The axes through P form
consequently a plane pencil in WV, and a pencil the plane of which
passes through J, hence:

the complex I consists of oo* plane pencils of parallel rays lying
in the planes of the sheaf round M.

From this there follows that I is invariant for any homothetic
transformation relative to J/; the complex cones corresponding to
the points of a straight line through Jf, have accordingly the same
enrve at infinity.

§ 9. All the straight lines of V, belong to T, hence the complex
curve of an arbitrary plane « touches the / of its plane. Besides
this straight line one more tangent may be drawn to the complex
curve out of each point P of this /_, namely the line of intersection
of x with the plane of the pencil of complex rays through P passing
through M. Consequently J, is a bi-tangent of the complex curve
of zr and also of all the planes in which it lies, or:

V. carries a field of double rays of T.

ao

56

§ 10. The complea curve of an arbitrary plane x is rational; the
Ll, of ws plane is its bi-tangent; single tangents are: the lines of
intersection of « with the perpendicular bisector planes of T.

Through its bi-tangent and the six single tangents the complex
curve of an arbitrary plane is defined; other tangerrts may be con-

strueted with the ruler.

§ 11. If the tetrahedon 7’ is cut by V,, we get the well known
contiguration of a complete quadrilateral. Polarisation of this figure
in the absolute polar field gives a complete quadrangle having D
as angular points; the straight lines at infinity of the perpendicular
bisector planes are the sides and the points H; are the diagonal
points of this quadrangle.

§ 12. In a plane a through one of the points H;, hence parallel
to a normal to 2 subtending sides of 7’, the complex rays consist of
a plane pencil round Hy; and the tangents of a parabola. If x passes
at the same time through MM, it contains atso a plane pencil round
M, hence also a third plane pencil; as the 7, of z is a double ray
of I, the centre of this third plane pencil lies also on /,.

In a plane z through 2 of the points Hy; there lie plane pencils
round both these points, hence also a third plane pencil; to this
belong the points of intersection of a with the perpendicular bisector
planes through the third of the points H;, hence:

to I there belong three bilinear congruences, which have as direc-
trices the join of 2 of the points H; and the line through the 3% of
the points H; and M.

If a passes through 2 points H; and through M, the complex
rays in a form the plane pencils round these three points.

In a plane 2 through one point H; and two of the points Di
there lie three plane pencils of complex rays round these points.
If « passes also through M it is a cardinal plane.

§ 13. Before investigating the planes through a point D; I shall
first consider the complex cone of a point P of the perpendicular
m; out of M to one of the side planes of 7. This complex cone is
apparently split up into three plane pencils, lying in the perpendi-
cular bisector planes through m;; m; is a threefold generatrix of the
complex cone of each of its points, hence:

the four straight lines m; are 3 fold rays of T.

In a plane a through 1; lies a plane pencil round M anda plane
pencil round D;; now the /, of a is a double ray and m; is a

57

threefold ray of IF, hence the third plane pencil in 2 has likewise
D; as vertex; the complex rays in a form accordingly a plane
pencil round MZ and a plane pencil round PD; which is to be counted
double.

§ 14. Consider an arbitrary plane z through one of the points
D;; in this there lies a plane pencil of complex rays round D;,
while the rest of the rays envelop a parabola. Out of each point P
of the J, of a there can be drawn besides /, one more tangent
to the parabola; P is the point of contact if this straight line coin-
cides with /. The plane of the pencil of complex rays through P
passes in this case through Jf and through Dj, hence through m,,
but then P coincides with D; or:

in a plane through one of the points D; (// to a straight line mij)
the complex rays consist of a plane pencil round this point and of
the tangents of a parabola with axis [/ mj.

§ 15. In a plane through M there lies a plane pencil of rays
round this point and as the J, of this plane p is a double ray of
I’ there lie 2 more plane pencils with centres P on p. The points
P and the straight lines p are conjugated in a null system [2,1].
By conjugating to each other the points P lying on the same straight
line, an involution of pairs [2] arises. This involution is quadratic,
for on an arbitrary straight line there lies one pair of conjugated
points.

The involution [2] is not a quadratic inversion as the joins of
conjugated points do not pass through a fixed point; consequently
[2] consists of the pairs of points conjugated to each other relative
to the conics of a pencil. This involution has 4 double points (the
base points of the pencil), in this case the points D;, and 3 cardinal
points, the diagonal points of the complete quadrangle of the base
points, in our case the points H;, hence:

the complex T consists of pairs of plane pencils of parallel rays
lying in planes through M. The vertices of the two plane pencils
lying in the same plane, are conjugated points of a quadratic invo-
lution in Vy.

§ 16. If a straight line p of V,, revolves round one of its points
Q, the points associated to p in the null system [2,1] describe a
curve &* of the 8rd order; this curve passes through O, through H;
and touches the straight lines OD; at D;. The curves &* belonging
to all the plane pencils of V_, form a net with seven base points,

ER and D;.

58

§ 17. In order to get the complex cone of an arbitrary point P,
we consider a plane a through MP; let O be the intersection of
MP, p the intersection of a with V,. If P, and ZP, correspond to
p, PO, PP, and PP, are the lines of intersection of the complex
cone of P with az. If a revolves round PO it appears that:

the complex cone of a point P passes through the straight lines
PM and PH; and touches the planes MPD; along the lines PD,

At the same time it appears again that if ? moves along a straight
line through M, the curve at infinity of the complex cone of P
remains unaltered (ef. § 8).

§ 18. Out of a point O, 4 real tangents OD; may be drawn to
the corresponding curve 4°, hence the curves 4? and also the complex
cones consist of two parts.

The caracteristic of a curve 4? is defined by the 4 straight lines
OD;. Through D; there pass 3 conics through the points O of which
there pass 4 harmonical rays through D;, hence:

the locus of the points with harmonical complex cones consists of
3 quadratic cones the vertices of which lie in M and which pass
through the straight lines mi, and also:

the complex cones of the points lying on a quadratic cone through
the 4 straight lines m;, have the same characteristic.

§ 19. The curve of Jacopi of the net of the curves 4° consists of
the six sides of the complete quadrangle of the points D;. No rational
curves 4° belong to the net, only curves degenerated in a side of
the quadrangle and a conic through the 4 points D; and H; that
do not lie on this side, accordingly :

there are no points with rational complex cones; for any point of
a perpendicular bisector plane the complex cone degenerates into a
plane pencil and a quadratic cone; for a point V, the complex cone
consists of a plane pencil in V,, to be counted double, and a single
plane pencil.

§ 20. As each complex curve has a double tangent, we might
call those planes where the double tangent is an inflexional tangent,
singular planes. In this case the two points P corresponding to_the
straight line p in the null system [2,1], must coincide. This happens
only when a plane a passes through one of the points D;, but
then the system of complex rays in zr splits up into a plane pencil
and the tangents of a parabola; consequently non-degenerate complex
curves with an inflecional tangent do not occur.

59

$ 21. If in a there lies a plane pencil with centre P at finite
distance, there are also 2 plane pencils with their centres on the
Ll, of z; if a does not pass through one of the cardinal points at
infinity, the planes of these latter pencils pass through J/, hence:

only the planes through the 8 cardinal points contain degenerate
complex curves (ef. §§ 12, 13 and 14).

§ 22. As the null system [2,1] and the involution [2] are
invariant for central projection, we can construct the complex cone
of an arbitrary point P in the following way :

We determine the points of intersection D; of the perpendiculars
out of P to the side planes of 7’ with an arbitrary image plane r
and also the intersection O of TM with t. Then we construct the
double points of the quadratic involution in which the conics of the
pencil through D; cut an arbitrary straight line / through O; we
fix this involution by means of the points of intersection of / with
2 degenerate conics of this pencil. The straight lines joining P to
the double points in question, are generatrices of the complex cone

or. PP

§ 23. If the points A; are coplanar, their plane « cuts an QO? of
the system in consideration along a conic 4’ through A; or is a
part of the Q*. In the first case the axis of OV? lies in one of the
planes through the axes of symmetry of 4? perpendicular to «a; in
the second case the axis of O? is a straight line perpendicular to a.
The axes of symmetry of the conics through A; are tangents to a
curve of the 3rd class touching the line /, of a twice; the planes
through these axes and. 4 a touch a cylinder of the 3"¢ class with
V,, as double tangent plane.

The rays of F in an arbitrary plane a touch also in this case at
a curve of the 3'¢ class that has the /_ of its plane as a bitangent.
The complex cone of an arbitrary point P, however, splits up into
3 plane pencils the planes of which touch at the cylinder in question ;
a perpendicular to a is a triple generatrix of the complex cone of
each of its points, hence:

if the 4 points A; are coplanar, F consists of the tangents to a
cylinder of the 3rd class; V, is the bearer of a field of double
rays; the vertex of the cylinder at infinity is the bearer of a sheaf
of triple rays.

§ 24. Now consider the case that 3 of the points A; lie on a
straight line a; then the O*’s must pass through a fixed point A

60

and a fixed straight line a. If A is to lie on the quadratic surface
which a describes when it revolves round a straight line /, the circle
which A deseribes when it revolves round /, must cut the straight
line a; accordingly / must lie in the plane which bisects perpendi-
cularly the straight line joining A to a point of a. These planes
touch a parabolical cylinder that has for directrix the parabola of
which A is the focus and a the director line and the generatrices
of which are perpendicular to the plane (A,q).

If a revolves round a straight line crossing it at right angles, a
plane is produced which, completed by the plane through A parallel
to it, gives another QO? that satisfies the conditions mentioned, hence:

if three of the four points A; are collinear, [ splits up into a
pencil of rays with the axis at infinity, and the tangents to a para-
bolical cylinder.

Mathematics. — “Axes of Rotation and Planes of Symmetry of
Quadratic Surfaces of Revolution through 5,6 and 7 Given
Points.” By H. J. van Veen. (Communicated by Prof.
JAN DE VRIES).

(Communicated at the meeting of April 29, 1922).

§ 1. Let there be given five points A, A, B; (j = 1, 2, 3). I consider
the complexes I’, and TP, belonging to the points A, B; and A, B; ’).
Generally a common ray lof I, and I, is the axis of an O* through
the 5 points; for / is the axis of an 0? through A, 6; and of an
O? through A, B;; these two O?’s have in common the 3 parallel
circles on which the Bj lie; hence they coincide. An exception
exists for the straight lines in the perpendicular bisector plane of
the join of 2 of the points B;, and also for the straight lines of
V,,- The field degree of the congruence of axes is therefore

3.3 —3—2.2=2.

At the same time there must be split off: the sheaf of the rays
which are perpendicular to the plane through the points Bj. Let D
be the centre at infinity of this sheaf; both the complex cones of
a point P touch the plane through P M, M, and D along P D, hence:

the axes of the O”s through 5 given points form a congruence of
the sheaf degree 7 and the field degree 2, Ct.

§ 2. To C%? belong the complex rays of I, lying in the perpen-
dicular bisector plane of a straight line A, B;, hence:

the 10 perpendicular bisector planes of the joins of the 5 given
points are singular planes of the order 3.

§ 3. In the two null systems belonging to FP, and I, the curves
kt and k,? (O's through 4 points § 16) are associated to a plane
pencil round a point O of V,,; these curves pass through OQ,
touch O D at D and have accordingly six more points in common.
Consequently through O there pass six straight lines on which the
two pairs of points which through the two null systems are asso-
ciated to them, have one point in common.

1) Cf. my paper “Axes of Rotation of Quadratic Surfaces through 4 Given
Points.”

62

The complex curves in an arbitrary plane through such a straight
line touch each other at the point in question, so that the two
complex curves have 5 coinciding tangents in common in the /,
of their plane. Now we have split off the straight lines of V_ as
4-fold rays of the congruence of the intersection of the two com-
plexes, hence:

Vis a singular plane of the order 6

§ 4. We can also arrive at this last result in the following way.
The quadratic surfaces through 5 points form a linear system of
oof individuals; these cut V, in a (#°),; the conic of the double
straight lines of this (47), belongs to the parabolical cylinders of
(07), Let C be such a eylinder, 7’ its vertex, c the line along which
C touches V

The polar plane of 7’ relative to C' is indefinite, hence 7’ has a
fixed polar plane relative to all O’s of the pencil through 4, B,
which touch y? in its points of intersection with c. This fixed polar
plane is at the same time the plane of the centres of the individuals
of the pencil; it passes through the polar line p of 7’ relative to

‚In the null system [2,1] belonging to I’, the pole P ofc relative
A y’ is associated to p.

As the fixed polar plane of 7’ relative to the O7’s head ADB;
that touch y? at its points of intersection with c, pass likewise throubh
p, in the two null systems corresponding to I, and T, the pes P
is associated to p. |

P was the pole of c relative to y?, hence the locus of P is a
conic. The order of the null systems is three; accordingly the locus
of the straight line p is a curve of the sixth class.

We remark also that to each parabolical cylinder one axis in
V., remains associated (O7’s through 4 points, § 2), namely the
polar line of its vertex relative to y’.

§ 5. If sr points are given I consider a group of 4 and a group
of 5 of these points which have 3 points in common. To the
group of 4 points there belongs a complex I’, to that of 5 points
a congruence (72 The axes in question are part of the common
rays of complex and congruence; however, we must split off: the
tangents of three curves of the 3rd class and twice the tangents of
a curve of the sixth class, so that we arrive at a ruled surface of
the order 3(7 + 2) — 3.3 — 2.6 = 6, hence:

the aves of the O”s through sia points form a ruled surface of
the sixth order, o°.

63

§ 6. Through consideration of the perpendicular bisector plane of
the straight line through the 2 points that belong to the group of
5 and not to the group of 4 points, we find that in this plane and
accordingly in each of the 15 perpendicular bisector planes, there
lie 2 generatrices of 9°.

The Lhe Sage surfaces through six points cut V, in a linear
system of o° conics (£*),. These define together with y? a linear
system (£°),; the tangents of the conic of the double lines of (4°),
are the chords of contact of the O?’s through the six points; polari-
sation of these straight lines relative to y° gives a conic 4”; to (4),
there belong four double lines, originating from parabolical cylinders
(ef. § 4), so that the loeus of the axes has a conic £* and 4 straight
lines in common with VV, hence:

e° is rational; it has a double curve of the order 10; the 15 perpen-
dicular bisector planes of the joins of the six points are bi-tangent
planes; Vis a 4-fold tangent plane.

§ 7. In order to investigate the axes of the Os through seven
points, we consider a group of 4 and a group of 6 of these points
_ that have 3 points in common. We get in this way a complex I’,
and a ruled surface g° that have 18 straight lines in common. If we
subtract from them three times two straight lines lying in the
perpendicular bisector planes of the joins of the 3 common points, and
twice 4 straight lines in V,, we have + straight lines left, hence:

through 7 points there pass 4 O's

§ 8. We can also arrive at this result in the following way. All
quadratic surfaces through 7 points cut V, in a (4*),; in connection
with y? this gives a (47), with 4 double straight lines, consequently
in (47), there are four individuals touching y* twice. These belong
to the surfaces of rotation through the 7 points.

$ 9. A quadratic surface of revolution O? has a pencil of planes
of symmetry passing through the axis of rotation and therefore
defined together with this axis, and further generally one more plane
of symmetry perpendicular to the axis. I shall investigate these latter
planes for O?’s through given points and I define as a plane of
symmetry of an O* the polar plane of the point P at infinity of
the axis of rotation; if this polar plane is indefinite the planes
through the chord of contact p ot the O* are considered as planes
of symmetry.

64

§ 10. An arbitrary plane a is a plane of symmetry of one 0?
through four given points A;; for through A; there passes a pencil
of Os touching y? at its points of intersection with 2; generally
one of these O*’s passes through the mirror image of one of the
points A; relative to a and this surface satisfies the conditions.

It may happen that the mirror image in question lies on the base
curve of the pencil; then a is a plane of symmetry of all indivi-
duals of the pencil. As the sphere B theough A; belongs to the
pencil, * must pass in this case through the centre M of this sphere.

$ 11. The o’ planes of symmetry of the O?’s through /ive points
envelop a surface of which I shall determine the class. The O*’s the
planes of symmetry of which pass through a point P of V,, cut
V, along conics that touch y? at its points of intersection with a
ray of the plane pencil round P. The image of all such conics in
Rk, is a quadratic cone K (O0*’s through + points § 3).

The quadratic surfaces through the 5 given points cut into V_
a (k*) that has an R, as image in R,; this R, cuts A along a
conic k° 1.

To the degenerate conies of V, there corresponds in Rk, a cubic
hypersurface, V*,, that has a double surface O*, of the 4" order
(a surface of Veronese). Besides its two points of intersection with
k?; (Os through 4 points, $ 3) that lie on O“,, k’j7 has 2 more
points in common with V*,, hence to the O?’s through the 5 given
points the planes of symmetry of which pass through P, there belong
two paraboloids of revolution; these have V, as a plane of sym-
metry. Through a ray p of the plane pencil round P there passes
one more plane of symmetry that does not coincide with VV,
consequently the planes of symmetry through P envelop a cone
that has P for vertex and that touches V,, twice. An arbitrary
straight line / through P bears therefore 3 planes of symmetry;
through a line of V, there passes besides V, only one more plane
of symmetry, hence:

the planes of symmetry of the Os through 5 given points envelop
a surface of the 3™ class of which V, is a double-tangent plane.

$ 12. The conic along which this surface touches WV, has six
tangents that are the bearers of pencils of tangent planes; these
cannot belong to different O?’s for in that case through the 5 given
points there would pass a pencil of O*’s touching y° at its points
of intersection with a straight line p and from this would follow
that the 5 given points must lie on a sphere.

65

To each of the six straight lines p belongs therefore one (? that
has a pencil of parallel planes of symmetry, or:

through 5 given points there pass six cylinders of revolution; their
generatrices are parallel to 6 sides of a quadratic cone.

§ 13. The planes of symmetry through an arbitrary point touch
a cone of the 3rd class; let a be such a plane through the centre
M of the sphere B through 4 of the 5 given points; 7 is then a
plane of symmetry of an O* through the 5 points and also of the
sphere B, hence of a pencil of O*’s through those 4 points, or:

through the centre of the. sphere through 4 given points there pass
oe! planes each of which is a plane of symmetry of a pencil of O*'s
through those 4 points; these planes envelop a cone of the 3” class.

Such a plane a is also a plane of symmetry of the base curve
of the corresponding pencil, consequently to this pencil there belongs
a cylinder of revolution of which the generatrices are perpendicular
to a, hence:

through 4 points there pass w* cylinders of revolution of which the
generatrices are parallel to the generatrices of a cone of the 3° order.

§ 14. If sew points are given, we consider two groups of five
points; these have 4 points in common. Tbe surfaces of the 3" class
corresponding to these two groups, have in common the tangent
planes of a developable surface of the 9" class that has Vas a
4-fold tangent plane. However, we must subtract from this the
tangent planes through the centre of the sphere through the 4 com-
mon points, hence:

the planes of symmetry of the O's through six given points envelop
a developable surface of the 6% class that has V, as a 4-fold
tangent plane.

§ 15. The quadratic surfaces through six points cut V, in a
(k*),; to this there belong 4 double straight lines; how many degene-
rate curves touching y° twice, belong to (47), ?

In order to determine this number we remark that the cone in
Rk, formed by the straight lines joining the image of y? to 0%,
($ 11), cuts the image R, of (k?), along a curve k* of the 4%
order; this curve has besides the 4 points that are the images of
the double lines of (47), and that are to be counted twice, 4 more
points in common with V*,, hence:

through six points there pass 4 parabolical cylinders and 4 para-
boloids of revolution.

66

As through an arbitrary point P of VV, there pass 2 more planes
of symmetry, (for the conie of the double lines of (47), defined by
y? and (k?), sends two of them through P), we find also in this
way, that the planes of symmetry in consideration envelop a
developable surface of the sixth class with V, as a 4-fold tangent
plane.

§ 16. In order to find the planes of symmetry through seven
given points, we consider a group of six and a group of five of
these points that have 4 points in common. The corresponding
surfaces have 3.618 tangent planes in common. If we subtract
from them 2.4=8 times V_ and further 6 planes through the
centre of the sphere through the 4 common points, it appears
again that:

through seven given points there pass 4 quadratic surfaces of
revolution.

(Cf. $$ 7 and 8).

Physics — “A Connection between the Spectra of Ionized Potas-

stum and Argon.” (First Communication.) By Prof. P. Zeeman
and H. W. J. Dix. ,

(Communicated at the meeting of April 29, 1922).

According to the conception of RurnrrForD-Bonr an atom consists
of a very small positively charged nucleus, which contains almost
the whole mass of the atom, and of a number of electrons revolving
round the nucleus. The number of electrons moving round the
nucleus, is equal to the atomic number of the element; hence this
also indicates the number of units of charge which an atom that is
neutral taken as a whole, possesses in the nucleus.

It has been made plausible that the electrons are arranged in
shells or sheaths with the nucleus as centre. In particular the regular
changes which the chemical properties undergo with the increase
of the atomic number, make this probable. Regularly elements occur
in the periodic system which easily cede one electron (the alkalis),
regular is also the succession of the inert gases. This becomes com-
prehensible when it is assumed that a shell can become full, and that
then the configuration will be very stable: helium, neon, argon ete.
The atoms of lithium, sodium, potassium ete. have only one electron
in the outer shell. On this similarity in structure rests also the
resemblance which has been observed at an early date in the are-
spectra of the alkalis. The one outer electron can be removed by
the electric forces which are active in a spark. Then the atom is
ionized, and the electron combination which has remained, can emit
the spark spectrum. :

On these general features of the atomic model, in particular on
the number of outer electrons which increases at every step in the
periodic system, rests a displacement law enunciated by Kossrr and
SOMMERFELD'), which establishes a connection between the spark
spectrum of an element and the are-spectrum of another element
which precedes it in the periodic system. If e.g. an electron of the
potassium-atom has been driven out, the remaining electron system
must present the greatest resemblance with that of argon, and only

1) KossEL u. SOMMERFELD, Auswahlprincip und Verschiebungssatz bei Serien-
spectren. Verh. deutsch. physik. Gesellsch. 21. Jahrgang 240, 1919.
5
Proceedings Royal Acad. Amsterdam. Vol. XXV.

68

differ from it in that the positive nucleus of potassium possesses
one unit of charge more. Like the arc-spectrum of argon, the spark-
spectrum of potassium must be composed of a great number of
lines, and not show series. As yet the relation which the displace-
ment law renders probable, is only qualitatively known.

For some time some researches have been in progress in the
Amsterdam laboratory to determine the relation quantitatively.

We will here communicate some results to which the investiga-
tion of potasstum has led. These facts retain their value whatever
interpretation may have to be given to them.

Besides the arc-spectrum of potassium with the so well-known
spectrum series which according to SOMMERFELD’s opinion originates
from the neutral atom, Eprr and VaLentra’) observed in 1894 a
spectrum, emitted by ionized potassium, which was very rich in
lines. Eper and -Varunta observed simultaneously are- and spark
lines; in 1907 Gorpsrrin®) however, succeeded in observing in the
intensely luminous line of discharge occurring in the passage of vigor-
ous electric discharges through powdered salts, a spectrum in which
only lines are seen which have not been ranged into series, and in
which even the distinct arc-lines did not appear. GOLDsTEIN points
out that these lines owe their origin to circumstances which differ
essentially from those which give rise to the arc-lines, and he
introduces the name of ‘ground” spectrum. We are undoubtedly
justified in attributing the ground spectra to the emission of the
once ionized atom.

In the subjoined Table | a * denotes the strongest lines, those
published by GOLDSTEIN.

With better appliances Eprr’s pupil ScHILLINGER®) could supple-
ment GoLDsTEIN’s observations by investigating also the ultra-violet.
He worked with vigorous discharges between potassium electrodes
in a bulb with hydrogen. His observations are given under S in
Table I.

In 1915 some observations of NerrnorPe*) were published for
potassium lying between 6307 A and 3898 A. He employed
another type of tube than GorpsrriN, and recorded by means of a
spectrograph. On his plates the arc-lines are absent, the ground-
spectrum of GoLpsrEIN coinciding with his strongest lines. The
doubt expressed by Karser whether Gotpsrein’s failure to see the

1) Eper u. VALENTA, Denkschriften Wien. Akad. 61. 347, 1894.
*) Gorpsrein, Verh. deutsch. physik. Ges. 321. 1907; 426, 1910.
3) SCHILLINGER, Wiener Sitz. Ber. 118 [2a] 605. 1909.

+) NELTHORPE. Astroph. Journ. 41. 16. 1909. .

69

Potassium lines with electrode less discharge.

Remarks

——OOOOOOOOO

TABLE I.
Intensity.

EV | SyioN ViMcke
Sn TD

8| 5

Be| 6

7 4

— 1 =

— | 2) 3

— | 1

= 2 |: 8
i—i | 3
3) | AES

Di Bles

ZN Se

3) |) SE
—|—|—]| 2
SEZ ES

1 1 | —=
BEN

2 1 |=

2 1

2 TRES

life wiet

na

ee eli

nr
oo
S
3
P A wp ©

eN
oO
ie)
ao © BW N

17324

17715
18064
18286

18817

19778

Arc-line

Pi
H 6563?

Q
, P,

Arc-line

»

Arc-line
>
>

Are-line

Intensity.

EV | Sa IN» |McL
2) Bel 5

| ee ee ee

Ed, e=
a Mt Mn 3
3 Dial?
—|—|—- 1
—|}—|{|—|] 1
—|-—|;-—| 1
oh ke
il 1
enke kl
== en | 1
SPE

Zola EN pee te ee
il 1
6) 4] 15

Jl 4168

Dl 25 05

Ill 2

Wa |

3 340
—|—|—]| 2
lek ol 5

AF) REZ

7 ae ld

D

15

TABLE | (Continued).

5005.5 *
4965.5
4958
4943.2
4863
4829.2 *
4805
4190
4769
4760
4744
4720
4688
4659 8
4650.7
4643
4608.5 *
4596.0
4505.6 *
4467.5 *
4455.5
4423.6
4388.3 *
4365. 1
4339. 9
4309.5 4
4305.0
4288.6
4285.1

70

19978

20230

20707

21079

21460

21699
21758
22195
22384
22444
22606
22788
22909
23042
23204
23229
23317
23337

Remarks.

R3
Arc-line
Ps

Arc-line

Arc-line

>

Qs

Ry

Arc-line

71

TABLE I (Continued).

Intensity.
A y Remarks.
EV | S | N |McL| D
6 | 8 | 10 30 4263.5 * 23455 Rs
B14) 0 30 4225.7 > 23665 Qn
Bua) 8 30 4223.2 23679
A Pans 9 4208.9 23759 Qie
8 | 10 | 20 30 4186.2 * 23888 R;
Bef 5-| 10 30 4149 1 * 24102 Pis
6 | 5-40 30 4134.7 * 24185 Rio
deld. | 218 30 4115.1 * 24301 Se
—|—|] 5;—|— 4106.8
—|{—| 7] If 4104.2
ae) a a | 4098.6
=| 1-42 15 4093.5 24429 Pis
—}|}—| 2 — 4086.8
—|—| 3| =| — 4075.6
—j;—| 2/-—|—- 4072.3
ae eee ae 10 4065.2 24599 Rie
— 2: — 4058. 1
10 | 10 | — — 4047.4 Arc-line
10 | 20 | — — 4044.3 Arc-line
al ine ae oe, 15 4042.5 24731 Pi: S7
Be igi = 10 4039 .9 24753
Belt lei — 10 4024.9 24845 Pig
th ae EEE, 9 4018.9 24882 Pig
mel A BEN. 10 4012.2 24924 Ss
Bal! 5. 8 15 4001.1 24993 Pao So
Br, Aat 3 10 3995.0 25031 Sto
— [|= 8 3992.0 25050 Po,
Sil Be) ot 15 3972.8 25171 Poo
S| ood 15 3966 7 25210 Pos

72

TABLE 1 (Continued).

Intensity.
À y Remarks.
Ev | S | N |McL} D
4} 4] 8 15 3955.5 25281 Qis
ai A 4 10 3943.3 25359 Si
l | 9 3934.6 25416
1 1 2 9 3927.3 25463 Si2
1 1| — 9 3923.8 25485 Pog
8| 8| 10 15 3898.0 25654
— | — —| 3 3887.2 25726 Qi
oe 5 3884.5 25743 Siz
| 1 8 3879.2 25779 Py
2 i 10 3874.5 25810 Ri4
et 10 3861.9 25894 Q»;
— |= — | 3 3844.8 26009 Poe
1 2 15 3818.6 26187 Po7
= | — 3816.9 |
Bali 2 15 3800.8 26310 Ris
a he: 15 3783.2 26433 Riz
1 3 15 3767 1 26546 Ris
1 1 6 3756.0 26624 Qos
1 | — —|— 3749.1
1 1 9 3745.2 26701 Roo
1 1 9 3139 2 26744 Ro}
WS 3121 5
-- 1 9 3122.4 26866 Roo
1 1 9 3716.9 26904 Ros
a — | — 3713.2
—]| 1 — 3683.7
4| 4 15 3682.3 27157 Sis
— 1 8 3677.6 27192 Pog Rog
1 1 10 3670.2 27246 P39

73

TABLE I (Continued).

Intensity.
ees A y Remarks.
al S Ab McL
— | — — 3660
a en = 3650.6 27393 Sis
—|1 4 3639.8 27474 Ros
—| 1 9 3627.1 215710 Qos
= ee 15 3618.4 27636 P3,
A 12 3609.4 27105 Rog
— | — fae 3593.8 27826
—|— ee 2 3587. 1 21818 Roz
—|— 1 | — 3572
— | 1 8 3562.5 28070 P35
Bae OS 20 3530.9 28321 Sos
—| 1 1 3518.8 28419 Rog
== 1 ii 3514.0 28458 P33
—|— 1 | — 3489
ed ae | 8 3481.3 28725 P35 So7
1 1 8 3476.9 28761
— | 1 7 3468.7 28830 P55
= 2 3457.8 28920 Qn
2 1 3447.5 29006 Arc-line
a 3 — 3446.5 +
ob 3 12 3440.5 29065
1 | 2 10 3433.7 29123 P37
arent 8 3422.4 29219
1 | — — | 4 3421.5 29227
BZ 10 3404.7 29371 P38
— | 1 1 3393. 2 294711 P39
6| 4 10 3385.3 29539 Qa
6| 4 10 3381 .4 29573 Q35
E83 10 3374.0 29638 P4o

74

TABLE 1 (Continued).

Intensity. |
A y Remarks.

al S | N [MeL/ D
deelen Ne mn men ee en
46 3364.7 29720

18 Ee 3363.4 29132 Sa
il Til. a 29770 R32
=) 2 7 3357.2 29781 S30
8} 5 6 | 12 3345.8 29888 Py
—|— 3] 1 3337.7 29961

= =| 3326.4

ien Ae 3 | 9 3322. 1 30101 Pa»
84 5| 9 3312.8 30186 Si
—|— aN 3302.0 30284

311 C9 5| 9 3291.1 30385 Ra
—| 4 =) 5 3289.1 30404

—| 3 Bal bay 3278.8 30499 P43
—|2 BAe d6 3262.0 30656

—|— 3/74 3258.8 30686

— | — eal a2 3253.9 30732 Qu
— | 2 3716 3241.1 30854

ee al 1] 5 3224.8 31010 Ss
2452 EB 3220.9 31047

—| 1 ae 3219.1 31064 R3s
2 | — | — 3207.5 Arc-line
| 4 —| 5 3209. 1 31161 R39
—|— 4 | — 3205.6

1113 2S) 5 3202.1 31230 Si
hik EG 3190 6 31342 Re
ae Its) 5| 6 3188.3 31365 S36
==) |) = 2|— 3174.0

{Al 4/3 3170.0 31546

Wel ey ari 1 3157.6 31670 S37

75

TABLE I (Continued)

Intensity.
A y Remarks.

Ev S | N |McL} D
Pe Te een
— | — 2\|— 3148.6

3} — — | — 3143.7

ade 45 3129.5 31954

5| 4 6| 6 3105.4 32202 R43

1} 1 —\|=— 3103.1

1 1 2/;— 3074.6

1|— —|- 3067.3

Ber 5 Sen 3062.6 32652 S42

said arc-lines might possibly have to be attributed to a less good
observational power in the extreme red and violet, appears therefore
unfounded.

The importance of the ground spectra made it desirable to perform
new measurements. The best method to obtain the first spark
spectrum of potassium in great purity and completeness we found
to be exciting the luminosity of very diluted incandescent potassium
vapour under the influence of very rapidly varying electrical forces.

When our investigation was in progress, there appeared a publi-
cation by Mc Lennan') on the spectrum of ionized potassium.
His tables present a close resemblance to ours, but in his Table I
Mc Leynan gives the lines which he has observed besides those of
Scur~uincer. Hence he also finds the arc-lines, which we succeeded
in eliminating.

Besides both in his and in Scam..inerr’s observations a few important
lines are wanting. Important because they have been serviceable in
the search for the regularities to be mentioned presently. By the
aid of Table I it is possible to compare the measurements of our
second (D) with those of the other observers, besides the data in the
column “remarks” show which P,Q, ete. could only be determined
by the new lines. At the same time it is at once clear which of the
lines are arc-lines. We estimate the accuracy of the measurements

„

1) Mc LENNAN, Proc. R. S. Vol. 100. 182. 1921.

76

from 4700 A al 0,2 A. To some lines a + is added to show that
they are not sufficiently accurate. (Cf. Table 1).

Argon can emit two types of spectra. One is the so-called red
spectrum, which is formed under the influence of weak electric
forces, and must, therefore, be called the are-spectrum of argon.
The other is formed by strong electric discharges, and is called the
blue spectrum because of its colour; it is the spark spectrum of
argon. No spectrum series are known in the red spectrum, but it

exhibits the regularity found by Ryppere') that for 4< 4704 A
the frequencies of almost all the lines may be arranged in a Table
the four columns of which present a constant difference. Paulson *)
extended these results to the less refrangible part of the spectrum.
Ryppere’s and PaursoN’s tables are reproduced here in Table II,
somewhat abbreviated, but with continuous notation. It gives the

constant differences for the wave-lengths of 29233—3319 A. (Cf.
Table II). The relations are:

bB=A-+ 846,1

C= A-+ 1649,3

D=A- 2256,1

The frequencies in Table I] followed by an M have been taken

from Merecers*). They are more accurate than the frequencies in
the original tables of RypBrra and Pavrson. For this reason the
mean value of Meraarrs has been put at the head of the Av-column
and not the mean value of all Ap’s.

The spark spectrum of potassium possesses the same property
Ryppere found in argon, for the examined region between 6594—

3063 A. This appears from Table III, which has been obtained by
the aid of the data in Table I. Under the heading “Remarks” in
Table I the lines inserted and arranged in Table III are indicated
by symbols (See Table III). .

The relations for the lines of ionized potassium are:

Dee PG
R= P +1695
Sedes

The first spark speetrum of potassium is, therefore, still somewhat
simpler than the red spectrum of argon, the differences being:

1) RypBEeRG. On the constitution of the red spectrum of argon. Astroph. Journ.
Vol. 6. 338. 1897.

2) PAULSON, Rhysik. Z. S. 15. 831. 1914.

3) Mraaurs, Scientific Papers, Bureau of Standards N°, 414, 1918

77

TABLE II. Arc-Spectrum of Argon. (RYDBERG and PAuLson).

Ay

ae x | Sree er 4846.2 Elek s A 4 2256.1
1 10353.2 607.3 | 10960.5
2 11533.6 M | 803.1 | 12336.7 M | 606.8 | 12943.5 M
3 | 10837.7 M (1649.3) | 12487.0 M | 606.8 | 13093.8 M
4 11896.7 (1410.4) | 13307.1
5 | 11731.9 M | 846.2 | 12578.1 M (1409.9) | 13988.0 M
6 | 11889.9 M (1649.2) | 13539.1 M | 606.8 | 14145.9 M
7 | 12096.6 M | 846.2 | 12942.8 M | 803.0 | 13745.8 M | 606.9 | 14352.7 M
8 | 12477.0 (2258.1)| 14735.1
9 | 13326.2 (2258.5) | 15584.7
10 15012.9 606.7 | 15619.6
11 | 13668.4 847.9 | 14516.3 (1410.3) | 15926.6
12 15429.3 606.7 | 16036.0
13 | 14223.7 (1651.8) | 15875.5
14 15078.3 (1409 9)| 16488.2
15 | 14413.4 (1651.2) | 16064.6 |
16 15398.6 (1409.6) | 16808. 2
17 16219.8 606.9 | 16826.7
18 16340.6 606.5 | 16947.1
19 15699.2 803.5 | 16502.7
20 | 14972.3 (1651.7) | 16624.0
21 16716.2 607.3 | 17323.5
22 16029.3 802.7 | 16832.0
23 16130.5 (1409.7) | 17540.2
24 16144.0 803.1 | 16947.1
25 16164. 2 (1409.9) | 17574.1
26 16431.4 802.7 | 17234.1
27 16481 .3 (1409.7) | 17891.0
28 16520.9 802.6 | 17323.5
29 | 15699.2 847.6 | 16546.8
30 | 15787.2 847.3 | 16634.5
31 | 15853.1 848.1 | 16701.2

16298 .2
16334.7
16617.8

18098 .7
21260.2
21599.5
21751.9
21783.8
22163.2
23013.3
23059 .9
23069 .2
23477.0
24794 .8

25675 .3

25864 . 2

26077 .2
27208 .3

27242, 1
27119.2

27992 .3
28201 .2

= = WA —

Ay
846.2

847.7

846.1
846.2
846.4
846.1
846.1
845.8

846.8
846.6
846.7
846.6

845.9

846.3

78

TABLE II (Continued).

B Ay
A-+ 846.2 | 803.1

16866. 1
17145.9

17863 .9

18373.8

18474.7

22106 3

22598. 1

23859 .7

23906 .0

23915.3

25640 .6

26522. 1

26710.8

28055 .0

28063 .4

28088 . 7
28625. 1

29047.5

803.4

(1651.1)

(1651.2)

802.5
(1651.7)

M | 803.1

(1649.3)

M | 802.7

(1649.2)
(1649.2)
803.3

M | 803.1
M | 803.2

(1649.8)
(1650.0)

(1649.9)

(1649.3)

(1649.2)

(1649.7)

(1649.7)

(1649.8)

C
A } 1649.3

17669.5

17985 .8
18269.0

19277.2
19750.4
22909 . 4
23248 .8
23400.8
23433 .0
23812.4
24663 .0
24709. 1
24718.5
25126.8
26444 .8
26486 .7
27325 .2
27448 .2
21513.5
215271.2
27126 .4

28891 .8
29428 .9
29518 .6
29642 1

aR ei

Ay
606.8

(1409 6)
(1410.4)

607.0
606.8
606.8
606.9

606.8
606.9

607.2
606.2

606.8
606.9
606.7

(1410.1)
(1410.0)

607.1

606.8

D
A + 2256.1

19273.5
19784 .2

23516.4
23855 . 6
24007.6
24039.9

25315.9
25325 .4

27052 .0
27092 .9

28055 .0
28120.4
28133.9

29465. 1

29473.4

29498 .9

30125.4

Rm Bm

79

TABLE III. First Spark-Spectrum of Potassium.

o DO ml Oo A PP |W WN

B | een aa =P 1605 i En
+ 844 16009 +(2550)| + 17715
+1724) | + 18064
(1692)| 19978
(1682) | _ 21460
849 21079
848 22606 849 23455 846 24301
847 23042 846 23888 849 24737
845 23229 (1695) 24924
(2549)| 24993
23337 848 24185 |, 846 25031
23665 (1694)| 25359
850 23159 840 24599 864 25463
2539 25743
(1708) | 25810
852 25281
26310 | 847 27157
(1696) | 26433
(1701)| 26546 847 27393
844 25126
(1708)| 26701
844 25804 | 850 26144
(1695) | 26866
(1694)| 26904
(1707)| 27192
845 26624 | 850 21414 | 847 28321
(1696)| 27705
(1691)| 27878 847 28725
27570 849 28419

(2540) 29732
(2541) 29787
(2550) 30186

80

TABLE III (Continued).

N°, P | & eten Ahold nooi fe zei zé
32| 28070 | 850 | 28920 | 850 | 29770

33 | 28458 (2552) |__ 31010
34 29539 | 846 | 30385 | 845 31230
35 | 28725 | 848 | _ 20573

36 | 28830 (2535) | 31365
37 | 29123 (2547) | 31670
38) 20371 (1693) |__ 31064

39 | 20471 (1690)| 31161 ;

40 | 29638 (1704)| 31342

41} 29888 | 844 | 30732

42) - 30101 | (2551)| 32652

43 30499 (1703)| _ 32202
|

1 > 847, 2 X 848, 3 X 847. From this ensues that Table III is not
unequivocally determined, like II, because when e.g. only P and Q
occur in a row, they can now equally well be placed in another
row in the Q and R or R and S columns.

it makes the impression that the number 847 — D has a physical
meaning, as also a value 846,2 occurs in the argon spectrum, which
may possibly be a more accurate value for D.

One more detail of the experiments deserves to be mentioned,
In some cases the argon spectrum was observed in the potassium
tube at the same time with the first spark spectrum of potassium.
We have not to do here with a case of transmutation of potassium
into argon, but with the penetration of atmospheric air, of which
the argon has been finally left. When, however, all precautions are
taken, the spark spectrum of potassium is emitted without argon lines.

Mathematics. — ““Keplanation of some Interference-Curves of
Uni-axial and Bi-axial Crystals by Superposition of Elliptic
Pencils.” (Third paper.) By J. W.N. Le Hevx. (Communicated
by Prof. Hunprik pr Vries.) —

(Communicated at the meeting of March 25, 1922).

Some well-known interference-curves, f.i. the hyperbola’s and the
lemniscates are obtained by superposition of two equal unissons,
under certain conditions, as was remarked in my first paper’).

From this observation we may derive a parameter-equation for
both cases, which enables us to construct the curves in a simple
manner.

The axes being at right angles, the unisson may be given by

& == T6032 P
y = 17 cos 2 (p 4- a).

Each value of the phase-difference 2@ corresponds to an ellipse;

when we suppose, that this phase-difference increases each time

Tt . .
with da =S the unisson has 7 ellipses.
n

With regard to an easy construction, the angle 2p may also be

. . as

supposed to increase with —.
2n

The two equal unissons, partially covering each other, are given by:

e=rcossagp-+a I
y=reos?(p +a)+ ay
“=r cos 2g — A

, age cee CD
y= rcos2(g'+a') —a ue)

where a is constant and < r.
The distance between the centres is 2a //2.

= aU
By altering 2a (and also 2e’) from O to 9 the image of the hy-
It
perbola’s is obtained, and from 5 to zr, that of the lemniscates.

1) These Proceedings Vol. XXII, p. 1223—1225.

82

Each curve of the moiré-image corresponds to a certain constant
difference (or sum) of phase.

The equation will first be derived for a constant difference of
phase 2a—2a’ = 26.

This condition, together with (I) and (II) gives:

Ane lt
x == COB a.
r
FTA
«Ja eo
—— = cos2p
Lf
dd : :
S= 082 p cos Za — sin 2 sin 2 a
(LY)
y+a . oe td
SO — cos 2(p'—A)cos 2 a—sin 2 (p'— 0) sin2a
r
Eliminating 2a from (JV) by means of the relation
sin? Za + cos? Za =1
we get:
y a 3 y—a 2 3
: — sin 2 p cos 2 p —__ cos 2 p — sin 2 gp
r by 2) ee
q
ia sin 2 (p'—O)| [cos 2 (g'—@) ine cos2(p' — 0) — sin2 (p'—@)
r r

or after reduction:

LE

r*

2__93
cos* {2 (pp) + 20} — 2 en cos {2(p—q') + 265+ 2

When in this equation cosp and cos p’

x—a xda
—— and ——
H fe i he

are replaced, resp. by

we get the equation of the moiré-image in ay co-

‚

ordinates.
It is, however, preferable to seek parameter equations.
Suppose 2 (p—p') + 26 = 24, then (V) becomes:
r? cos? 2 A — 2 (y2—a") cos 2 A + 2(y?+a07)—r?7=0 . (VL)
which gives for 4:
jr San neten gar,
The value of « follows from:
2(gp——) + 202A
cos 2 p cos 2 pl + sin2 p sin 2 pl = cos 2 (A—@)
or, with regard to (III) and after reduction:
r? cos? 2 (A —O) — 2 (x? —a*) cos 2 (A—@) + 2 (#74 a7) — 7? = 0.
This equation, being of the same form as (VI), we get for w:
ot Vr ee) ene

83

When the original angles p‚, g’, a and «/ are again introduced,
the parameter equations become:

@ = + Vr? cos? (pp!) — a? cotg? (p—-y')

EE 0 2 { eS A EN EN = ef AT (VIII)
y= r® cos” \(p—y') + (a—a')} —a’ cotg’ (pp) + (a—a’)!

For a constant sum of phase, we find the same equations by
changing g’ and a’ into — p/ and — a’.

In both cases, the image is the reflexion of the part in the first
quadrant with regard to the axes.

Characteristic is the function

FEE cosy Sa tp:

which is real for sin p > —.
da
ae SE: ;
It has an initial value 0 for y = bg sin —, a fast reached maxi-
pn

; a : : :
mum for sin? p= — and it becomes for this maximum = 7r—a.
f fe

This is in accordance to the fact, that the circumscribed squares
of the partially covering unissons have a common square with sides
= 2(r—a), in which square the moiré-image is inscribed.

For the more general case:

2=r,cs2gm+ b wr, cos2 pl — b
y=r,cos2(p + ea) Ha y=r, cos 2 (p + ed) —a
we find:

2 Vr? cos* (p—gp') — b? cot” (p—g’)

y = + Vr,? cos? (ep — g') + (a — a) — at cote? (ap — @') -+ (a—@)}.

Construction of the Hyperbola’s.

The construction is similiar to that, used for a Lissasous-curve,
that is: straight lines are drawn parallel to the scaled axes of an
orthogonal system and the points of intersection are joined diagonally.

Fig. 1 shows a diagram of the funtion

TP Vr cos? g—a’ cotg? op
for a= 8, r=30. gp is given in units of $¢{—3#° and so, the
unisson has 2=—=12 ellipses.
The maximum ordinate is r—a = 22, for p + 30°

(f (80°) =V483 while 22? = 484).

TIDAL a ;
The initial value of p = 15°, — being = = }.
ge

Proceedings Royal Acad. Amsterdam. Vol. XXV.

84

Between tne initial and the maximum value of », there are but
three ordinates and so, the sealed axes have three dividing-points
and the image has three interference-curves, each consisting of four
equal parts (Fig. 2).

In the formula, y—’ increases from 15° to 30° and the phase-
difference a—e«’ from —15° to +15°.

The construeted curves may be compared to the experimental
curves in fig. 3, obtained by superposition of two equal unissons,

Pea Goa

a
=
ae on
o

4 En
Le]
iS
Se

hed o

i ttt nen mts
ond 78 gn VON 42 REN 1S, EE RUG en A EEL EE

Fig. 1.

each containing 12 ellipses. A much finer result is obtained with
unissons of f.i. 50 ellipses, or by comparing to constructed unissons
in superposition — these drawings, however, require much time.

It will be evident, that an image with more interference-curves
may be obtained by interpolating a same number of curves between
two succeeding curves of fig. 2.

‘

Jonstruction of the Lemniscates.

This construction is more difficult than that of the hyperbola’s,
because the image, going to the centre, shows three different species
of curves, viz.: ovals, flattened ovals and hyperbola’s with doubled
ovals.

Only the outer curves are seen in the case of few isophasic lines;
they are as easily to construct as the hyperbola’s, viz.: by joining
the points of intersection, but now following the other diagonal
(tig. 4), according to a phase-difference, that begins with 90°.

The constructed curves of fig. 4 may be compared to the expe-
rimental curves of fig. 5, the unissons having 12 ellipses each.
Fig. 5 is somewhat irregular, owing to the small number of ellipses.

A new difficulty arises from observing, that the axes of co-ordi-
nates are not axes of symmetry for the image of the lemniscates,
as is required in the found formula. Still, this image was built in

85

some experiments, while another time, under apparently the same
conditions, a family of ovals appeared. At last, it was found, that
the angle between the planes of the pendulums caused the difference :
the image of the lemniscates is not built, unless this angle differs
from 90° and with a very large number of ellipses per unisson.
So in fig. 6, where the angle between the directions of the two
composing movements is + 145° and each unisson has + 120 ellipses.

The reason for this large number of ellipses proceeds from the
swift rising of the function in fig. 1. Dividing-points near the centre
are not obtained, unless the interval 4—5 is divided into f.i. 15
parts, corresponding to a phase-difference of +°= 15’ and a number
of 180 ellipses per unisson.

The experimental number however is limited in consequence of
the thickness of the ink-lines.

The phaenomenon is mathematically explained as follows:

The unisson

MEOS AGE
y' =rcos2(p~ + a)

upon a system with angle 25, becomes upon an orthogonal system
with the same bisectrix:

w' =r sin (8 + 45°) cos 2 p + roos (B + 45°) cos 2 (p + a)
y' = rcos (8 + 45°) cos 2p + r sin (B + 45°) cos 2 (p + a)

When 8 4 45° = y and seeking the equations of the moiré-image
in a similiar manner as before, the composing (oblique) unissons are :

(1X)

2 —=rsinycos2p + rcos ycos2(y + a) +a
y=reosycos2p+ rsinyeos 2 (p Ja) Ha
and
© == r sin y cos 3 p' + r cos y cos 2 (pl + a') — a
y =reos y cos 2 pl + rsin y cos 2 (pl + a!) — a
and a point of the moiré-image has the parameter-equations:

x sin Y—Y COS Y [
EI ein Zy) eo (ep) — @ col” (—)
cos y — sin y
& cos Y—y sin y

cos y — SUNY
== Ver (1 + sin y) cos* (gp) + (aa); — a? col" pa!) + (a—@)}
Now
== + Vrt cos? (pg!) — @° cot? (pg)
y = + Vrt (oP) a} a cotg? pp) + (a—«’)}
where

86

r= ry 2.sin(y + 45°)
is a moiré-image of two orthogonal unissons.
sin y only alters the magnitude.

The constant factor cos 7

When
wv sin y — y cosy — «a
uv COSY — ysny=—y
it follows, that
y cosy — w siny sin y

>= (y tg y— wv
ar BA (y cotg y—#x)

ysiny— xcosy smy

(y—« cotg 7)

cos 2 y cos 2"
A; sin y
Omitting the constant OE that does not alter the form,

we find at last, that the moiré-image for oblique unissons proceeds
from that for orthogonal unissons by the linear substitution

x, —_ 2 +y cotg y

= y x cotg y.
The form, thus chosen, gives rise to an easy construction, exe-
cuted in fig. 7. The new ordi-
nate, f.i. is found by drawing

from a point P (a, y) a straight
line, that builds an angle = y
with the ordinate of P.

By this construction, the
double symmetry is lost; the
axes turn to each other over
an angle 90°—y.

In fig. 7, a flattened oval is
obtained '); when the original
curve lies nearer to the centre
Fig. 7. and turns its convex side to

the axes, the hyperbola’s *) are built.

1) See the experimental, curves in my first paper, fig. 4.

3) A mathematical explanation of interference-curves, wholly different from the
here given. is to be found in Mr. T. K. CHINMAYANANDAM: On Haidinger’s Rings
in Mica. Proc. Royal Society. Vol. XCV, p. 176—-189.

The author maintains the pure hyperbola’s and the ovals of Cassini, which,
however, build a rather rough approximation.

J. W. N. LE HEUX: “Explanation of some Interference-Curves of Uni-axial and
Bi-axial Crystals by Superposition of Elliptic Pencils’’,

a
er

‘
?

4
,
r

Bigs 2: Fig. 3.

Fig. 4. Fig: '5.

Fig. 6.
Proceedings Royal Acad. Amsterdam. Vol. XXV, 1922.

Bacteriology. — “Studies on the bacteriophagus of p’Hururrn.” I.
By J. W. Janzen and L. K. Worrr. (Communicated by
Prof. C. Eykman).

(Communicated at the meeting of March 25, 1922).
Ul. The Bacteriophagus with regard to flagellates.

We have been informed by p’Hrrenie that the water of some
Indian rivers possess the bacteriophagus properties.

In connection with that we have considered it of importance to
see how far flagellates out of a mixture of bacteria and bacterio-
phagus also eat the latter. ;

Ie order to do this we prepared a suspension of dead typhoid
bacilli in saltsolution, and to a third part of this we added 2 ¢M®
canalwater; a second portion was mixed with bacteriophagus and
2eM? canalwater; a third portion was only mixed with the same
quantity bacteriophagus as the second.

After 9 days the two first portions had become considerably
clearer and we could distinctly show flagellates in the microscopic
preparation.

Now dilutions were made, the number of bacteriophagus germs
of which was stated in the wellknown way.

We found:

II emulsion + canalwater + bacteriophagus in

1/400.000 cM? 71 islands.

HI emulsion + bacteriophagus in 1/400.000 cM* 380 islands.

With another trial we found after 14 days:

Il emulsion + canalwater + bacteriophagus in

1/4000 mill. eM? | 120 islands.

[IL emulsion + bacteriophagus in 1/400 mill. eM? 50 islands.

This numbers are of the same range; the differences range within
the mistakes of the experiments.

The suspensions without canalwater remained absolutely turbid,
because the bacteriophagus does not affect dead bacilli.

From these two experiments we wish to conclude that the bacterio-
phagus is not being affected by flagellates.

88

III. Constancy of the bactertophagus properties.

In our first communication we have proved that various bacterio-
phagus strains behave differently with regard to different typhoid
bacilli.

Here follows a comparition of the bacteriophagus Sm in the sixth
and tenth generation with regard to four different typhoid strains;
the bacteriophagus was always fed with typhoid Sm.

1. Clearing. 2. Checking. 3. Islandformation.
| 6th generation . | 10th generation
Strains | | | 2 | 3 | 1 | 2 | 3
Wi — ++ - — ++ =
23 ++ 4+ | +44 | +t +) +++
24 — — — — o —
25 Hede | tt++ [dt | t4t4 | dd | +++4

So here we see an absolute conformity.

The behaviour of bacteriophagus Sm with regard to strain Wi is
somewhat strange; in some generations we did not find any effect;
in some others’ as above mentioned we did find shecking of the
growth in broth, but no islandformation.

We have now observed whether the properties of the bacterio-
phagus change when it is cultivated on different bacteriastrains.

In the following tabels the results are given in which

I. Bacteriophagus Re direct from faeces,

I]. é Re after having been fed with typhoidbacilli Sm,
iO, in Wi direet from faeces,

IV. Y Wi after having been fed with typhoidbacilli Wi,
V. i Wi after having been fed with typhoidbacilli Sin,
VI. ne Sm after having been fed with typhoidbacilli Sm.

The thus obtained bacteriophagi were examined with regard to
5 typhoidstrains.

From this we see that the properties of the bacteriophagus do
change when another bacillus has served as food in this sense, that
no bacilli which used to affect are now left uninfluenced, but
that an increase can appear in the number of strains which are
influenced by the bacteriophagus; except for this strengthening
however the bacteriophagus retains its specific properties, which in
our opinion pleads more for a living being than for a ferment.

89

3. Islandformation.

II Bact. Re after having been
fed with typhoidbacilli Sm.

| | 2 | 3

— | +444 | Ht
= + | +4++4+
neten

1. Clearing. 2. Checking.
I Bact. Re direct from faeces.
Typhoid
strains i 2 3
Wi — = —
— +++ | +++
24 = = —
27 — = =
29 — ze Ln
III Bact. Wi. direct from faeces.
Typhoid
strains I | 2 | 3
Wi | +++ | 444+ | +4+4++
1 a Ab of
24 — ++ | +44++
27 — + | +4+4++
29 =) RE | E+

V Bact. Wi after having been fed
with typhoidbacilli Sm.

Typhoid

IV Bact. Wi after having been
fed with typhoidbacilli Wi.

| 2 | 3
++++ | +444 | +444
— ++ | ++++
= + | ++++
— | 4444+ | +444

VI Bact. Sm after having been
fed with typhoidbacilli Sm.

strains | ! | ¢ | = : | je | 5
Wi Borg Eat er aa on raad Pen ag oe = Ee =
1 fetes) Shisha i sete sre eis
24 = ni ai pee oy a = = =
27 a ae lignes EN = =
29 ran ar Wee TLS ITALY “Ti Ti En
_ Lab. for hyg. of the University.

Amsterdam, March 1922.

Physics. — G. Hertz: “On the Mean Free Path of Slow Electrons

in Neon and Argon.” (Communicated by Prof. P. Karenrest).
(Communicated at the meeting of March 25, 1922).

The reason for undertaking these measurements was given by
researches concerning the efficiency of non-elastic impacts of electrons
in neon and argon at potentials just above the excitation-potential.
It is known, that those collisions between electrons and the atoms
of rare gases, which take place below the excitation-potential
characteristic for each gas follow the laws of elastic collisions. As
soon as the kinetic energy of an electron surpasses the value
corresponding to the excitation potential, it can, on collision with
an atom, transfer energy to the latter and thereby raise it from its
normal state to a higher quantum-state. This, however, does not take
place at every collision between a sufficiently fast electron and an
atom; only a certain part, in the case of rare gases most probably
only-a small fraction, of these collisions is non-elastie and causes
excitation of the colliding atom. This fraction we call the efficiency
of the particular non-elastie impact. It is equal to the probability
that an impact of an electron possessing the required energy really
leads to a transfer of energy. It is naturally a function of the
velocity of the electron. The form of this function however is not
vet known.

In a glow-discharge the two rare gases neon and argon show a
characteristically different behaviour, which among other things
manifests itself under similar circumstances by producing in neon
a much more intensive emission of light than in argon. The reason
for this different behaviour according to G. Horst and E. Oostrruuis *)
probably lies in the fact, that in argon electrons having a velocity
above the excitation-potential readily transfer their kinetic energy
to the argon-atoms thereby exciting the emission of ultraviolet rays
(resonance), while in neon only a small fraction of the impacts leads

) G. Horsr and G. OosreRauis, Physica. 1, 78, 1921.

91

to radiation the majority of the electrons only imparting their energy
to the neon-atoms after falling through a potential-difference equal
to the ionization-potential, thus causing ionization.

In consequence one would expect a great difference in the effi-
ciency of the first non-elastic impact in neon and argon. Preliminary
experiments concerning the relative value of the efficiency in these
gases however have shown, that this difference is not large enough
to explain the different behaviour. So there must be another reason.
Beside the excitation-potential and the efficiency there is only one
quantity which determines the number of the non-elastic impacts,
and that is the mean free path of the electrons. Up to now it was
assumed, that the value derived from the kinetic theory of gases
for particles of infinitesimal small dimensions and large velocity,
viz. 4/2 times the mean free path of a gas-molecule, should hold for
the electrons. Recently however, H. F. Mayer’) and C. Ramsavrr *)
have found, from the measurement of the mean free path of electrons,
that also for slow moving electrons this quantity depends on the
velocity of the electrons, this dependence being different for different
gases. Especially between neon and argon RAMSsAUER found a very
marked difference. While in neon the mean free path depends only toa
slight degree on the velocity of the electrons and is nearly equal to
the value of the kinetic theory, argon shows for very slow moving
electrons, below 1 volt anomalously large values of the mean free
path. The mean free path then decreases and becomes a minimum
at approx. 12 volts, the minimum being about one third of the value
of the kinetic theory. This fact must be of importance for the pheno-
mena produced by electrons passing through a gas, especially in the
case of argon, where the mean free path has its minimum value
at a potential nearly equal to the excitation potential.

Considering the great importance of the dependence of the mean
free path on the velocity, not only for the understanding of the
action of electrons in gases, but also for the theory of the atom, it
appeared desirable to me, to verify this dependence by direct ex-
periments, in order to obtain accurate values for the ratio of the
mean free paths in neon and argon, this ratio being of importance
for the evaluation of comparative measurements in the two gases.
The applied method is based on the following idea: If in an appa-
ratus of given geometrical dimensions electrons of a certain velocity
are allowed to move in a rare gas in a space, in which there is

1) H. F. Mayer, Ann. d. Phys. 64, 451, 1921.
*) C. RAMsAUER, Physik. Zeitschr. 22, 613, 1921.

92

no electric field, the mean free path alone will determine their.
movement and distribution, so long as the velocity of the electrons
is not larger than that corresponding to the excitation potential,
that is: so long as the impacts are entirely elastic. If the apparatus
is then filled suecessively with different rare gases, the movement
of the electrons in the one gas must be the same as that in the
other, provided the pressures are chosen in such a way that the
mean free path is the same. If, on the contrary, the pressures
of both gases has been adjusted so as to make the movement of
the electrons the same, the inverse ratio of the corresponding
pressures will give the required ratio of the mean free paths under
equal pressure. This ratio must be found to be independent of the
pressure used in the experiments.

The apparatus used is shown in fig. 1. G is a
tungsten filament, MN, and AN, are grids P is a
receiving plate, and H is a metal shield which
prevents electrons from coming from G to P by
any other way, than through the space between
the two grids. All metal parts were made of copper.
Before mounting the apparatus they were treated
with nitric acid and showed a clean metallic surface
after the tube had been exhausted during 5 hours
at 400°. The gases used were so pure that no
non-elastie impacts, below the excitation potential
could be detected even by a very sensitive device.

Before the final measurements, preliminary mea-
surements were made with a simpler device, which
differed from that of fig. 1 by omission of the grid JN,.
Though the experiments made in this way do not
allow an accurate quantitative evaluation, the results
are given here briefly, as they show very simply and clearly
the different behaviour of neon and argon. During these prelimi-
nary measurements the entire apparatus was at earth-potential,
except the filament which was brought at a variable negative
potential, so as to produce an accelerating electric field between
filament and grid. The electron-current passing on to the receiving
plate P was measured by a galvanometer. The measurement consisted
simply in noting the current as a function of the accelerating
potential between G and N,, in neon and argon under various
pressures. In order to be independent of slow variations of the
current in the filament, a second galvanometer registered the total
electron current, and the quotient of the plate-current and the total

iS i 1 Ce a et

Fig. 1.

93

©

5
3
3
v
is]
>
IN

8

a
=

20 Volt.

are oe

Fig: .3:

; 94

electron current from the filament was calculated. As the tempe-
rature of the filament was always low, this quotient was independent
of the intensity of the electron emission of the filament.

This quotient, multiplied by a constant is plotted in the curves of
the figs 2 and 3 for a series of pressures in neon and argon as a
function of the potential difference between Gand N,. The numbers
near the curves show the gas pressure in m.m. mercury. We see
immediately the extra-ordinary difference in the behaviour of both
gases. While in neon an increase of pressure for all velocities
reduces the plate-current in about the same degree, argon shows at
10 volts a remarkable decrease of current at pressures, where at
1 volt practically no influence is observed. As the observed decrease
of current can result only from the collisions between the electrons
and the atoms of the gas, we can deduce from these measurements
qualitatively, that the mean free path of electrons in argon varies
strongly with the velocity of the electrons, while in neon this is
not the case, or at any rate only to a small degree. A quantitative
calculation in the sense of the above consideration can only be
taken from these measurings for slow electrons up to about 10 volts;
at higher velocities the electrons produce secondary electron emission
from the metalwalls. To retain these secondary electrons, the second
grid N, was introduced a retarding potential equal to */, of the
accelerating potential between Gand N, being applied between
N, and P. The result of such series of measurements is shown in

2

figs. 4 and 5 wherein the numbers near the curves again show

O 00210

© 00297

LU 4 8 12 1S 20 Volk.

95

the gaspressure in millimetres mercury. For the evaluation of
these measurements the distribution of the electron velocities was
first measured in vacuo by means of a variable retarding field with
the result, that, in consequence of the initial velocity of the electrons,
the potential gradient at the filament and the Volta-potential difference

|
|

== Vacuum

_AXrgon_

6 4 8 ; ee Se ie eS

Fig. 5.

between filament and grid, 0.7 volt had to be added to the applied
accelerating potential, in order to obtain the true velocity of the
electrons. For a series of electron velocities the logarithm of the
plate-current was registered as a function of the pressure in neon
and argon. A similar character of the curves in neon and argon
is to be expected, assuming that the method is correct, in such a way
that for each velocity the proportion of corresponding pressures in
neon and argon (i.e. pressures giving equal plate-currents) is constant.
This is in fact the case for all electron-velocities up to 16 volts. To
show this, the curves so obtained for a number of velocities are
reproduced in fig. 6. The evaluation is simplified by the fact that
the first part of the curves is straight. From the slope of these
straight portions we can obtain directly the ratio of the corresponding
pressures and so also the ratio of the mean free paths of the
electrons.

A condition for the correctness of the method here applied is, that
all collisions between electrons and atoms are absolutely elastic. By
reason of the very low efficiency of the non-elastic impacts below the
ionization potential in the rare gases this is no doubt the case for

96

potentials between the excitation- and the ionization-potential and for
the low pressures used here. Things are different above approx.16 volts,
the ionization potential of argon. This already can be observed at
the curves for argon at higher pressures in fig. 5, by a bend in
the curves at 16 volts; consequently the ratio of corresponding
pressures is no more accurately constant there, as is to be seen in
fig. 6 at the curves for 18 volt. At the same time this curve shows,

06

0%

02

0 002 006 006 "Ym

42 Volt.

0 ope 00% 006%, 0

5 Fig. 6.

that for the lower pressures the number of ionising impacts is so
small as to play no part, so that there is no objection against
deducing the ratio of the mean free paths from the ratio of the
slopes of the first straight parts of the curves.

As a result of the measurement, the values for the ratio of the
mean free paths of electrons in neon and argon obtained in this
way are shown in fig. 7 as a function of the potential corresponding
to the velocity of the electrons; in fig. 8 they are plotted as a
function of the root of this potential, being proportional with the

97

velocity of the electrons. The dotted line in fig. 8 shows for comp-
arison the values of this ratio as deduced from Ramsavurr’s measure-
ments. It will be seen that our measurements verify not only the
fact of the variation of the mean free path of the electrons with
their velocity, as found by Ramsaver, but also the general character
of this variation. The maximum of the curves was found in the
present measurements at a potential about 2 volts less than in
RAMSAUERS.

The action of the slowest electrons is theoretically of special interest.
As however the accuracy of such measurings decreases for ex-
tremely slow electrons an extrapolation in the direction of the

ANe_
Abr ee

Fig. 7. Fig. 8.

velocity zero is always doubtful. If we stipulate, according to the
results of Ramsaver that the electrons in neon show nearly normal
values of the mean free path, it appears that, according to the here
obtained results, the mean free path of electrons in argon on
approaching zero-velocity, do not reach an infinite value, but one
about 3 times that calculated from the kinetic theory for very
rapidly moving particles of infinitesimal small dimensions. This figure
can however, by no means lay claim to accuracy.

The number of collisions of an electron passing through a unit

length under the influence of an electric field #, in a gas, in which
; v' UT
its mean free path is 4, is — —, that is, inversely proportional
e
pn
m
of the square of the mean free path. In argon the mean free path, just
below 12 volts, the excitation potential, reaches its minimum of about
‘/, of the value derived from the kinetic theory. We can therefore
conclude that an electron of this velocity in argon in passing

98

through a length unit makes about 9 times as many collisions as
would be expected from the kinetic theory, while in neon the
number of collisions is nearly normal. This shows clearly, why
tn argon non-elastic impacts above the excitation potential have a
marked effect, while under similar conditions in neon they are
hardly noticeable.

Eindhoven, Laboratory of the
Philips Incandescent Lamp Works.

Anatomy. — “On the morphology of the testis of Rana fusca Rösel”
By G. J. van Oorpt. (Communicated by Prof. J. Borkr.)

(Communicated at the meeting of April 29, 1922.)

Ln trod u.e tio n.

In recent years several investigations have given us a better
insight into the course and the structure of the seminiferous tubules
of a number of Mammals and of one Bird (cock). Formerly it was
tried to isolate these tubules by the process of maceration and teasing
in order to establish their form, their mutual relation and their con-
nection with the rete testis. The results were not convincing, however,
because it could not be traced with certainty whether the free ends
found were natural or had originated by tearing.

By means of complete series of sections and wax-reconstructions
Brumer (1911) succeeded in disclosing the complicated structure of
the embryonic human testis. He discovered that the testis tubules
form a closed network. Employing a new, good injection method,
followed by maceration and teasing, Huser and Curtis (1913) isolated
in the testis of the adult rabbit several arch-shaped seminiferous
tubules, connected to the rete testis with both extremities. Besides
these simple “single-arched” (n-like) tubules, ‘“double-arched” (m-like)
tubules, connected with the three free ends to the rete, were met
with. Relatively simple tubules as well as canal-systems of compli-
cated structure were found in the rabbit’s testis; canals terminating
in blind ends or diverticula were not described, however. Applying
the same method Huser (1916) discovered in the testis of the cock
that the seminiferous tubules form a network, in which no blind
ends occur.

Studying complete series of sections Curtis (1913) met with
various single-arched tubules in the testis of the mouse. Anastomoses
between two arches occur but rarily. Later on (1918) Curtis inves-
tigated the testes of mouse, rabbit and dog and in these animals he
also found the simple n-like tubule to be the original one. However,
the testis of the mouse shows the simplest structure, then the testis
of the dog and next that of the rabbit follows as to complication.

Independent of Curtis , pr Burrer and pr Ruiter (1920) came to
the same results in studying a number of complete series of sections

d

Proceedings Royal Acad. Amsterdam. Vol. XXV.

100

of testes of mouse-embryos of 9—17 mm. length. The fundamental
form of the embryonic testis tubule is a simple n-like tube, of which
the convex side is directed towards the periphery and of which the
extremities are connected with the future rete testis. A number of
these tubes are placed serially behind each other; anastomoses between
the arches and double-arched, m-like tubes occur also. The plane of
the arch is perpendicular to the longitudinal axis of the testis.
Tubules, terminating in blind ends, were rarely found. In the caudal
part of the testes of embryos of 13 mm. and smaller a so-called
,caval-complex” occurs, from which later on — for in older testes
more arches are to be found than in younger ones — additional
arches probably develop. The tubules number from 10 to 13 in the
mouse. After the ,,canal-complex” has disappeared, the longitudinal
growth of the testis-tubules sets in and then the tubules begin to coil
strongly. From the longitudinal stem, originally epithelial, the rete
testis develops.

In a second paper pr Burrer (1921) traced the morphology of a few
Marsupialian testes (Perameles obesula, Didelphys spec., Halmaturus
Bennetti). The single-arched tubule was found again; in Perameles
the testis (embryo of 50 mm.) is still more simply built than in the
mouse; the testis of Didelphys (embryo of 20 mm.) is composed of
two long, strongly twisted tubules. These tubules are very numerous
in Halmaturus (embryo of 105 mm.), where they vary from 200
to 300.

Starting from the above investigations it was but natural to trace
in one of the representatives of the other Vertebrate groups, how
the shape of the adult seminiferous tubule derives from the embryonic
one. After consulting Dr. H. M. pe Bertier, to whom I wish to
express my thanks for his interest in this work, I chose the co m-
mon Frog, Rana fusca Rösel. As it appeared during the investi-
gation that in immature frogs the course of the vasa efferentia,
the ducts through which later on the spermatozoa pass to the kidney,
show different peculiarities, | decided to communicate simultaneously
a few remarks concerning the course of these channels in immature
frogs in the beginning of their second year.

Material and methods.

All specimens of the common frog were caught at Bilthoven
(near Utrecht) in Sept. 1920. The smallest, immature frogs measured
2.8 em. (from the head to the rump), the largest, adult spec. 6.3 cm.
According to Gaupp (1904, III, pp. 298—300) frogs measuring circ.

101

30 mm. are in their second, those measuring cire. 50 mm. in their
third year, whilst they become mature in the end of the fourth year.
The gonads of the immature frogs were taken from the body,
together with the kidney; they were fixed in Bouin’s solution and
after 5 days they were transferred to alc. 90 */,. Subsequently the
testes were cut — mostly frontally, but in a few cases transversely
— into complete series of sections of 10u. The sections were
generally stained with DerarieLp’s hematoxylin and van Girson’s
solution, sometimes eosin or nigrosin was used instead of vaN Girson’s
solution. Especially with van Gigson’s solution the connective tissue
between the seminiferous tubules assumes a deep red colour.

From the testes of the adult frogs only the middle part was
sectioned, from all other testes complete series of sections were made.
As far as necessary, the sections were drawn on-transparent paper
at a magnification of 100, with the aid of the large projection-
apparatus of Zuiss.') By laying these transparent papers on each
Other, it is generally not difficult to trace the course of the tubules,
which are cut transversely. Originally 1 had the intention to project
on a certain plane several tubules, passing over into the rete testis
with a common stem, but in many cases this method proved not
practicable, especially in adult testes, as here the tubules are too
close to each other and too much twisted. Fig. 10 is even so
schematized that only the mutual relations of the tubules, drawn in
one plane, are shown. In order to get an exact insight into the
course of the seminiferous tubules a few sections of the part of the
testis, in which these tubules occur, are also reproduced.

In the following the development and structure of the testis tubules
are described in the first place and further the particular course of
the vasa efferentia in six immature testes is treated.

The development and structure of the seminiferous

tubules. .

An extensive literature deals with the development of the gonads of
frog-embryos. As most of these investigations do not bear upon my
subject, I will only communicate the results of Wirscui, who in his
„Experimentelle Untersuchungen über die Entwicklungsgescliichte
der Keimdriisen von Rana temporaria” (1914) not only traced the
different developmental stages of the gonad, but also drew attention

1) | have to thank Prof. A. J. P. van pen Broek, whose kindness enabled me
to use the apparatus of the Anatomical Institution of the University at Utrecht.

7*

102

to the morphology of the testis tubules of newly metamorphosed frogs.
After deseribing the development of the so-called indifferent gonad
— which possesses a germinal epithelium consisting of one layer
and surrounding a central lumen, the
primary genital space, in which eetl-strands,
-SSÛ the sexual strands, situated at regular
distances behind each other, have origin-
ated from the mesonephros — Wrrscar
traces the development of the ovary and
the direct testis-development. The indirect
testis-development, which takes place in
the so-called hermaphrodites of
Prrücer is elaborately described; in this
‘ase the testis originates from an Ovarium-

siti like gonad’). As this development does

Var

not bear directly upon my subject and
as the final stage of both direct and
indirect testis-development is the same,
I will not enter any further upon this
question. Shortly, the direct testis-develop-
ment is as follows. The germ cells leave
the germinal epithelium, wander through

Fig. 1.

Schematized longitudinal
section of the testis of a newly
metamorphosed frog. After the primary genital space and settle on

Witscut (1914). the sexual strands. All germ cells leave
the germinal epithelium about simultaneously, so that only the
peritoneum remains. Between the germ cells and the compact core
of the sexual strands several slits originate: the anlages of the
lumina of the testis-ampullae. Then the ampullae differentiate from
each other and in this way the anlages of the testis tubules develop.
These ampullae are short, almost globular tubules, with a lumen
disappearing later on.

The convex side of the ampullae is directed towards the periphery
of the testis; with the other side they are attached to the central
strand. The sexual strands are connected with the mesonephros. The
distal ends of these strands thicken, fuse and in this way the central
strand originates in the longitudinal axis of the juvenile testis. After
some time the inner-testicular network or rete testis originates from
the central strand, as well as the vasa efferentia from the compact
sexual strands.

A schematized longitudinal section of the testis of a newly meta-

1) Witscu’s latest publication (1921) treats the same subject.

103

morphosed frog is reproduced in fig. 1, which is drawn after Wirscu
(1914, fig. A, p. 21.)

In the literature, dealing with the further development of the testis,
only some scattered remarks on the testis tubules are to be found.
“Damit (i.e. when the stage, reproduced in fig. 1 is reached) haben
die Samenkanälchen im wesentlichen ilren definitiven Zustand erreicht”
(Wrrscur 1914, p. 20). Then the testis ampullae grow out “zu
den bekannten schlauchförmigen und gewundenen Samenkanälchen,
während sich die Keimzellen ziemlich rasch vermehren” (Wrrscui1
1914, p. 20). However, nothing is mentioned about this outgrowth
and about the question whether the tubules are connected with each
other.

Gaupp describes the form of the testis tubules of the adult frog
as follows (1904, III, p. 307): “Sie beginnen an der Oberfläche
gerade und mit radiärer Anordnung gegen das Centrum hin, laufen
dagegen mehr central vielfach gewunden durch einander. Die radiären
Canalabschnitte der peripheren Zone beginnen blind unter der Tunica
albuginea, und häufig sieht man hier, wie zwei gesondert entstehende
sich mehr central mit einander vereinigen”’.

It is my intention to trace how the structure of the adult testis
originates from the simple one of newly metamorphosed frogs, the
latter having been described by Wrrscat.

I started with the study of testes of frogs in the beginning of
the second year. It proved easiest to get an insight into the form
of the testis tubules by studying frontal testis-sections, in which a
great number of transversely cut tubules are visible (ef. figs. 2, 3,
6, 7, 8, 9). These sections were drawn on transparent paper and
then compared.

In figg. 2 and 3 parts of two frontal sections of the right testis
(long 1.8, broad 1 mm.) of a com-
mon frog with a head-rump length
of 3.5 ¢c.m. are reproduced. Fig. 2
is a section close to the rete;
many tubules transversely cut,
are distinctly visible. On tracing
the course of the three tubules,
designated A, B and C, to the
periphery, we observe that in most

A I hs
N Y
A <\
< Ve
rae ENG
Section of the testis of a juvenile Cases these tubules branch, like
frog (beginning of second year), near the fingers of a hand, into anumber

the rete testis (X 100). of tubules (fig. 3, which is drawn
after a section close to the periphery) and that all these tubules are

104

terminating in blind ends. Tubule A ramifies into five tubules (A /,
All...AV), B into two tubules (BJ, BI), while C remains
single. Already in fig. 2 it is visible
that the tubules A and B divide
into a certain number of branches,
for these tubules are designated
Al—V and B/—/T in this figure.
On comparing figs. 2 and 3 we see
that the space between the tubules,
the interstitium, is larger near to
the rete than towards the periphery.
As has already been mentioned, fig. 3
is drawn after a section close to the

Fig. 3. testis-surface, so that not all testis
Section as in fig. 2, but more tubules are cut transversely. Many
near the periphery (< 100). tubules, which were not cross-cut,

were indistinctly visible and for this reason this part of the section
is shaded by oblique lines.

To elucidate the course of the seminiferous tubules, I have projected
the circumferences of the testis tubules A, B and C on a sagittal
plane of the testis (this plane is marked by a —.—.— line in
fig. 3). This is reproduced in fig. 4, in which the course of these
tubules can be seen. Moreover it is visible that the ducts of the

„en

rete into which the tubules 4, ArArAr 3! Ay BI C

¢
id

B and C pass over, are directly Fig.3—
connected with each other.
The left testis of the same
frog was cut transversely. The
testis tubules are built in the
same manner as those of the ioe
right testis. However, on com- 7
paring the form of the tubules
of the cranial and caudal part
of the left testis with the form Fig. 4.
of the tubules of the middle Projection of the tubules (designated
part of the right testis, we see in figs. 2 and 3) on a sagittal testis-
that in the former the number Plane (X< 150).
of simple, not branching tubules is much larger than in the latter.
A peculiarity of this left testis is that the most caudal vas efferens
is not connected with the rete testis. In this testis there is a small
caudal part, consisting only of three testis tubules, which do not
open into the rete, but are directly connected with the mesonephros

—-" edad

105

by an efferent duct. In fig. 5 this is figured. Only these candal vasa
efferentia are projected on the mid-sagittal plane of the testis. Moreover,
two-single testis tubules, directly
passing over into the rete testis,
are sketched; the vas efferens,
previous to the last, gives off a
side branch to the last efferent
duct, but a connection is not
established, however.

Two frontal sections of the left
testis (long 6, broad 3,5 m.m.) of
a frog in the beginning of the third
year (4,75 ¢.m. in length) are
reproduced. Fig. 6 shows a section,
close to the rete testis, of which
different parts are visible. The
tubules A, B, C and D are sepa-
rately connected with the rete;
tubule B just ends in the rete in
the section reproduced; in a neigh-
bouring section tubule C' is con- Fig. 5.
nected with this same rete canal.

Projection of the two posterior vasa
In this figure arrows indicate with efferentia on the sagittal longitudinal
which part of the rete a few of testis-plane. Frog from the beginning
the testis tubules are connected. of the second year (X 100).

When we trace the course of the testis tubules, indicated A, B, C
and ) towards the periphery, we see that here also these tubules
divide into many others; e.g. tubule A splits up into seven, B into
five, C into four and D into six others. Fig. 7 shows a section of
the same testis about halfway the periphery. At this level tubule A
has divided into 3 branches (A /—//, A III-—V, A VI—V1/1), B
into three (B V, branched off nearer to the rete is very short), D
into four, while tubule C has not divided as yet; this will take
place closer to the periphery. The space between the tubules, being
rather wide near the rete, is very narrow at this level. Most tubules
end near the periphery; anastomoses are never found.

On comparing the testis of a newly metamorphosed frog (fig. 1)
with that of a second or third-year one (figs. 2—7), we find that the
testis tubules, which are single originally and terminate in blind ends,
divide already in the second year into a number of branches (like
the fingers of a hand) and that this subdivision has increased in the

106

third year. The testis having strongly increased in size during this
time, it is impossible that several testis-ampullae have fused to form
such acanal system. On the
contrary, we must conelude
from the stages, described
above, that the testis tubules,
which are originally simple
and very short and which
are called testis ampullae
then, divide toward the
periphery into a number
of tubules and that these
branches are connected with
the rete by the proximal
part of the ampulla. On

Fig. 6. comparing the different sec-
Section of the testis of a frog of the third tions’) we see that both
year; the rete is partly visible (X 50). length and diameter of the

seminiferous tubules have strongly increased.

Turning now to the testis of the adult frog, we observe almost the
same here. In figs. 8 and 9 parts of two frontal sections of the left
testis (long 10.5, broad 7 mm.) of ~
an adult common frog (length
6.3 cm.) are reproduced. The
tracing of the course of the strongly
ramified testis tubules and the
graphic reconstruction of this taking
too much time, I can only des-
cribe a few tubules, not very
strongly branched. They are
reproduced in figs. 8 and 9 and a
reconstruction of the same tubules,
beside each other and in one Fig. 7.
plane is given in fig. 10. This had Section as in fig. 6, but about half-
to be done, because the tubules, way the periphery (X 50).
winding too much around each other, especially in the neighbour-
hood of the rete, could not be reproduced, projected on a certain
plane.

The tubules, designated AJ and A // in fig. 8 do not branch

: 1) Originally [ had the intention to reproduce all the figures at the same magni-
fication (XX 100); this proved impossible, however, the figures of immature frog-
testes then becoming too small and those of adult frog-testes becoming too large.

107

further towards the periphery; tubule B /—// (fig. 8) splits up
into two tubules towards the periphery (fig. 9), while B /// is very

short and ends blindly about halfway the periphery (fig. 10). If the
testis had developed further, this short tubule would probably have
grown peripherally. Tubule C divides into 5 parts. A, B and Care
connected with the rete close to each other.

On comparing this testis with those, described above, we see that
apart from the size, there is no fundamental difference in the shape
of the tubules. The seminiferous tubules of the adult testis have the
same shape, but are longer and thicker. They form no anastomoses
and all end blindly. Most of them are strongly branched. The
tubules twist, especially near to the rete. Towards the periphery
the tubules are situated so close to each other that there is but a

108

very narrow space left for the interstitium. Towards the rete testis
this space increases in width (cf. figs. 9 and 8).

Fig. 10. Schema of the course of the testis-tubules, designated
in figs. 8 en 9 (XxX 50).

The course of the vasa efferentia in frogs
in the beginning of the second year.

It is generally known that in adult frogs the vasa efferentia,
which arise at the medial side of the testis, form a network, the
extratesticular network, between testis and kidney. The number
of these channels greatly varies. According to Gaupp (1904, III,
p. 355) they number from 4 to 11 in Rana fusca. These differences
are not only individual, but occur also in the right and left testis
of one and the same animal. Channels which terminate blindly and
do not reach the kidney are numerous, according to GAUPP.

Investigating a number of testes of immature frogs, I found that
here these particuliarities were also present. A conspicuous differ-
ence is that the extratesticular network has not developed as well
as in adult frogs, the vasa efferentia being still situated serially
close behind each other in the mesorchium.

I will describe six testes, derived from two frogs of 2.8 cm. and
one frog of 3 em. in length. With regard to the vasa efferentia,

109

they show the following particuliarities and differences, sketched
schematically in fig. 11 a—/; testes, corpora adiposa and kidney
are dotted, while rete testis and vasa efferentia are black. For sim-
plicity’s sake all the ducts are indicated by successive numbers.

Fig. 11a gives a schema of the right testis of a frog, measuring
2.8 cm. in length. From the testis to the mesonephros 4 efferent
ducts run, of which the two last have fused over some distance.
At the cranial side of the testis there is also a vas efferens (N°. 2)
but this one is not connected with the mesonephros. It runs cranial-
ward and ends in the fat body. Still more in front of the fat
body there is a very short vas efferens, connected neither with the
testis nor with the kidney.

In fig. 115 a schema of the left testis of the same juvenile frog,
with 10 efferent ducts is reproduced. The most cranial one, running
only over a short distance in the fat body, can be compared to the
first vas efferens of the right testis of the same frog. The rete testis
is connected by 8 different vasa efferentia (N° 2—9) with the
mesonephros. N°s 5 and 6 arise from the rete at some distance from
each other, but quite near to the testis-surface they come close
together and run parallel without fusing, however, to the mesone-
phros. The two ducts (Nes 8 and 9) at the caudal side of the testis
arise close to each other but separately, from the testis, and unite
just outside the testis to form a common duct. As is the case in
the testis described above (p. 8) and sketched in fig. 5, the 10 vas
efferens is not connected with the rete testis. Only a few semini-
ferous tubules open into this duct; so these are directly connected
with the kidney.

The two testes sketched in fig. 11c and 11d belonged to a frog,
also measuring 2.8 em. in length. In both the most cranial efferent
ducts have no direct connection with the mesonephros, but run
cranialward to the fat-body and from here to the kidney. In the
right testis, behind this efferent duct, there are still six others, from
which Nes 3 and 4 are only separated over a short distance, quite
near to the kidney.

In the left testis of the same animal the 2d and 3¢ vasa efferentia
arise separately from the rete; they fuse near the mesonepbros to
form a common duct. The caudal vasa efferentia, N°s 5 and 6, run
parallel in the testis and unite there, where they leave the testis;
then they split, subsequently they again form one duct and finally
they enter the kidney separately.

The right testis of the specimen, the last to be described (3 cm.
in length), shows only one peculiarity (fig. 11e) ie. the 3td and 4"

Fig. 11. Schemata of the course of the efferent ducts in
6 testes of juvenile frogs.

111

vasa efferentia, running close to each other, fuse near the kidney.

The left testis is remarkable for the following facts (fig. 11/).
The most cranial vas efferens runs like the most cranial ones, sketched
in fig. 11a and 116; the third vas efferens runs like both cranial
efferent ducts of fig. 11¢ and 11d and moreover, a short side-duct
(N°. 2), coming from the fatbody, opens into it. The vasa efferentia
Nes 5 and 6 are close to each other, especially outside the testis,
but enter the mesonephros separately. The 7‘ and 8 vasa efferentia
leave the rete testis united and split outside it; the 9" vas efferens
finally is connected with the kidney, but does not reach the testis.

So we have seen that the course of the efferent ducts in immature
frogs is as variable as in adult ones and that there is no symmetry
between left and right testis of the same animal.

SUMMARY.

I. According to Wrrscm the testis of a newly metamorphosed
Rana fusca is composed of a great number of short tubules, the
testis-ampullae, which end blindly, and are implanted around and
perpendicular to a longitudinal stem, the central strand. With this
central strand the mesonephros is connected by the sexual strands.
The ampullae, which possess a lumen, disappearing later on, form
no anastomoses and are not branched. Later on the rete testis
originates from the central strand, the vasa efferentia from the
sexual strands.

II. During the further development of the testis, the testis-ampullae
increase in length as well as in diameter and they simultaneously
divide towards the periphery into a great number of branches, which
nearly all grow out till they reach the periphery. Only a few short
tubules, not reaching the testis-surface, were noted.

Ill. The testis-tubules of an adult frog, are composed in the same
way: towards the periphery they split up more and more. All tubules
terminate in blind ends, and they never form anastomoses. The
tubules, which are straight near the periphery, are often somewhat
bent and twisted near to the rete.

IV. In two testes of immature frogs it was observed that a small
caudal part of the testis is not connected with the rete, but that
the tubules, composing it, opened directly into an efferent duct.

V. The courses of the vasa efferentia of six immature frogs in
the beginning of the second year show several peculiarities:

1. A real network, as in adult frogs, was not noted.

2. In the fat-body short tubules often occur, neither connected
with the testis nor with the kidney.

112

3. In .some cases the cranial part of the rete testis is connected
with the kidney by an efferent duct, which first passes through the
fatbody. In one case a short side-duct, coming from the fatbody,
opened into such a duct.

4. It was often observed that vasa efferentia, which run close
together, fuse. This fusion can take place near the testis as well as
near the kidney.

5. In a few cases an efferent duct was found, which, originating
from the mesonephros, did not reach the testis.

6. The vasa efferentia between rete testis and mesonephros number
from four to nine, this agreeing with the number, observed in adult
frogs. In the left and the right testis of the same animal the number
can vary.

Utrecht, April 1922. Zoological Laboratory, Veterinary College.

LITERATURE CITED.

Bremer, J. L. 1911. The morphology of the tubules of the human testis
and epididymis. Amer. Journ. of Anat., Vol. 11.

De Burtet, H. M. und De Ruiter, H. J. 1920. Zur Entwicklung und Morpho-
logie des Säugerhodens. I. Der Hoden von Mus musculus. Anat. Hefte, Bd. 59.

De Burrer, H. M. 1921. Zur Entwicklung und Morphologie des Säuger-
hodens. II. Marsupialier. Zeitschr. f. Anat. u. Entw., Bd. 61.

Curtis, G. M. 1913. Reconstruction of a seminiferous tubule of the albino
mouse. Proc. Amer. Ass. of Anat. Anatomical Record, Vol. 7.

—— 1918. The morphology of the mammalian seminiferous tubule. Am.
Journal. of Anat., Vol. 24.

_ Gaupp, E. 1904. Anatomie des Frosches. III Abt. Braunschweig.

Huser, G. C. and Curtis, G. M. 1913. The morphology of the seminiferous
tubules of Mammalia. Anat. Record, Vol. 7.

WitscuHi, E. 1914. Experimentelle Untersuchungen über die Entwicklungs-
geschichte der Keimdrüsen von Rana temporaria. Arch. f. Mikr. Anat., Bd. 85,
II. Abt.

—— 1921. Der Hermaphroditismus der Frösche und seine Bedeutung für
das Geschlechtsproblem und die Lehre von der inneren Sekretion der Keim-
driisen. Arch. f. Entw. Mech., Bd. 49.

ABBREVIATIONS.

= corpus adiposum, fat body.
. = central strand.
interstitium.
kidney.
peritoneum.
rete testis.
sexual strand.
testis.
testis-ampulla.
= tubuli seminiferi, testis tubules.
— vas efferens.

°°
u '
kn *
>}

S

>
a

UE Tet on

Shae
nw
|

Mathematics. — “A New Method for the Solution of the Problem
of the Characteristics in the Hnumerative Geometry.” By
G. SCHaAAKE. (Communicated by Prof. Henprik pr Vrins.)

(Communicated at the meeting of April 29, 1922).

§ 1. In this paper a general method will be set forth for the
determination of the expressions through which the problem of the
characteristics in the enumerative geometry is solved. These are the
expressions indicating how many individuals two algebraical systems
resp. of oo? en oo” figures, depending on ” parameters, have in
common.

The method in question will be best explained by application to
a special example. We shall therefore by the aid of it solve the
problem of the characteristics for the straight line in a space of an
arbitrary number of dimensions. ')

§ 2. We shall first confine ourselves to the straight lines of a
plane V. In V we assume a point C and a straight line c by the
aid of which we represent the plane homographically on itself.
With a view to this we associate to a point P of V the point 2”
of the straight line CP that together with C, the point of inter-
section C’ of CP and c, and P’ forms an anharmonic ratio that
is equal to a constant number À. Through this transformation a
straight line / of V is transformed into a straight line /’ cutting
lon c.

Especially we consider the transformation for which à==0. In
this case for an arbitrary point P the distance C’P’ =O, so that
the point P’ corresponding to a point P generally lies in the inter-
section of CP with c. If, however, P lies in C, together with the
straight line CP also the distance C’P’ becomes indefinite, so that
to the point C' all the points of V are associated.

For an arbitrary straight line / the corresponding line /’ coincides
with c. If, however, / passes through #, there are o' associated

) Cf. for other applications Cap. Vl of my academical dissertation which will

shortly appear, entitled: Afbeeldingen van figuren op de punten eener lineaire
ruimte, Groningen, P. NoorpHorr, 1922.

114

straight lines, which form a plane pencil that has the intersection
of / and ec for vertex.

If 2 changes continuously, out of a system S of op! straight lines
through the homographic representation described above, oo! new
systems are derived forming a coherent set, which contains S (for
A= 1) and of which we shall especially consider S’, the system
arising from S through the transformation belonging to A—0. The
number of straight lines which a system of this set has in common
with a system of oc! straight lines not belonging to the set, is apparently
independent of 2. In order therefore to know how many straight
lines SS has in common with another system ‚S* of o* straigh lines,
we may equally well investigate the same for S’.

Now any straight line of S is transformed into the line c, which
may always be chosen outside S*. If, however, S contains & straight
lines / passing through an arbitrary point, so that 4 is the class
of the curve enveloped by the lines /, the & straight lines of S
through C' are transformed into as many plane pencils of straight
lines /'. S* contains k' lines of each of these plane pencils, if the
straight lines of S? envelop a curve of the class 4. From this we
conclude that S' and S', hence also S and SS’, have £4' straight
lines in common.

§ 3. In order to apply the same method to the straight lines of
space, we assume a point C and a plane y, and we make use of
the homographic representation arising if to each point P we associate
the point P’ that forms with C, the point of intersection C’ of CP
with y, and P an anharmonic ratio == 4; in this representation there
corresponds to any straight line / another straight line / cutting /
on y. If again we take the case 2— 0, to any straight line / a
straight line /' of y is associated, the intersection of the plane (C;, /)
with y, unless 7 passes through C in which case there are ow’
associated lines /’, which form a sheaf of rays that has the point
of intersection of / and y for vertex.

In this way a ruled surface R is represented in a system &’ of
ow rays | of y. These envelop a curve of the class @, if @ is the
order of Fk. For through a point P of y there pass those straight
lines /' that are the images of the straight lines / of R cutting CP.
If now we consider a complex A of the order x, this has in y
opt rays enveloping a curve of the class x, so that A has x@ rays
in common with A.

A line complex of the order x has therefore x@ lines in common
with a ruled surface of the order o.

115

Through our transformation a congruence G passes into a system
G’ that consists first of all the rays of y, each counted #-fold, if
8 represents the class of G. For each line / of y is associated to
the 8 lines J of G lying in the plane Cl’. Further, if a is the order
of G, there are «a rays of G which pass through C and are trans-
formed into as many sheaves of rays of G’. Another congruence
with the order @ and the class § has aa’ + 38 rays in common
with G’. From this follows the well known theorem of HarPaur:

Two line congruences (a, 8) and (a',B') have aa + BB! lines in
common.

§ 4. Before we give the general solution of our problem in an
R,, we consider the special case that we have to do with the a‘
straight lines of an A. By the aid of a point C and a space T in
R,, we arrive at the o’ homographic representations that are each
characterised by a value of the anharmonic ratio 4—=(CC’ PP’) if
C’ is the point of intersection of CP en I Again we consider
especially the representation belonging to 4= 0.

If we take a system S, of oo! rays, this is transformed by the
latter representation into a ruled surface S,’ of the order @ lying
in I, if @ represents the numbe# of straight lines of S, cutting a
plane. If we consider further a system S, of o® straight lines
of which an arbitrary plane pencil contains x, the rays that S, has
in common with I form a complex of the order x, so that S, con-
tains ox rays of 5S,’.

A system S, of the order 9 has ex rays in common with a system
S, of the order x.

A system S, of oo’ rays is represented on S,’, a congruence
(a, B) of I’, if « is the number of rays of S, cutting an arbitrary
straight line (through C), and p the number of straight lines of
S, lying in an arbitrary space (through C). A system S, has a
congruence (~,w) in common with I, if p and wp represent the
numbers of straight lines of S, resp. belonging to a (three-dimen-
sional) sheaf of rays or lying in a plane. S, has «ap + Bw rays in
common with S,’.

A system S, (a,8) has ap + Bw rays in common with a system
S, (2, |). f

A system S, is transformed through our representation into a
system JS,’ consisting first of a complex of the order v lying in TI,
if v is the number of rays of S, lying in a (three-dimensional) special
linear complex. Further, if S, contains u rays through a given point,
to each of the p straight lines / through C there are associated the

8

Proceedings Royal Acad. Amsterdam. Vol. XXV.

116

oo® rays / passing through the point of intersection of 7 and TI, so
that 5S,’ contains also u four-dimensional sheaves of rays. If besides
S,, we have another system S,' with the characteristic numbers
u, and »,, this has in J’ a ruled surface of the order v, and it
contains mw, straight lines of each of the four-dimensional sheaves in
S,’. iS,’ and $,’ have accordingly wu, + »v, rays in common.

Two systems S, (u,v) and S,* (u,,%,) have uu, + vr, rays in
common.

§ 5. Bij means of complete induction the following results may
be easily proved, through which the problem of the characteristics
is solved for the straight line in: /,.

The characteristic numbers of a system S, of oo rays in R,,
indicate how many straight lines of Sp there are in an Bet lying
in R‚ which eut an A,4,-,-2 in the aforesaid A#,—,+41 for all values

&

of u satisfying the inequalities: u > 0, n+ u—p—2<cn—u+1
3
or jd and n 4u pl or u pri.
From this follows that the p-fold number of characteristics for
ae or = A,

according to whether p is odd or even, and for p2n equal to

2(n—1)—p-+1 "a 2(n—1)—p
2 2

or even. The p-fold number of characteristics is, therefore, equal to

the 2(2—1)—p-fold number.

The expression indicating how many lines an S, and an aen
have in common, is a polynome of which all the terms are found
by multiplying each time those characteristic numbers of S, and
Oi that belong to conditions which together define a straight
line in A.

the straight line in &,, if p<{n, is equal to

+1 according to whether p is odd

$ 6. It is clear that the indicated method may also be applied to
the case when we have to do with figures composed of a definite
number of points, straight lines, planes etc. If the parts of these
figures are independent of each other, it will often be desirable
to transform them by different homographie representations.

The system e.g. of the oo” groups of n points (P, P,,..., Pn) of
a straight line / may in the following way be represented homo-

graphically on itself. We assume on / 2n arbitrary points (\,..., Ch,
F.E and associate to a point P; of a group of n points

(n-group) the point P'; defined by: (CT; P;P')= A.

117

If we take all 2;—=0, there belongs to an arbitrary n-group the
n-group (/,,...,/); if, however, a point P; coincides with C;,
the associated point P’;, becomes indefinite, so that to an ”-group of
which the % points ia Ee Te Bir coincide resp. with Cis De arr Ci,

there are associated ook groups that have the 7— points li in U

in common.
el n
Let us now consider a system Sp of ook n-groups with the i

characteristic numbers «a; indicating how many groups of
: ty y 8

ty eee ij»
the system there are for which the points Pi Pig sah, Pi, are de-
fined. Through our representation Sp is transformed into a system S'z

f : . f

consisting of @ separate systems of ook groups. Such a system is
k

formed e.g. by the n-groups that have their points Pury nae Ae ack

resp. in Tyger Ui, and of which the remaining points P are

indefinite. Each group of this system is associated to the Oi igs ++ iy

groups of Sj that have their points vars! Arte Pi, in Ci, Len: Ci, and

is therefore an aj, -ifold group of S', If we take another

t . .
2
system Sp of o”—* groups, with the characteristic numbers
Pi, ip- +i, y» We find from the number of common groups of
S'. and Sys:

A system Spr (ei, ij) of ook n-groups of points has with a system

nk (Bi, + i

common.
Finally we remark that the expounded method may also be

applied to curves, surfaces etc,

Bias) of wk n-groups Zei, vi Bia ……i, groups wn

?

8*

Physics. — “On the diffraction of Röntgen-rays in liquids.” By
Prof. W. H. Keresom and Prof. J. De Smepvr. (Communication
N°. 10 from the Laboratory of Physics and Physical Chemistry
of the Veterinary College). (Communicated by Prof. H.
KAMERLINGH ONNks.)

(Communicated at the meeting of March 25, 1922).

§ 1. Zntroduction. The investigation by means of Röntgen-rays
of the structure of substances that are in liquid or solid state at
temperatures lower than the ordinary one, seems us to be of extra-
ordinary importance. These substances namely belong to those that
possess the most simple chemical structure (in the gaseous state
several of them are mon- or diatomic). In most cases their molecules
consist of light atoms small number of electrons). Therefore the ex-
perimental results obtained with these substances will lead more easily
than other ones to conclusions* of importance for the structure not
only of the crystalline state but also of the molecule and the atom.

We thus gladly followed the invitation of Prof. KAMERLINGH ONNES to
make such an investigation on the diatomic elements oxygen, nitrogen,
if possible on hydrogen ete. and the monatomic elements as f.i. argon.
In the discussion of the scheme for this investigation, for which we
made at Leiden some preparatory experiments, the first question
was the following: Will liquefied gases also give a diffraction figure
when they are crossed by a beam of Röntgen rays as it was the case
with the liquids that were investigated by DrBije and SCHERRER ') ?
As some Röntgen-technical difficulties had to be overcome we
agreed to continue the preparatory experiments at Utrecht, as far as
we should be able to obtain there the liquid gases and work there
with them. Some of the results of these experiments will be given
in this paper. In these investigations we did not only use liquid
oxygen and argon’) but also some substances that are liquid at
ordinary temperatures.

§ 2. The apparatus. Fig. 1 shows the vacuum glass g and fixed

1) P. DeBije and P. Scuerrer, Nachrichten Göttingen 1916.
*) The argon was put at our disposal by N.V. Philips’ Gloeilampenfabrieken,
for which we wish to express here our thanks.

119

to it the camera c, into which the liquid gas is poured and in which
it will be radiated by the Röntgen beam which is bounded by the
diaphragm d of tin (length 34 mm., diameter of the opening 2 mm.)
shut by a leaf of aluminium. The lower
part of the inner tube is narrow. First
it consisted of a small tube of aluminium
thick 0,015 mm. and with a diameter of
3 mm. which was soldered to a copper
tube by means of wolframine. Later on this
aluminium tube was replaced by a glass
tube thick 0,002° to 0,01 mm.!) and
with diameter 2 mm., blown to a wider
glass tube. Except between 6, and 6, the
glass was silvered.

The camera (radius 27,5 mm.) is fixed
to the outer glass by means of a ground
plug. In the camera along the cylinder
wall the film f is stretched (Eastman
duplitized X-ray film) in the same way
as was done by DpBijr and Scurerrer. For
taking in and out the film, which was
wrapped up in black paper, the camera

Fig. 1. was detached from the plate p to which
its ground border had been cemented. The vacuum was obtained with
a LANGMUIR condensation pump with the rotating mereury pump of
Garpr as a forepump. This vacuum sufficed to expose with one single
filling of 200 cM? of the liquefied gas during more than 5 hours.

The Röntgen-rays were excited by a metal SrrGBanN tube with
Cu-anticathode. The Ks; rays were filtered away by a Ni-plate of
0,01 mm. The current given by an inductorium with gas interruptor
was + 10 mA. tension + 25 KV., time of exposition as a rule
5 hours.

For a photograph of the Röntgen interference figure of ice (see
§ 3) we used a glass tube partly filled with water. The lower part
of this tube consisted again of a thin glass tube as described above.
The tube with water was let down into a vacuum vessel with a
lower part of thin-walled glass filled with liquid air. During the
exposition the tube was rotated from time to time.

') These thin tubes of aluminium and glass are proofs of the ability of the
amanuenses Ist class J. J. VAN DER SLUIS and A. R. B. Gerritse, the last of
whom has also made several of the here mentioned photographs.

120

The substances that are liquid at ordinary temperatures were
exposed in a more simple glass apparatus with a thin walled lower
part, which fitted on the same camera, while again the camera
was evacuated.

§ 3. Results. We have exposed liquid oxygen, liquid argon, benzene,
water, aethylalcohol, aethylaether, formic acid, carbonic disulphide,
bromium.

Of these carbonic disulphide and bromium (in glass tube) gave
no distinet diffraction figure *).

The other liquids gave first an intense almost circular diffraction
ring. Fig. 2 shows the diffraction ring of oxygen.

Argon was exposed twice, once in an aluminium tube and once
in a glass tube. Of these only *) the first one gave a distinct diffrac-
tion figure.

In table I p represents the half top-angle of the cone formed by
the diffracted Röntgen rays.

TABLE I.
3 Su
Substance p a 1.33 ig
oxygen 27° 4.0 A 4.0 A
argon 27 4.0 4.1
benzene 18 6.0° 5.9
water 29 Pb 3.6
aethylalcohol 22 4.9 52
aethylaether 19 5.7 6.2
formic acid 24 4.5 4.5

By the agreement between the diffraction rings of oxygen and
argon we might come to the hypothesis that these rings are due
to the same impurity fi. to small ice crystals. This was however
proved to be not the case. Therefore oxygen namely was first dried
by KOH and P,O,, then liquefied and destilled in apparatus dried
beforehand and finally poured through a filter of cotton wool into

') The probable reason for this is, that the Röntgen rays are absorbed to such
a high degree by these substances, that the Röntgen-light diffracted by the liquid
on account of its small intensity cannot be distinguished from that diffracted by
the glass.

2) Probably by the reason mentioned in note 1.

121

the vacuum glass that was filled with dry air *) and in whieh such
a filter was placed again at the entrance of the narrow part. This
oxygen now gave the same ring. On the other hand a photograph
of ice (see § 2) surrounded by liquid air taught us that none of the
interference lines of ice coincide with the ring of oxygen.

The diffraction image of water shows still an interesting detail
(see fig. 3 of the plate). Immediately following on the intense diffrac-
tion ring the film shows a very considerable almost uniform blackening
with a rather sharp outline at p == 46°.

For some other liquids too we found weak indications of a similar
blackening.

For oxygen and argon the best films show beside the ring given
in table I still a weak second ring, for oxygen at v= 46°, for
argon at p= 49°.

§ 4. The intense diffraction ring ts due to the cooperation of
neighbouring molecules. As was shown by Enreneust*) and at the
same time by DrBijn and SCHERRER (Le) a diffraction ring like that
of §3 may be due to the interference of Röntgen-rays diffracted by
arbitrarily orientated systems each of two (or more) particles,
which have a definite mutual distance (fi. the two atoms in a
diatomic molecule, where each of the atoms is regarded as one
single diffracting centre.) Between the angle p and the distance a
of the two diffracting particles we have then (see Enrenrest Lc.)
the following relation

dg tara
ee ee SY et Is ee
sem
4” sin —
2

where 4 is the wavelength of the Röntgenrays.

The values of a caleulated in this way (with 4 = 1,54 A) are
given in table I.

In the first place the fact, that also argon has a similar diffrac-
tion ring, involves that, at least for argon, this diffraction ring is
not due to the cooperation of atoms in the molecule. *)

That this is neither the case for oxygen is to be expected by the

1) By a small window v in the vacuumglass we could state that the liquid was
perfectly clear.

3) P, EHRENFEST. These proceedings Vol. XVII, p. 1184. See also P. Desir
Ann. d. Phys. (4) 46, p. 809, 1915

3) Unless argon should be more-atomic in the liquid state, which is not made
probable by the following.

122

improbable if not impossible great distance, which the centres of the
atoms should have then (see table 1).

The distance of the interfering particles calculated with (1) however
agrees with the distance of the centres of neighbouring molecules,
when we think us these arranged as the centres of spheres packed
possibly close together. This distance is found in the last column
of tabel | (M = molecular weight, d == density). Small deviations,
as far as they do not fall within the limits of experimental accuracy,
might be ascribed to deviations from the spherical form or to the
circumstance that will be discussed in $ 6.

From this we think it justified to draw the conclusion, that the
intense diffraction ring found above is caused by the interference of
Röntgen light diffracted by neigbouring molecules *) *).

For benzene too the above mentioned agreement between a and
the distance of neighbouring molecules arranged in closest packing
has been stated. From this we think it evident that the above con-
siderations also hold for this substance in contradiction with the
opinion of Design and Scuerrer (Le) that this diffraction ring should
be due to the atoms in the molecule.

§ 5. When our view that the observed diffraction ring is due to the
interference of Röntgen light diffracted by neighbouring molecules
is right, the dimensions of these diffracting particles may no longer
be neglected compared with their mutual distance and we may ask :

1) This does not involve that we have to do with the cooperation of only two
molecules at a time. On the contrary, as far as it is not due to the particular
form of the relation between the quantity of Röntgen light and the blackening of
the film caused by it, the relative sharpness of the diffraction ring might point
at a cooperation of more molecules at a time.

These molecules might then be arranged in the liquid in groups more or less
regularly under the influence of the forces which below the melting point condition
the regular structure in the crystalline state.

In this way fi. both rings of argon might be explained by assuming that in
the liquid a great number of groups is present in which the atoms are arranged
in a centered cubical lattice. The mentioned rings correspond then to the planes

(110) and (211), the edge of the lattice would be 4,65 A. For the distance of.

two neighbouring atom centres follows then again 4,0 A as in table I.

Because of the perfect analogy in the behaviour of oxygen and argon we should
have to replace for oxygen these atom centres by molecule centres. [Later experi-
ments have shown that the ratio of the values of sin4/,9 for the two rings does
not quite agree with the ratio 1:3, as should be the case if the supposition
made above were valid. Added in the translation].

2) The possibility of this has already been acknowledged by DeBiE and
SCHERRER (l.c.).

123

in how far may we regard the distance calculated with (1) as the
distance of the centres of the molecules?

As in reality the electrons are the diffracting particles, this question
may only be answered when the true position of the eleetrons in
the molecule is known for every instant.

In order however to form us still an opinion in this problem we
shall consider the case of molecules each consisting of a nucleus
(which is supposed not to contribute to the diffraction) and one
electron that is freely moving in a sphere with radius r (so that
it passes in all volume elements equally long times). A system of
arbitrarily orientated pairs of such molecules all with the same
distance a between the molecule centres gives then in a direction
which makes an angle p with the direction of the incident light
an intensity proportional with

{sinar—arcosar}* sinaa
bite? ar "aa i)
when
4 7
a= ting wih el be ob onda AS)

This expression may be easily deduced by an extension of the
calculation given by Enrenrest for the case of two simple diffraction
centres.

When r is not small compared with a, the first maximum does
no longer correspond with the relation (1). In this case an other
factor must be substituted for 7,72 in this formula. When f.i. we

take mo dik f= 1,25 A, this factor is 7,42.

Evidently the influence of the dimensions of the molecule is small.
The more will this be the case as the (mean) density of the electrons
in the molecule is greater in the central parts than near the periphery,

When the molecules come so near to each other, that they are
in conctact the influence is greater. For the simple molecule models,
described above, the factor in (1) would then become 10 °/, smaller.

§ 6. Water. The blackening which is found in the diffraction
image for water round the above mentioned diffraction ring seems
to point at a rather great number of pairs of molecules with a
mutual distance smaller than that wich we shall call here the
normal one‘). On this supposition the limit of this blackening

1) With the above is in good agreement, that in table I the mean distance

(3,6 A) for water is smaller than the normal one (3,75 A).

124

(p= 46°) corresponds to the smallest distance between the centres

of two neighbouring molecules. Formula (1) gives for this 2,4 A.

The further examination of the blackening in the diffraction image
of the liquids thus gives a direct method of research for the way
in which the molecules are distributed in the liquid as to their
mutual distances. Some conclusions may be drawn then also on the
field of force of the molecules.

The fact, that in water a relatively great number of pairs of
molecules occurs with a distance smaller than the normal one will
be related with the peculiarities in the thermodynamic properties
by which water is regarded as an associating substance. However,
we do not find an extraordinarily great number of double or multiple
molecules which should have been formed by juxtaposition of simple
molecules so as to ly as close as possible to each other.

§ 7. Oxygen and argon. By analogous considerations as in $ 6
we probably must ascribe the second weak ring for oxygen and
argon to pairs of molecules which touch each other *).

According to (1) this would give for the distance of the centres
for oxygen 2.4 A, for argon DS

Because of the last remark of $ 5 these values might however
still undergo a small variation.

Comparing these results with those obtained for water we find:
firstly, that in oxygen and argon there is a considerably smaller
number of pairs of molecules with a distance below the normal one,
secondly that for oxygen and argon in the greater part of these
molecule-pairs the molecules are lying together as close as possible.

We might ascribe this different behaviour to a difference in the
fields of force: the water should have then a more intense field,
which extends over a greater distance, while oxygen and argon
should have a field of force which makes itself more felt in the
immediate neighbourhood of the molecule. In this way the dipolar
character of the water molecule becomes manifest on one hand, the
quadrupolar (resp. perhaps octopolar) character of the oxygen and
the argon molecule (atom) on the other hand.

1) See also p. 122 note 1.

W. H. KEESOM and J. DE SMEDT: ,,On the diffraction of Réntgen-

rays in liquids.”’

Eiam2:
Oxygen, with Kz-rays of copper.

Bis;:3:
Water, with Kzx-rays of copper.

Proceedings Royal Acad. Amsterdam. Vol. XXV, 1922.

Physics. — “The crystal structure of germanium”. By Dr. N. H.
KorKMEIJER. (Communication N°. 11 from the Laboratory of
Physics and Physical Chemistry of the Veterinary College at
Utrecht). (Communicated by Prof. H. KAMERLINGH Onnes).

(Communicated at the meeting of April 29, 1922).

§ 1. lntroduction. From a medical-biologieal point of view too,
a possibly complete knowledge of the quadruvalent elements as f.i.
C and Si will be of great importance. The only one among the
elements of the fourth group of the periodic system the crystal
structure of which has not yet been investigated is germanium *).

For this reason the author undertook the investigation of this
structure with the same apparatus that lad already been used in
the investigation of tin?) and in that of NaClO, and NaBrO,’), that
has been described in preceding papers. Only the diaphragm of lead
in the camera was replaced by one of tin*) while before it a Ni-
filter of 0,01 mm. thickness was placed in order to weaken the
8 radiation from the Cu-anticathode. The germanium (from Dr. TH.
SCRÜCHARDT, Görlitz), in the form of a fine powder, was cemented
to a thin glass rod, with Canada-balsam. | |

$ 2. The crystal structure. The observations were in good agreement
with a structure like that of diamond. In the table this is evident
from the satisfactory agreement between the values of sin? 46°)
derived from the observations with the calculated ones. For tbe

latter we chose as value of the lattice parameter a = 5,61 A. From
the density at 20°,4 viz. 5,459°), the atomic weight 72,4187) and

the number of Avocapro 6,062 .107* we deduce a = 5,594 A.

1) As has been remarked by D. Coster (These Proceedings 21, 1294, 1919)
the knowledge of this structure might also be of importance for the question of
the eventual existence of binding rings of circulating electrons.

2) A. J. Buu and N. H. KorkmeirRr. These Comm. Nos. 1 and 2. These Pro-
ceedings 21, 405, 494, 1918.

8) N. H. Koixmewer, J. M. Buyvorr and A. KARSSEN. These Comm. N°. 5,
These Proceedings 23, 644, 1920.

4) W. H. Kersom and J. De Smept. These Comm. Nr. 10. These Proceedings
25, 118, 1922. By a sufficiently high tension the L-radiation of the Pb might
namely be excited by the heterogeneous radiation of the Cu, which would cause
a blackening ‘of the film. For tin this is much less probable.

5) 9 is the angle between the rays incident on the substance and those diffracted
by it.

6) CL. WINKLER, Journ. f. prakt. Chem. 34, 177, 1887.
7) J. H Mürrer, Journ. Am. Chem. Soc. 43, 1085, 1921.

126

| | Calculated ').
Observed. |
z-lines. 2-lines.
Intensity|sin? !/,6.103 hy hg hg |sin?!/,6.103| Intensity || h‚ hy hg |sin? '/,4.10% Intensity
vs 59 Ll thal ankee 1.3
vf 124 220| 122 1.5
s—vs| 153 ||220] 151 1.5
fff 168 | ota 167 1.1
S—vs Miervdvaitalth sy id
f 2495 400| 243 0.4
f 296 Â-001 St 04 “3 3'1 |’ “280 0.6
m--s | 363 3 3 1| 358 0.6 | 42 2| 363 1.0
s—vs | 454 422| 452 1.0
f (double) 511 drin sos 0.6 4 2 halt in Aa
f 5995 | 440) 603 0.4 | 6201 609 0.6
Sih 652. sail. 059 “0.1 || 52331... 654 0.3
m 745 6 2 0| 753 ale. apie? 1 716 0.5
f 801 5 33 | 810 0.3
ff 848 Ba pol 052 0.9
f 892 444| 904 0.2 SZ 898 0.6
s-m | 948 Ba of 960 0.5
f 966 8 0 0| 974 0.1
m 904 ' 73.3 |... 1019 0.2

From the fact that of C, Si, Ge and Sn we know modifications
with the same structure as diamond, while this is not the case for
Ti, Zr and Th, we might conelude that C and Si are somewhat
more intimately connected with the elements of group [V6 than
with (bose of group [Va.

To Prof. Dr. W. H. Kersom I am much indebted for his interest
and his kind help in this investigation.

1) In the calculation of the intensities, only the structure factor, the LoRENTz-
factor and the number of planes factor have been used, not the polarisation factor
and the temperature factor.

Physiology. — “An Objective Method for determining the Co-
agulation-time of Blood.” By R. J. Wonvius. (Communicated
by Prof. A. A. HiJMANS VAN DEN BERGH.)

(Communicated at the meeting of December 23, 1921).

The usual methods for determining the coagulation-time of blood
aim at detecting the right moment at which the phase of complete
solidification of the blood has just set in.

At first I myself adopted the method suggested by Fonio and
FRANK, viz. by observing, with strict precaution, the coagulation of
the blood on a watchglass and by noting down the moment at
which the phase of complete solidification had apparently been
reached. However I was always in doubt whether complete solidifi-
cation had been accomplished at a certain moment, or whether it
had not, so that I always hesitated in fixing the right moment.

In this connection Hayrm’) says: “On sait, en effet, que la solidi-
fication du sang ne se fait pas brusquement, c'est a dire d'un seul
coup, à un moment précis. Le phenomène, évolue d'une manière
progressive, a tel point, que pendant une periode relativement assez
longue, on reste dans lhésitation, en se demandant si la prise en gelée
est effectuée ou n’est encore qu’imminente.”’

What tells most against these methods, is that the degree of
solidification has to be determined by subjective observation. I, there-
fore, looked for some phenomenon that goes on pari passu with
the solidification and admits directly of measurement. I found that
phenomenon in the turbidity which attends the salting out of fibrin
and consequently decided to measure it. Preliminary experiments
had shown that at the very outset of thickening of the blood a
clouding commences that increases with the further progress of the
thickening and ultimately remains stable as soon as coagulation
has reached its completion. Now, it being my purpose to observe
the time in relation to solidification, I might as well ascertain the
time taken up by the clouding process. In order to measure this
growing turbidity I made use of a new apparatus, the extinction

) Hayem, Du Sang, quoted from Marcen Biocu, La coagulabilité sanguine
pag. 22. These, Paris 1914.

128

meter’) of Dr. W. J. H. Morr, which enables us to measure the
turbidity from moment to moment.

The principle of this apparatus may be discussed in a few words:

A powerful light-source is firmly set up between two surface
thermobatteries I and IJ, after Morr. They are both connected to
a mirror-galvanometer, thus counteracting each other. Between the
lamp and the thermobattery I is placed a cuvette filled with water;
between the lamp and the thermo-battery II a cuvette filled with
the blood-plasm.

Consequently the light that is directed on to the thermo-batteries
is weakened on the one side by water, and on the other by blood-
plasm. Through displacement of one of the thermo-batteries or through
changing the position of the lamp the unevenly weakened light may
be made to fall upon the thermo-batteries with equal force. The
two thermo-electric currents thus elicited, will then be equal, the
galvanometer will receive a current O, the image reflected by the
mirror will occupy the O-position. The apparatus has then been
“adjusted”. The slightest change in the turbidity of the plasm
disturbs the equilibrium and yields a deflection of the galvanometer ;
the apparatus acts so quickly that after a contingent sudden change
in the turbidity the reflected image will come to rest again within
a few seconds. Moreover a procentic measurement may be taken
of the changed turbidity with the aid of a so-called compensation-
switch.

Now our procedure is as follows: Into a sterile, dry Record-
syringe of 10 ¢.c. with a sharp, dry needle, 1 c.c. of a clear sterile
solution of 1°/, potassium oxalate in 0.85 °/, common salt is sucked
up; the needle is inserted into a cubital vein and the blood is
aspirated to 10 ec.c. Due regard should be given to an easy flow
of the blood into the syringe, so that no air is drawn in along
with it. The mixture thus obtained, is centrifugalized during 20
minutes in sterile centrifugation-tubes, which causes the blood-
corpuscles and the blood-platelets to precipitate and the supernatant,
more or less turbid plasm can be pipetted off and transmitted to
sterile tubes. Three c.c. of this oxalate-plasm (measured very care-
fully with sterile pipettes) are put into pure, and dry cuvettes. The
cuvettes used by me are made of the same glass and have precisely
the same dimensions, so that not only the thickness of the fluid-
layer, but also the level to which the cuvette is filled, is always
the same in every one of them; in other words the contact-plane

Hitte W.J. H. Morr, Een extinctiemeter. Verslag Koninklijke Akademie van
Wetenschappen, Wis- en Natuurkundige Afdeeling, 27 Maart 1920. Deel XXVIII.

129

between plasma and glass is the same. This cuvette is placed in
another one of special construction, which acts as a thermostat, is
filled with water and is heated electrically.

The measurement proceeds as follows:

The cuvette is placed in the thermostat so as to make the light
of the lamp reach the thermo-battery II and pass through the plasm.
By its side, in the same thermostat, stands a test-tube containing

bee. 1/,°/, CaCl, The extinctionmeter is “adjusted”. Then follows
a 20 minutes’ wait, after which the plasm and the CaCl, will be
of the temperature of the thermostat and the galvanometer will be
completely quiescent and in the zero-position. The work-room is
made semi-dark and from this moment photographical readings are
taken from the galvanometer. A registering instrument is used that
is moved by a perfectly reliable clockwork.

After some moments the 14 ce. '/,°/, CaCl, are added to the
plasm, the whole mixture is rapidly stirred for half a minute with
a sterile glass rod and is then left to itself. The galvanometer then
traces on the sensitive paper of the registering instrument the
“turbidity-curve”’.

Fig. 1 is a faithful reproduction (natural size) of such a curve, in

C

Biga,

130

which three horizontal portions A, B, and Care to be distinguished.

A indicates the motionless phase of the galvanometer during the
time when there is only the oxalate-plasm between light-source and
thermo-battery ; a. indicates the moment when CaCl, is added; the
first moment the plasm becomes clearer, see b., which is owing to
the dilution of the plasm. But directly after this the liquid becomes
very turbid which is due to the forming calciumoxalate; the curve
ascends almost vertically, see c., and would gradually have reached
the A-level, if not an irregular weakening of the light had been
brought about by the stirring rod; the jerks in the curve at d.
illustrate this irregularity, so that they have nothing to do with the
process of turbidity. The calcium oxalate is not precipitated but
remains in suspension; for a few minutes the galvanometer remains
constant, as shown in the ZB-portion.

Up to this moment coagulation is out of the question. Soli-
dification commences at e. at a certain moment, apparently quite
independently from the inital turbidity (formation of caleium-oxalate),
and simultaneously the second phase of turbidity begins. It is this
portion of the curve that interests us most. Its shape is an objective
illustration of the coagulation process.

It appears that this coagulation starts very slowly, then proceeds
more quickly until a maximum rate is attained, after which a
retardation sets in again until the terminal value is ultimately
reached.

I will not discuss here the nature of this curve, but only point
to the method, which enabled me to typify any given portion of
the curve by a tigure. I note the exact time at which certain levels,
e.g. '/, and */, of the difference of the B-, and C-level are reached ;
the time-difference is my control-number.

My researches were performed in the Physical Laboratory of the
Utrecht State-University, where I had the freedom of the instruments.

Utrecht, December 1921.

Physiology. — “A contribution to the physiology of the electrical
organ of Torpedo” By Prof. F. J. J. BurreNpijk. (Communi-
cated by Prof. G. van RIJNBERK).

(Communicated at the meeting of April 29, 1922).

In the winter of 1911 I had the opportunity to investigate the
function of the electrical organ of Torpedo in the Zoological Station
of Naples. The aim of part of this research was to study the
magnitude and character of its diseharges under different cireum-
stances. For this purpose a string-galvanometer (large type of Eprr-
MANN) was available at Naples and with this apparatus I made many
records. From these records and from test-records of the apparatus
it appeared, that the string-galvanometer is not the most suitable
instrument for the registration of the discharges of the organ of
Torpedo which reach their maximum within 0,002—0,008 sec. This
does not astonish us in connection with the investigations of GARTEN ’).
For this reason I intended to continue this research with an appa-
ratus more suitable for this purpose foscillograpbion, Fty1’), string-
electrometer, Cremrer*). However, as circumstances prevented me
from carrying out this plan, I now communicate the results of my
research.

Marry, SCHöNLeIN and Gorcu *) have already observed that the reflex-
discharge of the electric ray has a rhythmical character. In many
records 1 found that as a rule many discharges succeed each other,

Fig. 1. Reflex-discharge in Torpedo after mechanical stimulation.
Test-record 4 volt. Time 1/5) sec.

1) GARTEN. Abh. d. Kgl. Sachs. Ges. d. Wiss. 1899.
2) Fuur. Journ. of the College of Science Univers. Tokio 1914, Vol. 37.
3) CREMER. Sitz. Ber. Physiol. Geselsch. Berlin 1912. Mediz. Klinik 1912, N°. 42.
4) S. Garren. Handb. d. Vergl. Physiol. 3e Bd. 2e H., p. 177.

9
Proceedings Royal Acad. Amsterdam. Vol. XXV.

132

mostly 5—8 in number with an interval of 50. Fig. 1 represents
one such discharge, where the shocks came with an interval of
5,66. Cremer found an average of 5,66 in reflex-discharge. Most
striking in these rhythmical discharges is the regularity and the
equal amplitude of the single shocks, as appears clearly from my
figure. In the periodical discharges after stimulation of the nerve
of the excised organ, I never obtained such regularity and asa rule
inequal amplitude. Usually the shoeks diminish gradually, sometimes
they first increase, then decrease. Fig. 5a and 56 illustrate this more
clearly. The periodical discharges in reflex-action therefore give the
impression of being caused by a series of central impulses from my
nervous system, whereas the periodical discharges after stimulation
of the organ or the nerve seem to be due to secondary self-stimu-
lation. This is especially and to a greater extent true in the case
of the stimulation of the nerve. After direct stimulation of the organ
usually only two small, secondary discharges occur, provided that
the nerve has been eut at the very spot of its entrance into the
organ. Fosr however has registered reflex-discharges (in Astrape
japonica) in which only two shocks occurred in every group
followed by a small one. The same result was also obtained after
stimulation of the nerve stem. For this reason Fuj believes that
the successive discharges occur by self-stimulation. The solution of
this question has importance for the question which has been solved
by Garten’) in Malapterurus, i.e. in how far the discharges of
both organs occur simultaneously.

In a detailed research Bernstein and TscHermak ’) have tried to
find out whether the current which the electrical organ produces
during activity is caused by a concentration-chain or whether a so-
called chemical chain here causes the difference in potential. To
solve this question the .temperature-coefficient of the force of the
current in the organ was investigated within certain limits of tem-
perature.

From theoretical considerations it is known, that in a concen-
tration-chain the E. M. F. is nearly proportional to the absolute
temperature. Brrnstein already had found a positive temperature-
coefficient for the current in muscles and nerves and within normal
limits of temperature the E. M. F. proved to be nearly proportional
to the absolute temperature.

In their study on the electrical organ the authors mentioned above

lj GARTEN. Zeitschr. f. Biol. 1910. Bd. 54. S. 399—480.
2) BERNSTEIN und TscHERMAK. Pflügers Archiv. 1906, p. 112.

133

always stimulated the nerves of. the organ by means of a single
induction-shock (make-induction) and read the deviation of a galvano-
meter with not too great inertia on a scale. The deviations of such
galvanometers are nearly proportional to the average EK. M. F. of
short currents, if the external resistance and the path of the current
remain constant. The latter condition, however, was surely not
complied with at different temperatures.

From the investigations of Gorcu on the capillary electrometer
it had already become known that the velocity of the movement
at low temperature (38° C.) is retarded and differs rather strongly
from that at moderate temperature (15—20° C.). Such change in
the record of the current must magnify the movements at low tem-
perature. In that way the difference with those found at higher
temperature is bound to become smaller than corresponds to reality
and the observed temperature-coefficients must be too small as
GARTEN has already observed. Moreover, it has become evident from the
experiments of ScHONBEIN and GARTEN, that after indirect stimulation
of the electrical organ by induction-shocks a repeated discharge
frequently occurs, which of course does not show up with the slow
galvanometer.

My own experience has shown that especially in the cooled organ
this repeated discharge occurs very frequently. In this way the very
low temperature-coefficients, found by BeRENSTEIN and TscHERMAK may
partly be explained.

At any rate, it seemed advisable to try to secure more data on
the process and the E.M.¥. of the shock. Of freshly caught specimens
of Torpedo marmorata and T. occalata the electrical organ was
prepared free with its nerves after removal of the skin. The organ
was now enclosed between two zine electrodes by means of two
rubber rings. Two bars for the conduction of the electrical shock
were attached to the zine electrodes.

The conductors were passed through a rubber stopper which also
held the platinum electrodes used for the stimulation. This rubber
stopper served to close a glass-vessel, in which the organ could be
enclosed and through which a stream of liquid could be passed.
The strength of the electrical discharge could thus be studied under
different circumstances.

Moreover, a thermometer was inserted into the stopper. If one
allows the liquid to flow into the vessel through the lower tube
(Fig. 2) and to leave the apparatus by the upper one, it is possible
to regulate conditions so as to keep the organ in the fluid and to
keep the nerves in the air.

Ox

134

This arrangement had the advantage that it enabled me to repeat
the indirect stimulation under very constant conditions. In this way
one succeeds in keeping the organ in good condition for 2—3 hours,

Fig. 2. Apparatus for study of electrical Fig. 3.

discharge in different fluids, gases lo = electr. organ s = string-galv.m.
and temperature. /=slate-resistance 7= induction-app.
v = Volt-meter pho = apparatus for

w = resistance-box photogr. registrat.

so that if one stimulates once every 15 minutes the deviations of
the galvanometer remain constant.

The discharge was led to an ordinary resistance-box and a slate-
resistance (of 800,000 £2). From the resistance-box a circuit could
be branched off to the string-galvanometer. By means of a key,
connected with the recording apparatus, a definite potential difference
could be thrown into the chief circuit for the purpose of testing the
movements of the string (Fig. 3).

A tuning fork of 50 vibrations per second marked the time on
the photographical plate, while a very sensitive signal of Dupriz
indicated the moment of stimulation. The nerves were stimulated
by means of induction-shocks. Sometimes part of it was thrown into
the string-circuit so as to have the string itself mark the moment
of stimulation.

It is clear that this method does not enable one to study the
question of the relation of a stimulus to its effect.

This question has been thoroughly investigated by Fun with the
oscillographion.

In my experiments I could not state anything but the fact thata
weaker stimulus gave a less noticeable effect than a strong one and

135

that make induction-shocks are more effective than break-shocks (Fig. 4).

ese ee To get an impression of the
[nace Ww conditions on which the magni-

. tude of the discharge depends,
| |
>

I first investigated the question

| OE in whether organs which had been
OPO ONO kept in different liquids for
| : some hours, as a result showed
ae “a change of the discharge-shock.
Fig. 4. Example of discharge after Qf course, the nerves were
indirect nerve stimulation with make

and break induction shock.

always stimulated with maximal
stimuli.
In this way it appeared that an organ (without skin) kept in:

Experiment 1.

2,50/, NaCl-solution lost its irritability after three hours. The same thing was
true for sea water. In Fiihner’s solution + urea’) the irritability strongly diminished
after three hours.

Experiment 2.

Organ 1: in (NaCl 2,5 °/, + KCl 0,1 °/,) no shock could be obtained after 40 min.

Organ 2: in (NaCl 2,5 °/, + CaCl, 0,2°/,). After 40 min. the shock had diminished
slightly.

Organ 3: in F. sol. after 40 min. shock not changed.

Experiment 3 (see fig. 5).

a NaCl ax Fahnersche oplossing. + 0,

Fig. 5.

A preparation made from Torpedo marmorata (size 15 c.m.) from 3.50—4.10,
Organ 1 is put into NaCl 3°/). From 3.50—5.28 four records were made (fig. 3.
a,b,c, d), the preparation was then put into Fühner’s solution + O,. After about
60 min. record e, after another 38 min. record f, after 20 min. record g.

1) Fühner Zeitschr. f. allgem. Physiol. (1908) Bd. 85. 485.
Used solution was:

Na gCO; 0.2

CaCl, 0.2
KCl 0.1 > per 1 L. water.
NaC] 20.

Urea 25;

136

It appears that after the discharge has decreased in the NaCl solution, it again
increases in Fiihner’s solution + Og.

The other organ (2) has been kept in moist air from 4.10 until 6.47, then it
is put into Fiihner’s solution + O,. It becomes apparent that this organ also
shows a considerable increase in magnitude of the discharge after 30 minutes.

The result of experiment 3 is therefore that O, causes the shock to increase
and that sol. F. shows the same activity even though the discharge had been
weakened by an immersion in NaCl-solution.

Experiment 4 (Fig. 6 and Fig. 7).

A Natl ox
B NaCl 1%
G NaCl +0,

Fig 6.

Preparation of small Torpedo (15 c.m.).

Organ 1 (Fig. 6): At 3.53 in 3%, NaCl. Record A. After two hours record B.

0, is now bubbled through the NaCl. After 30 min. record (.

Organ 2 (Fig. 7): At 4.50 in 3°/) NaCl. Record Aj. After 70 min. record B.

NaCl replaced by Fükner's solution. After 30 min. record Cj.

Result: O, restores the discharge even if the organ remains in NaCl-solution.
Sol. F. restores the discharge which has been diminished in NaCl. solution.

Experiment 5.

The preparations were made at 10.36 in the morning.

Organ 1: kept for 4 hours 40 min: in F. sol. poor in oxygen (boiled).

Record a: deviation is 0,25 volt. After 14 min. exposure to the air.

Record hb: deviation is 0-31 volt. After the preparation had been kept for 23 min.
in well-aerated F. sol.

Record c: deviation is 1,4 voit.

Organ 2: kept for 4 hours 30 min. in F. sol. (O, bubbling through).

137

Record a: deviation is 3 volt (followed by a series on spontaneous discharges).

In F. sol. free of O; the deviation diminishes considerably. After the preparation
has been kept for a long time in F. sol. rich in O3, a repealed discharge follows
after one indirect stimulation.

In two other experiments in duplicate it could be shown that also
after keeping the organ in F, sol. which had been saturated with
H, and more so yet in one with CO,, O, causes the deviation to
increase.

After this series of experiments another one followed in which
the same apparatus was used (Fig. 2). The Fiibner’s solution, poor
in QO, or saturated with, it was here kept at certain definite
temperatures by immersing the whole apparatus in a thermostat.

Experiment 8.

Organ 1: Temp. 18°. Deviation about 25 volt. Latent period 5,5c.

After 30 min. Temp 11°. Deviation 24,2 volt. Latent period 6,8c.

After 22 min. Temp. 28°. Deviation 0,3 volt. Latent period 4,2c.

Organ 2: Temp. 18°. Deviation 20,6 volt. Latent period 6,4c.

After 40 minutes: Temp. 30°. Deviation 0,25 volt. Latent period 3,4c.

After 26 minutes: Temp. 15°. Deviation > 4 volt. Latent period 6,5c.

Experiment 9.

Piece of organ of large Torpedo between zinc electrodes, two nerves being
intact. Thermometer lies in immediate neighbourhood of organ. Length of nerves
15 mm. Distance of stimulating electrodes 3 m.m.

ee) Te | deviation Pe | Lat per

20 5.05 a 4 volt 5 > 40 5,2
13 5.15 b 4 volt 5 + 30 Wed

7 A] 5.37 Cc 4 volt 5 32 12

6 5.53 d 4 volt 5 1005 20

5 6.32 e ‘Jo volt 5.0 0.27 Zed
10 6.47 iff Ijs volt 9 0.31 16

15 7.16 zg '/, volt 550 0.67 8.7
15 9 h /, volt 14 0

As mentioned before we can not attribute any absolute value to
the volt-values given for the discharges, since the galvanometer-
records require a correction which can not be calculated very
easily. After cooling, however, the string will more easily follow
the potential difference, because it develops more slowly in the cold.

Whatever may be their absolute value we can see easily from

138

figures of exp. 9 that as long the organ is cooled, up to about 7,5°,
the discharge diminishes slightly, though not very considerably.
From 5—15° a rapid decrease follows with a slight recovery. Then
the organ apparently is dying.

The changes in deviation of the test-potential were obtained by
changing the side-chain or the resistance, not by changing the sensi-
tiveness of the string (tension).

Experiment 10.
Large organ, kept in F. sol. containing Os.

Latent

Time. Temp. aoe ee ee Period
m.m. in ¢
Eee el ESTE BEEREN DANS KN REBT VERSE SS Eee ere ES
4.23 5 1 iiD 0.33 12.26
4.38 10 1 14 0.49 9.33
503 19 1 cee 3.3 5.6
5.14 26 | CH) 0.67 4.66

The temperatures given are presumably not those of the inside of the organ
because the temperature changed too rapidly. Consequently the large organ conld
not have assumed the temperature of the environment.

Heating to above 22° gives a considerable decrease as appears
from :

Experiment 11.

At 3.05 ’o clock. Temp. 21°. 1 volt = 2,6 m.m. Deviation 25 m m.

At 3.30 ’o clock. Temp. 28°. 1 volt = 2,6 mm. Deviation 2,1 m.m.

The rise in temperature has diminished the deviation to 1/10.

Experiment 14.

At 5 ’o clock. Temp. 20°. 1 volt = 5,5 m.m. Deviation 32 m.m.

At 5.30 ’o clock. Temp. 25°. 1 volt = 5 m.m. Deviation 17 m.m.

The rise in temperature has caused the deviation to diminish to 1/5.

In Fig. 8 and 9 the string-record of the discharge at different temperatures
has been pictured together with the test-record. | have reconstructed it to the
best of my ability from the not absolutely focussed photographs.

Large organ in F. opl. at 28° C. (since 12.55).

Time. en Deviation.
if Ul 5 mm. 35.5 m.m.
12 5 m.m. 34 _m.m.

Now 8 stimuli are given at intervals of 30 sec.

14531 | 5 m.m. | 4.8 m.m.

139

In that way it is evident that at high temperatures fatigue oecurs
very rapidly. A attempt to study the influence of O, at different
temperatures could not be carried out systematically.

Est

Fig. 9.

140

From the experiments it appeared however that at high tempera-
tures (22°—28°) O, did not cause an inerease in discharge. The
latter was the case at lower temperatures. Experiments on the
influence of narcoties had to be given up at an inopportune moment.

Fig. 10 demonstrates that by chloral-hydrate the discharge disappears
nearly completely.

In the apparatus nerve and organ were kept at the same tempe-
rature. [t seemed important in order to judge about the change

Fig. 10a. Fig. 100.
a. Record of discharge small electrical b. The same after exposure to chloral-
organ). Test !/, volt. hydrate dissolved in Fihner’s solution.

in the values for the latent period, to submit the nerves separately
to changes in temperature.

Experiment 16.

Preparation of large Torpedo (28 c.m.) made between 11.45 and 12.45 and
put into apparatus.

Piece of organ with two nerves, the nerves led through glass tubes, in which
stimulating electrodes. Tubes surrounded by glass-mantle, in which water circulates
at different temperatures.

After the experiment has been ended a control is made by tying off the nerves,
which causes a complete breaking of the conduction.

The magnitude of the deviation remained the same although the
temperature of the nerve varied from 20'—6°.

The values of the latent periods actually were lower at lower
temperatures. The measurements are, however, not sufficiently
accurate to allow a calculation of the velocity of the conduction.
That, however, the differences in latent period found in the other
experiments are due to changes in the electrical organ, is evident
from the fact, that in this experiment the difference between 6°— 20°
only amounted to 1.8 6.

Having thus obtained an impression on the influence of tempera-
ture O, and different salt-solutions on the strengih of the discharge
as a responce to indirect stimulation. I have tried to study the
gaseous exchange of the electrical organ in rest and during activity.

For this purpose the electrical organ was enclosed in a very thin

141

dialysing sac of collodion. The oxygen of the surrounding liquid
passes through these sacs without difficulty, as could be shown in
preliminary experiments, but only a very small quantity of organic
substances passed through so that the method of WinkLer for the
determination of O, dissolved in water, could be used with a slight
correction. This very useful method of Winkier can only be used
in the absence of organic substances in the liquid or after a cor-
rection has been made *).

This dialysing sac was put into a bottle, which was completely
filled with Fiuner’s solution of known O, content. After some time
(12 hours) a certain quantity of the contents of the bottle was
again secured for a WiNKLeR’s determination of its O, percentage.

In order to stimulate the organ during its stay in the liquid, two
silver electrodes were tied to the organ. Organ and electrodes were
then put into the dialysing sac and immersed into the liquid. The
organ was stimulated directly once every 5 sec.

The results are given in the following table:

TABLE I.
Exp. Welant Stim. + dine Gk Temp. fe Gee note andes
No, organ In Nesis resp. In oC.
Sus enue Not stimul. | Stimul.
6 35 = 2 18 60
1 36 = 11/4 18 62
Taner 56 + I, 18 103
8 Al ae wil 21 220
8a 4l en 1 19 #00
9 57 — 1 21 103
9a 57 Le 1 19 74
10 18.3 ae 1 21 306
10a 18.3 a 1 sou 440
12 28 = 1 6 136
12a 28 a 1 6 160
13 41 — 1 19 93
13a 41 + 1 -19 100

1) See Henze Abderh. Handb. der Biochem. Arbeitsmeth. Ill, p. 1067.

142

In the first place it became evident that though the results varied

considerably — this is easily explained by the changing condition
of weight ete. of the organ and the varying conditions for the
diffusion of oxygen — the figures in the first place give a very

definite idea about the gaseous exchange in the electrical organ.
The electrical organ appears to consume 6—18 m.m’*. O, per gram-
hour, a quantity which is of the order of the O, consumption of
the peripheral nervous system (THUNBERG)*) which consumes about
‘/,, of the quantity that is used by the central nervous system.

In 1883 Werr tried to demonstrate some chemical changes in the
electrical organ after it had shown vigorous activity. He found a
change in reaction (hydrogen-ion concentration) i.e. an increase in
acidity after activity. Moreover, he tried to estimate the production
of CO, by the organ. Wryr found that 17,5 gms. produced 4 mgms.
CO, in two hours. After stimulation he found a decrease instead of
an increase. The alcohol-extracts of a stimulated organ and one
which had not been stimulated, did not show any differences. The
watery extract of the stimulated organ was larger. | myself have
tried in vain to demonstrate the change in reaction after stimulation.
I have tried to demonstrate two chemical substances in the electrical
organ i.e. xanthin-bases and glycogen. This seemed to me to be of
importance, because we know that the electrical organ must be
derived from muscles in which both substances occur abundantly.

The xanthin-bases were determined according to the method of
Burian:

100 gr. of the organ are boiled for 12 hours in 1 L. of 0,5°/) H,SO,. After
filtration the sulfuric acid is precipitated with Ba(OH), and the liquid which is
now alcaline is filtered. The filtrate is saturated with CO,. The BaCO is removed
by filtering and the filtrate, after acidification with acetic acid, is evaporated down
to 100 c.c. These 100 c.c. are boiled for some time with a smaller quantity of
concentrated NaOH + Na,€O, and filtered. The filtrate is acidified with HCl. A
precipitate of xanthin bases now comes out on addition of an excess of NH; + AgNOs.
In this precipitate nitrogen can be determined according to KJEHLDAHL.

The following table gives the results of this investigation: (See
Table 2, following page).

We may therefore conclude that the electrical organ contains no
xanthin-bases or a neglegible quantity.

Determinations of glycogen were made in two very large animals
and in two young ones.

') TuunBERG. Zbl. Physiol. 28 (1904). See also BuvreNpiJk. Kon. Ak. v. Wetensch.
1910 (615—621).

143

TABLE 2.

| Result.
Expert: 107,5 gm. electric organ. Very slight precip.
Exp: 1a: 55 gm. muscle Heavy precip.
Exp 2 106 gm. electric organ. No precip.
Exp. 3a. 120 gm. electric organ. Very slight precip.
Exp. 4. 122 gm. electric organ. No precip.
Exp. 4a. 52 gm. muscle Heavy precip.

The determination was made according to PrrüGer :

TABLE 3.
Exp. | Size of animal in c.m. | Quantity of organ. 0, Glycogen.
: el taken out of the 313 0.051
2 45 nnen 1288 4 0.031
3 15 freshly caught animal. 20 0.787
4 5 6specim.; just born. 13.5 1.02

If we compare these results with those of BaAGLIONr '), we see that
the glycogen values in exp. 1 and 2 are lower than those given by
Baeionr (0,09 °/,), but of the same order. The figures in very young
animals (exp. 3 and 4) are very much higher.

If the electrical organ functions by splitting up ion-proteids,
we may expect salts to become free. This might be the
explanation of the increase of the watery extract found by Whryt.
The electrical organ reacts to mechanical stimulation, e.g. mincing
or pressure, by strong activity. Therefore I have tried to divide
electrical organs finely by gradually cooling and finally freezing
them. In that way no discharges occurred. In centrifuging the frozen
organ after it had been ground up, I could obtain a very complete
separation of the organ-fluid. This fluid as obtained from stimulated
and fresh organs, was used for the present research.

In the liquid thus obtained I made a determination of the ash-
compounds, which led to the following results:

1) Baauiont. Hofmeister’s Beiträge 1906. Bd. VIII, p. 456—471.

144

TABLE 4.
Ash (mgs per c.c. organ-fluid) determined after the wet method (SO, ash).

Exp. Not stimul. Stimul. Difference.
| 31.8 31 — 0.8
2 30.4 31.2 + 0.8
3 38.6 35.5 — 3.1
4 26 28 + 2

We see at once that there is no difference in ash-content in the
fluid of a stimulated organ and of one which bad not been stimulated.
Moreover | made treezing-point determinations in both liquids.

TABLE 5.
A in ° in organ-fluid.
Exp. Not stimul. Stimul. | Difference.
1 Zane 2.215 + 0.095
2.12 2:21 + 0.09
2, 2.145 2.30 + 0.155
2.135 2.295 + 0 160
3 2.16 2723 + 0.07
2.15 2.24 + 0.10
4 2.095 2.18 + 0.085
Ground Ground when
when frozen. warm (20°).
5 2.08 2.20 0.17

From these experiments it appears that during activity substances
pass into the organ-fluid which must be considered to be organic
substance, because the ash-content is not increased, whereas the
freezing point shows a very definite lowering.

However incomplete these investigations may be, I have felt the
desirability of communicating them very briefly, the more because
I shall most probably not be in a position to take up the whole
problem once more and because the data published in the present
paper, to my opinion, may be a stimulus to a continued research
of the physical and chemical processes which take place during the
discharge of the electrical organ.

Physiology. — “On the Significance of Caleium- and Potassium-
ons for the artificial Oedema and for the lumen of the
bloodvessels”. By Ruporr J. HAMBURGER. (Communicated by
Prof. H. J. HAMBURGER).

(Communicated at the meeting of March 25, 1922).

Of late years a series of researches have been carried out in the
Groningen Physiological Laboratory, which demonstrated, among
other things, that the solution used by Srpney RINGER in his remark-
able experiments on the frog’s heart, is not suitable for other
organs of the frog. As known, this solution is composed as
follows: NaCl 0,7 °/,, NaHCO, 0,02 °/,, CaCl,6 aq. 0,04 °/,, and
KCl 0,01 °/,. HAMBURGER and BrinkMAN') found that when, after
the addition of a little glucose, this solution is allowed to perfuse
the kidney, the glomerular epithelium does not retain any glucose.
Systematical investigation, however, enabled them to modify the
circulating fluid in such a way that the glomerular epithelium
obtained the property to retain the physiological amount of glucose
(0,060—07°/,) This circulating fluid was of the following composition:
NaCl 0,5 °/,, NaHCO, 0,2 —0,285 °/,, CaCl,°6 aq 0,04 °/,, KCI 0,01 °/,.
Also for other organs of the frog the proper physiological fluid was
found after systematical investigation (for the movements of the
stomach on excitation of the N. vagus’), for the movements of the
rectum *), for formation and solution of biliary concrements) *). All these
researches have shown that the efficiency of the circulating fluid
depends on the amount of free calcium-ions °). Also in warm-blooded
animals the concentration of Ca-ions appeared to play a prominent
part: here we allude to the investigations on haemolysis ®) and on

1) H. J. HAMBURGER and R. BRINKMAN, These Proceedings Vol. XIX, p. 989
and Vol. XX, p, 668. See also Biochem. Zeitschr. 88, 97, 1918.

2) BRINKMAN and vAN Dam, These Proc. 18 Dec. 1920.

5) Demonstration by van Crevetp at the Conference of Physiologists at Amst.
22 Dec. 1921, ]

*) Borr and Heeres, Ned. Tijdschr. v. Geneesk. 65, 2d half NO. 10, 1921. Also
Pfliiger’s Archiv f. d. ges. Physiol. (not out yet).

5) Cf. also H. J. Hamsurcer, Permeability in Physiology and Pathology, Lancet 2,
1056, 1921.

6) BRINKMAN, Biochem. Zeitschr. 95, 101, 1919.

146

the origin of spasmophilic phenomena consequent on decrease of
the concentration Ca-ions of the blood *). ‘This concentration of depends
upon Ca-ions the NaHCO, and on the H-ion concentration.

As for the influence of the concentration of the Ca-ions upon the
permeability of the glomerular epithelium, it is so great that, even
when a potassium-free liquid is sent through the kidney, retention
of the physiological quantity of glucose was still observable *®).

This being the fact, it seemed interesting to us to investigate with
what liquid the vascular system of the frog had to be perfused
in order to prevent the production of wdema in the hindlimb.

We were all the more induced to inquire into this matter, since
some years back GunzBure *) occupied himself with this question in
the Utrecht Physiological Laboratory. He found that, when perfusing
the vascular system of the frog with a fluid such as Ringer had
used for the heart, and which differed from ours in NaHCO, 0.02 °/,
being used instead of 0,2 °/,—0,285 °/,, KCl 0,01 °/, was indispens-
able to prevent oedema. So, in Gunzpure’s experiments oedema
arose when the fluid was potassium-free or when too large an
amount of K was present. Instead of K he could use also Uranium,
Thorium or Rubidium in definite quantities. It is evident, therefore,
that, according to GunzpurG, K is indispensable in this case, and
this indispensability is, according to him, due to the specifically
radio-active effect of this element.

But Gunzpure also detected that in Rinewr’s mixture K could be
left out, when the mixture was saturated with oxygen, in which
case cedema was also prevented. We shall revert to this point.

It has been stated that in the circulating fluid HAMBURGER and
BRINKMAN could do entirely without K. In that case, however, the
Ca-ion concentration should have a definite value. The question
now arose: can wdema be prevented in the frogs limb with a
potassium-free circulating fluid, the Ca-ions concentration being ac:
curately fixed ?

In order to find an answer to this question we have a series of
experiments which yielded unexpected results with reference to the
influence of the Ca-ions concentration on the lumen of the blood-
vessels (capillaries).

Of course the inquiry was begun by repeating Gunzpure’s experi-
ments. A perfusion of the ordinary Rineer’s liquid (NaHCO, 0,02°/,)

') Van Paassen, Ned. Tijdschr. v. Geneesk. 65, 2e helft, nr. 17, 1921.

3) Hameurncer and Brinkman, These Proceedings Vol. XX, p. 668; Biochem.
Zeitschr. 88, 97, 1918.

5) Gunzsura, Arch. Néerl. d. Physiol. 2, 364, 1918.

147

did not cause cedema, which indeed came forth, when K was left
out, just as GunzBure has shown.

Now mixtures were applied of NaCl 0,6 °/, with several quanta
of CaCl, . 6 aq. The result was that cedema appeared when
CaCl, .6 aq. 0,003 °/,, 0,005 °/,, 0,006 °/, was applied, but that zt
stayed away when CaCl, .6 aq. 0,007 °/, was used, even when the
hydrostatic pressure was raised from 85 to 70 cm.

These experiments, therefore, went to show that, contrary to
GuNzBURG’s opinion, K may be taken from the circulating fluid,
without evoking cedema'‘), in other words, that no radioactive sub-
stance is required to prevent cedema.

Now it seemed to be interesting to add some K to this circulating
fluid (NaCl 0,6 °/, + CaCl, .6 aq. 0,007 °/,), which, as has been said,
does not cause oedema. The addition of KCl 0,01 °/, produced
cedema. It may be concluded, therefore, that the absence of wdema
on adding KCl in the experiments of GunzBure cannot be due to a
specific Potassium-action. On the other hand, it became rather evident,
that when a definite concentration of it is present in our NaCl—
CaCl, mixture, cedema is sure to appear on that account, so that
it becomes. obvious, that the prevention of cedema by the 0,007 °/,
CaCl, 6 aq. solution is balanced, and even more than balanced,
(this depends on the amount) by the antagonistic Potassium.

Now, how are we to account for GunzBurg’s finding that a pot-
assium-free Rinerr’s mixture evokes cedema? It is probably to be
ascribed to the fact that this circulating fluid contained only 0,02°/,
of NaHCO,, of which according to Rona and Takanasut’s’) formula
a large amount of Ca-ions is the consequence.

A direct measurement of the Ca-ions concentration after BRINKMAN
and van Dam®*) proved that the Ca-ions concentration used by GUNZBURG
was, indeed, much greater than in the above-named mixture of
NaCl 0,6 °/, + CaCl, .6 aq. 0,007 °/,.

We found experimentally that in our mixture NaCl-CaCl,, which
did not bring about cedema, contained 13 mgrms of Ca-ions per
Litre, whereas the liquid used by GunzBure contained 20 mgrs per
Litre, which makes a difference of 35 °/,.

Now we know that K and Ca are antagonists; the action of K
being liquifying, that of Ca tending towards coagulation. It is not

1) It has been shown that, with other kinds of frogs, there are sometimes other
Ca-ion concentrations needed to prevent cedema.

2) Rona u. Takanasut, Biochem. Zeitschr. 49, 370, 1913.
3) BRINKMAN and van Dam, These Proceedings, Vol. XXII, p. 762.

148

surprising, therefore, that the ratio of K- en Ca-ions is of great
importance for the permeability of the vascular wall. It is evident
that in an’ NaCl-CaCl, mixture the constricting power of 13 mgr.
Ca-ions per Litre is so great, as to keep away cedema. In the
presence of more than 13 mgr. Ca-ions e.g. 20 mgrs, as is the case
in Gunzpura’s fluid, cedema will ensue, if not a certain amount of
K is added to counteract their effect. A similar phenomenon appeared
in the case of the kidneys viz. that an excess of Ca-ions content of
the circulating fluid produced permeability of the glomerular epithe-
lium for glucose *). The same thing was found by BRINKMAN *) with
regard to the red blood corpuscles. Likewise Nruscu.osz *) physico-
chemical experiments demonstrated that the surface-tension of a
lecithin-suspension in NaCl is as well influenced in the same manner
by too little as by too much Ca.

We now tried to ascertain, whether cedema would arise when
using a mixture of NaCl—CaCl, which contained much more than
0,007 °/, of CaCl,. 6 aq., just as had occurred when the amount
was 0,006 °/,.

With a view to this 0.01 °/, CaCl, 6 aq. (instead of 0,007 °/,) was
dissolved in NaCl 0.6*/,. We expected cedema to come forth. It did
not come forth, though, which was owing to a quite unexpected
phenomenon: the perfusion of the liquid through the vessels stopped
abruptly. It could not be restored even through a considerable rise
of the hydrostatic pressure. When the same result was obtained
several times running, also with higher Ca-ions concentrations ‘),
further experiments concerning the influence of a higher Ca-ions
concentration on the producing of cedema had to be relinquished,
and vascular contraction was supposed to come into play.

Now the assumption was warrantable that the vascular contraction
(spasm, tonus) would disappear on addition of K. It appeared, indeed
that when to the circulating fluid (NaCl 0,6°/, + CaCl, . 6 ag. 0.01 °/,)
0.01 °/, KCl was added the perfusion of the liquid was restored again.

We are justified in coneluding from this that when, in a system
Na + Ca, the Ca-ions concentration is higher than agrees with CaCl, .
6 aq. 0.007 °/,, a constricting influence is exercised on the vessels,
which may be counteracted by K-ions. This action seems to be
reversible; it may be repeated several times.

‘) Hampcrcer u. BRINKMAN, Biochem. Zeitschr, 95, 101, 1919.

2) R. BRINKMAN, Broch. Zeitschr. 95, 101 (1919).

3) Neusenrosz, Pfltiger’s Archiv f. d. ges. Physiol. 181, 17, 1920.
4) More about this in a subsequent publication.

149

In correlating this result with the well-known observations of
Crrarr and JANUSCHKE *), according to which the process of conjunctival
inflammation may be arrested by instillation of a CaCl,-solution, we
are led to suppose that a definite concentration of Ca-ions exercises
a constricting influence upon the vessels and at the same time a
coagulating action upon the vascular wall. It appears then that both
these actions are neutralised by K.

That the contracting and the coagulating action may coincide,
is substantiated by the observations on the influence of oxygen.
Séverini’) found that oxygen brings about contraction of the vessels;
while GUNZBURG?®), reports that a potassium-free Rincur’s mixture,
which in other cases always caused cedema, did not cause it when
the mixture was saturated with oxygen. From this it seems probable
that vascular contraction coincides with decrease of permeability of
the vessel-wall not only with a definite concentration of Ca-ions,
but also under the influence of oxygen.

As regards the inhibition of vascular constriction through the
addition of KCl to the mixture NaCl 0,6°/, + CaCl,.6 aq. 0.01°,,, it
appears that the minimal required concentration of KCl is about

KCl 0,004 °/,.

Sr aie Rey:

The described researches, of which a detailed report appeared
in the Biochemische Zeitschrift*), may be summarized as follows:

1. When perfusing the frog’s leg with an aqueous solution of
NaCl and CaCl,, potassium may be absent in the circulating fluid,
without cedema being evoked. The circulating fluid, however, should
contain a definite concentration of calcium-ions. NaCl 0.6°/, CaCl, .
6 aq. 0.007°/, will serve our purpose here. When using CaCl, . 6 aq.
0.006°/, cedema will arise. This will occur also when to the first-
named mixture 0.01°/, KCl is added. This phenomenon finds .an
explanation in the fact that the coagulating action of the Ca-ions is
counteracted by the antagonistic K-ions.

2. That GunzBure wanted potassium in his solution to prevent
oedema is to be ascribed to the fact that he used an excess of cal-
cium-ions. The arrest of cedema in GuNzBurG’s experiments is,

) Crrarr u. Januscuxe, Arch. f. exper. Pathol. u. Pharmakol. 65, 120/126, 1911.

2) Luiat Severinit, ,Ricerche sulla innervazione dei vasi sanguigni’’. Perugia
Boncompagni et Cie (See Baytiss: „Principles of General Physiology”, 1915, p. 534.

3) GunzBure, l.c.

4) Ruporr J. Hampureer, Bioch. Zeitschr. 129, 153, 1922.

150

therefore, not owing to a specifically radio-active potassium-action
but only to the long known potassium-caleium antagonism.

3. The influence of the K-ion concentration upon the permeability
of the vessel-wall (mentioned sub 1 and 2) coincides with an
influence upon the capillary lumen. A perfusion of the vascular
system of the frog with a mixture of NaCl 0.6 °/, +CaCl, .6 aq
0.01 °/, produces so considerable a constriction of the vessels that
no fluid can pass through any more. When to this mixture a little
KCl, say, 0.01°/, KCl is added, the vessels dilate and the fluid
runs on as before. This process is reversible.

4. The parallelism of decrease of permeability and of constriction
of the vessel-wall manifests itself not only under the influence of
Ca-ions, but also under that of oxygen.

5. In a quantitative determination of the dilating and constricting
action of pharmaca after TRENDELENBURG, due regard should be
paid in future to the ratio of Potassium- and Calcium-ions in the
circulating fluid.

From the Physiological Laboratory of the

5 March 1922. University of Groningen.

ERRATUM.

In these Proceedings of June 1912 (Vol. XV), p. 276, Table II,
column 5, line 12 from the bottom to replace the there printed
number 1.18908 by the number 1.69487.

KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM.

PROCEEDINGS

VOLUME XXV
Nes. 5 and 6.

President: Prof. F. A. F. C. WENT.
Secretary: Prof. L. BOLK.

(Translated from: ‘Verslag van de gewone vergaderingen der Wis- en

Natuurkundige Afdeeling," Vol. XXXI).

CONTENTS.

H. ZWAARDEMAKER: “On the Alpha-automaticity of the Autonomous Organs”, p. 152.

C. E. B. BREMEKAMP: “Further researches on the antiphototropic curvatures occurring in the
coleoptiles of Avena”. (Communicated by Prof. F. A. F. C. WENT), p. 158.

R. WEITZENBOCK: “Ueber Wirkungsfunktionen”. (Communicated by Prof. L. E. J. BROUWER), p. 166.

J. W. JANZEN and L K. WOLFF: “Studies on the bacteriophagus of D’HERELLE”. (Communicated
by Prof. C. EYKMAN), p. 171.

A. W. K. DE JONG: “The Biscoumaric Acids”, p. 175.

G. HERTZ: “On the Excitation and Ionization Potentials of Neon and Argon”. (Communicated by
Prof. P. EHRENFEST), p. 179.

C. A. H. VON WOLZOGEN KüHR: “On the Occurrence of Sulphate-reduction in the deeper layers
of the Earth”. (Communicated by Prof. G. VAN ITERSON Jr.), p. 188.

E. VAN THIEL: “The Influence of a Catalyst on the Thermodynamic Quantities Regulating the
Velocity of a Reaction”. (Communicated by Prof. J. BOESEKEN), p. 199.

J. BOESEKEN: “The Dislocation Theory of Catalysis”, p. 210.

W.E. DE MOL: “The disappearance of the diploid and triploid magnicoronate narcissi from the
larger cultures and the appearance in their place of tetraploid forms”. (Communicated by Prof.
G. VAN ITERSON Jr.), p. 216.

L. J. SMID Jr.: “Numbers of Circles Touching Plane Curves Defined by Representation on Point
Space”. (Communicated by Prof. HENDRIK DE VRIES), p. 221.

A. F. HOLLEMAN: “Monochloro-trinitrobenzenes”, p. 223.

A. A. WEINBERG: “On Respiratory Oscillations in the Galvanogram of Man”. (Communicated by
Prof. E. D. WIERSMA), p. 225.

10
Proceedings Royal Acad. Amsterdam. Vol. XXV.

Physiology. — “On the Alpha-automaticity of the . Autonomous
Organs.” By Prof. H. ZWAARDEMAKER.

(Communicated at the meeting of June 24, 1922).

In the organism there are some organs which perform automatic
movements and whose movements are continued also in parts that
have been isolated from the body. Without any outward stimulation,
simply by watehing those parts we can follow up the continuation
of this action in its causal and conditional relations. The type of
such an organ is the heart. It is the musclecells themselves that
pulsate, from the earliest embryonal existence up to death. Such a
pulsating heart-cell is comparatively a simple system of phases, *)
which, if the nucleus is left out of consideration, is made up of the
following components: 1st. 7 ions, H, OH, Na, K, Ca, HCO. eo:
(resp. HPO,); 2™¢. 2 lipoids, cholesterin and lecithin; 3'4. a carbo-
hydrate, glycogen, which is alternately combined with phosphoric
acid and isolated from it again; 4”. oxygen; St. proteins and
water as a solvent. The absolute quantity of every component exerts,
according to the rules of the equilibrium of the phases, an influence
upon the whole. Influence may be exerted, a component may even
be given a certain concentration, by surrounding the cell with a
nutrient liquid composed for the purpose. In so doing substitution
appeared to be possible. Na may be replaced by Li or by highly
purified Cs; K by all radio-active elements’); Ca by Sr and Ba;
lecithin by sodiumoleonate. Besides the absolute quantity also the
mutual relations carry weight, notably H:OH, H: HCO,, K : Ca.
Such interrelations must keep within certain bounds. To test this
various qualities of the function may be considered: first of all the
so-called tonus-condition, i.e. the degree of continued contraction
between the limits of atony and maximal tonus; next the excitability
in the several intervals of a period; lastly the automatic movement
itself. Now granting the conditions of the system to be so regulated
that the bounds we alluded to, have been kept in view, and each

1) H. ZwAARDEMAKER, Erg. des Physiol. Bd. 5. p. 135. 1906.
2) H. Zwaarpemaker, These Proceedings Vol. XIX, p. 633. (1916).

153

of the three fundamental manifestations, i.e. tonus, excitability and
automaticity persist freely, two sorts of automaticity can be elicited
by superadding successively the several radioactive elements to
the nutrient liquid which surrounds the cells. Two sorts we say,
because there are two groups of radio-active elements, which thus
far I have been able to use as medium in the solutions of Ringer
or Tryropr to substitute vice versa: 1st. an «-group: uranium,
radium, emanation, polonium, thorium, 2"¢ a g-group: potassium,
rubidium.

We shall now discuss the points of distinction and of agreement
between these alpha-, and beta-automaticities.

The principal feature of an automatic, periodic movement is its
tempo, which in its turn depends again on the so-called refractory
stage inserted into every period. Now this tempo is determined by
the amount of radio-activity for the alpha-group, as well as for the
beta-group. A minimum amount is required for the movements to
reveal themselves at all, and a maximum quantum that should on
no account be surpassed. This allows a certain latitute for dosages,
which is narrow for the alpha-, and broad for the beta-group.

Somewhere in this latitude there is a point of greatest frequency,
the optimum. This point being established for the two sorts of rayers,
the frequencies will be the same for either group.

Such an investigation evidently requires a constant temperature.
It is also clear that, when the temperature is variable the two
determining factors: amount of radio-active matter and degree of
the temperature, may cooperate or counteract each other. It has
already been shown that there is a law, which determines these
relations, but I do not intend to enter into it here. Now, when both
for potassium and for uranium the optimum ‘doses have been found,
which yield the highest frequency, the frequencies for potassium-
and for uranium-automaticity are equal. This is instanced in Fig. 1.
In the centre the potassium-beat is shown, separated to the right
and to the left by a standstill from two other pulsations; these two
other pulsations represent. the paradoxical phenomenon appearing
when passing from perfect . potassium-dosis to a perfect uranium-
dosis, and conversely *). To the right and to the left the uranium-
beat can be observed. Its frequency does not differ from that of the
automaticity in the centre of the figure.

Another property the two automaticities have in common is a

1) These: Proceedings Vol. XIX, p. 1043, (1917) C.R. Soc. de Biol. t. 84 p. 704.
Paris 1921.

(Vas

154

similar need for radio-activity in the several subdivisions of the
heart. This is seen best when passing from a perfect uranium-dosis

mT

bit) jill his ii

UN
Hi

|

Fig. 1.
Frog’s heart Kronecker’s canula 14° C., red light.

Transition from a circulating fluid with 25 mgr. uranylnitrate to another with
300 mgr. potassiumchlorid per litre, and then back again to 25 mgr. uranylnitrate.
The transitions generally took place resp. 40 and 60 seconds before the paradox-
ical standstills, indicated in the figure by a white line. Potassium pulsation in the
centre. Time '/, min.

to a perfect potassium-dosis or the reverse with a simultaneous
registration of the sinus, atrium, ventricle. If no conductive disturb-
ances occur, it will be seen that the three divisions of the heart
will stand still and resume their beats at the same moment with
automaticities of their own. This is illustrated below in fig. 2 for
an eel-heart in situ, which was perfused first with a uranium-liquid
and at a moment designated in the time-line by S witb a potassium-
liquid.

The phenomenon, instanced in fig. 2 requires, however, accurate
dosage of uranium as well as of potassium. It would not be surprising,
if inaccuracy in this respect should engender dromotropism.

A third property the two automaticities have in common is
the self-regulation after extrasystole, for a-conditions as complete as
for the g-conditions.

The fourth common property is the initial similarity of the alpha-
and the beta-electrogram, though I must admit that afterwards a
difference may come forth through secondary influences”).

Only in adventitious respects do the two automaticities differ.

Of the greatest importance in this respect is the tonicity of the
heart. The conditions determining the auto-tonus of the cardiac
muscle are:

1) Klinische Wochenschrift Jahrg. I NO. 12 (or Diss. H. Sroorr, Utrecht
4 July 1922).

155

a. the number of calcium-ions placed or not placed over against
univalent-ions.

6. the number of H-ions.

c. the amount of light incident upon the heart, especially: in the
presence of a fluorescent substance.

DONNE ANN

2 VIN mm mmm a

3
4 8

4

Fig. 2.

Eel’s heart in situ. Perfusion from vena cava, first with a circulating fluid,
containing 15 mgr. thorium-nitrate per litre, then with a circulating fluid, containing
100 mgr potassium-nitrate. 1 sinus, 2 atrium, 3 ventricle. Time in sec. At S
transition from one fluid (thorium-beat) to the other (potassium-beat). Only in the
ventricle a light tonus is noticeable during the thorium-beat. It has disappeared
already for the greater part in the first beat performed by the heart during the
paradoxon.

When applying uranium as an a-rayer each of the three above
conditions is modified. Sub a undergoes a change because over
against the calecium-ion not only univalent ions are placed, but
also uranyl. Sub 6 is modified, because a solution of uranyl-salt
causes a small increase of H-ions in Ringer’s solution. True, this
factor may be eliminated by the addition of a trace of CaCO,, but
let it be supposed that this did not take place. Sub c has been
modified, because in the organ perfused with a potassium-fluid the
incident light has only an inappreciable influence unless its strength
be enormous, while in the presence of a fluorescent uranium-liquid
also ordinary light will show its tonie action.

It will, therefore, be considered quite rational that in fig. 1 the
bases of the uranium-elevations are not so low as those of the po-
tassium-elevations. When thorium is substituted for uranium the
phenomenon is less pronounced, still, it is certain that even then
the tonus is not quite absent.

156

With emanation-beats') and with pulsation evoked by outside
radiations with polonium, there is often some increase of tonus,

Fig. 3.
Frog’s heart, ‘KRoNECKER’s cannula.

Deprived for some hours by potassium-free perfusion of diffusing potassium
and of part of the depot. Then pulsating during the night with 100 mgr. of potas-
sium-chlorid per litre. Next morning standstill with potassium-free Ringer’s mixture.
Recovery of pulsation due to omnilateral polonium radiation. At the beginning of
the curve the polonium was taken away.

Nearly half an hour later the polonium-beats cease. They had caused no increase
of tonus worth mentioning.

which need not surprise us if we consider what has been stated sub a.
Increase of tonus, however, is not a typical feature of alpha-auto-
maticity, since it can exist without this increase when it is brought
about from the outside by polonium-radiation. This is illustrated in
Fig. 3’). A heart that after cautious, prolonged perfusion with pot-
assium-free Ringer’s solution, had been deprived of a considerable
portion of its potassium depot, continued pulsating for a Jong time
also when subjected from the outside to omnilateral polonium-radi-
ation. These pulsations occur without additional increase of tonus.
The polonium is taken away at the beginning of the figure.

Besides in the tonus-condition, the two automaticities are also
distinguished in the relation of the regularly pulsating hearts to the
action of the constant current, to the alternating current and to dia-
thermy. These distinctions have been described by Dr. DEN Boer *) in
his Thesis, so that I will not revert to them.

1) ZwWAARDEMAKER and T. P. Feenstra, C. R. Soc. de biologie, t. 84, p. 377.
Paris 1921. ZwAARDEMAKER, Klin. Wochenschr. Jahrg. I, N°. 11. 1922. Arch.
intern. de Physiol. vol. 18, p. 284, 1921.

2) Another instance is giften by ZwAARDEMAKER and G. Grins, Arch. néerland. de
physiol. t. 2, p. 502, 1918.

3) M. pen Boer, Dissertation. Utrecht 1 Maart 1921.

157

The heart has served us as a type of the two automaticities; the
natural one depending on the radio-activity of potassium, or rubidium,
and the artificial one, that can be evoked by the radio-activity of
uranium, thorium, ionium, radium, emanation. In quite the same
way there is a mutual resemblance between the alpha- and beta-
automaticities of the gut and the uterus.

Botany. — “Further researches on the antiphototropic curvatures
occurring in the coleoptiles of Avena.” By Dr. C. E. B.
BREMEKAMP. (Communicated by Prof. F. A. F. C. Wenr.)

(Communicated at the meeting of May 27, 1922).

As I have shown in my former communication‘), the conditions
under which the coleoptiles of Avena produce an antiphototropic
curvature, may be summed up in this way:

1st. At the end of the one-sided illumination the rate of growth
should have about the same value at both sides of the coleoptile?).
This result is only to be obtained with light of rather strong inten-
sity. If this is provided for, the product of the intensity and the
exposition-time should exceed a certain value.

nd, After the close of the illumination, there should be a more
rapid increase of the growth-rate, in the side that has received the
greatest quantity of light. In this way it should reach here a higher
value.

An explanation of the way wherein a difference in the rate of
increase may come about, was given in my paper entitled: “Theorie
des Phototropismus’’*). After a previous diminution in consequence
of the illumination, the rate of growth after some time increases
again. This process commences probably the sooner, according as
the diminution has been the greater. In this way the increase of
the growth-rate in the side which has received the greatest quantity

1!) C. E. B. Bremexamp. On antiphototropic curvatures occurring in the coleo-
ptiles of Avena. Proceedings Kon. Akad. v. Wetensch. te Amsterdam. Vol. XXIV,
peel. li 92de

2) In my previous work in stead of the expression “the rate of growth at the
end of the illumination” I used the ampler expression “the rate of growth
belonging to the grade of sensibility existing at the end of the illumination”. In
this way | reckoned with the possibility that it would give a latent period between
the phototropical reaction i.e. the change of the rate of growth, and the absorption
of the light with its influence on the sensibility. However, a critical examination
of the literature on this subject, has convinced me that the evidence in favour of
the existence of this latent period, is not conclusive. The investigations of Bose
and others have made it very probable that the reaction follows the illumination
almost immediately.

5) G.E. B. Bremexamp. Theorie des Phototropismus. Rec. d. trav. bot. Néer-
landais Vol. XV. p. 123. 1918.

159

of light, may gain an advantage of that in the other side. This
advantage will be the greater, according as there lies more time
between the moment whereon the growth-rate in the anterior side
has reached its lowest value, and the moment whereon this is the
case in the posterior side. If it is sufficiently great, the rate of growth
in the first-named side with the aid of it will reach at the end of
the illumination or shortly afterwards a higher value. In any case the
exposition-time should be long enough that an advantage of sufficient
extent may be gained.

However, in my previous communication [ showed that an anti-
phototropie curvature may come about also, if the expositiontime
is very short. As in this case the explanation given above naturally
fails, 1 suggested that the theory of Bosk') might give us here the
clue to get out of the difficulty.

According to this theory, a disturbance of equilibrium in the
organism generally manifests itself in a local contraction (the direct
effect) which is accompanied by an expansion in the adjoining tissue
(the indirect effect). In the latter, the turgescence would be heightened
by the water expelled from the contracted portion, and accordingly
a temporary enhancement of the growth-rate would be the result.
In this way a normal curvature in one part of an organ would
always go together with an antitropie one in the adjoining region.
Only if an increase of the rate of growth in that part, should be
impossible, the antitropic curvature would remain out. In our case
then, the origin of the antiphototropic curvature in the tip of the
coleoptile might be connected with the origin of a normal photo-
tropic curvature in the basal part.

To test the correctness of this supposition, [ made a number of
experiments wherein the phototropic reaction of coleuptiles exposed
in the whole of their length, was compared with the reaction of
coleptiles illuminated at the tip only, or illuminated also in the
whole of their length, but after an exposition of the basal part to
a two-sided illumination of rather great strength.

Before I enter into the details of these experiments, I will give
a survey of the results which previous investigators have obtained
in their researches on the influence of an illumination of one part,
on the phototropic reaction of another.

First of all then, we have to consider the experiments on photo-
tropism made by Bost’) himself. They are rather few in number,

h J. C. Bose. Plant Respose. London 1906.
*) J.C. Bose assisted by Jyotiprakash Sircar. The transmitted effect of photic
stimulation. Life Movements in Plants. Calcutta 1918/19. p. 362—3877.

160

and form only a subordinate part in the general frame of his work.
His experimental objects were seedlings of Setaria and roots of
Sinapis.

The choice of the first-named object is not very happy, as the
direct effect of the exposition of the coleoptile is not outwardly
visible, and its existence therefore, as yet purely hypothetical. The
indirect effect consists in an antitropic curvature of the axis. This
curvature which appears almost immediately, is followed in about
25 minutes by a normal one. The latter should be the result of
the propagation of the invisible direct effect. An illumination of
the growing region gives a normal curvature. ,

That the antitropic curvature of the axis occurring with an
exposition of the coleoptile should be the indirect effect of this
illumination in the sense of Bosr, is possible. [t should be remarked
however, that it is not proved. As yet, we don’t know with
certainty, if in this case the direct effect consists really in a
contraction, as no sign thereof becomes outwardly visible.

The roots of Sinapis show a negative phototropism. At least this
is the case, when both the tip and the growing region are exposed
to the light. The curvature appears in the growing region, the tip
always remaining straight. An exposition of the tip also gives a
negative curvature of the growing region, but if this part itself is
exposed to the light, there appears at first a positive curvature
which only after some time is followed by a weak negative one.

Bose considers the negative curvature in the growing region pro-
duced by an exposition of the tip, as the indirect effect, the direct
effect as in Setaria remaining concealed. That this curvature is not,
as in Setaria, followed by a positive one, he explains by assuming
that the intervening tissue would be practically unable to conduct
the direct effect. In the case of an exposition of the growing region,
the positive curvature is considered as the direct effect, whereas the
negative curvature appearing a little later, is said to arise on account
of transverse conduction of the direct effect under continued
illumination.

However, this explanation is not very convincing. That a neutra-
lisation of the curvature might come about by transverse conduction,
is quite conceivable, but how a reversion of the curvature might
be explained in this way, I fail to understand. Moreover, as a
conductivity for the direct effect in the longitudinal direction is
supposed to be absent, it is not readily admissible that is should be
very efficacious in the transverse direction. Therefore, in this case
the interpretation of Bose cannot be considered as sufficiently founded.

161

The explanations of these negative curvatures given by other inves-
tigators are, however, hardly more convincing.

Information about the influence of an illumination of the basal
part on the reaction of the tip, is to be found in papers by van
DER Work !), GuTTENBERG *) and Arisz ®), all dealing with the photo-
tropism of Avena.

According io VAN DER Work the results of an illumination of the
basal half of the coleoptile on the upper half, is to be seen in the
fact, that an illumination of 12 MCS gives in these seedlings a
curvature of the same strength as an illumination of 85 MCS in a
wholly etiolated coleoptile. This greater curvability of the upper
half might, perhaps, be explained by assuming that the contraction
of the tissue in this part was facilitated by the decrease of turges-
cence in the basal half: the expulsion of the water would find
here less resistance.

GUTTENBERG on the contrary, tried to show, that the curvability
of the tip of the coleoptile is not altered by an illumination of the
basal part. In his experiments three sets of seedlings were compared.
They were all illuminated unilaterally with 22,2 or 33,3 MCS; but
in the second and third set the basal part was exposed previously
during one hour to an illumination with 11,1 MC; in the second
set the seedlings rotated during this time round a vertical axis,
whereas in the third set they stood still. In this case the after-
illumination took place from the opposite side. GurreNBerG found
that the phototropic curvature in the third set was a little weaker
than in the other two.

This result seems at first in flagrant contradiction to the statement
of VAN DER Work cited above, but it should be remembered that in
the experiments of vaN DER Work, the light was very strong, and
the exposition only short, whereas GurreNBERG used light of rather
feeble intensity and a very long exposition. Therefore, in the seed-
lings of vaN DER Work the decrease of turgescence in the basal
part, might have been greater, and consequently the effect on the
curvability of the tip more important than in the seedlings of
GUTTENBERG. This explanation would probably suffice, if there was
no difference at all between the curvatures in the three sets. Gur-

1) P. G. van ver Work. Investigations of the transmission of light stimuli in
the seedlings of Avena. These Proceedings, Vol. XIV, p. 327.

2) H Ritter von Gurtenserc. Ueber akropetale Reizleiting. Jhrb. f. wis. Bot.
Bd. 52 p. 333. 1913.

5) W.H. Arisz. Untersuchungen über den Phototropismus. Rec. d trav. bot.
Néerlandais. Vol. XII p. 44. 1915.

162

TENBERG stated however, that the curvature in the third set was
smaller than in the other two, and explained this discrepancy by
assuming a propagation of the basal curvature to the tip. In my
opinion it might have its cause in the circumstance, that these
seedlings were already slightly curved at the moment of the after-
illumination. If this had been the case, the tip would have received
here a smaller quantity of light and this moreover partly under a
less favourable angle than in the other sets, and consequently, the
phototropic curvature would not have attained the same value. It
should also be mentioned, that a repetition of these experiments by
Arisz (le. p. 105) gave only doubtful results, the sources of error
being very great. In any case, we dare not say, that the acropetal
propagation of the basal curvature has been demonstrated, and for
the solution of the question, whether an exposition of the basal
part exercises any influence on the curvability of the tip, the
experiments are not suitable, the intensity of the light being too
weak.

Nevertheless, there are in the paper of GUTTENBERG a few indi-
cations, which seem to show that the illumination of the basal part
influences the curvability of the tip, in the way described by: van
perk Work. On p. 341 one may read: “Kin deutlicher Unter-
schied zwischen den Kriimmungswinkeln der beiden Serien war dabei
nicht zu konstatieren; doch verhielten sich die allseits vorbeleuchte-
ten Pflanzen zunächst etwas anders als die verdunkelten. Bei ersteren
erfährt nämlich das oberste Drittel der Koleoptile eine etwas
stärkere Kriimmung als bei letzteren. dafür ist aber bei diesen die
Kriimmung bereits weiter nach unten fortgeschritten”. That these
differences were only very small (further data le. p. 437) and quan-
titatively very different from those observed by van per Work, may
find its explanation, as I have pointed out-already, in the feeble
intensity of GUrTENBERG’s illumination.

Arisz mentions (l.e. p. 103), that he has repeated the experiments
of van DER Work, and deseribes his results in this way: ,,Wohl ist
in vielen Fallen eine kleine Vergrésserung der Spitzenkriimmung
beobachtet worden, welche auch etwas früher sichtbar wurde,
aber so eklatant, wie vaN DER Work seine Resultate beschreibt, war
es nicht”. Arisz therefore does not deny, that the illumination of
the basal part enhances the curvability of the tip; only he awards
this influence less importance than vaN DER Work does.

Summing up, we may state that our knowledge of the influence
which an exposition of the basal part exercises on the tip, is far
from complete. Moreover, it cannot be said that the available data

163

are very valuable for our supposition, that the antiphototropie cur-
vatures of Avena might find their explanation in this way.

In the experiments of Arisz (le. p. 97), the exposition of the
basal part gave a normal curvature’), which did not extend itself
beyond the limits of the part exposed. As the occurrence of an
antiphototropie curvature in the tip is never mentioned, we must
assume that under the circumstances of these experiments, the tip
remained perfectly straight. At first sight, this seems to clash with
our supposition, but we should remember, that in these experiments
the tip remained continually in the dark, so that its turgescence
underwent no decrease. Now in consequence of this circumstance,
an increase of the rate of growth might be difficult or even im-
possible.

In my own experiments I compared in the first place the reaction
of coleoptiles exposed at the tip only, with the reaction of coleo-
ptiles exposed in the whole of their length. The result was very
clear. Whereas in the first case antitropic curvatures were never
found, in the second case they could be obtained without difficulty.

The etiolated seedlings used for these experiments, were planted
in a single row in oblong zine boxes. Each box got about 15 seed-
lings, so orientated, that their plane of symmetry was parallel to
the small side of the box. During the exposition, the boxes were
placed perpendicular to the rays of light. The seedlings that should
be exposed at the tip only, stood with their basal part behind a
screen, so that only 24—3 mm. of the tip protruded. This screen
was prepared in the following way. A feeble red light was placed
just in front of the experimental lamp, and the silhouette of the
coleoptiles caught on a piece of black paste-board standing just
behind them. The place of the tip was marked thereon with the
aid of a pencil. Above these marks the paste-board was cut away
and then the screen pushed 2'/,—3 mm. deeper in the earth. After
that the box was turned round and the red light removed. During
the illumination with the experimental Jamp, in this way just 2°/,—
3 mm. of the tip was exposed.

The intensity of the illumination was in all experiments 750 MC;

1) In two experiments out of a very great number, Arisz mentions to have
obtained antitropic curvatures in the part exposed. In one case (illumination during
1 minute with 330 MC), the curvatures are stated to have been feebly normal or
antitropic, in the other ease (illumination during 1 minute with 200 MC), they
were antitropic or absent. As these cases, however, stand wholly isolated among
the rest of his results, it seems probable that these antitropic curvatures are due
to some experimental error.

164

the exposition-time 12, 15, 18 and 21 seconds. The temperature
varied between 15° and 20° C., but in each series of experiments
it remained nearly constant. After the illumination the boxes came
on the clinostat.

With an exposition of 12 seconds (light-quantity 9000 MCS), after
3'/, hours the coleoptiles exposed in the whole of their length,
were feebly antitropic (S-shaped), the coleoptiles exposed at the tip
only, feebly curved in the normal way.

With an exposition of 15 seconds (light-quantity 11250 MCS), the
results were nearly the same.

With an exposition of 18 seconds (light-quantity 13500 MCS),
after 3'/, hours the coleoptiles exposed totally, were clearly antitropic
(feebly S-shaped), the coleoptiles exposed at the tip only, nearly
straight.

With an exposition of 21 seconds (light-quantity 15750 MCS),
after 3'/, hours the coleoptiles were all nearly straight.

The experiment with the exposition-time of 15 seconds, was
repeated 5 times, always with the same result. That in this case,
the occurrence of an antitropic curvature at the tip of the totally
exposed coleoptiles, is dependant upon the exposition of the basal
part, cannot be doubted.

The results of the experiments wherein the basal part of the coleo-
ptiles was previously exposed to a very strong illumination, and
where, therefore, the unilateral after-illumination of the whole
coleoptile did not give a normal curvature in the basal part, demon-
strate the significance of this influence also clearly.

In these experiments, | compared the result of an unilateral illu-
mination of the whole coleoptile after a twosided exposition of the
basal part, with that of an unilateral illumination of seedlings previ-
ously kept in the dark. During the fore-illumination two screens
of the same shape were used, one in front of the coleoptiles, and
one behind them. They were prepared in the same way as those
used in the previous experiments, the only difference being that in
this case, the basal part of the paste-board was for the greater part
cut away. In this way during the illumination, at the tip of the
coleoptiles a piece of 2'/,—3 mm. remained in the dark. The fore-
illumination lasted 60 seconds, and during this time, every 10 seconds
the box was turned round. At the end of the fore-illumination the
box was turned round for the last time, then the screens ware taken
away, and the seedlings once more exposed to the same light. This
time the illumination lasted 12 or 15 seconds. The intensity of the
illumination was always 750 MC. The result of these experiments

165

was, that the coleoptiles, whereof the basal part was previously
exposed, remained straight, whereas the others showed the usual
antiphototropie curvature.

In my former communication I admitted that in coleoptiles previ-
ously submitted to an omnilateral illumination of a definite value,
an antiphototropic curvature might, perhaps, be obtained with the
aid of a rather weak after-illumination. This seems now not very
probable, as under these circumstances, the occurrence of a normal
curvature in the basal part, may hardly be expected. Therefore,
in this case neither of the causes hitherto discovered, by which an
antiphototropic curvature may be produced, is present.

The relative importance of the two causes is as yet wholly un-
known, but that the cause discussed in this paper, must be very
efficient, follows from the experiments described in my former com-
munication (le. p. 182). The antiphototropic curvatures produced
by an illumination with a given quantity of light, showed but little
difference if the exposition-time varied between 1 and 256 or between
*/, and 192 seconds. Now, as we have seen that with a very short
exposition-time, the presence of the cause discussed in my earlier
work, is wholly excluded, we must conclude that its influence in
the experiments with a longer exposition, was here also rather weak.

S U-M'MA RY.

The antiphototropic curvature which appears at the tip of the
coleoptile of Avena with a very short exposition, does not show
itself, if the illamination is limited to the tip, or if the basal part
has previously been exposed to a rather strong illumination.

Therefore we should assume, that with an unilateral illumination
of the whole coleoptile, the rate of growth of the tip, is enhanced
by an influence proceeding from the basal part. This influence must
be greatest in the side, which underwent the greatest contraction,
that is to say in the side, which during the exposition faced the
lamp. The origin of an antiphototropic curvature of this kind is,
therefore, always connected with the origin of a normal curvature
in the basal part.

Mathematics. — ,, Veber Wirkungsfunktionen”. By Prof. R. Werr-
ZENBÖCK. (Communicated by Prof. L. E. J. Brouwer).

(Communicated at the meeting of May 27, 1922.)

§ 1. Einleitung.

Bei der Ableitung der Feldgesetze und der Erhaltungssätze in der
allgemeinen Relativitätstheorie und deren Erweiterungen steht man
vor folgender Aufgabe: wenn gip und p; die Komponenten eines
Kovarianten Tensors. 2. resp. 1. Stufe sind und

Ogik 0 gik Oy; Opi

i
ku = kep = ie == DE
Jika = De » Gik,uf TOE Oz: > Piz = one » Piag =

(1)
gesetzt wird, so ist aus diesen Funktionen eine absolute Invariante
W wu bilden. Wg wird dann eine relative Differentialinvariante

vom Gewichte eins (=, eine scalare Dichte) und

eas woa || fw va ae, de,de,de,. . (2)

wird eine absolute Integralinvariante.
Man nennt Y die Wirkungsfunktion. Bedeutet d eine Variation
der gip und g;, so gibt die Gleichung

Oa, Vag

af dr = (hin allecd gi nde OE) JI oe Ulan

die Feldgesetze.

Die Frage nach allen Differentialinvarianten zweiter Ordnung der
beiden Tensonen giz und p; wird zurückgeführt auf die einfachere
Frage nach allen ganzen, rationalen Differentialinvarianten dieser
Tensoren. Hierauf gibt ein Reduktionssatz von Ricer und Lervi-
‘vita *) die Antwort: man hat alle projektiven Invarianten der
folgenden 5 Tensonen zu suchen:

gik == metrischer Fundamentaltensor

gyi =electromagnetisches Potential

Rix,2g = (Riemann-Christoffel’scher) Kriimmungstensor . (4)
Pia) == erste kovariante Ableitung der p;

Pias — Zweite kovariante Ableitung der p;.

1) Mathem. Ann. 54, (1901), p. 138.

167

Die Frage nach allen projektiven Invarianten dieser Tensoren’
bildet ein sehr kompliziertes algebraïsches Problem. (Nach dem all-
gemeinen Endlichkeitssatz von HirBerr gibt es endlich-viele ganze
rationale Invarianten, durch die sich alle iibrigen ganz und rational
ausdrücken lassen.)

Gliicklicherweise ist hier die Sache nicht so trostlos verwickelt,
indem zwei sehr einschränkende Forderungen gestellt werden: in
der Ernstein’schen Theorie wird verlangt, dass die Feldgesetze Diffe-
rentialgleichungen höchstens zweiter Ordnung werden; in der Theorie
von Wer müssen die aus den Tensoren (4) gebildeten Wirkungs-
funktionen auch masstabsinvariant sein.

Wir behandeln zuerst den zweiten Fall.

§ 2. Die Theorie von Werr.

In der durch Wey. gegebenen Erweiterung der allgemeiner Rela-
tivitätstheorie muss die aus den Tensoren (4) gebildete Wirkungs-
funktion absolut-invariant gegenüber Masstabstransformationen sein.
Diese Transformationen sind gegeben durch

0 log a
Ii = git Pre ae sty tO)

woraus noch entsprechende Gleichungen für R'jz22, p'iay und pins
folgen.

Die Forderung 8’ — (fiir alle 2) erniedrigt dann die Anzahl
5 der Tensoren (4) auf 4 masstabinvariante Tensoren:

Jiu == metrischer Fundamentaltensor (g'i,== À giz) ,

fin = electromagnetisches Feld (f'#=2 Fiz) |
*Fy23—= Richtungskriimmung CP hig A ij) ) . (6)

Kik,« = Fine — (foe pit fia P+ 2fik pa Gai fae p?—guk fig 1) |

B ie == Eire).

Der gegenüber W—=Wi’g etwas allgemeinere Ansatz W—= Wo",
wobei W keinen Faktor g mehr enthält, führt weiters auf die
Gleichung

In, + In, + 3n, =d,
wobei W ganz und rational vom Grade n,‚n‚‚n, in den Ti birde
und iz ist. Daher ist n, =O und für n, und n, bleiben: nur die
drei Möglichkeiten (2,0), (1,1) und (0,2) übrig. Man kann dann be-
weisen *), dass sich unter diesen Annahmen nur die folgenden sechs
Wirkungsfunktionen ergeben :

1) R. WerrzenBöck, Wiener Ber. 129, (1920), p. 683 und p. 697; dito, 180,
(1921), p. 15.
Ki
Proceedings Royal Acad. Amsterdam. Vol. XXV.

168
, = ffe =2 (fia tua tha tas this Sas)
W, = Sik fe Vg

i
Wo EZ *F i im FF
Vg ik Im wi nodniiabreyy

—

= 00,

eS ae + Sig OLN
ik ik,oo

om — (x oe: bi

Se Orgs ( ae al g

QS, = * Fill * Py gn Y q
Hiezu machen wir die folgenden Bemerkungen'). 28, und Y%,
kommen als Wirkingsfunktionen nicht in Betracht, da ihre Variationen
identisch Null geben, wie R. Bacu bewiesen hat’). W, ist die
Maxwerr’sche Wirkingsfunktion, bei Wey mit { bezeichnet*). Auch
Wo = Hg wird von WEYL verwendet.
An Stelle von YW, kann man auch die Invariante

WSE or Sel Wt git eee A oe ata
verwenden; es ist nämlich :
tn - 7%, od es gt es GERNE bac (9)

Die Variationen von %8', und ®, wurden von W. Pavuni‘t) und
R. Bacn’) berechnet.

§ 3. Die Theorie von EINSTEIN.

In der Ernsrein’schen Theorie ist W— Wg und W ist aus den
Tensoren (4) zusammen gesetzt: rational in den giz, ganz und rational
in den iibrigen vier Tensoren.

Variieren wir die gj, allein, so bekommen wir die Gravitations-
gleichungen Wik; die Variation von p; ergibt die verallgemei-
nerten Maxwerr’schen Gleichungen wi==0. Dabei sind diese ,,Tensor-
dichten”’ *) gegeben durch:

we 208 ne ( aw )+ 0? ( ADI ). an

: Ogik O2'y Ogik, a. Oa, dap Ògir.ag bh:

we in gon) + af ( 08 ) (11)
\ Opi. PEA 2 Or. Ore \Ogics/

1) H. Weyr, Phys. Zeitschr., 22, (1921), p. 473.
3) R. Bacu, Mathem. Zeitschr. 9, (1921), p. 124.
5) H Weyu, Raum, Zeit, Materie, 4. Aufl., (1921), p. 268.
4) W. Paurr, Phys. Zeitschr., 20, (1919), p. 457; Verhdl. d. Deutsch. Phys.
Ges. 21, (1919), p. 742.
5) D. Hinpert, Göttinger Nachr. 20. 11. 1915.
R. WerrzenBöck, Wiener Ber. 130, (1921), p. 15.

169

?

Berechnet man diese ,,Variations-Ableitungen” und verlangt man,
dass sie Differentialquotienten von höchstens zweiter Ordnung ent-
halten, so ergeben sich die drei folgenden Möglichkeiten :

A. W enthält die Frog linear, keine pic) und keine pigs):

BAS (te Wigs) Rigter Va Wah. €12)
B. W enthält die gaya) linear, keine Rirse und keine pi»):
Weites Pis Perlin are oe (ES)

C. W enthält keine Ry. und keine yaya):
Een GE 4. Pita hen een ta. Can lan 0 CS)

Wir behandeln diese drei Fälle der Reihe nach. Bei A kann man
zeigen, dass man nur die zwei Invarianten erhält:

ASR ERK EEK ES)
A, ist das von Einstein verwendete R.

Im Falle B haben wir drei Invarianten:

odo

B, ER vof ’ B, ape Bi (a) pi ’ B, — Pia pp pe pe. (16)

Die neben B, noch mögliche Invariante
Be
ist mit Hilfe von B, und A, ausdrückbar:

a Bi =y

a AD)

Komplizierter ist der dritte Fall C. Hier ist die Anzahl der In-
varianten sehr gross: das Aufsuchen aller Invarianten kommt hinaus
auf das Berechnen eines vollen Systems von orthogonalen Invari-
anten einer quaternären Linearform gy; und einer ebensolchen (un-
symmetrischen) Bilinearform pis. Dies ist eine bisher noch ungelöste
Aufgabe. |

Wir führen einige der einfachsten Invarianten vom Typus C an.
Enthält C erstens keine Picoy SO haben wir die einzige Invariante

Oi igg pi PE en en ee ~ (18)

Wenn C die pic) linear enthält, haben wir zwei Invarianten
i rede dior Mio)
EDE) = Vg Da:

Die Wirkungsfunktion C,Vg gibt zu den Feldgesetzen keinen
Beidrag, da C,V’g eine Divergenz ist.

Von den in den p;,) quadratischen Invarianten C nennen wir
nur noch

C. =a. C= (19)

C,=2 (Vie PO — pie) GO) = fir fly. . … « (20)
11*

170

Hier ist fiz das elektromagnetische Feld und C,q_ ist die
Maxwerr’sche Wirkungsfunktion.

Sind f(p) Polynome von p (Vel. (18) mit constanten Koeffi-
zienten, so hat die allgemeinste Wirkungsfunktion die Gestalt
23 == NAC) (PA, +S ADA, t+f(g)B, +H A(PBLAS (DB, a C] Vg (21)
C' bedeutet hier eine ganze rationale Funktion von Invarianten (14).

Von dieser Wirkungsfunktion ausgehend, wären nun die Feld-
gesetze aufzustellen. Dies ist bisher nur für die einfachsten Invari-
anten durchgefübrt worden.

Bacteriology. — ““Studies on the bacteriophagus of D’HererrE”’.
By J. W. Janzen and L. K. Worrr. (Communicated by Prof.
C. Eykman).

(Communicated at the meeting of May 27, 1922).
IV. About the relation between bacteriophagus and resistant bacteria.

D Herenie tells us in his book that, when a weak bacteriophagus
is added to a thick emulsion of bacteria, the former will have
disappeared from the suspension after some time.

Then he says that the bacteriophagus also seems to penetrate into
the bacteria, but that, now that the bacilli eould not increase, the
bacterium resists the bacteriophagus, which is destroyed in vivo.
We have considered it important to study this phenomon carefully
once more; for this we have used some typhoidbacteriophagi, one
resistant and one not resistant typhoidstrain out of our collection.

We have found that the disappearance of the bacteriopliagus as
described by p’Herrerve for thick emulsions also takes place in the
ordinary thin emulsions, this time not of normal but of resistant
bacilli.

We have also found that old non resistant bacilli, which are not
being dissolved by the bacteriophagus in consequence of their age,
do absorb the latter; in this case however, the bacteriophagus only
increases when the bacteria multiplicate and so get young again.

Some of the series of experiments about this subject are as
follows:

Series of experiments I.

Resistant strain. — T 20. Non resistant strain = T Wi.

Determination of the number of bacteriophagus germs by counting
the number of islands (on agarplate).

Bacteriophagus Wi,

Adding equal portions of bacteriophagus Wi to equally turbid
suspension in broth of T 20 and T Wi.

Number of bacteriophagus germs per cM’.

172

| T 20 T Wi.
Directly | (18 milliard) 18 milliard
1/, hour 0.6 a On Ae
3/, hour 2.4 E innumerable

1!/, hours 08 5

24 hours ONZ

A second experiment with T(Sm) instead of T (Wi) offered an
analogous result.

T 20 | T Sm.
Directly (30 milliard) 30 milliard
after '/, hour| 1.7 E 4 -
a Or 1” Z a 100 a
~ 24 hours) 168, innumerable

After a week the number of bacteriophagus germs with the resist-
ant strain was about the same as the number found after 24 hours;
with the non resistant strain it had greatly increased.

We have regularly found the slight increase (in comparison with
the number after */, hour and after */,—1 hour) with the resistant
strain; the explanation seems to us as follows: the resistant strain
also has some weaker descendants which can be dissolved by the
bacteriophagus; hence an increase of the bacteriophagus, which is
now being caught by the stronger brothers.

We can easily succeed in destroying the bacteriophagus by cul-
turing three of four times on broth with new bacilli the mixture
of bacteriophagus-resistant strains in fresh broth.

1. Ist culture of bacteriophagus germs| 60 milliard per cM3

2nd ” ” ” » 24 ” ” »
3rd ” ” ” ” yy 4 ” ” ”
4th ,, > 4 * disappeared?

sth Sy zl * ie disappeared

173

II. Ist culture of bacteriophagus germs | 18 milliard per cM3
2nd ” ” ” 0 02 ” ” ”
3rd ch - A disappeared

Finally an experiment with old non resistant bacilli.
A. 14 days old bacilli Sm in broth.
B. 6 hours old bacilli Sm in broth.

A. B.
Directly (30 milliard) 30 milliard
after '/4, hour4 , 6 pe
AMER Ie en 800
after 2 „32000, Innumerable.

Our typhoid bacilli that are resistant by nature to the bacterio-
phagus do not even lose their resistance after being subeultured
repeatedly in contradistinction to what p’Hererre tells us in his
book (pag. 67) about the bacilli, who are been made resistant by
influence of the bacteriophagus.

V. About big and small islands.

O. Bam and T. WaranaBE have said that, in plating a mixture
of bacteriophagus and bacteriacultures on agarplates, the islands are
not always equally big, but that sometimes big ones, medium ones
and small ones are to be found.

They have tried to cultivate the bacteriophagus of these islands
purely; they say that they have succeeded in doing this with the
small islands, not with the big ones however.

We too had already been struck by this before Barr’s communi-
cation reached us, and we have tried to isolate these bacteriophagi,
forming big and small islands, from each other, but we did not
succeed. We have stated though, that it could not be possible in
our cases, as a bacteriophagus which exclusively formed big islands
with regard to one typhoidstrain, made nothing but small islands
with regard to another typhoidstrain, and as to a third, both big
and small ones. So we do not believe that Bam’s and WATANABE’s
explanation is right, but we think the difference in size of the

174

islands must be attributed to a difference of virulence as to the
various strains. Big islands point to a strong effect with regard to
the typhoidstrain; small ones to a weaker effect. This has also been
proved by a still to be published investigation of Dr. Krorpverp in
our laboratory, about staphylococci-bacteriophagi.

Bacteriophagus Wi always gives both big and small islands with
regard to T Wi.

Small and big islands are cultured over separatly 9 times, small
islands always being used for the series of small ones, big islands
for the series of big ones in this process.

The last culture of both always gave a mixture of big and small
islands again.

Finally we have tried’ both bacteriophagi Wi big *® and Wi
small *® as to 4 typhoidstrains.

With both bacteriophagusstrains we got exactly the same result
which is only following once.

1. Clearing. 2. Checking. 3. Islandformation.

Typhoid 9 +++-+ ++-+-++ ane big islands.
U b+ Ht ++++ big islands.
see 2 — ze JHH very small islands.

Wiee shoe AH big and small islands.

Laboratorium of Hygiene.
Amsterdam, May 1922.

Chemistry. — “The Biscoumaric Acids’. By A. W. K. pr Jone.
(Communicated at the meeting of May 27, 1922).

Some time ago’) | communicated that the product of illumination
of coumarin is not identical with hydrodicoumarin of Firria and
Dyson, as CLAMICIAN and StrBeR had thought, but that it must have
another structure, because when treated with alkalis it does not
give a mono-basic, but a di-basic acid.

It is natural to suppose that the produet of illumination of coumarin
is formed from coumarin in the same way as a@- and g-truxillie
acid are formed from the forms of normal cinnamic acid by the
combination with formation of a tetramethylene ring between the
doubly bound C-atoms of the two molecules.

As two molecules of normal cinnamic acid can combine in four
different ways to a truxillie acid’) also the combination of two
molecules of coumarin will give four different biscoumarins, which
will, vas the truxillie acids, belong to two series according to the
arrangement of the C-atoms with unequal (1) or equal (Il) atom-
groups next to each other in the tetramethylene ring.

Of both structural formulae two different biscoumarins can exist
according to the situation of the coumarinrings on different sides or
on the same side of the tetramethylene ring.

1) These proceedings Vol. XX, 875.
2) These proceedings Vol. XX, 590.

176

To the product of illumination of coumarin one of these four
structural formulae must be assigned.

Also another biscoumarin is known, obtained by Knut T. Srröm ')
by boiling biscoumarie acid, formed by illumination of coumaric
acid, with anhydrous acetic acid. This biscoumarin is, as Strom
already communicated, different from the biscoumarin obtained by
illumination of coumarin, nor is it identical with the hydrodicou-
marin of Firrig and Dyson.

The biscoumaric acid of Strém is formed from coumaric acid, of
which no metastable forms are known till now, in a conformable
way as a-truxillie acid of @-normal cinnamie acid, and therefore it
is very likely that this biscoumaric acid will have a conformable
structure to a-truxilliec acid. The properties of this biscoumaric acid
known at present are in agreement with this, as will be shown.

The biscoumarin of Srröm would then possess the structual
formula I, the coumarin-rings being situated on different sides of
the ring.

To distinguish the different biscoumaric acids I propose to give
to these acids similar names as to the truxillie acids, and then the
biscoumaric acid of SrrÖM must be called a-biscoumaric acid, and
its biscoumarin a-biscoumarin. The melting- at the same time
decomposition-points of the two substances are the same, viz.
318° (Srröm stated them to be above 275°); a-biscoumaric acid also
changes into its biscoumarin when heated to 250°. The biscoumarin
obtained by illumination of coumarin might be different from a-bis-
coumarin by the position of its coumarin-rings situated, on the
same side of the tetramethylene-ring or it might be one of the two
other possible biscoumarins indicated by figure II. The first sup-
position was not very likely, the two biscoumarins showing no
change when heated at 210° with the acetic acid anhydride, whilst,
when they had. only a difference in the situation of the coumarin-
rings with respect to the tetramethylene-ring, a change of one into
the other was probable. This experiment is, however, not a con-
clusive proof of a different binding of the coumarin-molecules in
the biscoumarins. The best way to decide this is to prepare the acid
of the biscoumarin, converting it to the dimethylether, and to try if
through heating with the acetic acid anhydride at 210° an anhy-
dride is formed which gives a dimethylether of another biscoumaric
acid. If the two coumarin-rings are situated on the same side of
the tetramethylene ring, no other biscoumaric acid is formed, whilst -

1) Ber. 37, 1883.

ti

when they are on different sides, a new biscoumaric acid will be
obtained.

The methylation of «-biscoumaric acid by dimethylsulfate gives the
dimethylester of the dimethylether crystallized into needles, melting
at 133° and sparingly soluble in ether. On boiling with alkalis
the dimethylether was obtained melting at 261°—262°. BERTRAM
and Kirsten') found the melting point of this substance, obtained
by illumination of the methylether of coumaric acid, to be
260—262°.

When the dimethylether is heated with the acetic acid anhydride
at 210°, the anhydride of the dimethylether of y-biscoumaric acid
was formed, which crystallized in pretty large bright yellow crystals
out of the anhydride of acetic acid, melting at 186°-—187°. The
dimethylether itself was obtained in fine needles melting at 234°.

When the a-biscoumaric acid is heated with KOH the acid corre-
sponding to 8 cocaic acid was obtained, which separated in an
ether solution by addition of petrolether in rhomb-shaped crystals
melting 212°. As it whould be strange to give this acid a name
connected with coca, | propose to call it ¢-biscoumarie acid. With
a similar treatment also the dimethylether of a-biscumaric acid gave
the same acid, which shows that the methylgroups are split off
through melting with KOH.

These transformations of the a-biscoumaric acid, respectively the
dimethylether, are wholly analogous to these of a-truxillie acid.

The dimethylester of the dimethylether of the biscoumaric acid
of the product of illumination of coumarin, for which I propose
the name of À-biscoumaric acid, melts at 112°—113°; the dimethyl-
ether itself at 134°.

By heating the dimethylether with acetic acid anhydride at 210°
and after evaporating the solvent in a glycerine bath at about 130°
a brown sirup was obtained, which did not crystallize. The acid
obtained by boiling the sirup with alkali crystallizes out of an ether-
petrolether solution in fine needles melting at 203°: On account of
its resemblance in structure with ¢ truxillie acid [ propose to call
this substance the dimethylether of ¢ biscoumarie acid. This trans-
formation proves that the coumarin-rings of the illumination product
are situated on different sides of the tetramethylene ring and as
also a-biscoumarin possesses the same situation of the coumarin-
rings and the two substances are different, 4-biscoumarin must have
the structure of fig. If and by the removing of a carboxylgroup

1) Journ. f. pr. Ch. (2) 51, 328.

178

from one side of the tetramethylene ring to another an o-dioxy-e-
truxillie acid is formed.

By melting with KOH 2-biscoumaric acid is converted into
d-biscoumaric acid, crystallizing in needles melting at 157°.

I hope to make further communications on other possible trans-
formations of the biscoumaric acids, while it will also be tried to
obtain them from the truxillie acids, by which the proposed names
and the structural formulae will obtain more security.

Laboratory of the Colonial Museum, Haarlem.

Physics. — “On the Excitation and Ionization Potentials of Neon and
Argon’. By G. Hertz. (Communicated by Prof. P. Eurenrsst).

(Communicated at the meeting of May 27, 1922).

_ lt is known that rare gases and metallic vapours behave in a
very simple way on collision with slow electrons. Then there can
be, exchange of energy between electrons and atóms only in one
way, viz. that in which the transferred energy is used to bring the
colliding atom into a higher quantum condition. Hence on collision
with the atoms the electrons can transfer only very definite energy
quanta to them, which according to Bonr’s theory, are in direct
connection with the series-spectrum of the atom. For a great many
metallic vapours this transition of energy in quanta has already
been investigated and the relation to the optie spectra has been
shown. Of the rare gases accurate measurements have only been
carried out for helium *), on the ground of which Franck succeeded
in making the system of the series-spectra of helium complete, and
in showing the connection between the. ortho-helium and the par-
helium spectrum. Several observations have, indeed, been made for
neon and argon’), but the results are inaccurate for the greater
part, and partly in conflict with each other. Besides in the great
sensitiveness of noble gases to traces of impurities, the excitation
and ionization potentials of which lie nearly always below that of
the rare gas, the cause of these conflicting results seems to lie
chiefly in this that the efficiency of the unelastic collisions in the rare
gases is much smaller than in the metallic vapours, so that the
methods which lead to good results for the latter, cannot be applied
here. In order to attain reliable results, it seemed, therefore, neces-
sary to me, to refine the methods for the investigation of the quantum

1) F. Horton and A. C. Davies, Proc. Roy. Soc. London (A) 95, 408, 1919.
“J. Franck and P. Kyippina, Zeitschr. f. Physik, 1, 320, 1920.

K. T. Compton, Phil. Mag. 40, 553, 1920.
72) EF. Horton and A. C. Davins, Proc. Roy. Soc. London, (A), 97, 1, 1920-and
98, 124, 1920.

G. STEAD and P. S. Gosring, Phil. Mag. 40, 413, 1920.
_H. C. Renrscuuer, Phys. Rev. 14, 503, 1913.
~G. Désarpin, C.R. 172, 1847, 1921.

180

transition of energy between electrons and atoms, and supplement
it by a method which admits of a clear distinction between light
emission and ionization also in the case of unelastic collisions of
small efficiency.

The methods applied up to now for the study of the quantum emis-
sion of energy consist in this that either the radiation or ionization
that take place starting from a definite potential, or the phenomenon
that the impinging electrons lose energy, is used as a proof of the
occurrence of unelastic collisions. In this way a curve is obtained
in which the different steps of energy appear as breaks; an accurate
measurement of them is often difficult, especially for the higher
steps of energy. It seemed, therefore, desirable to me to use as
criterion for the quantum transition of energy a characteristic that
immediately disappears again when the critical potential is exceeded,
and consequently causes the separate steps of energy to stand forth
as sharp maxima. Such a characteristic is the occurrence of electrons
with the velocity zero. For as soon as an electron possesses exactly
the energy required for the excitation of a definite quantum transition,
it may lose all its energy at the collision, and be left behind as
an electron with the velocity zero. If, however, it possesses a greater
energy, it retains the rest after the collision, and remains behind as
an electron with a velocity which, though smaller, is yet different
from zero. If, therefore, electrons of a definite velocity, are admitted
into a space in which they collide with atoms of a noble gas,
electrons of the velocity zero will only occur when the energy of
the electrons is precisely equal to the work required for the excitation
of a quantum transition. When, therefore, the number of electrons
which are left behind with the velocity zero, is plotted as function
of the accelerating potential, a sharp maximum must be obtained for
every potential corresponding with an energy-quantum that can be
transferred at a collision of electrons. In consequence of the inevitable
distribution of velocity of the electrons it is not possible to determine
the number of electrons which have rigorously a velocity zero.
Therefore the number of those electrons the velocity of which lies
below a definite small value (in our measurements mostly 0.2 Volt)
~ will be plotted as function of the tension.

The measurements according to this principle are carried out in
the following way :

The electrons emitted by a short incandescent wire D of tungsten
(Fig. 1) enter the field-free space A through the gauze JN, after
acceleration through an electric field, in which space they collide
with the atoms of a rare gas. Part of the electrons passes through

181

the cylindrical gauze. NV, after numerous collisions; opposite this

cm gauze a receiving plate has been adjusted,

Polina? “Tonle also cylindrical. (The cylindrical arrange-
| 5 ment of N, and P appeared to be prefer-
i! |, able, though good results were also ob-
| R N, P | tained with an apparatus with two parallel
pieces of gauze and a plane receiving plate).
| 2 When between V, and Pa small retarding
‚ potential is applied, all the electrons, the
N, | : velocity of which corresponds to smaller
D potentials, are held back. A certain part

| of the faster electrons will likewise be

Pig. 1. retained by the weak counter-field, but

as appears on closer consideration, this part greatly decreases with
increasing velocity. The difference between the stream of electrons
received on the plate with and without the small counterfield,
therefore, gives a measure for the number of electrons having about
the velocity zero. In order to be able to measure this difference with
great accuracy, an arrangement was chosen which rendered it
_ possible to insert and cut out the field alternately; the part of the
potentiometer from which the small counter-potential had been branched
off, could be short-circuited by a mercury contact in vacuum. By
alternate reading of the deviation with and without counterfield the
difference could be accurately read, and an error in consequence
of a possible change of the zero-point was out of the question. It is
further possible to render oneself independent of a slow change in
the emission of electrons of the incandescent wire, by dividing the
difference measured by the total deviation. For the efficiency of the
method it is of importance that the metal surfaces should have the
greatest purity possible, as small impurities can already cause Volta-
potential differences of the order of magnitude of the small counter
potential. The copper used had been cauterized with nitric acid
immediately before the construction and the sealing in of the apparatus.
The whole apparatus was mounted on a pretty large glass foot, as
is used for incandescent lamps, so that it could be fused into a
glass globe without the metal parts being heated too much. It was
heated at 400° in high vacuum for six hours; after this the copper,
even though it was a little tarnished before in a few places, presented
a perfectly pure metallic surface.

In figures 2 to 4 curves are represented as instances of the results
of such measurements, which refer to neon of a pressure of
0,51 m.m., to a neon-helium mixture of 30°/, helium and a pressure

182

of 0,56 m.m. and argon of 0,36 m.m. pressure. Especially fig. 3
shows the efficiency of the method. In spite of the comparatively
small percentage of helium, the two first excitation tensions of
helium, though they lie above the strong excitation tensions of neon,

10 - =

8

6r

“

2 | = jn el

pier ds L [Volt]

4 6 18 20 22

Fig. 2. Fig. 3.

stand out as two sharp maxima at a distance of 0,8 Volt. These
maxima were used to obtain the absolute value of the excitation
tensions of neon, in which the value of 20,45 Volts measured by
Franck and Kwyrppinc') for the lowest excitation tension of helium,
was used as basis. The values thus obtained appeared to be inde-
pendent to a high degree of the circumstances of the experiment.

This method is entirely unsuitable for the measurement of the
ionization-potential. For then the impinging electron or the electron
that has been liberated from the atom by the collision can have
the velocity zero after an ionizing collision, also when the energy
of the colliding electron was greater than the work of ionization.
As moreover at first the effect brought about by ionizing collision
evidently rapidly increases with increasing tension, the curve shows
no maximum here, but only a rise, which is besides influenced by
the positive ions, and does not admit an accurate determination of
the ionization-potential. For this reason the arrangement usual
with a strong counter-field between MN, and P was used for the
measurement of the tension of ionisation for some measurements ;
most observations were, however, made according to anew method,

1) J. FRANcK and P. KNiPPiNg, l.c.

183

in which a very reliable criterion is applied for the first appearance
of the ionization. For this purpose a second, very thin incandescent
wire G of the shape represented in Fig. 5 was placed in the field-

Cm
5

4 | !
' ! 3

G :
Nailp Fe

2 - Ee a P| 1 1
| Wam nnn | 4

be
Js
i
CS
b=]
o

10 pale Ti Wk

Fig. 4. Fig. 5.

free space A; the positive end of this wire (on the left side of the
figure) was connected with the walls of A, so that the field round
the wire, which moreover remains restricted to its immediate neigh-
bourhood on account of the. slight thickness of the wire, can by no
means accelerate the electrons coming from D. This incandescent
wire was heated to such a temperature that the stream of electrons
flowing from the wire to the metal wall, is limited by the space
charge. So long as the energy of the electrons coming from D is
not sufficient for the formation of positive ions, they have no in-
fluence at all on the amonnt of the stream of electrons issuing from
G. Nor could a photo-electric effect, if it took place, even apart
from the fact that it is so small, have any influence on the amount
of this stream of electrons, limited by the space charge. As soon,
however, as positive ions are formed, and some of them get into
the neighbourhood of G, the space charge is partly annihilated, and
the stream starting from G suddenly rises. Figures 6 and 7 show
the results of these measurements in neon and argon. It is seen that
not even the slightest discontinuity can be perceived in the curve
when the lower excitation tensions are passed, while at the tension
of ionisation the stream begins to rise rapidly. To obtain the absolute
value of the ionization potential, the maximum corresponding to the
first excitation potential was determined at the same time by the aid
12
Proceedings Royal Acad. Amsterdam. Vol. XXV.

184

of N, and P according to the method discussed above, which is

2

likewise expressed in the figures. In this it should be taken into

Fig. 6.

account that this maximum slightly differs with respect to the
tension at which unelastie collisions take place, viz. the amount
equal to the small counter-potential (here 0,2 Volt). It may also be
mentioned that the measured stream in these experiments was about

Fig. 7.

thirty times the flow of electrons issuing from D, so that in this
way an accurate measurement of the ionization potential is possible,
even with an ordinary millivoltmeter.

185

Results. Starting from the value of 20,45 Volts for the lowest
excitation potential of helium, two rather pronounced excitation
potentials were found for neon at 17,35 and 19,15 Volts, 22,2 Volts
was found for the ionization-potential of neon; for argon two excita-
tion potentials were found at 12,25 and 13,7 Volts, a less distinct
one at 14,7 Volts; the ionization-potential at 16,0 Volts.

With the very complicated structure of the optical spectrum of
neon the occurrence of discrete fairly pronounced excitation potentials
seems surprising at first sight. If, however, the serial scheme of
neon drawn up by Pascuen') (fig. 8) is plotted in a scheme in the
way given by Bonr, it is directly seen that the values found are
in very good harmony with the optical measurement. The term

100.070

|| 135s, lass, 22.2 Volt
Il} 135s2 lisse 055
IIL Isss, JO ee (7,35Nele
IL Isssa lissa
IL Iasse hisss
II sp, lap,
IL Ispe laps eid
IL sp, laps
II lap. lapa
Il t3ps la,
IL 1 Lape laps
ILL lap, lap,
UREN laps
IL Lap, las,
ILL Iapg lane
i [ee SEE
III Isa,
len tea
Hille Tia
TEMES fsa
it | laas
|
i
Fig. 8.

corresponding with the normal state and denoted by me as 0,5s
has been added in the scheme, the value of this term has been
calculated from the ionization-potential. This term 0.5 s is first of
all followed by a group of four terms of the type of 1.55; these
lie close together within a region which, expressed in Volts, is
smaller than 0,2 Volt., and can, therefore, not be separated in
measurements with colliding electrons. Then follows a group of 2 p
terms, the greater part of which lies again within 0.1 Volt. After
this come, about 1 Volt higher, the 3d terms. The other terms
succeed each other at distances of at most some hundredths of Volts,

1) F. PASCHEN, Ann. d. Phys. 60, 405, 1919.
12*

186

so that the methods of the collisions of electrons is not sufficient to
separate them, only a “continuous spectrum” can be observed. When
the curve given in fig. 3 is compared with this, the serial system
is clearly found back in it. The first maximum corresponds to the
group of the quantum transitions 0.5 s—1,5s, the second to the group
0.5s—2p, and then at a distance of 1 Volt follows the spectrum
of the transitions to higher quantum conditions, which seems conti-
nuous on account of the small dissolving power. Also quantitative
the agreement is good, as is seen in fig. 8, where the quantum tran-
sitions observed with collisions of electrons have been indicated by
arrows, of which the projection on the axis of abscissae is equal to
the observed value of the potentials of excitation resp. ionization.
It is, therefore, seen that the serial scheme of neon has become
complete by the addition of the term 0.5s = 179800 + 1000.
There is no room in this serial system for a resonance-potential
of 11.8 Volts and ionization-potentials at 16.7 and 20 Volts, which
values were derived by Horton and Davies *) from their experiments,
nor was there any indication at all in my measurements of the
occurrence of resonance or ionisation at these potentials. On the other
hand the experiments of the same investigators on excitation of
light in neon through collision of electrons *) are in good agreement
with the conclusions which may be derived from the completed
scheme. As can at once be read from the figure, the lines of the
principal series must first appear alone starting from 19.2 Volts,
then from about 20.2 Volts the lines of the secondary series must
gradually begin to make their appearance, while the whole spectrum
only can be emitted above the ionization-potential. Horton and
Davies actually found that at 20 Volts only the lines of the principal
series were emitted, the whole spectrum not appearing before 22.8 Volts.

It would be of importance to ascertain whether there may perhaps
be terms for neon that correspond to metastable states, as Franck
has found them for helium and mercury ®). To find this out it would,
however, be necessary really to separate the different terms, and
for this the dissolving power of the method of the collisions of the
electrons is not yet sufficient. Measurements with the usual arrange-
ment for showing photo-electric radiation proved, as was to be
expected, the occurrence of photo-electrically active radiation at
both the excitation potentials observed.

As was already stated above, in argon there likewise appear two

1) F. Horton and A. C. Davies, l.c.
2) F. Horton and A. C. Davies, Phil. Mag. 41, 921, 1921.
3) J. Franck, Phys. Zeitschr. 22, 388, 1921.

187

excitation potentials (at 12.25 and 13.7 Volts), and a less distinct one
at 14.7 Volts, which is followed by a series of energy steps which
has not yet been dissolved. Here too the apparently sharp excitation
potentials will no doubt correspond with undissolved groups of terms
lying close together, on account of the complication of the argon
spectrum. The argon spectrum not yet having been split up into
series, a comparison is not vet possible. When a similar structure
is assumed for the speetrum of argon as for neon, then starting
from the measured values for excitation and ionization potentials,
the following mean values for the first groups of terms are to be
expected :

0.5 s = 130000 += 1000
1.5 s — 30400
2 p — 18600
higher terms < 10500

The serial terms calculated by Nissen *) do not fit in with this
scheme. Also the fact that according to Nissen lines of the red and
the blue argon spectra are considered as members of the same
series, though the condition for the excitation of the two spectra
are different, pleads in my opinion against the validity of the terms
calculated by him.

For the rest more complications may possibly be expected for
argon than for neon. The fact found by Pascuen’) that for part of
the neon series the limits are shifted by a constant amount in
comparison with the other series, was explained by Grorrian *) by
the aid of the L-doublet of neon. He has also already pointed out
that it must be expected for argon thad the multiple M-limits will
manifest themselves in an analogous way.

Physical Laboratory of the “N.V. Philips
Gloeilampenfabrieken’’.

(Philips Incandescent Lamp Works).
Eindhoven.

1) K. A. Nissen, Phys. Zeitschr. 21, 25, 1920.
3) F. PAscHEN, Ann. d. Phys. 63, 201, 1920.
3) W. GROTRIAN, Zeitschr. f. Phys. 8, 116, 1921.

Microbiology. “On the Occurrence of Sulphate-reduction in the
deeper layers of the Earth’. By C. A. H. von Worzocen
Könr. (Communicated by Prof. G. van Iverson JR).

(Communicated at the meeting of April 29, 1922).

§ 1. Introduction.

The disappearance of organic matter at greater depths in the soil
has since long occupied the minds of investigators. The difficulties
associated with their inquiries regard especially that of obtaining
sterile samples from such depths, which is essential to microbiolo-
gieal inquiry.

The process of oxidation, which causes organic matter to disappear,
can be effected by free as well as by combined oxygen. When the
air is shut off, as is the case in the lower strata, oxidation is of
course brought about by combined oxygen.

Now the question is how this process can take place microbio-
logically.

The term sulphate-reduction designates the process by which,
with the exclusion of air, organic matter in the soil is oxidized
under the influence of combined sulphate-oxygen. This anaerobic
process is effected by Microspira desulfuricans, discovered in 1895
by BeiJERINCK *). It being an exothermic process energy is set free
through this oxidation, which is utilized physiologically by the
sulphate reducing spirilla. The rough equation for sulphate-reduction
gives the following formula:

2C...+ CaSO, + H,O CaO, + CO, + HS,
in whieh C... is the symbol for the source of carbon.

Microspira desulfuricans occurs in the mud of ditches and the
ooze of the Dutch “Wadden”. The grey, bluish-black to black colour
of the soils in which sulphate-reduction takes place, must be ascribed
to ferric sulphid, in which form the liberated hydrogen sulphid is
combined by iron-compounds present in the soil.

The occurrence of the sulphate-reducing microbe at the greater
depths in the terrestrial soil has been less frequently observed and,

1) Ueber Spirillum desulfuricans als Ursache von Sulfatreduktion. Verzamelde
Geschriften. 3de deel, pg. 102.

189

to my knowledge, statements about it are few and far between.
JunTzscH’) e.g. records that in the deeper ooze-layers of the ocean
of about 40 m. and more, reduction-processes occur, in which hydro-
gen sulphid and ferric sulpbid are formed, which are ascribed by
him to decomposition of proteins. It is more likely, however, that
here also we have to do with sulphate-reduction, since it has been
proved that this is of frequent occurrence under the circumstances
alluded to.

Another statement is given by Eve. Dougpors °®) who observed the
transformation of sulphate into ferric sulphid in the lower alluvial
clay-layers underneath the Dutch Dunes.

An opportunity to ascertain the occurrence of sulphate reduction
in deeper layers was offered, when in the autumn of 1921 a number
of new wells were dug along the Sprenkelkanaal on the source of
supply of the Amsterdam Dune Waterworks.

§ 2. How the samples of sand, clay and peat were obtained
from the well-shafts.

In connection with the bacteriological sampling it will be well to
set forth, in principle, the way in which the new wells were sunk.

A wide iron tube is driven vertically into a dug, shallow cavity.
The sand is excavated from a greater depth than is at first reached
by the tube, which can consequently sink gradually deeper. By
means of a screw-thread one length of tube is screwed on to the
other, so that a system of tubes is procured of the length necessary
to reach a certain depth.

The masses of sand and the occasional lumps of clay and peat
are removed from the tubes with a so-called ““puls’”’, consisting of
a hollow iron cylinder of smaller diameter than the tube’s. At the
lower end it is sharp-edged to facilitate the sinking, while the bottom
is provided with a valve, opening to the inside. By means of two
iron bars that are fastened to the edge of the open top-part of the
cylinder and are suspended on the same point of support, it is
possible to connect the apparatus to a pulley-block. When moving
the “puls” foreibly up and down in the wet mass of sand present
in the shaft, it is ultimately filled with a pap of sand. The filled
“puls” is then hoisted up and emptied by overturning it. This process
of removing the sand from the well-shaft is briefly called “pulsen”.

1) Zeitschrift d. Geol. Ges. 1902. 54, p. 144. Cf. Ramann, Bodenkunde, p. 180.
2) Het Leidsche Duinwater. Eene hydrologische studie. 1912, p. 19 en 20.

190

§ 3. The examination of the sand- and clay-samples for
sulphate-reduction.

From a chemico-biological point of view it is interesting to
ascertain the origin of the ferric sulphid, which gives a dull-grey,
greyish blue to blnish-black colour to the soil-samples. The obvious
hypothesis that the ferric sulphid was formed by sulphate-reduction,
was in every respect substantiated by the examination of the many
sand-, and clay-samples procured by means of the “puls”. Thus the
sulphate reduction in the deeper layers of the earth underneath the
dunes appeared to be a bacteriological process of common occurrence.

The demonstration of sulphate reducing spirilla was performed
after the accumulation-method of Beijerinck, the culture-medium *)
used veing:

Fapwaterts abel hace dl 00

Na-laetate” 2.02 zen 0.5

ASPATAGINI ix, eid ate) 0.1

MSO: ZM AUKE ek alte 0.05 (or gypsum)
Fes, Trader <4 the 0.001

with which sterile stoppered bottles of + 150 cc. capacity were
filled after infection with a quantity of the sand-, or clay-samples
under examination. They were filled up to the neck, then cautiously
stoppered and placed under 25° C.

BeigeRINCK?) showed that in this anaerobic procedure Microspira
desulfuricans is exclusively the causative agent of the sulphate-
reduction manifesting itself, as appears from the formation of hydro-
gen sulphid and the black ferric sulphid.

My culture bottles showed in every respect the same progress
of the reduction process, so that hereby the examined sand-, and
clay-samples gave evidence of the presence of Microspira desulfuricans.

The material used for infection of the medium was drawn from
the inner portion of the sand-mass in the ‘“puls” by means of a
sterile spatula, and deposited in sterile wide-mouthed stoppered
bottles. Directly when the samples were received at the laboratory
they were subjected to investigation.

Sterile sampling could be effected to perfection only in clay-, and
peat-samples. This was performed after BrijerINCK’s®) method. The
sample was split in two. From the fracture laid bare, the required

1) A. van DELDEN. Beitrage z. Kenntn. d. Sulfaatreduktion durch Bakt. Centralbl.
f. Bakt. 2e Abt. 1903. Bd. XI, p. 83.

2) Verzamelde Geschriften. (Collected Papers) Vol. 4, p. 53.

5) Verzamelde Geschriften. (Collected Papers) Vol. 2, p 354. Note 2.

)

191

inoculation material was taken by means of a sterile spatula. The
lumps of clay and peat suited our purpose well, since in the splitting
the fracture was not contaminated by crumbling particles of the
edges, which was owing to the solid structure of the sam ples
resulting from their humidity.

The time in which the formation of hydrogen sulphid in the
culture-bottles commenced was very different for the same inoculation-
substance and especially for the sulphate reduction it largely depends
on the number of viable germs present at the outset of the experiment.

The clay-, and the peat-samples dredged up with the puls:
were derived from the clay-, and the peat-banks underlying the
dunes. They were all compact masses, in which the original stratified
structure, arising from sedimentation, had been preserved. These
clay-, and peat-layers being all but impermeable to water, their
inside represents the original bacteriological condition of the stratum,
from which the sample has been taken.

The clay- and peat-lumps were on the outside wet and on the
inside, judging superficially at least, moderately humid. The water-
content of the clay amounted to about 26°/,; in the clay-samples
which contained peat in the stratified structure, the content of
moisture was considerably higher, viz. about 50°/,. The peat-samples
exhibited the largest amount of water, viz. rather more than 77°/,.

The clay- and the peat-lumps varied from very large ones to
those of the size of a fist and appeared to meet the bacteriological
requirements in every respect.

§ 4. Summary of results and observations on the inquiry about
sulphate-reduction.

The number of soil-samples of the 9 wells which were examined
for sulphate-reduction, have been summarized in the subjoined table.

The quantum of infection-material used for every sulphatereduction-
test amounted to from 5 to 10 grs. of the soil-sample. After an
interval of from 8 to 20 days sulphate-reduction revealed itself at
25° C., which period rose to 5 weeks in the case of the peat-
sample B 31.

In every well, even the deepest of 34.50 m. below A.P., we
chiefly found sand over the whole depth, in which irregularly spread
lens-shaped clay-, and peat-layers occurred alternately.

With a“ few exceptions all the sand- and clay-samples indicated
in the subjoined table, yielded on examination for sulphate-reduction a
conclusive positive result. Consequently the dull-grey or grey colour

192

of the sand-samples and the mostly blue to bluish-black colour of
the clay-samples points to prevailing sulphate-reduction. This com-

te B 24 B 25 B 26 B 21 B 28 B 29 B 30 B 31

21.6 M. 35 34 M./35.30 M.| 6.50 M.| 8.00 M. 6.50 9.50 M.| 8.00 M.
10.50 M./12.50 » |74.00 »
15.10 » |z3.25*)» | 6.co M./14.00 |18.50 » [25.30 »

to (peat)
17.50 » 6.50 » (16.25 » (32,50 »
28.50 » 16.50 » |20.50*)» [34.50 »
32.50 » 29.00 » [23.10 »

34.50 »

B 22, B 24, etc. = wells.

The values express in metres the depths below A.P. (= Amsterdam level)
from which the soil samples have been drawn.

The figures in italics refer to clay-samples which enclose organic particles
or peat-layers.

The figures in ordinary type are sand-samples.

(*) = no sulphate reduction in culture bottle.

mences at about 10 m. below the surface (7.5 m. —A.P.)') to =
37 m. (34.50 m.—A.P.) the largest depth examined here.

The conditions under which sulphate-reduction appears are:

1°. Absence of oxygen *).

2°. The occurrence of organic compounds.

3°. The presence of sulphate and the required mineral compounds.

The first condition, the absence of oxygen, is satisfied in conse-
quence of the considerable depth below the level of the ground.

The second condition: the occurrence of organic compounds, is
fulfilled already to the eye by the peat-sample and also by the
clay-sample with enclosed peat-layers. That the sand-, and clay-
samples, which do not enclose immediately distinguishable organic
particles, also contain organic matter, can be demonstrated chemically,
by the potassiumpermanganate method. This is conducted as follows:
The soil-sample is boiled with diluted sulphuric acid and filtered.
The filtrate is cooled down under the tap; now potassiumpermanganate
(0.01 norm.) is instilled. The first drops are directly decolorized.
which is owing to the oxidation of ferro- and mangano-compounds,

1) The grounds of the wells at the Sprenkelkanaal is lying at 2.5 M. above A.P.
*) Traces of oxygen are left out of consideration here.

193

Then a moment follows in which the colour of the added potassium-
permanganate disappears only slowly: this is the oxidation of the
organic matter, extracted by the diluted sulphurie acid, for in a
drop of this extract, placed on a piece of filterpaper soaked with
potassium ferrocyanid no ferro can be demonstrated any more.

The sand-samples are most often not so rich in organic compounds
as the clay-samples, which often contain peat. Presumably this
generates a stronger sulphate-reduction than is possible in the sand-
samples, and this is probably the reason why clay can be darker
in colour than sand.

Van Deven *) has shown that for sulphate-reduction organic bodies
are required which are easily oxidizable. This justities the assumption
that in the organic substances, demonstrated by us, there are some
bodies difficult of oxidation and others again which are easily oxidi-
zable, which is proved indirectly by the sulphate-reduction that
manifests itself in the sand-, clay-, and peat-samples.

Also the 8rd condition, the presence of the required mineral
compounds, was satisfied. In our examination for sulphate only small
amounts could be demonstrated, which is explained by the disappearance
of sulphate through sulphate-reduction.

One of the mineral combinations is that of the insoluble, black-
coloured ferric sulphid, formed by the iron and the liberated hydrogen
sulphid, as pointed out already in §3.

From the foregoing we may deduce that the conditions of
anaerobic life which we found in the deeper layers of the soil,
fairly agree with the prevailing sulphate-reduction.

5. The content of ,,aerobic’ and ,,anaerobic” germs of the
À 9
deeper layers of the soil.

Besides the demonstration of sulphate-reducing spirilla in the soil-
samples, another question arises, viz. whether they contain other
germs and whether these belong to the aerobes or the anaerobes. We
examined the samples:

B 28 29.00 M — A.P. (clay with peat)
B 29 6.50 — 10.50 M — A.P. (clay).
B 31 25.30 M — A.P. (peat).

The number of germs was ascertained in the way described in
§ 3. With a sterilized spatula inoculation-material was taken from
the soil-samples, it was then shaken up in sterile tapwater and

1) Centralbl. f. Bakt. Bd. XI, 2te Abt. 1903, p. 83.

194

subsequently weighed. This material was used for making counting-
tests by sowing the micro-organisms on nutrient gelatin. The counting
of the microbe-colonies for the aerobic plate-cultures took place after
48 and 72 hours, after which there was hardly any increase of the
colonies worth mentioning.

The anaerobic culture plates for the counting-tests were made
after Wricut and Burris’) culture method, modified by me. As
this strictly anaerobic method of cultivation yields very good results,
it will not be amiss to state our procedure.

In a glass box closed tightly by a glass stopper with a ground
rim a smaller petri-dish is placed containing a solidified culture-
medium on which the anaerobes are sown in streaks. The circular
open space left round the dish is first stopped up with non-absorbent
cotton-wool on which a layer of absorbent cotton-wool is laid. The
latter is soaked with 20 °/, potassium hydrate and finally with an
equal volume of 20°/, pyrogallic acid.

Throughout this procedure the petri-dish remains covered. After
tbe cotton-wool has been soaked with pyrogallic acid the dishcover
is removed, while the glassbox is closed by its cover-glass of
which the glass-rim is smeared with vaselin. The rim of the glass-
box may also be shut off with paraffin after the lid has been
adjusted. In order to facilitate the opening of the glass-boxes, the
wall is provided with a little hole which is shut off with paraffin
and is opened again before taking off the lid of the box, in

Aerobes. | Anaerobes.
Soil-sample.
number of germs number of germs
per c.c. of soil. per cc. of soil.
After 48 hrs./After 72 hrs.| After 4 days. | After 12 days.
B 28 29.00 M. — A.P.
clay + peat.
15400 20000 409000
B29 6.50—10.50 M. —A.P.
5 IE ee
B 31 25.30 M. — AP.
peat. | 103600 160000

1) J. H. Wrieut. A method for cultivation of anaerobic bacteria. Centralbl. f.
Bakt. lte Abt. 29, 1901, pg. 61. R. Burri. 2te Abt. 1902. 8, pg. 533.

195

order to admit the air. Now the cover of the petri dish is easily
removed.

The number of anaerobes was counted in the same way as that
of the aerobes in the same sample.

Because we had determined the specific weight of the soil-samples,
we could establish the number of germs per cc.

Our results we have tabulated on page 7.

The time in which the anaerobes yielded a constant number of
colonies was considerably longer than that of the aerobes.

It strikes us that the anaerobic test yields a total of germs which
is much greater than that of the aerobic one, while the amount of germs
in B 28 and B 31 is much higher than that of B 29. The last-
named fact is perhaps due to the higher content of organic matter
in the first two soil-samples.

For the sake of comparison we may add that in raw water from
the dunes the number of bacteria per e.c. varies in round numbers
from 400 to 1800.

§ 6. Jt appears that microbes derived from aerobie and anaerobic
cultivation belong for the greater part to the facultative anaerobes.

The number of species of bacteria obtained in the preceding para-
graph by the method described, appeared to be only small when
we examined their qualities. Generally the anaerobes and the aerobes *)
were not identical. The following table shows the number of species
of microbes we found:

Soil-sample. Aerobes. Anaerobes.
B 28 29.00 M. — A.P. 2 species 4 species
B 29 6.50 — 10.50 M — AP. RRS dend
B 31 25.30 M. — A.P. 1 = 4 =

As to their properties aerobes revealed some resemblance in
acidformation from glucose, Berlin-blue formation from ferri-ferri-
eyanid, the formation of hydrogen-sulphid from broth (lead-carbonate
test), the splitting of aesculin, the formation of katalase, and most
often in the inability to ferment glucose, to form lipase and diastase.
Spores were not formed.

1) Probably B 29 anaerobe and one of the species B 29 aerobe were identic.

196

A difference in the properties of the two microbe-groups appeared
from the following reactions: Anaerobes form nitrite from nitrate
in a marked degree, indican is split extensively in most cases
(oxidation of indoxyl to indigo-blue), a moderate amount of invertase
is formed, a large amount of slime (wall-matter) is formed from
saccharose. Aerobes lack these qualities. They liquefy gelatin, whereas
the anaerobes do not.

My investigation into the properties of the microbes did not put
me in a position to classify them.

When examining microbes derived from aerobic cultivation for
their anaerobie behaviour, it appeared that only B31 grew very
well without air, those of B28 and B29, however, very badly.
The occurrence of these aerobes seems to show that presumably
very small quantities of air are to be found at larger depths in the
soil, and that they are carried along with the rainwater that
penetrates at a very slow rate into the deeper layers of the earth. If
the layer, as is the case here with clay, is only sparingly permeable
to water, the dissolved oxygen is allowed to diffuse to the places
where it is to be consumed. .

The microbes obtained from anaerobic cultivation developed
enormously when living in air. This appeared conclusively when
the. anaerobic culture-boxes after being opened had been standing
for some time exposed to the air. Then the microbe colonies grew
larger and larger in a very short time. These bacteria grew very
well as aerobes, also on nutrient agar-slants. Tested in this way
the majority of the isolated bacteria appeared to belong to the
facultative anaerobes, which is consistent with the occurrence of
these microbes at greater depths.

§ 7. Research for some other specific species of microbes.

We endeavoured to ascertain the occurrence of. obligate-aerobic
nitrifying bacteria and of Azotobacter chroococcum, however, with
negative result, as could be expected.

Nor could denitrifying microbes be demonstrated; no more could
we detect anaerobic butyric bacteria and anaerobic bacteria which
break down cellulose.

§ 8. Van DER SLmEN’s Manganese-Theory for the oxidation of
organic matter at greater depths in the soil.

The problem of oxidation of the organic matter in the deeper
layers of the earth has been discussed by W. G. N. van DER SLEEN

197

in his publication: „Bijdrage tot de kennis der chemische samen-
stelling van het duinwater in verband met de geo-mineralogische
gesteldheid van den bodem.” The writer says (p. 50) that at such
a great depth bacterial influence on the oxidation of organic matter
seems to be out of the question and he suspects manganese salts to
act as oxygen-carriers. Further on (pg. 62) the writer says: ,,.... I
do not think that Microspira desulfuricans oceurs at such a depth
as has to be assumed when ascribing sulphate-reduction only to
this micro-organisme’’.

On pag. 51 the author records some experiments which go to
show that manganese can transmit oxygen from the sulphates to
an organic compound such as hydrochinon. To conelude from this
that the oxidation of organic matter at the lower depths in the soil
could occur in the same way,.seems to me hardly admissible unless
experimental evidence be brought forward that biological oxidation
is out of the question. Such evidence has not been produced as yet.
It may be deemed surprising that the author, who, as appears from
the passage in his publication that we quoted just: now, had taken
cognizance of the bacteriological sulphate reduction has omitted to
inquire into it. This is the more surprising since on the ground of
its anaerobic behaviour Microspira desulfuricans is adapted to living
at greather depths in the soil.

The evidence produced by our investigation set forth in the
preceding paragraphs, by which it has been established that sulphate-
reduction is of common occurrence at the greater depths underneath
the dunes, warrant the conclusion that oxidation of organic matter
can be effected by Microspira desulfuricans, without the additional
influence of manganese compounds.

§ 9. The tran{formation of sulphate in the clay-containing
soul of the dunes and sulphate-reduction by Microspira
desulfuricans.

The “Koninklijke Academie van Wetenschappen te Amsterdam” *)
has brought forth a report on the question to what the presence of
so called Artesian water in the dune-soil is due, in a preliminary
advice from G. A. F. MoreNGRAAFF and Kuve. Dusors. In an enume-
ration of the chemical properties of dune-water the report contains
the following statement:

1) Verslag v. d. gewone vergaderingen der Wis- en Natuurk. Afd. Vol. XXX,
p. 212.

198

“From the surface downwards in and underneath the dune-masses
the sulphuric acid content diminishes proportionally to the total
thickness of the clay-layers occurring in them, i.e. in proportion
to the increase of the volume of clay-soil, through which the water
has percolated downwards.

This phenomenon is the result of the power of clay-soil to convert
sulphurie acid and then retain it”.

In the study by Eve. Dusois’) already quoted above, a detailed
exposition is given of the transformation of sulphuric acid in the
clay-layers, which consists in a reduction-process in the presence
of organic matters, with formation of ferric sulphid.

It is evident from the foregoing that sulphate-reduction, which
occurs not only in the deeper clay-layers, but also in the sand-soil,
is brought about by Microspira desulfuricans. The life of this microbe,
which ws adapted to anaerobic conditions, accounts for the common
occurrence of sulphate-reduction in the deeper layers of the earth and
especially in the clay-soil, which generally has a higher content of
organic matter.

So long as the conditions of this typically ymicrobiological process
are fulfilled, transformation of sulphate into ferric sulphid will
hereby be generated, to which is to be ascribed the partial or total
absence of sulphuric-acid salts in deep-dune water.

Heemstede, February 24 1922.

1) „Het Leidsche Duinwater”’. Een hydrologische studie, 1912, p. 20.

Chemistry. — “The Influence of a Catalyst on the Thermodynamic
Quantities Regulating the Velocity of a Reaction.” By E. van
Ture. (Communicated by Prof. J. BörsrKEN.)

(Communicated at the meeting of May 27, 1922).

According to GurpBerG and Waace’s hypothesis the velocity of
reaction in a homogeneous system of constant temperature is equal
to the product of the active masses of the converted substances
multiplied by the velocity constant. This constant is, of course,
variable with the temperature, and dependent on the nature of the
reacting molecules. The differential equations of G. and W. only
indicate the number of molecules decomposed in the time unit; they
do not indicate precisely how the reaction(s) takes place; hence they
do not show either how the reaction constant depends on the
nature of the substances and on the temperature.

Disregarding Nernst’s formulation, in which the velocity of reac-

chemical force

tion is put = a formula that proved untenable,

chem. resistance’
GoLDscHMIDT’s attempt’) to give an explanation of the nature of the
reaction constant may be called the first. Starting-point for these
and following theories were especially two considerations referring
to bi-molecular gas reactions:

1. the reaction constant (velocity for concentration = 1) is doubled
about per 10° of increase of temperature, so long as the observations
are not too far from room temperature. The number of collisions
of the molecules is proportional to the translatory velocity, hence
proportional to 7. The increase of this kinetic energy can, there-
fore, contribute to a maximum of 2°/, to the increase of the velocity
of the reaction found. Hence a deeper insight into the nature of
the reaction than is given by G. and W.’s theory is necessary.

2. if all the molecules of the decomposed gas were in the same
state, every collision would be followed by a reaction. Every reaction
would then take place with the same explosive velocity. This not
being the case, all molecules are not equally reactive. A fraction of
them is in a more favourable condition. It is, therefore, possible
that the velocity of reaction is proportional to the number of these

1) Diss. Breslau, 1907. Cf. also Topp and Owen, Phil. Mag. 37, 224.

13
Proceedings Royal Acad. Amsterdam. Vol. XXV.

200

favoured molecules. Whether it is necessary for the reaction that
two active molecules collide, or whether it is sufficient when one of
them is active, must for the present remain an open question.

GoLDscHMIDT assumed that the velocity of reaction is about pro-
portional to the number of molecules the translatory velocity of
which exceeds a definite minimum value. Only these molecules, the
number of which is given by Maxwerr’s law of partition, would
be active. This restriction to the velocity of translation, is however,
entirely unfounded; it is on the other hand more probable that
also the intermolecular and interatomic energies play a part in the
reaction, it is, therefore, more plausible to assume a threshold value
also for these energies.

Krüaer’s theory is of a more exact character; it has, however,
only been elaborated for the simplest cases, as e.g. the dissociation
I, 21, in which the reacting substances are already in atomic
(active) condition. Trautz gave a more general theory of velocities
of reaction. Starting from van ’t Horr’s reaction-isochore:

| k
ae = hen he substituted for ay and for
1

OEE „fe dT — Ey, fen aed".

0 0

He further assumed that £, resp. &, depends only on the proper-
ties of the initial resp. resulting substances, and therefore split the
reaction isochore into two parts, each referring to this. For this it
must also be possible to split Q, rationally, for which purpose T.
introduces the conception intermediate substances (which have an
exceedingly short period of existence). In the case of the splitting
up of 2HI=H, + 1, these intermediate substances might be H- and
l-atoms. For the decomposition of HI into H- and I-atoms a disso-
ciation energy is again required, in the formation of H, and I, from
these atoms a heat Q, is liberated. It is clear that Q, = Q, —Q,.
Now all the obstacles to the splitting up of the reaction isochore
were removed, and the following equation resulted :

Th

dln k Q
Ui ‘— — Er en n fen aT / prs.

0
By integration and further elaboration Trautz obtained a formula
which in approximation could be reduced to a considerably simpler
form, and from which some important conclusions may be drawn:

201

Q,
4,571 T
while the following form may be derived for the temperature coef-
ficient of the reaction constant:

Ts T,
TE Th: ie f Ev dT f
24 „ai enn „dT.
bink K did R Tid EE nts, ;

kr,

log k = (25 to 35) — —2v.1,5logT— J v.1,1

From the first of the two equations may be read that in bi-mole-
cular reactions the velocity is greater, as the Q, is smaller, while
it follows from the second equation that the temperature coefficient
increases on increase of the Q,. When, therefore, the same reaction is
brought about without, and one with exceedingly little catalyst under for
the rest identical circumstances, the catalysed reaction, which proceeds
more quickly, will require a smaller heat of activation for its mole-
cules, and possess a smaller coefficient of temperature than the not
catalyzed reaction, two conclusions which may be verified experi-
mentally.

Briefly T.’s train of thought comes to this that he assumes that
it is required both on formation and decomposition of molecules
that they pass into a reactive form (not always atoms) with absorp-
tion of energy and that on collision of these active molecules the
reaction always takes place. Van ’r Horr’s reaction isochore being
the starting point in Traurz’s theory, it is comprehensible that the
stress has been laid on the changes of energy taking place in the
reaction, and that the importance of the constant of integration is
not sufficiently brought out. And yet it is clear on some consider-
ation that the only thing required for a bi-molecular reaction is
not a collision, but a collision at the right place (perhaps with the
exception of very simple molecules). This favourable constellation
which may be expressed in the form of a quantity of entropy, does
not occur in the reaction isochore. Accordingly in Travtz’s theory
changes of entropy in the reaction have only been considered in
so far as the number of collisions are concerned.

That with by far the majority of the reactions change of the
internal energy of the molecules is accompanied with change of the
molecular entropy *), is not sufficiently taken into account in Lrwis’s
theorie either. There, too, it is assumed that before being able to
react, every molecule must have a certain excess of energy, called
by L imerement of energy. This increment would be absorbed in

1) TrestinG, These Proc. Vol. XXIII, p. 148.
Ta*

202

the form of infra-red radiation of very definite frequency, which
radiation is present in the medium in virtue of its thermal condition.
3y the application of Pranck’s law of the normal partition of energy,
the density of radiation of this frequency can be calculated at every
temperature, and from this the fraction of the molecules that are
in reactive condition. Lewis derives that the increment of energy E.
is equal to a quantum (of the absorbable type) per molecule.

a= Ni Vreagents+

Lewis derives for the constant of reaction of a bi-molecular
reaction :
— h(va + rvB)/rr

== ar VT oe ae e
in which P,==eonstant, 7’= absolute temp., m4 and nz = index of
refraction of the substance A resp. B, and k= gas constant per
molecule. The formula shows very clearly the rapid increase of 4
on rise of temperature.

The nearer the value of the critical energy is to that of the
mean energy per molecule, the greater will be the number of
molecules becoming active per second, hence also the velocity of
reaction, the same conclusion, therefore, to which Traurz came. By
taking the logarithm of the above formula, and differentiating this
with respect to time, the following form results:

dink Nhk(vat va) +'/, RE E+ %/, RT
EE HRT rn RTS

Of reactions which take place as much as possible under the same
circumstances, only more slowly or more quickly (to be realized
with little catalyst), the quicker reaction must have a smaller £
din k

dt
become smaller, hence also the temperature coefficient of the reaction
constant, for the temp.coéf.

according to the above, from which it then follows that has

k dk
kr lime dk dink
LO a let a pase gy TG a ee
kr kr krdt die

Lewis (like Trautz) draws the conclusion that a strongly catalyzed
reaction will indicate a decrease of the temperature coefficient
compared with the same reaction weakly or not catalyzed.

On half thermodynamic, half kinetic grounds Konnstamm and
ScHEFFER have derived a relation between the velocities of reaction
and the thermodynamic potentials of the substances participating in

203

a reaction. Starting from this Scherrer drew up a simple formula
which agrees with a formula derived at about the same time in an
entirely different way by Marcruin, viz.:

Ink = A B
ae meter

in which £ represents the difference of energy between the inter-
mediate state which is rich in energy, and the mean condition of
the reacting substances in the reaction, and B is a quantity which
does not contain constants dependent on the nature of the substances,
except the difference of entropy. This term takes the effective chance
of collision into account. It follows from the formula that increase
of the energy increment diminishes the velocity of reaction, increase
of the difference of entropy on the other hand increases it. In contra-
distinetion with the formulae discussed before, a catalyst need not
necessarily decrease the energy increment; it is even possible that
as a result the energy increment is increased, provided the increase
of factor 6 more than neutralizes this unfavourable action. The
increase of the energy increment means fewer active molecules,
increase of B is equivalent to a more favourable chance of collision.
It is, therefore, possible that the action of a catalyst would consist
in this that though the threshold of energy should be raised, the
number of favourable collisions has been so much increased that
the reaction nevertheless proceeds more rapidly.

In the not catalysed reaction by no means every collision between
active molecules would eventuate in a reaction. This is a priori
sooner to be expected for complicated than for simple molecules ;
instances are, therefore, especially to be found in erganic chemistry.

From increase of the energy-increment ensues increase of the
temperature coefficient, hence the catalysed reaction can have a
greater temperature coefficient than the not catalysed reaction.
Entirely in contradiction with Traurz’s and Luwis’s conclusions the
catalysed reaction can have a temp. coef. and an energy increment
which are greater than those of the same reaction without catalyst.

Measurements of the velocity of one and the same reaction between
complicated molecules with and without catalyst and at different tempe-
ratures might give a decision in favour of Scurrrer’s theory, if a
reaction could be found which, catalysed, presented a greater tem-
perature coefficient than not catalysed. As will be seen in what
follows, this appeared to be the case in the acetylation of diphe-
nylamin.

The reaction was carried out at 0°, 20°, 30°, 40°, and 50° C.

204

The excess of acetic acid anhydride was taken so great that the
variations of concentration of this component could be neglected
with respect to those of the component diphenylamin. Hence the
reaction was pseudo-mono-molecular. Many catalysts were tried *)
before some substances were found which were not paralysed during
the reaction; they were p. bromo-benzene-sulphonic acid and p.
toluene-sulphonic acid.

The following tables give the observations from 0— 50° without
catalyst. j

temp. 0° 1 mol diph. 121/5 mol. anh. temp. 20° 1 mol. diph. 12!/, mol anh.
t 0/9 converted GEN 9/pconverted
2.303 :
1.— uur | 0.0048 0.30 uur 0.8
2 1.4 0.0031 130. 3 2.4
33 erp aed 0.0031 2,30; 3.8
4.— , 2,3 0.0025 3:30 5.5
5.— » 2.4 0.0021 4.300, 1.3
0:15 5 3.0 0.0021 6.— „ §.1

temp. 30° 1 mol diph. 12!/, mol. anh. temp. 40° 1 mol. diph. 12!/2 mol anh.

t 0/9 converted ade t 9/9 converted nS
2.303 2 2.303

0.30 uur 1.6 _0.0127 0.33 uur 25 0.0220
1204 pe 2.8 0.0121 Oras 4.3 0.0208
2.— » 5.5 0.0123 2.— y 8.9 0.0202
3.— „ 8.2 0.0124 25594 12.9 0.0201
4.— y 10.8 0.0124 i 2155 0.C210
605) 5 16.3 0.0129 1. 4 29.0 0.0212

Taking into consideration that in the first table the converted
quantities are so small, the most probable values of the reaction
constants are respectively; 0,0021—0,0070—0,0124—0,0209 and
0,0384.

1) Diss. Delft 1922.

205

temp. 50° 1 mol. diph. 12!/, mol. anh.

t 9/) converted oe
0.30 uur 4.4 0.0391
1.— , 8.4 0.0381
2.— » 15.2 0.0358
3.— y 22.6 0.0371
5.— 4 36.1 0.0389
ley 46.5 0.0388

The reaction constants of the catalysed reactions are recorded in
the following table:

p.bromo-benzene-sulphonicac. cat.) p. toluene-sulphonic acid catal

0.00089 mol. 0.00178 mol. 0.00089 mol. 0.00178 mol.
ko 0.0018 0.0027 0.0021 0.0024
kao 0.0102 0.0197 0.0105 0.0134
k30 0.0243 0.0523 0.0235 0.0340
ee 0.0598 0.143 0.0558 0.0819
on 0.153 0.383 0.123 0.194

It is remarkable that the activity of the catalyst decreases at low
temperatures, and becomes about O at 0°. At lower temperature the
catalyst is paralysed, to which we shall revert later on. The energy
increment can be calculated from two observations by the aid of

ig Ey ek 1
the formula nii) In the calculation of the energy-

1

increment of the catalysed reactions it should be borne in mind
that this must not be done in the usual way, if the measured reac-
tion is a combination of two or more reactions taking place side
by side ’). The hypothesis according to which it is assumed that
with a small catalyst concentration, the number of collisions of the
kind as occur in the non-catalysed reaction, remains the same, and
that only another kind of collisions is added to them, is permissible
in my opinion. In this case the measured constant of reaction

1) LACOMBLÉ, Diss. Leiden 1920, p. 80.

206

represents the sum of that of the non-catalysed and that of the
purely catalysed reaction. In order to obtain the constants of the
purely catalysed reactions, which are recorded in the above table,
the reaction constants of the non-catalysed reactions must be sub-
tracted from the measured ones. It has been tacitly assumed, what
is, indeed, shown by the constancy of the measured reaction con-
stants, that the two reactions proceeding side by side, are of the
same order, as otherwise this operation is not allowed.

p. bromo benzene sulph. ac. catal. p. toluene sulphonic catal.
0.00089 mol. 0.00178 mol. 0.00089 mol. 0.00178 mol.

0.0006 = 0.0003
0.0127 0.0035 0.0064
0.0399 0.0111 0.0216
0.122 0.0349 0.0610
0.345 0.0846 0.156

The energy increment calculated from the 1“t series of observations
without catalyst, and from these 2rd, 3rd, 4th, and 5t series is
respectively + 10.000 calories — 23000 cal. — 20500 cal. — 20500
cal. — 20800 cal.

The acetylation of diphenylamin decides, therefore, in favour of
ScHEFFER’s theory, as it would e.g. be entirely inexplicable according
to Lewis, why the sulphonic acid can act as catalyst, as the addition
of this substance about doubles the energy-increment; the number
of active molecules would, accordingly, be much smaller, hence also
the number of effective collisions.

In the calculation of the factor B from ScueErrer’s formula, it
appears to be more than doubled by the catalyst. The favourable
chance of collision has, therefere, been enlarged, notwithstanding
the number of active molecules has become smaller. Hence if the
conversion is to be inereased, this smaller number of active mole-
cules must collide more favourably. Accordingly every collision
between molecules that are sufficiently rich in energy does not
always eventuate in conversion, it is probably only a small percentage
of them that enters into reaction.

One can form the following conception of this.

It is not immaterial what part of the acetic acid anhydride
molecule impinges with the diphenylamin-molecule, nor with what
part of the latter. The reactive molecule parts, in this case the

207

Ist series. 2nd series. 3rd series.
| E B | | E B |
| |
kao : Koo | 23200 | 34.7 k3o : kao | 20200 | 31.1
kao: k39 23000 | 34.4 kao : k39 20800 | 32.0
Kso : kao | 22600 | 33.8 k5o : kao | 20800 | 32.1

4th series. 5th series.
| | E | B E | B
|
kao : kop | 20400 | 30.1 ka, : Kop | 21600 | 32.7
kao : k3 21000 31 . 1 kao à kao 20800 31 3
Ks : kao 20200 29.8 kso 5 ka, 20200 30.4

oxygen bridge of the anhydride and the aminohydrogen of the amin,
must be in each other's immediate neighbourhood. In a substance
which exercises an attraction on these two parts, these molecule
parts will be turned towards each other at a collision of the three
molecules (more probable is a collision of a molecule with the
complex of the two others). The sulphonic acids used certainly
exert an attraction on the amino hydrogen, and most likely also on
the bridge oxygen, because sulphuric acid impinges with the anhy-
dride at that place, and the sulphon group is the active component
in both substances. In my opinion the catalytic action of sulphonic
acid is for the greater part due to its directive action, and it owes
this directive action to its affinity towards the reaction components,
as BörseKeN’s dislocation theory demands for every catalyst, without
this affinity leading to such a firm bond, that the affinity, hence also
the directive action on the other kind of molecule, would be
eliminated.

Against these conclusions the question might be raised whether
the measured temperature coefficient represents indeed the real one.
The nature of the catalyst leads to the supposition that a part of the
sulphonic acid is bound to the diphenylamin resp. anhydride (or
both), and that this might not be active (or much less so). On rise
of temperature a stronger dissociation would appear in the components,
hence more free (i.e. more active) catalyst would be present. Then

208

kro kT 410. , Ceat T+10
‚but = TX.

kr kr Ceat T

Accordingly the real temp. coef. would be smaller than the

the measured temp. coeff. is not =

measured one.

Let us suppose the bound catalyst to be totally inactive, and the
true temp. coef. to have remained of the same value as was
found in the non-catalysed reaction. The measured temp. coéf.

/ /
from which de
C cat C cat
confronted by the question whether it is possible that in the neigh-
bourhood of room temperature the concentration of the components
increases by 67 °/, per 10° increase of temperature.

Let us take 300° and 310° absolute for the two temperatures,
0,1111 as constant of equilibrium at 300° (hence 90°/, bound cat,
10°/, free cat), and let us put the heat of dissociation = 5000 cal,

a heat which may be called normal.

So a = 1,67, in other words one is

10 X ca ® Xe 4
Kos = ER oa 310 102
in which ¢4 —c’a4 may be put:
K. ‘
310 ze v 9
Koe 100—z#

It follows from the reaction-isochore that:

Ke Oe abe, OOV OR)

log = eye = == ; ==) Olas 76
ibs Nh LEL) Ri Ae Bo 4,571 93000
from whieh:
Karo li ia sae
GE 100—-ea
from which:
c' cat
a= 12,7 Sand a= ON
c cat

Hence even in the most unfavourable case conceivable that the
bound catalyst would be totally inactive, the increasing dissociation
per 10° increase of temperature is only able to account for a small
part of the increase of the temp. coef. of the catalysed reaction
above that of the non-catalysed reaction.

SCHEFFER pointed out that in many cases the / may be put
practically constant over a limited range of temperature, and that
in this case B is also pretty well constant. If the region from
20°—50° lies within this limited range, the values of Ink drawn

209

as function of 7 must lie on a straight line, for every equation of
the form y=ma-+06 represents a straight line. Expressed in a
graphical representation this appears really to be the case’), and
the course of the lines suggests that the energy-increment is little,
if at all, dependent on the quantity of added catalyst. The values
of Ink at O° fall outside the straight line in the catalysed reactions.

As on account of the slight velocity of the reaction at 0° the
observations need not be very accurate, I repeated two measurements
at O°, viz. of the non-catalysed reaction, and of that with 0,00178
mol. p. bromobenzene sulphonic acid. I extended the observations
over fully two days instead of over seven hours.

temp. 0° 1 mol. diph. 121/, mol. anh.

temp. 0° 1 mol. diph. 12!/, mol. anh. 0.00178 mol. acid.

| t 0/9 converted os t %o converted =
21.55 uur 8.0 0.00165 21 48 uur 10.3 0.00216
28.26 > 10.1 0.00162 28.19 » 12.9 0.00212
44.55 » 14.5 0.00152 44.48 » 19.4 0.00210
52.52 » 17.6 0.00159 52.44 » 23.8 0.00224

0.00226

Though the values which I found, were indeed lower, the constant
of the purely catalysed reaction appeared to have the same value
as was determined in former experiments, viz. 0,00218—0,00160 =
= 0,00058 (found formerly = 0,0006).

0,0127

To be expected was a value + BD == =-0,00132, henee’ for
the gross catalysed reaction 0,00132 + 0,00160 — + 0,0029; a
value that exceeds the error of observation many times.

In FeCl, I think I have found a catalyst which is catalytically
active undiminished down to 0°. As these experiments have not yet
been completed, they will be discussed in a later publication ; I may
conclude from the experiments already made that also ferri-chloride
enlarges the “hill” of energy and that accordingly also this catalytic
action can alone be explained by the aid of Scuerrer’s theory.

1) Diss. Delft 1922.

Chemistry. — “The Dislocation Theory of Catalysis.” By Prof. J.
BOESUKEN.

(Communicated at the meeting of May 27, 1922).

The explanation of the catalytic phenomena has always presented
great difficulties, and has never been satisfactory as yet, because
‘the cause of changes of reaction-velocity was to be ascertained with-
out there seeming to be a clear relation between the velocity of
reaction and the quantity of energy that came into play.

Before the catalytic phenomena had been brought in connection
with the conception of free energy, satisfaction might be found in
establishing the fact that one or more intermediate reactions took
place, which together proceeded more rapidly than the reaction
without catalyst.

And it is still possible to be satisfied with such an explanation
when it can also be shown that the catalyst in quantity and quality
is eventually regained unchanged from the reaction mass.

It should, however, be fully realized that no answer is given to
the question why these intermediate reactions proceed more rapidly
than the principal reaction.

This is the more striking, because in these intermediate reactions
the catalyst disappears from the reaction-mass at least temporarily
and partially. I have, therefore, pointed out that the ideal catalysts
are exactly those that are not fixed in intermediate reactions, and
that the real catalysis is the interaction between the catalyst and
the molecules, which has nothing to do with the formation of a
compound as such.

This interaction, which I have called dislocation, may be seen as
a change of the paths of the electrons; it is very well possible that
it cannot take place until the catalyst has formed a compound with
the molecules, but at any rate it must be possible to show it in
some way or other and to express it in a mathematical form.

On one side it is therefore necessary to form a clear conception
of the dislocation, on the other side the modifications which take
place in the thermodynamic relations through the presence of a
catalyst and to which the changes of the reaction velocities respond,
must be fixed in a mathematical formula by establishing a connec-

211

tion between the reaction velocities and the thermodynamic relations.

As regards the former, in the owidation of alcohols with coopera-
tion of aromatic ketones activated by light | have found a reaction,
in which the catalysis proper (the dislocation) could be sharply
distinguished from the formation of a coumpound between catalyst
and the molecules present. *)

When an alcoholic solution of benzophenon, which is kept
saturate with oxygen, is exposed to violet light, the alcohol is oxi-
dized to aldehyde and water, the ketone remaining unchanged.

A closer study brought to light that above a certain concentration
of the ketone the velocity of reaction became independent of this
concentration, and further that it was proportional to the square of
the intensity of the light and to the first power of the cone. of the
alcohol.

This may be explained as follows:

The ketone absorbs part of the light and is activated by it.
According to the laws of absorption the quantity of active ketone
will be proportional to: }

[Ae hed) in which # = absorption coefficient
c = concentration ketone
d = thickness of layer

Le-ked is the light that is transmitted. If 4, c, and d are pretty
great, this is very little, and all the light is absorbed. The quantity
of activated ketone then becomes proportional to Z and independent
of c, its concentration.

When we assume that among others the two following processes
take place:

“2 active ketone + alcohol = (active ketone), alcohol
and
(active ketone), alcohol + O — ketone + aldehyde + H,O,

the former of which proceeds much more slowly than the latter,
the oxygen absorption (which was measured) will be determined by
the first process, the velocity of formation of the ternary compound.
This velocity of reaction must then be proportional to the square
of / and to the concentration of the alcohol.

I will not enter here into a fuller discussion bow this might be
proved in different other ways”). The whole process can now be
described as follows:

Under the influence of the light there is suddenly formed a

') Recueil 40, 433—445.
2) 1c. p. 439—442.

212

quantity of photo-ketone = kl (1—e~-"«¢) approaching to kl.

I. ketone + light = photo-ketone ;
as this quantity is formed at the moment that the solution is illumi-
nated, it is as if with the velocity of light a plate of a catalyst
slides on the light side of some vessel or other, in which the solu-
tion is put.

Then the reaction takes place the velocity of which regulates the
process: the meeting of the alcohol molecules and those of the
photo-ketone :

II. 2 photo-ketone + aleobol = (photo-ketone), alcohol.

By this meeting two H-atoms of the alcohol are activated:

Ill. (photo-ketone), alcohol — [(photo-ketone), active alcohol].

This process, which probably takes place with the velocity of
light, as the real catalysis, the dislocation.

The alcohol-molecules are enabled to react with the oxygen accord-
ing to the scheme:

IV. 2 [(photo-ketone) active alcohol} + O, =

4 ketone + 2 aldehyde + 2H,O,
which last process also takes place with great velocity.

We see that the actual catalysis has to do with the formation of
the ternary compound only in so far as the photo-activity of the
C == O-groups of the ketone can be transferred to the H-atoms of
the alcohol. Here the distinction of the catalysis and of the forma-
tion of the compound is, indeed, very clear, for the ternary compound
is also formed in the dark, and then there is no question of any
catalytic action.

When the photo-ketone is thought replaced by an ordinary cata-
lyst, e.g. a plate of paladium, it is clear that the combining of this
metal with the aleohol is not the essential part of the catalysis, but
what happens with the alcohol molecules at the moment that the
atoms Pd get into contact with them, through which two of the
H-atoms are activated. This the paladium can do by itself, without
being activated by a stimulus from outside.

It appeared from the light-investigation that the oxidation of the
activated alcohol molecules took place very rapidly. This will as a
rule also be the case in the ordinary catalysis, but this velocity
can be different for each case.

If, however, a catalyst in very small quantities is to accelerate
a given reaction considerably, every contact of its molecules with
those of the substance that is to be activated, must give rise to a
dislocation that sets in very rapidly.

213

It is clear that this can hardly take place otherwise than on
intimate contact, and here the significance of the formation of a
compound between catalyst and the molecules to be activated, even
though it be one that can very easily be dissociated, comes to the
fore. In the light investigation it was only the primary and secondary
alcohols that were easily oxidized, and not the hydrogen itself and
a number of hydrogen compounds, evidently because the former
could, the latter could not be attached by the ketone.

As has been said in the introduction, not only must the conception
of dislocation be defined more closely, but it must also be tried to
find a mathematical form for it through the consideration of the
thermo-dynamic and kinetic relations.

Of late years many scientists have occupied themselves with studies
of the reaction velocities, which are also the subject of this investi-
gation. We may mention the names of Traurz, Marcerin, Lewis,
Perrin, and SCHEFFER *).

It seems to me that ScHEFFER’s considerations have the greatest
value for the knowledge of the significance of the dislocation, because
there the question is put whether a formula for the phenomena of
diffusion (drawn up by Kounstamm) is also valid for the description
of the reaction velocities, and this question is answered in an
affirmative sense.

For the chemical phenomena are essentially phenomena of diffusion
in which particularities will occur only in the partial mutual pene-
tration of atoms and molecules. In Scuerrer’s theoretical research
the significance of these particularities, which were represented in
the form of thermo-dynamic relations of the “intermediate states’,
was clear. It is self-evident that it is exactly these relations which
are modified by the catalyst, and that comparison of these relations
without and with the catalyst, must lead to a standard of the
dislocation.

SCHEFFER’s simple equation of the relation between the reaction
constant, the quantities in question, and the temperature is:

EE
nk=— nm + B.
n RT +
In this #, — # is a measure for the difference of energy

between the reacting substances and the intermediate state at the
reaction”), B contains the differences of entropy and constants
1) These Proceedings Vol. XIII, p. 789 and Vol. XV, p. 1109.

4) It is the energy which a gram-molecule requires above the mean energy al

the temp. 7 in order to react, and which is sometimes expressed by the name
of energy-increment.

214

which do not depend on the nature of the reacting substances.

As a difference of entropy is a measure for a greater or less
probability, and as this probability must refer to the reaction setting
in more or less easily, both this difference of energy and this pro-
bability can be calculated by the, aid of this formula from two
observations at different temperatures, and by carrying out this cal-
culation with and without a catalyst it can be ascertained in what
way these two relations are modified by the catalyst.

As appears from the following communication, this calculation
has been applied by B. van Trier to the acetylation of diphenyl-
amin with acetic acid anhydride both in presence of p-bromo (methy])-
phenylsulphonie acid as catalyst and without it, and the remarkable
result has been obtained that in the presence of a catalyst the
factor (f,— E) is about doubled, B becoming also considerably
larger. The conclusion may be drawn from this that in this case
by the addition of a catalyst more than double the energy is, indeed,
required to cause the molecules to react than without it, but that
this unfavourable factor is far more than compensated by the so
much greater probability for the setting in of the reaction in the
presence of the catalyst.

In his address at the spring meeting of the Ned. Chem. Ver.
(Duteh Chemical Association) of April 20 1922 ScuErrer expressed
this as follows: the hill of energy that is to be surmounted becomes,
indeed, higher, but the road across it, becomes very much broader.

Though it may be more or less a coincidence that in the case
examined by van Trier, the hill of energy is so much higher in
the presence of a catalyst than without it, it is yet the confirmation
of my view that the formation of a compound between the catalyst
and the substances to be activated sooner hampers than promotes
the reaction, and that the catalyst performs its accelerating action
not by combining with these molecules, but 2m spite of this combination.

The acceleration of the reaction takes place because simultaneously
with the formation of this compound a change of condition sets in,
the dislocation, in which the conditions for the occurrence of the
reaction become so much more favourable. The conception of dislo-
cation has found a confirmation through Scuerrrr’s theoretical investi-
gation, and a measure in the variation of the quantity B of his
formula.

In conclusion it may still be pointed out that the thermo-dynamic-
kinetic considerations have not brought the question why a catalyst
creates favourable conditions, nearer to its solution. The possibility
may be considered of the molecules assuming a certain position,

215

which causes the collisions to take place on the reactive parts of
the molecules (vaN Tairr, see following communication), or it may
be supposed that the reactive surface is enlarged, etc. etc. It is
certain that these changes of position or of form must take place
very rapidly, and the catalyst must be under very favourable con-
ditions with regard to the molecules that are to be activated, which
can hardly be imagined in another way than ensuing from a che-
mical affinity, which leads to dissociation equilibria that are esta-
blished very rapidly.

Delft, May 1922.

14
Proceedings Royal Acad. Amsterdam. Vol. XXV.

Botany. — “The disappearance of the diploid and triploid magni-
coronate narcisst from the larger cultures and the appearance
in their place of tetraploid forms’. By Dr. W. E. pr Mot.
(Communicated by Prof. G. van [TERSON JR.).

(Communicated at the meeting of June 24, 1922).

I. Introduction.

Simultaneously with my investigations into the causes which lead
to the immense variety of size and form in the Hyacinthus orientalis
in Holland, I commenced a similar research with respect to the
species of narcissi and narcissus-hybrids under cultivation. These
comparative researches have led to some noteworthy results. One
conclusion I arrived at was that, as is the case with Hyacinthus
orientalis, the remarkable size of the bulbs, leaves and flowers which
characterize the bastards of Narcissus Pseudonarcissus now cultivated,
correspond mainly with the number of chromosomes of which,
according to my cytological observations, the somatic nuciei consist.

This feature which, as far as I have been able to observe, occurs
in Hyacinthus orientalis only in the Dutch cultures, is found both
in England and in the Netherlands in Narcissus Pseudonarcissus,
and is more pronounced than in the hyacinth. In the latter there
are probably no tetraploid plants yet, whereas there are several in
the Narcissus Pseudonarcissus.

Il. Some results of the cytological investigation.

The preparations which I used in my cytological researches were
made in the same way as those for hyacintbs. The thickness of the
sections is 10 or 154 according to the size of the cells and nuclei.

ASCHERSON and GRAEBNER (1) give the Magnicoronati as the 1st
section of the sub-genus Hunarcissus. This section is entirely formed
by the class NW. Pseudonarcissus, which they divide into 2 sub-
classes, MN. festalis and N. minor. For convenience sake in describing
the varieties studied, I shall keep to this classification, except that
I shall place the sub-division MN. minor first.

1. N. minor.

The somatic nuclei of NM. minor (the type), NV. nanus, N. minimus
and N. cyclamineus (which is best classed with the sub-species

217

N. minor) consist of 14 cylindrical chromosomes, 10 long ones and
10 short ones.

2. N. festalis.

a. Diploid varieties.

The somatic nuclei of MN. muticus (syn. abscissus), Capax plenus
(which perhaps ought to be classed under N. minor), Telamonius
plenus (Double Sion, Wilmer’s great double golden yellow Daffodil),
large old double yellow trumpet Daffodil) also comprise 14 chromo-
somes which [ cannot distinguish from the former ones.

b. Heteroploid varieties.

N. Johnstoni Queen of Spain possesses somatic nuclei with 20
chromosomes. In Maximus and Golden Spur these nuclei consist
. of 21 chromosomes, so that judging from the number these varieties
are triploid.

The nuclei of Bicolor Victoria and Buttonhole (obtained from
Bicolor Victoria by budvariation) contain 22 chromosomes. The
chromosomes-garniture of both forms is the same.

The varieties King Alfred and van Waveren’s Giant are, to judge
from the number of chromosomes, tetraploid, for here the somatic
nuclei consist of 28 chromosomes.

In all the 14 forms above-mentioned and examined, the chromo-
somes — both long ones and short ones — correspond in size and
shape. The diploid nuclei always consist of 10 longer and 4 shorter
chromosomes. [ cannot yet state the exact number of long and short
chromosomes of the nuclei of the heteroploid forms. To do this it is
necessary to examine over 3000 good sections with dividing nuclei;
I have now examined this number. Probably the longer and shorter
chromosomes do not differ in length and breadth from each other,
and as in Hyacinthus orientalis the pairs of long and short chromo-
somes will not be distinguishable from each other by any characteristic
constant difference in form, as is described of NV. poeticus by
Stomps (3).

Ill. Self-pollination in diploid, triploid and tetraploid forms.

In contrast with Hyacinthus orientalis, in such categories as can
be distinguished cytologically, self-pollination yields good practical
results. From the few seeds of the diploid MN. minimus, minor,
cyclamineus (and WN. triandrus albus), taken in 1913, 1914 and 1915,
I have reared plants which are not distinguishable in bulb leaf and
flower from the parent species.

In the case of the triploid Golden Spur self-pollination yielded

14*

218

plants which in form and size differed from each other and from
the parent species.

By means of self-pollination of the tetraploid King Alfred 1 got
hundreds of seeds in 1914 and 1915. In 1916 I had about 1400
small bulbs. This spring 50 flowers came out, which differed greatly
in form and size from each other and from King Alfred. Most of
them were smaller than the parent species. The tetraploid Van
Waveren’s Giant can also be self-pollinated successfully.

IV. Conclusion.

1. Of the variety Maximus which I examined we are aware that
it was already known in 1600, from which it may be inferred that
even three hundred years ago there was triploidia in the magni-
coronate narcissi. Triploidia must have commenced with the wild
species or those again run wild, as the above-mentioned variety
and Golden Spur (first cultivated between 1885 and 1888) were
probably not obtained in nurseries (see 6). Regarding the wild
variety of MN. Johnstont Queen of Spain, BAKER assumes that this is
a hybrid between N. Pseudonarcissus and N. triandrus. If this is
correct — and the bastards cultivated of these two varieties leave
no room for doubt — this variety of Queen of Spain is in all
probability a bastard between a heteroploid form of N. Pseudonar-
cissus and WN. triandrus, as my experience shows the latter to be
diploid and to possess the same chromosome garniture as the diploid
narcissi already mentioned.

2. If we keep to the classification of AsCHERSON and GRAEBNER we shall
see that the feature of the heteroploidia was first seen in the genus or
group of N. Pseudonarcissus festalis major, the diversity which by
hybridization has principally yielded the large garden forms of the
present day.

It is very interesting how the increase in the size of these varie-
ties now cultivated can be traced. Up till 1885 — the diploid
varieties were chiefly grown. The culture of the Golden Spur marks
the beginning of the era of the triploid garden forms.

Bastards between Mazximus, Golden Spur and other valuable
kinds are grown, with the result that larger specimens have been
obtained, of which King Alfred (England; tirm of KeNparL) is the
finest. From this dates the advent of the tetraploid varieties (1899).

Just as the climax in point of size of the diploids seems to have
been reached in 7elamonius plenus, and of the triploids in Golden
Spur, the culminating point among the tetraploid forms seems to
have been reached in Van Waveren’s Giant. Nevertheless this

219

has been surpassed again by magnicoronate narcissi, the dimensions
of which are greater in one or two respects (e. g. Harly Giant,
Apotheose, Ajax Grand Vizier, Imperator and Mammoth; (see for
this the “Weekblad voor Bloembollencultuur”, 32nd. Year, 1922,
Nos. 85, 87, 89, 91 and 93), so that we may suppose that there
are already hypertetraploid forms. In this connection the significant
question: arises as to whether the number of chromosomes may go
on increasing indefinitely. Or, in other’ words: Is there any limit,
and if so, where?

The same question has been asked by Beumer with regard to the
increasing size. (“Weekblad” n°. 101). In the following table some
of the measurements are given in millimetres; they are nearly the
same as those given in the publication of SyprNHAM (4), with the
exception of those for Mammoth, which are mentioned in “Week-
blad’? n° 93.

, Tepals Paracorolla
Name of variety | Diameter i ieee
length | breadth] length Leca
Queen of Spain 82 35 15 28 28 20
Bicolor Victoria 101 + 35 44 44 22
King Alfred 107 40 28 44 50 28
Van Waveren’s Giant 127 50 38 50 50 28
Mammoth 140 7 ? 5 60 ?

3. It goes without saying that I cannot now sacrifice the plants
that I have obtained from King Alfred and Golden Spur for a
cytological examination. But even without this examination it seems
to me highly probable, especially when I test these observations by
those conducted by WinkKrer with Solanum (5) and those of van
OvererM with Oenothera (2), that these conspicuous differences in
form and size are primarily due to an unequal distribution of the
chromosomes in the reduction-dividing of which an unequal combi-
nation of the sex nuclei is the inevitable result.

LITERATURE.

1. PAUL ASCHERSON and PAUL GRAEBNER. Synopsis der mitteleuropaïschen Flora,
Bd. 3, Leipzig, Wilhelm Engelmann, 1905—1907.

2. CASPER VAN OVEREEM. Ueber Formen mit abweichender Chromosomenzahl
bei Oenothera. Beihefte zum Bot. Centralbl., Bd. 38, Abt. I, Heft 2, 1921.

220

3. THEO J. Sromps. Gigas-Mutation mit und ohne Verdoppelung der Chromo-
somenzahl. Zeitschr. f. ind. Abst. u. Vererb. Bd. 21, Heft 2, 1919.

4. Robert SyDENHAM. All about Daffodils. Sec. edition, Midland Daffodil Society,
1911.

5. Hans Winger. Ueber die Entstehung von genotypischer Verschiedenheit
innerhalb einer reinen Linie. Deutsche Gesellschaft für Vererbungswissenschaft.

Bericht über die Griindung und die erste Jahresversammlung. Leipzig. Borntraeger
1921.

6. D. M. Wiistennorr and R. H. Beeruorst. De Narcis. ato Batteljee en
Terpstra, 1908.

Plant physiological Laboratory of Prof. Ep. VerscHarre.t,
Hortus Botanicus, at Amsterdam.

Mathematics. — “Numbers of Circles Touching Plane Curves
Defined by Representation on Point Space.” By L.J. Smip Jr.
(Communicated by Prof. Henprik pe Veres),

(Communicated at the meeting of June 24, 1922).

The circles of a plane (degenerations included) may be represented
without exception through a one-one representation on the points
of a projective space. (R. Menke, Zeitschrift fiir Mathematik und
Physik 24 (1879)). We can arrive at it among others in the
following way:

Let W be an umbilical point of a quadric O? and let w be the
tangent plane at that point, B a plane parallel tow. A plane section
of O? with its pole relative to 0? is projected out of W on B as
a circle with its centre, and inversely. We consider this pole as
the image of the circle.

As a special case we may take for 0? a quadric of revolution of
which W is a vertex. If moreover (0? is a sphere, we get the repre-
sentation of Prof. Jan pe Vries (Verhandelingen 29); if W moves
to infinity it becomes the representation of Dr. K. W. Warsrra
(Verhandelingen 25).

Prof. Hx. pr Vrins has studied cyelographically the circles touching
a curve C in B of the order u, the class v, passing ¢ times through
both the circle points (with e different tangents in finite space which
cut C at those points in e +1 points), touching the line g,, singly in o
different points and having further no other singularities than d
nodes, * cusps, rt bi-tangents and « inflexional tangents (Verhande-
lingen 8).

We arrive at the same results through the above mentioned
representation. We shall only consider the principal ones.

The curve C' is projected out of W on O? as a curve consisting
of the two generatrices through W, counted « times, and a curve £
of the order n = 2u — Je passing (u—2e)-times through W. o pairs
of tangents at W coincide, because the parabolic branches of C
give rise to cusps of k in W. Further & has d nodes, x cusps and
(u—e) (u-—e—1) apparent nodes and no stationary tangents. By
means of PLickrr’s formulas we find other numbers characteristic of &.

From the nature of the representation there follows that the points
of the surface Z of the tangents of / represent the circles cutting
C at right angles. The tangent planes to O° at the points of &

222

envelop a developable surface K the points of which represent the
circles touching C and the points of the cuspidal curve / of K
represent the osculation circles of C. There exists a polar relation
between the points, tangents, and planes of osculation of & and the
planes of osculation, tangents, and points of /. Out of the characte-
ristie numbers of & and L we find accordingly through dualisation
the characteristic numbers of / and K, for instance:

Order of J: mtd 3u — be — 20

Order of K: r = Qu + r— 4e—o

Cusps of J: B = 5u-- 3y + 31 — Be — 30

Order of the nodal curve of K: rv = 4${(Qu + »— de —o)’— 13u—»
— St + 24e + 70}.

From this follows among others:

To a given pencil there belong r tangent circles of C, but to a
concentric pencil only r— (u — 2e) in finite space (class of the
evolute). If we have 3 curves C,,C,,C,, the surfaces K,,K,,K,, have
in all v,r,r, points in common, of which however there lie
Alu, — 2e,)(u, — Ze) (u, — 2e,) in W. The rest is the number of
circles touching the 3 curves.

Through a given point there pass m osculating circles of C. The
projection of / out of W on & is the evolute; / passes 5 times
through W, hence the order of the evolute is m—o. The evolute
has 2 cusps (vertices of C) in finite space and moreover u—2e—2o
at infinity, arising because u — 2e — 2o tangents of / pass through
W, lie in w and have their points of contact outside W.

Through a point there pass « circles touching C twice. The locus
of the centres of these bi-tangent circles is the projection of the
nodal curve of K. This curve however passes s = (tt— 28) (a —2e—1)—o
times through W, so that the order of the projection is only 2— s.

The number of tangents to 7 cutting / once more, is y= rm
+12, — 14m —6n. Of these 2o(u — Ze — 2) lie in w through W.
The rest gives the number of circles of curvature touching C once
more.

The number of triple points of K is:

t = 4 fr? — 3r (r + n + 38m) — 58r + 42n + 78m}.
Of these however
4 (u — 2e) (u — Ze — 1) (u — Je — 2)
jhe 2. 3
lie in W. The rest gives the number of circles touching C thrice.

If we work out these formulas they get the same form as those

of Prof. pe Vrins as is to be expected.

BO) a (re aes

Chemistry. — ‘Monochloro-trinitrobenzenes.” By Prof. A. F.
HOLLEMAN.

(Communicated at the meeting of June 24, 1922.)

So far only two of the six possible isomers were known, viz.
pierylehloride and a product obtained by Nierzxi (see below). For
an inquiry into the replaceability of substituents it was required to
prepare also the other four isomers. | have only been able so far
to lay hands on three, and without doubt I should have waited
with the publication of my results till the whole investigation had
been completed, if ] had not happened to hear that also others are
engaged in a study of the same subject.

CI 1-chloro-3, 4, 5-trinitrobenzene. This compound is
a easily accessible; it is indeed surprising that it has
I. | not been known long since. The starting-point for
NO Lo, its preparation is chlorodinitraniline 1, 4, 2,6, in which
4 NO, was substituted for the NH, group according
to the method of Körner and Conrarpr. The yield Cl
of raw compound amounts to 70°/, of the theory, Gs

and there is only little loss in the purification. The
substance may be recrystallized from benzene. It NO NO,
then melts at 168°. Large yellow erystals. NH,

CI 1-chloro-2, 3, 5-trinitrobenzene. This compound is

ar formed on very energetic nitration of 1-chloro-2,3-

* dinitrobenzene with a mixture of fuming nitric acid

NO,\ NO, and oleum of 50°/,. The heating of 160—170° i
continued for 5 hours. When the mixture is poured out into water, an
oil is obtained, in which crystals are formed after some time. By centrifu-
gation these are separated and then recrystallized from alcohol. Melting-
point 106°. The structure of this compound was verified by a treatment
with alcoholic ammonia, through which 2-chloro-4,6- CI
dinitraniline is obtained, melting-point 159°. This com- ZA na
pound is known. Much more easily, however, than | i
according to the methods used up to now it could be NON /NO,
prepared by chlorination of NH 2-4-dinitraniline with KCIO,
in hydrochloric acid solution. __/N NO The entrance of a NO,-group
at the place 5 in 1-mono- | | chloro-2,3-dinitrobenzene is
very surprising, as this ea group takes a position at mm
with regard to Cl and at p with regard to a nitro-group.

LI:

224

‘al 1-chloro-2,3,4-trinitrobenzene. In the nitration of
/\yo 1-chloro-2,3-dinitrobenzene by the method given
DEN ~~? under II, the oil from which Il was erystallized

\/NO, contains this third isomer. When the oil stands for
NO, a long time, the isomer crystallizes out of it in
colourless needles of the melting-point of 69°. They are purified by
recrystallization from alcohol. The structure of this compound can
also be determined by treatment with alcoholic ammonia. If the
action of the ammonia is allowed to last only for a short time,

only one of the nitro-groups is replaced by NH, CI
The aniline formed is 3-chloro-2, 6-dinitraniline for TR NO
1-chloro-2, 4-dinitrobenzene is obtained from it lise Thar 4
by deamidation. This aniline has the melting-point Ny NE
112°; it was unknown up to now. NO

CI 1-chloro-3, 4, 6-trinitrobenzene. This compound was

NO, ZN already prepared by Nretzxi by nitration of 1-chloro-
Weet al | 3,4-dinitrobenzene. On repetition of his experiments
\/NO, it appeared to me that the yield was small, and
2 especially very uncertain, because either the nitration
remains incomplete, or the reaction is so violent that total destruction
ensues. It is therefore, better to proceed as follows:
Cl NH, NO,
NOLY\ NON NO,/N
(lennard. elites ade ad)
we \ Jel \ /el
NO, NO, NO,

The substitution of NH, for Cl takes place in alcoholic solution
on the waterbath with addition of gaseous ammonia, till a test-
sample shows the correct melting-point of 174°. According to KORNER
and Conrarpi NO, tan then be substituted for NH,. The crude
product is coloured black. It can be purified by boiling with nitric
acid 1.4, followed by reerystallisation from alcohol. The melting-
point is 116°, as has been given by Nrierzk1.

No method of preparation Cl has as yet been found for the
last isomer, the dichloro: RIAN 6-trinitro-benzene ; probably
it is also present in the oil obtained in the nitration of
1-chloro-2,3-dinitrobenzene. ALP

Amsterdam, June 1922. Org. Chem. Lab. of the University.

|

Physiology. — “On Respiratory Oscillations in the Galvanogram
of Man.” By A. A. WernBero. (Communicated by Prof.
E. D. WikrsMa.) .

(Communicated at the meeting of June 24, 1922),

An inquiry into the psycho-physiological significance of the psycho-
galvanic reflex, which will ere long be reported in detail, gave rise
to the question whether the respiratory arhythmiae in the plethysmo-
gram which result from a predominating influence of the sympathetic
nerve, or of the vagus, on the heart), may be attended with
oscillations in the so-called rest-current of the galvanogram. In order
to set this question at rest the following experimental arrangement
was set up.

Our subjects were healthy individuals from 20 to 40 years of age, without any
anomalies of the heart or the urine. The current was lead off by non- polarizable
electrodes from the baths of a four-cell bath, and was registered with the quick
sensitive electrocardiograph of Siemens and Harske. The non-polarizable electrodes
consisted of porcus pots filled with a saturated zinc-sulphate solution, with a zinc
rod. These pots were placed in the baths, which contained a physiological NaCl-
solution heated to body-temperature. The current was recorded by the compensation-
method, as the condensator-method!) does not enable us to observe the slow
oscillations of the current. The sensitivity of the galvanometer, which was controlled
for each separate registration, amounted to 4 m.V. per cm. For convenience’ sake
I selected the three leads which are generally used for taking an electrocardiogram.
The method of EtHoven and Roos), which implies the use of fingerelectrodes
and has-the advantage of not being complicated by the electrocardiogram, did not
yield satisfactory results in these experiments. For further particulars of the pro-
cedure of the experiments I refer the reader to my article in the “Nederlandsche
Tijdschrift voor Geneeskunde” (1.c.).

With all the subjects thus far examined in this way (fifteen)
respiratory oscillations were noticeable in the level of the electric
curve. The only requisite was that the subjects had to be in a
condition of perfect quiescence, and that their attention be not
diverted by anything. Directly when they were more or less pre-

1) A. A. Wetnpera, Ned. Tijdschrift v. Geneeskunde; 66, II, 343, 1922.
*) W. EintHoven and J. Roos, Pfliiger’s Archiv; 189, 126, 1921.

226

occupied, either in consequence of the experiment or through the
after-effect of emotional occurrences, the respiratory oscillations dis-
appeared from the galvanogram, while in the case of still intenser
preoccupation other modifications in the level of the curve appeared,
which were independent of respiration. All these modifications in
the shape of the galvanic curve run parallel with the oscillations in
the level of the plethysmogram, either in the same or in the opposite
direction. Curve I is an illustration of the respiratory oscillations
in the galvanogram.

The following objections may be raised to the hypothesis that
these oscillations are connected with the respiratory oscillations in
the equilibrium between the sympathetic and the parasympathetic
(vagus resp.) nervous system :

a. The oscillations are effected by the movements of the respir-
ation-muscles.

b. They are caused by the changes in the electrical resistance
which are brought about by rhythmic movements of the arm during
respiration.

c. They are caused by the respiratory oscillations in the blood-
filling of the extremities. f

The first objection is done away with by the fact that in the case
of preoccupation the fluctuations disappear (curve II) whereas the
movements of the respiration-muscles continue. This phenomenon
might likewise tell against the second objection, just as the fact
that the subject always rested his hand on the bottom of the arm-
baths, Hereby the movements of the upper-arm, which were already
none too vigorous at first, were considerably relaxed if not checked
entirely. However, with six subjects I have registered the movements
of the upper-arm with the aid of a very sensitive tambour affixed
to the arm-bath, its rubber membrane, which is provided with a
knob, resting on the m. biceps. Hereby it was proved that the move-
ments of the upper-arm do not affeet the shape of the galvano-
gram. This is illustrated in Curve II] where the movements of the
upper-arm are reproduced graphically ; of oscillations in the level
of the galvanic curve, on the other hand, no trace is to be seen.
Curve IV further shows that even considerably stronger involuntary
arm-movements do not alter the shape of the galvanogram.

Finally, that the electric modifications in respiration cannot be
ascribed to the bloodfilling of the extremities is demonstrated by
curve V, which exhibits distinct respiratory oscillations of the galvano-
gram, although the extremities, from which current were derived,
had been made bloodless by bandaging.

Plethysmogram

Insp

Respiration
Exp

Galvanogram

Time (ls sec.)

Movement-curve ;
right upper-arm.

Pores eee eee Pe a tee tel
mah ih Bee : os ee geh |

Soa ze Ae - ZE ese Eken Deh NE Vets ates a rk ee rde EE

II. The same. 3 VI ’22 Lead I. Comp. IES: vid. G. 2°3lyears, 19 Vie 22:
Pre-occupation curve. Lead II. Comp. Pre-occupation-
curve, with control.

Movement-
curve; left
upper-arm

IV. G.T. 2 39 years 6 VI’ 22. V. D.T. d 21 years 9 VI’22. Lead II. Comp.
Lead III. Comp. Rest-curve, Rest-curve with dehematized right arm and
with control. left leg. Plethysmogram left hand,

228
SUMMARY.

The galvanogram of Man displays with a low degree of conscious-
ness, oscillations which run parallel to respiration and are very likely
connected with the respiratory oscillations in the condition of balance
in the involuntary nervous system, as these oscillations disappear
with preoccupation and as they are not influenced by the involuntary
respiratory movements of the arms and are not the outcome of the
modifications in the bloodfilling of the extremities, from which the
current is derived.

From the Laboratory for Psychiatry
June 1922. of the Groningen University.

end

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KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM.

PROCEEDINGS

VOLUME XXV
N°s, 7 and 8.

President: Prof. F. A. F. C. WENT.
Secretary: Prof. L. BOLK.

(Transiated from: “Verslag van de gewone vergaderingen der Wis- en

Natuurkundige Afdeeling,” Vol. XXXI).

CONTENTS.

EuG. DUBOIS: “Phylogenetic and Ontogenetic Increase of the Volume of the Brain in Vertebrata”,
p. 230.

R. MAGNUS and A. DE KLEYN: “A further Contribution concerning the function of the Otolithic
Apparatus”, p. 256.

L. RUTTEN: “Cuba, The Antilles and the Southern Moluccas”, p. 263. (with one plate).

B. SJOLLEMA and J. E. VAN DER ZANDE: “Changes in Milk due to Sterile Inflammation of the
Udder”. (Communicated by Prof. C. EYKMAN), p. 275.

M. W. BEIJERINCK and L. E. DEN DOOREN DE JONG: “On Bacillus polymyxa”, p. 279.

W. VAN DER WOUDE: “On the Light Path in the General Theory of Relativity”. (Communicated by
Prof. H. A. LORENTZ), p. 288.

G. BREIT: “Calculations of the effective permeability and dielectric constant of a powder’. (Com-
municated by Prof. H. KAMERLINGH ONNES), p. 293.

J. J. VAN LAAR: “On the Heat of Mixing of Normal and Associating Liquids”. (Communicated by
Prof. H. A. LORENTZ), p. 309.

J. BOEKE: “On the Regeneration of Sensitive End-corpuscles after section of the nerve”, p. 319.

H. R. KRUYT and C.F. VAN DUIN: “Heterogeneous catalysis and the orientation of adsorbed
molecules”, p. 324.

H. A. BROUWER: “Fractures and Faults near the Surface of Moving Geanticlines. II. Abnormal
Strikes near the Bending-points of the horizontal projection of the Geanticlinal axis”, p. 327.

P. VAN ROMBURGH and J. H. N. VAN DER BURG: “Cyclic Derivatives of Mannitol”, p. 335.

F. A. H. SCHREINEMAKERS: “In-, mono- and divariant equilibria’. XXII, p. 341.

B. L. VAN DER WAERDEN: “Ueber Determinanten aus Formenkoeffizienten”. (Communicated by
Prof. L. E. J. BROUWER), p. 354.

H. J. BACKER: “The dissociation constants of sulphonacetic and z-sulphonpropionic acids”. (Com-
municated by Prof. P. VAN ROMBURGH), p. 359.

ARIE QUERIDO: “On the progress of the veratrin-poisoning of the striated frog-muscle”. (Commu-
nicated by Prof. G. VAN RIJNBERK), p. 364.

L. BOLK: “The Problem of Orthognathism”, p. 371.

Erratum, p. 381.

Proceedings Royal Acad. Amsterdam. Vol. XXV.

Palaeontology and Zodlogy. — “Phylogenetic and Ontogenetic
Increase of the. Volume of the Brain in Vertebrata’. By
Prof. Eve. Dusois.

(Communicated at the meeting of June 24, 1922).

One of the most striking and important palaeontological facts ever
brought to light in the investigation of the strata of the earth, is
that of the extremely slight volume which the encephalon possesses
in the earliest forms of Reptiles, Birds and Mammals. By this
feature do these for the rest very differentinted and often gigantic
earliest representatives of their class differ from the forms immediately
following them and from the modern ones, in a way which must
almost seem ridiculous to the comparative anatomist.

As regards Reptiles this has especially become known, by the
discoveries of Marsu, about the Dinosauria, the principal terrestrial
animals of the Mesozoic Era. In them the spinal canal, in its whole
length, was not seldom wider than the cranial cavity. In Stegosau-
rus, from the Lowest Cretaceous in Wyoming, the cross-section of
the sacral enlargement of the spinal canal (this in connection with
the large hind-legs) was ten times as large as the cranial cavity. In
a Diplodocus of a computed body length of 24 meters, from the same
strata, this cavity is only 9 em. long and 5 cm. wide, whereas that
of an adult alligator, with a tenth of that maximum body length of
its mesozoic distant relation, has a length of 6'/, cm. and a width
of 3 cm. Also in Theromorpha and Pterosauria the cranial cavity
is very small.

Ichthyornis, described by Marsn from the Upper Cretaceous of
Kansas, possessed only the third of the cranial capacity of the Large
Sea Swallow (Sterna cantiaca), with which this toothed Mesozoic bird
bore considerable resemblance in size and structure of its skeleton,
probably also the mode of life of the two birds was similar.

In the class of the Mammalia, the Eocene primitive Carnivora, the
Creodontia, possessed very little encephalon, which appears clearly
on comparison of the cast of the brain-cavity of Aretocyon, from
the Basal Eocene of Reims, with that of a dog of similar size of
body (Fig. 1, A). The Condylarthra from the Lower Eocene, from
which the existing sub-orders, the Perissodactyla and Artiodactyla

231

both originated, had also brains of incomparably small volume; side
by side with the brain cast of Phenacodus, from the Wasatch
Formation of Wyoming, that of a pig of similar size of the body
appears as gigantic (Fig. 1, B). Also other Eocene Hoofed Mammalia,
the Amblypoda, had very small brains. Thus Coryphodon, from the
Wasatch Formation, in comparison with a Rhinoceros of similar
size (Fig. 1, C).

Fig. 1. Brain cast of: A. Arctocyon and Canis; B. Phenacodus
and Sus; C. Coryphodon and Rhinoceros. (After OsBorn) !).

In all these cases the most compounded, functionally most intri-
cate parts of the encephalon, especially the cerebrum (hatched in
Fig. 1), have the smallest volume. They in particular have not yet
come to a fuller growth. But in the Miocene, partly already in the
Eocene Period, the brain in the Mammalia reaches the volume and
the proportion of its sub-divisions of most modern types.

As remarkable as this sudden, at all events comparatively rapid
increase of the volume of the brain in the classes of Reptiles, Birds,
and Mammals is the other paleontological fact, that in the Hominides,
which geologically do not appear until very. late, the brain imme-
diately possessed the same volume already in the earliest of the
known crania as in modern ones. The expectation that by means of
these skulls a gradual increase of the volume of the brain might
be shown, up to the exceptional capacity whose possession raises

1) H. F. Ossporn, The Age of Mammals in Europe, Asia and North America,
p. 173. New York 1910.
15*

232

modern Man so high above the animals, has not been realized.
This however does not apply to Pithecanthropus, if this fossil
anthropomorphous Primate is not considered to be of a separate
family, but reckoned to belong to the Hominides. For he possessed
only two thirds of the cerebral volume of the Australian aboriginal
(which he resembled in body size and also in the main features of
his skeleton), but twice that of anthropoid apes of the same body
size. But also this “precursor of Man” is of a late date — probably
not before the Pliocene. The transition from such a volume of brain
as that of the Anthropoid Apes to the modern human volume seems
at all events to have been a rapid one, and halfway there is still
that of Pithecanthropus.

This organ, upon which depend inscrutable attributes of animal
life, of the greatest degree, shows therefore an indubitable progress
in the geological past. But it is also certain that this phylogenetic
growth of the encephalon, as a whole and in its most compounded
parts, took place with starts, and much seldomer than that of the
other parts of the body, of which now one part, now another is
again and again seen, in the most diversified ways, to increase in
volume and complexity, the whole body not seldom growing into
gigantic dimensions.

The question now suggests itself what the proportion has become
between the volume of the brain and the size of the body through
phylogenetic and ontogenetic growth, i.e. increase from species to
species and from individual to individual, in adult animals of the
present time.

It can easily be ascertained that the brain volume, reached by a
species of animals in adult state, depends both on the size of the
body and on the stage of development attained by the brain, which
determines the degree of the functions of the organ.

It is not astonishing that the absolute brain weight of Man is
surpassed by that of the Elephant and the large whale species.
The largest whale species, which is a thousand times heavier than
Man, possesses five times his brain weight. It is also self-evident
that such a gigantic species of the cat family as the Tiger has much
larger brain than the Domestic Cat; to sixty-four times the body
weight of the latter, the Tiger has ten times its brain weight. Keeping
to the same species we find in an adult dog of the size of the
Wolf, of about 40 kg. body weight, double the brain weight
of a lap-dog weighing about 2 kg.

But besides on the size of the body, the brain volume depends
also on the stage of development of this organ, on the particular

233

structure and functions of other organs, and on other not easily
measurable factors which determine the cephalisation of the
central nervous system. When we compare Man with animals of
the same body weight, when, in other words, we eliminate the factor
body weight, we see that he far surpasses all fhe animals. He
possesses three times the brain weight of a species of anthropoid
apes of the same weight and more than six times that of an equally
heavy gazelle. We may also say that the coefficient of cephalisation
x of Man is three times as great as that of Anthropoid Apes and
more than six times as great as that of the Gazelle.

We may assume equal cephalisation for the Cat and the Tiger,
and yet we see the body weight increase in a much greater pro-
portion than the brain weight. The same fact is found on comparison
of the Mouse with the Rat, of the Pigmy Antilope with the Beisa-
Antilope ete. Evidently the weights of brain and body, also with
equal development of that organ, are not simply proportional to
each other. The large species of the same genus, and also the large
adult individual of the Domestic Dog species always has less brain
weight in ratio to the body weight than the small species and the
small adult individual. On account of the equality of the densities,
the volumes may be substituted for the weights, and itis, therefore,
possible that another measure of the body than the volume, for
instance the surface, which is proportional to the 2/3; power of the
volume, — for which the weight P of the large animal may be put,
and the weight p of the small one, — determines the quantity of brain
— volume or weight — of the species. A priori it seems, indeed, that
there is a good deal to be said for this view, for the sensual areas, the
physiological cross-sections of the muscles, which determine muscular
force, the superficial extent of the body, on which metabolism
depends, are proportional to the surface of the body. The brain
weights # and e of two animals differing only in body weight, but
with for the rest quite identical organisation, may always be put
K=xP and e=<xp"; then the exponent of relation r, indicating
the power of the body weight with which the brain weight increases
log E—loge
log P—log p

or decreases, can be calculated from the equation r=

E
and == Pp will be found.
Twenty-five years ago, making use of the observations of weight
published by Max WeBer *) a year before, I found thus 5/9 as mean

1) Max Weger, Vorstudien über das Hirngewicht der Säugethiere, in Festschrift
für CARL GEGENBAUR, p. 105—123. Leipzig 1896.

234

value of 7 in seven pair of mammalian species, i.e. a slightly smaller
exponent than would correspond to the proportionality of the brain
weight with the surface dimensions of the body’). The discrepancy
appeared to be constant, and the same exponent was found for
Birds by Louis Laricqur and Pierre Girarp in 19057), and for
Reptiles and Fishes by me in 1913*). The exponent 5/9 holds un-
doubtedly for all Vertebrata. Certainly this “strange power” of the
body weight cannot be attributed to insufficiency of the data; it is
impossible that we have to do here with a “rough empirical law,
as limit of a sum of different functions”. The relation found between
the weights of the brain and the body must be a simple, rational
one. As this exponent indicates the relation of species to species, a
relation which must have come about with the origination of the species,
I will designate it here as phylogenetic exponent.

In the system of coördinates of Fig. 2 the body weights in kg.

200

150.

100.

Fig. 2

1) Eve. Duvgors, De verhouding van het gewicht der hersenen tot de grootte van
het lichaam by de Zoogdieren. Verhandelingen der Kon. Akademie van Weten-
schappen te Amsterdam. Tweede Sectie. Deel V, N°. 10. 1897. — Also: Sur le
rapport du poids de l'encéphale avec la grandeur du corps chez les Mammifères,
in Bulletins de la Société d'Anthropologie de Paris 1897, p. 337—376.

*) Comptes Rendus des séances de l'Academie des Sciences. Paris 1905, 1,
Tome 140, p. 1057 — 1059.

5) These Proceedings, Vol XVI, p. 651—654. 1914.

235

are indicated on the abscissa, the brain weights in gr. on the
ordinate. The points Z, V, ¥, and L refer to the averages of those
weights of the species Canis zerda, Canis vulpes, Canis familiaris
and Canis lupus. The relation of brain weight and body weight in
these species of the genus Canis is here graphically represented by
the full exponential curve Z V L, defined by the equation H = 0.41
Ph, and by the point F, whose position is defined by the
equation 89 — 0.385 « 18000%. In Fig. 3 the same relation is
fog 1000 3.0

C.lupus 40000 147.6
6 C.famil. 18000 89

ale C.vulpes «120 52

ZE C.zerda 2000 279 or |
JERE Ga
fe dae OE a EKE
| all sr Eel NT la I

(ce) Ea a

EERE
ame dE
EERE

un

=

°
2 .

to)

fog. 10! 1.0
SOM ue eer OON (fe Oe Oe Oele Od
loq tooo log.10000

‘o
ow
oo

Fig. 3

represented by the full logarithmie line, a straight line with which
the lines of genera and species with other cephalisation would run
parallel. |

An entirely different exponent of relation, viz. about 1/4, i.e. less
than 5/13, half the value of the exponent holding from species to
species, was found on comparison of large adult individuals of one
and the same species by Lapicque for the Domestic Dog *) in 1898,

5) L. Laricque, Sur la relation du poids de l'encéphale au poids du corps.
Comptes rendus de la Société de Biologie. Paris 1898, p. 63.

236

and independently of the distinguished French physiologist, in the
same year, by me for Man'). In 1907 this result was confirmed by
Lapicgue’) for Man; at present, from the new observations of weight
on 150 Berlin dogs by Berrnorp Krarr®) I can corroborate the
result obtained by Laricqur from Ricuptr’s 188 Paris dogs *).

Similar low interindividual exponents of relation as for Man and
the Domestic Dog are now also valid within other species. For
obvious reasons: very important differences of the body weights in
one case, numerousness of the observations of weight in the other,
the species Domestic Dog and Man are most suitable for a comparison
of the individuals. But we so often meet with similar values, lying
in the neighbourhood of 5/18 == 0.27 or lower, within other species,
that here the existence of another, but equally real law may be
admitted.

The same relation of brain weight and body weight as between
large and small adult individuals of Man and the Dog is certainly
also valid for the Horse. The data are not very numerous here,
but the differences in body weight are comparatively large. A
heavy Belgian horse, according to Cornnvin’), weighed 1040 kg.
when alive, and its cranial capacity was 805 c.c.; a light Camargue
horse had only 320 kg. living weight, and its cranial capacity
was determined at 585 c.c. From this an exponent of relation of
0.2708 can be calculated. Prof. J. C. Ewart at Edinburgh was so
kind as to send me, for measurement, the skull of a very typical
Shetland pony, a mare of 36'/, inches or 92'/, em. height. Length
of skull, from ineisivi to oceiput, 40'/, cm. The capacity is 475 c.c.
lowe to Dr. C. KerBerT the communication of the body weight
of such a pony living in the Amsterdam zoological gardens, a male

1) Eva. Dupois, Ueber die Abhängigkeit des Hirngewichtes von der Körper-
grösse beim Menschen. Archiv für Anthropologie. Band 25, p. 423—441. Braunsch-
weig. 1898.

*) L. Lapicgue, Le poids encéphalique en fonction du poids corporel entre
individus d'une même espèce. Bulletins et mémoires de la Société d’ Anthropologie
de Paris. Séance du 6 Juin 1907. 5™e Série, Tome 8, p. 315. Paris 1908.

8) BertHotp Karr, Studien zum Domestikationsproblem. Untersuchungen am
Hirn. Bibliotheca Genetica (E. Baur). Band II. 180 pag. My calculations are to be
published in Bijdragen tot de Dierkunde. XXII. Hat sich das Gehirn beim Haus-
hunde, im Vergleich mit Wildhundarten, vergrössert, oder verkleinert ? Leiden 1922.

4) Crarres Ricuet, Poids du cerveau, de la rate et du foie, chez les Chiens de
différentes tailles. Physiologie. Travaux du Laboratoire de M. Crarres RicHEr.
Tome Deuxième, p. 381—397.

5) CH. CORNEVIN, Examen comparé de la capacité cranienne dans les diverses
races des espèces domestiques. Journal de médecine vétérinaire et de zootechnie,
publié a l'École de Lyon, 3me Série, Tome 14, p. 24. 1889.

237

horse of the same height (92 em.) and skull length (41 em); it
was 128 kg. By comparison with Cornnvin’s heavy Belgian horse
I now find and exponent of relation of 0.2528. The heaviest of 15
male horses, according to Conin'), a Percheron of 501 kg. dead
weight, compared with the lightest male horse (‘de petite taille”) of
this group, of 288 kg. dead weight, gives an exponent of relation
of 0.1855. The heaviest horse was probably less emaciated than
the lightest; hence the exceedingly low exponent.

For two groups, each of six domestic rabbits, formed from
Mi.ver’s records *), one of an average body weight of 4386 gr.
the other of 1727 gr, I find an exponent of relation of 0.2512.
Two groups, each of five male moles, from MANouvrier ®), yield 0.234.

Hight domestic ducks, of 1756 gr. average body weight, compared
with a dwarf of the same domestic species, of 755 gr. body weight,
according to Timmann’s*) records, yield an exponent of relation of
0.3096. A cock of 1745,7 gr. body weight with a hen of 985.2 mrs
from Fatck’s *) report, yield an exponent of relation of 0.2248.

Two groups, each of six Bull Frogs (Rana catesby ana), according
to Donarpson *), of 244.5 and 164 gr. mean body weight, give an
exponent of relation of 0,2516. Also the average cranial capacities
of 9 male and 11 female Australian aboriginals in relation to the
mean volumes of the six long bones, from Havenr's observations’),
yield an exponent of 0.2770.

In the Figures 2 and 3 the dotted lines give a graphical record
of the relations of the weights of the brain and the body between

') G. Gorin, Traité de physiologie comparée des animaux. 8™¢ Edition, Tome E
p- 302. Paris 1886.

%) E. Miter, Vergleichende Untersuchungen an Haus- und Wildkaninchen.
Zoologische Jahrbiicher. (Spengel). Abteilung fiir Allgem. Zoologie and Physiologie
der Tiere. Band 36, p. 585. Gesamttabelle XXVa. Jena 1919.

5). L. MANoUvRIER in Dictionnaire de Physiologie par Cg. RicHer, article
»Cerveau”, p. 680. Paris 1898.

*) O. TiMMANN, Vergleichende Untersuchungen an Haus- und Wildenten. Zoolo-
gische Jahrbiicher, ibid., p. 653.

*) CG. Pu. Faucx, Beiträge zur Kenntnis der Bildungs- und Wachsthumsgeschichte
der Thierkörper. Schriften der Gesellschaft zur Beförderung der gesammten Natur-
wissenschaften zu Marburg. Band 8, p. 242. Marburg 1857.

8) H. H. DoNArpson, On a Formula for Determining the Weight of the Central
Nervous System of the Frog from the Weight and Length of its Entire Body.
University of Chicago. Decennial Publications. Vol. 10. (1902), pu a.

1) Orro Haveer, Der Gehirnreichtum der Australier und anderer Hominiden,
beurteilt nach ihrem Skelet. Anatomische Hefte (Merken und Bonnet). 1. Abteilung.
Heft 179. Band 59, p. 589: Tabelle I, p. 616—617: Tabelle Ill. München und
Wiesbaden 1921.

238

adult individuals of four species of the genus Canis. In Fig. 2 they
are again exponential curves, defined, for the Domestic Dog, by the
equation LH = f P°*4—=8.475 POB (in which f is found from
89 = f X 18000), and for the wild Canidae, # = 4.615 Pm which
52
6120 ‘hs
less steep than the lines for these relations from species to species,
which they intersect in the points of the means, as far as the wild
species are concerned. | have derived the mean point for the Domestic
Dog, and the line for theindividual relation within this species from
observations of weight on 434 dogs, i.e. 152 new ones by Krarr '),
Rrcnet’s 188 observations *), Laricqur and DnérÉ's 47 *), RÜpinarr’s
19 *), Wirper’s 16°), Max Weper’s 12°). On the ground of these
data 18 kg. may be admitted for the mean weight of the Domestic
Dog, 89 gr. for its mean brain weight. The brain weight is certainly
at least 6°/,, probably 10°/, lower than in a wild species of Canis
of the same weight. This can only be considered as a consequence
of domestication, i. e. of unnatural mode of living. Something of
the same kind was found by DoNaLpsoN and Harta‘) in the domesti-
cated albino-form of the Brown Rat (Mus norvegicus). Not only
the body weight has been reduced in this domestic Rat, but the
brain weight comparatively to a greater degree, a phenomenon of
domestication due to a diminished growth of the brain, which was
already known to Darwin (1868) for the domestic Rabbit *), and
which was afterwards confirmed by Laricque’), Kuatt’’), and

4.615 = ) In Fig. 3 they are straight lines, both of them

1) B. Krarr, lc. Haupttabelle at the end of his work.

8) Cu. Ricuet, l.c.

5) L. Laricgue in Bulletins et mémoires de la Société d’Anthropologie de Paris
1907, p. 316.

4) N. Rüpinger, Ueber die Hirne verschiedener Hunderassen. Verhandlungen der
Anatomischen Gesellschaft. Jena 1894. Ergänzungsheft zum 9. Band (1894) des
Anatomischen Anzeigers, p. 173—176. ;

5) B. G. Wiper, Cerebral Variation in Domestic Dogs. Proceedings of the
American Association for the Advancement of Science, 224 Meeting (1873), p. 235—
236. Salem 1874.

6) Max Weger, Vorstudien über das Hirngewicht der Säugethiere l.c, p 112.

7) H. H. DonNaLpsonN and Srinkismi Harar, A Comparison of the Norway Rat
with the Albino Rat. Journal of Comparative Neurology. Vol. 21 (1911), p. 417 —
458, particularly p. 454—455.

8) Ga. Darwin, The Variation of Animals and Plants under Domestication. Chap. IV.

9) L. LaPicqve in Bulletins et mémoires de la Société d’Anthropologie de Paris
1907, p. 331—337: „Régression cérébrale des animaux domestiques”’.

10) B. Krarr, Ueber die Veränderung der Schädelkapazität in der Domestikation.
Sitzungsberichte der Gesellschaft Naturforschender Freunde zu Berlin. 1912, p. 155

239

Mörrer |). The same cerebral regression by domestication was found
by Lapicqur’) for the Ox and the Sheep, by Krarrt *) and Brricke *)
for the Ferret, by Lapicque*) and Timmann ‘) for the domestic Duck,
and now by me for the Domestic Dog. For 72 of Donarpson and
Hatar’s wild Mus norvegicus‘) of both sexes, of 335 to 525 gr.,
averagely 389.861 gr. body weight, with averagely 2.402 gr. brain
weight, and 71 male and female wild rats of 275 to 325 gr.,
averagely 300.211 gr. body weight, with an average brain weight
of 2.299 gr, I calculate an exponent of relation of 0.1674. That
this exponent is considerably smaller than is usually found between
individuals of one species, may be readily explained in this way
that DoNALDSON and Harar give the body weights irrespective of
the state of adolescence and the fat percentage (of which they state
that it augments with age); part of the increase of the body weight
is, therefore, not accompanied by increase of the brain weight, as
is the case on comparison of adult individuals only, and which are
in a medium condition.

In Fig. 4, after DoNALpsonN ®) the exponent of the individuals with
body weights between 250 and 446 gr. may be calculated at 0.1572
for the male wild Mus norvegicus (from observations of weights on
232 male specimens of all ages). From Donatpson’s Table 85 *)
the exponent 0.1554 may be calculated for body weight of 301.0
to 389.7 gr. The exponent is 0.1342 for the male albino of this
species of 181 to 350 gr. body weight. The relatively smaller increase
of the brain weight with increasing body weight of the (domestic)
albino Rat finds expression in the slower ascent of the curve and
the lower value of the exponent. It may be admitted that the
exponent is in general somewhat lower in the domesticated species
(not leading a natural life), because the brain increases somewhat

‘) E. Mürrer, Vergleichende Untersuchungen an Haus- und Wildkaninchen.
Loe. cit. p. 503—588.

8) See note 9 foregoing page.

$) See note 10 foregoing page.

4) H. BerncKe, Vergleichende Untersuchungen an Frettchen und Iltissen. [bid.,
p. 589—620.

5) O. TimMANN, Vergleichende Untersuchungen an Haus- und Wildenten. Ibid.,
p. 621—656.

6) DoNALDSON and Harar, l.c., p. 426—427.

1) From Chart 3), p. 201 in H. H. Donatspon, The Rat. Reference Tables
and Data for the Albino Rat (Mus norvegicus albinus) and the Norway Rat (Mus
norvegicus). Memoirs of the Wistar Institute of Anatomy and Biology. N°. 6.
Philadelphia 1915.

8) Ibid, p. 208:

240

less under these circumstances, in proportion to the body weight
grows in a less degree than in the natural state.

ie) 50 100 150 200 250 300 350 400 450

Fig. 4.

In 1918 I found an exponent of 5/13 = 0,27, Le. of precisely
half the value of the exponent holding for the relative brain weights
from species to species, on comparison of the volumes of largest,
Le. of full-grown, homologous nerve or ganglion cells
in relation to the body weights of adult animals of very different
sizes, both of one species and of different species. Compare Tables |
ange tl +):

Though in the microscopical image of the grey cortex the nerve
cells are placed as densely and are as unequal in size as the stars
in the telescopic image of the Milky Way, we may yet admit a
relation between the average size of these cells and the size of the
body, and look for the explanation of the relation holding for the
volume of the brain in the nerve cells, the elements from which
the brain is composed.

The exponent holding between the adult individuals of one and
the same species, in the relation of the body weight to the brain
weight, may now be distinguished as ontogenetic exponent from

1) These Proceedings, Vol. XX, p. 1828—1334. There too the fuller references
to the works of the authors mentioned in the last column of Table I.

241

T ABEE.
Body Nerve cell
Reference to authors,
weight MAS, ee date and page of reported
(grammes) aa, En abn measurements
1, Elephas indicus 3600000 84.4 Col. ant. | I. Hardesty. (1902). 160, 161
2. Equus caballus 562500 61.9 ek al er : ‘ en el
3. Homo sapiens 72000 58.0 x STEN 3 „ 169, 160
4. Lepus cuniculus dom. A. 2000 39.2 en aa 2 2 160
5. Mus norvegicus albinus. A 250 34.7 se ie a _ a B
6. Mus musculus albinus 20 27.4 - = . pl a» 160, 164
7. Lepus cuniculus dom. B 2000 56.0 Spin. G. Levi. (1908). 200
8. Mus musculus. A 20 37.2 5 ” ” » ”
9. Canis familiaris. A 23000 80.8 7 » (1906). 331, 332
10, Canis familiaris. B 3150 67.5 7 5 5 “ - 7
11. Mus norvegicus albinus. B 250 16.5 Purk. | Addison. (1911). 469
12. Mus musculus. B 20 13.0 2 Obersteiner. (1913). 5
13. Felis leo 119500 69.5 max. Betz Brodmann. (1909). 83
14. Felis pardalis 10433 66.5 med. a Bevan Lewis. (1880). 53
69.0 max. + Brodman (Lewis) (1909). 83
15. Felis domestica 3300
60.0 med. ia Bevan Lewis. (1880). 85

the exponent holding from species to species, as it expresses the
relative individual growth of the brain to the adult state.
In consequence of this difference in the fixed relations of the

weights of the brain and the body, between homoneuric species
on one side, individuals of a species on the other side, i.e. the
difference between the phylogenetic and the ontogenetic exponent,
small individuals have comparatively more, large individuals compa-
ratively less brain than species of corresponding mean body weight.

This appears graphically in Figures 2 and 3. The difference ean
become very great in dwarfs and giants of one species; it is very
striking in the Figures 5 and 6, which give the accurate outlines, in
natural size, of the skull of a medium sized fennec (Canis zerda), the
smallest species of the genus Canis, and one of the smallest
individuals of the species Domestic Dog, of a diminutive breed,

242

E-ARBMEIEN Ul

Calculated Values of the Exponent r for the Increase of the Volume
of the Nerve Cells with the Body Weight

Proportion
DE sotien of the | Exponent

body weight
1. Elephas indicus and Mus musculus albinus Col. ant. 180000 : 1 0.2789
2. Equus caballus and Mus musculus albinus s . 28125: 1 0.2387
3. Homo sapiens and Mus musculus albinus - es 3600 : 1 0.2747
4. Lepus cuniculus dom. A and Mus musculus albinus Dn pe 100: 1 0.2333
5. Mus norvegicus albinus. A and Mus musculus albinus 5 Ps Pa | 0.2805
6. Lepus cuniculus dom. B and Mus musculus. A Spin. 100: 1 0.2665
7. Canis familiaris. A and Canis familiaris. B a Dok 0.2975
8. Mus norvegicus albinus. B and Mus musculus. B Purk. Pt! 0.2832
9, Felis leo and Felis domestica Betz 36 : 1 0.2804
10. Felis pardalis and Felis domestica . Jl 0.2681

probably a toy-terrier, of the same body weight, after photographs
which | owe to Prof. W. Lrcur at Stockholm. The brain weight
in the diminutive individual of Domestic Dog, with only a ninth
of the mean body weight of the species, is indeed quite 87°/,
more than the mean of the smallest species of Canidae’). The
amount and the plus or minus sense of this difference with species
ig dependent on their body weight. The smaller the species
of the genus Canis, the more it is exceeded in brain weight by
an individual of the same size of the Domestic Dog species.
Domestic dogs of the size (the body weight) of the common (Euro-

1) The body weight of a female fennec, killed in its African home, was 1.5 kg.
according to KiLatr (Studien zum Domestikationsproblem, p. 36), the weight of
the brain was 25.2 g. The capacity of an almost adult female skull in the Leiden
Museum of Natural History, observed by me, was 20 ec.c., of two other skulls,
of which the sex is not indicated, in the Berlin Zoological Museum, the capacity
observed by Kuarr, is resp. 20 and 18 c.c. When for the species 2 kg. body
weight, and 27.9 gr. brain weight is assumed, this gives certainly about the true
ratio; absolutely these weights are possibly estimated too high. From the observa-
tions of Krarr (Ibid., Haupttabelle) on 17 adult toy-terriers (Zwergpinscher), of
an average body weight of 3.11 kg. with 58.1 gr. brain weight, I calculate for
2 kg. body weight of this diminutive breed the brain weight at 52.3 gr.

243

pean) Fox have only slightly more than 28°/, more brain weight
than this small species. Very large domestic dogs, of about 40 kg.,

Fig. 5.

Fig. 6. Skull of a domestic dog of diminutive breed, in natural size.

i.e. the mean body weight of the Wolf, have 25°/, less brain
weight than this largest member of the Canidae’).

It is now of great importance that the ontogenetic exponent is
equal to the exponent indicating the relation of the body weights or

1) Through comparison with two foxes from France and one wolf from America
LAPICQuE (loc.cit. p. 329) had already pointed out these differences in 1907.
Afterwards Krarr (Ibid, p. 36) corroborated them with more numerous data
through a comparison with the Jackal and the Wolf. According to KLarrt's
records on ten (German) foxes (Ibid. p. 37) and eleven domestic dogs (Haupt-
tabelle) of about the same size, 6.12 kg. may be taken for the body weight of

244

volumes to the volumes of homologousnerveorganglion cells,
both between adult individuals of one species and between different
species. This confirms that, with increasing body weight, from adult
individual to adult individual of one and the same species, only
the volume of each nerve cell in the brain increases, but from
species to species at the same time the number of these cells, and
that the number does so in the same ratio as the volume increases, which
had already been rendered probable by other facts. Comparison of
the brain weight in function of the body weight between the two
sexes') had led me to the result, on the ground of the measurements
of the diameter of the muscle fibres by Bowman and by ScHwALBE
and Marepa, and the observations of muscle weights by THeEILe,
that the number of muscle fibres of Man is equal to that of Woman.
From the comparison of the relative quantity of brain and muscularity
of the Europeans and the Japanese it had appeared to me that the
relatively larger volume of the brain and of the muscles of the
latter finds its explanation, not in the different number of the neu-
rones and the muscle fibres, but in the larger cross-section of the
separate muscle fibres, larger separate volume of the nerve cells ’).
Hence, between Man and Woman, between the Japanese and
the European, i. e. within the species of Homo sapiens, only the
volume, not the number of the nerve cells and of the muscle
fibres differ.

the Fox, 52 gr. for its brain weight; the average body weight of the eleven
domestic dogs is 6.6 kg., their average brain weight 68 gr. Hence with equal
body weight, the latter brain weight is 28.40/, more than for the Fox. Gompa-
rison of these dogs with the jackals (Canis aureus) leads to similar results. The
average body weight of fourteen jackals according to Krart's observations (Haupt-
tabelle) is 6.836 kg., their average brain weight 57.1 gr. The difference with dogs
of the some body weight is 20.1 °/,, somewhat less than the difference of these
with the Fox, because the cephalisation of the Jackal is a little higher. In contrast
with domestic dogs of the size of these small Canidae, domestic dogs of the size
of the Wolf have 24.8°/, less brain than averagely this largest species of the
genus Canis. From Kuarr’s records. (Haupttabelle) of brain weights of six and
body weights of four Lapland and Russian wolves, and of cranial capacities of
23 European and American wolves (Krarr, Ueber die Veränderung der Schädel-
kapazität, p. 166), averagely 161 e.c., | derived a body weight of the species of
40 kg., a brain weight of 147.6 gr. Absolutely both weights may be a little
too high, relatively most likely they are about right. Accordingly the Wolf is
about equal in its cephalisation with the Fox. But twenty dogs of KLATT's observa-
tions, of 30 to 48 kg. averagely 37.6 kg. body weight, have an average brain
weight of 109.4 gr.

1) Under this title in these Proceedings, Vol. XXI, p. 868—869. (1919).

2) Eve. Dusois, On the Significance of the Large Cranial Capacity of Homo
neandertalensis. These Proceedings, Vol. XXIII, p. 1281. (1921).

245

From the still little known, but very important measurements of
muscle fibres by von per MarsBurG ') the same may be derived for
individuals of unequal size of different Mammalia.

In Table II some individuals of five species, being in a fairly
good condition, and of a body weight as different as possible, are
compared as regards the relation between the latter and the cross-
section of homologous muscle fibres. This cross-section appears to
increase in direct ratio to the surface of the body, hence to the
cross-section of homologous muscles, which means that the number
of muscle fibres within a species does not change with increasing
size of the body. Also the number of nerve fibres and that of the
nerve cells of the brain may then be admitted as being the same
within a species.

This is certainly not the case between different species, for when
the specific differences of caliber are taken into account, through
which homologous muscle fibres of different species of animals (just as
not homologous muscles of the same species) are distinguished, not
much remains of a direct influence of the size of the body on this
caliber of the muscle fibre. The number of the muscle fibres must,
therefore, greatly increase with the size of the animal species.
According to von prR Matspure the average diameter of the muscle
fibres in the rectus abdominis and the gastrocnemius is for the Ox
45.88 micra (in its different breeds 35.35 to 63.37 micra), for the
Horse 39.20 micra (breeds 33.26 to 48.60 micra), for the Pig 42
micra, for the Sheep 22.61 micra (breeds from 18.50 to 30.85 miera),
for the Goat 18.90 micra. For the average diameter of the muscle
fibres in the gastrocnemius of the Dog (calculated from v. p. M.’s
records, applied to the mean body weight of this species) 21 micra
may be assumed, the average of four hares is 19.20 micra, and of
five mice 17.40 micra, the body weights of these two last species
being to each other as 200: 1.

With not inconsiderable specific differences (but much smaller
than between the different breeds and individuals), only small differ-
ences between these species are to be ascribed to the influence of
the size of the body. Thus also Marrpa and ScnwarLBeE*) found in

1) KaroL von DER MarsBure, Die Zellengrösse als Form- und Leistungsfaktor der
landwirtschaftlichen Nutzliere. Arbeiten der Deutschen Gesellschaft für Züchtungs-
kunde. Heft 10. 367 pag. Hannover 1911.

8) R. Mayepa, Ueber die Kaliberverhältnisse der quergestreiften Muskelfasern.
Zeitschrift für Biologie. (Kiiu#NE und Voir). N.F. Bd. 9, der ganzen Serie Bd. 27,
p. 129. München und Leipzig 1890. — G. ScHwALBE und R. Mayepa, Ueber die
Kaliberverhältnisse der quergestreiften Muskelfasern des Menschen. I|bid,p. 487,489,515.

16

Proceedings Royal Acad. Amsterdam. Vol. XXV.

246

TABL EF Lit

Relation of the Cross-Section of Homologous Muscle Fibres to the Body Weight,
in Individuals of Different Sizes of one Species

m
is P Ln of the [Calculated
& muscle fibres, in micra
bor power of
54 : Hey Mean of ichi
we Species Bein ‘ome P, which is
e
Ss ent Gastro- abdominis propor-
Bit in kg. | cnemius and
> Gastro- |tional tom?
cnemius
Horse
146 4 heavy, average 712.5 46.16
0.6459
146 2 light zs 290 34.53
102 Belgian male 850 49.60
0.6750
102 Pony, male 300 34.90
102 5 males, average 740 48.79
0.7218
104 4 4 P 437.5 40.36
Ox
95 4 bulls, average 662.5 45.17
0.6670
97 er 3 416.6 38.10
95 Bos taur. primig. var. Sarm. 600 45.00
0.6030
98 » » n ”» » 350 38.25
Pig
108 Wild, male 130 48.25
0.7800
108 „ female 80 40.10
149 Yorkshire 100 44.00
0 5480
much
149 „dwarf ( emee alt 24.50
Dog
109 Newfoundland (emaciated) 49 38.10
0.7402
109 Fox-Terrier 9 20.35
Rabbit
326 |Domestic, large breeds, average 3.3 36.65
0.6946
326 » small B Ml 1.5 27.87
Mean 0.6751

247

their measurements the muscle fibres in the gastrocnemius of a
mouse about as thick as in the homologous muscle of a woman
and of a dog (but thinner than in that of a man). In the masseter
of their mouse the muscle fibres were about as thick as in the
masseter of the man, but less thick than in the dog. That the size
of the body from species to species has only little influence on the
caliber of the muscle fibres appears also from this that G. Levi ')
found the diameter of the thickest muscle fibres in the rectus femoris
of a mouse not below that in a rat (twenty times as heavy).

It may, therefore, be admitted that in homoneuric species the
number of muscle fibres, and then also proportionally that of the
ganglion cells in the brain, greatly increases with the size of the body.
But the available data do not enable us to calculate the exact
relation of the body weight to the number of the muscle fibres
in these species. On the ground, however, on one side of the
relation found for the brain weight # to the body weight P,
according to which # increases proportionally to P*s between
homoneuric species, and proportionally to Phs between adult indi-
viduals of the same species, and on the other side, on the ground
of the relation found for the volume of the separate nerve
cells C to the body weight, according to which C inereases in
the ratio of Phs, both between individuals and between species;
further on the ground of the established fact that between large
and small individuals the number of the muscle fibres, hence
proportionally that of the nerve cells in the brain, does not differ,
but that it differs greatly between large and small species, we may
conclude, that also the number of the nerve cells between
homoneuric species increases in the ratio of P's.

The difference between the phylogenetic and the ontogenetic
exponent is thus rationally explained. It means that in the origina-
tion of the species, increase of the size of the body is accompanied
with multiplication of the nerve cells, through cell division (in non-
homoneuric species this multiplication is greater in certain parts of
the brain) ’). With the establishment of larger adult individuals

1) GiusEPPE Levi, Studi sulla grandezza delle cellule. Archivio di Anatomia e
di Embriologia. Vol. V, p. 327. Firenze 1906.

2) Direct counting of the cells in the grey cortex of Monkeys by Orto Mayer
(Mikrometrische Untersuchungen tiber die Zelldichtigkeit der Grosshirnrinde bei
den Affen, Journal fiir Psychologie und Neurologie, Bd. 19, p. 237. Leipzig 1912)
teaches that per m.m.*, calculated throughout the cortex, only about the same
number of cells occur in the small Hapale (3448) as in the larger Chrysothrix
(3603) and in the still larger Cebus (3581). As the brain weights in these hetero-
neuric and from the smallest to the largest species higher cephalized American

155

248

of a species, there is no nerve cell division; these cells only increase
in volume, which they also do with the origination of larger
species. For this increase of the nerve cell volume is a mechanical
necessity, as may appear further below.

That phylogenetic increase of the volume of the brain is actually
brought about by cell division, associated with equivalent increase
of the separate cell volume, is also proved by the fact that in
related, but heteroneuric species, with equal body weight, the volumes
(or weights) of the brain or — what comes to the same — with
inequal body weight, the calculated coefficients of cephalisation,
in many cases, are to each other as 1, 2, 3,4. The cranial capacities
of the Chimpanzee (450 c.c.), of Pithecanthropus (900 c.c.), and
of the male Australian aboriginal (1350 ¢.c.) are to each other as
the numbers 1: 2:3. The coefficient of cephalisation of the Man-like
Apes is twice that of the Old World Monkeys and Baboons; Cebus
has double the cephalisation coefficient of Cbrysothrix; in the
Megachiroptera it is twice that of the Microchiroptera. The coefficient
of the Tree Shrew (Tupaja) is four times that of the Common Shrew
(Sorex) and the Musk Shrew (Crocidura). The coefficients of the
genera Mus, Lepus, and Sciurus are to each other as 1:2:3. The
genera Tapir, Sus, and Hippopotamus have a coefficient of cepha-
lisation half as great as that of the Horses, the Deer, the Giraffe,
the Antilopes, and the Oxen. The Chevrotain (Tragulus) also has
a coefficient only half so great as the modern-type Ruminants. It
is extremely interesting that among the Mustelidae, the Polecat
(Putorius putorius), the Stoat (Putorins ermineus), and the Weasel
(Putorius nivalis) possess a coefficient of cephalisation only half so
great as the Beech-Marten (Mustela foina) and the Pine-Marten (Mustela
martes). In this respect the Badger (Meles) agrees with the former,
the Otter (Lutra) with the latter group.

We meet here with an important phenomenon, analogous to the
‘“parameter-law” of crystals, and, undoubtedly, intimately connected
with the polyploidy of nuclei and consequent rational increase of
cell volume.

It may, further, be pointed out that most of the heteroneuric
species mentioned with low cephalisation, are small, in comparison
with the allied species with high cephalisation. This proves that the
phylogenetic growth of the brain, in which — different from what

Monkeys are to each other as 8:24:70, the absolute number of cells increases
considerably more than would correspond with the same size of body of homo-
neurie species. In the nearly homoneuric Gibbon (Siamang) and Chimpanzee those
numbers are 3160 and 1765, and the brain weights to each other as about 1:3.

249

is found in the establishment of a new homoneuric species — certain
parts of this organ increase to a greater degree than the other parts,
and accordingly a heteroneuric species originates, is probably always
too accompanied with increase of the bulk of the body. Only with
the same increase of the bulk of the body, the increase of the
volume of the brain is comparatively greater than in the establishment
of a new homoneuric species.

Another peculiarity of the Polecat may be considered in connection
with what has been said about its lower cephalisation. When
with the observations of weight of the body and the brain by
Burncke') of ten certainly adult polecats, the ontogenetic exponent
is calculated, from the five with body weights above 1000 gr.
(average 1281.5 gr.) and the five under 1000 gr. (average 769 gr),
0.42 is found for it, the same value as is obtained from the weights
of a very large polecat (of 1700 gr), from the observations of
LapicQqur®), and a very small one (of 593 gr), of my own obser-
vations®), both adult animals. This exponent is exactly halfway
between °/18 and °/9. In a graph the direction of the ontogenetic line
of the Polecat would be seen to deviate from other ontogenetic lines,
and approach to coincidence with the phylogenetic line of the genus
Putorius. Evidently the species of Polecat is in a state of disintegration.
Probably the other Putorius species are too. Well-known is, indeed,
the great variability of all the species of this genus.

In the ontogenetic growth there is an important difference between
the nerve cells and the other cells of the body. It is the great
merit of Giuseppe Levi and of Epwin CoNKLIN to have pointed this
out. In 1906 Levi‘) proved for a great number of Mammalia and
in 1908 for the Vertebrates in general‘), that in contrast with most
cells, except probably the muscle fibres (and those of the crystalline
lens), the size of the nerve cell increases with the size of the
animal’). The other cells increase in number, not separately in size.

1) Loc. cit., p. 613.

4) Comptes rendus. Académie des Sciences. (2), Tome 151, p. 1393. Paris 19192.

8) Verhandeling of 1897, p. 36. Also: Bulletins de la Société d’Anthropologie
de Paris, 1897, p. 371.

4) Loc. cit.

5) Giuseppe Levi, I Gangli cerebrospinali. Supplementa al Vol. VII dell’ “Archivio
Italiano di Anatomia e di Embriologia”. Firenze 1908.

6) Irving Harpesty, already in 1902, found that the size of the motor nerve
cells from the spinal chord of various Mammals increases with the size of the
body. (Observations on the Medulla spinalis of the Elephant with some Comparative
Studies of the Intumescentia Cervicalis and the Neurones of the Columna Anterior.
Journal of Comparative Neurology. Vol. XII, p. 125 seq. Philadelphia 1902).

250

In 1912 Conxktin') showed for different species and individuals of
one species of Boat Shell (Crepidula), that in spite of the very great
differences in body size, “the size of tissue cells is approximately
the same in all species examined, and in all individuals of both
sexes and of very different sizes. In the main, differences in body
size are due to differences in the number of cells present, and not
to variations in the size of individual cells. Ganglion cells and muscle
cells form the principal exception to this rule’. (According to his
measurements the diameter of muscle fibres is not greater in the
larger species, and only a little greater in large-sized individuals of
one species). From his measurements of a gigantic female and a
medium-sized male individual of Crepidula plana I find for the
exponent of relation of the volume of the body and the volume of
the ganglion cells the value of 0.3149, whieh is sufficiently near
5/8 to prove the existence of the same ontogenetic relation also in
the Invertebrates.

As was already mentioned, Levi is less certain in his conclusion
about the muscle fibres; he generally finds them thicker in large
animals than in small ones, but the thickness changes much less
than the length, and there are many exceptions to the rule. This
uncertainty is, indeed, explicable by what was derived above from
von DER Matspura’s measurements with regard to the larger differ-
ences between individuals than between the species.

The nerve cells and the muscle cells are distinguished from
most other cells (only the fibres of the crystalline lens make an
exception to the general rule) in that early in life — in Man and all
Mammalia examined on this point about birth-time — they cease
increasing in number through division, but then continue for some
time to increase separately in volume. The other cells go on multi-
plying by division throughout life. The muscle cells continue increas-
ing their separate volume at least up to the adult state of the
individual. But the nerve cells also stop doing this in the early
youth of the individual.

A consequence of this peculiarity of the nerve cells is, that
early in the life of the individual the brain assumes the volume of
the adult state of the body; in a male child for instance, at the
age of nine, in a female child when six years old. But a similar
remark holds among others for the Dog, the Rat, the Great Ant-
Kater, the Sparrow, the Chicken, the Crocodile, the Frog, the Salmon,

1) Epwin G. Conxurn, Body Size and Cell Size. Journal of Morphology. Vol. 23,
p. 159—188. Philadelphia 1912.

251

in short for all the Vertebrata, and also for the Invertebrata. At
birth the brain weight of Man is 4/9, and in the adult state of the
body 1/47 of the body weight. At its birth a dachshund has !/29, and
in the adult state !/i35 of its weight in brains. With a body weight
of 7 grams the Brown Rat has less than 1/49, and when it is full
grown 1/16 of its weight in brains. In the Bull Frog of 4'/, grams
of body weight, the brain weight constitutes '/jo9 of it, and when
the body weight has increased to 200 grams, the ratio of the brain
weight is only */so000. This gives the skulls, of them all in their first
youth, a much more humanlike appearance than they have in the
adult state. The great resemblance of the skull of young Apes with
that of Man cannot, therefore, have the special significance that is
sometimes ascribed to it.

The peculiarity of the nerve cells manifested in this early cessa-
tion of cell division in the ontogenetic growth, now accounts also
for the long interruptions in the phylogenetic growth, (also resting
on cell division), especially if this growth is stronger in certain parts
of the brain and mostly in those with the highest integrative action.
This phylogenetic growth then takes place with long intervals, as
shown anatomically in the brain quantities of allied heteroneuric
species of the present animal world, paleontologically by comparison
of animal forms of the present time with those of a former world order.

But why arethe nerve cells distinguished in this conspicuous way
from all other cells, with the exception of the muscle cells, which
act under their influence? We find the volume of the nerve cells to
be in a particular, in what precedes not yet causally explained relation
to the body weight. What is the meaning of that “strange” °/13 power?
To a proportionality with the °/;g or '/; power of the body weight,
i.e. with the linear dimension of the body, we could readily ascribe
a dynamic significance; as the mass of the body increases as P,
the physiological cross-sections of the muscles, which determine
the muscular force, the sensual areas, the areas that determine
metabolism increase only proportional to P*%, it would be compre-
hensible if this inadequacy implied an increase of the volume of
the nerve cell proportional to P%. But this takes place in a definite,
smaller proportion, according to Phs.

In order to detect the meaning of this latter proportionality |
examined on a former occasion *) in what relation the volumes of
the principal constituents of the nerve cell, the nucleus and the
plasma, are to each other and to the body weight. The result
of this examination is recorded in Table LV.

1) These Proceedings, Vol. XXII, p. 671—675. (1920).

no

252

TrAcB A. BY.

Calculated values of the exponents d, ~(=5/;gd) and k for the increase of the

plasma volume D with the cell volume C and with the body weight P, and of

the nucleus volume K with the cell volume C. (From measurements of the diameters

of ganglion cells and their nuclei by GrusePPe Levi, and corresponding linear
dimensions of their plasma). ')

. . d in A in k in
Situation of th .
Species sea ae (END | (EPD | (EK
ganglion cells GD PD Gi, Ki
. Bos taurus, 1 and Mus
musculus, 8 Gangl. spin. 1.198 0.3327 0.5348
Bos taurus, 2 and Mus
musculus, 8 id. id. 1.203 0.3342 0.5268
Lepus cuniculus, 4 and Mus
norvegicus, 7 id. id. 1.202 0.3338 0.5987
. Lepus cuniculus, 4and Mus
musculus, 8 id. id. 1.206 0.3351 0.6143
. Mus norvegicus, 7 and Mus
musculus, 8 id. id. 1.210 0.3362 0.6288
. Cavia cobaia, 5 and Arvi-
cola arvalis, 9 id. id. 1.216 0.3378 0.6703
. Cavia cobaia, 6 and Arvi-
cola arvalis, 9 id. id. 1.259 0.3497 0.6025
. Felis domestica, 10 and 11,
gin. cerv. V and cocc. I id. id. 1.123 03119 0.6466
. Python (species), 12 and
Seps chalcides, 14 id. id. 1.187 0.3296 0.5892
. Varanus arenarius, 13 and
Seps chalcides, 14 id. id. 1.203 0.3341 0.5386
. Bos taurus, 15 and Mus
musculus, 16 Rad. ant. spin. 1.195 0.3320 0.6555
. Canis familiaris, 17 and
Canis vulpes, 18 Purkinje cerebell. 1.199 0.3330 0.6651
. Canis familiaris, 21 and Gangl. cerv. sup.
Putorius putorius, 22 n. sympath. 1.248 0.3466 0.6523
Mean | 1.204 | 0.3344 | 0.6095

The cells compared there are all adult, and homologous as regards
their general character, but not being in each case of accurately
corresponding places in the central nervous system, they cannot be
directly referred to the body weights.

') Cf. in these Proceedings, Vol. XXIII, p. 672, Table I. There on p. 674 also
the above calculations were already published in T-ble II.

253

When now the power of the cell volume C, is calculated, by
which the plasma volume D increases, we find for it 1.2 or §/5.
We find 0.6 or 3/5 for the power of the cell volume by which the
nucleus volume K increases proportionally. On increase of the nerve
cell the plasma volume varies, therefore, proportionally as the square
of the nucleus volume. As °/5 >< °/1g=/1g or 1/3, the plasma volume
appears to increase proportional to the third root of the body weight
or P's, and the nucleus volume proportional to the sixth root of
the body weight or Ph,

Thus it appears that only the plasma, which is directly connected
with the nerve fibre, in such a way that the axis cylinder passes
into it, has the said direct dynamic significance. The nucleus, which is
always separated from the plasma by a membrane, is directly concerned
only with the life of the cell and its intern mechanism. The nucleus,
in the common opinion, is the bearer of the hereditary properties
in the nervous system, and it regulates the constructive metabolism,
growth, and reproduction of the cell.

But still this “strange” exponent °/ig is only partly accounted
for. Why does the volume of the nucleus A vary proportional
to the sixth root of the body weight, i.e. to the square root of the
body length, VL, or K? to L?

This too I already discussed on that former occasion. The follow-
ing remarks may now be added.

It has appeared chiefly from the then cited cytological researches
and studies by Grrassimow, Boveri and R. Hertwie that the volume
of the plasma depends on that of the nucleus: The relative size of
the nucleus is determined by a dynamic state of equilibrium between
the volume of the nuclear substance and the free surface of the cell,
i. e. of the plasma. Further that with such a constant ratio the rate
of cell division also remains constant. Now we actually see in the
largest, i.e. full-grown humologous ganglion cells, in every case com-
pared above, the volume of the nuclear substance increase in nearly
quite the same relation with the body weight as the free surtace of
the cell, for P% = P% and P%isX%s — P's, It may, therefore, be
admitted that these cells are in such a dynamic state of equilibrium.
The volume of the nucleus increases, indeed, somewhat less than
exactly proportional with the surface of the cell (which would be
required for cell division), but in this condition of the cell it remains
in equilibrium with the general dynamic condition of the body. For
the metabolism of the cytoplasma increases in the same rate with
the increasing volume of the nuclear substance K, and consequently
the kinetic energy issuing from the nucleus proportionally to A’.

254

But we found also K* increasing proportionally to L or P%s. And
this is the same ratio as exists between the mass of the body and
the muscular force, the metabolism, the rate of conduction of the
nerve impulses.

It has been found cytologically that with constant relation of
nucleus and plasma also the rate of cell division remains con-
stant. And already in 1895 ALuxaNber SuTHERLAND') had shown that
the time of incubation of bird species and the time of gestation of
related species of mammals increases proportional to P% or VL;
weight und length being those of the full-grown animal’s body.

In general this time is 7’ = Ay, P, in which n is a constant,
almost the same for all bird species, but different for every order
or family of the Mammalia, which tends to increase with the
increase of “nerve complexity, as gauged by size and efficiency of
brain”. Its amount is in indubitable connection with that of the
coefficient of cephalisation x, which is determined by the hetero-
neuric increase of the number of nerve cells; but m certainly
increases less greatly and is, in Mammalia, also dependent on other
circumstances (as the non-coincidence of the dates of copulation
and fecundation). The values n and x are highest in Man, Apes,
and the Elephant. The 105 bird species mentioned by SUTHERLAND
differ relatively little inter se in their cephalisation, but in some its
influence on the time of incubation can yet be recognized, such in
the Owls in comparison with the Gallinae. Thus the time of growth,
determined by cell division, to birth appears to be in the same
relation to the body weight of the adult animals as the nucleus
volume of full-grown homologous nerve cells, which cease dividing
at birth. This means equal increase of the number of nerve cells
to their separate volume. Again, finished cell division in the brain
implying completion of linkage in the nervous integrative machinery,
it thereby causes mechanically birth, of mammal as well as bird.

In the origination of a heteroneurie species the phylogenetic
growth of the brain volume is not uniform, in simple mechanical
accordance with the phylogenetic growth of the body, as in the
establishment of a larger homoneuric species, but it is stronger in
those most compounded parts of the brain, where new chains of cells
are superposed upon the preéxisting chains, superiorly integrating

1) ALEXANDER SUTHERLAND, Some Quantitative Laws of Incubation and Gestation.
Proceedings of the Royal Society of Victoria. Vol. VII. (New Series), p. 270 — 286.
Melbourne 1895. Also in The Origin and Growth of the Moral Instinct, p. 69—71 and
101—102. London 1898.

255

parts upon the inferiorly integrating parts of the brain. Yet the brain
volumes, corresponding to equal body weights, of heteroneuric species
are to each other as 1 to 2, 3 or 4, which implies that the volume
of those superposed chains of cells, in the origination of a heteroneuric
species, is equal to, double or triple the volume of the preéxisting
chains. We may infer from this, that the phylogenetic progress of
the brain, by evident discontinuous variation (mutation), after all
depends on segregation of aliquot parts from polyploidly increased
nuclear substance. i

As, again, the size of the nerve cell body and its chief component
parts is adjusted to the mechanism of the whole animal, and every
nerve cell is bound to coöperation with many homologous,
and non-homologous nerve cells, its relatively stable character,
manifested in the ontogenetically limited, and phylogenetically in-
frequently, but then from the beginning definitely increased multi-
plication by division, becomes comprehensible, especially when —
in the origination of a heteroneuric species — the multiplication
must be greater in the most compounded and intricately functionating
parts of the brain.

Physiology. “A further Contribution concerning the function of
the Otolithic Apparatus.” By Prof. R. Maenus and A. pr Kueyn.

(Communicated at the meeting of May 27, 1922).

In a previous publication ') we demonstrated that when caviae are
centrifuged by Wirrmaack’s method, being thereby deprived of otolithie
membranes, the labyrinth-reflexes resulting from position (tonic
labyrinth-reflexes on the extremities, “Labyrinth stell-reflexes’”’, and
compensatory eye-positions) will disappear, but that, on the other
hand, the labyrinth-reflexes responding to movement (rotatory actions
and after-reactions on head and eyes and the reflexes on progression-
movements) will persist. It follows that the above position labyrinth-
reflexes are otolithic reflexes, since change of position of the head in
space does not enable us to elicit a change of the stimulation in the
sensory epithelium of the otolithic maculae, but does not at all
mean that the sensory epithelium cannot, under these circumstances,
be in a permanent condition of stimulation. It is a priori quite
possible that the sensory epithelium of the maculae, like that of the
retina, continually produces stimuli, whose magnitude, in the absence
of the removed otolithic membranes, can no more be altered by the
changes of position of the head in space.

This conception was brought home to us by experiments to be
published afterwards.

In order to go further into this subject we started from the
following consideration :

The extirpation of one labyrinth in a-normal animal brings about
an intricate complex of phenomena. A previous minute inquiry *)
into these phenomena enabled us to establish the following symptoms
as resulting directly from the unilateral extirpation of the otoliths
(membranes + sensory epithelium) or rather from the activity of
the otolithic organs on one side only:

a. Rotation and flexion of the head towards the missing labyrinth.

b. Eye-deviation: the eye on the side of the removed labyrinth,
deviating downwards, the other upwards..

') These Proceedings, Vol. XXIII, p. 907.
2) Pflügers Archiv. 154. 178. (1918).

257

As secondary results from the rotation of the head sub a appear
change of posture of the whole body, difference of tonus in the
extremities, rolling movements etc.

We do not know as yet which part of the labyrinth is responsible
for a transitory difference of tonus in the extremities, which persists
also with the head in the normal position towards the trunk. This
symptom has, therefore, to be left out of consideration in the
following discussion.

On the basis of these findings we performed the following expe-
riments :

Caviae were centrifuged after the familiar method of Wrirrmaack.
Now only those animals were used for further experimentation in
which clinically all labyrinth-reflexes of position disappeared and all
movement-reflexes maintained themselves, or, in other words, animals
in which it could be expected that all the otoliths had been completely
detached on either side.

In order to eliminate as much as possible a stimulating, or
paralysing influence of the removal itself on the sensory epithelium,
the animals were regularly examined and the experiment proper
was started only from 7 to 9 days after the centrifugation.

In this procedure about 0.1 ce. of a 5°/, cocain solution was
injected unilaterally through the ear-drum into the middle-ear, in
order to paralyse the whole labyrinth on that side.

If it should now appear that, after the removal of the otoliths,
the sensory epithelium of the maculae was not in a condition
of stimulation, it could be expected that no phenomena should reveal
themselves after the cocain injection, with the exception only of a
nystagmus consequent on the elimination of the semicircular canals
on the injected side.

If, however, there is indeed, after the removal of the otoliths a
stimulation in the sensory epithelium of the maculae, we may look
for asymmetrical phenomena after the cocain-injection, since at the
injected side the sensory epithelium is completely paralysed and there
is a constant condition of stimulation at the other side.

After the cocain-injection a rotation of the head towards the
injected side (“Grunddrehbung”; utriculus) and an eye-deviation (eye
at the injected side down, the other eye upwards; sacculus.) may
then be expected, i.e. phenomena agreeing with those appearing in
normal animals, if ipsilaterally the labyrinth is paralysed through
extirpation or through injection. With this difference, however, that
the phenomena in animals with removed otoliths do not vary, as
is the case in uormal animals after unilateral extirpation of the

258

labyrinth, with the various positions of the head in space consequent
on the varying influence of the otoliths of the unimpaired side, but
that these phenomena are constantly the same whatever the position
of the head of the animal under examination may be, when it is
held up freely in the air.

Five similar experiments were made, which are instanced in the
following three protocols:

98/6 1921:

2/7 1921:
4/7 1921:

5/7 1921:

11h 39’.

11h 41’.

11h 43’.
11h 47’.

11h 49’.

11h 51’.

11h 54’.

12h.

12h 3’.
12h 6’.

Cavia R:

All labyrinth-reflexes normal.

Centrifugation: head up, chest inward, time 2 minutes, rate 1000 m.
per minute.

Total lack of tonic reflexes.

Reflexes of the semi-circular canal: rotation-reactions towards the
right positive, to the left weak.

Progression-reactions: doubtful or lacking.

Total lack of tonic reflexes.

Reflexes of the semi-circular canal (also progression-reactions) all
present and symmetrical.

Tonic reflexes: all present. Sits symmetrically, no eye-deviations. In
dorsal position with head in normal position to the trunk: no distinct
difference of tonus in the extremities.

0.1 ce of 5°/) cocain solution into left middle-ear.

Held up in the air with head down: head 90° towards the right.
When sitting OD!) down OS?) up (consequently stimulation of the
left labyrinth).

Head down: head symmetrical again.

Head down: head 20—80° rotation to the left, slightly turned to the
left. When sitting a slight levoversion of the head, no distinct eye- -
deviations.

Head down, 45° levo-rotation. When sitting falls on the left side.
Head in normal position: no distinct difference of tonus in the
extremities. If moved on the ground to the right much greater resi-
stance then against moving to the left, strong inclination to the left
(incipient paralysis of the left labyrinth).

Head down: 70° levo-rotation. When sitting head-nystagmus towards
the right. ls moved on the ground: rolling to the left. No distinct
eye-deviation.

Head down 90° levo-rotation. OS slightly downwards. OD upwards.
OS weak nystagmus beats anteriorly upwards. OD posteriorly down-
wards. No change of the phenomena with a change of the position
of the head in space.

Marked spontaneous nystagmus, direction as at 12h,

Marked deviation and nystagmus, do not change with a different
position of the head in space.

1) OD means Right eyeball.
2) OS means Left eyeball.

6/7 1921:

12h,

28/6 1921:

4/7 1921:

7/7 1921:

Injection
12h 30’.

12h301/,/,
12131’.

12n311/,
12133’.

12h 34’.

12h 341/,/,

12h 36’.

12h 38’,
12h 40’.

12h 52’.

259

Reflexes of the semicircular canal: all present and symmetrical.
Tonic reflexes: all absent, asymmetry of cocain-test quite disappeared.
Decerebration, fair stiffness.

Shifting from ventral to dorsal position: no trace of tonic labyrinth-
reflexes. Rotation of the head in lateral position: Typical cervical
reflexes, no labyrinth-reflexes.

Cavia WN.

All labyrinth reflexes present and normal.

Centrifugation: head up, chest inward, time 2 minutes, rate 1000 m.

per minute.

Reflexes of semicircular canal: asymmetric reflexes. Rotation-reactions

on head and eyes with rotation to the right weak, with rotation to

the left strong.

Progression-reactions: weak; extension of the legs even lacking.

Tonic reflexes: lacking, only slight „Grunddrehung” to the left.

Reflexes of semicircular canal: present and symmetrical. Progession-

reactions weak but present.

Tonic reflexes: lacking, no more ,Grunddehung”’. Sits symmetrically.

No eye-deviation.

Dorsal position head in normal position towards the trunk; no diffe-

rence of tonus in the extremities.

of cocain in the left middle-ear.

Held up in the air, head down: dextro-rotation of head (stimulation

of the left labyrinth).

Head down: head, in normal position, not turned.

Head down: levo-rotation of the head (incipient paralysis of left laby-

rinth).

Head down: 60° levo-rotation of the head.

When sitting, head turned and flexed to the left: clock-hand move-

ments to the left, no nystagmus.

OS downward, OD upward; no nystagmus.

Marked eye-deviation, no nystagmus: no difference of deviation with

change of position of head in space. Head down: head turned 90°

to the left.

Right lateral position : head in position

of normal sitting animal.

Left lateral position: head in dorsal

position.

Dorsal position: head right lateral pos.

Head up : head left lateral position.

No nystagmus.

Rotation to the right and to the left : eye-rotation reaction and nystagmus.
5 F bigs : head rotation reaction spositive.

On the ground: clock-hand- igvements to the left; pushed with expe-

rimentator’s foot: rolling once to the left.

Kvident eye-deviation: for the first time very strong spontaneous ny-

stagmus, OS anteriorly upward, OD posteriorly downward.

No change of the rotation
of the head with different po-
sition of the head in space.

4h,

8/7 1921:
9/7 1921:

28/5 1921:

31/5 1921:

9/6 1921:

5h 19%
6 hour.

6h 7’.

6h 10’.

6h 18.

6h 33’.

260

When sitting, head flexed and with maximum rotation to the left,
marked rolling movements, strong spontaneous nystagmus.

Tonic reflex entirely lacking. Yesterday’s asymmetry quite disappeared.
Animal dyspnoeic. Decerebrate rigidity not good.

Tonic labyrinth reflexes decidedly not present.

Cavia F.

All labyrinth-reflexes positive.

Centrifuged with head up, chest inward, time 2 minutes, rate 1000
m. per minute.

Semicircular canal reflexes: Rotation-reactions and after-reactions:

positive.

Progression-reactions: lift-reaction positive, the others weak.

Tonic reflexes: lacking.

Reflexes of semicircular canal: all positive. Tonic reflexes: lacking.
0,05 ee. 10°/, cocain through left tympanum.

Sitting with head placed in tbe normal position: OD upward, OS
downward (incipient paralysis of left labyrinth).

Sitting with head turned a little towards the left, the whole animal
inclines to the left.

Hanging with head down: “Grunddrehung” 90° to the left.
Rotating with head inward, rotating to the left, weak rotation-reaction
of the head, distinct after-reaction. Dextro-rotation: marked rotation-
reaction of the head and no after reaction.

Eye-rotation reactions: dextro rotation, distinct reaction with nystagmus,
no after-reaction. With levo-rotation: reaction and afterreaction.
Progression-reaction: Liftreaction not distinct.

“Springing reflex’’ positive.

Muscular tremor: positive in all directions except posteriorly.
Tonic labyrinth-reflexes negative.

Position of the head in the air with:

Right lateral position: head in normal position |
to the trunk through ‘Grunddrehung”’, often
hangs down.

Left lateral position: head in dorsal position
through “Grunddrehung”’.

Head up: head in left lateral position, animal
now becomes restless (cocain-action).

Head down: head turns 90° to the left.

Dorsal position: head in right lateral position
through levorotation, often also in dorsal position
with left flexion.

When sitting with head placed in the normal position: OD anteriorly
upward, OS posteriorly downward. Nystagmus just the opposite way.
Right lateral position: OS posteriorly downward, nystagmus the
opposite way. Eye-deviation and nystagmus of the left eye are the

Ergo constant
rotation of the
head, which does
not change with
change of position
ofthe headinspace.

_ same with right and left lateral position of the head and equally

strong; the same holds good also for OD.

261

1/6 1921: Animal sits symmetrically, no eye-deviation.
Reactions of semicircular canal: all positive.
Tonic reflexes: all lacking. Asymmetrical phenomena quite gone as
in cocain-test.

8/6 1921: Like previous day. When sitting, head sometimes turned very slightly
to the right, for the rest animal sits symmetrycally, no eye-deviations.

Anatomical examination by Dr. M. pe Bur et. All otolithic membranes detached.

Right sacculus; sensory epithelium without membrane; the otolithic membrane
isolated in the sacculus between ductus endolymphaticus and the
back-part of the sensory epithelium.

Right utriculus; sensory epithelium without membrane; the otolithic membrane lies
between the posterior portion of the macula and the entrance to
the crus commune.

Left sacculus; sensory epithelium without membrane: the otolithic membrane
rests against the lateral wall of the sacculus and above the macula.

Left utriculus: sensory epithelium without membrane; the otolithic membrane
is detached towards the inner side and above the macula but lies
in the utriculus.

These experiments go to show that for more than a week after
the removal of the otolithie membranes the sensory epithelium is still
in a constant condition of stimulation. When one labyrinth is for
some time eliminated by cocain, the stimuli emanating from the
non-injected labyrinth will induce asymmetrical phenomena, similar
to those after unilateral extirpation of the labyrinth in normal
animals, with this difference, however, that in the centrifuged
animals injected unilaterally with cocain, these phenomena do not
change with a change of position of the head in the air.

Considering that there was a week’s wait after the centrifugation,
it is probable that the above condition of stimulation should no
longer be ascribed to centrifugation, and that, therefore, to the
sensory epithelium of the maculae the power should be assigned of
eliciting stimuli, which, owing to the absence of the otolithic mem-
brane, do not vary much as to strength.

The function of the otolithie membranes, then, consists in altering
the intensity of this condition of stimulation of the sensory epithelium.
This stimulation will be stronger or weaker according as the mem-
branes pull at the epithelium or press upon it.

Relative to the portion of the sacculus (the main part) innervated
by the N. saccularis it has been previously demonstrated that the
stimulation decreases with pressure and increases with pulling. This

mechanism exists probably also for the utriculusmaculae.
AW
Proceedings Royal Acad. Amsterdam. Vol. XXV.

262

s

It appears that for the division of the sacculus (sacculus corner)
innervated by the N. utricularis the relations are more intricate.

Our results may perhaps be conducive to the proper conception
of the function of the sensory epithelium of the otolithic maculae.

The above-named property of the otolithic apparatus to elicit
continuous stimuli even after the otolithie membranes are detached
— as here described — undoubledly demands attention in the
further study of the unilateral affection of these organs.

From the Pharmacological Institute of the
Utrecht University.

Geology. — „Cuba, The Antilles and the Southern Moluccas.” By
L. Rotten.

(Communicated at the meeting of May 27, 1922).

In 1865 HE. Suess endeavoured to show in which way North-,
and South-America are connected geologically *). Basing upon the then
scant geological literature of the borderlands, he partly adopted the
conceptions of some few of the older explorers. He observed that
the mountain systems of Western North-America do not directly
merge into those of Western South-America, but that in South-
Mexico and in Guatemala the coastal ranges bend round, ramifying
there in different chains, which cross transversely the narrow Central
America, to proceed on their course in the Greater Antilles. All
along the row of the Antilles Suess imagined to observe the traces
of a large chain of folded-mountains,- which he conceived to extend
along the North Coast of South America, as far as the boundary of
Venezuela and Columbia to merge there into the Andes. So he
considers the Andes of South-America as a continuation of the
mountains of Western North America, but looks upon the curving
chain of mountains via the Antilles as the connecting link.

In the region of the Antilles Sumss distinguished three zones: an
interior zone of small islands all composed of young volcanic rocks
with very young coastal limestones and allied formations, extending
from Grenada to Saba; a middle zone, in which in many places
older, folded rocks emerge, building up the Antillean-Cordillera
proper, extending from Trinidad via Barbados as far as Haiti,
branching out there in at least two chains, of which the southmost
proceeds via Jamaica to Honduras, while the most northern runs
via Cuba to Yucatan; lastly an exterior zone, stretching from
Barbuda via the Bahama Islands and Florida to Yucatan and which
is supposed to be the remainder of the unfolded and disrupted
“Vorland” of the Antillean Cordillera.

Already Surss had pointed to the striking analogy between the
row of the Antilles and the Southern Moluccas. A few years later

1) E. Suess, Das Antlitz der Erde. I. 1885.
17*

264

this analogy was discussed further by Wicamann:') and Martin *).
In the Southern Moluccas we also distinguish an interior curve of
voleanic islands, an intermediate curve, consisting of the remains of
folded mountains, and farther to the east the remainder of the almost
undisturbed ‘‘Vorland”’.

In many points the hypothesis of Suwss has been corroborated
by subsequent. researches. K. Sapper*) has demonstrated that the
peculiar curvature and ramification of the tectonical units in
Northern Central America, which Suxss only suspected, really exist.
W. Sievers *) has proved it to be probable that the eastern Corde-
rillas of Columbia split up in the North into different branches,
then bend round to the North-east and to the east, and can be
traced as far as Trinidad with rather great distinctness. Lacroix °)
found in young volcanic rocks of Martinique xenoliths of mica-
schist, proving thereby that in the subsoil of this island there still
must exist old, metamorphic sediments. HöeBom has pointed out the
remarkable analogy *) between the eruptive rocks of the Virgin
Isles and those of the Andes of South-America. In the collections
of the chemist RicHarp Lupwie W. Sievers has found a young
eruptive rock from Alta Vela, a small island south of Haiti, and
has proved the possibility that this islet may be the continuation
of the volcanic interior curve of the Lesser Antilles’). Finally
W. Beret *), who arranged the above-named collections petrograph-
ically, has shown the occurrence of old schists in Haiti. Lastly
DE La Torre’) discovered in Western Cuba a fauna of Malm-
ammonites and M. Sancngz Roie’*) established that this fauna bears
a close resemblance to the jurassic fauna of San Pedro del Gallo
in Mexico, which has been treated in such a masterly way by
BURCKHARDT **).

On the other hand Suwss’s theory has not been universally accepted

IG. E. A. WicHMANN, Samml. Geol. Reichsmus. Il, 1887, p. 198 sqq.
2) K. Martin, Tijdschr. Kon. Ned. Aardr. Gen. VII, 1890, p. 260 sqq.
3) K. Sapper, Peterm. Geogr. Mitt. Erg. Hefte 127, 1899, 151, 1905; Report
8th Int. Geogr. Congr., held in the Un. States, 1904.
4) W. Srevers, Peterm. Geogr. Mitt. 1896, p. 125 —129.
5) A. Lacroix, La Montagne Pelée et ses éruptions, 1904.
6) A. Héasom, Bull. Geol. Inst. Upsala, VI, 1905.
7) W. Srevers, Zeitschr. Ges. fiir Erdkunde Berlin, 33, 1898.
8) W. Beret, Abhandl. Gesellschaft Isis. Dresden. 1897, p. 61—64.
9) C.pE LA Torre, C.R. Congrès Intern. Géol. XI, Stockholm, 1910, p. 1021—-1022.
lo) M. Sancnrz— Rore, Boletin especial de la Secretaria de agricultura, comercio
y trabajo, Habana, 1920.
1!) G. BurcKHarpt, Bolet. Instit. Geologico Mexico, 29, 1912.

265

in America. The investigations of Americans have negatived rather
than substantiated Suxss’s conceptions in some respects. J. W. SPENCER *),
for instance, came to the conclusion, chiefly after the study of charts
and morphological speculations in connection with them, that the
Antilles were not the remains of an old cordillera. This researcher
maintained that the whole tract of the Caribbean Sea, the Antilles
and the Gulf of Mexico constituted an ancient continental region,
which ever since the Miocene had executed the most stupendous vertical
fluctuations of an amplitude of many thousands of meters. RT. Hur ®),
however, who visited many of the Antilles, is by no means inclined
to consider most of these islands as other than true oceanic formations
and refuses to believe that there is any connection between the
northern Antilles and Barbados-Trinidad, the latter being by him
assigned to the South-America mainland. In his aversion to the
assumption of old-sedimentery cores in the Antilles east of Western
Cuba he even goes the length of questioning the results of Beret (l.c)
who had established the occurrence of old schists in Haiti ou the
basis of simple petrographic work.

Neither were the long-continued explorations of T. W. VaueHan ®),
who has contributed so largely to the knowledge of the geology of
Central America in modern time, based upon the ideas of Surss,
which, as shown above, were of such pregnant significance for
many a European explorer.

Particularly the island of Cuba, where since the Spanish-American
war a number of American explorers have been working, seemed
to have many features not belonging to the other Antilles. The
Spanish mining-engineer SALTERAIN already had mistaken a group of
sharply folded rocks from the environs of Habana, where fossils
had never been found for cretaceous sediments *) and the later
American’) explorers adhered to this view or contended it only

1) J. W. Spencer, Geol. Magazine (4), I, 1894, p. 448—451; Bull. Geol. Soc.
America VI, 1895, p. 108—140; Transactions Canad. Instit., V, 1898, p. 359—368,
and many: other publications.

*) R. T. Hier, Bull Museum. Comp. Zoology, Harvard Goll, 34, 1899, p. 225
sqq.: Bull. Geol. Soe. America, XVI, 1905, p. 243—288, and many other publications.

5) T. WayLAND VAUGHAN, Bulletin U.S. National Museum, Washirgton, 1038,
1919; Contributions to the geology and paleontology of the West Indies, publ. by
the Carnegie Inst. of Washington, 1919, in which older publicatious are cited in
extenso.

4) P. SALTERAIN, Boletin Mapa geologico de Espaiia, VII, 1880.

5) R. T. Hitt, Amer. Journal of Science, (3), 48, 1894, p. 196— 212. Bull. Mus
Compar. Zoology Harvard Univ. Geol. Series IJ, 1895, p. 243 — 288; B. WILLIS,
Index to the stratigraphy of North America, US, Geol. Survey, Profess. Papers,
71,/4912.

266

reservedly *). However, the petrographic habitus of this would-be
cretaceous formation, made up of white limestones, of soft, white
marls and of loose calcareous sandstones, is quite different from all
the cretaceous rocks known from the other Antilles, Central America
and Northern South-America, sothat Cuba seemed to be isolated
from the rest in this respect. Another peculiarity of Cuba seemed
to be that on the whole the tertiary is not very thick and only feebly
folded: Hit?) says that the tertiary is merely a thin veneer over-
lying the older formations sothat its thickness does not excel 1000
feet, and Havyrs-VAUGHAN-SPENCER have reproduced profiles of the
island in which everywhere a very feebly folded tertiary formation
is marked’). If this is correct, Cuba differs very much from the
other Antilles, for in Haiti‘), Babados as well asin Trinidad ®) there
are very thick and intensely folded tertiary deposits, as may be
expected in a young mountain-range, such as Surss asserts the
Antilles to be composed of.

A two months’ stay in Cuba, in the months of March and August
of the past year, put me in a position to explain this seeming con-
tradiction and to detect some striking resemblances between Cuba
and the other Antilles. |

First of all the so-called cretaceous deposits in the environs of
Habana were explored. They can readily be examined in numerous
exposures along roads and railway cuts in and near the capital.
They are composed of white soft, sometimes nodular, fine-grained
marls; of light-coloured, youngish looking, organogenetic limestones,
which are seldom very pure, most often however contain some
voleanic tuff-material; of true submarine tuffs; while sometimes also
peculiar fine-grained limestone-breccias occur in the formation. In
numerous spots I found in the limestones and in the submarine
tuffs micro-organisms, which could be determined in microscopical
sections. It now appeared that besides a number of Foraminifera,
insignificant for the age of the formation, and besides Lithothamnia,

1) C. W. Hayes, T. W. VAUGHAN and A. CG. SPENCER, Geology of Cuba, 1901
reprinted in 1918 by the Dirección de Montes y Minas at Habana.

AR. DT. Arun, Jc.

8) CG. W. Hayes, T. W. VAUGHAN and A. C. SPENCER, l.c.

4) L. TiPPENHAUER, Peterm. Geogr. Mitteilungen, 1899, p. 25—29, 153—155,
201 —204; 1901, p. 121—127, 169—178, 193—199; 1909, p. 49—57. W. F.
Jones, Journal of Geology, 26, 1918, p. 728—758.

5) 1. B. Harrison and A. J. Jukes Brown, The geology of Barbados, 1890,
and other publications. G. WALL and J. Sawkins, Report on the geology of Tri-
nidad, Memoirs Geol. Survey, London, 1860.

267

also small Nummulinae and Orthophragminae occur in various local-
ities and Nummulinae and Lepidocyclinae in other places. I encount-
ered in various tuffish limestones between Ardai and Arroyo Naranjo
small Nummulites and Orthophragminae, while in limes, south-east
of Regla, to the south of the bay of Habana and to the north of
Guanabacoa, besides Nummulites also small Lepidocyclinae were
found, which also occur in the railway-cut, north-east of Palatino
(the finding-places are marked on the accompanying map).') This
“Older Habanaformation” is intensely folded, with dominant W—HE.
strike, and rapidly alternating steep dips, so that no positive opinion
can be formed about the thickness of the whole complex of layers
with its few well-continuous sections. This thickness however is
sure to be very considerable. It is evident that this formation, which
contains Nummulites and Orbitoides, and which, in concurrence
with SALTERAIN (l.e.) was generally mistaken for cretaceous, is of
a distinctly more modern type, being nothing else but the well-
developed and intensely folded eogene, which we recognize with
the same tectonic and partly also with the same petrographic features
in so many localities of the Antilles. The occurrence of Orthophrag-
mina implies that part of this intensely folded formation is decidedly
eocene. We will endeavour to ascertain whether perhaps subsequent
parts of the Tertiary are represented in this complex. .

If the fossils, occurring in the “Older Habana-formation”’, had
been found in Europe or Asia, there would be no doubt whatever
about the occurrence also of oligocene and maybe even of old-
miocene rocks in this complex, as in Europe as well as in Asia
Lepidocyclinae are characteristic of tbe oligocene and the older
miocene (Stampian to Burdigalian). However, in America Lepidocy-
clinae have been found also in unmistakably eocene deposits, *) so
that their occurrence in the vicinity of Habana is in itself no evidence
at all. Now, the American species in positively eocene rocks (south-
eastern part of the United States), are all large species, except one
(L. floridana Cushmann with a diameter of 4—8 mm.). In San
Bartholomew (L. antillea Cushmann with 5 mm.) and in the zone
of the Panama-canal (L. Macdonaldi with 5—7 mm.) there occur,
it is true, some smaller species in rocks, taken to be eocene, but
the age of these deposits is not so well established as that of the

1) It is a pity that the names in the map are rather illegible but with the
aid of a reading-glass it will be possible to recognize most of them.
2) J. CusHmann, U.S. Geological Survey, Professional Paper, 125D, 1920.
T. W. VauaHan, Proceedings First Pan Pacific Conference, Honolulu, 1921,
p. 754—755.

268

formations of the South-east of the United States. Now, in the
Habana rocks, described above, large Lepidocyclinae are absolutely
lacking; they contain only dwarf-species which — as experience
in Asia and Europe has taught us — are more or less indicative
of younger formations, so that part of the “Older Habanaformation”
must very likely still be referred to the Oligocene. And this is not
all. In the city of Habana and west of it the Older Habanaformation
is overlain by rocks of quite similar petrographic habitus, but they
are much less disturbed. These rocks of the „Younger Habana-
formation” (organogenetie limestones, white and yellow marls, sub-
marine tuffs) form namely a monocline, whose core still exhibits
steep dips — up to 40° and higher —. The younger portions of this
formation, however, which in its totality is dipping towards the
sea, are much less steep. In the suburb of Vedado the marls of
this formation are overlain by coral-limestones which are also dipping
down towards the sea. The rocks of this “Younger Habanaformation”’,
which are so beautifully exposed in the marlpits of Puentes Grandes
and of Cienaga and at the Castillo del Principe, are lying uncon-
formably — as the accompanying map indicates — on the rocks
of the “Older Habanaformation”: while the strike of the older rocks
is E.—W., that of the vounger is about N.E.—N.N.E. The facts,
however, that in the deeper parts of the younger formation the
layers are very sharply inclined, and that there is a remarkable petro-
graphic similarity between the two formations tend to show that
the stratigraphical gaping between the two formations is only very
inconsiderable ; nay, in all probability, the unconformity is only
“tectonic”, is originated during the folding, and the two formations
succeed each other most likely without a significant stratigra-
pbical gap.

Now, M. Sancenrz Roie') has for several years been collecting fossils
from the marlpits of Cienaga. It is especially the teeth of Selachii
that were encountered here. They point to a miocene age, while
the more southern limestones of Vedado belong even to the Pliocene.

The foregoing no doubt justifies the conclusion that the rocks of
the “Older Habana formation” belong partly to the eocene, partly
to the oligocene, that the tertiary orogenetic movements in this part
of Cuba began towards the close of the Oligocene, and that they
continued even in the Pliocene.

So while in the North the layers of the “Older Habanaformation”
are overlain unconformably by miopliocene rocks, which have still

1) M. SancHez Rora, Boletin de Minas, Habana, NO. 6, 1920.

269

co-operated in the crustal movements, in the South near Arroyo
Narranjo limestones are overlying the “Older Habanaformation’’,
which are perfectly horizontal and can be traced southward as far
as Guira, invariably in horizontal position. Near Arroyo Narranjo
these limestones, which in their habitus differ greatly from the
rocks of the “Older Habanaformation”, are coastal limestones;
farther to the south also Globigerina limestones occur. As a matter
of fact these limestones, which have had no share in the latest
orogenetie movements, must be of more recent date than the mio-
pliocene rocks of the “Younger Habanaformation” and belong con-
sequently to the Youngest Pliocene or Pleistocene. These limestones,
which the Geological survey-map of North-America’) still marks as
Old Tertiary, have lent support to the opinion that the Cuban
Tertiary is only feebly folded, and that the Tertiary constitutes only
a thin varnish overlying the older formations.

This does away with the seeming contrasts between Cuba and
the other Antilles and replaces the island in the homogeneous range
of the Antillean Cordillera. |

In an excursion to San Diego de los Baïos, about 100 k.m. to
the west of the capital [ encountered also here a well-developed
and intensely folded eogene formation; to the North of this small
town mesozoic limestones emerge, but farther to the south intensely
folded rocks (strike E.-W.) are exposed everywhere — especially
submarine tuffs — containing Lithothamnia, Nummulites and Ortho-
phragminae. Globigerina marls also occur.

The Petrographic composition of the Cuban Tertiary is interesting
also in other respects. First of all, in the Older as well as in the
Younger Habanaformation limestones occur that, being examined
microscopically, appear to contain much young volcanic material,
nay in many cases, even change into true calcite-poor, submarine
tuffs. Sharp angular splinters of plagioclase and quartz are numerous.
Likewise numerous grains present themselves, of a substance con-
taining plagioclase microlites, granules of ore and glass, which are
to be considered as ground-mass fragments of an andesitic or dacitic
rock. Similar eogene, submarine tuffs were also recognized in the
Tertiary of San Diego. Much volcanic material also occurs in mio-
pliocene deposits of a shallow sea (coralligene limestones, marls,
calcareous sandstones and finely granular conglomerates), which are
excellently exposed in the Yumuri cleft near Matanzas, about 75 k.m.
east of Habana. On the contrary volcanic material seems to be
lacking entirely in the very young, horizontally disposed limestones

270

found near Arroyo Naranjo, Rincón, San Antonio de los Banos and
Guira. In one of the younger portions of the Yumurt cleft-profile
feldspars were so numerous that they could readily be examined in
the pulverized rock. All the splinters that were examined, had a
higher refractive index than canada balsam, so that there is a
complete lack of orthoclase and albite. Among 20 splinters examined
13 had a higher, 7 an equal or a lower refractive index than
eugenol (1.546), so the latter belong to oligoclase. Nearly all the
splinters have a lower refractive index than nitrobenzol (1,556), so
that among the larger feldspar splinters, which are of course
fragments of phenocrysts from the dacitiec-andesitic rocks, from which
also the ground-mass originates, no plagioclases occur that are more
basic than andesine'). The effusive rocks supplying the material for
submarine tuffs, must then have been a highly acid, potassium-
poor dacite i.e., a rock in all points of the type of the “Pacific Roek”.

It should be observed that the fragments of the ground-mass
occurring in the tuffs, very often have a diameter of 1 mm. It is
not out of the bounds of possibility of course, that similar volcanic
material could have reached Cuba during an eruption of rather
remote volcanoes, if at the time of the eruption a violent storm had
been blowing in the direction of the island. The coarseness of the
fragments, however, together with the very high frequency of
volcanic material in formations extending from the eocene into the
pliocene in localities nearly 200 k.m. apart, indicate that this
material has not “come over” under “peculiar” circumstances from
far-away volcanic centra. These submarine volcanic tuffs that are
so widely diffused both stratigraphically and geographically, must
be regarded as evidence that in the Tertiary the voleanic activity
in the Antillean region extended over a much larger area than at
present and that it did not settle down before the close of the
Tertiary. This fact also tends to strengthen our view that the Antilles
are geologically ‘homogeneous.

It is likewise deserving of note, that no remains whatever are to
be found of the voleanoes that must have existed as late as the
latter half of the Tertiary in the neighbourhood of Cuba. This
proves that already since the beginning of the Tertiary Cuba must
have been subject to violent distarbances, where denudation destroyed
rapidly what had been built up by volcanic and orogenetic processes.

1) The refractive indices of the fluids used in the Utrecht geological institute
for the determination of the refractive indices of minerals, have been verified only
a short time ago by Prof. ScHoort for which we tender our thanks.

271

Presently we shall see that other facts also corroborate this hypothesis.

In the vicinity of Habana a deeply weathered serpentine-massif
(see sketchmap) has long (SALTERAIN |. c. and others) been known.
In two localities — south of Guanabacoa and due south of the bay of
Habana — quartzamphibole diorites are found as a dyke. These
moderately acidic plagioclase rocks forcibly reminded me of the
granular crystalline rocks of the “Pacific type”, described by Héegom (lc)
and derived from the Virgin Isles. The felspars of this quartz-
amphibolediorite all had a refractive index higher than canada
balsam, but the refractive index of most of them was lower than
that of quartz, to which they often are contiguous in the micro-
scopical sections. Consequently they belong to the acid portions of
the plagioclase series. Indeed the fact that this rock is poor in
potassium and comparatively rich in silicic acid (much quartz and
many acidic plagioclases) reminds us forcibly of many ‘‘Andes-rocks’’.
Also by the occurrence of granular rocks of this type Cuba is united
to the American continent on the one side and on the other to the
Virgin Isles.

When perusing the literature concerning the Antilles we are
impressed with an other incongruity between Cuba and the other
Antilles. Already long ago young Radiolaria-bearing deposits became
known in Barbados (Harrison and Jukes Brown, |. c.) which many
geologists regard as true deepsea-deposits. R. T. Hir also described
tertiary Radiolaria-deposits in the east of Cuba (Baracoa). However,
whereas in Barbados the Radiolaria deposits overlie unconformably
the older tertiary — which developed there as a terrigenic deposit —
and have only been subject there to faulting and not to folding,
the Radiolaria deposits of Baracoa have a steep dip, so that there
seemed to exist a stratigraphical incongruity between these deposits
in the two islands. In the neighbourhood of Habana I encountered
Radiolaria-bearing rocks in two levels of the Tertiary. In the first
place white marls in the “Older Habanaformation” near Cerro,
with a dip of 75° southward. They are entirely filled up with
Radiolaria that belong for the major part to the Spumellaria, for
a small part however also to the Nasselaria (fig. 1). Secondly, in
the most recent part of the “Younger Habanaformation’’, i. a. in
the marlpits of La Cienaga, white Globigerina marls occur which
contain a not inconsiderable amount of Radiolaria. Now it is very
well possible that the Radiolaria-marls of Cerro are the equivalent
of those of Baracoa in East-Cuba, whereas the Radiolaria-bearing
Globigerina marls of La Cienaga are stratigraphically more like the
deposits in Barbados. Also the contrast which apparently exists in

272

this respect between Cuba and some of the other Antilles finds an
explanation in the above.

Indications of the homogeneity of the row of Antilles can also
be found in the older formations of Cuba. As stated previously, of
late years Malm-ammonites have been found near Viüales, in the
most western part of Cuba. These Upper-jurassic layers, which dip
away to the North at a rather small gradient, are overlain by thick,
old-looking grey limestones with intermediate layers of sandstones,
which, therefore, are probably to be referred to the Cretaceous
system. In one place I fownd in these limestones small nests of red
chert; under the microscope this red chert appeared to be a true
Radiolarite, very much like the Radiolarites so widely diffused in
the mesozoic rocks of the southern Molucean-cordillere (fig. 2). The
geological institute at Utrecht possesses a number of rocks from the
islands of Curacao, Bonaire and Aruba, collected by Dr. I. Bor.pinen.
Among the rocks from Bonaire and Curacao it was not difficult to
recognize Radiolarites — probably mesozoie — bearing close resem-
blance to those from Cuba.') This is not all. In the coral-limestones
of the Yumuri-cleft near Matanzas coarse clastic material was found;
boulders to a maximum of 7 mm. in diameter. Four of them were
ground, of which two appeared to be red radiolarites like those
found to the north of Vinales, while in our days mesozoic sediments
are lacking in this part of the island.

It is evident, therefore, that such a peculiar sediment as the mesozoic,
red radiolarite is found at the extremities of the Antillean region:
in the most western part of Cuba and in Bonaire and Curacao.
This, no doubt, warrants the assumption that the Antillean region
is one continuous whole, parts of which, in spite of their different
appearance, have many features in common, that point to an
historical homogeneity. :

From the occurrence of much voleanic material in the whole
tertiary of Cuba, in the neighbourhood of which no volcanoes exist
any more, we may conclude that the island must have been subject
to great geological disturbances in recent times. A similar conclusion
may be deduced from the great abundance of boulders of cretaceous
Radiolarites in the miopliocene of the Yumurt-cleft, as these boulders

1) K. MARTIN, Bericht über eine Reise nach Niederl. West Indien, II, 1888,
p. 28 and 73 and J. H. Kroos, Samml. Geol. Reichs-Museums, Leiden II, 1, 1887,
already demonstrated the occurrence of Radiolaria-bearing rocks in Curagao and
Bonaire. From their descriptions it is not evident, however, that we have to do
here with typical Radiolarites, which at that time did not receive so much
attention from geologists as nowadays.

273

point to: a powerful post-eocretaceous mountain-building by which
the deep-seated Radiolaria-deposits were uplifted beyond the sea-
level, while in the Tertiary the mountains were entirely denuded
again. .

In the foregoing Radiolaria-bearing deposits have been described
from three levels of the series of sediments of Cuba: a fourth level
can still be added. Between Bacuranao and the boring-field which
is located to the north of this village, green sediments were observed
in the centre of the serpentine-area. These sediments are distinctly
seen to dip away below the serpentine. Under the microscope they
appeared to be in part voleanic tuffs, in part remarkable radiola-
rites, which consist chiefly of skeletons of Radiolaria, but also
contain spiculae of sponges, while the ,silicie acid of the Radio-
laria as well as of the sponges spiculae is still perfectly amorphous
(fig. 3). These siliceous sediments are closely connected with the
volcanic tuffs; not only do the Radiolaria-layers and the tuffs possess
equal dip and equal strike, but sometimes the siliceous sedi-
ments contain splinters of plagioclase, and in one of the micro-
scopical sections the tuff even passes into the siliceous sediment.
These Radiolarites of Bacuranao certainly belong to an older level
than the tertiary Radiolarites, as the former dip away below the
serpentine, whereas the whole tertiary is more recent than the
serpentine, whose water-worn fragments are found here and there
in the tertiary limestones and calcareous sandstones. They belong
moreover to another level than the red Radiolarites of Vinales and
Matanzas, for the thick limestones bearing the red Radiolarites of
Viüales are not found near Bacuranao. The siliceous sediments are
closely related to the Cuban serpentines.

Now it is very remarkable that in Cuba such extreme deposits
as Radiolarites appear in four different levels. Even when not
assuming that Radiolarites are true deepsea deposits, we must be
convinced that the formation of these calcium-free or calcium-poor
siliceous sediments requires conditions that do not exist in the shallow
epi-continental seas. At all events the occurrence of these deposits
in at least four levels of the island of Cuba justifies the conclusion,
that the area in which the island is now situated, was in the latter
half of the Mesozoicum an extremely restless region, where now
deposits of a shallow epicontinental sea (sandstones in the Chalk,
Nummulites and Orbitoide-bearing limestones in the Tertiary), then
again such peculiar sediments as Radiolarites') could be formed.

1) One more fact may be adduced to confirm the conception that at least one
level of the Radiolaria-bearing deposits in Cuba is formed, if not in a true deep-

274

There are, indeed, two more arguments for the conclusion that
Cuba has ever been a very inconstant region, at least since the
Tertiary.

In the outset we reminded the reader that already Suess, WIcHMANN
and Martin had pointed out the analogy between the Antilles and
the southern Moluceas, which analogy is brought out in a similar
arrangement of the tectonic elements. Two points have been discussed
above to emphasize this analogy. In the first place the occurrence
of Red Radiolarites, so very typical of the Mesozoicum of the
Moluceas, in the two extremities of the Antilles. In the second
place the conception that in the latter geological periods the Antillean
region was so extremely restless. It is known, indeed also of the
southern Moluceas, that their region was very changeable, and was
characterized by great instability in the relations of land and sea:
also there the formation and the denudation of mountains took place
in such rapid succession, that it is difficult to disentangle the develop-
ment of the geological history. We may add even one more detail
in comparing the instability of the Antillean region with that of
the southern Moluceas. In the Antilles it struck us that in one and
the same island Radiolaria-deposits occur at least in four different
levels. Why, also of the island of Rotti, near Timor, Brouwer has
described’) Radiolaria-bearing deposits in three totally different levels:
Upper Trias, Malm and Tertiary.

Utrecht, May 1922.

sea, anyhow in a sea of considerable depth. In the white marls of La Cienaga,
where many Globigerina and also numerous Radiolaria occur Sanchez-Roig (Lc.)
has found numerous teeth of Selachii. A large number of these teeth (though by
far not all) display the peculiarity that only the enamel of the teeth is left, while
the dentin has completely disappeared. This state of preservation is exclusively
characteristic of Selachii-teeth that are encountered in the deepest sea and in
deepsea deposits.

Cf. MoLENGRAAFF and BEAUFORT, Proceedings XXIX, 1921, p. 677—692.

') H. A. Brouwer, De Nederlandsche Timor Expeditie, III, 1921. Geologische
onderzoekingen op het eiland Rotti.

DESCRIPTION OF THE PLATES.

Fig. 1. White Radiolariamarl. Older Habanaformation. > 26.
Fig. 2. Red Radiolarite. Vifiales. > 26.
Fig. 3. Silicious rock with Radiolaria and Sponge-spiculae. Bacuranao. X 26.
Fig. 4. Geological Sketchmap and transverse profile of the vicinity of Habana.
—,.—,— Railways.
ABC—CD Line of Profile.
S. Serpentine.
D. Quartzhornblendediorite.
A. Petroleum Rigs.

L. RUTTEN: “Cuba, The Antilles and the Southern Moluccas’’.

we

Figo 26.

i*
Fig. 3. X 26.
|

Fig. 4.

Proceedings Royal Acad. Amsterdam. Vol. XXV.

Bio-chemistry. — “Changes in Milk due to Sterile Inflammation
of the Udder.” By Prof. B. Ssoutema and J. E. van DER ZANDE.
(Communicated by Prof. C. Eykmay.)

(Communicated at the meeting of May 27, 1922).

The examination of a number of samples of abnormal milk from
cows suffering from clinically observable affections of the udder,
as well as from cows in which clinically no anomalies of the
udder were noticeable, impressed us in 1921 with the idea that
too great an importance is ascribed to streptococci as causative
agents of the secretion of abnormal milk. We found for instance
that in very abnormal milk streptococci are often absent.') We,
therefore, decided to go further into this subject and produced
sterile inflammation of one of the quarters (R. F.) of the udder of
a milch-cow in full lactation, with the aid of a suitable injection.
On the suggestion of Prof. Parmans a solution was administered of
of silver-nitrate of 0,2 °/,.*)

In the same cow a sterile abscess had previously been developed
through injection of oil of turpentine in the region of the neck with
a view to ascertain whether such a sterile inflammation exerted
any influence on the secretion of milk. We were induced to do so,
because in a previous investigation in our laboratory anomalies had
been found in the milk yielded by animals which were affected by
inflammation of quite other parts of the body than the udder.

The results obtained after the injection of oil of turpentine need
not take us long. Although a considerable abscess had developed,
the composition of the milk did not undergo a notable change,
neither during the development, nor after the abscess had become
mature.

Once the sediment of the milk from one of the quarters had
increased a little, of which the abscess may not have been the

‘) Our report pertinent to the matter in question appeared in Tijdschrift voor
Vergelijkende Geneeskunde enz. Band 7 1922.

*) We were in a position to prosecute this inquiry thanks to the aid of Prof.
W. J. Parmans and the Conservator for Obstetrics, Mr. J. A. J. M. Kircu, whose
assistance we acknowledge with gratitude.

276

cause. It would seem, therefore, that a sterile inflammation does
not affect the secretion of milk in the same way as a bacterial in-
flammation has in our earlier researches repeatedly proved to do;
this result could be expected.

The effect of the sterile inflammation of the udder with silver-
nitrate solution was quite different. The very next day (9 March)
the composition of the milk had changed very much, as was also
the case on the following days, when the milk presented also a
very abnormal aspect.

Gradually composition and aspect improved; however, this quarter
became choked before the milk was quite normal; at all events not
a trace of milk could be drawn on March 19 and following days.
The examination of the milk-samples gave the results tabulated on the
following page. For the sake of comparison we have also tabulated the
figures of some abnormal milk-samples with (N°. 164 and 142) and
without (N°. 181 and 267) streptococci, which samples were examined
in 1921. For the same reason we included the figures obtained from
the same quarter (R. F.) of the injected cow before this treatment
(N°. 343 and 337) and from other quarters (N°. 385 and 381) after
the injection.

The table shows that the milk from the quarter injected with
silver-nitrate possessed, — with the exception of the presence of
streptococci, — all the properties of milk from animals, suffering
in a high degree from. udder-affections e.g. streptococci mastitis).
Acidity, p,, sediment after centrifugation in Trommsdorff-tubes,
leucocytes, chlorin-, and lactose-content, were all changed in the
same measure,') as were also the total protein-content and the
calcium-content.

Furthermore the content of total, combined-, and free carbonic
acid appeared to have increased, just as in milk from cows with
diseased udder. This anomaly and its connection with the bydrogen-
ions concentration of milk has been pointed out in 1919 by L. L.
VAN SLIJKE and J. C. Baker’).

Lastly, the tryptophane-content appeared to be considerably in-
creased. In 1921 we found this content in abnormal milk (derived
from diseased udders), and in colostrum to be very high. This is no
doubt due to the occurrence in these kinds of milk of much protein,
which is identic with, or related to the globulins of bloodserum,
just as the other anomalies of the milk from cows with diseased

1) Milk containing streptococcci has sometimes a high degree of acidity.
2) Journ. Biol. Chem. 40. 335 (1919).

277

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278

udders are connected with the transit of bloodplasma-components
in abnormal milk. While 100 ¢.c. normal milk — after removal
of casein and fat with the aid of potassium-alum contain according
to our investigations about 14—20 mers. of tryptophane, as much
as 348 mgrs. occurred in the milk-samples after the injection of
silvernitrate, that is about twenty times more.

The determination of the tryptophane-content, easily executed by
the colorimetrical method of von Fürrn and Noset'), is no doubt
one of the most accurate methods for examining the normality
of milk.

The foregoing experiments tend to show that the anomalies
characteristic of streptococci-containing milk, arise also from sterile
inflammation of the udder-tissue, so that streptococci need not always
be essential to the occurrence of similar anomalies. The question
whether, in the case of streptococci-mastitis, these bacteria are very
often only of secondary importance can of course not be answered
on the basis of this investigation.

From the Chemical Laboratory of the Veterinary
University of Utrecht.

1) Biochem. Zts. 109. 108. (1920).

Microbiology. — “On Bacillus polymyxa’'). By Prof. M. W.
BEIJERINCK and L. E. pen DOOREN DE Jon.

(Communicated at the meeting of September 30, 1922).

If the species-conception is taken in a not too limited sense, the
closely related, but not identic forms mentioned in Note 1, may be
said to comprise the only known aérobic spore-forming bacterium-
species, which causes fermentation in a sugar-containing medium.
We call it Bacillus polymyaa.

It is rather generally spread in fertile soils; its properties are
very characteristic and give rise to interesting experiments. The
production of aceton first observed by SCHARDINGER, has in the later
years drawn attention on this microbe, but the quantity formed is
small and from malt or potatoes it does not amount to 1 °/, of the
weight. But the conditions for its formation are not yet well-known
and might perhaps be greatly improved as to the quantity. Alcohol
is also generated and to a somewhat greater amount than aceton.
Besides, a little acetic- and formic acid seem to be produced. Par-
ticularly the secretion of the enzyme pectinase and of much slime
by the chief variety is of interest.

1) The literature of this Bacterium and its nearest relations is to be found under:
Clostridium polymyxa Prazmowski, Granulobacter polymyxa Beuserinek, Bacillus
macerans SCHARDINGER and Bacillus asterosporus A. Meyer. — A. PRazmowski, Ent-
wickelung und Fermentwirkung einiger Bacterién. Dissert. Leipzig 1880, p. 37. —
Tu. Gruger, Identifizierung von Clostridium Polymyxa Prazmowskt, Centralbl. f.
Bakteriol. 2te Abt. Bd. 14, 1905, pag. 353.-— F. Scuarpincer, Bacillus macerans,
Acetonbildender Rottebacillus, Centralbl. f. Bakt. 2te Abt. Bd. 14, 1905, pag. 772.
Zur Biochemie von B. macerans. Centralbl. f. Bakt. 2te Abt. Bd. 19, 1907, p. 161.
Kristallisierte Polysaccharide aus Stärke durch Mikrobien. Centralbl. f. Bakter. 2te
Abt. Bd. 22, 1909, p. 98 and Bd. 29, 1911, p. 189. — A. Meiser und G.
BREDEMANN, Variation und Stickstoffbindung durch Bacillus asterosporus. Centralbl.
f. Bakteriol. 2te Abt. Bd. 22, 1909, p. 44.

The name asterosporus is derived from 9 or 10 rims on the exosporium of
the oblong spores, which make the transversal section star-like. By abundant
feeding, as on wort-gelatin, many rodlets change into narrow clostridia con-
taining somewhat granulose, colored blue by jodine; so the species may also be
called Granulobacter polymyxa.

18*

280

Accumulation and occurrence.

Long ago the following experiment for the accumulation of this
species was described *).

Coarsely ground rye with some chalk and inoculated with fertile
garden soil is mixed with water in a deep beaker to a thick solid
paste, boiled during some seconds to kill the non-spore-formers and
cultivated at 25° to 30° C. As the spores of B. polymyza soon die
at boiling, the heating must last but a short time. After a few days
the surface is covered with a coherent film of B. mesentericus *) and
other closely related species, while in the depth a butyric-acid fer-
mentation takes place, usually simultaneously with butylic-alcohol-
and polymyxa fermentation.

It is clear that this accumulation reposes essentially on a tempo-
rary anaérobiosis of B. polymyra, which can also grow aërobie and
so behaves like the aleohol yeast and the Aérobacter-Coligroup among
the bacteria. The rye produces the sugar causing the fermentation,
i.e. the source of energy, which makes the anaérobiosis possible so
long as the “excitation oxygen” is still sufficiently present, albeit
chemically non-demonstrable, whereas the want of ‘oxidation
oxygen’, which is required for aërobiosis in much larger quantity
as source of energy, is temporarily excluded. Pastrur’s statement:
‘la fermentation est la vie sans air” is evidently applicable to B.
polymyxa.

By sowing out the fermenting matter from the depth on wort-
agar, ordinarily already after few days the polymyxa colonies become
visible as lumps of slime, together with the unavoidable flat spread-
ing colonies of B. mesentericus.

This method can only produce those varieties of B. polymyxa
which are able to resist a relatively high concentration of the food.
Another accumulation method by which also forms adapted to a.
lower concentration of food are obtained is based on the aérobiosis
of our bacterium.

After the observation had been made that flasks of boiled wort, not
sufficiently sterilised, were not seldom spoiled at the low temperature
of 15° C. by the development of B. megatherium and never by 5.
mesentericus, whose germs were certainly also present, the question

1) M. W. Bewerincx. De butylalcoholgisting en het butylferment. Academy of Sciences.
Amsterdam 1893.

*) This film may be colourless, brown, red, and even jet black according to the
accidentally present varieties of B. mesentericus. The black form is rare and
sometimes obtained by the “mesentericus experiment’’ with unwashed currants
(boiling with chalk, cultivating at aëration at 30° to 40° C.).

281

arose: which are the aërobie spore-forming bacteria, which can
develop at temperatures of 15° C. or lower and under favorable
feeding conditions? We knew already that the obtaining of -B.
megatherium might give an answer to the question, for example in
case the spores of this species were only present with those of
B. mesentericus, but it seemed possible that free competition with
the soil bacteria would exclude B. megatherium and that some other
species could appear. The chief aim of the experiment was to
exclude B. mesentericus, the common hay bacterium, which produces
substances very noxious to other species, and this is to be reached
by the low temperature, as the minimum for the growth of this
species is at about 20° C. The simultaneous development of B.
megatherium is of less importance as it is innocuous to other kinds.
Of course we had to reckon with the butyric-acid and butylic fer-
mentations, which may very well occur at 15° C, but strong aéra-
tion prevents them efficiently.

Although we could expect that the one or more species that were
to develop under the chosen conditions would possess a higher
temperature optimum than that used by us, we had not to fear a
failure if only we cultivated above their minimum.

Knowing that the spores of some spore-formers, for example those
of the butylic ferments, and thus perhaps, too, those of the species
we sought for, could not or hardly resist boiling, the heating of
the culture liquid containing the inoculation material and wanted
for killing the non-spore forming species, was not continued much
above 85° or 90° C. and only for a few seconds. We used flasks
half filled with about 30 cM’ liquid, and in order not to miss
somewhat rarer species, we inoculated with so much soil that on
the bottom a layer of about 1 cM precipitated. This soil had
previously been well-divided and freed from coarse particles. In
such a thick layer a beginning of anaérobiosis is possible, but by
shaking, butyric-acid or butylic fermentation may easily be stopped.

For food we used at first malt-wort, diluted to 2° to 5° BaLuine,
later broth-bouillon with 2°/, to 5°/, cane sugar, or glucose. Addition
of chalk is not absolutely wanted for the success of the experiment
but its presence proved favorable.

After we had ascertained with pure cultures of B. polymyaa that
ammonium salts, nitrates and asparagine are very good sources of
nitrogen, we also accumulated with sugars and ammonium sul-
phate, in a solution of tapwater 100, 2 to 5°/, glucose or cane
sugar, 0,05 °/, (NH,),SO,, and 0,02°/, K, HPO, with some chalk.
The execution of the experiment is as above, but after pasteurising,

282

the butyric-acid fermentation must be more completely excluded
than when using broth-bouillon or malt-wort. For although the latter
liquids contain an excellent nitrogen food for B. polymyxa, they are
of Jess value for the butyric-acid ferments, for which the ammonium
salts are preferable. Hence, in this case it is advisable to use a large
ERLENMEIJERflask, as the great volume of soil which sinks to the
bottom as inoculation material, can then be better aérated, by which
butyric fermentation is prevented.

Although the growth is slow at the low temperature the liquid
becomes distinctly turbid and in most cases this is accompanied
with fermentation. This fermentation especially awakened our atten-
tion as we had expected an accumulation of B. megatherium, which
causes no fermentation at all.

As the Col- and Aérogenesfermentations had been prevented by
the previous heating, the butyric-acid and butylic fermentations by
the aëration, we now expected that the fermentation of B. polymyza
was obtained, and this was confirmed by the pure culture. The
fermentation which is chiefly an alcoholic one, proves that our bacte-
rium belongs to the facultative (temporary) anaérobes, and the exa-
mination of the gas showed that it is almost pure carbonic acid.

One of the most notable qualities of B. polymyxa is its secretion
of pectinase, i.e. the enzyme by which some microbes dissolve the
central lamellum of plant tissues, thereby disintegrating them into cells.
Hence, B. polymyxa like B. mesentericus may under certain cireum-
stances play a part in the retting of flax, although the real agent in
this case is the anaërobie B. pectinovorum.

Beans, peas and other plant seeds, left to spontaneous corruption,
may change into rich cultures of B. polymyaa, the cell-walls of
cotyledons and of endosperm being easily attacked by pectinase,
whereby the interior of the seeds is changed to a pulpous mass !).
For the preparation of a pure culture this method is less recom-
mendable than the two foregoing accumulations, on account of the
numerous hay bacteria which thereby simultaneously develop; it is,
however, a good way to get an initial material for the said accu-
mulations themselves.

It seems to us that the generality of B. polymywa in our surroun-
dings and particularly in the soil should be explained by its pectinase
secretion, which must give this species, in combination with its little
want of air, a great advantage over the other saprophytes.

1) The enzyme seminase, which changes the endosperm of the Leguminosae
(Indigofera, Ceratonia) into mannose, is perhaps identic with the pectinas of
B. polymyxa.

283

The very common presence of B. polymyxa in the bark of the
nodules of the Leguminosae is certainly also a direct consequence of
its pectinase production. Its presence there is of so general occurrence,
that it reminds more of symbiosis than of saprophytism. In the
bacteroidal tissue B. polymyza is however completely absent.

Properties of the colonies.

~The colonies on agar as well as those on gelatin are characteristic.
On malt-wort gelatin they resemble at first thin, watery, sideways
quickly extending, slowly liquefying layers, which by and by
become deeper and cloudy by their strong growth. At length the
gelatin is completely liquefied and then these cultures resemble those
of common hay bacteria. On malt-wort agar there is a profuse produc-
tion of slime, whence very distinct voluminous and wrinkled
colonies appear. The slime attracts part of the pigment from the
wort-agar thereby becoming brown-coloured, which gives a character-
istic appearance to the colonies.

On glucose-kalium-phosphate-ammonium-phosphate-agar they be-
come glass-like transparent, somewhat resembling glass globules, so
peculiar that at estimating the number of germs in soil samples, they
may directly be recognised and counted. Silica plates, saturated with
food, also produce such drop-like colonies from soil. Some varieties form
much less slime than others and this slime is either tough or soft.

Microscopically those with soft slime consist of much shorter
rodlets. Hence, one is at first disposed to think of different species,
but further research shows the similarity, which is the more con-
vincing, when beside the natural varieties, the mutation phenomena
in the pure cultures are studied. On cane-sugar-asparagine agar
many colonies, at first quite homogeneous and soft, when getting
older produce small, rather solid, transparent, secundary colonies
which, after separation from their surrounding (which is not easy)
prove to be constant. On malt-wort agar the variety with tough
slime, when growing older produces extensive, flat secundary colo-
nies, showing a hereditary loss of the factors for slime formation.

In liquid nutritive media the form resistent to high concentrations
of the food gives remarkable cultures.

In a malt-wort of 10° BarrinG at 30° they consist of excessively
voluminous slime masses, forming after one or two weeks a thick,
coherent, floating film, inflated by carbonic acid, whilst no hydrogen
is detectable. Only in the anaërobic butylic fermentation something
of the like may be observed but then much hydrogen is present.

284

Even the most slimy Aërobacter forms produce quite different sub-
merged cultures equally dispersed through the solution.

The vigorously fermenting slime varieties of B. polymy«a produce
aceton, probably after the formula

C,H,,0, + 20, = C,H,O + 3CO, + 3H,0.

To the products of the anaérobic fermentation belong in parti-
cular aethyl alcohol, with traces of acetic acid and formic acid
beside some other products, such as butylic glycol, in small quantities.

The less slimy varieties of B. polymyxa can only live in food of
lower concentration and spread through the solution as Lact. aérogenes.
Also in other respects there is similarity between Bact. aérogenes and
B. polymyxa, so that there is cause to conclude to a real relationship.
Still there is a great difference in so far as aérogenes can assimilate
many organic salts, a power quite absent in B. polymyaa.

Nutrition.

For the investigation of the substances which can be assimilated
by B. polymyxa, the auxanographic method is very convenient,
particularly in relation to the carbohydrates, B. polymyxa being a
real “sugar bacterium”, which produces much cell-wall matter,
which makes the auxanograms very distinct. In judging the latter
it should be kept in view that, beside pectinase, B. polymyaa
produces diastase, invertase and emulsine. In presence of sugar
various nitrogen compounds are assimilable, of which, however,
only nitrogen is taken up. We preferently used peptone, asparagine
ureum, ammonium sulphate and saltpeter. Urease is not secreted ;
saltpeter is reduced to nitrite, not to nitrogen.

As in absence of sugar the carbon cannot be withdrawn from
nitrogen compounds, such as peptone and asparagine, the growth,
even on broth-bouillon-agar is but slight and is a eriterion for the
quantity of sugar present. Hence, if on this medium B. polymyaa
is densely sown, only small, hardly visible colonies grow, consisting,
however, of bacteria with abundant protoplasm and commonly
motile. If on such a culture an assimilable carbohydrate is locally
distributed, vigorous growth ensues, chiefly reposing on slime for-
mation and a distinct auxanogram results, demarcated by the limit
of diffusion of the substance. It is in fact the presence of a small
amount of complete food at the starting of the experiment, together
with excess of by themselves unassimilable nitrogen compounds,
which enables the germs to change into small colonies, which

285

renders the further growth after addition of the carbohydrate very
clear.

Most sugars and polyalcohols are readily assimilated by B. poly-
myxa. This we have ascertained for arabinose, glucose, levulose,
mannose, galactose, cane-sugar, maltose, lactose, melibiose, raffinose,
rhamnose, glycerin and mannite. On the other hand sorbite, dulcite,
erythrite and quercite are not attacked. It is very notable that we
did not find any organic salt assimilable by this organism.

The “sugar bacteria’, to which B. polymyza belongs, produce from
carbohydrates much more visible cell-wall substance than protoplasm,
if the carbohydrates exceed the nitrogen food and vice versa.

Hence, B. polymyaa may be found, as was observed above, in two
microscopically greatly different conditions. At insufficient feeding with
carbohydrates, for example on broth agar, it grows as highly motile
rodlets, without slime wall; at copious feeding with carbohydrates,
as immotile rodlets with a thick slime wall’). This circumstance
leads to the following experiment, only adapted to the variety of
B. polymyxa which produces voluminous slime and grows strongly
on malt-wort.

The bacterium densely sown on cane-sugar-kaliumphosphate-agar,
containing but few nitrogen compounds, may form fairly large
colonies consisting, however, almost entirely of the strongly swollen
walls of the cells. By addition to the said medium of a few drops
of complete food, for example a little broth or malt-wort, con-
taining an excess of sugar, the slime walls grow surprisingly so
that the plate covers with a relatively thick slime coat. This slime
is built up of the sugars by ope or more synthetically acting
enzymes, that might be named “cyteses’’ and should be considered
as the genes or factors of the cell-walls.

This slime has the remarkable property of being able to become
itself a source of carbon food, but only at the moment when all
the cane sugar and all the assimilable nitrogen compounds have been
used. If at this time some such nitrogen compound as ammonium-
sulphate or asparagin are brought on the slime coat of the plate, the
bacteria begin anew to grow and produce new protoplasm from their
own cell-walls. This leads to the peculiar consequence, that an aux-
anogram is produced sinking deep into the layer of slime. For, by the
growth the bulk of thebacteriais diminished, because the walls, which
chiefly consisted of water and were very voluminous, disappear
and are replaced by living protoplasm. So the appearance of the auxa-

1) Medici give to the cell-wall of bacteria the singular name of “capsule”.

286

nograms is quite changed when compared with the original state,
for by their intense increase the opaque bacteria produce an also
Opaque auxanogram, whilst the original slime was transparent like
glass. This proves that, in this case at least, the biological function
of the slime is that of a reserve food.

In this experiment cane sugar was the food for the slime pro-
duction; as hereby inversion takes place, glucose and levulose are
probably the building materials of the slime; that these sugars are
assimilated was stated above, and that glucose may also serve for
the described experiment we ascertained particularly.

The other sugars have not yet been extensively examined from
this point of view, but it seems that all give the same result. This
leads to the conclusion that probably no more than two or three
factors or genes (endoenzymes) are active in the production of the
cell-wall. The problem is evidently of theoretic interest and deserves
nearer research.

The wall-substance, which certainly belongs to the cellulose group
and therefore may be called cellulan, must have a high power of
attraction for water, for else its surprising volume cannot be explained.
Nevertheless its molecules cannot be very small as they cannot diffuse
at all in water. It is not colored by jodine, nor is it attacked by
diastase. But as B. polymyaxa may use it as a food-substance, this
species evidently can excrete an enzyme which dissolves it. It is
not improbable that this enzyme is pectinase, but this question is
not yet answered. Should this really prove to be true, then the other
question arises whether the so-called pectose of the central lamellum
of the tissues of the higher plants may not also be a cellulose
modification, as it is also easily dissolved by pectinase. This view
seems to be much more acceptable than the current hypothesis:
the central lamellum should be the calcium salt of an acid, isomeric
with arabin-acid.

On the great similarity between pectinase and the seminase of
the seeds of the Leguminosae, I already earlier directed the atten-
tion. That the latter enzyme does not attack true cellulose is in
accordance with the same property of pectinase.

SUMMARY.

With a not too limited species-conception Clostridium polymyza,
Granulobacter polymyxa, Bacillus macerans, and Bacillus asterosporus
may be brought to one single species: Bacillus polymyxa.

It is the only hitherto known aërobie spore-former, which, in

287

neutral sugar-containing media excites fermentation and thereby
proves able to live as a temporary anaérobe.

The chief products of the fermentation are carbonic acid and
alcohol. At the aérobic life a little aceton results, evidently from
oxidation of sugar.

Anaérobie accumulation is possible in rye paste at 30° C. after
short boiling. Aérobic accumulation takes place in dilute malt-wort
or broth with 2°/, to 5°/, sugar, after heating at 85° to 90° C.
or short boiling with much garden soil and cultivation at 15° C.
by which B. mesentericus is excluded, whose growth minimum is
at about 20° C.

The general distribution of B. polymyxa in decayed plants and
its occurrence in the bark of plant roots and of the nodules of the
Leguminosae reposes on the production of pectinase, which dissolves
the central lamellum of the cellular tissues.

B. polymyxa forms much slime from sugar, which must be consi-
dered as cell-wall substance. Without carbohydrates or polyalcohols
its growth seems impossible, hence it develops but slightly on
broth agar.

The slime may serve as reserve food.

Laboratory for Microbiology of the Technical
High School at Delft.

Mathematics. — “On the Light Path in the General Theory of
Relativity.” By Prof. W. van pur Woupe. (Communicated
by Prof. H. A. Lorentz.)

(Communicated at the meeting of September 30, 1922).

In Einstein's theory the path of a ray of light is found by putting
the condition that it is a geodesic null line in the four-dimensional
time space’). If accordingly we represent the line element of this
time space by

En ORR Ea a ase EE taller)
ik
the light path satisfies equally the equations of the geodesic as
those of the null line

de Ege ay EME DE OC

As far as we know the remarkable relation existing between
these differential equations, has not yet been pointed out. We shall
prove that this may be expressed in the following way:

a geodesic having one element, i.e. one point with the tangent at that
point, in common with a null line, is itself a null line.

In order to prove this we shall first give the equations of the
geodesic a form different from the usual one ($1), as on account
of (2) it is not desirable to take s for the independent variable.
With a view to an application which we shall give later on, we
take one of the coordinates of the time space for the independent
variable.

We shall conclude by pointing out the (evident) physical meaning
of the theorem.

$ 1. If the line element is represented by
ds* — Sg. dx, dx, ,

ik
the equations of the geodesic are
dz, Au)de)d
es Bee Te SEE
ds? ‚u lv \ds ds

1) From this there follows for the statical field (gip independent of the time-
coordinate 2 and go; = 0 for 10) the principle of FERMAT for the minimum
time of light in three dimensional space.

289

has here the meaning :

À
= In

where g”” is the algebraical minor of g,- in the g-determinant divided
by this determinant, and

À u a 1 Og» | Ogu» 09),
Be, TE & + Ow Oay

As independent variable we chose one of the coordinates, e.g. 2,. |
In this case

day «ds da, da, (ds\* de, d's de, 5
ds “de, dz ds? \ du, BEAR dr A (4)

CuRISTOFFEL’s symbol Kie

Au
yv

especially for wv, =w,

daf de’ de, ds 1
EL o dat er ne ae (aA
lf therefore we multiply the former of the equations
day _ \Au) deden
ds? de (oP ds “da a
da, Au) deden — 5
ds? hat 0 deden.

ds \° ds \* dz,

a the latter a= : aye ;
by Ss , the latter by SS ane we find after subtraction by
the aid of (4) and (4’)

dees as |
dz, hp.
These are the equations of the geodesic which we had in

view. Taken as the equations of the geodesic of a two-dimen-
sional space (a surface in the usual meaning), they give

ze | (Ca) (Pe f-2 DE)
+ (2) i a lee he za

a well known form, which is often taken as the starting point for
the discussion of the properties of this line.

Al
yv

Au) de, | da) dx
es iB ee
0...) dede de,

290

d.
§ 2. We multiply (5) by Gatch and sum with respect tov and 9;

da,
the equation thus found

arj N Au A pj da, | daz) dz, \ dz
S Jip ; i Ss Ive | | av | | A PB. ae! =— 0 : (6)
„ dz, | » 0 \ dw, | dz, de, de,

Ap

may be reduced to a different form.
Let us consider the first term:

As g,.= 9 we may also write this

1 SE B 4. fe bd Ls =) d da, da, |
DA de*de, dx, de, Be der Ade, de,

In the second term

Au

v

de) de, da,

= 9 — —
oe de, dz, dx,

Ay 5%?

Au f
we replace 5 by its expression between the square brackets and
v

apply a reduction

= vT ~ da) dende, > aon dx) diy + VT da,
ae r |de, dede, armel t | da, da, vp aa de)

À vpt
ae eee,
wt. T Ide, dz, da,

as
val forno =S)
Sages 8 2
pe Pe SO (for 0 At)

According to the meaning of the symbols [ |, we may replace
the expression thus found by

1 Ee Ògu de, de, da, 1 > dx dtp, don
2 dur On, dx, dede, 2 i, da, de, de,

The two former terms of (6) may therefore be combined to:

ibid dx, dan _ le dh Wards eN
2 da, in)" du, dx, 2 de, \de,)

We write the third term

Au
yv

de, dx) da dx,

=
hj da, de, de, dx,

Arp

291

> 2 de, de, > " u de) de, EL ds = > 2 u de, de, f
re de, da, orn | 0 }de,de, de) xml 0 ) de, dz,
so that (6) is transformed into
de, de,

Ed fedeet de? Au
——— {| — } + | — ] 2 ——_= 90
2 de, \dz, a a We 0

— ni) DEN OY
dx, dx, (7)

as

§ 3. Let us now define a line in time space by
Ui — Pi (2),
where we require of the functions p:
1. that the line defined in this way satisfy the equations of the
geodesic ;
2. that in a definite point A

ds \? de; dx;
ne == Iik == == 10%
dz, JA ik de, de, JA

Of course we also suppose that the coordinates 2; are defined as
uniform continuous funetions of «, and that also gj, and its
derivatives are uniform continuous functions of the coordinates, at
least in the region in consideration.

We have in this way taken care that the line defined by (8) is
a geodesic and has a null element in A. As it is a geodesic
each of its points satisfies (7); each a; being a function of a,, we
may conclude that

elf GON: ds oe 0
de, de, De (z) = 0,

where ® is a uniform continuous function of a.
Hence, along each geodesic

ds \? ds \? ie (x9) dx
— =| — e To 8 ; Agta te, Weba (8)
dx, /]P de, JA

by a, and p, we understand the values which «, assumes at the
starting point A and an arbitrary point P of the line.

However, we have also made the assumption that the geodesic
in consideration has a null element in A. Accordingly here

( ds )
= 0.
dz,/]A

On the other hand there follows from (8) that along this line always

1 3
SE 0
de,

292

in other words that the line in consideration is a geodesic null
line, which was to be proved.

§ 4. Let #, be the time coordinate. In three-dimensional space
in a point A an arbitrary direction is defined by giving definite
day

ratios to Dr (L=t1, 2, 3). If inversely we assume these ratios as
U,

. do Mie
given, we can give such values to — that the condition

dx

0
(= )=2 donald Oy wv
dx, a Ju de, din, dar ma aX,
is satisfied.
The theorem which we have proved, has therefore the meaning:
In three-dimensional space there passes a ray of light at any
moment through any point in any direction.

Physics. — “Calculations of the effective permeability and dielectric
constant of a powder.’ By G. Breit, National Research
Fellow U.S.A. (Supplement N°. 46 to the Communications
from the Physical Laboratory at Leiden. (Communicated by
Prof. H. KAMERLINGH ONNgs).

(Communicated at the meeting of October 28, 1922).

Introductory.

The pure samples of some rare substances are available only in
powdered form and show particularly interesting magnetic properties.
For this reason it is desirable to know the relation between the
measured and the true permeability of a powdered substance.

If the susceptibility is small the effects of the demagnetizing field
are negligible and the magnetization of any individual particle of
the powder is the same as it would be if the particle were part of
a solid block. Supposing that the particles are crystalline, the measured
specific susceptibility is the mean specific susceptibility of a crystal
provided in taking the mean equal weights are given to all orien-
tations of the crystal.

In the case of gadolinium sulphate at 2° K. the magnetization is
considerable and the above approximation does not suffice. This fact
has been realized by Prof. H. KaAMERLINGH Onnes and a correction
has been made by him’). Prof. KAMERLINGH ONNes expressed his desire
to the author to see a more accurate correction. This forms the
subject of the following pages.

Approximations and statement of problem.

In view of the random distribution of the principal directions of
the individual crystalline particles the difference between suscepti-
bilities in different directions will be neglected. This probably intro-
duces an error in the calculations which however is likely to be
small.

It will be supposed that the applied field is so small that the
magnetization is proportional to the field. Some of the results of
the calculation are independent of this assumption as will be brought
out later.

1) Leiden Comm. Suppl. N°. 44a p. 10.
19
Proceedings Royal Acad. Amsterdam. Vol. XXV.

294

For convenience of notation the electrostatic problem of a powdered
dielectric in an electric field will be treated. The results are trans-
lated into the magnetic case by substituting the permeability u for
the dielectric constant €.

Our problem is to calculate the effective dielectric constant of a
powder under the above assumptions as to the smallness of the field
and the random distribution of the axes when the density of packing
of the powder and the dielectric constant of the material of the
powder are known.

Definition of “effective dielectric constant’.

Let us consider a portion of the powder which contains many
particles and let us take the mean electric intensity and the mean
electric displacement throughout this portion. (The mean being taken
with respect to volume). We define: “effective dielectric constant” =
mean electric displacement

mean electric intensity

We presuppose that this definition is unique which implies that
the powder is sufficiently fine for otherwise it is not possible to
include a sufficient number of particles without making the portion
so large that the field’ would vary in it, (from point to point) if the
powder were replaced by a solid.

Let us draw a spherical surface inside the powder. According to
the well known treatment of polarized media the electric intensity
inside the sphere is equal to the electric intensity due to charges
inside the sphere plus the intensity due to charges of polarization
on the surface of the sphere and plus the intensity due to charges
of polarization on the outer surface of the powder as well as that
due to charges outside and inside the powder. This means that the
electric intensity

= E; AR Ep ZIE B
where

E; = effect of charges inside the sphere

HL, = effect of charges of polarization on the surface of the sphere

E, = effect of charges of polarization on the outer surface of the
powder + external field

where “external field’ = field due to all real charges and the
charges of polarization not belonging to the powder.

Since each individual particle is uncharged £; is obtained by
summing the fields due to charges of polarization on the surfaces
of the particles inside the sphere.

295

If E, should denote the average value of Z, throughout the sphere

we have with a good approximation E,=E because the usual
treatment of polarized media may be applied to EZ and the result
is H, if the powder is fine.

Let a certain volume be occupied by the powder and put in an

external field €. Then 4, € on account of the charges of polari-
zation on the outer surface of the volume. It is for this fact that
the correction has been made by Prof. H. KAMERLINGH Onnes. We
shall suppose in what follows that this or an equivalent correction
is made in the final interpretation of the experiment. In order to
make such a correction however one must first obtain the effective
dielectric constant and then operate with this constant just as one
would in the case of a homogeneous medium. Thus e.g. it may be
shown') that the force on a sphere of radius a placed in a field
of force given by EL, + Bz parallel to the OZ axis of a rectangular
system of coördinates having its origin at the centre of the sphere

B ;
and —> along the radius @ perpendicular to the axis of z is
e—l a
= argc rs where #,, B are constants and « is the dielectric
é

constant. Hence
| oa ole Ba +1
1 wae Flos BE,

Preliminary approaimate solutions.

(a) A space lattice of spheres.

Consider a space lattice of spheres the density of packing being
not too great. We can get very easily an approximate solution for
this case. Let us suppose that each sphere has its boundary removed
so far from the surface of the adjacent spheres that the field acting

1) Using equation (6) (to be derived presently) we find that the density of the
fictitious distribution of charge is (using polar coördinates with OZ as axis)

Al 5 ee 1 EE Doe 2 (, 4 oe oF P 4
LE, Ula Erne e+ 2 oF 1 (008 ) + oe43 aP, (cos@) |.

Hence the force

41
a? d(e —1)
eo [E, + Ba P, (cos oi) — E, P, (cos 6) +
2 e+2
cos §=—1
CD BaP, (cos pd (eer jet EB
T Des a P, (cos | (cos eae: B.

19%

296

on it may be considered as uniform. Then the sphere is uniformly
&,—1
&,+2
trie constant of the sphere and F is the uniform field acting on
the sphere. If q should denote the fraction of the volume of the
lattice which is occupied by the spheres themselves, the average
polarization is

3
polarized, the polarization being res F, where e, is the dielec-

Sid EE de zel F
Ane, +2

Since now the effect of a uniformly polarized sphere at points
outside the sphere is equivalent to the effect of a doublet at the
centre of the sphere the contribution to /' of the particles of powder
situated inside the large spherical hole vanishes by a well known
reasoning of Lorentz’) and his result for F applies here so that

ners ag ee
ry Toa) oe im ergs
Le.
E
F=
oo 1
&,+2
and
3q EK e—l
Ar &, +2 An
mere
where e is the effective dielectric constant.
Thus
e—1 ze. 1 :
Le (1)
3 pale
and letting
p+q=1

ee ee i br eg eg Se TG
we have
e—1 1

ET

EE EE
d
te

Thus the effective susceptibility of a powder is not proportional

1) H. A. Lorentz, Theory of Electrons, p. 308.

297

to the density of packing but should be corrected by the factor
1
En
It is worth noting that (1) may be written as
e—l é,—1

oon an ay

which means that if the powder is moulded in a sphere then the
force on that sphere is a gt? part of the force which would be
exerted on a solid sphere of the same radius. In other words each
individual particle of the powder may be considered as acted on
only by the external force. (I have seen a very direct and simple
proof of this fact from Prof. Enrenrrst).

We see therefore that to within the approximations made so far

l
the factor — — — — used by Prof. H. KAMERLINGH Onnzus should be
4x od

| ed eT
ae 3 H
used with the value of the density in the solid — not the powdered

form.
(b) A space lattice of spherical holes’).

The case considered above may be expected to give a good ap-
proximation if the powder is packed loosely. If it is packed closely
a better approximation must be expected from a space lattice of holes.

It is not necessary to treat this case independently because use
can be made of formula (1) if it is remembered that in (1) e is the
ratio of the effective dielectric constant to the dielectric constant of
the space between the spheres of the lattice. Denoting by q as before
the proportion of the volume occupied by the substance (i.e. the
ratio to the total volame of total volume minus the volume of the
holes) and leaving (14) unchanged we arrive at

e— 1 1
Ee . 1. ss. 2)
TEI) 1+ po
3 + 2d
which may be also shown to be equivalent to
e—l1 1 !
at gale EN
€é,—l de, Pp
te Ea
1 + 2e, g

1) The possibilities of this case have been pointed out to me by Prof. H.
KAMERLINGH Onnes and Dr. H. R. Wotrser.

298

From either of these formulas we find
gh el
ond?
€+2 ee 2pd*
342d
This formula is analogous to (1") in (a) and shows that to within
the first power of d the force on a sphere having spherical holes in
it is the same as if the sphere were moulded into a smaller sphere
without holes. Thus the conclusions drawn in (a) for the correction factor

2")

— remain valid in this case.
4x od

3 4H

1+

(c) Laminary structure of powder the directions of the laminae
being distributed statistically. (See fig. 1).

Bur

MA"
SS

The electric intensity may be resolved into two components
normal and parallel to the laminae respectively.

(I) Normal component.

Letting H,, U, h,, h,, &, €, be respectively the normal components
of the field intensity, the thicknesses, and the dielectric constants
of the interspaces between the laminae and the laminae themselves
we have:

1 E, h, BE, de h, B,

6, | q € 33) he! Jkt

Writing
h, E, + h, E‚= (A, ai h,) E
and letting

Mette By

Einen
we obtain

atin h +h, 5: 1
he + he! op + ge,
having let
El Es de al
A, +h, hth,

This number «, is the effective dielectric constant for the component
normal to the laminae.
(II) Parallel component.
For this it is clear that the effective dielectric constant is
WEG aie Patan
aa ee are:
(LII) Both components present.

The electric displacement is re (en cos DB, &, sin) where 9 is the
JE

angle made by the mean electric intensity with the normal to the
laminae. Since the directions of the normals to the laminae are
entirely arbitrary with respect to the direction of the mean electric
intensity, the component of the electric displacement perpendicular
to the mean electric intensity is distributed at random. The only
component to be considered is then that parallel to the mean electric
intensity which is i (en cos? J + &, sin’? J). The effective dielectric
7
constant is
En + 2&
3

& == En cos* } + Ep sin? 9 =

Hence we get
rn 2
‘ie = aie d (3)
q Gy 1 a pd
To within the first power of Jd this is the same as (2) or (1’) so
that in this case the conclusions drawn as to a force on a sphere
are still valid. Rewriting (3) in the form

e—1 1
ban seller GAD naaister.) eeb ate (3)
dading van BS
3 + 2pd
it becomes apparent that the value of « obtained from (3) lies between
the values obtained from (1’) and (2).

300
Variable susceptibility.

To within the approximations made so far the case of variable
susceptibility offers no difficulty. Thus in the case (a) it was assumed
that the field acting on each particle of the powder is uniform.
Whether the susceptibility of this particle depends on the field or
not its polarization is uniform and is such that the electric intensity
K inside the particle is

3
E= —__———_
se, (ZH) + 2
where fis the intensity of the field acting on the particle and
e,(£) is the value of the dielectric constant of the material of the

= de:
particle corresponding to £. If the mean field is #, —= H+ Sis

uae
and P=q oe

simultaneous equations

i. Hence K and e, are the result of solving the

=|
The solution may be obtained graphically or otherwise.
In the calculations that follow the correction for variable suscep-
tibility is more complex and will not be considered.

The distribution of potential in a rectangular space lattice of
dielectric spheres.

In order to investigate the errors involved in the approximations
we shall look for an exact solution in the case of a space lattice
of dielectric spheres. The following notation will be employed:

h = distance between centres of adjacent spheres.

e, = dielectric constant of the material of the spheres.

(7, 7, p) = polar coördinates of a point referred to centre of sphere
placed at the origin. The polar axis is chosen along one of the
rectangular axes of the lattice.

(7,,9,,,) = polar codrdinates of a point referred to centre of
sphere whose Cartesian coördinates are:

(2, Yo, 2) and whose polar coördinates are:

(B, 0, PD).

The radius of each sphere is taken to be 1. The mean field is
also supposed to be 1 and directed along the polar axis.

301
Polarization of single sphere in external field.

Before proceeding with the solution of the problem it will be
convenient to derive an expression for the state of polarization of
a dielectric sphere placed in a known external field. Charges of
polarization are induced. If the electric intensity due to these charges
be H; and if the impressed electric intensity be Z,, the total intensity
is H= BE, + E;. Let us suppose that H; may be derived from a
potential

m

m
y—s A, Pr (cos ) cos mp
n,m rt

outside the sphere. Then it must be derivable from

(4)

= > An r Py (cos 9)cosmp . . … « « ~ (5)
n,m
inside the sphere since the potential is continuous at the surface.
Denoting the components along the outward drawn normal by the
suffix n and referring to the state just inside the sphere by n, and
to the state just outside by n, we have the boundary condition
&, (Ben + Ein) = Pea Eng
or
(e,;—1)} Len = Ein, me Ein
“ Using (4) and (5)
(&,—1) Een = = (ne, +n +1) An Pr (cos iP) cosmp . . (6)
n,m
Thus if E£., can be expanded in a series of surface harmonics
the coefficients Am may be determined from (6) and hence the state

of polarization of the sphere may be obtained.

Derivation of expansion for Ken.

In order to solve the problem it will be sufficient to express Ze,
in terms of A™ and substitute the result in (6).

A 0
The average polarization of the medium being —- we have
)

/
0
Fe =| 1 + pila cos 9 — = (= =; A, Py (cos 9) pees
3 A Or 1 n,m rth r=!

the first summation being extended over all the spheres inside a
large sphere having its centre at the origin, the dielectric sphere
situated at the origin being omitted from the summation as indicated
by the accent. Using the notation:

pan drm 7%
Loe Òzn— "Po
De gm om
á dem on™
f= 4 + 34, H=#%—ty
and letting
ps BA ES ee

it may be shown that [see appendix formula (14)]

cos mp, Px (cos 9) _ (—)" 2" bn om (1)

(c) (7)

ptt =i. (n—m) ! n
the differentiation being performed with respect to the end point of
the vector 7, i.e. with respect to (7, ”. p). Thus

An A 0 —)"27h,A” mn
En =(1 ieee noel = ( ) "De zz)
On (n— m)/ ae

oe 1
where R has been subtracted from — so as to secure absolute
1 ry
convergence of expansions that follow. Now
Ne Set eal ype ) ®,).
—— 8 PDP
a DE EERE Em) cos 9) (cos @,) cos m (p :

1
Mii==O eft

Py

When this is summed with respect to R,, @,, P, terms in sinm ®,
and all terms with an odd m drop out. Hence

m m

—)yn9uh. A D (

An A 0 f ( ) m n

Een (145 5 eo ed EAT nd P; (cos) au)

where

(v—p)! Py (cos O,) cos uP, (8)
Pu)! Rr PES
Now it may be shown that [see Appendix formula (24)]

m(r PS (cos) )cos up (—)" (vu)! pon PEAT" (eos9) cos(m+) p
a ee Ki 2m (punt my! binn FARK
which when substituted into the expression for Ee, just found gives:

0
Een =) En oa)? (cos 9) —

si —

bin ig An Ss prt n o
ees ( yee Pe (vp + pu)! (v—n) (cos) cos (m +) p REET
bn+u (nm)! (pun tm)!

> (ne, +n +1) An Py (cos F) cos mp

n,m é,—l

303

in virtue of (6). Equating coéfficients of P, we have

eo 4
Gi ze) All + #AVS94 649894... . . (10)
@; =
where use is made of the fact that S}— were = 0. In

order to obtain A® we are thus in need of Aj, Aj, etc. For these
it follows from (9) that

[Gs De, + 2942) Aregi 5 (Ast 2p + 2)! Soopopte

el gend (28)! @p+1)/ ay
(¢ == 1, 2, Sige)
the upper subscript being dropped for the present. Writing
; &, —l Aost1 (2s + 2p + 2)!
Gh Sh Sas (SP)
2s + 2 A, (2s + 1)/(2p + 1)!
a oo (11)
2s + 1
Soptos+2 = Op+s
we have
Os = Bs = (s, p) G45 ps CP ne eee De 1)
ps
or

a, = Bs (3,0) 6; + Bs s (35D) Opis Copiaaty nj (12’)
p=1

Substituting for ap on the right hand side the expression which
follows for it from (12') and proceeding in this manner indefinitely
we obtain purely symbolically on changing suffixes:

as = Bs (8,0) Gi > 8, Bs, (s, 8,) (s,, o) Os-+-5,,5, zE

+ = Bs Bs, Bs. (s, s,) (s‚, s,) (35, 0) Osten, 1+5p, Sa des

$1, Sa=l
+ & Bs Bs, - - Bs (8,81) (81184) « « (Sp—t, 8p) (Sp 0) Fst, 81+ 89,0048 ace ae ole sene
Sy yoy SQp—=1 7 P gee
where
Ox,y,2,.. == Ox Oy Gz +. ie i ae ee ed 0)

If the spacing of the lattice is large in comparison with the
diameter of each sphere this expansion may be expected to converge
rapidly. As a first approximation the first term will suffice giving

Be (26-192) Sees os se as (195)
Using (10) and (11) we have for the average polarization P=A, h~*
and the effective dielectric constant €

304

3q
e—l—4nr P=
&,+2

é&,—l

(14)

—gq— (2s + 2) a, 5;
1

An
where gE and denotes as before the proportion of the total

space occupied by the material of dielectric constant €,
So far we have considered the field only in the direction of one
of the axes of the lattice. If the lattice is rectangular and not cubical
the quantities 6, may be different for the three principal directions.
In the case of a cubical lattice however they are the same. Since
all the relations of the problem are linear the effective dielectric
constant in a cubical lattice is independent of the direction of the
field and may be thus justly compared with the effective dielectric
constant of a powder.
If the first approximation (13) is substituted for @, into (14) the
approximate formula
3q

Si

De : (14’)

&,—l

—g — 3 (201372, 0.
1

is obtained. In the summation of this formula the density of packing
enters through the quantities o, and the intensity of polarization
comes in through p,. The quantity e,—1 occurs in these to the
first power. If the more accurate formula (13) were used higher
powers of ¢,—1 would come in. Hence if the density of packing is
kept constant and if deviations from the simple formula (1”) just
become apparent due to an increase in se, formula (14) is the proper
one to use. On using (11) it may be simplified to

3
e—1l= oa ennn (14")
&,+2 pa s+ 1 : 6q 3
re DE tere (4)

ms . wu . . . .
where o, is the value of os for ES which is the maximum possi-

ble q for the lattice. The quantities o, are rapidly diminishing as s
increases. Thus we find
3 (46,)? = 0.0646, _ B (60,)* = 0.00082.
Writing

Pe A

Tu: 6q
logs Re tege 160) OEE
dte (7 (15)

305

we get on neglecting terms of higher order than the second in ¢,—1

e— 1 é,—l (e‚— KE, i
el, Le eee

Thus owing to the interaction among the particles of the powder
the force on a ball made of the powder can no longer be considered
as the sum of the forces on the individual particles independently.
The increase of the force to within terms in (¢,—1)’ is given by

Lye

the factor 1 + oe —_— q'. For the maximum possible value of q for

the ae ean: qg' = 0.065 and the correction factor becomes
2
= . If the quantity asi of Suppl: N°. 44a is 0.09 for
zee sulphate at 2° K. then since d was taken as 3 of the
actual density the quantity «,—1 becomes 0.36 and the correction
factor is 1.0028. Thus the effect discussed must be taken into account
if the measurements of the force are made to within 0.3°/,. If such
a correction is made it should be also borne in mind that even the
simple formula (1”) involves terms of the second order in the apparent
‘¢—1) if it is solved for ¢, as may be seen in the following way.
For small values of ¢,—1 we have gq (e«,—1) =x’ where F is
the force and x is a constant of the apparatus. For larger values
of e—1 this is not true but it is convenient to call the quantity
&,—1 defined by the above equation: “the apparent e—1”. If the
sample is spherical and if the powder may be considered as the
cubical lattice just discussed

é,—l 1 2 rp Eg—l
OS AONE NN na AEA veP
es q
3
Hence
ee ed
eet <a =S +(- Ae [lean
eae eee) (eel)? :

U
f
Thus 2 occurs here together with the larger term —.
q

If the demagnetizing field is negligible as in the case of a thin
long tube e-—1=>x#/'= gq (e,—1) where « is the effective suscepti-
bility. Hence by (14")

=i
pea EP TEGE a rg

p q :
1 — q (Ea1) De zal)

306

If the sample has the form of a thin slab normal to the lines
of force

—&g—l
e, —1l= sy, a (17%)

1+ 29 q
fed ETE (LE Ds
gee Dt glad)

Space lattice of spherical holes.

From (14") we get for this case to within the second power
of (e, —1)"

where p' is the same function of has q'. The corresponding formula
for the space lattice of spheres is

q (e.—1) i

Be | SS Se
jz q B
15e 1) — (6, —I)

/

The term = thus tends to reconcile the two expressions. However
q

for the case of touching spheres or touching holes the space lattice
of holes has a higher e than the space lattice of spheres even though
q is made the same for both. This means that the continuous path
of the flux between the holes contributes to a high value of the
effective «. It thus becomes apparent that qg and e, alone do not
suffice to determine e even if the structure is on the average isotropic.
The correction in (e,—1)? may therefore be never applied with
certainty and an estimate of its amount is all that the present theory
can offer.

SUMMARY.

1. The consideration of the effects of the demagnetizing field for
various models of the powder shows that to within the first order
terms the correction is the same for all models considered and may
be expressed by the fact that the force on a sphere of the powder
is equal to the force which would be exerted on the material if it
were moulded into a solid sphere instead of being powdered.

2. Different models give results differing in the second order terms
in the demagnetizing field.

307
APPENDIX.

1. It is shown in Maxwerr’s: Treatise that
yo = =» m |

m+l De —.
n n T
Now
oe seine : OP. 2cosm®
n antm(nf)? 7
and
m 2n / ee
6 2" (n—m)!n!
Hence

2 P, (cos 9) cosmD (—yr 2m ml
pnt ~ (n—m)/ nr

It is also well known that

ae

ml mn den

These two equations may be combined in:

cosmP P‚ (cos 9) (—)P2™b, mf
SSS SS = eee ed 7

putt Ee ln ET
where
b= Ts Dive bee =e

2. To show that:

Dr r’ P; (cos 9) cos uP (—)" (vp du)! rr AEM (cos) cos (mu) D '
Cc [Se a
n bn 2m (v--u—n-m)! bn (2.4)
We consider the following cases:
(L). =m = 0
We must a that
Ip n
5 (r’ P, (cos Ó)) = ——_—_ P_n (cos 9).
ENG (cos 1) = 7 7 „(cos 9)
Proof. Using sh: integral
1
P; (cos == = | om 7 + isin 3. cos PD) db
a
0

i. cap et
we have r’P,(cos 9) = 5 fe + iQ cos DY B where e= Vat + 4",

308

whence the formula follows on differentiation.
(TT). nmr #0
We must show that:

a pn—m PM (cos 9) . 2 cos my

9 m n—m

DE (r" P, (cos 3) =
Proof. Since 9? = En we have

—)p nl anp Erm?

rn lam i

p_ PP (pl)? (n—2p)!

Operating on this with D; and observing that
! cos"—2m—2p Ff sin?p H

PE (cos) = e sinng = (—)p
2 p (n—2m—2p)! 22 pl(m-p)!

the above written formula follows. An analogous formula holds of

course for the operator DY.

(ELI). m0, uil
Using (14) and (ID, (24) is found.
(IV). m = 0

This is also verified without difficulty.

Physics. — “On the Heat of Mixing of Normal and Associating
Liquids.” By Dr. J. J. van Laar. (Communicated by Prof.
H. A. Lorentz).

(Communicated at the meeting of September 30, 1922).

1. In connection with a study by J. R. Katz (published in „Ver-
slag der Wis- en Natuurk. Afdeeling Kon. Akad. v. Wetensch.”
Vol. XXXI, nos 5/6, p. 333—336) I wish to make a few remarks
on the heat of mixing of liquids, also in reference to the quantity
af: (or afgz).

Different authors, among others vaN DER WaaLs and myself, made
use of approximations some time ago, which seemed permissible;
but which gave no account, not even in approximation, of the heat-
effect, which is sometimes very slight, especially for normal substances.
For here the case presented itself that the neglected quantities
((v—6)? by the side of v’, p by that of 7/,2) would give a term of
higher order of magnitude in the results than that which results
from the not neglected part. The latter term appears to be of the
order of magnitude (6,/a,—6,Va,)’, whereas that of the neglected
part — yielding a term with (p + %/2) Av — is of the order
6,V.a,—b,Va, on account of Av; hence, when the difference of the
critical pressures of the components is small, the neglected part
will have a much greater value than the not neglected part.

And besides: While the first part — referring to the change of

the potential energy without reference to the contraction — will
always be positive, the second (neglected) part — which is in con-
nection with the volume contraction Av — is nearly always negative.

In ‘quasi-ideal” mixtures of two liquids (i.e. liquids the critical
pressures of which are about equal), the effect will nearly always
be negative (ie. heat is berated), and not positive, as the earlier
theoretical derivation indicated. In liquids the critical pressures of
which are not about equal, sometimes differ even considerably, it
will entirely depend on circumstances (relation of the a’s and 6’s
inter se, value of the mixing ratio #) whether the result will be
positive or negative.

In assvciated components, where Av can become much greater
than in mixtures of normal components (generally the critical pres-
sures also differ much more from each other), the above ratios will

20
Proceedings Royal Acad. Amsterdam. Vol. XXV.

310

be more greatly accentuated, and the negative term with (p + ¢/,2)Av
will predominate still more.

Already Baknuis RoozEBooM — now about twenty years ago —
drew my attention to the insufficiency of the approximative expres-
sion, but at the time we attributed this to other causes *), thinking
that -— especially in quasi-ideal mixtures — the possible volume-
contraction would probably be quite negligible. Not until 1912, when
in a letter my friend Prof. Kremann at Graz put a question to me
on this subject, was I led to carry out the perfectly accurate
calculation of the quantity Av”).

In what follows I may be allowed to give the exact theory, first
of all of mixtures of normal components. Here too the perfectly
accurate derivation appears to be by no means more difficult or
longer than the approximated derivation, and the result is almost
equally simple. The same thing is found here as before with the
exact derivation of the equations of the spinodal and the plaitpoint
line*). There the perfectly accurate results are even simpler than
the earlier approximated expressions.

2. Heat of mixing of normal components.
From the well-known expression for the total energy

Py thay rama
v

in which the energy constant €! is = 7,e’, + n,e',, and the heat capacity
at constant (infinitely great) volume k=n,k, +n,k,, we find for the
pure components:

U a j
ge, eN Se Pee

1
° ' as °
C= ep aem Ge
2

For the integral heat of mixing of n, gr. mol. of one component
and n, gr. mol. of the other component the expression

1) Inaccuracy of VAN DER WaaLs’ equation of state; non-validity of BERTHELOT’s

assumption dy, = Waag, etc. But since then I have got more than ever convinced
of the absolute validity (in liquids) of the said equation and B’s assumption. Of
course a and 5 then have other values than in the gaseous state, but this need,
of course, not be considered here.

*) Later inserted summarized in his valuable — unfortunately too little known
— book: “Die Eigenschaften der binären Flüssigkeitsgemische etc.” (Sammlung
(Herz) chemischer Vorträge Bd. 23, Stuttgart, Enke, 1916); see p. 170—171.

3) These Proc. Vol. VII, p. 646; Vol. VIII, p 33.

is at onee found from

we (n, e,° + un, Ek:

Now
a a a a a a
—=— + —— | == ——-_— Ap,
v Ve v Vo Ve vv,
in which v, = nv, + n,v,°, and v—v, = A is written. Further

“alee +n,Va,)’, and from this follows:
Zante nd n, eV ie (9g, Vlan wlan)

Vay. ies RORY

Remarks. a. Formerly *) the following equation was written:

Hence:

ne deld vot ye

ve Di v,°

a

r= ~ sE (S (v—b) + p(v—b) — (n, + 2.) Rr),

on account of the equation of state. This gives:
= = — (27h) + "p(o—b) (n,n) RP — (: ss (=) ) a
ae b v

7 P (v—b) ney (n, zE 74) RT,

exe + (: tale mR) r— (1 er) + pb,

for which e=e’ + k’T—+/, was written — with an apparently
perfectly justifiable neglect of some terms. Then we get:

(2, Va, ane b, Va,)’

eed iin bbs bt

hence:

W==n, Nn

: ‘ a : :
It is seen that the very essential term — Av is omitted.
vv,
b. We might also have written:

1 a, (v, Va, zer Va,)’
SER NI >,
v Vv, vv, U,
; ; Ov Ov ;
in which», =—— and v, = —. For according to a property of the
On, On,

1) Cf. among others Zeitschr. f. physik. Ch. 63, p. 219 (1908).
20*

312

homogeneous functions of the first degree with regard ton, and n,,
we have v= nv, +7,v,. And further according to (a):

LE: B +n, eo +
Vv

UU, Vv,

af P (nr, (v, at v,") 5 i ns (ets) )s

or also

rele ental OR (> + :) n, Av, + (» ip

vv, UV, Re ok

a
= ‚ads (19)
v

Vs U,

which expression will at once appear to be useful.
Here is »,—v,°= Av, and v,—v,°= Av, and evidently we have
Av = v—v, = (nv, + nv,)—(n,v,° + n,v,°) = 1, Av, + n,Arv,.
For the differential heats of mixing w, awe and poe we now
dn, On,
have from (19) *):

) — 250
een me Vaal 2. (*:) +(> En “ae,

vv, On, \ v

ke Ò (m‚N vnd Nd
dn, \v v? v?

2
1

vv
)
== n,? (v, Var Va.) a: (» Ai =) Av, |

2e
Vv, U3

(2)

Likewise

1) In these differentiations many parts have not been taken into account. For
in general vj and vz are still functions of m, and ,. But as the neglected parts

in w, and wy can always be represented by zj = ge and 2, => ‚in which 2,
1 2

just as w, will always be a homogeneous function of the first degree with respect
to 2, and no, necessarily 7,2 + 22, will have to be = 0, mw, + MW, already
being = w according to (2). Now also #2, + 23 =2, hence 2 is identically = 0,
hence also zj and zj.

lt would indeed not be difficult to show directly the disappearance of the parts
z, and zj, which have been left out of account. As to zj, we get the result:

1 ari a, dv, Ov,
ET mn tm 5)

pe : ¢ : 5 u :
in which the last factor will disappear in conseqence of ee a A vy, is a
1 Ne

homogeneous function of the Oth degree with respect to the molecular numbers
m and #3.

313

For liquids p may of course always be cancelled against the so
much greater molecular pressure 2/,2.
We will just mention that the earlier — inaccurate — expressions
were:
3 (6, Va,—b, wa)’ 3 (b, arb, Va.)
w, == Nn, ’ WwW, == u, = .
b°b, b'o,

3. Volume contraction with normal components.

We must now try to find an expression for Av, and then also
for Av, and Av,, in order to be able to substitute in (1) and (2),
and to form an opinion of the order of magnitude of the different
parts. As

Av=v—-v=v— (nv,° + n,v,°),
we have also:

Av = b —(n,b, + n,b,) + (v — 6) — n, (v,° — b,) — 2, (v,° — 4,).

Now b—=n,b, + n,b,, hence after application of the equation of
state, there remains:
jen (n, + ns) RT (sed dO ae BT

phe. pe tipsy Bt

Le. with neglect of p:

2 3
2 0 r)
1) v U
Av = RT Nn, a) — nl a en, ie
a a, a,
or
A hal RT 0 0 2 Fis A
ian ee a (n, a n,) (2, v, ots Ne, Vy ) a, 4, — n, U; aa,— nv, aa, ty
13

RT
+ ——(n, + n,) (2 Av (n, v‚° + 2, v,°) + (A0)'),
a
as v= (nv, + n,v,") + Av. In consequence of this, with a=
Ge (Aer
‘(n,+n,) RT

a

Av (2a» (v—Av) + (ao) =

RT 3 2 2
=F | ort nadine. my a,a,—(n,v,° a,+n,v,° a) acte) |

aa,a,

which, worked out with neglect of Av by the side of 2v, and
putting n, -+n,=1 at AT, gives:

314

nv,” + 2(n, +7,) v,°0,9 +n, 0,"

a, a, —

RT |
== n,n,

ae 9 0? °° va os
n‚v, a + 2(n, u a, 4-7, ¥,” @,)V ad, + nv," a,

= n, nm jee, vaer 20,'Va,) —v,° a,’

+n, Jota valet 2v,°) Va,—2r,° Va) aie

RL |
= n‚n,| n,

2v,°o, Va,w, V/a, —v, Va.) + a(v° 4,—v,° a,) | oP

a a,a,
zie Ns 20,” a,Va, wlan Va,) SE a, (v,°'@,—v," a) |
RT AM
NN ON Ee
a a,a,

i n,| aint Wag ede DD

For the form between | | we may further write:
(hea (v,°Va, +0,'Va,)—n,a,(v,°Ya, + ¥,°V a,)—2n,v,°a, Va, + 2n,v,°a, Va,
nie Pas (v,° Va, =e Va) malts (v,° Va,—v,° Va,) d
La a Va, (n,v,° st n,v,°) rage ms Va, (n‚v‚° te n‚v,°),

so that we finally get:

\

| 2RT HET;
Av (2 = I= nn, (v,° Va, —2," val |
- (3)

“/» aaa,

. E Vo (Va, Ce Wa.) Va,a, — (n‚a, = n‚d,) (v,” Va, Er v,° Al |

This almost quite exact result (only p has been neglected, and in
the 1st member Av by the side of 2v) shows that Av will be of
the order d= v,°Va,—v,°Va,, so that w consists of two parts, of
which the first is of the order d* (cf. equation (1), the second of
the order d. When the critical pressures differ little, dis very small,
and of the small heat of mixing w the second part (neglected before)
will certainly predominate.

In the case that the critical pressures differ little, expresion (3)
can be considerably simplified. For then v,°Va,—v,°Va, = 0 ean
be put between [ |, and there remains:

315

ART at v,° Va, \0,° Va, (Wa, — Wa.)

Av ¢ — an oa ib Li :
af, af v, Va, Va, a,

st v,°—v,

But because than Wa, = — a}, V4,-V8,=4 Va,
10 Vv,

BRT ART Ph,
hence Av{1— —— |= nN, Ny 1 — — (v,°—,°) p (32)
af, ef, Pr

As for ordinary substances in liquid state (below the boiling-point)
a), - TRT, and in the second member v,—v may be put, we find
with 1/7, = dik

ie m Ae
A= — 1 > Dn ite ERR 5
9 TE hl me) v,) (3°)

If eg. m='/,, we have with n,=1—2, n,=@ for Av the
value 1/,a(1—a)(1—-1) (v,°—v,°), so that the maximum contraction
(at «—'/,) becomes = */,,(1—V’)(v,°—v,°) — hence very small
and of the order 1—\).

With regard to the sign of Av it may be pointed out that 5, > b.,
e.g. b,—60b, corresponds with v,°>v,°. Then a, is approximately
= 4 a,, so that %/,, becomes — daf, or Ti, > Tr. But from this
it ensues that pz, is generally somewhat greater than pz,, in conse-
quence of which 1—) becomes negative. And the reverse when
v,° should be < v,°. The quantity Av will, therefore, nearly always
be negative, in other words volume contraction will take place.

With regard to the differential variations of volume Av, = v, —v,°=
= ze and Av‚,=v,—v,° = MEP grom the approximated expression

1 2
(3a) follows, when ¢/, is considered constant in the correction term
of the 18* member :

2RT 0 (n, v,
do, (1— )=2 Rtn, Aere )
af On,

v a
In approximation v,° Wa,=v,° Wa, was taken, so that a, is =

vi De v
= sy Va, and/a=n, Va, +n, Va, = Val, of + n, = Way.
a 2 2

0/ ny 0 n, vv,”
In consequence of this xz ( ) becomes = ( : 5 ie

a AR
dn, \ a On Een,
3 ,
Be OES (Now 2 anid TEM Ve N,v,"
= <— | — | in which — | — ]=—W¥.= ——.. Hence we have
as On, Vo On, 0 Vo Vo

316

0 (nv Brus Da
—{—" |} =n, -; +=n,—; therefore with the same approxi-
òn,\ a JE) a

mation as (3a):

2RT ORE
dut) = Ev eee)

efo afne 4
za RT) L\2ET ee hei,
Av,| 1 — —— —— n,? (lW) (v,°—», fi
af as) dl ge
We now duly get again n,Av, + n,Av, = Av,, because
Vs v,° Vv,
n,n," — -+ n,n," NN
a a a

4. Substitution of (3°) in (1).
We get for w, after substitution of (3e) in (1), with omission of
the external pressure p:

(v,° Ya,—v,’ Wa) a hm v,°Va,—v,°Va
n +

1
wn nn (y,°—v,°
a ve VP 0," vo, 1--*/,m' * v,° Va, 7%
or
w=n,n (VE ENT = bh) a 4 Var —v, Wa.) (v,°—2,°) dert
== nn, ve v,°v,° len vv, ep,

when ®/,, Wa is substituted for Wa, With m="/,andv==v,, this
passes into

ht: ne, = (¥,°V/a,—, val €, °Ya,—v,°Va,) — = 5 tne HG

The factor '/, is, of course, somewhat different, when m= gg
is not —‘/,. When the critical pressures are equal, the foregoing
factor is — 0, hence also the total heat of mixing. But when these
pressures do not differ too much, the first term between [ | will
all the same be small with regard to the second, and in approxi-
mation

1). magn

vm 0 Van Va) te) a … … (59

may be written.
But however this be, we shall always be allowed to write:

WES RIN dn
vv

OLK == Md nv. =(1—a)v,° + av,’ = v,° 1 AD, ==
9 ise) 33 1

= Vv, (Ll +72), when dick =r (hence ea =1+ r) is put, and

with alist =o OY
(v,’)
a va (la) a
w= x (1—z2) ; (6)

(Fre) +") } RTE } TT Pra pry
the old expressions, but in which « has now a somewhat different
value than before, and will also be dependent on the temperature
(through mm).

When in approximation

a
=

a
Aa 2 he
v

vv,
is written for (1) with omission of the first part, which is generally
much smaller, we get approximately :

Ww a
If the critical pressures of different substances do not diverge too

much, also the values of ¢/,2 do not lie far apart in mixtures of
different pairs of substances, and we shall find values of at least

the same order of magnitude for the quotient ree result to which
v

also Mr. Katz came experimentally in his latest paper (loc.cit.) *) —
at least as far as volume-contraction and heat of imbibition of
amorphous and crystalline swelling substances is concerned. That
the ratios there are quite analogous to those of liquid mixtures is
owing to this, that when one of the components is solid, it must
first be reduced to the liquid state, whence the pure heat of melting
of this components is simply added to w. But if Av predominates,
also this heat might be omitted with respect to the second part.

At any rate we shall never find exactly 4/2 Yor w/a», because the
omitted part can never be entirely disregarded. For this reason also
the values of ~/,, will differ somewhat, even with almost equal
values of @/,2, which was also found by Karz.

1) The curves of Fig. 1 and 2 are no hyperbolae, but oblique parabolae,
a(l—2z) a

l+re l+r
the integral heat of mixing (i.e. 1—a gr. mol. of 1 +a gr. mol. of 11) would
be a pure parabola. If, however, 7° is not =v,°, the top of the parabola will
have been displaced somewhat to the side of the component with the smallest

as according to (6) wis = . If r were =0 (Vz = 0,°), the curve of

molecular volume, as is easy to verify. From òw/òx =O we find x=1:(1+V 1 +7),
which gives x =1/, for r=o, but x<1/, for r >0. (v9 > vj).

318

The values of ¢/,: in our above formulae always refer exclusively
to the liguid mixture, even for solid components, for as we already
remarked above: this solid component must first be thought liquid,
so that after all we have always to do with quid mixtures.

Now that through the formulae derived by us above, the absolute
values of w and Av are known, which Mr. Karz so eagerly desired,
the problem has become clearer. Also when the components should
be associated, everything remains essentially the same, as I will
shortly show in a concluding paper. But then the preponderating
influence of Av will still be more pronounced, in consequence of
the great variation of volume on dissociation of the double molecules.

And finally as regards the “important as yet undiscovered prin-
ciples of the laws that govern molecular attraction” — I believe
that this principle too was solved long ago’). This subject will also
be discussed more fully in our concluding paper.

Tavel sur Clarens (Suisse), September 1922.

1) Compare my papers in These Proc. Vol. XVIII N°. 8, p. 1220—1235, and
following numbers; in the Journ. de Ch. physique 14, p. 1 et seq. (1916); in the
Z. f. anorg. und allg. Chemie 104, p. 57—156 (1918); in the Ch. Weekbl. of
1918 (p. 1124); in These Proc. Vol. XXI NO. 5, p. 644—655, and the J. de Ch.
ph. 16, 411 (1919), which possibly have escaped Mr. Katz’s notice.

Histology. — “On the Regeneration of Sensitive End-corpuscles
after section of the nerve’. By Prof. J. Bork.

(Communicated at the meeting of September 30, 1922).

During the process of regeneration of the motor endplates of
striated muscles we are in a position to observe not only that the
nerve-fibers put forth new shoots again and unite with the muscle-
fibers to form new end-plates, but also that all the surrounding
tissue elements: the connective tissue as well as the muscle-fibers,
the nerve-sheaths and the axis-cylinders of the nerves themselves,
play a part in the regeneration process and are instrumental in
ensuring its success.

In the case of sensitive nerve-endings it is more difficult to observe
this procedure: 1° because there is a greater variety in the shape
of these endings than in that of the motor end-plates, 2° because
many more varieties occur side by side in the same environment,
and 3° because sensory endings generally offer greater difficulty in
establishing the relation between the nerve-fibers and the surrounding
cells than motor end-plates do.

Now in the cere of the duck’s bill there are two sorts of
sensory end-bodies, viz. those of GRANDRY and Hersst, which are
very well adapted to such an investigation by their simple, well-
defined structure.

We examined the regeneration after cutting the nerve. The ope-
ration was well sustained by the animals and in a short time the
wound was healed in primam (among 24 cases one inconsiderable
suppuration) without any injury to the animals. |

After 4—5 days the severed nerves were completely degenerated ;
nothing was left of the axis-cylinder except a few granules staining
brownish black by BirrscHowKY’s method. After some days these
also disappeared.

An alteration of Granpry’s tactile cells or of Hergst’s core-cells,
described by Gastorowski years ago after cutting the nerve, consisting
in shrivelling of the cells and bulging and wrinkling of the nuclei,
[ have not been able to detect. In agreement with the aspect of
the soles of the motor endings the protoplasm became more coarse-
grained, swollen, while the impression was given that in the core

320

of Hersst’s corpuscles there were more nuclei than the normal
corpuscle presents. There also seemed to exist a slight increase in
the number of the capsule-cells of GRANDRY’s corpuscles.

While regenerating the nerve-fibers follow the old nerve-courses
(which have changed into strands of BinGNeER), and pass again into
the primary corpuscles. It seems, however, that all along also new
corpuscles, especially GRANDRY’s corpuscles, are formed, in which
process sheath-cells (lemnoblasts) grow larger and become tactile
cells, as Hertnea has established as to embryological development. As
soon as the nerve-fibers have reached the tactile cells of GRANDRY,
they branch out, grow sinuously round them, always embedded in
the protoplasm of the capsule-cells and at length force their way
between the tactile cells. Directly after this the neurofibrils begin to
branch, broadening reticulations appear, which gradually spread
between the tactile cells, first as a delicate retiform structure, after-
wards as a close-mesh network. In this way the whole interspace
between the two tactile cells is occupied again by a net-shaped
neurofibrillar nerve-plate.

Two things strike us here as being remarkable:

First of all that in the beginning of the process of regeneration
the nerve-fibers bend round the tactile cells in various convolutions
and ramifications, but that in the following stages (after 2 or 3
months) this process is less pronounced, so that gradually the normal
condition asserts itself in the same way as with the motor end-
plates; secondly that neither the nerve-fibers themselves nor their
terminal branches and terminal broadening ever run freely, but
always remain enclosed in the protoplasm of the conducting cells
and the capsule-cells, and that directly when they are within reach
of the tactile cells, a peculiar network is formed around them,
inside the protoplasm of the tactile cells, which could also be demon-
strated, in complete distribution, in the normal corpuscles of GRANDRY ;
lastly that here the process of regeneration of the intraprotoplasmic
network shows itself first round the end-branches (end-reticulations
and end-knots) of the nerve-fibers and then appears to extend gra-
dually over the whole extent of the flat tactile cells. The whole
regeneration-process takes two or three months.

In the case of Hersst’s corpuscles the in-growing nerve-fibers also
follow the old nerve-tracks. At their point of entrance into the core
of the corpuscle we see also here that the nerve-fiber not only
proceeds linearly into the protoplasm of the syneytially connected
celss of the core, but also that it throws out its branches and passes
with many convolutions through the protoplasm, so that the aspect

321

CF:

Fig. 1. GRANDRY's corpuscle. 36 days Fig. 2. GRANDRY’s corpuscle, 46 days
after cutting the nerve. Initial stage of after cutting the nerve. Complete
the surface-enlargement in the neu- regeneration, double growth round
rofibrillar apparatus of the nerve- the tactile cells. Longitudinal
threads that grow round the tactile section.

cells. Transverse section.

Fig. 3. Fig. 4.
GRANDRY’s corpuscle. 42 days after the cutting of the nerve. Transverse
section of the same end-body at different planes. Splitting of the in-growing
*nerve-thread. Intrusion between the tactile cells, formation of a protoplasmic
network (receptive substance, periterminal network) round the end-buds of
the neurofibrillar nerve-apparatus.

322

of the whole structure becomes much more complicated than that
of the primary nerve-fiber of the normal Hursst-corpuscles. However,
here also the normal relations gradually assert themselves. I have
not been able to ascertain whether new HerBsr-corpuscles are forming
in the course of the regeneration process.

Round the inner core in HerBst’s corpuscles are disposed a large
number of connective-tissue lamellae, separated by lymphspaces.

Fig. 5.

Transverse section of a Hersst-corpuscle, with a nerve-thread that not
only branches out in the protoplasm of the cells of the core, but proceeds
from there into the connective-tissue lamellae round the inner core, where
it continues its growth. 42 days after the cutting of the nerve.

These lamellae are connected by means of cellular processes, thus
forming a whole.

Now in watching the regeneration it may be repeatedly observed
that the nerve-thread, which has passed into the inner core of a
Hersst-corpuscle and ramifies in the protoplasm of the core, does
not remain enclosed here in its entirety, but that some of the end-
branches leave the core and intrude into the tissue of the connective-
tissue lamellae. This then is the very place to see quite clearly,

323

that these nerve-fibers do not force their way into the lacunae
between the connective-tissue lamellae, but that they lie in the
lamellae, enveloped by protoplasm, and remain there. This envelop
must decidedly partake of the nature of connective tissue. This
observation, therefore, is in perfect harmony with what could pre-
viously be established for the neuromuscular spindle of striated
muscles. In them also the in-growing regenerating nerve-threads
could be seen moving through the protoplasm of the connective-
tissue cells of the capsular space, which cells have developed into
a conductive-tissue.

Utrecht, August 1922.

Chemistry. — “Heterogeneous catalysis and the orientation of adsorbed
molecules’. By Prof. H. R. Kruyr and C. F. van Duin.

(Communicated at the meeting of September 30, 1922).

In a previous communication’) we published investigations on the
relation between the adsorbtion of reacting substances an the velocity
of the reaction, with the object of coming to a better understanding
of heterogeneous catalysis. In these investigations we found, that by
giving coal to the reacting system a decrease of the velocity sets
in, even in cases, where undoubtedly an increase of the reacting
components in the surface layer takes place.

In accordance with the theory of 1. Lanemuir*) and W. D. Harkins’)
concerning the special condition of molecules, which are situated in
surface layers, we tried to explain our results by the assumption
1. that adsorbed molecules bave partly lost their mobility and con-
sequently a great deal of the possibility of meeting and reacting
with other molecules, and 2. that adsorbtion can cause positive
catalysis only in the case, when the molecules are adsorbed in such
a way that the number of effective collissions increases.

That adsorbtion in itself can have a decreasing effect was found
when studying a monomolecular reaction, viz. the transformation of
racemic dibromo-succinnic acid into bromo fumaric acid and HBr‘).
The results are given in the tables I and II.

Evidently a marked decrease in the velocity occurs.

We discussed in the paper cited above, that a positive contact
catalysis can be expected only in the case, when the reacting group
is turned away from the adsorbent and towards the surrounding
liquid. With charcoal as an adsorbent, and water as milieu, all
electrically polar groups will be turned towards the water; we
therefore had chosen the reaction of «3 dibromo-propionic acid and
KJ (formation of acrylic acid, KBr and J,). As might have been

1) Rec. trav. chim. Pays Bas 40, 249 (1921).

3) Journ. amer. chem Soc. 39, 354 en 541 (1917).

3) Journ. amer. chem. Soc. 38, 2221 (1916) and 39, 1848 (1917).

4) Cf. HormBera, Journ. f. prakt. Chem. 84, 145 (1911) and Zeitschr. f. physik.
Chem. 79, 147 (1912).

325

TABLE I. Without coal. TABLE II. With coal.
Time |c-c. NaOH conc. k Time mr aa conc. k |
in ‘Noon |. m | mono- in 10 ob i0 cel in Zt. | Mono-
min. |p. 10 cc.|'" 499 | mol. min. ae pay ak ‘| 1 400 | mol.

0| 20.22 | 19.98 — 0 | 18.91 | 20.22 | 19.98 —
1371 21.53 17.36 |0.000103 1372 19.89 | 21.20 18.02 |0.000075
2991 22.70 15.02 095 2992 | 20.87 | 22.18 | 16.06 13
4288 | 23.57 13,28 095 4311 21.29 | 22.60 15:22 63
6771 24.88 | 10.66 093 6788: | ‘2z582 123.45 | 13.56 57

expected, we then have found and accelleration of the reaction. We
repeated these experiments in a ‘CO,-atmosphere and in the dark
room to avoid complications. The result was almost the same:
without coal we found k —0.000123 and when coal was added
k = 0.000149.

The place of the polar groups in dibromo-propionic acid is however
not symmetric; the possibility remains that the COOH-group exerts
a more vigorous orientating influence than the Br groups and con-
sequently the latter will not be in a most favourable condition. A
better result could be expectod therefore in the case of the reaction
of dibromo-succinie acid and KJ. A comparison between the
formulae

HC—CH—COH en HOC—CH—CH—COH

Br Br O O Br Br 0
will elucidate this inmmediately. Moreover, the stereochemical confi-
guration suggests a still better arrangement in the case of the
mesoform than in that of the racemic. In the tables IU and IV we
give the results obtained with the racemic, in the tables V and VI

TABLE III. TABLE IV.
Racemic-acid without coal. Racemic-acid with coal.

Time |c.c. thio} conc. k Time | c.c. Ix ac I conc. k
in ne a mono- in 0 fi mono-
min. 40 /go0 mol. min. |not corr.| corr. /800 | mol.
| SE | |
0}; 0.08 19.92 — 0 WEAN PAD we | 19.92 —
790 1.82 18.18 |0.000116 716 11.72 14.57 14.37 |0.000421
1392 | 2.99 17.01 113 | 1380 8.90 iis 11:55 395
k mean 0.000115 k mean 0.000408
21

Proceedings Royal Acad. Amsterdam. Vol. XXV.

326

TABLE V. TABLE VI.
Meso-acid without coal. Meso-acid with coal.
: : n n
Time |c.c. thio | conc. k Time | ce J 40| “© J conc. k
in n pe mo no- in 5 mono-
min. | 45 /800 | mol. min. |notcorr.| corr. /800 | mol.
0 | 0.06 19.94 — ON ABEL „20.14 19094 —
289 | 1.11 18.89 |0.000187 292 | 14.45 | 16.38 | 16.18 |0.000716
HIG | 2.12 17.88 189 582 | £1520 |: 13.13, |" 12,03 744
806 | 2.83 17.17 _186 809 9.47 | 11.40 | 11.20 713

k mean 0.000187 k mean 0.000724

hose with the meso-acid. The initial concentration of the acid was
/,, u., that of KJ 2n.; work is done at 25° centigrade, in CO,-
atmosphere, in the dark room; 1 gramm of coal was added per
100 cem.; in the experiments with 'coal-10 cem. of the reacting
mixture were poured into 20 eem. of thio-solution of 0.02525 n.;
he titration was done with a J-solution of */,, n.

These results, shewing a great accelleration of the reactions,
fully support our theory.

We have still other expirience, which is in, accordance with this
theory. Dr. C. F. van Duin wil give presently a detailed paper in
Recueil des Travaux chimiques des Pays Bas.

Utrecht, van ‘tr Horr-laboratory,

St. Andrews, United College of St. Leonards
and St. Salvador 1922.

Geology. — “Fractures and Faults near the Surface of Moving
Geanticlines. Il. Abnormal Strikes near the Bending-points of
the horizontal projection of the Geanticlinal, axis.” By Prof.
H. A. Brouwer.

(Communicated at the meeting of September 30, 1922).

In a previous paper') we have pointed to the occurrence of
considerable transverse fractures near the bending points of the hori-
zontal projection of the geanticlinal axis, which phenomenon has been
explained by velocity differences on either side of these bending
points.

Another phenomenon that may be observed near the bending
points is the occurrence of older strikes, inclined or normal to the
horizontal projection of the axis’). This may be seen in rows of
islands if the strikes in some islands do not coincide with the main
trend of the islands. It is of great interest for determining the
precise movements of the rows of islands, as will be shown in the
following discussion.

The row of Islands Sermata-Islands, Babber, Tenimber-/slands.

In the islands Letti, Moa, Luang and Sermata the principal strikes
are sometimes more or less parallel to the direction of the row,
e.g. in Letti. :

Fig. 1.
++:++ Horizontal projection of the geanticlinal axis (schematic representation).
—— Older strikes and coastlines.

In Moa some strikes are N.N.E. to N.E., so these are different
‘from the direction of the row; in Luang the permian strata are

1) These Proceedings XXIII, p. 570,
*) H. A. Brouwer, The horizontal movement of geanticlines and the fractures
near their surface. Journ. of Geology, XXIX, 1921, p. 560—577.

ai

328

intensely folded, with strong differences in strike and dip. If we
construct the geanticlinal axis, as is generally done, with right
angled bends, near Babber and near the southmost island Selaru of
the Tenimber-Islands, so that the geanticlinal axis between these two
islands is below: the surface of the sea, the Tertiary strike in Babber
(N.N.E.) is about normal to the direction of the row.

The connection of Halmahetra with the Pelew Islands.

The soundings between these islands do not go against the
assumption that the prolongation of the Northern Peninsula of
Halmaheira via Morotai towards the Helena-reef has a more or less
east-western direction and bends in a more or less north-eastern
direction towards the Pelew Islands. Even if considerable depths

A.

HALMA HEIR

Ow .

Fig. 2.
.1++ Horizontal projection of the geanticlinal axis (partly hypothetic).

— Older strikes and coast-lines.

should exist where the E-W. prolongation of Halmaheira’s northern
peninsula is supposed to be, these depths may be the result of gaping
fractures, that may exist near the bending-point. The known strikes -
on Morotai are in the direction of the longer axis of the island and
are oblique to the supposed direction of the geanticlinal axis. This
conception renders the resemblance between the outlines of Celebes

329

and Halmaheira more complete. The difference between them consists
chiefly in the eastern part of the northern peninsula of Halmaheira
being covered by the sea.

The row Formosa— Riukiu-lslands.

The prolongation of the Sakishima-group is generally considered
to be linked to North-Formosa '), also by authors whose interpretation
of the known facts differs from the one that will be put forward

Fig. 3.
Explanation of Fig. 2.

lower down. The older strikes in the major part of Formosa are
N.N.E. approximately parallel to the longer axis of the island. In
North Formosa, however, their trend is about E—W, and they are
cut off by the eastern coastline. In the Sakishima-group of the Riukiu-
islands the strikes are irregular and are oblique or normal to the
trend of the row of islands, while in the major part of the Riukiu

1) S. YosHirwARA, Geologie structure of the Riukiu Curve ete. Journ. Coll. of
Science, Tokyo. XVI. Part I, 1901.

330

Islands as far as Kiusjiu the strikes are again about parallel to the
direction of the row. This example seems to be similar to the two
preceding ones, but the areas near Babber, as well as those near
Morotai, from which this analogy might appear, are covered by
the sea. In Formosa the bending of the older strikes is visible
and moreover it can be seen that locally near the bending point of
the horizontal projection of the geanticlinal axis the older strikes are
normal, or approximately so, to this projection, while on either side
they are parallel to it.

The movement at the surface of horizontally moving geanticlines.

In another publication we have already pointed to the difference
in speed and direction of the movements at different depths’). The
points, which were originally on the same vertical line, will in a
later stage form an irregular curve in space. If the rate of movement
has a vertical component, the vertical movement near the surface
will be influenced by the vertical movement at greater depth.

The complicated horizontal and vertical movements, which differ
already at a comparatively short distance, will cause new portions
of the surface to form the crests of the moving geanticline. The
direction of the older strikes with regard to the new geanticlinal
axis in a subsequent phase of tlle movement, will depend upon the
rate of movement at greater depth and that near the surface and
upon the rate of erosion.

If the forees, which cause the movement of a geanticline, of
which the highest parts rise above the sea-level as rows of islands,
are deep-seated, the vertical movements will cause the uplift or
subsidence of the islands, while the rate of horizontal movement
at greater depth may differ considerably from the rate near the
surface. We distinguish two extreme types of movement: 1° The
horizontal movement near the surface is equal to zero. 2° The horizontal
movement near the surface is similar to the movement at greater
depth. In general neither of the extreme types will occur. In the
first case no horizontal fracture-movements will take place at the
surface, and straits generally correspond with a depression, islands
with a culmination of the geanticlinal axis in a given stage of the
movement.

In the second case the islands as such move ina horizontal direc-

!) H. A. Brouwer, The horizontal movement etc. loc. cit.
Id. The major tectonic features of the Dutch East Indies. Journ. Wash. Acad.
of Sciences, 1922, p. 172—185.

331

tion, and straits may originate near the fractures without a subsidence
of the geanticline along the axis. The movements near the surface
are not equal to those at greater depth. But we suppose an extreme
case, in which, considering broadly, the portions near the surface
move at the same rate as those at greater depth.

The vertical movement and the effect of erosion.

Considering that during the movement erosion will continuously be
at work in the portions above the sealevel, it will generally be possible
to compare in the terminal phase the direction of the geanticlinal
axis with the direction of the exposed older strikes. In case of a
brief and not very intensive erosion, the tectonic details of a more
plastic deformation at greater depths, are still invisible. The intensity
of erosion decreases if, as in many rows of islands, the deform-
ation of the geanticline takes place near the surface of the sea,
and it is especially, when the vertical component of the rate of
movement is great, that the tectonic details, which have been formed
by a more plastic deformation at greater depth will soon be visible.

Rectilinear old strikes and curved geanticlinal axis with a bending-
point in the last phase of movement under consideration.
The two extreme cases, mentioned above are:

1. No horizontal movement at the surface.

In the case represented by fig. + the old strikes cut the geanti-
clinal axes of the terminal phase on either side of the bending-point
of A’B’ at an angle of about 45°, while nearer to A’ and B’ the
older strike will gradually coincide with the new geanticlinal axis.
If we assume that in the portions AC and DB, the movement has

D

Er cS Tr a area a fad pe ro gga a Ly

meenen Older strike.

A C B = horizontal projection of the geanticlinal axis in the initial
stage of the movement under consideration.

A! C! D! B!= Ibid. in the last phase of the movement under
consideration.

332

taken place without velocity-differences and normal to the geanticlinal
axis, gaping fractures will nevertheless be lacking in the portion C’ )’,
and in the case of a row of islands a strait will correspond witha
minimum of the vertical projection of the geanticlinal axis.

2. Horizontal movement at the surface, corresponding with the
movement at greater depth. In the portion C’D’ gaping fractures
will be formed which — in so far as they occur near the surface
of the sea — may be visible as straits between the islands.

In the positions A’C’ and B’D’ the old strikes will not differ
from the direction of the new geanticlinal axis; to what extent they
will do so in the portion C’ D’, will depend on the movements near
the surface. If these movements are non-rotational, differences up
to 45° will oceur; with rotation of the portions of the fractured
surface the differences may be approximately zero.

Curving older strikes with a bending-point, and curving geanticlinal
axis with displaced bending-point in the final stage.

One of the numerous variations of this more general case is
represented in Fig. 5.

„ennen = Older strike.

ACDB and A’C’ D’ B’ = horizontal projection of the
geanticlinal axis, resp. in the initial-, and the terminal stage
of the period under consideration.

1. No horizontal movement at the surface. In the final stage the
old strikes are nearly all oblique to the geanticlinal axis, near the
bending-point even approximately normal to it. Straits will correspond
with depressions of the geanticlinal axis. If the geological structure
changes chiefly in the direction vertical to the old strike, islands of
highly different structure will in some places be located side by side. |

2. Horizontal movement at the surface corresponding with that at
greater depth. When, in the terminal stage of the considered period
of movement, the points A, B, C and D have reached respectively

333

A’, B’, C’ and D’, gaping fractures will appear all along the line
A’ C’ D’ B’, which may have helped to form straits. If during their
displacement the parts near the surface had at the same time
rotating movements, the angles between the old strikes and the
geanticlinal axis may approach zero in the final stage.

Explanation of the abnormal strikes near the bending-points.

The abnormal strike of the island of Babber (fig. 1) may be
accounted for by assuming that the deformation of the geanticline
at greater depth has been attended with similar horizontal movements
near the surface, so that e.g. the geanticlinal portion near the surface
of the Tenimber Islands may originally have been situated N.N.E.
of Babber, while these parts have since been displaced considerably
relative to each other in a horizontal direction.

When assuming that no horizontal movement has taken place
near the surface, the abnormal strike in Babber may also have
originated from the great velocity-differences in a horizontal direction
at greater depth, with this difference that the submarine geanticlinal
part between Babber and the Tenimber-Islands is not disrupted
near the surface. If the bending-point is the horizontal projection of
a point that gives a minimum in the vertical projection, it may be
that near it a large part of the geanticlinal axis is below the sea.
In that case data will be lacking for a comparison of the present
morphology with the older tectonic structure of the parts on either
side of the bending-point.

Likewise the connection of Halmaheira with the Pelew-Islands is
covered by the sea in a considerably area on either side of the
bending-point, but in Morotai, where the older strike is oblique to
the geanticlinal axis, the geanticline still emerges from the sea,
while here the resemblance of the coastline to that of the neigh-
bouring part of Halmaheira points to horizontal movements of the
islands as such. In the row Formosa-Riukiu Islands (Fig. 3), unlike
in the preceding instances, the bend of the older strikes is not
covered by the sea, which facilitates a more correct explanation of
the phenomenon. The dips in the older formations of the Taiwan-
mountains in Formosa point to WNW. movements, those in North-
Formosa to southward movements, those in the major part of the
Riukiu-Islands to S—E movements. It is evident therefore, that
already during the older phases of the orogenetic process, there was
a tendency to form a bending-point between Formosa and the Riukiu-
Islands. Similar movements during the youngest phase of the mountain-
building process gave origin to numerous fractures, e.g. those which

334

cut off the K- W strikes of North-Formosa at a right angle and

separate the Sakishima Islands from each other and from Formosae

According to our conception of the differences in character and
rate of movement at different depths, the absence of islands between
Formosa and the Sakishima Islands may be looked upon as resulting
from the formation -of gaping fractures, in connection with the
velocity-differences in a horizontal direction at the surface near the
bending-point, and from a minimum elevation of the geanticline near
the bending-point of the horizontal projection of the axis. The ab-
normal strikes of the Sakishima-Islands find an explanation in the
assumption of movements, such as have been referred to above in
the discussion of a geanticlanal movement with curving older strikes
and with a displaced bending-point in the final stage (Fig. 5). The
movement can be described only in broad outlines, the details can-
not be derived from the visible facts. Thus the strikes on the Saki-
shima-Islands have no constant direction, and differences occur between
the strikes of the older and those of the more recent deposits. Near
the bending-point, however, irregular movements can be expected,
while at the same time the rate of vertical movement, and conse-
quently the rate of erosion must in a high degree have influenced
the present-day tectonic structure.

The abnormal strikes of the Sakishima-Islands have been explained
differently by von RrcarHoreN '), who speaks of transverse subsidence
causing an abnormal dip of the strata in connection with his ex-
planation of the origin of the mountain ares of Eastern Asia by
tensional and not by compressional stress. In contradistinction to
this interpretation by vertical movements, we have compared the
features with those of other belts of islands and find an explanation
of the abnormal strikes near the bending-points of the geanticlinal
axis in considerable horizontal movements, which have already been
discussed by us for various geanticlines in connection with other
features.

1) F. von RicHtHoreNn, Geomorphologische Studien aus Ost-Asien. III. Sitz.
Ber. Akad. d. Wiss. Berlin. Phys.-math. klasse. 1902, p. 944 et sec.

Chemistry. — “Cyclic Derwatives of Mannitol’. By Prof. P. van
RompureuH and J. H. N. van DER Bora.

(Communicated at the meeting of October 28, 1922).

Many years ago the researches on the decomposition of the for-
mates of polyhydric alcohols, and also those on the 1.3.5. hexa-
triene, induced one of us (v. R.) in collaboration with Mr. Van MAANEN,
to study the action of formic acid on mannitol.’)

After they had succeeded in preparing the hexaformate of mannitol
it appeared against expectation that on being heated this substance
yielded no hexatriene or only traces of it; on the other hand it
yielded a product of the formula C,H,O, though in small quantities.
This product, which boiled at 107 —109°, had already been obtained
by Favconnirr’), together with isomannide, on heating mannitol with
formic acid.

Also the tetraformate of mannitane and the diformate of iso-
mannide were obtained by heating mannitol and formic acid, both
in pure state. FAUcoNNIER®) found already, that by heating the
diformate of isomannide only carbon oxide was evolved, with
formation of isomannide; when on the other hand the former was
heated, carbonic acid gas was formed, and again the oxide C,H,O
was obtained.

The following constants were found for this latter product, which
is very strongly levo-rotatory. Bp. 107°, di’ —0,9226, np, = 1,3567.
With bromine it gives a liquid dibromide, C,H,Br,O, dj” == 0,8622,
Bp. 15 mm. 118°.5. A tetrabromide could not be obtained.

Reduction with hydrogen, according to SABATIER and SENDERENS,
gave with C,H,O, both at 110° and at 180° a product of the
formula C,H,,0, which did not boil constantly under ordinary pressure
but at 16° at 23 mm. Hence only 1 mol. of hydrogen had been absorbed.

In virtue of the decomposition of the di-formate of isomannide, in
which only carbon oxide is formed, (so that it may be assumed not to

1) Van MAANEN, Diss. Utrecht, 1909.
2) C. r. 100, 914 (1885).
5) Bull. Soc. Chim. N.S. 41, 125 (1884).

336

contain two vicinal OH-groups) van RoMBuren and van MAANEN

OH
. |e a reaped
proposed among others the formula CH,.CH.CH.CH.CH. CH, for
| O | |
OH

nA

O— IT |

isomannide, and CH, VCH. CH’: OH. tia CH,OH
ou OH

for mannitane, the formate of which gave only carbon dioxide.

The compound C,H,O might therefore be represented by the formula
CH,.CH:CH.CH. CH: CH,, hence it would be a-vinyldihydrofurane.
beeen) |

In 1917 Winpavs and Tomicu') too studied the compound C,H,0,
and could obtain by its reduction with hydrogen under the influence
of palladium, an addition of two mol. of hydrogen, so that C,H,,O
was formed, which substance according to them should be identical
with a d-hexylene oxide described by Lipp’), in which not a 5-ring,
but a 6-ring occurs: CH,.CH,.CH,.CH,.CH—CH,, so that the

| 0 |
original oxide would have the formula CH : CH . CH: CH.CH. CH,,.
Ee folhates tM

They concluded to the identity of the two saturated oxides by
the equality of the boiling-point, both of the oxides and of the di-
bromides derived from them. Winpaus rejects the possibility of the
oxide being a furane-derivative, because then no asymmetric formula
would be possible. This argument is, however, not valid with regard
to the formula drawn up above.

It has appeared from investigations on the action of ozone on
the oxide C,H,O, undertaken by Mr. Bruins in the Utrecht Labor-
atory after the publishing of Winpavs and TomicH’s paper, that
in this reaction only carbonic acid, formaldehyde, and formic acid
could be found, but no products in which a CH,-group occurs,
which pleads against Wiunpbaus’s formula. This, however, did not
give a rigorous proof for the «-vinyldihydrofurane-formula. To
obtain perfect certainty, we have followed another course.

First of all by reduction of C,H,O with hydrogen of a pressure
of two atmospheres in the presence of palladiumsol the saturated

1) Göttinger Nachrichte Math. Phys. Kl. 1917, S. 462.
4) B. 18, 3275 (1885).

337

oxide C,H,,O was prepared. We used for this purpose an apparatus
as indicated by Skrra*), in which the process of the reaction can
be easily followed. During the fractionation the substance poly merizes
partially, so that a perfectly pure product only can be obtained
at the expense of considerable loss.

In spite of careful purification the possibility exists therefore that
a small quantity of unsaturated product is left behind.

The substance was optically inactive, and showed the following
constants :

bp. 103°—106° dij 0.8693 n, 1.42797
(analysis: found C 71.8 H12,3; cale. C 72,0 H 12,0).

In the way indicated by Lipp loc. cit. we have further prepared
the d-hexylene oxide, with the following constants:

bps 106°—106°.2, d!° 0.8617, n, 1.41887.

Since on reduction a-vinyldihydrofurane must yield y-hexylene oxide,
we have also prepared this oxide according to WouLcrmurH’), who
however, only gives its boiling-point, viz. 106°—108° at 770 mm.

The following constants were found: Bp,,, 106°.5—107°, d'® 0.8609,
Dp 1.41685.

The corresponding bromides were obtained by treatment of these
oxides with the 8-10-fold volume of hydrobromic acid (48 °/,) in a
sealed tube for 1 to 2 hours at 100°. The 1-5-dibromo hexane boiled
at 15 mm. at 105°—108° (analysis found Br. 65.3°/, calc. 65.5), the
1-4-dibromo hexane at 106°—108° at 15 mm. (Br. found 65.4). The
boiling-point of the di-bromide obtained from the reduced oxide C,H,,O
was 106°—110° at 14 mm. (Br. found 65.6). It is evident that from
the equation of the physical constants, both of the oxides and of
their di-bromides, no conclusion can be drawn about the structure
of the reduced oxide C,H,,O, unless there are large quantities of
the substances at our disposal. It was, therefore, necessary to try
to obtain crystallized compounds. An attempt to prepare crystallized
benzoates of the glycols corrésponding with the dibromides did not
meet with success. The action of piperidine on the di-bromides, on
the other hand, in which quaternary ammonium bromides were formed,
had a favourable result.

In analogy with von Braun’), who made act 1-5-dibromo pentane

\) B. 45, 3595 (1912).
2) C.r. 159, 80 (1914).
5) B. 89, 4347 (1906).

338

on piperidine in excess, we prepared, from the 1-5-dibromide, the
a-methylpentamethylene piperidinium bromide:

CH,—CH CH,—CH,

i‘ pee Nen, fa ost ib
NOOR lt NÓRESE A

Br

CH

CH,

By recrystallisation from alcohol-ether it is obtained as a white
crystalline substance, melting above 290° (Br found 32.63, cale. 32.5).

In an analogous way the 1-4-dibromide yielded the a-aethyltetra-
methylene piperidinium bromide:

CH, CHN HCH “i
CH,—CH” | \CH,—CH,~
Br

C,H,

This substance melted at 270° corr. (Br 32.58 found, 32.5 calc.).

The dibromide obtained from the reduced oxide, C,H,,0, treated
in the same way, yielded a substance melting at 269° (corr.). (HI).
A mixture of this substance and the preceding one melted sharply
at 269° corr.

Hence the 1-d-hexane dibromide and the dibromo derivative of
the reduced oxide are identical.

Moreover we prepared double salts with platini chloride which
likewise present the same analogy in their melting-points and in
those of their mixtures.

From (I) (C,,H,,NBr), PtCl, Pt. found 23.4
M.P. 247° corr.

From II MP. 260° _,, dah orn nn
Brom (lls MP5 2599 11,8 MUM Sak
Mixed melting-point I and IT 246° corr.

sa 5 Il and III 260°

”

Here again appears the analogy between the compound obtained
from the 1-4-oxide and that which was prepared from the reduced
oxide, C,H,,O. Consequently this reduced oxide may really be
regarded as a-ethyltetrahydrofurane and the unsaturated oxide C,H,O
of FAUCONNIER as a-vinyldihydrofurane :

309
on — Ci

| |
CH, CH—CH = CH,.
Nig ~

The place of the double bonds in this compound is now exactly
known. The substance being optically active, an asymmetric carbon
atom must be present in it; a formula, e.g. as the following:

O
CH,—CH,—C CH
| I
WAELE
would not satisfy, as has also been remarked by Winpaus.

As a-vinyldihydrofurane is formed from mannitane tetra for-
mate, it is now possible to draw up a structure formula for the
anhydrides of mannitol, viz. mannitane and isomannide.

We then arrive at the following scheme for mannitane:

OH
| 0 Rents)
CH, —CH— CH—CH—CH—CH, OH.
Mean el
OH OH
In connection with the spatial formula of mannitol:

OH OH

A CECE Or
a ot
We see that as soon as the oxide-ring is formed between the C-
atoms 1 and 4, the OH-groups at 2 and 3 will be at the same
side. Besides the molecule contains two OH-groups situated beside
each other at 5 and 6 (in perfect accordance with the pyrogenic
decomposition of the tetra-formate, in which formic acid and carbon
dioxide are split off from OH-groups placed: beside each other), so
that here a possibility must be for the formation of a di-acetone com-
pound. In fact this compound was obtained as a colourless substance
crystallizing in glossy leaflets, melting-point 155° (analysis C 58.83,
H 8.38; calculated C 59.0 H 8.2).
The conductivity, of boric acid will also be increased greatly by
mannitane. *)

1) Bogsexen, Rec. 40, 553 (1921).

340

Through the formation of a second oxide ring, we then arrive at
the following formula for the second anhydride

OH
EER NE |
CH,— CH—CH—CH—CH—CH, .
| LE ied
OH

The places of the OH-groups here are at 2.5; hence no acetone
derivative can be formed, nor will the conductivity of boric acid
be raised. On treatment with acetone and 1°/, hydrochloric acid
the isomannide was actually recovered. The results of the measure-
ments of the conductivity are recorded in the following table:

Capacity of the vessel 0.4106.
Conductivity of the boric acid 0.5 mol. Litre 30> 10-® = Kz.

In water In boric acid sol.
K; — (Ky + Ks).
A. | W. | K2X10-6| A. | W. xu
Mannitol 500 | 5660 12.5 | 500 | 1037) 396 | 294
Mannitane 500 | 3240 126.8 | 500 | 440) 933 116
Isomannide 480 |11000 34.4 4.4

The concentrations were 0,2 mol./Litre.

After deduction of the conduetivity for water 3 >< 10-°®, we
find therefore that iso-mannide in a very small, quite negligible
degree increases the conductivity, whereas this increase for man-
nitane exceeds that of mannitol more than 2*/, times.

Of the forgoing we may conclude that the structure of the un-
saturated oxide C,H,O is proved, likewise that of mannitane. The
given formula for isomannide seems to be exceedingly probable.

Utrecht, Org. Chem. Labor. of the University.

Chemistry. — ‘“Jn-, mono- and divariant equilibria’, XXII. By
Prof. F. A. H. SCHREINEMAKERS.

(Communicated at the meeting of October 28, 1922).

Equilibria of n components in n +1 phases, when the quantity of
one of the components approaches to zero. The influence
of a new substance on an invariant equilibrium.
For the equilibrium:
EE ele Bs ake in tt MED hast tases thy zat pny ley

of m components in n-+ 1 phases, as we have seen furtherly, are
valid the equations:

RENSE : . ° . ° (2)
wherein

and further:

ÒZ, ÒZ, OZn44 r
y= Zen == En 1G
Gat ane Ön |
(3
0Z, OZ, tn) py OZn44 |
dy, _ _òy, hete OYn44 Vay !
to which still must be added the corresponding equations for the
variables z,z,...U, U,... etc. As it is apparent from the number

of equations (viz. n* + ”) and the number of variables (viz. n° + n +1),
this equilibrium is monovariant, consequently, in the P,7-diagram
we represent it by a curve, which we call £.

When in this equilibrium £ all phases with constant composition
contain together only n—1 of the m components, so that in these
phases one of the components f.i. X is missing, then, in the phases
with variable composition the quantity of this component X may
approach to Zero.

Then the equilibrium / passes into an equilibrium, that we call
E(x=0) which consists of n—1 components in n-+ 1 phases and
that, consequently is invariant; in the P,7-diagram it is represented
therefore, by a point which we shall call 7(v=0). This point is

the invariant terminating — or beginning — point of curve Z£.
22
Proceedings Royal Acad. Amsterdam. Vol. XXV.

342

As we do approach the quantity of the component X to zero,
we put again:

Z,=2', + RTe, log z, 4,== 2, 4+- RTe, loge, . (4)
etc. In similar way as we have done formerly, now we find:
OZ
Aya? — VAPH Bet wd (Fo) bo ——dK . (5)
ee
i—1,2,.../(n +1)
*,— Us 7, Uy Mg Tjee es Eni nitie: … (6)
0z' 0Z' 0Z',
Zg EE EK Oe Ne
dy, d Oy, OYn44 ;

To these equations (7) must be added the corresponding equations
for the variables z,z,... u, u,. The sign d indicates that there
must be differentiated with respect to all variables.

Now we add to one another the n+1 equations (5) after having
multiplied the first with A,, the second with À,, ete. Then we obtain:

= (MH).dT — J (AV). dP 4+ RT > (da) + & (Ay) dKy + | (8)

+ 2 (Az). dK, 44... = SS (4). dK
Now we put:
= (4)=0 of A, +4, +....4 Ana = 0
= (Aa) ==0) Ok A a A ee ee end con = 0 (9)
= (Ay) = 0 of Ayr Age Heee Hr Anti Ya = 0

ete. but. not > (AH) and S (AV).
Then we have n equations, so that that the m ratio’s between
a,4,...- Anti are defined. The reaction:

AF, HAP, +e f+ An Pa = 0 Sal le AO)

which may occur in the monovariant equilibrium /, when the
quantity of the component X is infinetely small, is, therefore, also
defined. We shall call this equilibrium, which differs extremely
little from H(« =o) the equilibrium /# (Lim «= o) or shortly the
equilibrium (wv). With the aid of (9) now (8) passes into:

(5) (1) (1)
Ole ts (AV). ae /

wherein A, A, are defined by (9).

Consequently the direction of the tangent to curve £ in its
invariant point of beginning or terminating {(& = 0) is defined by
(11). The relation (7) (XIX) is, therefore, true also when the quan-
tity of one of the components approaches to zero.

343

Now we put:
= (A) =O conseq. 4, + 4... - s+ Aa 0
= (Ay) = 0 ” Ait iy Fo Pale ere + Anti Fite 0

By (Az) = 0 we Aye Aln tw. + Apes ents = 0 (12)

= (À vy = 0 i, À, Vi +HA,V, +... + Anti Vri
but not = (ax) and Z (AH). The n relations between A, A,... Angi
are then defined again. Those relations now define the isovolumetrical
reaction in the invariant equilibrium # (rz = 0).
Now it follows from (8)

/
/

RT > (Az)y
> ()H)y
wherein the index V indicates that 2, À,... 2,4: must be calculated

from (12) consequently from the isovolumetrical reaction.
Also we may put:
= (4) =.0 conseg. A, ay ee it Angas 0
= (Ay) =.0 ” AY, a AYs rie ES “fr Ani Int = 0
(Ae yaa0 Uig Are Rye, ie... eA ene =O . (14)

(AD =— (13)

SA ee We de Er a HLO
but not > (A) and Z(AV). The relations between A, a,... AH
are, therefore, defined and by this also the isentropical reaction,
which may occur in the invariant equilibrium E(&=0). Now it
follows from (8) :

RLS (do)

(dP). = SAN (15)

wherein the index // indicates that 4, 2,....4,41 must be calculated
from the isentropical reaction, therefore from (14).

From (114), (13) and (15) follows the relation

(AV). E(AH)y. ZE (Ae) + SUA). (AV). ZE (Ae)y =O (16)

While the direction of the tangent to curve Zin the point 2 (a= 0)
follows from (11), formula (13) is determining whether this curve is
going from this point towards heigher or towards lower temperatures
and (15) is determining whether it is going from this point to higher
or lower pressures.

We may express all this also in the following way. When we
add a new substance to an invariant equilibrium, then it becomes
monovariant, the partition of this substance between the different

22%

344
phases is defined by (6). By (13) is defined whether the temperature
is rising or falling; by, (45) is defined whether the pressure is in-
creasing or decreasing. |
We write the isovolumetrical reaction:
ES + ee + Ag+1 FH nn LEN

wherein all reaction-coefficients have been taken positive. Now we

A

have:
(hia Vy == A, Hg +. AH a i ee 4,0, —41,H,—....
= (As) 49% + yee) Bee ere) A, —i, a, —...

Now we assume that we have written reaction (17) in such a
way that it proceeds on addition of heat from the left to the right;
consequently (AH); is positive. In order to determine the sign of
= (ax)y we have to dissolve A, a,... from (12) and we must know
the partition of the new substance between the different phases ;
this may be found from (6).

In some cases the sign of > (Av)y is known, however, at once
without this calculation. When f.i. the new substance occurs only
in one or more of the phases, which arise in (17) on addition of
heat, consequently, in: B, Poa 5... then is 7, = Osj 0 nr dj 0
and, therefore 2 (2v)y is positive. It follows then from (13) that
(JT); is negative.

When, however, the new substance occurs only in one or more
of the phases, which arise in (17) on withdrawing heat, then
Ngati... are zero, so that &(dx)p is negative. Then it follows
from (13) that (d7’)z is positive.

When, however, the new substance occurs in both groups of
phases, then only a calculation more in detail may decide on the
sign of Z(Àr)y and consequently also on the sign of (d7’),.

Now we represent the isentropical reaction also by

RSM, A oP ee ok Doct wna cial ie a

However we have to take ‘in mind, that A, 4,... in this case,
must not be dissolved from (12) but from (14). Consequently in (18)
A,a,... shall have not only other values than in (17), but one or
more of them may have also other signs, so that they must be
transferred from the one part to the other. Now we have:

= (AV) a = 1g Vq + Agm Vom +....—4,V, — a, Va —....
= (A 2) =hg2_ + hg Cg H.A ge, ee.

Now we assume that reaction (18) is written in such a way that
it is proceeding from left to right with increase of volume. Conse-
quently > (2V)gy is positive. When the new substance occurs only

345

in one or more of the phases which arise at increase of volume, then
X(4x)y is positive and, in accordance with (15) therefore also (dP),.

When, however, the new substance occurs only in one or more
of the phases which arise on decrease of volume, then 2 (Av)j, is nega-
tive and therefore, also (dP), is negative.

Hence we may deduce the following rules:

When we add a new substance to an invariant equilibrium
(a= 0) then a monovariant equilibrium £ occurs, which we
represent in a P,7-diagram by a curve ZE; when the new substance
occurs only in one or more of the phases, which arise at the iso-
volumetrical reaction on addition (withdrawal) of heat, then the
temperature is lowered (raised); consequently curve £ proceeds
starting from its invariant beginning-point towards higher (lower)
pressures.

In some cases we may also deduce something on the direction of
curve ZE in its invariant beginning-point in the following way. We
assume that the new substance which is added to the invariant
equilibrium :

BG om et tot ne ye fA ete tel ray | ed
occurs only in the phases F1... Fo: and, therefore, not in
ff, F,...H,. This is surely the case when F,...F, are phases of
constant composition. When we take away from the equilibrium #
the phases Fo Fia than we keep an plurivariant equilibrium
F,...F,; this is represented in the P,7-diagram by a plurivariant
region. As curve / must be situated in this region, hence follows
the said-above. In the special case that the new substance occurs
in one of the phases only, curve / coincides, therefore, with one
of the monovariant equilibria of the equilibrium («= 0).

Before applying those considerations to some cases, firstly I will
draw the attention to some points, which have been already discussed
before. When we know of the isovolumetrical and isentropical
reaction the ratio of the coéfficients 2, 2,.... and also in which
direction those reactions proceed on addition of heat or on increase
of volume, then we shall say that those reactions are known quan-
titatively. When we know, however, only the signs of 4,A,....
and also in which direction the reactions are proceeding on addition
of heat or on increase of volume, then we shall say that the
reactions are known qualitatively. Then we only know which phases
are at the one side and which at the other side of tbe reaction-sign.

346

When we know of each phase of the invariant equilibrium («= 0)
the entropy, the volume and the composition, then with the aid
of (12) and (14) we may define the isovolumetrical and isentropical
reaction quantitatively. Consequently we are able to draw exactly
the direction of the different monovariant curves in the P, 7-diagram,
we call it a quantitative P,7-diagram.

When we only now both reactions qualitatively, then we can
define only whether the monovariant curves proceed, starting from
the invariant point towards higher or, lower temperatures and towards
higher or lower pressures; but then their situation with respect to
one another is still undefined; this we call a qualitative P, 7-diagram.

We take for example the reactions:

PEP SPE FA AH>0 AV=0

Fit ee Bee Fee AH=0 AV>0
of a ternary invariant equilibrium. The first is, according to the
supposition AV —0, the isovolumetrical reaction and it takes place,
according to the supposition 4 H >>0 from left to right on addition
of heat. It appears from A H—O and AV > 0 that the second
one is the isentropical reaction and that the volume increases from
lef to right.

In accordance to our former considerations, now we have:

[TEMS rs er tE AH>0 AV=0
CATGAY (a KOG,

: 19
towards lower 7’| towards higher 7’ OR
Further we have:
Ee ak Ts AH=0 AV>0
(EME) | BARRON
(20)

towards higher P | towards lower P

In accordance to our previous notation, herein is:

(F,)=F,+F,4F, +6, (F)=F, HF HF, + Fo etc.

Now we know qualitatively the P,7-diagram; we know viz. that
from the invariant point curve (/) is going towards higher 7’ and
lower P; curve (F,) goes towards higher 7’ and at the same time
towards higher P, etc.

Inversely we can also find from a qualitative P,7-diagram the
qualitative isovolumetrical and isentropical reaction. When weknow
fi. that the curves (#,) and (/’,) go towards higher temperatures
and (F,) (F,) and (F,) towards lower temperatures, then we have
to construe (19) in the inverse direction viz. from the bottom to the
top, in order to find the isovolumetrical reaction.

347

When we know that (F,) and (F,) go towards higher tempera-
tures, and (#) (F,) and (F) towards lower pressures, then we find
at once, by construing (20) in the inverse direction the isentropical
reaction. i

Firstly we shall apply those considerations to a simple case viz.
to the addition of a new substance to the invariant unary equili-
brium H(a#=0)=>F+4 24+ G. The P,T-diagram may belong to
two types, viz. when the volume decreases, on melting of the solid
substance, then fig 1 is true; when the volume increases, then fig 2
is valid. The regions in which occur the phases #, L and G are
indicated by the same letters, but in a circle; the curves are repre-
sented by (#), (L) and (G); in accordance with our notation is
(F)= L + G, ete.

When we add to H(2#=0O) a new substance, which occurs only
in the liquid, then the monovariant equilibrium H— #4 L+G
arises; when we take away from it ZL, then we keep the equilibrium
Ft G=(L).

Curve FE coincides therefore in figs 1 and 2 with curve (L) of
the invariant unary equilibrium Z(w — 0).

Fig. 1. Fig. 2.

When we add a volatile substance, then we must take away
from the monovariant equilibrium the phases L and G, so that we
keep F only. Therefore, curve # must be situated in the region #,
as f.i. va, 26 and ic in the figs 1 and 2.

When we add a substance, which is not volatile, which gives,
however, mixed-crystals with #, then we must take away from the
equilibrium EZ the phases # and JZ, so that the vapour G only
remains. Therefore, curve / must be situated in the region G.

We may obtain also these results by using the qualitative iso-
volumetrical and isentropical reaction, which we can deduce easily

348

from the figs 1 and 2. It follows trom the position of the curves
in fig 1.
towards lower 7'| towards higher 7’

5 Js’ i Vad EN
(L) (G) | 5)
FILLG AH>0 AV=0
and
towards higher P | towards lower P
| - Nie areal (EON
(F) (G) (L)
DG AH=0 AV>O0

so that both reactions are known qualitatively.

Now we add to this equilibrium Hi(2 = 0)= F+ L+ G a sub-
stance, which occurs in the liquid only. As in the isovolumetrical
reaction (21) ZL is placed at the right side of the reaction-sign,
consequently, in accordance with our rules, 7’ is lowered; as in the
isentropical reaction (22) L is placed at the left side of the reaction-
sign, the pressure is also lowered, therefore.

Consequently in fig. 1 curve ZE proceeds starting from point 7
towards lower 7’ and P; this is in accordance with the deduced
above, that curve MZ coincides with curve (L) in this case.

When we add a volatile substance, than it occurs in L and G.
As both those phases are placed in (21) at the right side of the
reaction-sign, consequently 7’ is lowered. As L and G are placed
in (22) at different sides of the reaction-sign, the pressure may be
as well increased as decreased. Therefore, curve Z may be represented
by ta or 76 in fig. 1. Which of these curves may occur in a
definite case, cannot be deduced in this, manner; we are able todo
this, as we shall see further, with the aid of the quantitative reactions.

In order to deduce the qualitative reactions from fig. 2, we write:

towards lower 7'| towards higher 7’

En el ee eae
(L) | (F) (6)
RIGE AH >0 AV=0
and
towards higher P! towards lower P (24)
(F) (6) (L)
beng AH=0 AV>o.

When we aid a new substance, which occurs in Z and G, then
we find that curve / may be represented in fig. 2 by za, 76 or te.
It is apparent from the previous that by simple considerations
we may deduce already something about the direction of curve £
from the qualitative P,7-diagram of an invariant equilibrium 4(¢= 0).

349

When, however, we know the quantitative reactions, then we are
able to deduce not only the quantitative P,7-diagram for the equili-
brium E(e=0) but also (dT): and (dP), for the equilibrium &
and consequently we can define exactly the direction of curve E.
When we represent entropy and volume of / by H and J, of
L by H, and V, and of G by A, and V,, and when we assume
that the substance melts on decrease of volume, then we have:

BE and) V, MEM ro rde)
We write the isovolumetrical reaction :
ANG OEM dS PNA eres, (26)

As, in accordance with (12):
Peep go “andl Va Va BR VSS ie O20K27)
it follows:
Vi.—V V—V.

7) ———— : A Saas : . e ° 28
i Er and A, RED (28)
so that 2, and 2, are both negative. Instead of (26) we now write:
PE LIE HGM ee |. (28)

wherein
ed 30
EV demen

and

Say WEL, HIER MM, aay

Now we may prove that =(AH)y is generally positive, so that,
on addition of heat the isovolumetrical reaction (29) proceeds from
left to right.

In a similar way we find for the isentropical reaction:

Belen Ce a. Ge et MS
and
= (AV a Ft ees STEM ie
wherein
EH EE 2
u, ee. en u, ora EEN ° ‘ “ ie ( )

so that u, and pw, are both positive.

As =(AV)pis positive, reaction (32) proceeds from left to right
with increase of volume.

With the aid of reactions (29) and (32), as is discussed in previous
communications we now can deduce the P,7-diagram quantitatively;
then we find ‘fig. 1.

Now we add a new substance which occurs in the liquid only.

350

When we call its concentration wv, then we have:
5 (Av)p ='4,a, and 2 (We) == ut,

so that, in accordance with (13) and (15):

ay yet

— RT p,«,
> (aH)y Tr

IT): = ANG Ove he = Sn eh
(AT) Ek Fran (34)

Consequently in fig. 1 curve E proceeds, starting from point «
towards lower P and 7.

It follows from (933):
(5) tt Bob. dln EH

Ee
dT x À ee u, Vm he Var: 4 rt} ( )

Hence it appears that in fig. 1 curve / coincides with curve (Z).
Also we may find (34) at once with the aid of (9) and (11). We
put viz.:

EDA A, =0 and Sax) =A2, = 0
so that 2 = 0 and A, — —1. Hence it follows:
S(\H)=H—H, and T(AV)=V—Y,,

2
consequently for (11) the same value as in (34). |

When the new substance occurs in liquid and vapour with the
concentrations «, and w, then we have:

in accordance with (29): = (av)y =de + 24,

and in accordance with (32): = («)7 = — p27, + 4,2,

so that (d7’), and (dP), are known again. We see that (d7’), is
negative, but that (dP)x may be as well positive as negative. Curve

FE, therefore, may be situated in fig. 1 as za or ib.
When we put:

u, HH
== =o: rns ee
us li :
then is
Sade ay (oF ENE HE (37)

wherein, in accordance to (35), A > 1.
Now we find:

for — > K is (dP), >0; consequently curve EH goes, starting
a,
from point 2 towards higher pressures ;
for a < K is (dP);< 0; consequently curve ZE goes, starting
1

from point 2 towards lower pressures.

351

When fi. is K—5, then the concentration of the new substance
in the vapour must be at least five times as large as in the liquid,
that curve Z is proceeding towards higher pressures, starting from ¢.

In order to define the direction of curve / we define the values
of 2, and A, according (9) from:

Ed, SO and Aj Ez = 6
(11) then passes into:
es ie, (EE) (ESH)

dT Jz «,(V,—V) —e, (V,—V)
by which the direction of curve / is defined. This direction, as
follows from (37), is dependent on the partition (w‚:w,) of the new
substance between gas and liquid. Also it follows from (37) that
curve E must be situated between the curves (1) and (G).

We now add a new substance which forms mixed-crystals with
F, but which does not occur in the vapour. When we represent
its concentration in F and L by « and z, then it follows from (29)
and (32):

> (As)y Aya, —e and 2 (la)q = 2 — ut,

(38)

consequently :
RT (Ar) RT («#—p,2,)
(dT ),== and (dP), =
= (2H)y = (AV)

It is apparent from (30) and (33) that 2, <1 and uw, >1, but
also that A, differs very little only from 1. It follows from (39):

for —>p, is (dT)z> O and (4P):>0;
vy

(39)

Curve £ is situated then, f.i. like curve zd in fig. 1

for #,>—>A, is (dT):2>0 and (dP), <0;
wy

Curve E is then situated, f.i. like curve je in fig. 1
for Ant vig (ATO .and.(éP):<0;
v,

Curve E then is situated f.i. as curve 7/ in fig. 1.
In order to define the direction of curve /# we take in accordance
with (9):
S)=—144,+2;=0' and J (Ae) 2 HA, =0.
With the values of 2, and 4, which follow from this we find for (11):
@) hay (EB) ee (Ey)

oh a (40)
at Jay, DD) A

352

so that the direction of curve Z is defined.

Also it is apparent from (39) that EZ must be situated between
the curves (F) and (ZL).

Finally we shall assume that the new substance divides itself over
the three phases, we call its concentration in # L and G aa, and
x,. We now have according to (29) and (32):

= (Ae)p = —a# + Ax, + 4,4, and = (Ao) =er — Ut, + Urs
wherein 2, + 2,—=1 and w,=—1-+4,, so that (dT), and (dP), are
known.

We now put: /
= (Ac) 7 = and VE NAE ee | a

As we are able to satisfy (40), independent on the values of
r and s, by positive values of # zv, and .z,, it follows that curve #
may go in every direction starting from point 2. It may be situated,
therefore, not only in one of the regions F’ and G, but also, like
f.i. curve ig, in the region L. Of course its situation is dependent
on the partition of the new substance between the three phases.

The same considerations as for fig 1 are also valid for fig 2, for
this we have to examine however more in detail the occurrence ot
curve 2¢.

Instead of (25) we have for fig 2:

Bs Hand. WA Wi Se ee AE

As A, is negative now, in accordance with (30) the isovolumetrical
reaction passes into:

PA dl OE Rn EL
wherein:
Vi.— Vi—V
eS yay and: 4, i= VV,
so that

= (4H) = 1,H, — H —2,G4
is generally positive; reaction (43) is proceeding therefore, on addi-
tion of heat from left to right.

When we now aid a new substance, which occurs in liquid and
vapour, then we have: > (Ar)y= Ae —A,v,. In order that (dT),
is positive, 2(Ax)y must be negative, consequently :

Pec ae e,. V,—V
ae or TE toes . … (44)

av

As in general V,—V is some thousand times larger than V,— V
curve zc therefore can, occur only in the very special case that the
concentration of the new substance is some thousand times larger
in the vapour than in the liquid.

0503

We may summarize some of the previous deductions in the
following way.

When we add a new substance to an invariant unary equlibrium
K(«=0)=F+L2+G, then an equilibrium H—=F+L+G
arises that is represented in the ?,7-diagram by a curve F/; this
curve begins in the invariant point z of the equilibrium («= 0).

When the new substance occurs in the liquid only, then curve #
coincides with curve (L)— # + G of the system H(« = 0).

When the new substance is occurring in liquid and vapour then
curve # is situated in the region /’; its direction is defined by the
partition of the new substance between vapour and liquid. A curve,
like zc in fig. 2 may, however, occur only in very special
circumstances.

When the new substance is occurring in liquid and solid phase
(consequently with formation of mixed crystals) then curve U is
situated in the region G'; its direction is defined by the partition of
the new substance between mixed crystals and liquid.

When the new substance occurs in the three phases, then curve
E may be situated in each of the three regions; its direction is
defined by the partition of the new substance between the three

phases.
(To be continued).
Leiden, Lab. of Inorganic Chemistry.

Mathematics. — ° Ueber Determinanten aus Hormenkoeffizienten’’.
By B. L. van DER WAERDEN. (Communicated by Prof. L. E. J.
BROUWER).

(Communicated at the meeting of October 28, 1922).

§ 1. Die Aufgabe.

Vier binäre Bilinearformen (az) (a’x’) bestimmen die Determinante
Lita lie. Ne hee dl
EN
41

(wo 1;, de Koeffizienten der ersten Form sind, usw), welche inva-
riant ist gegenüber unabhängigen linearen Transformationen der
beiden binären Gebiete # und 2’, weil bei diesen Transformationen
auch die Koeffizientenreihen linear transformiert werden.

Sechs lineare Komplexe im dreidimensionalen Raum *Z haben
ebenso eine Invariante

lag hig) laa ise Laa hea
A=| 3

612

Für das Problem: Derartige Invarianten symbolisch darzustellen,
werde ich im Folgenden eine allgemeine Methode angeben und
diese dann auf die genannten zwei Beispiele anwenden.

§ 2. Lemma.

Wenn eine Form f in n n-äüren Veründerlichen (eine n-dre Ver-
dinderliche ist ein Inbegrifi von n homogenen Grössen a, ... py), sich
gegeniiber Permutation dieser Verdinderlichen verhält wie eine alter-
merende Funktion, so enthdlt sie entweder den Klammerfaktor (ay ...),
oder sie verschwindet identisch.

Beweis. Setzt man zwei der Veränderlichen einander gleich, so
verschwindet f identisch, da dann (= — f wird. Wenn man dann
nach dem Gleichsetzen mit Polarenprozessen operiert, so erhält man
immer wieder identisch Null. Also verschwindet das erste Glied der
GORDAN-CaPeLLi-schen Reihenentwicklung der Form fidentisch. Alle
weiteren Glieder aber enthalten entweder den Faktor (ay...), oder
verschwinden. Daraus folgt das Lemma.

30D

Bemerkung. Für den Fall (den ich eben benötige), wo die a, y, .
in f linear auftreten, ist das Lemma elementarer zu beweisen. Es
ist dann nämlich symbolisch

hes Anale 2) Oy) 13%

Vertauscht man #,y,... in allen möglichen Weisen, und addiert

mit +, so kommt

| (ae) (ay)... |

n\ f= A! (b' w) (by)...

pe Ro

oder nach dem Multiplikationssatze der Determinanten

BNA Ax (a0... .) (anes

EN DTE A
fg).

’

§ 3. Die allgemeine Methode.

Es seien gegeben NV Formen derselben Art, mit je N Koeffizien-
ten. Ich setze voraus, dass man alie Invarianten vom 1. Grade in
den Koeffizienten dieser Formen, symbolisch hingeschrieben hat.
Verlangt wird dann, die Determinante A der N* Koeffizienten durch
diese Invarianten auszudrücken. Lösung: Man stelle aus diesen In-
varianten irgendeine alternierende Funktion der Koeftizientenreihen
her. Wenn diese nicht identisch verschwindet, so stellt sie nach
dem Lemma bis auf einen konstanten Faktor die gesuchte Deter-
minante A dar.

In manchen Fallen gelingt das Auffinden einer solchen alternie-
renden Funktion sogleich. Ist dies nicht der Fall, so kann man so
verfahren: Man wähle irgendeine lineare Invariante / des Systems,
und bilde

EELT
unter Vertauschung der Formen in allen möglichen Weisen. Es gibt
wegen der Existenz von A sicher mindestens eine Invariante J, für
welche diese Bildung nicht identisch verschwindet, und die Bildung
stellt dann nach § 2, weil sie alterniert, bis auf einen Konstanten
Faktor die gesuchte Invariante A dar.

§ 4. Erstes Beispiel. Vier Bilinearformen in zwei unabhängigen
bindren. Verdnderlichen.

Die Invarianten der, Formen (le) (1'2'),..., (4x) (dw) gehoren den

356

folgenden Typen an: *)
Bis = (12) (1' 2') = Bar
Fyo34 = (12) (2'3') (34) (41) = Faia = Fage = Feras
Die Invarianten vom 1. Grade in den Koeffizienten der 4 Formen
sind also:
Bie Bsa, B13 Bos, usw.
F1234 ‚ usw.

Nun ist
= + Bie B34 = 0

es bleibt also für A nur die Mögligkeit:
AS Ay tE Fia
= AA SFioza— Foz —F 1304 + F1a23 +- P1342 — F'1430 }.
Zur Bestimmung der Konstanten A geniigt das Zahlenbeispiel
1. 0500

N01

Das gibt
A= — ‚4 4
12
Um nun © + F934 in seiner einfachsten Form darzustellen, ver-
wenden wir die sich aus
(23!) (4'1') = (24°) (31) + (12) (84)
ergebende Identität
F'y934 = — F12a3 + Bie Bos
Diese erlaubt uns, zwei beliebige Fj, aufeinander zu reduzieren
(durch wiederholtes Vertauschen von aufeinanderfolgenden Indizes).
So reduzieren wir die letzten fiinf Glieder der angeschriebenen

Entwicklung für A auf das erste. Es kommt schliesslich

A = — 2F 034 + Bie B34 — Biz Boa + Bra Bos.
Wenn man will, kann man auch schreiben
A = — Frieza + Fogar-

§ 5. Zweites Beispiel. Sechs lineare Komplexe im Quaterndren.

Geschrieben in WeirzensockK—W axEtscn’schen Komplexsymbolen’),
sind alle Invarianten von linearen Komplexen reduzibel auf „Ketten”’,
wie

1) Da die beiden binären Gebiete unabhängig transformiert werden, so bestehen
die Invarianten aus Klammerfaktoren, deren Symbole beide demselben Gebiete
angehören.

2) Siehe R. WerrzeNBöckK, Komplex-Symbolik, Leipzig 1908, WarrscH, Wiener
Berichte Dec. 1889, oder besser den III. Abschnitt der in Kurzem bei Noordhoff
Groningen erscheinenden „Invariantentheorie” von R. WEITZENBOCK.

357

(RIT (2), (21!) == Ch PD elen. neiaiee hh)
[12'34'56'] = (12') (2/3) (34) (4'5) (56') (6'1) = [34'56'12"] =
— [56'12'34'] — [16'54'32'] — etc.

Die Viererkette ist reduzibel'), vermöge *)
[1234] = 4{[12'] [34] — [13'] [24] + [14] [28]} - . (8)
Zwei Sechserketten ‘die auseinander entstehen durch Vertauschen
zweier aufeinanderfolgender Indizes, sind zueinander reduzibel ver-

möge der ldentität ’)

(ep!) (p'q) (qu) + (wg) (VP) (pw!) = — 4 [pq] wy),
zufolge welcher
[12'34"...J 4 [18'24... JAREN 2 2. &

und dual dazu. Aus (3) und (4) folgt noch

[12'8.4'56'] — —[13'24'56"] —4[23'] {[14'][56'] — [15'] [46] + [16"] [45']}
und dual dazu .

[12'34'56"] — —[21'34'56] — 1[12']{[84'][56'] —[85'][46'] + [36'] [45']}

Um nun die Invariante

(5)

lia 113 lia Jaa Lao Ie
Ass
| 612 |
symbolisch darzustellen, bemerken wir, dass
> + [12'] [34'] [56] = 0.
Also bleibt als einzige Möglichkeit
A=A. = +[12'34'56').
Zur Bestimmung von A nehmen wir das Zahlenbeispiel
DiGi a.

Jy z= iO]

und erhalten

also
2
ey REE i, ar! ar eS)
Man könnte nun, so wie im vorigen $, diesen Ausdruck weiter

1) Die Sechserkette ist nicht reduzibel. Vergl. R. WeitrzeNBöck, Jahresber. D.
Math.-Ver. 19 (1910) und Wiener Ber. 122 (1913).
2) R. WeirzeNBöckK, Invariantentheorie Il, 8 5 Gl. (10).
8) Komplex-Symb. p. 8, (26) und (26a); Invariantentheorie HI, § 5 Gl. (4).
23
Proceedings Royal Acad. Amsterdam. Vol. XXV.

358

reduzieren mittels (5); dann aber hatte man 119 Glieder zu berech-
nen, und an jedem Gliede eine bis zehn Reduktionen vorzunehmen.
Man weiss aber im Voraus, dass das Resultat die Form

A = —2 [12/8456'].+- FRA os [DO Horde Re ae)
haben muss. Wenn diese Formel gilt, so muss die duale auch gelten.
Um A zu dualisieren, muss man 1,, durch 1',,, oder durch 1

'
13?

84
ersetzen, usw.: A geht dann über — A. Jede Zweierkette ist zu
sich selbst dual. Also kommt

si eben de FURNA eT ee

Subtrahiert man nun (7) und (8), so fällt die Funktion #’ heraus,
und man erhält A in der Form:
AE 1234567 + [12845670 0. (9)
Wenn man will, kann man fir [1’23’45’6] auch schreiben
[61’ 23’ 45’ |, und das zweite Glied durch wiederholte Anwendung
von (5) auf das erste reduzieren; es kommt schliesslich

A = — 2 [12'34'56'] — 4{[12'] [34] [56] + [28'] [45'] [61]}.
; + § 4121 [35] [46] + eykl}
— $t[14'] 123] [567] + ck} (10)

— & [14] [267] [35'] + ck}

+ [14] [25'] [367]
wo [..][..|[.-] + eykl. bedeutet: die Summe aller Glieder, die aus
dem angeschriebenen Gliede entstehen durch null- bis fünf-malige
123456
934561’ während [..][..|[..]- ck
bedeutet: die Summe aller Glieder, die aus dem angeschriebenen
entstehen durch null- bis zwei-malige Anwendung der Permutation
12 34 56
oa 56 12)

Anwendung der Permutation

Chemistry. — “The dissociation constants of sulphonacetic and
a-sulphonproptonic acids’. By Prof. H. J. Backer. (Communi-
cated by Prof. P. van RoMBURGH).

(Communicated at the meeting of September 30, 1922).

The a-sulphoncarbonic acids are dibasic acids with a strong anda
weak acid function.

Consequently, the free compounds belong to the strong acids,
whilst the acid salts behave as weak acids.

In the table the molecular conductivity of sulphonacetic and
a-sulphonpropionic acid is mentioned.

When the values at an infinite dilution u,‚, on account of the
number of atoms in a molecule *) are taken for the sulphonacetic
acid at 376, and for the sulphonpropionic acid at 373, then the mean
value of the dissociation constant, at the concentrations '/,, and '/,,
Grammolecule per litre, is found to be for the sulphonacetic acid
0.58 and for the sulphonpropionic acid 0.57.

Great accuracy can not be ascribed to these figures, as the uncer-
tainty in the determination of uw, in the case of these strong acids
has a great influence on the size of the constants.

However, the values are not improbable; for WrescurpEr’), who
has argued the validity of Osrwarp's dilution law for sulphonic
acids, has calculated for benzol sulphonic, p-toluolsulphonie and
B-naphtalinesulphonic acids, the constants 0.21, 0.214 and 0.267,
and for the m-sulphonbenzoie acid, related to the above-mentioned
acids, the constant 0.4.

In the solutions of the acid sodium salts of the sulphoncarbonic
acids chiefly the following ionic equilibria exist:

Rite Ae tee INE yO EA ats Rey zet ee hele CER)
BEES Alte gen oe een OE

Besides, molecules of the free acid may be formed:
BEBA ST HA TRE ee eran (KE)

The conductivity of the acid sodium salts is thus caused by the
ons. Na, BA H, A”
1) OsrwaLrp-LurHer, Hand- u. Hilfsbuch 1922, 482.
2) WeescHeiDeR, Monatshefte f. Ch. 23, 340, 341 (1902); 30, 440 (1909).
23*

360

Molecular conductivity at 25° C. in reciprocal Ohms '!).

V(Number of liters p. G. mol.) 16 | oe | 64 128 | 256 | 512 1024
Sulphonacetic acid | |
C‚H40;5S | 348.9 | 357.9 | 366.3 | 373.3 | 380.1 | 388.8 | 403.4
Monosodium sulphonacetate
C,H,0;SNa 88.4 | 98.4 | 110.1 | 123.9 | 141.0 | 163.2 | 191.4
Disodium sulphonacetate
C,H,O;SNay 162.5 | 180.0 | 194.0 | 206.0 | 215.2 | 223.0 | 228.8

Sulphonpropionic acid
C3H605S

345.5 | 355.5 | 362.8 | 369.0 | 313.3 | 319.4 | 381.4

Monosodium
sulphonpropionate
C3H;0;SNa 82.6 | 91.4 | 101.1 | 112.5 | 126.3 | 146.0 | 169.0

Disodium sulphonpropionate
C3H,O;SNag 154.8 | 169.3 | 182.0 | 192.6 | 201.0 | 208.0 | 213.2

Propionanilide-z-sulphonic
; acid
CoH, ,04SN 337.2 | 348.1 | 355.7 | 360.8 | 364.0 | 365.1 | 365.2

Sodium propionanilide-
«-sulphonate
CoH,00,SNNa 63.0 | 66.6 | 69.6 | 71.4 | 73.3 | 74.9 16.3

In order to get an idea of the dissociation constant k, of reaction
U, the conductivity of the acid salts must be diminished by the
contributions of the ions Na’ and HA’.

The conductivity of the HA-ions Ar’ may, on account of the number
of atoms, be estimated for the sulphonacetic acid at 36 and for the
sulphonpropionic acid at 33. .

Further, the dissociation degree «, of reaction | has to be known.

This value being not directly determinable, we may make use of
Brepie’s rule’), that the dissociation degree of the sodium salts of
different monobasic acids rises about equally rapidly on diluting the
solution. |

It is therefore allowable to take the dissociation degrees sought

‘) Only the conductivities of the neutral salts have been diminished by the
conductivity of the water (1.5—2.0 x 10-6).
2) Brepie, Z. f. phys. Gh. 18, 191) (1894). -

361

as equal to the values given by the sodium salt of an analogically
built acid in the same dilution. As the properties of the acid salts
of the a-sulphoncarbonic acids indicate the structure CHR (CO,H)SO,Na,
the sodium salt of a sulphonic acid may be chosen for the sake of
comparison.

Now, with a view to determine the dissociation degree of a
monobasic sulphonic acid, related to the acids in question, the anilide
of sulfonpropionic acid was prepared '). The conductivity mentioned
in the table shows that this propionanilide-a-sulphonic acid is a strong
acid, from which it follows with certainty, that the sulphonic acid
group is free and that the carboxylic group is changed into amide:
CH, . CH(CONHC,H,)..50,H.

If ug is assumed to be 368, a value resulting from the
conductivity of the sodium salts and also from the number of atoms,
then the mean dissociation constant for the dilutions 64, 128 and
256 is found to be 0,39.

For the sodium salt, the conductivities at the dilutions 256, 512
and 1024, extrapolated according to Brepic, give uy = 79,0.

From this results the ionisation degree « at the dilutions v:

eek NEE 32 64 128 256 512 1024
a=0,797 0,843 0,881 0,904 0,928 0,948 0,966

These values are also taken for a@,, the dissociation degree of
NaHA (reaction 1).

The conductivity of the acid salt unaua, diminished by a, (Anar 4-2 Ha’),
will give, as a first approximation, the conductivity due to the ions
B: and A”.

In order to get a value for k,, it is necessary to know the con-
ductivity which the ions H* and A" would give at a complete
ionisation according to reaction II.

The equivalent conductivity of the neutral sodium salts diminished
by Anat, gives Aa In this way the value 72 was found for sulphon-
acetic acid and 65 for sulphonpropionic acid.

The conductivity of the ions H* and A” at infinite dilution is
then expressed by Ay + 2Aagr.

The observed conductivity gnarra — 4,(ANa‘ + 4m’), divided by
this value a4y--+ 224 , gives, as a first approximation, the value
of a,, the dissociation degree of reaction LI.

1) Recueil d. tr. ch. 40, 585 (1921).

362

Ben
FA SS ee ee a AE NEL
po dra jan ok: he
= 300
nf
S 250 ge ant ne
Ei 200 L__, pe rr WE ac
150 En on al en
ih pel oe | bere
aide ton eee
RR Bom
116 132 164 1128 1256 1512 11024

— log v (number of litres per Grammolecule)

Molecular conductivity.

1. Sulphonacetic acid.
Sulphonpropionic acid.
Propionanilide-x-sulphonie acid.
Disodium sulphonacetate.
Disodium sulphonpropionate.
Monosodium sulphonacetate.
Monosodium sulphonpropionate.

mmm oT > pS

Sodium propionanilide-x-sulphonate.

Now, a correction may be made for the fact that the concen-
tration of the HA’-ions is smaller than agrees with reaction I,

363

these ions being further split up according to reaction II.
A corrected value for a, is obtained, from which k, may be
calculated.
In this way k, is found to be for the sulphonacetie acid:
Or SA (64 PE2O 256 “ola 1024
ero tee HAMO | 8.0 Rony ds e105

and for the sulphonpropionic acid:

v =) 16:32:64. 128.256 | 512. 1024
lee =a One O'6.300.8) 5.30 can (48 SCe10=5

The mean value of the second dissociation constant thus becomes
for the sulphonacetic acid 8.9 > 10—° and for the sulphonpropionie
acid 6.0 > 10-5.

In this statement of views no account is taken of the combi-
nation of the ions H’ and HA’, as shown by reaction III.

A correction for this last, however, that would somewhat increase
the second dissociation constant is of no value for these strongly
dissociated acids, as the uncertainty in the values of the conductivity
of the different ions has a greater influence.

Dr. O. Ringer and Drs. D. W. Dikstra have given their assistance
with some of the measurements.

A more detailed account will appear in the Recueil d. trav. chim.

Organic Chemical Laboratory of the University.

Groningen, 8 Sept. 1922.

Physiology. — “On the progress of the veratrin-poisoning of the
striated frog-muscle’. By Arie Qurripo. (Communicated by
Prof. G. vaN RIsNBERK).

(Communicated at the meeting of October 28, 1922.)

1. Concentration and dose.

The nature of the action of veratrin on the striated muscular
tissue still has not been sufficiently revealed, partly because of the
lack of knowledge of the conditions, associating the poisoning.
Repeatedly we read with various authors the remark, how fickle
and incalculable the veratrin-phenomenon is in its appearance,
seemingly independent of the quantity of poison used and the time
it could act. It is true in 1904 Mosrinsky ') examined the factors
- cooperating in the formation of a definite shape of curve and he
succeeded in ascertaining the conditions incidental to this; the modi-
fications however of these conditions in the course of an experiment,
i.e. the alterations during the poisoning of the balance between
muscle-metabolism and poison-action of which the curve is a result,
are unknown as yet. Closely connected with this is the question,
in what way the shape of the curve corresponds with the rate of
poisoning of the muscle. On this subject we have some information,
that is two types of contraction-shape are distinguished, viz. the
type with two and with one top (fusion type), the latter of which
corresponds to a stronger rate of poisoning (BorHM °), DrerMAN ®) ).

In order to study these questions further, I irritated muscle-
nerve-preparations, after their immersion in a veratrin-Ringer-solu-
tion, by induction-shocks with so long a pause between the stimu-
lations, that the influence of a contraction on the following need
not be taken into account (three minutes).

In this way I collected a great number of curves of veratrin-
poisonings for different concentrations of the poison. On contemplating
the modifications in the veratrinogram, we can get an idea of the
relation between curve and rate of poisoning, for if a poisoning is
seen to progress in the direction of a diminishing or vanishing

1) Arch. f. exp. Path. u. Pharm., 51, 1904,
4) Idem fies.
3) Contrib. to Biology from the Amsterdam University 1914—15.

365

poison-influence, proved by the final appearance of normal, single,
rapid contractions, we see, before this stage is reached, the second
shortening becoming lower, of a shorter duration and appearing
after a longer latent period; conversely it follows that a strong
poisoning will be expressed by a high, prolonged, second shortening,
having a short latent period and that the “fusion type” indeed cor-
responds with a stronger rate of poisoning than one with two tops,
for with the former the latent period has reached its minimum, i.e.
has grown equal to that of the first shortening; moreover the height
is greater than that of a non-fusion second top. These magnitudes
therefore, which may be expressed in the corresponding magnitudes
of the first contraction, give a relative standard, holding for each
separate muscle during the course of an experiment, for the poison-
ing at the moment of contraction, enabling us to picture to ourselves
the progress of the poisoning, without our being dependent on the
direct result, viz. the shape of the curve.

On studying the poisoning-process in this way, we notice in the
series of curves peculiar differences, dependent on the concentrations,
in which the poison has been applied.

1. In concentrations of 1: 1000 and higher the muscle contracts
as soon as it is brought into touch with the solution and maintains
that shortening. On being stimulated the muscle shows either a very

Fig. |.

Experimental-process, when a veratrin-Ringer solution 1: 1000 is poured on a
muscle-nerve-preparation.

1: Contraction before poisoning: Af<——>: pouring on the solution. 2: subsequent
contraction of the muscle; 3 and 4: contraction after electric stimulation, three,
resp. six minutes after application of the solution: at | the cylinder stopped.
Time !/s sec.

slight: veratin-effect, or there is no result at all of the veratrin-
poisoning, and the concentration is undistinguishable from the
contraction yielded by an unpoisoned muscle on single stimulation.

366

(Fig. 1). This reaction is soon succeeded by complete insensibility
for stimulation.

2. If the muscle has been put into a veratrin-solution weaker
than 1: 1000, but stronger than 1: 100000 a series of curves is
obtained, of which either the first or a following gives the strongest
picture of the typical veratrin-poisoning, after which this effect
diminishes till it finally disappears, so that the muscle, just as before
the poisoning, responds to the stimulation with a single, rapid
contraction, if at least it has not become insensitive, before this
stage has been reached.

3. If solutions of 1: 100000 and weaker are employed, a definite
effect of the veratrin-action is obtained, which can maintain itself
for hours together when the preparation is regularly stimulated.

There are three hypotheses which might explain the process
described sub 1 and 2.

A. When the muscle has absorbed a certain quantity of poison
and gradually diminishes the effect of this by its contractions — no
matter how this happens — it is no more able to stand the influence
of veratrin again.

B. The quantity of poison in the solution is not sufficient to
supply the quantity abolished by the muscle.

C. In the period between two contractions the muscle modifies
its character in such a way, that it grows less sensitive to veratrin-
influence.

Hypothesis A may be omitted: a muscle once poisoned by veratrin
can very well be influenced by veratrin-action again, after the
veratrin-effect has been abolished by repeated contracting (e.g. by
frequent stimulation), as the experiment teaches.

Hypothesis B may also be omitted, because von Frry’s') experi-
ments show, that minimum quantities are already sufficient to poison
a muscle. Therefore the hypothesis remains, that the muscle alters
its character in the period of time between two stimulations, a
modification which can only be attributed to the action of veratrin,
for if all circumstances are left unchanged and only the veratrin-
concentration is altered, a definite rate of poisoning occurs, which
appears to be constant (third process).

Evidently there exists, besides the veratrin-effect on the striated
muscle, causing the well-known second, shortening, another action,
having an unfavourable influence on the effect first-mentioned, and
causing a rapid and exhaustive effect in strong concentrations, in

1) Sitzungsber. der Physik.-Med. Geselsch., Wurzburg, 1912.

367

less strong ones a slow and gradual effect; while below a certain
concentration it can no more occur.

If the poisoning-process in a calf-muscle, which is left in situ is
studied here — again with a stimulation-interval of three minutes —
the process mentioned sub 1 is never observed, because the vera-
trin-concentration in the blood never reaches a sufficient height.
On employing large doses (e.g. 15 mgr. per 50 Gr. frog) the heart
is arrested after a short time as Bornu ') describes it and the muscle
is in no other relation — not considering a more intensive contact
with the veratrin-solution — than in a muscle-trough of Kerru
Lecas, filled with a solution of the concentration at which the
process mentioned sub 2 occurs; the conduct of the muscle is indeed
in absolute accordance with this. On using smaller doses (1—2 mer.
per 50 Gr. frog), the heart, at least during the first hours after
poisoning, keeps beating, only gradually diminishing its frequency ;
consequently the quantity of veratrin carried to the muscle is
steadily increased and it should be borne in mind, that when the
veratrin-concentration exceeds a definite threshold, the second effect
of veratrin mentioned above will make its influence felt, i.o.w.
the poisoning will seem less intensive: conversely every contraction
will abolish part of the veratrin-effect and it may be supposed that
in this way interference takes place between the influence of the
two factors, determining the effect of the rate of poisoning, viz. the
application and the rendering inactive of veratrin, when their two
causes, i.e. the heart-action and the lapse of time between two con-
tractions, occur in a definite proportion. As a result of this inter-
ference a periodicity occurs in the poisoning-process, i.e. the effects
of stronger poisoning (higher, more prolonged second top) vary with
those of less strong poisoning. At length the regularity of these
oscillations is interrupted, because the heart-action diminishes under
influence of the effect of the poison and the relation above-mentiond
exists no more.

A constant poisoning in a muscle in situ can only then be obtained
when the poison is applied without interference of the heart, e.g.
by subeutaneous muscular injection (BUCHANAN) °).

2. Combination of veratrin and curare.

De Borer’) communicates the possibility of leaving only the second
shortening by simultaneous application of veratrin and curare. He

1) Arch. f. exp. Path. u. Pharm., 71, 1913.

2) Journ. of Physiol. 1899.

3) Contributions Amsterdam 1914—15 and Zeitschr. f. Biol. 65.

368

gives few particulars however, so that I did not think it superfluous
to repeat this experiment. It appears that quite different processes
may arise, dependent on the lapse of time between the application
of the two drugs.

A. If veratrin is first injected and the application of curare is
put off till a distinet veratrinogram appears, the curare-injection
remains without perceptible effect, the veratrin-poisoning proceeds
as usual. |

B. If curare is injected either simultaneously with veratrin-or
so short a time after, that the veratrin-effect has not yet become
manifest in the shape of a curve, in the further course of the experiment
a typical veratrinogram appears, which shows that the two parts
are equally effected by curare, so that both of them diminish till
complete indirect insensibility; on direct stimulation the muscle even
then gives a typical veratrinogram.

C. If veratrin is applied, if there is already an outspoken curare-
poisoning, no veratrin-effect is shown, the poisoning behaves as a
common curare-action till complete indirect insensibility.

D. If veratrin is injected while there are slight effects of the
curare-action — it is of course impossible to mention objective data
on this subject — in the further progress a veratrinogram appears
with a usually very striking second top, wich is afterwards modified
into a normal-looking veratrinogram, which further behaves as such.

i. Finally veratrin may be injected between the stages C and
D; then there arises neither a rapid contraction nor a veratrino-
gram, but a musele-contraction, which should be identified the
second shortening of the veratrin-curve. On direct stimulation there
is also formed a typical veratrinogram in that case. (Fig. 2). The
further process may lead to complete indirect insensibility, or to
the fact that before this slow contraction there occurs a rapid one,
causing another typical veratrinogram. In shape the shortening thus
obtained is identical to the second contraction of a veratrinogram,
when this succeeds the first in isolated condition, as it is sometimes
‘seen during a poisoning-process.

Examined on a quick-turning cylinder its latent period appears to
be twice or four times as long again as that of a normal single
contraction; no top is formed, the highest part of the contraction is
a horizontal line; the crescent is much less steep than the decrescent ;
the duration amounts to one to four seconds.

3. Temperature.
As to the influence of temperature, I agree in Baat with BRUNTON

569

and ‚Casn *),: according to whom both higb and low temperatures
have an unfavourable influence on the veratrin-phenomenon.

Fig. 2.

Combined action of veratrin and curare; 1 and 8: contraction on indirect
stimulation; 2: contraction on direct stimulation; period between contractions:
three minutes; at J the cylinder stopped. Time !/, sec.

Here too a number of details are to be observed with respect
to the modifications, the veratrinogram undergoes at various tempe-
ratures.

If a frog is cooled to 4° C. or lower and a veratrin-injection
is given after that, no poisoning-effect is observed; the muscle behaves
as an unpoisoned, cooled muscle, giving a relatively long and low
contraction on induction-irritation. If the frog is subsequently heated,
the second shortening gradually appears, first rapidly and of a short
duration; above 14° C. the normal veratrinogram appears; conversely
if a frog already poisoned is cooled, the second shortening disappears
in quite the same way as it appears in the reverse experiment.
Here too the cooled muscle behaves like an unpoisoned one. On
heatng above room-temperature the second shortening is seen to
increase (in height as well as in duration). The first also increases
its height as the contraction of an unpoisoned muscle would do,
the second bowever increases more rapidly and consequently soon
ecxeeds the first in size, so that a “fusion” type of curve arises.

At about 30 degrees the second shortening still increases in size,
now however the first grows more rapidly and at + 36° the second
shortening begins to decrease also absolutely, the first behaves exactly
as thecontraction of an unpoisoned muscle would do; till the muscle
has become insensitive in consequence of heat-stiffness, there is still
some veratrin-effect left. (Fig. 3). All this occurs quite independently
of the poisoning: process ; from every temperature with its corresponding

1) Journ. of Physiol. 1883.

370

curve-shape, we can return to room-temperature and see a typical
veratrinogram arise.

NS a ga gg ag ey) (EE By ST Ee ey es NT LOE NN VN OPE DN ON VEE VN ES ee MTD)

Voor afkoeling = Before cooling.

Shapes of veratrinogram, yielded by one muscle at various temperatures. Time
I/g sec.

4. Strength of stimulus.

I have not succeeded in exercising an influence on one of the
two parts of the veratrinogram separately by means of the strength
of the stimulus. If the strength of the stimulus is gradually diminished,
we may observe as Mostinsxy') describes, the critical progress of
the excitability of the veratrin-muscle, ie. below a definite limit,
which is very exact, no reaction occurs on irritation, above this
limit a reaction, differing but little from the maximal; moreover
this always is a complete veratrinogram.

»A more detailed research concerning the problem of veratrin
will appear in the „Archives de Physiologie Neéerl.””’

1) loc. cit.

Anatomy. — “The Problem of Orthognathism’’. By Prof. L. Bork.

(Communicated at the meeting of October 28, 1922).

In the meeting of February 1921 I called attention to the fact
that the typically somatic human features are of a special character,
viz, they are persisting fetal properties and conditions. I referred
this fact to the influence of the endocrin system, which, through its
inhibitive action, fixes fetal morphogenetic relations. The character
of the human body, therefore, is its fetality, and this character
results from what | am inclined to term a process of fetalization.

When studying the structure of the human skull from this point
of view, it is surprising to note how all at once the whole complex
of the typically human features, — and there are many in the skull
— becomes easy of comprehension. Of all parts of the human body
the head is most indicative of its fetal character. Earlier researches
made by me had already favoured this view with regard to several
of these properties. Long before conception of the fetalization-prin-
ciple as the leading factor in the genesis of the human body as a
whole, I had already pointed out that many somatic property
of man represents an early stage of ontogenetic development.

However, there was one property of the skull about which I had
no fixed opinion, and it is just this property that determines so
emphatically the human physiognomy viz. its orthognathism. The
question urged itself upon me, whether also this feature should be
a persisting fetal property? I felt some diffidence in putting the
question, as’ the pronouncements laid down in the literature were
not very encouraging, the general conception being that the ortho-
gnathous (i.e. the human) skull-type has originated from the pro-
gnathous (i.e. the animal) type. The evolution is supposed to have
consisted in a shortening of the jaws, in connection with the
presumed reduction of the set of teeth. Now, to this conception
objections might be raised also from other quarters, but 1 deemed
it necessary, instead of opposing one speculation to another, to let
the facts speak for themselves. This led me to an inquiry into the
relation between prognathism and orthognathism. The results were
indeed surprising, for not only was I in a position to establish this
relation, but it also became evident that the whole complex of

372

human properties in the skull form one entity. However, in this
paper I shall confine myself to my real subject.

My first attempt was to ascertain the essential morphological fea-
tures of the prognathous and the orthognathous skull-type, for the
criterion of short or long jaws is inadequate. With the aid of Figs
1 and 2 these features are easy to establish. |

Fig. 1. Fig. 2.

Fig. 1 shows a median section of a human skull. Fig 2 asimilar
section of the skull of Lemur, a Prosimia. Three lines have been
drawn in both figures, viz the axis of the cranial cavity, the axis of
the nasal cavity and the axis of the base of the skull. The three
lines demonstrate in a simple way the essential features of the
orthognathous and the prognathous skull-type. They are the following:
In the orthognathous type the axis of the nasal cavity is approxi-
mately perpendicular to the axis of the cranial cavity, in other
words the nasal cavity is situated beneath the cranial cavity; in
the prognathous type, on the contrary, the axis extends more or less
in the same direction as the axis of the cranial cavity. As to the
axis of the base of the skull, it is flexed in either case, but in
opposite direction. In the orthognathous type it is flexed between
the basi- and the praesphenoid, an angle is formed with its open
side turned anteriorly downwards. It is known in the literature as
the sphenoidal angle. In the prognathous type the base is flexed
between the praesphenoid and the ethmoid. An angle is formed with
its open side turned posteriorly upwards. This angle I shall term
the ethmoidal angle.

So it appears that the typical differences between the orthognathous
and the prognathous skulls consist in the different situation of the
nasal-cavity, either subcerebral or praecerebral, and in the different
direction in which the base of the skull is flexed. The length of
the jaws I do not consider as a fit criterion.

373

Now, when we test the skulls of the various classes of mammals
by the criteria just mentioned, it appears that the whole class of
the Primates, so not only man, is characterized by an orthognathous
skull, in eontradistinetion to all the other mammalian classes. Applying
the degree of prominence of the jaws as a criterion for prognathism
is an erroneous method, which e.g. has led to the classification of
apes among the prognathous forms. Though their jaws may be ever
so much developed, the base of the skull never presents an ethmoidal
angle, while the nasal cavity is never situated before the cranial
cavity and in younger individuals there is even a sphenoidal angle.
The strongly developed facial part of the skull in several apes,
however, reminds us forcibly of a prognathous skull. These forms
I will, therefore, distinguish as pseudoprognathous.

In the foregoing the principle has been established for an inquiry
into the relation between prognathism and orthognathism. The
object of such an inquiry must be the answer to the question:
which skull-type is the primitive one and which is the specialized
type. First of all [ will report the result of my examination of
embryos of a number of mammals. It is the following: the fetus
of all mammals is initially orthognathous, i.e. has a sphenoidal angle
lacks an ethmoidal angle and the nasal cavity is subcerebral. Now,
whereas this condition persists in apes partly and in man completely,
in the other mammals the fetal orthognathous skull passes gradually
into the prognathous type; first the sphenoidal angle disappears,
then the ethmoidal angle is developed and coincidently the nasal
cavity rotates; its subeerebral position passes into a precerebral
position. So it becomes evident that the orthognathous condition in
man, which is the special feature of the human physiognomy, reveals
itself again as a persisting fetal property.

Before demonstrating this in a series of embryos, I will briefly
dwell on the fact that this transformation of the orthognathous skull
into the prognathous type is a process, with which we are confronted
already in Reptiles, so that it has evidently been inherited by the
Mammals from their reptilian ancestors.

Fig. 3 represents a median section through the head of an embryo
of Lacerta, length of the head 4 mm. The chorda is still present,
the vertebrae are not differentiated, likewise the cranio-vertebral
joint is still incomplete. Of the chondrocranium the basicranial plate
enclosing the Foramen can be recognized. This plate extends frontad
as far as the Hypophysis cerebri, which is still attached to the
epithelium of the roof of the mouth. In front of the Hypophysis lies
the prechordal plate. The latter presents two enlargements the one

24

Proceedings Royal Acad. Amsterdam. Vol. XXV.

374

turned upwards: the septum orbitale, and the other turned down:
the septum nasale.

Fig. 3. Fig. 4.

Now, two things should be observed: First that the prechordal plate
extending in front of the Hypophysis,forms an angle with the basicranial
plate behind it. This angle which is still more distinct in younger
embryos, is identical with the sphenoida angle, the typical feature of the
orthognathous buman skull. The second thing to be observed is the
direction of the septum nasale. In this young Lacerta embryo the
axis of this septum is perpendicular to the base of the skull, which
also is a typical feature of the orthognathous human skull. In pas-
sing, I wish to point out that in this phase of development the
entrance to the mouth is, in Lacerta, not apical, but points down-
ward. This reminds us incontinently of the permanent condition in
Plagiostomes.

So the verticality of the septum nasale is a characteristic which, in
this phase of development, the head of the Lacerta-embryo has in
common with the orthognathous type. Fig. 4 shows how this type
passes into the prognathous. In fig. 4¢ the median section through
a primordial cranium is given, head length 4.5 mm. In fig. 4°
the same with a length of 5 mm.; the enlargement in the two
figures differs. Relative to the younger stage, the septum orbitale
in the embryo with a head length of 4.5 mm. is considerably enlarged.
It is clear that the axis of the nasal septum is no longer perpen-
dicular to the base of the skull, but has rotated anteriorly. In the
5 mm. embryo this rotation is so considerable that the axis of the
septum nasale is nearly on a level with the base of the skull. In
this older embryo the septum orbitale exhibits marked signs of

375

resorption. So the figures 3 and 4 illustrate a rotation of the septum
nasale, and consequently of the facial skull. From its original sub-
cerebral position (orthognathism) it shifts into a precerebral position
(prognathism). That in connection with this rotation plagiostomy.
changes into teleostomy we will pass over in silence, although this
phenomenon would give ample scope for interesting observations.

It has thus been shown that the chondroeranium of Reptiles, in
its early phase of development, resembles the orthognathous type.
Now we are going to demonstrate that the process of development
in Mammals bears a great resemblance to that of Reptiles. 1 have
studied the ontogenesis of the skulls of a number of Mammals, and
in all of them I met with the phenomena that I am going to
describe for the skull of Mus decumanus.

Fig. 5 represents the median section of an embryo of Mus
decumanus of 11.5 mm. In this stage the primordial cranium is

Fig. 5. | Fig. 6.

sufficiently differentiated. We will confine ourselves to the skeleton,
omitting all further remarks that the following series of figures might
suggest. In this stage the Hypophysis has become a closed vesicle,
which, however, still adheres to the epithelium of the mouth. Behind
the Hypophysis lies the basicranial plate, which in Mus is subchordal
over its whole length. Frontal to the Hypophysis lie the prechordal
plate presenting a slight broadening dorsad, which is homologous
with the strongly developed Septum orbitale in Reptiles. At its lower
surface the Septum nasale is fastened. There is no denying that the
basicranial plate and the prechordal plate form an angle. This

angle, which we also found in Lacerta, is the sphenoidal angle that
we know to be the typical feature of the orthognathous skull. Whereas
the base of the skull is directed almost quite horizontally, the axis
of the septum nasale is directed perpendicularly. Therefore in
this stage of development the nasal cavity of Mus is subjacent to
the cranial cavity. The skull of this young embryo of Mus possesses,
therefore, two features, which are characteristic of the orthognathous
skull, viz. a sphenoidal angle and a subbasal situation of the nasal
cavity. That the latter condition is not the consequence of the intense
development of the cerebral hemispheres, is borne out by the fact
that in an early stage of development of Reptiles we find the same
direction of the septum nasale. The condition in Mus, just described,
is inherited from the reptilian ancestors of Mammals, which in
their turn have inherited it from more primitive vertebrates. Plagio-
stomy, to which we referred heretofore, and which, to some extent,
is encountered in the represented embryo of Mus, indicates in what
direction we have to look for an explanation of this condition.

Accordingly we conclude that orthognathism is the characteristic
of the young fetal mammalian skull. Now let us see how the prog-
nathous type is developed from the primitive type.

Fig. 6 illustrates the median section through the head of an embryo
of 13.5 mm. in length. The chorda begins to disappear, the Hypo-
physis lies within the cranial cavity, but is still attached to the
mouth-epithelium. The base of the chondrocranium begins to stretch,
but the sphenoidal angle is still recognizable. The axis of the septum
nasale is still perpendicular to the prechordal plate.

Fig. 7. Fig. 8.
Fig. 7. Embryo of 20 mm. The basis cranii is stretched, the

677

sphenoidal angle has disappeared. The axis of the nasal septum is
no longer vertical to the base of the skull, it has rotated, so that
it forms an angle of 115° with the axis of the base of the skull.

Fig. 8. Embryo of 25 mm. The canalis Hypophyseos is closed,
basal plate and prechordal plate have coalesced completely. The
septum nasale has rotated further, and is inclined to the base of
the skull at an angle of 130°, the part of this base to which the
septum nasale is attached is bent slightly upwards, which is the
first indication of the developing ethmoidal angle.

Fig. 10.

Fig. 9. Embryo of 35 mm. Three centra of ossification have
appeared in the basis cranii for the Basioccipitale, the Basisphenoid

378

and the Alisphenoid. The rotation of the septum nasale has conti-
nued; the nasal cavity now lies obliquely under and anteriorly to
the cavum cranii. This rotatory movement apparently results from
the further upward flexing of the frontal part of the basis cranii.
The ethmoidal angle now becomes distinctly visible, right in front
of the centrum of ossification of the Alisphenoid.

Fig. 10. Embryo of 43 mm. The ethmoidal angle has reached
its definite value for the skull of the adult rat, the frontal part of
the basis cranii has now become the anterior wall of the cranial
cavity, the nasal cavity is situated before the cranial cavity, the
skull has become prognathous.

It is evident, then, that the transformation from the orthognathous
into the prognathous skull-type in the mammalian embryos is a
regular process in which two succeeding phases are recognizable.
In the first phase a straightening of the basis cranii takes place;
the sphenoidal angle disappears. Its disappearance it attended with
a change in the direction of the septum nasale, which is now placed
obliquely to the base of the skull. After this the second fundamental
alteration in the basis cranii commences, viz. the formation of the
ethmoidal angle, the anterior (ethmoidal) portion of the base being
turned up together with the septum nasale, which is attached to it.
Consequently a part of the base of the fetal skull becomes the front
wall of the cranial cavity.

I shall not enter into details concerning the various mammalian
embryos that [ have examined but will only add a few general
remarks.

From the foregoing it is sufficiently evident that the orthognathous
skull of man is to be considered as a persisting early fetal form.
In stating this fact we have at the same time disproved the current
opinion, that the sphenoidal angle, which is so characteristic of the
human skull, is due to the intense development of the human brain.
This angle, indeed, is not only a feature of all fetal mammalian
skulls, but it occurs even in the chondrocranium of Reptiles. It is
an essential character of, let me say, the primordial cranium of
vertebrates in general. I shall not discuss this point any further.

The question now arises whether the intense growth of the
Hemispheres has had no influence whatever on the anatomical relations
of the skull, apart from the necessarily considerable enlargement of
the cerebral crane. Such an influence, and even a very remarkable
one, can indeed be demonstrated, as may be seen in comparing
Fig. 11 and 12.

Fig. 11 shows the median section through the head of a dog’s

379

fetus; length 32 mm.; Fig. 12 that of a human fetus 40 mm. long.
The peculiarity I wish to lay stress on, regards the insertion of the

Fig. 11. Fig. 12.
membranous vanlt of the crane on the cartilagenous nasal capsule.
In the dog the former attaches itself to the acute border where the
cranial base bends round in the nasal capsule, i.e. to the anterior
margin of the cranial base. In man, on the other hand, it attaches
itself in consequence of the intense development of the Hemispheres,
to the anterior surface of the nasal capsule. It is obvious that a
comparatively large portion of the nasal septum is hereby enclosed
in the cranial cavity. This fact elucidates several phenomena observable
at the human skull, [ will only name them parenthetically. The
shifting of the insertion of the membranous cranium to the anterior
surface of the cartilagenous nasal capsule accounts for the occurrence
of the Crista galli. This process, which is lacking in prognathous
skulls is merely the top part of the nasal septum and the apex of
the Crista galli indicates consequently the original frontal boundary
of the base of the skull. This transference of the insertion of the
membranous vault causes a shortening of the frontal part of the
nasal region in man and it is quite obvious that the human physi-
ognomy has been largely influenced by it. Earlier comparative
anatomical inquiries already led me to conclude that the top part
of the nose in Primates was reduced, and tbat the present boundary
between nose and vault of the skull is of a secondary nature’). The

1) Die Herkunft der Fontanella metopica beim Menschen. Anat. Anz. Ergänzungs-
heft. Bnd 38. Jena 1911.

380

suture between nasal and frontal bones was lying on the forehead
at the spot where in man not seldom the so-called Fonticulus
metopicus is situated. The results of the embryological research lend
support to this view.

Another phenomenon explained by this transference of the insertion
of the membranous vault on the nasal capsule is the intra-orbital
situation of the entrance to the lacrimal duct. In the half-apes this
Opening is extra-orbital; in the apes, on the other hand, it is taken
up in the medial wall of the orbit together with the os lacrymale,
in consequence of the shortening of the facial part of the skull in
this region.

It appears then that through this transference of the insertion
of the membranous vault to the anterior surface of the nasal capsule
in consequence of the intense development of the cerebral hemis-
pheres, we are able to interpret in a simple way three apparently
heterogeneous phenomena, viz. Crista galli, Fonticulus metopicus,
and intraorbital position of the lacrimal foramen. In this connection
I may still add a remark about the other Primates. We have stated
that apes, however much their jaws may project, possess in reality
an orthognathous skull like that of man; they are to be classed as
pseudoprognathous. The persistence of the subcerebral position of
the nasal cavity, also in,apes, is the reason why the human
physiognomy is ever more or less discernible in apes, which is to
be ascribed chiefly to the position of the eyes. Originally the eyes
of all mammalian embryos are disposed on the lateral surface of
the head. In the prognathous type, in which the nasal cavity rotates
before the cranial cavity the eyes retain their lateral position. In
the orthognathous type, on the contrary, in which the nasal cavity
persists under the cranial cavity the eyes can draw nearer to each
other, and instead of the nasal cavity the orbitae occupy a precerebral
position. Now this rotation obtains with all Primates, and this is
why, pbysiognomically, apes resemble man.

In conclusion another point of similarity is the fact that all
Primates possess a Crista galli, so in all of them the insertion of
the membranous vault of the crane is transferred to the nasal capsule
under the influence of the intense growth of the cerebral hemispheres,
which is proved also by the intraorbital position of the foramen
lacrymale in this class of mammals.

381
ERRATUM.

In these Proceedings Vol. XXV nes. 5 and 6, D. 202, line 15

from the bottom, to replace “with respect to time” by “with respect
10 TEMPERATURE”.

en ren
kad pend =
enn sehen

i accel Che ar .
al cds Oita A peel ie ALI

os :
oe 4” sq) | q ' : '
i j 4 LAP piss ie
Ere mal x : nis 1

Pars
'

=
Kar MEA
wat
=
ay
nd
mf!

je gean 1

KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN
TE AMSTERDAM.

PROCEEDINGS

VOLUME XXV
Nes, 9 and 10.

President: Prof. F. A. F. C. WENT.
Secretary: Prof. L. BOLk.

(Translated from: “Verslag van de gewone vergaderingen der Wis- en
Natuurkundige Afdeeling,” Vol. XXXI).

CONTENTS.

J. P. KUENEN +: “The Magneto-Thermic Effect according to Thermodynamics”, p. 384.

SHINKICHI HORIBA: “Determination of the Vapour Pressure of Metallic Arsenic”. (Communicated
by Prof. P. ZEEMAN), p. 387.

B. SJOLLEMA: “On the Influence of the Composition of the Food on the Calcium output”. (Commu-
nicated by Prof. H. ZWAARDEMAKER), p. 395.

J. J. VAN LAAR: “On Heats of Mixing of Normal and Associating Liquids”. (Communicated by Prof.
H. A. LORENTZ), p. 399.

H. A. LORENTZ: “On WHITTAKER’s Quantum mechanism in the atom”, p. 414.

E. D. WIERSMA: „Concordance of the Laws of some Psychological and Physiological Phenomena”,
p. 423.

G. HERTZ: “On the Separation of Gas Mixtures by Diffusion in a Flowing Gas”. (Communicated by
Prof. P. EHRENFEST), p. 434.

G. HERTZ: “On the Excitation and Ionization Potentials of Neon and Argon”. (Appendix). (Commu-
nicated by Prof. P. EHRENFEST), p. 442.

H. KAMERLINGH ONNES and W. TUYN: “Further experiments with liquid helium. Q. On the electric
resistance of pure metals etc. X. Measurements concerning the electric resistance of thallium
in the temperature field of liquid helium”, p. 443.

H. KAMERLINGH ONNES and W. TUYN: “Further experiments with liquid helium. R. On the electric
resistance of pure metals etc. XI. Measurements concerning the electric resistance of ordinary
lead and of uranium lead below 14° K.”, p. 451.

J. P. WIBAUT and ELISABETH DINGEMANSE: “The Action of Sodiumamide on Pyridine, and some
Properties of ¢-aminopyridine’. (Communicated by Prof. A. F. HOLLEMAN), p. 458.

L. HAMBURGER: “On Centres of Luminescence and Variations of the Gas Pressure in Spectrum
Tubes at Electrical Discharges”. Il (Communicated by Prof. H. A. LORENTZ), p. 463.

F. A. F. C. WENT: “On a new clinostat after DE BOUTER”, p. 475.

B. SJOLLEMA and J. E. VAN DER ZANDE: “Concerning the Synthetic Action of Bacteria in the
Paunch of the Cow”. (Communicated by Prof. H. ZWAARDEMAKER), p. 482.

25
Proceedings Royal Acad. Amsterdam. Vol. XXV.

Physics. — “The Magneto-Thermic Effect according to Thermo-
dynamics”. (Supplement N°. 47 to the Communications from
the Physical Laboratory at Leiden). By Prof. J. P. Kunnen +.

(Communicated at the meeting of December 30, 1922).

In experiments with ferro-magnetic substances Weiss and Piccarp *)
found that the heat-effect which accompanies a magnetic change,
assumes a relatively large value in the neighbourhood of the Curie-
point. According to them this phenomenon, just as the discontinuity
in the specific heat at the Curie-point?), is a consequence of the
“molecular field’, which plays a prominent rôle in Weiss’ theory
of ferro-magnetism.

It is natural to apply equations to this phenomenon which ensue
from the second law of the theory of heat. The question suggests itself
whether this is allowed, as non-reversible changes occur in ferro-
magnetism. Every condition — leaving disturbances out of account
— is indeed a condition of stable equilibrium, but in general the
substance cannot pass through a definite series in both directions.
This difficulty may be obviated by considering only those condi-
tions that arise under the influence of strong mechanic or electric
vibrations: these neutralize hysteresis, and with it also remanent
magnetism, and the conditions then become reversible. The results
obtained by the aid of thermodynamics, will in main lines most
likely also hold for the phenomena occurring under normal circum-
stances: above the Curie-point they are, of course, strictly valid.

The external work of a magnetized system being represented by
— Hdo, where H and o denote resp. the magnetic force and the
magnetisation, the chief equation of thermodynamics is:

de Ri eH do 00, oe af SEE
As it is most convenient if H is an independent variable, we
write:
d (e — Ho) SFP dy— 0 d-H oren mange (2)
from which follows:
1) P. Weiss et A. Piccarp, J. de Phys. (5) 7, p. 103, 1917.

*) P. Weiss, A. Piccarp et A. Caprera, Arch. de Genève 1917; J. de Phys.
(5) 7, p. 87, 1917.

385

oT dg T 06

DET anode, ven ET PEERS
Here cy is the specific beat for constant field. This equation
shows that the thermic effect in question is greatly dependent on
oe hence becomes abnormally high in the neigbourhood of the
Curie-point, and this is what we intended to prove.
a being <0, the temperature increases during the magnetisa-

tion, and reversely. According to the above-mentioned experiments
c would suddenly assume a lower value at the passing of the
Curie-point in upward direction, but this does not affect the con-
clusion drawn. The relation found is independent of Weiss’ hypo-
theses, and sets forth the inter-relation between heat-effect and
disappearance of ferro-magnetism more clearly than the equations
given by Weiss and Piccarp.
When, with Weiss and Prccarp, o is taken as independent vari-

able, the following is found from (1):

SR AH T 0H

Eon Ta ORT ser Baths: (4)

ij
Above the Curie-point a (T7—@) = C, where 6 and C are con-

stants, so that Eren 5 On substitution of this in (4) an equation
is obtained which also occurs in the cited paper, but which is
strictly proved here without having recourse to Wuiss’ special theory.

It will be vainly tried to estimate the said change of the specific
heat at the Curie-point purely thermodynamically. Thermodynamics
gives, indeed, the change of cy with the value of H (resp. of
c, with o), and the difference between c, and c,, but not the
dependence on the temperature in question. To find this a molecular
theory like that of Weiss, is indispensable. From this an expression
for the internal energy e will have to be derived, and also for the

de òg

de
c’s, because c‚= —— ande, = — = a
‘ da. EN Yer OTH

In connection with the preceding paper I may be allowed to add
a few remarks.
The late Professor KueNEN had the intention to make a commu-
nication on the subject mentioned in the title at the Meeting of the
25*

386

Royal Academy of Sept. 30 1922; a few days, however, before the
meeting death took him away. Among the papers found after his
death was the manuscript of the above communication, ready
for the press, and a few detached sheets, on which the author tried
to ascertain what follows from the equations :

(ii

yet TSS (A)
(5),
0H
Pec)
EP (B)

NC
(st) = (5m), de Te Maingate

0 (fc 071, (07 0?6
[a le toe (33 2) An Gr)
0° 00 GE er ee
(ie) ee Toa
(Gr),
which can be derived in a purely thermodynamic way, if they
are combined with the empirical data on the course of 6 = g (7, H)

in the neighbourhood of the Curie-point, or with the equation:
no"

which is the direct consequence of the formula for the molecular
field H,, used by Prof. Weiss:

de
Ie ich mh tv BAA ene
(55); nO (F)

It seems to have been his intention to throw light on the question
what suppositions are necessary to derive the change of the specific

heat of ferro-magnetic bodies at the Curie-point.
Pe

Chemistry. — ‘Determination of the Vapour Pressure of Metallic
Arsenic”. By Suinkicut HoriBa. (Communicated by Prof.
P. ZrEMAN).

(Communicated at the meeting of October 28, 1922).

Arsenic is one of the most interesting elements, which should be
studied from the view-point of the theory of allotropy. It is a well
known fact that arsenic can exist in three kinds of modification, i.e.
gray, black, and yellow; the gray modification is quite stable in a
wide range of temperature, while the others are rather metastable.
Although many investigations have been carried out about this
important element, yet it has never been tried to define the exact
lines of demarcation between these three modifications. Recently
some observations of its melting point have been reported by GouBrav’),
Heike *), Rassow ®), and some measurements of the vapour pressure of
its solid phase by Heike, but in the ease of the latter, an indirect
method was used, so that the results were not very accurate. The
vapour pressure of the liquid phase of this element has never been
determined. On the suggestion of Professor Smits, the author has
undertaken the measurements of the vapour pressure of this element
in the laboratory of the University of Amsterdam ; the object of
the present study is, of course, to investigate the whole system of
this element, but the author is not yet in the position to complete
this study, owing to the difficulties of the technics of the measure-
ments. The present communication will only represent the results
of the measurements of the vapour pressure of the gray modification
and give some thermal data which can be calculated from these
vapour pressure data.

The Method of Investigation.

The same method of investigation, used by Prof. Smits and Bokuorst ‘)
for the study of phosphorus, was applied; a small modification,
which was made in the present investigation, was that a quartz
indicator of pressure was used instead of the hard glass, in view

1) Compt. rend., 152, 1767, (1911).

2) Z. anorg. chem., 117, 147 (1921): the literature of the melting point was
given in this paper.

3) Z. anorg. chem., 114, 131 (1920).

4) Z. physik. chem., 91, 249 (1916).

388

of the high melting point of arsenic. Owing to the technical dif-
ficulties of making such an indicator, its sensibility was some-
what inferior to that of the indicator made of glass, still some of
the indicators which were used, could keep their sensibilities within
one centimeter of mercury, being sufficient for the present purpose.

The Material.

Merck’s metallic arsenic was used after several purifications. At
first the finely powdered sample was subjected to repeated subli-
mation in a vacuum by the aid of a large Heraeus electric furnace,
the temperature of the furnace was maintained at a little over
500° C. in the first sublimation and at nearly 600° C. in the final
one. The gray modification thus prepared was again very finely
powdered, and was extracted by carbon disulphide in a Soxlet appa-
ratus for 24 hours. A small quantity of arsenic oxide, which would
still remain in the above purified sample, must be reduced by
hydrogen current in the pressure indicator itself.

The Filling of the Sample in the Pressure Indicator.

About 10 gr. of the sample was placed into the bulb of a quartz
indicator, and a hard glass capillary tube was introduced into the
bulb of the indicator, so that the end of the capillary tube was just
in the spring of the indicator. Then the indicator was heated from
outside by Bunsen burners at 500° C; during the heating of the
indicator a current of purified hydrogen was passed into the bulb
and its spring through the above mentioned capillary tube, so that
a small quantity of arsenic oxide, which still remained in the sample,
was at first sublimated and the rest of it reduced to pure arsenic.
After a sufficient sublimation in this way, the remainder of the
sample in the bulb became perfectly pure brilliant metallic arsenic.
Then the indicator was completely evacuated and the bulb of it
was sealed up. It was always observed that if arsenic was sublimated
in a vacuum, even at room temperature, at first it appeared as the
yellow modification, which would be soon transformed into the black
modification.

The Furnace of the Pressure Measurement.

A special furnace was constructed for the purpose of keeping the
indicator at constant temperature, even at very high temperature.
A large iron block of 14 cm. in diameter and of 30 eem. in height
was heated electrically by nichrom wire. In the middle of this iron
block, a hole of 3 cm. in diameter and of 25 cm. in depth was

389

bored, in which the indicator and a thermoelement were placed.
This furnace was available till 900°. The temperature of the furnace
was measured by a Herauus platinum-rhodium thermoelement, which
was carefully adjusted before the experiment.

The Measurement of the Vapour Pressure.
The method of the pressure measurement by an indicator is exactly
the same as that applied by Prof. Smits and Bokuorst '). The equi-

TABLE I. Vapour Pressure of the Solid Phase.

a = 7357 — 8.279

t | p atm. (obs.) | Tlogp | a A eo) | p (calc.)
450 0.026 42 1127 — 230 0.013
500 0.076 — 844 7244 = 413 0.075
525 0.105 — 620 7227 150 0.094
550 0.222 — 538 7352 a 45 0.219
568 0.362 oil 1334 ot 28 0.340
502 0.584 — 202 7363 156 0.598
604 0.785 = 92 7353 ae 0.771
615.5 0.997 wae 7357 +0 0.997
631 1.395 131 1354 2 1.387
658 2.392 353 7354 eid 2.377
665 2.717 401 7365 + 8 2.729
672 3.035 456 7371 + 20 3.189
685 3.906 567 _ 1365 18 3.983 |
697 4.85 664 7368 ES 4.96 —
720.5 6.95 838 7386 +. 29 1.46
741 9.7 999 7396 + 39 10.6
158 13.3 _1157 1378 el 14.0
712 16.9 1281 1371 Ed 17.4
790 22.3 1432 7368 IER 22.8
801 26.1 1522 7370 lS 26.9
809 30.0 1595 1363 + 6 30.2
815 33.6 1662 7348 it 33.0

1) loc. cit.

390

TABLE II. Vapour Pressure of the Liquid Phase.

pen = 2450 C = 3.80
t | patm. (obs.) | Tlogp | ve | pn | p (calc.)
4.571 4.571
808 34.2 1658 2450 + 0 34.2
817 85 1693 2453 +3 35.9
830 38.1 1743 2448 —2 38.0
843 40.5 1793 2447 — 3 40.2
850 41.6 1818 2449 — 1 41.5
853 42.2 1829 2450 +0 42.2

librium between vapour and condensed phase of arsenic is not very
quickly established but the heating of the furnace was so slow
that there was no difficulty to measure the pressure at any desired
temperature. The whole measurement of the vapour pressure of the
gray modification of arsenic to its liquid phase, namely from 400° C.
to 850° C., required a continuous work of more than 12 hours. The
results of the vapour pressure measurement were tabulated as follows:
(See Table I, page 389).

Starting from Crausius and CrLAPAYRON’s equation and assuming that
the heat of vaporization Q, is constant, that the vapour of arsenic
follows the gas law and that the volume of the condensed phase
can be neglected with respect to that of the vapour, the vapour pressure

would be represented by a straight line 7’ log p= — — + CT.

When the value of 7’ log p, from the observed values of pressure,
was plotted against temperature, a good straight line was obtained
from 550° C. to 700° C. as shown in Fig. Il, from which we can
easily calculate Q/4.571 and C. The table contains in the last column the
values of the pressures calculated from this equation. Above 700° C.
however, the 7’ log p—t curve shows some deviation, and the calculated
values of Q/4.571, assuming C as a constant must deviate. The deviations
become gradually smaller as the temperature rises, Some of these
deviations may, of course, be experimental errors, because at high
temperature a little observation error of temperature would have a
great effect on the value of pressure, quite the contrary of the case
at low temperature, where a little error in the measurement of
pressure, owing to small value of pressure, would have a great
effect upon the calculated value of Q/4.571. But such a deviation

391

as observed here depends certainly on the inapplicability of the
assumptions which were used in the integration of the CLausitus—
CLAPAYRON equation.

In the case of the liquid phase, the observed vapour pressures

F ug L.
30 T RE
40
2
ml
xo
a
4 30
E
=<
a
a 20
uw)
Z
10 AE
(Opie ES 1 En 1. mn L = =|
400° 500° 600° 700° 800° 900°
“TEMPERATURE
Fig. 1.
Fig x,
+2000 =]

+1500

+1000

+500

T LoGP

- 500

TEMPERATURE
Figs'2.

392

were represented quite well by T/og p plotted against temperature
as a straight line as seen in the table II.

The Melting Point of Arsenic.

The direct measurement of the melting point of arsenic was im-
possible in the course of this experiment, because the thermo-element
was placed outside of the indicator.

As shown in figure I, the observed pressures ') of the gray modifica-
tion very near this melting point (represented by a dotted curve)
were always a little lower than the extrapolated pressure curve and
at the temperatures a few degrees higher than the melting point the
indicator showed the right pressure of the liquid phase. For determining
the melting point I have therefore extrapolated the pressure curve of
the solid phase as that of the liquid phase and it was found between
817° C.—-818° C. which agreed well with the value given by GouBrau®)
and Rassow’). The corresponding pressure is 35.8 atm. Of course,
we could find also the value of the melting point by the intersection
of the two 7T'log p—t lines of solid and liquid phases, but in this
case we find the following values.

fi Q/4.571 p
822076: dl) 36.5

These values of the triple-point are certainly too high due to the
deviation of the expression used, as was already mentioned.

As to the pressure of the triple-point, we can measure it directly
with a certain degree of accuracy. Arsenic shows a very large
effect of supercooling, sometimes more than 30 degrees in the authors
experiments. In the case of a sudden erystallisation of such a super-
cooled liquid, its temperature rose very quickly to the melting point;
consequently the pressure rose also suddenly several atmospheres, so
that it was almost impossible to follow this sudden change of the pres-
sure, applying the pressure outside the spring of the indicator so that,
the spring broke. But if the temperature of melted arsenic was kept
a few degrees below that of the melting point, and if the change of
the pressure was constantly watched for a long while, sometimes
longer than two hours, then it was possible to follow the sudden
change of the pressure by crystallisation. In this case the pressure
remained constant during the crystallisation This adjustment of
the pressure, however, requires much skill, otherwise the spring
will break. In this way we could read the pressure at the melting

1) These values were not given in the table.
2) loc. cit.

393

point, which coincided with the value found by the extrapolation
of the vapour pressure curve of the solid phase to that of the
liquid phase (35,8 atm.).

The Heats of Vaporization and Sublimation of Arsenic.

Heat of vaporization is, of course, a temperature function, but
its temperature coefficient dQ/dt is generally negative, so that
T log p—t curve should be concave to the straight line given by
the expression

eN
4.571
which was deduced from the assumption that Q is a constant. On the
contrary, the present experimental results show that the 7’ log p—t
curve is somewhat convex to the said expression of pressure, so
that we can see that the deviation of the assumption, that Q is a
constant, is smaller than the total effect of deviations from other
assumptions, so that we may say that the temperature coefficient of
the heat of vaporization is comparatively small. It is, therefore,
possible to calculate the heat of vaporization from the expression

spa
4.571
which was found to hold good for comparatively low temperatures.
For the molecular heat of sublimation we have
Q
——— — 7357
4.571

T log p= —

T log p= - + CT,

hence,
Qsc = 33.6 Kg. cal.
For the molecular heat of vaporization for the liquid phase, we have

Q
Dei 2450
hence,
re At ke cal.
From the difference of the above two heats of vaporization, we
have the molecular heat of fusion

Qsr == 22.4 kg. cal.

According to Trouron’s law, Lr CrarerieR showed, that the quotient
Q/T, where Q is the heat of sublimation at sublimation temperature
under one atmosphere and 7’ is the sublimation temperature, would
be 30 for all substances. In the case of arsenic, the temperature of
sublimation is 616° C. or 889 in absolute unit, then

394

Q_ 386 X 10° |
Pe eS:

This is a very high abnormal value, just as in the case of phosphorus.

The Black Modification of Arsenic.

It was tried to measure the vapour pressure of the black modi-
fication by means of the same indicator as was used in the above
experiments. But when the vapour pressure was high enough to
measure by this indicator, all the sample in it was transformed
into the gray modification’), so that it was necessary to find a
suitable negative catalyser for this transformation, which would not
disturb the pressure measurement. The author hopes to continue this
study on a future occasion.

SU. MM Ai

The vapour pressure of the gray modification of arsenic and its
liquid state were measured. From these data, the molecular heat
of sublimation, of vaporization and of fusion were calculated.

In conclusion, the author expresses his cordial thanks to Professor
A. Smits for his kind suggestion and for the excellent advice he
has given during the work.

Amsterdam, July 15, 1922.

1) LASCHTSCHENKO, (J. chem. Soc., 121. 972 (1922)) gave some remarks
on polymorphism of arsenic from the measurement of heat evolved on cooling.

Bio-chemistry. — “On the Influence of the Composition of the
Food on the Calcium output’. By Prof. B. Ssou1ema. (Com-
municated by Prof. H. ZwWAARDEMAKER).

(Communicated at the meeting of November 25, 1922).

In my experiments on the influence of cod-liver oil on calcium-,
and phosphorus metabolism I found that the economizing effect of
cod-liver oil on calcium and on phosphorus, was attended with a
decreased production of faeces *). The question naturally arose whether,
conversely, an augmented production of faeces should result from
an increase in the faecal output of caleium and of phosphorus.

The answer to this question is of great importance with regard
to our understanding the metabolic phenomena and the physiology
of the formation of faeces. The question may be looked at also from
a practical point, especially because in experiments with milk-cattle
results were repeatedly obtained of late years, which render it
highly probable that among the dietetic factors the mineral compo-
nents are often in the minimum.

In the experiments described below we observed especially the
influence of the increase of the quantity of indigestible foodstuffs
(ballast) on the caleium- and phosphorus-metabolism. Two ballast-
experiments have been performed this summer, both with rabbit LI,
which since November 1921, was always used for metabolic exper-
iments, and which for chief diet was given a ration of dextrin,
lactose, oatstraw boiled with acid and alkali, a calcium-free salt-
mixture, a pure protein, viz. casein (afterward partly substituted by
gluten of wheat) and a few grammes of butter.

Besides this food-mixture, wheat (whole kernels) was given in the
ratio 3 mixture to 1 wheat. In addition almost always 15 grms of
cabbage was administered per day. For some weeks the boiled oat-
straw was replaced by sawdust boiled with acid and alkali and the
cabbage by mangels or carrots.

The calcium-determinations’) were made, after destructio of the urine
or the faeces, titrimetrically after Mc CRUDDEN, as well as nephelo-

1) Jubilee-Volume ZwAARDEMAKER. Arch. nêerl. de Physiol. t. VII, 1922.
’) The analyses were performed by Miss J. E. van per ZANDE, conservatrix, and
by Messrs H. Hooenouprt, analyst and H. Giereina (volontaire).

396

metrically after Lyman. The phosphorus-content was determined (also
after destruction) nephelometrically and also colorimetrically, after
BeLL and Dorsy’s method altered by Briggs.

Both ballast-experiments consisted of: an initial, and a final period,
each of a fortnight, in which the food-mixture contained 3°/, ballast;
intermediate periods of a week, in which the ballast was raised to
15 °/,, respectively lowered to 3°/, and the experimental periods
proper, each lasting a fortnight. In the first ballast-experiment there
were three experimental periods proper, the middle one with an
increased protein-content (10°/, gluten of wheat) and cystin. During
this experiment 40 mgrms of Ca. (as Ca acetate) was given separately
per day, but only 15 mgrs in the final period. In the second
ballast-test calcium was administered separately to such an amount
(at the most 12.7 mgrms per day) that the calcium-content of the
food was the same all through the experiment.

As the diet (without cabbage) was composed of 3 parts of the
food-mixture and 1 part wheat, it contained less than 15°/, oat-
straw, viz. 11°’, °/,.

With a hereatened percentage of ballast or Bedien the procentic
amount of dextrin plus lactose in the food-mixture was lowered in
both experiments.

The food was always made into a pap with had distilled water.
The green-fodder, and in other cases the calcium-acetate was admi-
nistered separately. The animal was weighed every three days.
The weight varied from 3530 to 3570 grammes. The average amounts
per day of calcium given off in the faeces and present in the food
in the various periods of the two ballast-experiments are expressed
in mgr. Ca in the following table:

Experimental-

Initial-period . Final-period
period 5
Ist exp. 30.4 88.4 en 69.3 12.5
Output
2nd exp. 44.1 66.76 2E
Ist exp. 59. — 16. — 46.3
Intake |
2nd exp. 33.6 35. — 36.4

It appears distinctly from both experiments that the calcium-
output in the faeces is increased. The ratio of the output in the
initial period to that in the experimental period in the first experi-

397

ment is about 100: 250; in the second experiment the ratio is about
100 : 150.

That in the one experiment the rise of the calcium-output differed
from that in the other, is no doubt due to the very different amounts
of calcium administered along with the ingested food.

The extra-ballast in the experimental period as compared with
the initial-period (12°/, of the fodder-mixture) amounted in the first
experiment to about 19 mgrms per day; in the second (when no
sawdust plus straw, but only straw was given as ballast) to only
9.4 mgrms. The increase of the faecal calcium-output is therefore,
much larger than the amount of calcium present in the extra-ballast.
That the calcium in the faeces was only for a small part derived
directly from the food is also clear from the fact that especially
in the second experiment the faeces contained almost twice the
amount of calcium present in the ingested food.

The increase of the amounts of faeces (air-dried) that were pro-
duced in the ballast periods, was very large.

The subjoined table gives the production in grammes.

re . Experimental- & .

Initial-periods periods | Final-periods
Ist exp. 5.62 11.9 and 10.5 | 3.35
2nd exp. 3.62 Ale | 3.85

The 12°/, extra-ballast in the experimental periods averaged per
day in the first experiment about 6,6 grms, in the second 4.7 grms.
These values do not differ much from those showing the increments
of the faeces production.

In the first experiment the calcium-contents of the faeces (air-
dried) were considerably higher during the ballast-periods than in
the initial-period; they were lowest in the final-period. (This is most
likely due to the smaller quantity of calcium-salts that were admini-
stered). In the second experiment the calcium-content of the faeces
diminished after the initial-period, which is not surprising if we
_ consider the very great losses and the consequent highly negative
balance. In the second experiment the difference between the output
and the calcium in the food was about double the difference of the first.

The negative balance is no doubt also answerable for the fact
that in the final-period of the second experiment the metabolism of
calcium was much more economical than in the initial-period.

398

Whereas in either period the amount of calcium administered was
nearly equal, the output in the initial-period was about three times
that of the final-period. When comparing the values of the fore-
period and of the experimental period of the second experiment,
we see that whereas the quantity of faeces was about the double,
the Ca-loss in the faeces was about 14 times greater than in the
initial-period.

The calcium-output via the kidney was in the first experiment
during the ballastperiods higher than in the initial- and final-
period; in the second experiment there was a gradual decrease of
calcium in the urine. This is also most likely attributable to the
higbly negative balance.

The figures warrant the assumption of a rise of the calcium-
output in the urine resulting from a great amount of ballast, if the
diet is not too poor in calcium. The quantity of calcium in the
faeces was as a rule at least double the quantity of that in the urine.

Regarding the influence of ballast on the phosphorus output we
only wish to observe that it was not quite parallel to the influence
on the calcium-output. In the ballast-periods the phosphorus-content
of the faeces decreased considerably in both experiments.

In a subsequent paper I intend to discuss the nitrogen-, and the
iron-outputs in these experiments, and to give the results of the
experiments in which we examined the influence of the alkali metals
in the food on the calcium- and the phosphorus metabolism.

From the experiments here described it appears:

1. that an increase of the amount of indigestible matter in the
food causes a greater loss of calcium via the intestinal canal.

2. that not all the calcium present in the faeces is necessarily
derived directly from the food: a large portion of it may be given
off by the organism, from which we may conclude that calcium
plays a rôle in the production of faeces.

3. that in view of this it is only under certain conditions that
an examination of the faeces can show whether in the food or in
a part of it (e.g. caleium-salts) calcium occurs in an available form.

4. that in animals, yielding much milk, feeding with much ballast
enhances the danger of a negative calcium balance.

(From the Chemical Laboratory of the Utrecht
Veterinary University).

Physics. — “On Heats of Mixing of Normal and Associating
Liquids.” By Dr. J. J. van Laar. (Communicated by Prof.
H. A. Lorentz).

(Communicated at the meeting of November 25, 1922).

5. Some Remarks. Before proceeding to the case of anomalous
components we will make a few remarks.

a). So far we have always written n, and n, for the molecule
values. But often n, =1—.x and n,=—z is put, so that n, +-n‚=1.
The differential quotients of w with respect to n, and », can then
also be calculated by the differential quotient with respect to 2 by
means of the equations

Ow dw w Ow
Par sit bop : Pa ance an Ema
This immediatdly follows from w—=n,w, +n,w, and
0w Odwdn, Òw dn, dw dw
dz Òn, de On, da Ted an Dio tt 3 wn

The same thing, of course, holds not only for w, but for every
homogeneous function of the 1st degree with respect to the mole-
cular values n, and n, (e.g. wv).

For a homogeneous function of the O degree with respect to
n, and n, (e.g. w,,v,, ete.; the degree of dissociation of the double
molecules 3 (see further), ete.) we have:

0B 0p 0p dg
ld enen: Ve doalando yous
which follows from:
0B 08 08 0p op
ae at) in Aeg re),
aR +n, Sh and ze a Ze aE (see above)

b). We have seen that when v‚* Wa, —v,°Wa,=0 (i.e. when the
critical pressures of the two components are the same) Av becomes
=— 0 according to (3) (hence also Av, and Av,). But according to
(1) then also w =O (and this holds also for w, and w,).

Now

vv, + Av=n,0,°4+ nr, v,° + Av,
26

Proceedings Royal Acad. Amsterdam. Vol. XXV.

400

hence when Av =O, simply :
; dv : Ov 5
vnd 1,45 bot =] See SS See
On,
so that then v becomes a linear function of z, viz. v= v,° +2 (v,'—,°).
In the supposed case also the following equation may be written

(see § 2):

a a a, a,
ZnS IL ear
v v v, v

0 3

hence also
Ly ==. ee
ie. the critical temperature of the “ideal” mixture is also a linear
function of z, viz. Tr = Tj, + (Tr Ti).
For ¢/, holds:

Min A AC ere Va) a, a,

Van Med (n, v,° +.n, v,°)? v,°” 0”

when Va,/v,° is =Va,/v,° in consequence of the equality of the
critical pressures. In ideal mixtures the critical pressure remains,
therefore, constant = px, = pr, Whatever is the value of «.

6. Associated components.

For the calculation of w we can adopt the whole derivation of
§ 2 unchanged; it should only be borne in mind that, the degree
of dissociation of the double molecules of the components being 8,
and @, in the mixture, that of the pure components will be different,
viz. B,° and g,°. Thence

(n, €, En ns e's) Tar (n, €, + My é'a)o

will not be =O now. For we can write e.g.
a i,
Se ano
when (e',)q is the energy constant of a double molecule and (e',), of
a single molecule. A similar expression applies to e',. Here e', and
e', always refer, therefore, to single molecular quantities. The quan-
tities g, and q, are the “pure” heats of dissociation, i.e. without
the parts referring to the volume contraction (see further below).
For the above expression the following equation may, therefore, be
written :

(e‚ Da “eae (ee ra (e‚)ssa zi By He De—(e, )sga} = (€,')ud Bin

e

nj Wm) M1 si Nn, (te Phn ke
Further it should be borne in mind that @ remains unchanged
on dissociation, for on simple joining of two single molecules to
one double molecule, Wa will likewise become twice as great;

401

hence Wa will have the same value for '/, double molecule as for
1 single molecule.

The same thing is assumed with regard to the heat capacities
k, and k,. There too — especially for larger molecules — no con-
traction of the value is supposed. _

Thus instead of (1) the following form is found:

ve 4a,—0,°Va,)? a
pasta) ote? oe ek 2 tet) a (Lass)
0
The values of w, and w, are found in an entirely analogous way
as in § 2, viz. from (ef. equation (19):

——}} 5 2 a
wg nn, EM Gro W6) ++ (» | ; = st + (»+ Be ‚rates
~ eal

VV, V, 030,

in which further:
Ae = =| wa )+( Do eef de
viv, (v, EK: W)z, (x, EN (va (v,)a,° (v,)4,

en Wi eet B) 4,,

a,
(v,)3,0(v,) A,
as :

1—8,
WS 9 (va + 8, (ve = (v,)igd + B, ((v,e—(@,)s¢ ) = (v,)ud aedee A,

so that w‚)a —W‚)ge = (8,—38,°) A,. In this A, represents the change
of volume (contraction), when 7 the mixture '/, double molecule
becomes 1 single molecule.

This quantity A, can possess a considerable value. The pheno-
menon of the maaimum-density of water e.g. finds its explanation
in the great value of 4,, so that below 4°C. the thermal expansion
is even exceeded by the diminution of volume in consequence of
the progressing dissociation of the double molecules. Above 4° C.
the thermal expansion will predominate *).

; ‘ a : 5
The same thing holds for —~ Av,, so that, taking into account
Vv, 2

that also

Av, =(%,)2,—(1") a9 (vt ee ai (ez —(v,)2,° )=(Ar,) seh ne

Aveda vs) =(or vide Hoda) J=(A,) a0 + (8,82) A,

1) This explanation, given by me for the first time in the van ’r Horr-volume
of the Zeitschr. f. ph. Ch. (Bd. 31, 1899, p. 1 et seq.)) more than 20 years ago
(see particularly p. 12—16), is not yet found mentioned in any handbook. Except
for a few favourable exceptions this is also the case with many other theories,
rules and explanations given by me.

26%

402

we may finally write:

a
w= —6§,° : A
nent (een, )O] +

-+n,(8,—8,") E iin (»+ ) A, | + nn, Vie te) +-

UU, v,

(v, EN (v, ) By

Ir (x = maa) n, (Av‚)ae + (» =f =e) n, (Av,)3,9

In this the quantities

a, A a,
= ra ; = Tl A,
Gat (Pt Geter) z Oh cee

are the total (absorbed) heats of dissociation of the components in
the mixture, on transition of */, double molecule to 1 single molecule.
When we further write:

n, hit! Q, a n, (8,—p,") Q, == Q,

we get finally:
(‚Wa —v, Va) ers

VVV,

w=Q+n,n, (vv Das rk n‚(Av‚)ae SE

Gs )

min (» ate -) Ns (Av )a,0

EE 22°

Taking the same remark into consideration in the differentiation
as in $ 2, we find from this for w, and w,:

EAN AE 40,0, | tr Evo
tet gn) Gone

v ne a.)? ) (2ass)
=| 2090, 49,0, 9 49,0, F | pm AN

a,
a= (» In an) (Av 2) Fa

In the equation (Aass) we now have (see above):

1

Sy

Av = v—v, = 7, Av, + n, Av, =n (Aveo + 2,(Av,).0 +
+ n, (8—8,°) A, + n, (B,—8,") A,
in which the last two terms with A, and A, will be greatly predo-

minant. Even if the critical pressures of the two components
were about the same, so that (4v,)a0 and (Av,)ao will become — 0,

‚ (8)

403

Av will remain comparatively great, because A, and A, will retain
their values.

Hence in associating components the term with Av will still more
greatly predominate in (loss) than in mixtures of normal substances,
because also g, and g, will never be great. Just as with the capacities
of heat, these differences in the energy constants of the half double
molecules and of the single molecules will probably be even quite
negligible. Even more than for non-associated components now

may be put, which values will again not differ much in different
pairs of substances, when the critical pressures of these substances
do not differ too much.

7. Approximative value of §,—8,° with small values of
ji (Or 2).
From the perfectly accurate equation of dissociation’) of the 4st
component in the mixture, viz.:
p+4/ye
(1—#) 8," RE

K.
Lg) K mhd hea

EN se benee ’
2

in which £', is still a function of the temperature, or also

8 1 7 1
B, —_——_—— kK, ; 1. e. Pai eas eig ei
Re En) 4 Bd
; Hiel +B,
et 3
when —= zt is put, follows immediately:
l4-p
B =|/ wa Pilea os a, K, the K, p |
AE) ee Am drek K,
Here is evidentl [7 = 8,° (for p=0 when z=0); hence
TY TE
1+9@
B, = B, NR
148, p

1) See among other things Arch. Teyler XI, 3e Partie, 1908, p. 44 et seq.

404

which for smaller values of w (y) passes into

8, = 8, (1+ '/,(1— 8," ) 9),
so that we get:
« 1+8,
1—a1+8,

Now for small values of 2 we may put 8,1 and ~,=—8,°, so
that finally becomes in approximation:

B, BZU, B (LB p=, B (LB)

(@ small) Br ni te tal SI ee ees

and «8,°(iA—p,°) may be written for n,(8,—8,°) = (l—e) (3, — 8,°).

8. Reduction of the formula for w in normal components.

When we want to test the formulae derived above by some expe-
rimental data, we can only do so with mixtures of normal compo-
nents. With regard to anomalous components (water, alcohol, acids,
etc.) we lack the knowledge of the quantities g and A. On the
contrary we calculated them approximately at the time (loc. cit.)
from the experimental results, e.g. from the volume-contraction of
water-alcohol mixtures. We must, therefore, confine ourselves, to
formulae (1) and (3), and when we apply these also to abnormal
components, we shall be able to find something regarding the probable
values of q and A from the deviations between the calculated values
and those found experimentally.

For Av we found (cf. besides (3), also (3%) and (3%):

3 Walt 1 :
Av=n,n, CE Se) (Va,—Va,)/Va,a,—— (nya,+n,a,)— Va ant,
(mi Sara; 2 v, 5
when
vn Va, > bk Vax, Phy

is written. Therefore, according to (1), with omission of p, w becomes:

or also
dt 1 a v,° deal a,\v,° )
wann, (1—r)?+ — (1-1) l-y n,+n,— }—(1-t) |,
Dyer Wh 6 a, v Os) owe a,/ V, \

o° 5 8 ee
on ite i es Vian

2
Dv vv, lef, Mm a,d,

405

when in approximation m= 7: T7,='/, is put. When 7R7;, is

written for t/o and 7277, for ¢/,, and further
B, bra Et
aar, Jb Tpit”

in which: b;,: bz, can be calculated from (7%, : pr.) : (Pp, : pa), we

get finally :

fy

6
Vv,

w=Tn,n, RTy, — a =. | |
Vo
(10)
1D
bon 5 de) (nr, +-n, nl |
Ve
When eqwimolecular quantities of the components are used,

Bt fand also ===! and we get:

a+

meee
te t)

|

’ 1

Wig = ene ke Uv ®,°) En)

L/T + Treo) 1 v,"

nee (=9 [av gr tna |,
as vo = NV + n,v,°, and approximately 7; = '/, (7%, + Ti). The
latter is strictly accurate only when the critical pressures of the
two components are equal (see § 5 under 6). When by way of
abbreviation

sri nr og bale ey rice 1
(Seas erate Tr,
is put, then finally with R= 2, so that w is expressed in gr. kal.:

2

eer At lie yi |. aoe
og = 5 PT 2) +1/,2,1 1 -V 9) "A= -+@)j]. 109

This formula is, of course, asymmetrical on account of 7%, only
in appearance, in as much as we have placed v,°Va, in v,°Va,—
—v,°Va, outside the parentheses. If we had done this with v,’ Va,
Tj, would have appeared as fore-factor, but then (pz, :pz,)—1
would also have been substituted for 1—1/ (pz,:pz%,). We now hence-
forth take t always <1, so that that component is chosen as the
first, of which the critical pressure is lowest.

In consequence of the fore-factor RT, ='/, %/,.0, w is duly of
the dimensious of an energy. Further only ratos of quantities occur
in (107). If, therefore, the components belong to the same family
of substances, e.g. to the extensive family of “ordinary” substances
(critical temp. between 400° and 600° abs, y=0,9, f= 7,
7 — Up: Op — 2,1, vete), the error “committed by putting v,*} wv,
= by,: by, and a,:a, = az,: a,%, in t and 4g, is certainly negligible.

406

For the ratios in question are about the same for all these sub-
stances — provided only that they be in corresponding states (e.g.
m ='/,) — which will approximately be the case when the critical
temperatures are not too divergent. Only in the fore-factor “/,,0
care has of course been taken by means of the factor 7 that the
corrections in question are duly observed *).
As according to (1)
a a Av Av

wo APE nn ee IR. 4 (Th + Ti.)

UU, 0

(see above), it immediately follows from (107) that

Avy

]
== 4, 12) (LWD) — YA (LD (LFO) (HI)

Vv

from which Avy can be calculated (v = 1).

When the critical pressures of the two components are equal,
then t is =1 and w and Av both become = 0. As we already
pointed out in our first paper, then (i.e. with very small difference
of px, and pz) Ηr is greater than (1—+)’, so that the part with
Av will predominate in w. But if the critical pressures differ some-
what more, the first part will continue to predominate. As will
appear from the calculation in the following paragraph, the part
with Av is at most '/, of the first part, but often it is much less.
Hence the principal term of w remains AP, and this may be repre-
sented by the single formula (# = ‘*/,):

wie Ie Tr lr)

If one wants, therefore, to form an approximate idea of the value
of the heat of mixing w, it will mostly be sufficient to calculate
the said value of AP.

The value of Av will sometimes be positive, sometimes negative.
Not always are the conditions for contraction (Av negative) fulfilled
— see § 3: “As regards the sign of Av” etc. According to the
tables on p. 160—161, 169 and 176 of Kremann’s cited book there
are about an equal number of mixtures of normal liquids with
a positive as with a negative Av. Everything, of course, depends on
whether

(LVO) 2, (AD (1+) > of <0,

) As RT = 287A ils, in which A is about ?%/ for ordinary substances,
Ul, = Io RT. Now a at T=!/, T; is about 1,4a, andv = 0,73 by, so that
we have 2/y = 2%4/,, = TRT, .

407

i.e. whether (in approximation) Wp is < or >1—*/, 4, (1—r).
And, of course, nothing can be said beforehand with regard to this.

9. Some numerical results.

That in case of mixing of normal substances the heat of mixing
is actually =O or very slight (+ or —), when the critical pressures
are about equal, appears among others from the following examples
(compare also Table V on p. 64—65 in Kremann’s book).

C,H;Cl — C,H;Br Pb, = 44,6 and 44,6) |w=0to 3,3(YouNG1903 and KR.)
Dimethylaniline— m. Xylene (, > 35,8 » 35,8)| + 2,8

Amylformiate — Propylacetate (> » 341 » 348)| — 2,0 | grREMANN c.s

p-Xylene — m-Xylene (> » 35,0 » 35,8)| — 2,0 1914
p-Xylene — o- Xylene (> > 35,0 » 36,9) a
m-Xylene — o-Xylene (» » 35,8 » 36,9)| + 2,0

Of the many mixtures studied, of which the critical pressures
are more or less different, we have calculated *) the following ones
according to (10%) for a comparison with the results of the obser-
vation.

1. Toluene-Benzene. Here we have:

Lor, (rp, our peri |

Dy belen BG bela nae tr hele Py ied )
41.6 594 14.3 8490

aol sep ne E80 0.932 | 0.774 | 0.880 | 1.10 | 1.028

For the calculation of 4, = v,°:*/, (v,°+v,°) we may either take
the densities at the temperature of the experiment, or — as v,° and
v,° will be proportional to bj, and bj, — introduce the above values
of 0b, (A is a certain numerical value). We have done the latter.
We now find:
w=='/,< 1,1 562 (0,00462+ '/, 1,03: 0,068{0,120—*/, 1,1 .0,068. 1,744 5)

— 2162 (0,00462 + 0,0117 {0,120 — 0,033?)

— 2162 (0,00462 + 0,00102) — 2162 X0,00564 = 12,2 gr.cal.

ALExesew found 14,0 (from Youne follows 15,8, and Kr. found
18,9).

1) Both in Table 5 for w (on p. 164) and in Table 23 for Av (p, 175) the
“calculated” values in KREMANN's book are all inaccurate, because instead of
the accurate formula derived by me for Av, an approximate one was used. Besides
27/, RT; was put in w instead of 4/»=4/p =7RT,, which in itself already
causes the values calculated for w to be twice too small. Etc.

408

It is seen that here the value of the term Av is about 22°/, of
the principal term.

The discrepancies between calculated and found values — also
in the following examples — must be chiefly ascribed, besides to
experimental difficulties and small approximations in the derivation
of the formula, to the often inaccurately known values of the critical
pressures. Even a slight error in them gives already rise to a com-
paratively great change in the value of (1—r)’.

The following value is immediately found for 4”/, according
to (it):

dof, ==! X 1,1 X 0,068 X 0,087 = 0,00027.

The value 0,05: 100 =0,00050 was found (see Table 21 on

p. 160—161 and p. 175 in Kr.) ’).

2. Metaxylene-Benzene. There we have what follows.

jo | Th Obr | Ty. ad: | T p | Vp | 7 A;
id at a eae 0.864 | 0.608 | 0.780 | 1.20 | 1.053
47.9 562 | 11.7 6580 |

This gives:

w=!l,X1,2X562(0,0185 +'/, 1,05. 0,136 {0,220 -'/,1,2,0,136.1,608})

= 2351 (0,0185 + 0,0239 } 0,220 —0,065 })

= 2351 (0,0185 + 0,0037) = 2351 « 0,0222 — 52,2 er. cal.

KREMANN found 57 gr. cal. The agreement is again very satis-
factory (taking the above remarks into consideration). The term
with Av is 20°/, of the principal term. Further:

BS Yar 00136 >< 0,199 = 000105:

Kr. found 0,15 :100 = 0,00150. The order of magnitude is the

same in every case. :

The mixtures with CCl, as component all present deviations. Now
CCl, is certainly associated (see also Kr., p. 68 and 140), so that
this accounts for the deviations.

}) It is not very clear in KREMANN’s records whether we should divide by 100,
or by 1e (79 + v9 = 195,5. (Cf. p. 175). In the latter case .Av/, would be
= 0,00026, in perfect agreement with the calculated value. As regards Youna’s
value, it deviates considerably from that of KREMANN. He found viz. 0,16, instead
of 0,05 °/,, hence more than 3 times the value. Also for w there are often large
differences.

409

Thus according to calculation the mixture CCl,—C,H, (px = 45,0
and 47,9) would have to give a heat of mixing = + 2,0 gr. cal.,
whereas + 21,4 was found by Youne. The valne of 4”/,, viz. — 0,00130,
found by Youne, points to a pretty great volume contraction which,
however, does not account for the too great positive value for w.
Also the vapour-tension line deviates here.

The mixture C,H,—CCl, (pz = 41,6 and 45,0) leads us to expect
+ 3,9 for w, whereas w is =—8,5 according to Youne. To this
belongs 4°/, = — 0,00070 according to the same author, and accord-
ingly w and Av are both negative.

3. C,H,Ac—CCl,. The calculation of this mixture may be repro-

duced here. We have:

Py Vk

| |

38.0 523.21 13277 7204
0.9189 | 0.9543 | 0.9769 | 1.054
45.0 30052, 1) basco 6875

Ab}. lr, id. T p | Vp | Le | Ze

0.9704

giving:
w='/, X 1,054 X 556,2 (0,006577 +
+ 1/,0,9704 . 0,0811 §0,0231—*/, 1,054. 0,0811 . 1,95433)

= 2052 (0,006577 + 0,013812 §0,0231 —0,0418})

= 2052 (0,006577—0,000245) = 2052 « 0,006332 = 4 18,0 gr. cal.

Youne found — 20,1. Calculation here gives a negative value for
Av, the correction term not being even so much as 4°/, of the
principal term. For 4”/, we calculate:

Bol, == tf, >< 1,054 < 0,0811 X ( — 0,187) = — 0,00067.

The value + 0,00030 was found by Youne. Again w and Av

(found) have opposed signs, which is strange, and renders the accuracy

of Youne’s values somewhat questionable. (Cf. also the last Footnote).

Let us now give a few examples of recognized associated com-
ponents.
4. C,H,—C,H,OH. We have in this case:

P, Va gad Wits) AD

47.9 NGL.G.) Dh, 12 6582
63.0 516.2 8.194 4230

0.8720 | 0.6427 | 0.8017 | 1.177 | 1.044

from which follows:

410

w—="/, < 1,177 x 516,2 (0,01638 +
+17, 1,044 . 0,1280 {0,1983 — */, 1,177 . 0,1280 . 1,64273)
= 2126 (0,01638 + 0,02227 {0,1983—0,0619 })

= 2126 (0.01638 + 0,00304) = 2126 « 0,01942 = 41,3 gr. cal.

But + 120 is found (Young). [WinkeLMann (1872) gives —110].
The term with Av is here 19°/, of the principal term. We calculate
fore?

IIS SC LE CO T280 0, 15604 — 000086.

Youne found 0, and Gururin + (1884).

In the expression Av = (Av)norm—+ 7/5 (8,—8,°) A, (ef. (8) in $ 6)
A,, i.e. the volume contraction on transition of 1 ce We
C,H,OH to two single molecules, seems therefore to have a small
negative value. But in w= Wrorm + Q= wr, + '/, (B, —8,°) Q, =

=d (8, — aC qd area ee A) (cf. e.g. i Weak in $6) Q, should

also be negative then (leaving g, out of account). In reality 11,(8 (8,—8,°)Q,
seems, however, to be about 80 gr. cal., which would point to a
comparatively large positive value of Q, (hence also to a positive
value of A), but seeing the deviating value of WiNnKELMANN, little
can be said with certainty about this. Indeed, we know little or
nothing about the value of p—,.

5. C,H,OH—CH,OH. Here we have:

P, Th | Ab}. | dip eM T p | Vp
63.0 516.2 8.194 4230
18.5 513.1 6.536 3354

0.8959 | 0.7929 | 0.8904 | 1.113 | 1.003

This gives:

wtf, X 1,113 X 513,1 (0,01084 +
4 1/, 1,003. 0,1041 {0,1095'—*/, 1,113. 0,1041 . 1,7929})

— 1999 (0,01084 + 0,01740 §0,1095'—0,0519" 3)

= 1999 (0,01084 + 0,00100) = 1999 X 0,01184 = 23,7 gr. cal.

The term with Av would, therefore, in any case be about 9°/, of
the principal term. Further:

dv/, = 1/,, 1,113. 0,1041 . 0.0576? = 0,00028.

Accordingly more or less these values would have to be found, when
the alcohols were not associated. In reality, however 4’/, = 0,00004
is found, which points to a certain volume contraction in both

411

alcohols. Bose®) found about 0,8 for w at 17°,3. This is considerably
less than 23,7, so that actually heat is liberated in consequence of
the volume contraction.

If water is one of the components, the values of Av and w are
generally much greater. Thus e.g. Bosr*) (w) and Youne (Av) found:

a) CH,OH—H,O | w= — 196 | 4/, = — 0,030
6) C,H,OH—H,O — 114 — 0,026
c) C,H,OH—H,O + 6 — 0,030

To form again an idea of what actually takes place I have once
more calculated the quantities w and Av according to (10%) and (11)
— which formula is, strictly speaking, only valid for normal com-
ponents, but can yet in approximation be also applied for the calcu-
lation of the normal effect also in anomalous components. I have
done so for

6 C,H,OH—H,O. We have then:

aa a Vo | A, | A,

0.5382 | 0.4551 | 0.6746 | 1.467 | 0.8989

P,, | Ti | Ob; Tid

63.0 516.2 8.194 4230 |
217.5 647.1 2.975 1925 |

From this is calculated :

Ge rel Aad OAT, L(0,2153. 1.
+ '/, 0,8989 . 0,4618 {0,3254—1/, 1,467 . 0,4618 . 1,4551 )

= 3323 (0,2153 + 0,06919 | 0,3254—0,2464;)

— 3323 (0,2153 + 0,0055) = 8323 0,2208 — 734 er. cal.

For 4’/, would be found:

oul, == */,, 1.407 , 0.4618 . 0,0790.—= 0,00223.

And thus + 734 is reduced to —114, and + 0,0022 to — 0,0026.

The great volume contraction (for the greater part owing to the

water) certainly chiefly determines the strong liberated heat-effect.
We shall not enter further into this, and only briefly return to

lb) At 21° 0,007 x!/,(32 + 46) = 0,3, which reduced to 17°38 gives 0,8 (see
the tables of L. u. B.).

4) 50 mol. 0/, =64 weight °/) gives at a) —7,77 X Us (18 + 32) — —194 (19°,7)
or —196 at 17°38. Further at 72 weight.) of b) w = —3,55X 1/3 (18 +46) =
= —114 (17°,3). WinkELMANN found the same thing in 1907. And at 77 weight
Oo of c) is w= + 0,50 X 1/2 (18 + 60) = + 19,5 (21°) or +6 at 1793.

412

the question, why the values of “/,. will not differ much in many
cases, as Karz thinks he has observed.

10. Some remarks on the values of “/,..

In the first place it may be stated that in w=AP-+a/,2 Av, AP
is, of course, only negligible when in consequence of great volume
contraction in associating components (chiefly water) the term with
a/pAv greatly preponderates. Only then w/Av may, of course, be
put = “¢/,: in approximation.

But in the second place ¢/,2=4/,2 is not yet always constant
within narrow limits. A look at a table') of critical pressures is
enough to convince one of this. In water p,= 217,5 atm.; in many
elements (metals e.g.) still much higher. In many “ordinary” sub-
stances, however, especially organic ones), the critical pressures will
be about between 30 and 60 atm., as extreme values. And in many
only between 40 and 50 atm.

All this is the consequence of the fundamental atomistic values
of Va and 6, from which the values of Va and 6 for the molecule
can be calculated additatively in all compounds according to fixed
rules (see my papers on this subject already cited in 1).

As an example let us take the following principal elements, of
which organic substances are built up.

Calin ze ONE heit) | |t © Br I

1056 = 34(14) 160(75) ven 60(85) 140 70(50) 125 55--110 165 220

13a 6 3.1 es 2.8 6.3 | 2.854) 6.9 9

10% b/,-q= 21(9) 32(24) 21 25(18) 20 | 20 20 24 24

And as the values of °/,,_ do not differ so very much, this will,
of course, not be the case either for the compounds built up of
these elements, since — as was already mentioned — the values of
b and Va can be additatively calculated from the fundamental values
recorded above.

Before concluding I will just draw attention in this connection
to the fundamental values of Wa in carbon. In four single bonds
the C-atom is towards the outside quite shaded as regards its attract-
1) Cf. eg. p. 7 of my first Paper on the additivity ef b and Va in the J. d.
Ch. ph. (1916) or These Proc. Vol. XVII N°. 8 p. 1220 et seq.

413

ive action, by the surrounding atoms or atom groups (Examples
Ci eclce-u,, CH.Cl, CHC),; etc, ete. —ef. also p. 22° J. d. Ch.
ph.; also SnCl,, GeCl,, etc).

In double bonds, on the contrary, part of the C-atom are left
free again, and is 10°W/a=—1,55, exactly half’) of the normal value
3,1. In triple bonds the whole C-atom can exert an attractive action
towards the outside, so that then 10? Va=83,1.

Accordingly in the compound under consideration the value of
10? Va is 1,55 greater for every C-atom with double bond, than
corresponding single bond. The amount of energy e, which contains
the term — “/,, will, therefore, be smaller by a proportional value.
Wisaut (Ch. Weekblad N°. 24 of 17% June 1922, p. 259) really
states that the value of the energy of a double bond is from 10
to 20 cal. smaller than in a single bond. All this finds its explana-
tion in the theory concerning Wa and 6 for all possible kinds of
compounds given by me in 1916, which theory has, unfortunately,
remained unnoticed by many up to now.

Tavel sur Clarens (Suisse), Sept.— Oct. 1912.

1) Thus e.g. in all aromatic compounds, in C,H, etc.; compare the table on
p. 20 J. de Ch. ph.

Physics. — “On Wuittaker’s Quantum mechanism in the atom”.
By Prof. H. A. Lorentz.

(Communicated at the meeting of October 28, 1922).

§ 1. Some months ago WarirrakKeEr *) has proposed an interesting
model by means of which the quantum properties of the atom can
be accounted for to a certain extent, the model showing in the first
place how it may be that, in the collision of an electron against
an atom, the former loses either no energy at all, or just a detinite
amount of it. In what follows I shall offer some remarks about the
action between an atom and an electron, as it would be according
to WHITTAKER’S views.

WHITTAKPR supposes that, when an electron approaches an atom,
a “magnetic current” is set up in this particle, comparable with the
electric current that is excited in a diamagnetic particle by the
_ approach of a magnetic pole. In this latter case the induced current
makes the particle repel the pole (Lenz’s law) and similarly in the
former case the magnetic current gives rise to a pee tending to
stop the motion of the electron.

The theory takes the simplest form when it is assumed that there
are not only ‘electric charges’, but also “magnetic” ones, accumu-
lations of positive or negative magnetism. By the introduction of
these into the fundamental equations, the parallelism between the
electric and the magnetic quantities can be clearly brought out.

§ 2. Let o be the density of the electric charge, v the velocity of
one of its points, and similarly u the density of magnetic charge,
w its velocity; further d the electric force or the dielectric displace-
ment in the aether, and h the magnetic force or magnetic induction.
Then we have the fundamental equations

dvd ==, (chia, ae we ee ee RED
EON ni RR ee

roth =—(d + ev) ni RS

j ae
rob = = (hw) + <i ea DIE SIMEK (4)

DE. T. Wairraker, On the quantum mechanism in the atom, Proc. Royal
Society Edinburgh 42 (1922), p. 129.

415

The force with which the field acts on unit of electric charge is
given by

1
and there is a corresponding force
1

klade . … e . . . (6)

acting on unit of magnetic charge.

Remarks on the fundamental equations.

1. In order to simplify the mathematical treatment all quantities
occurring in the equations are considered as continuous functions
of the coordinates.

2. We shall suppose that, while points of an element of volume
move with the velocity v varying from point to point, the electric
charge of the element remains constant, so that the density o changes
in the inverse ratio as the size of the element. We shall make a
similar assumption concerning the magnetic charge. By these assump-
tions the distributions, both of the electric current d +ov and of
the magnetic current h + uw are made to be solenoidal, as they
must be if equations (3) and (4) shall be true.

3. For the sake of generality we have introduced different symbols
v and w for the velocities of the electric and the magnetic charges.
These charges may be imagined as penetrating each other and
having independent motions.

§ 3. The fundamental equations form a consistent system and
are in good agreement with ideas and theorems which physicists
would be very unwilling to give up.

The force acting on the electric and the magnetic charges con-
tained in an element of volume, taken per unit of volume, is
given by

1 1
ef +ug=od+uh+—f[ev.h]——[uw.d]

and for the z-component of this force one finds after some trans-
formations

dent DE ID, MGE

et de oy dz Ot

where

27
Proceedings Royal Acad. Amsterdam. Vol. XXV.

416

X, = 4 (d.” dada d,’ rd d-°) + 4 (he ak h‚” ir hz»
4 „=de d, + hz hy, X,=d:dz+ hr hz, etc.

1

This shows that the ponderomotive forces can still be expressed
by means of Maxweri’s stresses and of the electromagnetic momen-
tum G. It should be noticed that this is possible because we have
the positive sign in (5) and the negative sign in (6).

The well known expressions for the electric and the magnetic
energy and for the flow of energy likewise remain unchanged.
Indeed, starting from the fundamental equations, one finds for the
work, per unit of time and unit of volume, of the forces exerted
by the field

HY den
(ef.v) + wg w)= — 5 — div,
kid hy a= )a ny.

§ 4. If the distribution and the motion of the charges are known,
the field can be calculated by means of two scalar potentials ¢, x
and two vector potentials a,b. These functions are given by the
formulae

An r
1 ig 1
ie f v| dS, pia fr dS.
4 ne r Anc r

in which the integrations have to be extended over all space. The
distance from the point for which one wants to determine the poten-
tials for the time ¢ is denoted by 7 and the meaning of the square
brackets is that the quantities @, ete. have to be taken such as they

N a
are at the time f — —.
Cc

In terms of the potentials we have for the field

1 .
d = — — a — grad p — roth,
c

1 . s
h = — —b — grad y + rota.
c

$ 5. We shall now suppose, following Wuitraker, that in the
atom there is a circular ring A, over which magnetism is uniformly
distributed. We shall consider it as very thin, so that we may speak

41?

of a “line”, and we shall denote by a the radius and by & the
amount of magnefism per unit of length. Let the centre VU be taken
as origin of coordinates, the axes VO Y and OZ being in the plane
of the circle, and let s be the distance from a fixed point, measured
along the circle. The positive direction of s will be determined by
the rotation O Y — OZ, and will therefore correspond, as we
shall say, to the direction of U X. We shall finally suppose the
ring to be a rigid body that can only rotate about O X, and we
shall in the first place calculate the couple acting on it when an
electron with charge e moves in tbe neighbourhood.

The force on an element ds is kgds and its moment with
respect to O X akg,ds=akhsds. Thus the resultant couple is

ak | h,ds, where the value of the integral may be deduced from

(3). For this purpose we imagine some stationary surface o having
the circle A for its boundary and the normal ” to which is drawn
in a direction corresponding to the positive direction of s. Then, if
this surface does not intersect the electron,

ret fdrao= 5 fey do 7
s zl n ¢ =—5 fi age re Beg as gts (7)

We shall suppose the motion of the electron to be so slow and
to change so slowly that it may be said, in any of its positions P,
to be surrounded by the electric field that would exist if the electron
were at rest in that position. Then the last integral in (7) has the value
e . N
ere if w is the solid angle subtended at P by the ring R, the
n
sign of w depending on the direction, towards the positive or the
negative side, in which straight lines drawn from P pass through
the surface. Hence, the equation of motion of the ring will be (&
angular velocity, Q moment of inertia)

dy ake dw
dt Arce dt

Q (8)

If this equation is to hold for a certain lapse of time, the surface
o must be chosen in such a way as not to be traversed by the
electron during that interval. N

Now, two cases must be distinguished, the electron passing or
not passing across the circular plane within the ring, or, as we
shall say, through the ring. In the latter case, 6 may be made to
coincide with the circular plane and we shall have, both before
and after the encounter, if the electron is at a great distance,

2t*

418

w—0. In the former case this will not be true. Let us suppose
that the electron goes through the ring once, in the positive direction,
and let A and B be two positions, before and after the encounter,
both far away from the ring. Then, whatever be these positions,
provided only that they do not coincide, we can choose the surface
o in such a way that it is not intersected by the path of the
particle . from A to B, and that w =O at the point A. It is easily
seen that then the final value will be w = 42.
Bij integration of (8) one finds

=a . . lee ° . ° (9)

if 9, is the angular velocity which the ring may have had before

the encounter.

§ 6. We have next to consider the motion of the electron. The
rotation of the ring constitutes a magnetic current

sak rewekrat van. pee ane WA

giving rise to an electric field that is easily determined if we sup-
pose it not to differ appreciably from the field that would exist if
2 were constant. The calculation, exactly similar to that of the
magnetic field due to an electric current (the vector potential b is

first determined and then d = — rotb) leads to the result
d i Òw [as i 0w pk t dw a
Edmon Nen Ade di eee Ancdz °° ba,

from which, combined with (10) and (9), we can deduce that the
force ed acting on the electron depends on a potential

ake he a p

Sepa a hag ar ENC RRR a) vett Bel CHN

If we wanted exactly to determine the motion we should also

have to take into account the force with which, owing to its velo-

city, the electron is acted on by the magnetic field that is due to

the ring and to stationary magnetic charges eventually existing in

the atom, and so the problem would become very difficult. Since,

however, the latter force does no work, we can write down the
equation of energy

imv? =i mu,* — ¥, 5 A a = e . . (13)

(v, the initial velocity at a point where w = 0) and this is sufficient
for some interesting conclusions.

419

Indeed, if the electron has not passed through the ring, we shall
have finally w =0, y=0O, so that at the end of the encounter the
angular velocity of the ring and the velocity of the electron will
again have their initial values #,, v,. This will also be the case if
the electron goes twice through the ring, first in the positive and
then in the negative direction.

If, however, it goes through the ring no more than once, the
final value of w will be +a and according to (12) and (13) the
electron will have lost an amount of energy

ake a“ hie?
err 2e°Q

The ring will have gained just as much. This follows directly
from (9) and also from the remark that, as may be seen by (9)
and (13),

mv +4 Qo
remains constant during the motion.

In the case #,=0O the energy that is imparted to the ring by
an ‘effective’ encounter is given by

a* ke
200

This agrees with Wuittaker’s result. In his calculations he has
confined himself to a motion of the electron along the axis of the
ring, but the preceding considerations show that the theory can
easily be generalized. However, it is also seen that, if in an effect-
ive encounter the ring is to receive the amount of energy repre-
sented by (14), the rotation which may have been imparted to it
by a previons encounter, must first have disappeared in one way
or another.

(14)

§ 7. If, in the case %,—0, the electron is to pass through the
ring for good and all, it must initially have at least the amount of
energy (14). If it has less, it can by no means get beyond a point,
where

Wash MOE e=

oe Wadi roos 8 ei)

Such a point is really reached, the electron returning after having
got to it, when the motion is along the axis. In general, however,
the problem is less simple. The locus of the points which satisfy
the condition (15) is a surface limited by the cirele R and having,
for a somewhat high value of v,, the shape of a wide bag lying
on the positive side of the circle, which forms its opening. An

v \

420

electron that flies into this bag can never leave it across the surface
which it will perhaps not reach at all. Indeed, it may be that,
before the velocity is exhausted, its direction comes to be tangential
to a surface w == const, characterized by a value of w smaller than
the one given by (15). It seems probable that in such a case the
electron, after having moved in the bag for a certain length of time,
will leave it through the opening, but it is difficult to make sure
of this. *)

§ 8. In Whuirraker’s model the ring & is made up of the poles,
of equal signs, of a number of magnets arranged along radii of the
circle and having their opposite poles at or near the centre. It might
seem at first sight that in a structure of this kind the magnets can
be replaced by perfectly conducting solenoids carrying pre-existent
electric currents, so that we can do without magnetic charges.

In reality, however, no satisfactory model can be obtained in this
way. This is seen most easily when the electron is supposed to
move along the axis O_Y. In the magnetic field due to this motion
‘the lines of force are circles around the axis, and therefore the force
acting on an element of current at a point P, is directed along a
line lying in the plane PO X. For such a force the moment with
respect to O X is zero; consequently, neither a solenoid nor a system
of solenoids can be acted on by a couple tending to produce a
rotation about OX.

Thus it would seem that the hypothesis of ‘‘magnetism’’ existing
independently of electric currents is quite essential in WuirTaker’s
model. I need not speak at length of the reasons for which such an
assumption is not to be readily admitted. Let it be remarked only
that the equations (1)—(6), though forming a consistent system, do
not allow us to establish variation theorems of the kind of Hamiron’s
principle. In this principle we are concerned with the difference
between the potential and the kinetic energy, so that, in the equations,
the two energies do not occur in the same way. Now, if there are
only electric charges, we can, as is well known, arrive at an equation
of the Hamiltonian form, in which 4d? takes the place of the
potential and th’ that of the kinetic energy. If there are only magnetic
charges, there is a similar formula, in which, however, the electric

1) An interesting discussion of this question has been given (Phil. Mag. 44, 1922,
p. 777) by Mr. B. B. Baker, wo has considered the case of an electron not moving
along the axis of the ring, without, however, taking into account the forces that
may arise from the existence of a magnetic field,

421

and the magnetic energy bave changed their parts. It is clear that
it must be difficult to combine the two theorems into one.

I must not omit to say that Wurrraker does not want to attach
too great importance to the special form of bis model. He aptly
remarks that, after having obtained a satisfactory system of equations,
we may discard the model by which we have been led to it. What
is especially interesting in Wuirrakrr’s idea seems to me to be this,
that it shows the possibility of a sharp criterion by means of which
it can be decided whether an encounter is effective or otherwise.
Such a criterion there must certainly be.

§ 9. Generalization of the model. Suppose that there is in the
atom a definite closed circuit s, in which a magnetic current 2 may
circulate, the energy being 4 Lc. Then we have the differential

equation
di
1H = = fh. ds,
dt

or, if an electron moves near the atom,
dt e dw
“dt Ane dt’

Take this instead of (8), and combine it with (11). The amount
of energy that is transmitted in an effective encounter (initially
2= 0) is now found to be

e?
QL *

In order to obtain a “vibrator” *) we can link the circuit s with
another circuit s’, in which an electric current can circulate (no
resistance, energy 4 L'v'?); indeed, we have

(16)

dpe ls, di! is
hin, ee
dt „€ dt c
The frequency is given by
1
LS
2acV LL!

If now an electron passes through the circuit s in a time that is
short in comparison with the period, the vibrator receives the
amount of energy (16) and this amount will subsequently be radiated.
It will be equal to hv if

mee" En
— —=h.
c L

1) Cf. Wuittaker, lc. 8 5, p. 139,

122

One can also try to illustrate other phenomena by means of the
model. In its passage from one stationary state of motion to another
an electron may be imagined to go through the circuit s of a
vibrator, so that the energy which it loses is first imparted to the
vibrator and then radiated by it. Conversely, after having taken in
some way from a beam of incident light the energy Av, the vibrator
could give this energy to an electron that passes through it at the
right moment. But in all this we are confronted with very
serious difficulties.

Psychiatry. — “Concordance of the Laws of some Psychological
and Physiological Phenomena’. By Prof. E. D. Wirrsma.

(Communicated at the meeting of September 30, 1922).

The phenomena of consciousness are attended with material
changes in the brain. There is an uninterrupted continuity in the
anatomic as well as in the psychic phenomena. The two groups of
phenomena run parallel. A change in the one will be accompanied
by a change in the other. Whether we consider the phenomena of
consciousness from the psychological or the physiological standpoint,
in both cases the result will be the same, because the changes in
the one differ from those in the other not intrinsically but only in
form. Memory, which we conceive to be the retention and repro-
duction of previous impressions, has been considered physiologically
and psychologically. First Aristorne and afterwards Herine have
looked upon it as a general function of the organised matter. SEMON,
who has written a pre-eminent monograph on the Mneme, deemed
the ordinary terminology inadequate, as it concerned chiefly the
phenomena of consciousness. He, therefore, introduces other terms,
as’ engrams, i.e. the organic changes evoked by a stimulus; the
retention of those impressions, which afterwards may again come
to us as consciousnesses, is the mneme; and the stimuli by which
the action of the primary stimulus can be re-aroused, are termed
ekphorie stimuli. Under certain conditions permanent connections are
formed between the several engrams, which have been termed
“regular tracks”. By the side of this anatomical interpretation the
psychological explanation may be put forward. We know for certain
that every impression leaves an after-effect in consciousness. Mental
tests on secondary function, psycho-analysis, the symptoms of hysteria,
hypnosis have conclusively established the existence of these after-
effects. That these after-effects may become consciousnesses again
through association, is borne out by self-observation and by experiment.
Thus the psychological conception may be formed directly, whereas
for the physiological we have first to pre-suppose all sorts of organic
changes, for we are still completely ignorant of the real existence
of the organic engrams and the regular tracks. In strictness this

424

interpretation is physiological only on the outside; at bottom it is
psychological.

Emotions reveal themselves in two ways: Self-observation tells us
what emotion in reality is, and from the expression of emotions we
deduce what the feelings of the affected individual really are. We
know that these peripheral phenomena play so important a rôle that
some regard the expression of an emotion in reality as the source
of emotion, as a conscious progress. Many psychologists still adhere
to this “James-LANGE-theory”’. However, LEHMANN has shown by dint
of many arguments that emotion is primary and expressional
movement is secondary. One of his arguments is that the change in
the blood-supply, in respiration ete, is posterior to the real emotion.
The experiment upon which this argument is based, is open to
objection, as it is often difficult to make out where exactly the change
in the plethysmogram or the breathing begins. This induced me to
repeat the experiment registering at the same time the psychogalvanic
reaction. In comparing the plethysmogram with the psycho-galvano-
gram the latter appears to be more reliable, as is borne out by the
subjoined curves.

Respiration

| did

Galvanogram

Plethysmogram QQ NN in.

Wen en we WAN

The beginning of the reaction is clearly marked, whereas in the
plethysmogram it is often doubtful with which pulsebeat the reaction
really begins. The subjoined table also clearly indicates that the

Physiological reactiontimes to pain-sensations
in !/199 Sec.

Galvanogram Plethysmogram
220 335
230 360
210 280

210 350

425

reaction-times of the psycho-galvanogram are shorter and much
more constant.

These physiological reactions times, of which I mention only a
few, are considerably longer than the psychological reaction times
to pain-stimuli which occur directly after the touch-stimuli.
~ Thus, although emotion i.e. the psychical, is to be considered as
primary, if is nevertheless a fact that the expressional movements
largely influence the nature and the intensity of emotion. Intense
emotions become less vivid through strong expressional movements.

Having a good cry and screaming lessens our grief, hysteric
affective conditions, which accompany weeping and screaming are
of short duration, the raptus melancholicus. has soon spent itself.
Here we have to do with an inhibitory process of two co-existing
complexes of consciousness. The experience of the violent expressional
movements inhibits the emotion.

This accounts for the custom among some uncivilised peoples of
dissipating grief by selfmutilation. Not only involuntary but also
voluntary expressional movements inhibit emotion. The intensity
of a sad mood is often lessened by assuming the attitude and the
countenance of cheerfulness.

So far we have seen that conscious as well as unconscious
will-acts bear upon emotion in the same way. Conversely, we will
now discuss the way in which emotion affects the will-acts.

Emotions exert a great influence upon other complexes of con-
sciousness. They largely inhibit them, because attention clings to
them tenaciously. Regular thinking is impossible. Voluntary move-
ments are also inhibited. We don’t get on. with our work, all our
activities slacken, and in pathological cases, such as melancholy, a
complete relapse may ultimately set in. Again, this does not apply
to voluntary movements only. Also the unconscious efferent impulses
are subject to the same influence. Cannon’) showed that in cats, in
a state of emotion, the food remained in the stomach longer than
in that of normal cats. Similar inhibitory processes occur in man.
A melancholiac secretes less saliva and fewer tears. This can be
established experimentally.

Furthermore a distinct decrease of motility of the stomach and
the intestine is demonstrable in man. When administering 0,11. K.
in the empty stomach according to Sanmi’s*) prescription, iodine
will be found in the urine and in the saliva under normal condi-
tions after 15 minutes. According to Sauri I. K. is not resorbed

1) CANNON: Bodily Changes in Pain, Hunger, Fear and Rage. 1918.
2) Sanur: Klinische Untersuchungsmethoden I, p. 564 u. p. 568.

426

at all in the stomach, or only after a long interval, so that with a
decreased motility of the stomach the I-reaction in urine and saliva
will appear later than in normal cases. This experiment was per-
formed with some melancholiaes and with some normal persons:

lodine-reaction in urine | lodine reaction in saliva
Melancholy | Normal | Melancholy | Normal
A 105 min. | K 15. min. A — min. | K 15 min.
B 105,65 EL Die) B fost; Ly AS
C DO 5 M (Des 7 op" Ve M een
D 60, N TON ja D — »y N 15.
E Bar O Lie E 90, O 15 san
F Toit; F 45)
G 45,5 G 90
H 60) > H 6D
I 45.» Kabel AS obey

This table shows distinctly the retardation of the reaction in
urine and saliva in cases of melancholy. It is very well possible
that this retardation is not due only to the gastrie function, but
that at the same time a slower resorption has taken place in the
intestine and inhibition in the seeretion of the kidneys and the
salivary glands.

Conclusive evidence regarding the retardation of the movement
of the stomach and the intestine can be afforded by Röntgenograms.

In the morning 150 grs of bariumsulphate was administered with
500 grs of porridge in the empty stomach. Normally the stomach
will then be quite empty again after 4—6 hours. In the stomach
of a melancholiae I found after 4 hours still a very large quantity;
after 10 hours a rather large quantum and after 24 hours still
distinct traces of the bariumsulphate. After a 10 hours’ fast this
patient took food again, so that the bariumsulphate, then present,
may have been mixed up with the food. The latter nce
therefore, is not quite reliable. ;

The decreased motility of the intestine also manifests itself distinctly.
Under normal conditions all the bariumsulphate is removed from
the small intestine after 10 hours. The examination of another

427

melancholiac proved clearly that after this lapse of time still -con-
siderable amounts are present.

In the same way slower motility of the large intestine can also
be established. In one patient the food remained in the large intestine
for 4 days, in others for more than 5 days.

It is evident that relative to the emotions the conscious will-acts
and the unconscious centrifugal impulses are subject to the same
rules.

In discussing the reflexes it appeared that mutual inhibition of
co-existing phenomena of consciousness also applies to simultaneous
unconscious centrifugal impulses. Basinski’s reflex is superseded by
the normal plantar reflex, the sucking- and the gait-reflex by other
movements, arising later, the diminution of the patellar reflex is
the result of centrifugal impulses that are always present, the tonus
of the antagonists diminishes through contraction of the agonists.
All this proves that the co-incidence of involuntary efferent impulses
gives rise to a mutual inhibition in precisely the same way as with
the co-incidence of conscious will-acts. Hereby a complete co-opera-
tion of the muscles is rendered possible.

Closely related to this are the associated movements. When a
child begins to grasp at things with the right band, the left one
accompanies it. A few years later these ‘‘co-operations’ disappear.
They are inhibited. Whence does this inhibition arise? An incessant
flux of impressions passes from the extremities to the area of con-
sciousness, imparting information regarding attitude and position of
the limbs, so that the easiest attitude will be selected and every
undesired movement will be counteracted. At first this occurs arbitra-
rily, afterwards involuntarily and reflexly. A gymnast and a skater
will first try to counteract the unnecessary movements, afterwards
this happens involuntarily. That the inhibitory action is exerted by
these simultaneous centrifugal reflex impulses may be gathered from
the following facts:

Associated movements are strongest in the first years of life.
When the position reflexes begin to develop, the associated move-
ments will gradually cease.

They will recur or intensify in highly emotional situations. The
pre-occupation resulting from them will not only eliminate all com-
plexes of the central area of consciousness, but also the subliminal
position-reflexes will be affected by them, so that the associated
movements of a deeper level will recur. In the same way in con-

428

ditions of dementia, as with dementia paralytica and dementia senilis,
in which a general diminution occurs of the degree of consciousness,
the position-reflexes are affected prior to the associated movements.
It is obvious, therefore, that the associated movements will recur.

Associated movements manifest themselves most distinctly with an
affection of the pyramidal tract, because then the conduction of the
centrifugal impulse, which acts inhibitively, is lacking. This is easy
to demonstrate in patients with cerebral hemiplegia, because in these
cases the associated movement of the paretic leg can be directly
compared with the movement of the healthy leg. In my investigation
I availed myself of the following associated movement. When a
subject, in dorsal position, is instructed to raise the right leg, the
left leg will be pressed down, of which fact the experimenter may
readily convince himself by putting his hand under the left heel.
A distinet pressure will then be perceived, which will increase with
a greater effort of the right leg. The associated movement of the
left leg may be reinforced by opposing a resistance to the movement
of the right leg. The registration of the associated movement happens
in the following way. The left leg is suspended in a loop a little
way above the heel. The loop is attached to a steel-yard by means
of a cord that passes over a pulley. When the leg is pressed down
the force of the effort can be read accurately from the steel-yard.
To the cord is fastened a stylus, which records the movement directly
on a rotating kymograph. In patients with cerebral hemiplegia the
associated movement on the paretic side appears to be much more
pronounced than on the healthy side. In the subjoined curves A’,
A" and A" represent the associated movements of the normal leg;

A’ Associated movement
of the normal leg.

chal / hs Se es. ecg Zer B’ Associated movement
i

of the paretic leg.

ie, Ga deal VTE ne A” Associated movement

yan —— of the normal leg.
eef \ Pe RO crt B’ Associated movement
U

of the paretic leg.

wes el Agfa A” Associated movement
of the normal leg.

RN B” Associated movement
£ of the paretic leg.
Ft.

429

B', B’ and B” those of the paretic leg. In curve I the associated
movement is registered without any impediment to the other leg.
In curve II the leg is weighted with 1700 grms, and in curve III
with 2900 grms.

The annexed table also shows clearly that the associated movement
of the normal side is invariably inferior to the one on the paretic
side.

Curve I | Curve II Curve Ill
normal paretic normal paretic normal paretic
leg leg leg leg leg leg
gr. er. | gr. | gr. | gr. | gr.
162 167 225 975 1247 1175
490 767 427 873 1302 1201
438 151 592 876 1064 1453

Associated movements are on a par with the associations of the
phenomena of consciousness. As known, the laws under which these
associations originate have been reduced to the simultaneous
associations. That this is also the case with the asssociated movements
is evident. The child begins to stretch both hands when grasping
at something, which evolves a simultaneous association. When, in
later years the grasping right hand is accompanied by a movement
of the left one, this is in reality an association effected in precisely.
the same way, in which e.g. the image of a person is called up
when hearing his name.

Associations can be facilitated or inhibited. In this also the asso-
ciated movements bear so close a resemblance to associations, that
the two processes must be considered analogous.

Associations are inter alia facilitated by greater intensity of the
associated ideas. EBBINGHAUS introduced meaningless syllables to be
learned by heart in a certain order. Reproduction in a reversed
order was not possible. Of this MünsrerBERG has put forward an
explanation: In reciting the alphabet, a and b remain for some time
in consciousness. In hearing b there is still a faint after-effect of a.
Therefore, in hearing a, b will be reproduced sooner than, conver-
sely, a will be reproduced in hearing b. In the associated move-

430

-

ments the same phenomenon manifests itself. The intensest associated
movements persist longest. They display a much greater resistance
to the inhibiton. There are people with whom some associated
movements persist through life e.g. the mouth-movements when they
are using scissors.

Associations are also promoted by the intensity of the associating
idea. Memory-images will be reproduced the more readily according
as the associating idea is more intense and distinct. Experience e.g.
teaches us that visual, and auditory sensations arouse associations
sooner and more distinetly than the vague olfactory, and gustatory
sensations. We can observe a similar phenomenon in the associated
movements. The curves obtained from the above experiments go to
show that, when the movement of the one leg is interfered with
by a weight thus inciting the subject to greater exertion, the asso-
ciated movements of the other leg also increases.

In curve II the weighting of both the paretic, and the normal
leg considerably increased the associated movements on either side.
When, as in curve III the weight is very heavy, the demand upon
the paretic leg is so great, that the ensuing associated movement
of the normal leg does not differ much from that of the paretic leg.
Curves I and II also demonstrate that, with a series of movements
of the paretic leg the associated movements of the normal leg
increase in magaitude. This is due to a greater demand upon the
paretic leg consequent on fatigue.

The associations of the phenomena of consciousness can also be
inhibited. Here again the associated movements exhibit analogous
phenomena. As known, the association of the phenomena of con-
sciousness is interfered with by co-existing complexes of conscious-
ness and the degree of the interference depends on their homogeneity.
The reproduction of visual ideas is counterected by other sight-
experiences in a higher degree than e.g. by auditory experiences.
In forming a visual image of a situation, we shut our eyes. Speaking
a foreign language is more difficult than to read it, because the
word in our native tongue arouses many associations which act
inhibitively, whereas the foreign word awakens no other associations
than those called up by the native word. It is just the same with
the associated movements. The impulses exciting them, are ousted
already by the co-existing efferent impulses of the position reflexes.
It is evident, that also here there is an analogy to the inhibition
exerted upon sight-associations by other visual impressions, and to
the inhibition, exerted by the multitude of associations, upon our
efforts to speak a foreign language.

431

The so-called mediate associations occur, when memory-images
flash into consciousness that seem to have no connection with the
associating idea. On closer inspection it will appear that the associ-
ated idea has not linked itself directly to the associating idea, but
to an unconscious memory-image. Without this intermediary the
association would not have originated. The strange freaks of normal
men, of hystericae and in cases of dementia praecox, may often be
assigned to these intermediary ideas unsuspected at the moment of
the association. Afterwards they crop up again by concentrating
ourselves entirely upon the association, or by other means, such as
association experiments, hypnosis, etc. Similar phenomena occur in
physiological processes. Many renal diseases are attended with hyper-
trophy of the heart. The real relation is still a moot point; probably
the enlargement of the heart arises from the increase of the blood-
pressure, which some believe to result again from the retention
of the intermediary products of metabolism, or, according to
others, from an excess of adrenalin-products. It is evident, then,
that here also we have to do with two phenomena mediately con-
nected. A similar example is afforded by hypertrophy of the uterus
in pregnancy. This is not a direct action of the foetus upon the
uterus, as this hypertrophy also reveals itself in extra-uterine preg-
nancy. Now, inquiries have proved that most probably internal
secretion of the corpus luteum comes into play here. So, here again
we observe a connection between the two phenomena through the
mediation of one that has long remained unsuspected. The hyper-
trophy of the mammary tissue in pregnancy is assignable to the
same cause.

We have already referred to the phenomena of ousting the centri-
fugal impulses by conscious will-manifestations and even by other
reflex-impulses, nearer to the threshold of consciousness. Definite
proof of it is afforded by the superseded reflexes, as that of BaBINSKI
and the sucking reflex, and the superseded associated movements.
As stated above, these reflexes have not disappeared; they recur
when the inhibitory influences do not exist any more. In this respect
they resemble retrograde amnesia. Here also memory images are
stamped out by intensely operating, often highly emotional, impres-
sions. The memories closest to the threshold of consciousness, still
exerting their after-effect upon the centre of consciousness (which
peoves them to be still coexistent with the superseding stimulus),
are thrown back farthest from the view-point. We may, then, put
it in this way that HryMaAns’s ingenious idea is applicable to the
superseded reflexes as well as to the superseded thoughts, viz.

28
Proceedings Royal Acad. Amsterdam. Vol. XXV.

433

that their distance-energy is enlarged and their level-energy has
decreased. °

It seems to me that there is another resemblance of some signi-
ficance. Perceptions, as we observed, do not fade out altogether,
they leave traces, which will be present in consciousness again
through association, but which, of themselves, also possess a tendency,
a certain potency to emerge. There is a continual competition among
the subconscious tendencies. Their potency varies with various
conditions inter alia of novelty, emotionality, fortuitous associations.
In ordinary circumstances there is an uninterrupted inhibition exerted
by other ideas. When this inhibition is taken away, as is the case
in dozing and during sleep, these subconscious ideas may be present
in consciousness again. This may be brought about by association,
but surely their own energy may also co-operate. This appears from
the difference in own energy appropriate to various ideas. For
example: a personal name may recall the image of the person, but
the latter does not always call up the name. An accident will be
reproduced more readily when witnessed than when only read
about. That own energy of ideas or perceptions to become central
consciousnesses, which energy has been termed by Heymans distance-
energy, is utilized partly by obviating resistances and, when at the
ingress into consciousness some energy is still left, this remainder
is spent entirely in repulsing the resisting complexes of consciousness
as far as possible into unconscionsness. These conditions occur with
the just-mentioned retrograde amnesia, analogous phenomena of
which are met with in the repulse of some reflexes by others, which
lie still nearer to the threshold of consciousness. But Hrymans also
puts the case that there are hardly any resistances, so that there
cannot be any question about a loss of distance-energy through
repulse. In such a case that energy will be applied in consciousness
as energy of association, of sentiment, of thought and of will. Now,
do similar manifestations also arise with subconscious phenomena?
As regards some reflex manifestations, we are in a position to select
such conditions as are perfectly similar to those required for the
phenomena of consciousness, so that when they occur there will be
no resistances in their way. In this connection we may take it for
granted, that knee-jerks are inhibited by simultaneous centrifugal
cerebral impulses. Affections of the pyramidal tract have disturbed
the conduction of these impulses, so that the knee-jerks are no longer
subject to inhibition. Well then, in these conditions many reflex-
associations occur, viz. contraction of the adductors, and also frequently
of the m. quadriceps of the other leg.

433

I annex a few other examples, the number of which may still
be enlarged.

It is known that the direction of voluntary thinking and acting
is determined by the intentional idea in its after-effect. The bias of
the mind arouses the most serviceable thoughts and motives; the
others are inhibited. This is the course of every process of thought
as well when we are simply designing a travelling plan, as when
we are working out the most intricate scientific problem. The same
holds also for mental development at large. From our earliest youth
upwards there is an unconscious tendency by which the adult mind
is developed from the simplest data. Physiologically we observe the
same process, by which a single ovum develops into the full-grown
body. In either case there is a tendency in the line determined by
the result to be attained, i.e. the intentional idea.

True, this result is not present in consciousness, but for the rest
it is perfectly similar to the intentional idea in its secondary function,
because either of them determines the developing process.

In mental growth the innate tendency dictates a certain trend.
Great disparities present themselves, e.g. in the types of observation
and in individual character. Interest, which is chiefly innate, plays
a prominent role in the formation of the types of observation. The
visual type e.g. shows an affinity for sight-impressions, while it
neglects the auditive-, and the motor impressions. In physical
development we distinguish a similar difference in trend. The fertilized
ovum cell is omnipotent. In it is hidden the power for development
of all tissues. Differentiation of this potency appears after repeated
division of the cell. Some cells can supply only epithelium, others
only connective tissue, or muscular and bony tissue.

From the facts above stated it appears that there is a far-reaching
concordance between the laws of some psychological, and, let me
put it cautiously, some physiological phenomena. Our results justify
us in suspecting that with a fuller knowledge of both groups of
phenomena a psychological equivalent may be found for every
physiological phenomenon.

28*

Physics. “On the Separation of Gas Mixtures by Diffusion in a
Flowing Gas’. By Dr. G. Hertz. (Communicated by Prof.
P. EaRENFEST.)

(Communicated at the meeting of November 25, 1922).

As is well known, the differential equation: Ag=—0O, in which e
represents the density of the diffusing gas, is valid for stationary
phenomena of diffusion in media at rest. This equation does not
contain the constant of diffusion of the diffusing gas at all. If,
therefore, the diffusion of a gas mixture is considered, the ratio of
the partial pressures of the components of the mixture is constant
throughout the space, i.e. unmixing does not occur with such a
stationary diffusion phenomenon. This however, is different, as will
be shown in. what follows, with stationary phenomena of diffusion
in a moving medium. As such a moving medium we take a flowing
gas. Let the velocity of this gas medium be »v, and let it satisfy the
condition div » = 0. The constant of diffusion of the diffusing gas
under definite circumstances be 0, its density e, which for the cal-
culation we shall assume to be small compared with the density of
the gas medium. The quantity of the diffusing gas passing through
the unit surface in the unit of time hence its current density, is equal
to the sum of the diffusion and the convection current; it is:

i=—dgrade + on
For stationary phenomena dwi==0, so that taking into account

that div » = 0, we get the following differential equation for such
phenomena:

1
de grad o)

In contrast with the equation 4 9 =O holding for a medium at
rest, this equation contains the constant of diffusion d. Accordingly
the distribution of the density in space is here dependent upon the
constant of diffusion. If, therefore, a gas mixture is made to diffuse
in a stationary medium the ratio of the partial pressures is constant.
On the other hand this ratio is variable in a moving medium; and
this brings about the possibility to use this phenomenon for the
separation of gas mixtures.

435

In what follows two special cases will be treated, which it has
been possible to realize experimentally, and which can be used for
the separation of gas mixtures. In both cases a gas medium flowing
with a constant velocity » is used, the direction of which will be
chosen as direction of the negative z-axis. For this case the differ-
ential equation is:

v dg *)
6 0x

When we assume 9 =o, for x=0, and e=0O for r=, we
get as a first example the case of diffusion against the gas current.
The solution is easily seen to be:

ae LK

The density of the gas diffusing against the current decreases,
therefore, according to an exponential function, the gradient of which
depends on the ratio of the current velocity to the diffusion constant.
When now a mixture of two gases whose partial pressures for «= 0
are g, resp. Q', diffuses against the current, the following equation
is found for the ratio of their partial pressures as function of the
place :

This distribution agrees in form with the distribution of the partial
pressures in the field of gravitation determined by the barometer

nD
formula, with the exception only that here the quantity 5 takes the

place of the specific gravity, and the whole pressure gradient can
be brought about at a distance of the order of a millimeter.

If this phenomenon is to be used for the separation of a mixture,
the gas present at a certain place, e.g. at «—J/, must be pumped
off. The limiting conditions then become @ =o, for 2=0O and
o = 0 for wl. The solution then becomes:

eso
e=c(- er ’)
vl

in which C is a constant. If, as in practice, e 5 is small compared
with 1, C is approximatiely equal to 9,. We thus find for the

1) Compare S. Horst WeBer, Handelingen van het 17e Nederlandsch Natuur-
en Geneeskundig Congres, Leiden 1919.

436

current density of the diffusing gas, ie. the quantity which diffuses
per unit of time through the unit of crosssection against the current:

ul
t= v0, ¢ ‘

If a mixture of two gases which at «—O have the densities o,
and go’, diffuses, the ratio of the quantities of the two gases which
diffuse per unit of time against the current is equal to:

ita)

tO

This quantity represents, therefore, the degree of unmixing reached
in such a diffusion process; inversely the product vl is determ-
ined by the diffusion constants of the gases that are to be
separated, and by the degree of unmixing required. In order to
make the efficiency also as large as possible, v should be chosen
as large as possible and in accordance with this / small, as follows
from the equation of the current density.

The second case, which in practice has been realized, is the
following one: let again v be the constant velocity of the flowing
gas, and let the direction of the current be that of the negative
x-axis. At a certain point in this current we now admit the other
gas. This gas will then be carried along with the current, and
at the same time be scattered to all sides by diffusion. In this
case the distribution of the diffusing gas is found by integration of
the differential equation :

with the limiting condition that at infinity the density of the diffusing
gas must be zero. When the point where the gas enters the current,
is chosen as origin of the system of coordinates, and the radius
vector is called 7, we find the solution:

in which Cis a constant. The factor — represents diffusion in the
is

medium at rest, the exponential function which is due to the
current, is of the same nature as in the first case; only instead of

7
vr, we have here If, therefore, a gas mixture is introduced

into the current, unmixing takes place in this case as well. Further

437

the same remarks are valid here as in the first case; thus it is
also practical here to choose the current velocity great and geo-
metrical dimensions small to render the quantity attained as great as
possible.

All these considerations have completely been confirmed by expe-
riment. In order to effect the separation of gas mixtures by diffusion
in a flowing gas in practice, it is first of all required that as a medium
a gas be chosen that can be easily separated from the diffusing gases.
This can be attained in a simple way by using a vapour as medium
gas, which can be condensed after having passed the place where
the diffusion is brought about. All the experiments made so far,
were carried out with water vapour of 15 to 60 cm. pressure.
The use of mercury vapour of lower pressure may, possibly, be still
more efficient; this will be further investigated.

The chief point in the construction of apparatus for
carrying out the process described above, is the produc-
tion of a constant vapour current. When a gas passes
over a sufficient distance through a cylindrical tube, a
current is obtained with parallel stream lines, but the
velocity is not constant; it decreases from the axis
towards the walls of the tube, as is represented in

Fig. 1. fig. 1. It is, however, possible to get a current of constant
velocity, though over a short distance only, when the gas passes
through a wide tube with a suddenly decreasing diameter or when
the gas escapes from a vessel through a small hole in the wall.
When in this way the medium gas flows
from a vessel A into a vessel B (fig. 2),
and when the gas mixture that is to be
separated, is admitted to the vessel 5, the
case of diffusion against the gas current is
realized. The velocity of the current can
then always be chosen such that only the Fig. 2.
component of the gas mixture that diffuses more rapidly, diffuses
against the current and reaches the vessel A, from which it can
be pumped off together with part of the medium gas.

This idea was carried out experimentally as follows: the water
vapour generated in a vessel heated electrically, flows through S (tig. 3)
into a tube closed at the bottom by a metal plate D of a thickness
of 1 m.m. This circular plate of a diameter of 28 m.m. has 30
holes of 1 m.m., each, distributed uniformly over its surface.
Through these holes the water vapour enters the vessel V, the
lower part of which is surrounded by a cooling jacket, so that

438

the water vapour is condensed. The gas mixture to be separated is
admitted through the tube G. A part of this mixture diffuses against
the current through the holes in D; this part can be pumped off with
part of the water vapour through the tube

H. The temperature of the water in the

f cooling jacket must be regulated in such a

2 way, that the sum of the partial pressure

q of the water vapour and the pressure of
SY the gas mixture in the vessel V is exactly
< so much smaller than the pressure of the

Q water vapour admitted through the tube,

= that the required current velocity is obtained.

=| The appliances used to attain this regulation,

4, will be discussed later. The method described

has so far been chiefly used to separate

v helium-neon mixtures, and has proved very
satisfactory. Even, when the process of

à diffusion was executed only onee, from such

a mixture containing 30 °/, helium, helium

Tek could be obtained, the purity of which was

: so great, that in a Geissler-tube at a pressure
X Ak of 1 m.m. the neon-lines were not visible

with an ordiuary spéctros cope. Considering
the exceedingly great spectral sensitiveness
of Helium with regard to very small quan-
tities of Neon, this shows already a very
great degree.of purity.

Though the unmixing of the gas mixture

Fig. 3. by diffusion against the gas current was
actually as great as was to be expected according to theory, the
quantities obtained remained below expectation. This may be ex-
plained by considering, that in the method described only part
of the cross section of the vapour current is used, because the gas
must diffuse from the outside into the jets that issue separately
from each hole. In order to deal with greater quantities another
apparatus appeared to be more suitable, working according to the
second example discussed above. This second case is in so far
much more easily realized, as it is not necessary here to keep the
current velocity accurately constant. It is immediately seen that with
a current as represented in fig. 1, also unmixing of a mixture is
to be expected, when this mixture is introduced at a point in
the axis of symmetry of the current. The principal part of the

USGA RERUN AARDE

OA URE EGA TG rn

439

apparatus is reproduced in fig. 4. The water vapour enters through
the tube A, which is ground off at the end, so that the water vapour
leaves the tube in acylindrical jet. The gas mixture enters through the
tube G, ending in a capillary concentric with &, the
end of which is in a plane with the endplane of AR.
Opposite the tube A at a distance of 3 mm. there
is a tube D, the opening of which is formed by a
circular sharp edge of a diameter of 6 mm., and
manufactured from metal for the purpose. The outer
part of the cylindrical jet coming from A is as it
were peeled off by the sharp edge. With a suitable
choice of the current velocity this outer part of the
vapour current practically contains only the com-
ponent of the mixture which diffuses more rapidly ;
this component is separated from the water vapour
by condensation, and collected in a vessel. By far the
greater part of the gas mixture admitted through G
passes on through the tube M with the inner part

Fig. 4. of the vapour current, is also freed of the water
vapour by condensation, and again admitted through G by means
of a circulation pump.

If the apparatus is to work well it is chiefly necessary that the
velocity of the current is accurately regulated, and besides it is
practical to lead the condensed water vapour back; else the water
in the heating vessel would diminish too rapidly. Fig. 5 represents
the whole apparatus. In the glass vessel W, which is 50 cm.
long and has a diameter of 10 cm. the water is heated electrically
by means of a heating wire wound on a layer of asbestos. The
pressure of the water vapour in this space can be determined by
means of a thermometer 7’ suspended in the vapour. This water-
vapour flows through a tube to a bulb B, and from. there to the
tube R of the diffusion apparatus, while simultaneously the gas
mixture to be separated, enters the tube G through a very narrow
capillary tube. By the regulation of the pressure of the gas
mixture before it enters the capillary tube, an accurate control of
the velocity with which the mixture is admitted, is made possible.
The two parts, into which the gas current is split up by D,
pass on through the tubes H M resp. and reach the condensation
vessels C, and C,, which are provided with cooling jackets A, and
K,. Here the water vapour is condensed, and the water runs back,
to W as is seen in the tigure. The part separated by diffusion is
collected in C,, and the rest of the gas mixtures in C,. Both

440

these parts tog ether with some water-vapour leave the appara-
tus each through a very narrow
capillary. The water vapour is
removed by freezing it out. The
separated part is received in a
vessel, the rest of the gas mixture,
however, is again led back to
the apparatus by means of a
circulation pump.

The vapour current is con-
troled by regulating the current
in the heating spiral wound on
W, and the temperatures in A;
and K,. The latter is effected
in such a way that the water
flowing through the cooling
jackets with accurately con-
stant velocity is beforehand led
through a copper tube, surround-
ed by a heating coil, so that
the temperature of the water
depends on the current passing
through this heating coil. The
check on the current velocity
is made possible by the capil-
laries between H and C,, and
between M and C,, these causing
a difference of pressure between
W and C, resp. C, that is in direct
ratio to the current velocity in H resp. M. This difference of pressure
can be measured by the difference of level between the condensed
water in C, resp. C, and the water in W. Neither the absolute
value of the current velocity nor the temperature of (he water
in K, and K, need be known; when the level of the water
in the two tubes with regard to the level in W is such, that
the unmixing of the gas mixture is satisfactory, the heating current
need only be regulated so, that this position is maintained.

It is not necessary to keep the temperature, and with it the
density of the vapour, accurately constant, for both the current
velocity corresponding to a given difference of pressure between the
ends of the capillary tube, and the diffusion constants of the diffusing
gases are approximately inversely proportional to the density of the

®
:

LAE MBS MOE LAD ELT.

(FREY AURELIA INN

EAT TOON ESE EMEA

|
à

NEETER ANS REAR DI ee ead ee

WREDE ACIER SART UITDELEN SERIE
= =

441

. . v . . . . .
vapour; accordingly the relation zs characteristic of the diffusion in

a flowing gas is not affected by small fluctuations in the vapour
density. In order to prevent condensation of the water vapour
against the walls, the whole apparatus is enclosed in a box, in
which the air is heated a few degrees above the temperature in W.

The same degree of the separation is obtained by the first and
the second method. As regards the quantity obtained the second
method however, is considerably better. Only when it is required to
separate small quantities, the former method is preferable, as in
the second method a certain minimum quantity is required for the
circulation.

It is of importance to consider whether our method of the diffusion
in a gas current is more efficient with regard to the separation of
isotopes than the methods used up to now. This new method is
no doubt superior to the usual way of separation by diffusion. It
is, however, possible, that when we apply this method to gases
with diffusion-constants differing as little as they do for isotopes,
small irregularities in the current may have much greater disturbing
influence than in neon-helium mixtures. Nor can it, of course,
be expected that a mixture of isotopes should be completely separated
by a single process of diffusion, for such a process, supposing it
be possible in principle, would require a very long time, as can
be calculated from the above given formulae. On the other hand,
e.g. in neon, a change in the ratio of mixing of the isotopes of
about 30°/, could be expected as the result of one process of
diffusion, so that it might be expected that a fairly far advanced
separation can be obtained after not too many repetitions. It is
not our intention to use the apparatus described above for the
separation of isotopes, as it must undoubtedly be possible to
construct apparatus on the same principle, working considerably
more rapidly.

Eindhoven, 1922. Physical Laboratory of the

“N.V. Philips’ Gloeilampenfabrieken.”’
(Philips’ Incandescent Lamp Works).

Physics. — “On the Excitation and Llonization Potentials of Neon
and Argon’. (Appendix). By Dr. G. Hertz. (Communicated
by Prof. P. EHRENFEST).

(Communicated at the meeting of November 25, 1922).

In the measurements of the excitation and ionization potentials
of neon and argon discussed recently’), the value of 20,45 Volts
measured by Franck and Knippinc was used as the first excitation
potential of helium, in order to determine the absolute value of
these potentials. Since then ‘LyMAN®) succeeded in measuring the
spectrum of Helinm in the extreme ultra-violet directly. [t .can be
shown from his results, that the values found by Franck and KNIPPING
for the critical potentials of helium, like Horton and Davies’ values,
which are in close agreement with them, are too high. As FRANCK *)
shows by a comparison of the values measured optically and electri-
cally, 19.75 Volts must now be taken to be the first excitation
potential, which value is accurate within 0.1 Volt. In connection
herewith the excitation and ionization potentials of neon and argon,
having been measured relatively to helium must also be diminished
by 0.7 Volt so that the following values are obtained:

Neon: Excitation potentials: 16.65 and 18.45 Volts.

Ionization potential : 21.5 Volts.

Argon: Excitation potentials: 11.55; 13.0 and 14.0 Volts.

lonization potential : 15.3 Volts. |

The conclusions relating to the optical spectrum are not affected
by this correction, as only the potential differences are used for
them. Only the term 0.5 s., which corresponds to the normal state
of the atom, must be diminished, and becomes 174000 + 1000 for
neon, and 124000 + 1000 for argon.

Eindhoven. Physical Laboratory of the
N.V. Philips’ Gloeilampenfabrieken.

1) These: Proc. Vol. XXV N°. 5 and 6, p. 179.
2) Tr. Lyman, Nature, 110, 278, 1922.
5) J. Franck, Zeitschrift f. Phys. 11. 155, 1922.

Physics. — “Further experiments with liquid helium. @. On the
electric resistance of pure metals etc. X. Measurements con-
cerning the electric resistance of thallium in the temperature
field of liquid helium.’ (Comm. N°. 160a from the Physical
Laboratory at Leiden). By Prof. H. KaMERLINGH ONNEs and
We Lury,

(Communicated at the meeting of October 28, 1922).

§ 1. Object of the research. Method of preparing the resistances.
The place of thallium in the periodic system of elements, between
the super-conducting metals mercury and lead, made it seem pro-
bable that it would become super-conducting at helium temperatures.

We had at our disposal only rods of thallium from KanrBavM ').
From this Mr. P. J. v. p. Baan, instrumentmaker of the Phys.
Lab., extruded wires of 0.2 and 0.5 m.m. thickness; they were
bright at first, but quickly became tarnished and grey in colour.
At the distance of a few c.m. from the ends of each wire a
second short wire was melted on in a small gas-flame; during
this process the thallium was protected from oxidation by a layer
of melted candle grease. The wire was then wound bifilarly upon
a porcelain tube with a double screw thread baked into it, (these
tubes were made by the Königliche Porzellan-Manufaktur, Berlin and
have been mentioned before in Comm. N°. 152c § 2) and then the
four thallium ends were each soldered to a copper wire, previously
attached to the tube. The resistance thus prepared was enclosed in
a glass tube made by the chief glass blower of the Phys. Lab. Mr. O.
KrsseLRING, in the following manner. The ends of this tube through
which the copper wires protuded were platinised, coppered, provided
with copper caps and sealed up (see also Comm. N°. 133d, p. 60).
To remove the oxidation layer on the 7'/-wire the resistance was
rinsed through the opening at the other end of the glass tube and
dried by a moisture absorber and carbon tube; a tap attached

') According to a letter from the firm the thallium contained the usual amount
of lead; about other impurities nothing was said. The same letter said that the
firm did not prepare any “extra” pure material. M. Levin (Z.S. f. An. Chem. 45
(1905), p. 31) states that KaAHLBAUM-thallium contains 99,910/, Tl, N. Kurnakow,

S. Zemozuzny and V. TARARIN (ZS. f. An. Chem. 83 (1913), p. 200), only say
that they used pure T] from KAHLBAUM.

+44

to this end of the tube was then closed. By means of a Töpler
pump and a suitable arrangement of glass connecting pieces the
resistance was then twice rinsed with helium and finally helium to
a pressure of 51 ¢c.m. was admitted; after this the glass tube was
sealed at the narrow part provided for the purpose. (For the final
form see fig. 2 of Comm. N°. 1606.) In this way in Dec. 1916
were prepared 77-VIII-19/6, diameter 0.2 m.m. with a joint in
the bifilar wire, and 77-IX-19/6, diameter 0.5 m.m.

§ 2. Zero determinations. For determining the zeros, the resistances
PI-VIIL-1916 and PLIX-1916 were placed in glass tubes filled with
liquid paraffin (owing to the war conditions no isopentane could be
had) or with distilled benzine; the tubes were closed by corks, over
which a layer of paraffin was laid. They were placed in ground ice,
and the first measurement was made two hours later and repeated
with intervals of about half-an-hour. The method of measuring used
is either that of overlapping shunts in accordance with KonLrausch,
or that of the compensation of the potential at the terminals of an
unknown and a known resistance, connected in series, by means
of a compensation apparatus free of thermo-forces in accordance
with DiessELHORST and provided by O. Worrr. Enclosing the wires

TABLE I.

Datum. Ti —VIUI—1916. | Ti.—IX—1916.

5 January 1917. 1.1499 02

6 January 1917. 4.439 () |
Immersed in liquid air.
8 January 1917. 4.4415 () |

Immersed in O, liq. and Ho lig.

2 February 1917. 4.447, 0)
6 February 1917. 4.448 () 1.150; 0
13 February 1919. 4.446 {

19 February 1919. 4.446 )

1.150, £2

30 January 1917. 1.150, 0
20 February 1919. |

445

in an atmosphere of helium proved to be completely sufficient;
the results of the zero point determinations are found in Table I
(see p. 444). The zero point measurements are partly due to Dr.
J. M. Bureers, now Professor at Delft.

§ 3. Measurements in liquid helium; determination of the vanishing
point temperature. The resistances were placed in the cryostat
provided with a stirring apparatus shown in Comm. N°. 124c,
fig. 4. For determining the amount of their resistance the second
method mentioned in §¢ 2 was used. The measurements were
always made with both directions of current in the circuit of the
resistances, care being taken that to each. of them the direction
of the current in the compensation apparatus corresponded. More-
over, in measurements below the vanishing point temperature the
galvanometer was observed when the current was reversed in the
circuit of the resistances only (this betrays super-conductivity more
quickly): in the case of super-conductivity there must be no
change of position observable.

The temperatures are determined by the measurements of the
vapour pressure of the helium bath, the connection between pressure
and temperature having been derived graphically from the results
in Comms. N°. 119 and N°. 1475. Close to the vanishing point
temperature the pressure of the bath was followed with the katheto-
meter (June 5% 1919); we give below the diagram of a series
of observations (in this field of temperature 1 m.m. pressure = about
0.01 of a degree).

gota EINE
somme MAAND Ë Le
Fig. ae

In spite of the fact that the wires were not in contact with the
liquid helium, in the measurement of their resistances the galvano-
meter reacted with surprising rapidity to the changes of tempe-
rature of the bath. The results are given in Table II.

From Table II it appears that a constant difference Aw exists for
all temperatures; in spite of this additive resistance’) of 77/-VIII-1916
with regard to 7/-IX-1916 both become super-conducting at the same

') If this additive resistance is taken constant, it becomes 0,00083 W,=0,00372;
we must assume in the meantime that it is largely due to the joint.

446
Hg, corresponding to 0.006 of a degree;

is caused by the pressure variations of the bath over

temperature. The behaviour of 77-VIII confirms the experience gained

with Pb-wires (Comm. N°. 133d § 15), that joints in a wire do not
affect its becoming super-conducting. The unsteadiness of the resistance

a range of 0.6 m.m.

at .2°.33 K.

Tl ATaVL

00000°0 00000°0 00000°0 00000°0 Eee
“p000'0 9} z000 0}
ee ee cee
°9000°0 641000 °%000:0 99000 Pez
890000 °c100:0 82000°0 *9900'0 882
'g100°0 L900°0 ep
690000 '¢100°0 60000 L900°0 672
“L000°0 *¢100°0 *8000°0 6900'0 Soc
¥g000°0 89100°0 °6000°0 6L00'0 tb
00000 1 00000 1 U Zoer [U py |'M6O'oELZ
(© SSRI“? (Mya IITA-1Laa S16I-XIIL 4 | ST6T IITA TL 4 | 7

9°8¢ |

€°6S
== "09
pee)
= OF
—"08

‘Sy ‘ww

yeoo] ul
wnlsHg

447

in this field of temperature thallium is in the same condition as is
shown for mercury in Comm. N°. 133a p. 24, fig. 6. At a current

© TI Vill. 1916.
OT. IX 7916.

©,

0,001

Fig. 2.

strength of 3,1 m.A. through the resistances the resistance falls, thus,
within a smaller temperature range than in mercury; a similar
difference had been found earlier between mercury and tin.') At
T= 2°.32 K. all measurable resistance has disappeared.

§ 4. Highest limit of a microresidual resistance. This limit is found
from the quotient of the smallest observable potential difference and
the threshold value of the current, it being assumed that Onm’s law
still holds. We found:

15 April 1919, for 7/-VIII aa — < 14.100 at p=2.3 m.m. Hg and
2730.K.

—< 24.10—! at p=2.6 m.m. He.
Wanze.k

The difference in the results may be due to the inequality of
temperature, but more to the difference of current threshold value

27 May 1919, for TLIX

of the two wires (see further § 5). If the value for thallium

273°K,

1) This comparison is defective, for as yet the fall of resistance in mercury, tin
and thallium not has observed on: wires of the same diameter by using the same
strength of measuring current. [Note added in the translation.]

29

Proceedings Royal Acad. Amsterdam. Vol. XXV.

448

is compared with that for other super-conductors (Comm. N°. 133d,
p. 67) the retrogression of the limit caused by a greater decrease
of temperature below the vanishing point temperature would seem
to be recognisable in the measurements of wires of different metals,
as has been ascertained already by measurements of one wire of
one metal. But we must point out that this general conclusion
cannot be drawn before the value of the threshold current as a
function of TZ\anishing point—Z’ and of the dimensions of the wire
is known and after it has been ascertained whether a returning
resistance is due to a single ‘bad place”, or whether it is distributed
over the whole length of the wire.

§ 5. Threshold value. At some temperatures we tried to determine
the treshold value of the current, that is the strength of the current
sent through the wire, which again generates a measurable potential
difference. The results are given in Table III.

The two. first observations in Table III show that for wires of
different diameter at the same temperature the quantity - seems to
be much more a constant than the current density. The latter
quantity occurs in the expression for the magnetic field at the surface
of the wire through which a current passes.

F. B. Stisspen') drew special attention to the influence of this field.
The determination of the threshold value of the magnetic field for
thallium by means of external fields, and the comparison of it with
A, derived from the two first observations in Table III] by means

9;
of ee (the wires 77-VII] and 7V-IX therefore being regarded as
r

straight), must prove whether these two strengths of field are equal,
and that therefore the magnetic field is the primary factor in tbe
disturbance of super-conductivity. Then the “bad places” referred to
more than once, are the places with the smallest diameter; the returning
of the resistance caused by the current, occurs first in these places
only. The above mentioned experiment with thallium is prepared
and also a similar one on a more extensive scale with the more
easily manipulated tin; it must not be forgotten, that at the return
of the resistance at great strengths of current such a development
of heat soon takes place, that first the wire and if this melts the
galvanometer is in danger; this makes the determination of large
current threshold values rather risky.

1) F. B. SmsBee, Scient. Pap. Bur. of Stand. No. 307 (1917).

alg
Ele -~ + Oo wm w
Oo OA ae N OS
~ Eu
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50de REE EN VT
OSE
Td
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emi; er 19 ©
dn 3 On if PEEN
DVE B Wiek en
[=
Esa = 0 © ss oO
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Ne So "S

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SE
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EE . A A A
lavf ke lep)
…_ 5
Q:=
ou Owe
LS) an —
c — n
ow . _
— .
a Se LA” ea pin
n an)
Bene
~% EB e
a lep) a
— _— _—
ep) a an
a _ Ka ae
_—
a 5 > a = A
Q 3
<n = 5
Ye) = Te]
N lan |

—

') The two first temperatures in this table are derived graphically by means of
a formula slightly differing from that given in Comm. No. 159 in the „ Discussion”.

*) Referring to § 3 concerning the heat conductivity of helium vapour, yet the
threshold values might have been found greater, when the resistances would have
been surrounded directly by liquid helium. [Note added in the translation].

29*

450

If we assume, that in super-conductivity the current runs only
in an extremely thin layer at or along the surface of the wire
and that each element of a section of this layer ceases to be super-
conducting at a certain current saturation dependent upon the tems
perature, integration over the whole layer yields the threshold current

me 1
and for wires of different diameter we get the constancy of —.
fs

The assumption of current saturation along the surface does not,
however, explain the connection, suggested by SisBre, between the
threshold values of the current and the magnetic field.

Physics. — ‘Further experiments with liquid helium. R. On the
electric resistance of pure metals etc. XI. Measurements con-
cerning the electric resistance of ordinary lead and of uranium
lead below 14° K.” (Comm. N°. 1606 from the Physical Labo-
ratory at Leiden). By Prof. H. KAMERLINGH Onnzs and W. Turn.

(Communicated at the meeting of October 28, 1922.)

§ 1. Object of the research. Method of preparing the resistances.

In Comm. N°. 133d § 133 we reported that “Kahlbaum”’ lead
became superconducting at the boiling point of liquid helium, and
remained so at 4,°3 K., the highest temperature attainable with the
usual cryostat for liquid helium; in § 15 of the same Comm. from
the threshold value of the current at 4,°25 K. the vanishing point
temperature was estimated at about 6° K. The object of the invest-
igation described below was to establish the vanishing point tempe-
rature of lead more accurately, as well as to trace the difference
in the vanishing point temperature of lead and uranium lead (Ra G)
and to follow the course of the change in the resistance of lead
with the temperature above the vanishing point, if possible up to
14°,0 K, the lowest liquid hydrogen temperature. Regarding a possible
difference of vanishing point temperature for isotopes it seemed not
impossible that the occurrence of the superconductivity might be
influenced by the mass of the nucleus. *).

For the preparation of the resistances we used ‘“Kahlbaum”’ lead
and uranium lead (Ra G), of which Prof. Héxigscumip of Vienna
very kindly put 16,5 gr. at our disposal; the atomic weight of
ordinary lead from non-radio-active sources is 207,20, that of Ra G
from Brocerrit used is 206,067). Wires were drawn from both kinds
of lead and resistances prepared from them in the manner described
in $ 1 of Comm. N°. 1604; the chemical properties of the metal

1) Concerning the properties of isotopes see the article by K. Fasans in the
Elster-Geitel-Festschrift (Vieweg) and the Presidential Address to the American
Association at Baltimore, Dec. 1918 by T. W. RicHarps.

2) According to a letter from the firm of May 17th, 1916, “Kahlbaum” lead
contains a trace of Cu and Fe, the total impurity is less than 0,01°/,; in a letter
of Dec. 8th, 1916 they give a more precise calculation of impurity : 0,002°/, Cu
and Fe. For an account of the atomic weight of lead isotopes cf. F. W. ASTON
“Isotopes”, London 1922.

452

made it possible to extend less care on them than on the prepara-
tion of the 7/-resistances, so that it is not necessary that the
resistances should be shut off from the air in a glass tube with
helium gas. We used the resistances Pb-1919-B, diameter 0,5 m.m.
not enclosed in a helium atmosphere, Pb-1919-/, diameter 0,12 m.m.
enclosed in a helium atmosphere and /sotope
P6-1919-/, in dimensions as much as possible
the same as Pb-1919-/ and treated in the
same way.

ELIE S

fl aL ALI E Eh

SLSTLLIDIEPTOETL DX

SE,

$ 2. Arrangement of the cryostat. The eryostat
with which the experiments were made, is
executed by and under the supervision of the
chief of the Techn. Dep. of the Cryog. Lab.,
Mr. G.J. Frm. Roughly speaking, it is the same
as that described in Comm. N°.1246. A charact-
eristic of the present cryostat is that objects to
be measured are surrounded by helium vapour
or gas (the latter at very low temperature); by
using it, the temperature field between the
boiling point of helium (4°,2 K.) and the
lowest temp. obtainable with liquid hydrogen
(14°,0 K.) is bridged over for the first time.
For the arrangement see fig. 1. In the entirely
silvered vacuum glass A, an also entirely
silvered vacuum glass B hangs in an inverted
position, ending in a single silvered glass tube ;
the bell-shaped space inside this glass is the ex-
perimental chamber. In this space are found the
resistances (in fig. 1 there is only one, marked
W) and the heliumgas-thermometer 7. The
upper end of B opens out outside the cryostat
and is connected with the gasholder; £ is
there provided with a regulating tap A for
blowing off (not visible in the drawing). The
liquid helium comes in through the entrance
D; the floater C shows the height of the
helium level. If the tap A, leading to the
gasholder, stands open, the helium will fill
both A and B; at the beginning of the ex-
periment measurements can thus be made
Fig. 1. at the boiling point of liquid helium, If the

SAIENS

453

tap AK is closed, the helium vapour formed will quickly drive the
liquid helium out of the bell-shaped cryostat space; by opening the
tap. K and putting on the electric heating in the spiral 7’, a constant
vapour stream may be sent through the cryostat; the stream may
be brought to the temperature desired by electric heating of the
spiral G; thus the liquid level of the evaporating helium remains
between PF and G. The copper mantle £ inside the bell contributes to
the acquiring of an even temperature over the whole space; further
experiments must show in how far uniformity of temperature has
been achieved with the arrangement as described. The first cooling
uses a great deal of liquid helium. |

§ 3. Resistance and temperature determinations.

The resistances are measured by comparison of the deflections of
the galvanometer, when connected with the extremities of an unknown
and a known resistance (0,001 or 0,01 2 O. Worrr); the resistances
are proportional to the means of the deflections for both directions
of the current, as follows from the comparison of the deflections
for 0,001 and 0,01 &.

The temperatures are determined with a heliumgasthermometer
of constant volume and with open manometer, the height of the
barometer is read from an aneroid. In the measurements of May
18 1920 the zero pressure of the thermometer was calculated to
be about 1140 e.m.; as it was not easy to determine this pressure
accurately, the pressure at the temperature of liquid helium was
taken as calibration point (this temperature followed from the vapour
pressure of the bath).

For the measurements of May 28" 1920 the zero-pressure of the
thermometer was decreased to 290 cm., in order to have less difficulty
with the corrections on the provisional international Kelvin scale,
these corrections in and below the field of liquid hydrogen being
insufficiently known. As two calibration points the tensions of the
thermometer served, placed in liquid helium (May 28th 1920) and in
liquid hydrogen (May 29th 1920); the temperatures of these points
again follow from the vapour pressure of the bath, using the data
from Comm. N°. 1475 and N°. 1565.

For the correction of the indications of the thermometer on the
provisional international Kelvin scale, we had at our disposal the
data of Comm. Suppl. N°. 34a, p. 17, note 4 (obtained from the
data of Comm. N°. 102c), in which B_o54°¢, has been taken zero,

454

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*), in which v is the volume

TBr—T)Bo
Vv

of gas in the thermometer, expressed in, the theoretic normal volume;
may, according to calculation, be neglected even with a large density.

Tio0 Bioo—To Bo
100 v

) At= rr

the C’s

455

and also from Comm. N°. 119 §56 Bio gok. = — 0,000047'); Table
V of Comm. N*.156a gives a resumé of the corrections, calculated
with the above data. In accordance with note 1 and 3, p. 27,
Comm. N°. 156a here B, = 0,000499, Bioo = 0,000476, «ine =
= 0,0036614 are taken, and the influence of the C’s is neglected ’).

New determinations, to be published shortly, of helium isotherms
at 7’= 20°,5, 4°,2, 3°,7 and 3°,4 K. gave provisional new values
for B, which therefore infer the introduction of different corrections
in the provisional intern. Kelvin-scale; they are larger than those in
Table V, Comm. N°. 156a and they do not come into line so well
with those for higher temperatures. For the sake of completeness
we give a comparison of these in Table 1. (cf. p. 387).

§ 4. Temperature of the vanishing point. On May 18% and 28th
1920 all three resistances proved superconducting in liquid helium
and. behaved, therefore, in the usual way. After this the cryostat
was gradually brought to a higher temperature by electric heating
of the vaporised helinm. At a certain moment the galvanometer
moved quickly over 35 e.m. on the scale and the vanishing point
was apparently reached; the suddenness of the deflection speaks
well for the usefulness of the cryostat if not too high demands are
put upon it. A repetition of the heating (very gradually) confirmed
the first result. While the temperature was kept constant the thermo-
meter was read at the vanishing point. The results are given in Table III.

TABLE III.

Data. Filling. Pas thermom. in Tue, uncorrected ru t. T.
local m.m. Hé.

May 18, 1920.| I 263.6 6.2 0.58 6.8 K.
May 28, 1920.| I 73.9 a. 1.0 0.15 a. 1.2
bY Td, 0.15 b. 7.25

B
1) The B= — 0,000047 is that derived according to pv = RT + a the B’s

‘ : : BY! .
further mentioned in this number are those according to pv = RT (: + =) in

agreement with the change of notation mentioned in note 360 of Comm. Suppl. N°. 23.

*) These values for Bo, Bioo and «ine must be retained to get the corrections
on the provisional internat. Kelvin-scale. Measurements have sliown that it would
have been more correct to use By =0,000513, Boo = 0,000492 and «; He =
0,0036613 (Comm. N°. 1025, Table | and Com. N°. 1564, p. 22, note 1); this
would lead to a second provisional intern. Kelvin-scale (helium-Avogadro-scale) for
which reason we retain the first B's.

456

In filling Il a is calculated by interpolation between calibration
points 20°,24 and 4°,07 K., 6 by using only the calibration point
20°,24 K. in the same way as in filling I only calibration point 3°,60 K.
needed to be used.

The agreement between the measurements with filling I and II
is bad. If in filling Il we calculate, with the pressure increase
of 10,3° mm. per degree, the temperature of the helium on May
28th, 1920, the calculation yields 4°,27 K, while the vapour pressure
gave 4°,22 K (table II); this is in favour of the measurements on
May 28%. If we further take the large Af's in filling I into
consideration, a determination with filling I deserves less confidence
than one with filling I]. We take T' vanishing point lead = 7°,2 K,
although it is still desirable to make a more accurate determination.

§ 5. Comparison of the vanishing point temperatures of lead and
uranium lead (Ra G).

On May 18, 1920 the cross-thread of the kathetometer was
adjusted to the mercury meniscus in the open tube of the thermo-
meter at the pressure belonging to the vanishing point temperature
of Pb-1919-/ (the meniseus in the closed tube must of course always
be kept on the same mark).

After a decrease of temperature /sotope [b-1919-/ was inserted
in the resistance circuit and the temperature again raised. If the
galvanometer moved, because the resistance passed through the
vanishing point, the meniscus in the tube of the thermometer passed
the cross. thread; this phenomenon was certain up to 1 mm. Heg:
“Kahlbaum” lead, atomic weight 207,20 and wranium lead (Ra G),
atomic weight 206,06 have the same vanishing point temperature within
the accuracy of */,, degree. The same result was yielded by P5-1919-5;
an influence of the smaller current density in consequence of the
larger diameter could not be detected (the strength of the measuring
current was always 7,8 m.A.).

§ 6. Resistances above the temperature of the vanishing point.

The results of these measurements are given in fig. 2; the point
most to the right, placed within a square, is the result of a mea-
surement in liquid hydrogen. As vanishing point 7°,2. was taken.
To make the curve join on properly to the one in the field of liquid
hydrogen it must be traced as in the diagram; that is why corres-
pondence with the points marked is defective. The broken crosses
have the following meaning: if the difference between the vanishing

457
point temperatures found on May 18 and May 28 may be
attributed entirely to At having been taken too large on May 18",
all the other temperatures must be recalculated, this recalculation
yields the crosses. Although this approximation is theoretically not
quite correct, as 7’— At and not 7’ ought to rise at every temperature

in the same ratio, yet the results are in favour of the suggested
assumption.

6570 9,0 11,0 i30 AT
Fig. 2.
e Pb—1919—TI,
© _ Isotope Ph—1919—I, 18 May 1920.

(4) Pb—1919—B,

net Pb-1919-2R 28 May 1920.

* Reduced observations: § 6.

Chemistry. — “The Action of Sodiwmamide on Pyridine, and
some Properties of a-aminopyridine”’. By J. P. Wipaur
and ErisaBera DiINGEMANSE. (Communicated by Prof. A. F.
HOLLEMAN).

(Communicated at the meeting of December 30, 1922).

Through TscarrscmBABIN's *) beautiful researches @-aminopyridine
has become easily accessible. This investigator found that sodium
amide acts on pyridine as follows:

1,H,N + NaNH, = C,H,N.NHNa + H,.

On decomposition of the reaction product with water, aminopyridine
and sodium hydroxide is formed.

As we required this substance as starting material for synthetic
investigations, we have applied the method of preparation found by
TSCHITSCHIBABIN. Though also in our experiments a-aminopyridine
was formed as chief product, we found other substances than the
Russian investigator among the by-products.

We experienced that the action of sodium amide on pyridine can
take place in different ways, dependent on the nature of the sodium
amide preparation used. We have prepared sodium amide according
to TiTHERLeEY’s indication by the action of carefully dried ammonia
on melted sodium at 350—400° C. The preparation obtained was
a pure white, showed a crystalline fracture, and contained no free
sodium. This preparation did not react with pyridine. A preparation
prepared at 300°, reacted very slowly with pyridine. In this expe-
riment very little e-amino pyridine was however, formed; further
a little y-y-dipyridyl, and some other products, which we did not
examine.

A sodium amide preparation of KanrBaum, which was pretty
impure, as it contained free sodium and also sodium hydroxide,
acted vigorously on pyridine, as TscHiTsCHIBABIN states. Another
preparation of KanrBauMm, which was apparently much purer, acted
in exactly the same way. A mol. of pyridine is diluted with toluene,
and this mixture is heated with « mol. of finely powdered sodium
amide at 120—125° for seven hours.

1) Journal de la Société Physico-Chimique Russe, 46, 1216 (1914).
Chem. Zentral Blatt 1915. I. 1065.

459

We have decomposed the reaction product with water according
to TSCHITSCHIBABIN’S direction, dissolved it in ether, and distilled
it at a pressure of 15 m.m. The bulk went over at 104—125°,
and was almost pure aminopyridine in agreement with the records
of the investigator mentioned. At 180—180° and 15 m.m. an oil
distilled, which soon gets a dark colour when exposed to the air.
After some time white crystals separated out of this oil. Recrystallized
out of water these crystals became colourless, long needles melting
at 73°. This substance is the hydrate of y-y-dipyridyl, which has
already been described by ANDERSON. After drying in a vacuum
exsiccator we obtained the y-y-pyridyl itself, which melts at 112°.
We identified this substance by analysis and by oxidation with
potassium permanganate. We obtained white crystals melting at
307°, which agrees with the melting-point of iso-nicotinic acid. On
action of picric acid on y-y-dipyridyl, both dissolved in alcohol,
we obtained a picrate crystallizing in fine yellow needles, and
melting at 252°. As appears from analysis this picrate contains 1
mol. of picric acid to 1 mol. of y-y-dipyridyl. With anhydrous acetic .
acid and zine dust the y-y-dipyridyl gave the intensive violet colour
reaction, which was lately described by Dimroru and Hrenr.

There are still some more substances to be found in the oil that
distilling at 130—180° and 15 m.m. pressure. After the bulk of
the y-y-dipyridyl had been removed from this oil, we treated the
liquid with hydrochloric acid. Two chlorides were then obtained,
which both crystallized in white needles. After recrystallisation from
diluted hydrochloric acid one melted at 115—116°; the second
melted above 280°. The latter substance appeared to be the salt of
y-y-dipyridyl.

We have liberated the base from the chloride of 115—116°, and
obtained white crystals melting at 94—95°. This melting-point agrees
with the «-a-dipyridyl-amine (C,H,N.),NH, which was obtained by
SremnAusrr and Dinpotper') from a-chloro pyridine and «-amino
pyridine by heating with barium oxide.

The nitrogen percentage of our crystals, which melt at 94—95°,
agrees with the value calculated for dipyridyl amine.

TSCHITSCHIBABIN says that this dipyridyl amine is formed through
the action of two molecules of pyridine on 1 mol. of sodium amide,
but does not yet describe the experiments from which this appears.
When speaking of the action of 1 mol. of pyridine on 1 mol of
sodium amide (the same way as we performed the reaction) Tscxit-

1) Journ. f. prakt. Chem. 93, 393 (1916).

460 ’

SCHIBABIN does not mention the dipyridyl amine. He prepared the
dipyridylamine from a-chloorpyridine and a-aminopyridine by heating
with zine chloride, and gives as meltingpoint 86—87°.

We have prepared a picrate from the dipyridylamine, which melts
at 227°.

Our observations on the melting-points of dipyridylamine itself,
on the salt with hydrochloric acid, and on the picrate of this base
are in perfect harmony with STrINHÄUSER and DieporLper’s records,
so that we have no reason to doubt the identity of our preparation.

The investigation of the components of the oil that goes over
at 130—180° and 15 m.m. pressure, was not yet completed then,
for a large part of this oil remained liquid after treatment with
hydrochloric acid. We removed the hydrochloric acid from this
liquid part, and then distilled the oil at ordinary pressure. We. col-
lected three fractions, viz. of 293—295°, of 295—300° and above
300°. The first two fractions had a nitrogen percentage of 13.9°/,;
the fraction above 300° had 16.4°/, of nitrogen. From this last
fraction a little dipyridylamine was still deposited. The first two
fractions were joined; this liquid appeared to be strongly unsaturated:
it immediately decolours a solution of permanganate and soda at
ordinary temperature. We have subjected part of this liquid to the
oxidation with sodium permanganate in sulphuric acid solution. A
white substance, which crystallized in white leaves and melted at
74°, could be isolated. The nitrogen percentage of it was 8.0 °/,.
This shows that it cannot be a dipyridylamine or a dipyridyl.

Besides these crystals, a viscid liquid was obtained from the oxi-
dation product. The investigation of these substances is being con-
tinued.

It appears from all this that on action of sodium amide on pyri-
dine there are formed, besides aminopyridine, several other pyridine
derivates, among which the y-y-dipyridyl seems to preponderate
quantitatively. TscuirscHiBaBIn likewise observed by-products in the
reactionproduct which arises from sodium amide and pyridine.
After the e«-aminopyridine had been distilled off, he states that an
oil went over which distilled at 120—180° and at 15—20 m.m.,
and besides a fraction that went over at 180—250° and 15—20 m.m.

From the fraction of 120—180° crystals are deposited which,
after recrystallisation from benzene, melted at 158°. TscHiTSCHIBABIN
supposed these crystals to be y-aminopyridine, but he could not
identify the substance for want of material. From the oil distilled
at 180—250° this investigator isolated the «-a’ diaminopyridine ;
there were also other substances present, which he did not identify.

461

In many experiments we prepared some hundreds of grammes of
amino pyridine; the reaction always proceeded as we described
above. We never observed a substance with a melting-point of 158°;
nor did we ever observe a diamino pyridine.

Accordingly the action of sodium amide on pyridine can evidently
give rise to the formation of different substances. We have not been
able to find out why with some sodium amide preparations amino
pyridine was not formed. Addition of small quantities of water or
free sodium had no influence on this. We also caused sodium to
act on a mixture of pyridine and toluene, both at the ordinary
temperature and at the temperature of boiling. In this case there
was formed a tough amorphous mass, insoluble in water and in
organic solvents, soluble in acids. By extraction with ether we could
isolate only a small quantity of y-r-dipyridyl. This result is in
accordance with the early experiments of ANDERSON.

The formation of the important quantities of y-y-dipyridyl in our
amidisation seems, therefore, not to be in connection with a possible
percentage of sodium in the sodium amide preparation used.

As amino pyridine seems comparable with aniline, we examined
the action of oxidizers on this pyridine base. For so far as we know,
nothing is known about this.

Bichromate and diluted sulphuric acid change a diluted solution
of amino pyridine only slowly at ordinary temperature. When the
mixture is left standing for some days, the liquid gets dark. From
this solution an amorphous green substance is isolated, insoluble in
water, alcohol, and ether, soluble with emerald green colour in
diluted hydrochloric acid. On evaporation of the hydrochloric acid
an amorphous blue substance was left behind. At 90° the action
of sulphuric acid and bichromate on amino pyridine takes place
more violently; and amorphous products are also formed. In these
experiments part of the amino pyridine however remained unchanged.

The action of potassium bichromate in acid solution on this base
takes place much less rapidly than in case of aniline.

The action of potassium permanganate proceeds in an entirely
different way. Amino pyridine is rapidly changed by permanganate
in acid solution; after a few minutes all the permanganate has
disappeared. When a diluted solution of amino pyridine is added
to a diluted permanganate solution containing soda, a slow action
takes place. When, however, first a neutral permanganate solution
is added to a diluted solution of amino pyridine, and then a few
drops of 10°/, sodium hydroxide, a change of colour is immediately
seen. When we start from a 0.1°/, solution of amino pyridine, the

462

liquid first becomes dark violet, then pure blue, after a few minutes
the colour has become emerald green. This green colour does not
change again, when there is no excess of permanganate present. If
the solution of the amino pyridine is somewhat more concentrated,
the green colour at once sets in after a transient dark colouring.

This reaction is characteristic of amino pyridine and very sensitive.
In acetyl amino pyridine this colour reaction does not set in at the
ordinary temperature until after some hours, soon however on boiling.

Whether the acetyl rest is split off primarily here, has not yet
been examined.

A more detailed account of the observations discussed briefly here
will be published in the Recueil des Travaux chimiques.

Physics. — “On Centres of Luminescence and Variations of the
Gas Pressure in Spectrum Tubes at Electrical Discharges’ 11. *)
By Dr. L. HAMBURGER. (Communicated by Prof. H. A. Lorentz).

(Communicated at the meeting of October 28, 1922).

§ 1. Zntroduction.

Experiments made by the author in 1916 showed that continuous
current-discharges when passing through not too rarefied gases, gave
rise to differences of pressure, the value of which, with sufficient
current density can amount to thirty per cent of the total pressure.
A first communication on this subject appeared in the author’s thesis
for the doctorate in the beginning of July 19177). In these investi-
gations such variations of pressure were observed in numbers of
gases of very different natures, as argon, neon, helium, nitrogen,
hydrogen; it was found that the effects observed are very great in
argon, hardly perceptible in hydrogen, and it was seen that the
pressure effect must increase with the intensity of the current (loc.
cit. p. 94), and with the root of the moleculair weight (loc. cit. p. 107).

Four months after the publication of this Thesis for the Doctorate
F. Sxaupy*) published a sbort paper,in which he mentioned differences
of pressure in continuous current discharges observed by him (only)
in the case of noble gases; these differences of pressure were small
compared with the effect found by us owing to the small current
density applied by him.

In April 1920 the author of this communication *) published some
further theoretical views and quantitative calculations about the
effects found, F. Skaupy confining himself in the course of the same
year to some qualitative remarks‘), which indeed referred more to
the phenomenon of electro-striction, which in our opinion can only
play a subordinate part.

Finally in the middle of 1922 there appeared a publication by
A. Révrrenaver*) on an important experimental investigation, in

1) Cf. for l: L. HAMBURGER, These Proc. Vol. XXIII N°, 2 and 3, p. 379.

2) L. HAMBURGER, Thesis for the doctorate, Delft 1917. Cf. These Proc. 20,
1043 (1917). Zeitschr. f. Wissensch. Phot., 18, 1 (19).

3) F. Skaupy, Verh. d. Deutsch. Phys. Ges. 19, 264—’67. Nov. Heft, °17.

4) F. Skaupy, Zeitschr. f. Physik 2, 215. Aug. Heft, °20.

5) A. RürreNAUER, Zeitschr. f. Physik 10, 269—274 (22).

30
Proceedings Royal Acad. Amsterdam. Vol. XXV.

464

which the variations of pressure of noble gases were subjected to
a closer examination and the dependence of the effects found
on different variables was given in an approximative “empirical”
formula.

§ 2. Purpose.

After having thus established our priority, we set ourselves the
task :

1st. to show that the experimental results obtained by A. Rür-
TENAUER in his extension of the investigations on the pressure effect
correspond to the theoretical formulae developed by us in J, in
which also the practical part of RürrrNAuwR's empirical formula is
included ;

2>d. to prove that serious objections may be raised against SkAuPyY’s
theoretical view of the pressure effect;

3d, to draw further conclusions from RÜrreNAUER’s important
determinations, also in connection with our earlier data on this
subject, and our objective, quantitative determinations on light
emission in continuous current discharges in spectrum tubes likewise
published in our Thesis.

§ 3. Formula for the calculation of the pressure-efject.
RUTTENAUER gives the empirical formula:

AGVM I
Ap = f ———..

Q

in which Ap represents the difference of pressure found, fa constant,
A the current density, g the gradient of tension, M the molecular
weight, p the total gas pressure, / the length of the pos. pile, Q
its cross section.

It is seen from this that Rirrenaver finds experimentally that the
pressure effect would be in inverse ratio to the total gas pressure’),
whereas the author of this paper found — also experimentally
that with not too great variations of p, Ap varied little, if at all,
with p. °)

How is this difference in result to be accounted for ?

1) Which was, indeed, also mentioned by F. SkAupy in his first publication
(1917).

2) RUTTENAUER is erroneously of opinion that it would have been found both by
me and by SkaAupy that in argon the pressure effect is in inverse ratio to the
gas pressure. It was on the contrary observed by us that within certain limits
the pressure effect showed a very slight variability with regard to the gas pressure.

465

On comparison of Rirrinavuur’s researches with ours it appears
that we made use of comparatively narrow capillary tubes as circuit
of the current, the German investigator on the other hand of com-
paratively wide tubes. We derived, however, already before, that
two different formulae must be valid for these cases, and this as a
consequence of the fact that in the case of wide tubes the laws of
PorskuILLE should be applied when taking the diffusion phenomena
into account, for narrow tubes those of KNupsen-Lanemuir. For in

Q*)

; A
the first case the electric mass-transportation c,—— / may be put
ale

D' 7 3 *
En Pa) [es

in the second ease to:

D° pp, ed ak)
ER Ma Ge
107 Pp M

In the first case the theoretical formula for the pressure effect —

equal to:

oe nD?
taking into account that Q= Tae for tudes with round cross-section

— is equal to:

AO” so. Llp ad gnd
p= fh p= fa VEN MoO. OE
Pa: Pr P Ji ap D* + Ji a'p Q ( )
in the second case to:
AOR M4, PUPA 3)
A» =f, —.—VMU=f:—.—VmM etheen CER
P Nie a dD Ss a! D ~ ( )
in which
6 3 C, =) 2 4
SS Es We Je ed dk and a =a—
h (Vad au J GAT 5 mr

When on grounds to be given later, the gradient g is taken
inversely proportional to a, we may write equations / and // as
follows:

TN a a aaa eth a teat EEE
p Q

resp.

1) In which cj is a constant. Compare further Equation 9, p. 390, These Proc.
XXIII, No. 2 and 3. The factor Q has been introduced, because A now denotes
current density, in our former paper current intensity.

3) Compare Equation 3, p. 382, These Proc. XXIII, No. 2 and 3, 1920.

3) Compare Equation 1, p. 582, loc. cit.

*) These equations have been obtained from the Equations 1 and 3, p. 382,
These Proc. XXIII, 2 and 3, after multiplication by 1/p. This has been done on
the strength of what was said in footnote 3, p. 385 of our paper of 1920.

30%

466

Bide
Ap=fhgn VH. or nn EN

in which equation /// must be valid for tubes the diameter of
which is large with respect to the free path of the corpuscles, which
is actually the case in Rérrenaver’s experiments. It is seen that
equation /// is identical with Rirrmnavurr’s empirical approximative
formula.

§ 4. On the influence of the potential gradient on the pressure effect.

The “empirical” introduction of the potential gradient by Rirren-
AUER in the pressure effect equation rests on the testing by three
kinds of observations:

a. the dependence of the observed values of the pressure effect
on the potential gradient with one and the same current tube and
the same gas with different current densities.

b. the dependence when the diameter of the discharging tube is
varied ;

c. the dependence when the nature of the gas is changed.

With reference to a we must remark that a critical consideration
of the values published by Rirrenaver shows that the variation of
the gradient is irregular, and besides smaller than the deviation of

the values found for a interse, which values should be appro-
ximately constant. Thus in table 4 p. 272 of Rirrenaver’s publication
the gradient for argon varies e.g. between 1,87 and 2,36, while the

p&p
Ag.iVv M
4,98. For the rest the uncertainty in the determinations of the
gradient seems to have been considerable. Where in our Thesis the
gradient decreased with increase of current density, it appears to
increase in a slight degree in the investigations recorded by Rürrer-
AUER in table 3, whereas it decreased in a great degree in table 5.
For this category of cases a constant value had, therefore, better
be substituted for g, and the empirical formula becomes identical
with our theoretical equation (1).

This is, therefore, in harmony with the statement expressed in
our former publication (loc. cit. p. 390) that ‘in the case that the
nature of the bearers is not modified” (bence for a definite gas) and
“with not greatly varying tension” (potential gradient) a is a constant.

With reference to case 6 we remark that the experimentally determ-
ined influence of yg is unmistakable. So far as the consequences of

“constant value” as a maximum varies between 3,70 and’

467

g for a definite gas are concerned, this influence is also theoretically
comprehensible. It already follows directly from the equation (4) of
our former communication (Ll loc. cit. p. 384) which is based on
the equation of motion of the electrically charged particles in the
electric field, and from which appears the proportionality with the
potential gradient V, provided the nature of the bearers undergo
no change with V.

Already for this reason we may express this also in the equation
of the mass-transportation by the electric current:

1 760
mass-transportation = — Q.A.—. 2,32 10-4 3)
a I.

: AGidl 1
(equation (9) communication I), by replacing — there by a factor
a

{ 1
bg, in which 6 is a constant for a definite gas. Hence — —=b or
; a.g
ag = constant.

Let us also try to derive this directly from the nature of the
electric conduction, and at the same time ascertain from it whether
or no 6 has the same value for different gases. We then remind
the reader that equation (9) of communication [ teaches us that the

1
pressure effect must be proportional to the part — of the conduction,
a

which takes place through ions charged with mass. This part is in
direct ratio to the concentration of the ponderable ions. The problem
may, therefore, be reduced to the question whether increase of g
can cause increase of the concentration of the ions. In case of
proportionality the equation ay = constant may then be applied. *)

This relation will actually have validity for electropositive and
noble gases, when J. Franck and G. Hmrtz’s?) elementary theory
is adopted, according to which, as is known, perfectly elastic collis-
ions between electron and atoms are assumed to take place, till —
under influence of the electric field — the electron has passed over
such a distance, and in this has obtained so much energy that its
energy exceeds the value connected with the ionisation tension. The
greater g, the shorter the time in which this value is obtained; the

1) With regard to the factor Q in the numerator, see note 1, p. 465.

*) We neglect the electrons liberated at the formation of the positive ions, sup-
posing that within stationary conditions as many of these electrons are disappearing
by recombination and formation of negative ions charged with mass. Additionally
it may be remarked, that in the field of this investigation the number of ions
compared with the number of free electrons is very small.

We intend to deal within short time more fully with this part of the subject.
4) J. Franck and G. Herrz. Verh. d. D. phys. Ges. 18, 213 (16).

468

number of ionisations per time-unit will be directly proportional to g.

Later Franck and Hertz *), just as C. D. Cap’), in connection
with N. Bour’s theory have assumed that unelastic collision can also
already take place before the tension of ionisation has been reached,
in whieh then removal of one of the electrons of the atom to a
path lying more outward, takes place. On return to the normal
path this energy can then be emitted. Yet the result of the elementary °
theory will be approximated by three cases:

I. Through absorption of the radiated energy by neighbouring
atoms (Compton) °).

Il. By increase according in quanta of the energy of slow electrons
on collision with dislocated atoms (‘collisions of the second kind”
in the theory of O. Krein and S. Rosserann; ef. also § 5).

Ill. (In a slight degree) through the renewed collision between
dislocated atom and (rapid) electron, before the former has lost
energy by radiation (K. J. van per Bri‘) ).

In agreement with our conclusion from equation (4) communica-
tion I it may therefore really be expected that in approximation the
relation a.g== const. will hold for each of these gases separately,
so long as the nature of the bearers is not subjected to any charac-
teristic modification. For in this case the energy-compensation ensuing
from I—III will always be the same percentage. This compensation
must, however, be very different for different gases. So that, the
tensions of ionisation also being so greatly divergent, we are led to
accept the obvious conclusion that the value of ag will be different
for different (noble) gases. We shall revert to this when discussing c.

That for the rest deviation is to be empirically observed ad 6
between a calculation based on formula III and observation (chiefly
as a consequence of errors of observation), may appear from the
following example (argon); though formula III would lead us to
expect that the value:

would be constant, a consideration of the values published by Rúür-
TENAUER shows that in table 5 e.g. the “constant” which amounts
to about 2,3.10-5, for one and the same noble gas in a definite
case (in which the pressure varies from 0,5 to 0,64 mm., the current
density from 1,49 to 1,21 A/em?. and the bore of the tube from

1) J. FRANCK and G. Hertz. Phys. Zeitschr. 20, 133 (719).

4) C. D. Carp. Phil. Mag. (6) 278 (14). Phys. Rev. (2) 15, 33 ('20).

. T. Compton. Phys. Review (2) 15, 476, 1920.

J. VAN DER BIJL. Phys. Rev. 10, 546 (17).

)
3)
5 K.

469

2,01 cm?. to 0,454 cm?.) shows the maximum deviation of 0,7 . 105.

In opposition to the fact of such a maximum deviation of about
30°’, it may be stated that the values of the tension gradient for
one and the same gas in RÜTrrrNAUER’s observations inter se are to
each other as a maximum as 1 to 4. We therefore consider (see
also our calculation for nitrogen p. 472 footnote) the effect of g
exceeding the errors of observation to be present.

We consider the fact of this theoretical and empirical determi-
nation of the approximated proportionality of the pressure effect with
Ag, hence with the added energy, of great importance. It is in perfect
harmony with the proportionality of the light emission of the pos.
pile with the added energy, which had been established by our
objective measurements. We will presently come back to this point
of simultaneous and quantitative parallelism. (See § 5).

With respect to case c we already remarked that divergent values
should be expected for ag resp. 6 for different gases. This is opposed
to Rorrenaver’s view; for this investigator thinks — with reference
to his empirical formule — to be allowed to consider the pressure
effects comparable for different kinds of gases, and assumes / to
have the same value for different gases. In our opinion the way in
which Rérrenaver introduced g into the empirical formula of the
pressure effect, cannot very well be accepted. He was in this
evidently led by the results for argon and helium (table 4 of his
communication); in fact we find here only a maximum deviation
of about 15°/,*). Besides on the ground of the theoretical expectation,
we have, however, reason to think here of chance, also on the
ground of what follows. In the absence of determinations of the
value of g, neon has not been taken for a comparison by RÜTTENAUER
in the corresponding calculated constants. For this purpose we can,
however, derive with amply sufficient accuracy from the determi-
nations of the terminal voltage communicated in our Thesis that
under comparable circumstances the potential gradient in neon
amounts to about 24 times that in argon’). When we, therefore,

1) In RiitrenaveR’s tabel 4 we find for helium and argon for the same tube
a maximum deviation in the “constant” EN which amounts to about
Ag V M1
46. 10-5, of a value of 0,75. 10-5
(in which p varies from 0.618 to 0,776 m.m.)
(974, fs ils oi 11.86. oet Tal ramp: /ec,m:®),

2) In the derivation from the terminal voltage cathode- and anode gradient
have been taken into account. That irregularilies at the electrodes cannot play an
important part in our case, appears among other things when also the ratio of
the tension-gradients for argon and helium are derived from the terminal voltages;

470

place the values of Ap, A, and p found for neon (RGTTENAUER,
table 1 of his publication) in his table 4, we can write g=5 for
neon, g being put at 2,0 for argon. Then we find:

TABLE A.
dh a ay h | A
Tube | | P | Ap A g arn 05 = constant
Wot |
Ill 7 = 60 Neon 0.776 | 0.026 | 1.13 | 5. - 1.33
Ill 2 = 60 Argon 0.741 | 0.062 | 1.21 | 2.0 4.98
Ill / = 60 Helium 0.785 | 0.079 | 1.13 | 9.67 4.73

in other words the value of the “constant” is from 300 to 400°/,
higher for argon and helium than for neon. This shows in our
opinion that it is injustifiable to put the pressure effects for different
gases comparable on such a basis.

Conclusion. It is necessary to replace Ritrrenaver’s empirical
formula by the theoretical formula:

AV MI

AVMI
— — - p (9) resp. Ee Wiep

NS Dp
p =f D De (9)

in which p(g) represents a function of the tension gradient, which
in definite regions can approximately assume the form bg, in which
b represents a constant the value of which is not the same for
different gases.

§ 5. Region of validity.

We pointed in our previous communication that the phenomena
in the path of the current are very complicated, and that our for-
mulae are drawn up for more or less idealized cases. What makes
A. RirrenaveEr’s determinations also so interesting is that they were
carried out with noble gases, in which the conditions in the path
of the current are naturally much less complicated than in the
multi-atomic not-noble gases. Besides this investigator used a very
long and wide positive pile, which brings out the influence of what
happens in the positive pile better.

We mentioned already that in his second publication F. SKAUPY

then the ratio appears to agree with that which ensues from the values of the
potential gradient as they have been measured by A. RiirrENAUER with the
positive pile.

471

as appears from some remarks, was inclined to the belief that the
pressure effect might be referred to the phenomena of electrostric-
tion. On page 215 loc.cit. it says about this: „In meiner schon
erwähnten Arbeit über die Druckdifferenzen wurde gezeigt, dass
bei Argonröhren innerhalb eines gewissen Druckgebietes (etwa 0,5
bis 3mm. Hg) die sich bei einer gegebenen Stromstärke einstellende
Druckdifferenz zwischen den Enden der 600 mm. langen, 0,8 cm.
weiten Réhre umgekehrt proportional dem in der Röhre berrschenden
Druck war. Durch einen Irritum wurde diese Beziehung für alle
Edelgasse als gültig angenommen und darauf eine Theorie der Er-
scheinung gegründet. Diese kann wohl nicht richtig sein, da die
Beziehung nur für Argon in dem genannten: Druckgebiet erfüllt ist,
aber nicht z. B. für Neon oder Helium.”

We point out, however, that A. RÜrTENAUER does not only find
the dependence on p for argon, but also for the noble gases neon
and helium, so that here no argument is present to induce us to
look for the central point of the explanation of the phenomena in
another region. We also remarked before that already in 1880 D.
Bos') showed that the effects which can ensue from the electro-
striction for gases, are exceedingly small.

Besides, as we could show that the region covered by A.
RGTTENAUER quantitatively continued that examined by us, if only
the right laws of diffusion are applied for every region, the validity
of our theoretical conception is confirmed for investigations in which

TABLE B.
RDP ast Ws 71090 or cal to 40
Q 0.03) ta +2 OF Cark to- 10
p O85, toric Be2’ tor teas Leto 8
A Obe toe t2.! or ca “I” to 20
id 0.6 to 45 oren iet te 75: 2)
M 4 to 40 orRea. st ito: 10
l 5 to 60 or yea." tto 12

') Diss. Groningen.

2) That for the tension gradient in this record of the ratios also observations
made on nitrogen, are included, may be justified thus. We published the following
measurements already before: p, = 1.18 m.m. Hg. Terminal voltage 288 V.
hl =6.5 em. g,=3.15 mm.*. M, = 28, A, = 12.7 Amp. cm, pj =0.18 mm.
Po = 0.15, 1, =5, Qo = 3.15, My = 28, A. = 127. For nitrogen in uviol-glass with
Q= 38.15 m.m.2 there are known to the author (Tabel C) the following three obser-
vations of p in connection with the terminal voltage, from which we arrive at the
bracketed values for the potential difference between the ends of the positive pile

472

the values of the different quantities, are as a maximum to each
other in the ratio as recorded in table B.

Continued experimental investigation on others than the examined
gases but also on the latter themselves can, however, still reveal
much. For all these investigations have been made within limits
for which if may be assumed that the nature of the luminescent
centres and of the current-conducting ions does not undergo any
essential change. We pointed out before that it follows from the
researches of J. Srark'), A. Wenner and J. Franck’) that when
p is sufficiently reduced, and g sufficiently raised, the pressure-offect
reverses it sign*), It may, however, also be questioned, what happens,
when the nature of the discharge is maintained, but the current-
density is greatly increased. We know only one indication of an
essential change taking place in this case; already in I we expressed *)
the desirability of examining by means of continued investigations
of the pressure-effect, whether anything could be derived from this

[by making by estimation, an approximate calculation of the cathode and anode
gradient and the loss of potential between the electrodes end the entrances of

TABLE G
p in m.m. Hg Terminal voltage | Pot. diff. pos. column Thesis
0.34 212 Volt (ca. 170 Volt) table 4
1.19 ZS, (ca. 240°", ) . 10
2.38 350 „ (ca. 290) ..2.) 4 14

the capillary path of the current]. Extrapolating we then find for p=0.15:
pot. gradient in the pos. pile: about 145 Volts. If in connection with this we
assume the pot. gradient to be %/; at 0.15 mm. of that at p, =1.19 m.m.

hence a = =| and if we bear in mind that we must apply here the formula
2

A p= fag VA, the following formula would follow from this

ED py 99; Lae. ER
Dip, hype ses

the ratio measured on nitrogen being a == os

)

More and more sharply defined measurements are very desirable also here.

1) J. STARK. BOLTZMANN-Festschrift 1904.

4) A. WEHNEL? and J. Franck. Verh. d. D. phys. Ges. 12, 444 (1910).

3) For convenience sake we shall distinguish this as “negative” effect from the
“positive” effect found by us.

4) Communication | loc, cit. 1178.

473

about change of the luminescent cenires on the transition from the
blue to the red argon-spectrum. On this head A. RürrrNAuwr’s
experiments give no decisive result, because the current-densities
applied by this investigator, are too small. The author expresses
the hope that — experimenting in this region being impossible to
him for the present — this remark may induce others to undertake
a further investigation.

§ 6. Quantitative and Simultaneous Parallelism of Light Emission
and Pressure Effect.

We derived in our former publication that the pressure-effects are
chiefly due to the transportation of ions by the electric current (mass-
transportation), which ions have originated at the impact between
electrons and atoms. Where the extension of the experiments corro-
borates our theoretical conception quantitatively, we think that itis
not devoid of interest to remark here that the theory of quanta
manifests its simultaneous and quantitative validity with respect to
light emission and pressure effect by means of the positive pile.

We have, indeed, to do here with two typical regions of the
application of the theory of quanta:

1. With light emission, the region of spectroscopy, in which the
phenomena should be studied, which present themselves on the return
of electrons from abnormal to less abnormal paths;

2. With the region of the pressure effects, in which the collisions
should be studied between electrons and atoms, the formation of ions,
hence*) the passing of the atom-electrons from normal to abnormal paths.

As soon as the ‘bearers’ change their character, both the character
of the light emission and of the pressure effect changes. The latter
may reverse its sign; as regards the light emission the change finds
among others a pregnant expression in the law of displacement
already cited in our previous paper.

If on the other hand the electric conditions do not change
characteristically, if the bearers continue to preserve the same
character, our quantitative objective measurements of the light emission
and our and Rirrenaurr’s manometric determinations of the pressure
effect prove the simultaneous quantitative proportionality of light- and
pressure effect with the added energy. That the light emission does
not change its character through increase of the added quantity of
energy, was only what was to be expected according to the theory
of quanta. Accordingly we consider particularly the fact that the
same thing holds simultaneously for the pressure-effect, a contribution

*) As far as the positive ions are concerned,

474

to our knowledge. We see tn this a confirmation of the view that
the atoms both absorb and emit energy in quanta, at the same time
an interaction between the two regions, which latter finds expression
in a related region of investigation, among others in Krein and
RossELANb’s theory *).

The well-known theoretical parallelism between these two regions
and the simultaneous parallelism between the observations on the
pressure effects and the light emission which have now been expe-
rimentally shown objectively, corroborate anew the close relation,
the wnity between these two classes of phenomena.

§ 7. Summary.

1. Our priority with regard to the “positive” pressure effect is
established.

It is shown that A. Rirrenaver’s experimental investigations quan-
titatively confirm the theoretical view and formulae about the pressure
effect found by us, which we gave before. This establishes confirms
for an extensive region of validity defined in $ 5 that the pressure
differences chiefly occur in consequence of mass-transportation by the
electric current.

2. It is desirable to replace the emperical formula given by
A. Rérrenaver for the pressure effect by two formulae derivable
from the theory, dependent on the ratio between the free path of
the corpuscles and the (round) diameter of the tube, viz.:

AV M1 AVM!
Ap= f su eles po) aresprs o-Aipia=z ae. . p (9)
in which p(g) represents a function of the potential gradient, which
_can assume approximately the form bg in definite regions; in which
b represents a constant the value of which is diferent for different
gases.

3. It is shown that the opinion advanced by F. Skaupy that the
pressure effect would be determined by the elastic electron impact,
is untenable.

4. The significance of the simultaneous parallelism of the quan-
titatively and objectively measured light and pressure effects with
regard to the theory of the quanta is pointed ont. It confirms that
the atoms both emit and absorb energy in quanta.

5.‘ Attention is drawn to the desirability of extending the investi-
gations, in particular also to argon.

Dordrecht, October 11, 1922.

1) KLEIN en RossELAND. Zeitschr. f. Physik. 4, 46 (21).

Botany. — “On a new clinostat after pr Bovurer’. By Prof.
B: Ay RC: Went.

(Communicated at the meeting of December 30, 1922).

It has been known to every botanist for more than 15 years,
that the clinostats in present use are not satisfactory with regard
to great precision. Already in 1907 van HarrrveLD*) made the
errors of those instruments known to us in a detailed study. He him-
self constructed a much better clinostat, satisfying high requirements,
but nevertheless introduced only in a few laboratories. This will be
chiefly due to the great costs, unsurmountable for most laboratories.

To the above fact it has been chiefly due, that Mr. P. A. pe
Bouter, mechanic of the Botanical Laboratory at Utrecht, asked
himself, whether it would not be possible to construct a much
cheaper clinostat, nevertheless coming up to high requirements.
Those considerations have led to the construction of a new clinostat,
the description of which follows.

Fig. 1 shows the clinostat in a more or less schematic way. 1 is
a shuntmotor, running directly full speed, and connected by a belt
3, with a flywheel 2, to the axis of which a pinion has been fixed.
With the aid of cog-wheels its motion is transmitted to the proper
clinostat 5. The axis of the fly-wheel turns on ball-bearings. Now
the question is, to make this fly-wheel revolve exactly once a second ;
this cannot be attained by altering the speed of the motor or by
regulating the diameter of the grooved wheels because of a too
great oscillation of the voltage of the town-plant. Neither does the
motor run regularly with equal voltage; namely with excentric load.
For this reason a different construction has been used here.

Into the circuit + — of the motor a resistance 12 has been
inserted in the form of a lamp, in consequence of which the fly-
wheel runs a little too slowly, e.g. half a rotation a second. It
however this resistance is put out of circuit, the fly-wheel revolves
a little too fast, e.g. two rotations a second. This putting out takes

1) PH. vAN HARREVELD, Die Unzulänglichkeit der heutigen Klinostaten für reiz-
physiologische Untersuchungen. Recueil des Travaux botaniques néerlandais. III.
1907, p. 178.

476

place every second with the aid of the pendulum of a clock keeping

exact time.

SDIDIPN DDN,

pJ
uy
J
Ine

a ee
Fig. 1. Sketch of the new clinostat; description in the text.

At 6 we see an electro-magnet every second turning magnetic
for an instant and attracting the spring-armature 7. The turning-over
switch 8 is drawn to one side by the spring 9, in consequence
of which the contact 10 is made. The current passes from + through
the motor straight to contact 10, next through a part of the switch
8, through the spring 9 and finally to —; in this way the motor
runs full speed.

But on the fly-wheel a cam 11 has been fixed; this makes the
switch 8 catch behind the armature 7, in consequence of which the
circuit is broken at 10. Then the current has to pass through the
resistance and the motor runs slower.

The final result is that the fly-wheel makes exactly one revolution
a second. Even considerable oscillations of the voltage of the light

477

and power-station are of no consequence, the only result will be,
that the cam 11 is a little more to the right or to the left at the
moment, at which the second circuit is closed, so that only the ratio
of the rapidly and slowly revolving parts of the axis of the fly-wheel
may be altered every second. This is of no importance, because the
axis of the clinostat revolves at a much slower rate and the movement
is transmitted to this by means of the cog-wheels 4, ete.

To the horizontal axis of the clinostat a conical cog-weel has
been fixed, in which another conical cog-wheel catches, fastened to
an adjustable axis 5. This latter axis has been fitted on in such a.
way, that it can revolve on the horizontal axis and can be fixed,
while the rotatory movement is not impeded. This enables us to
give the axis of the clinostat any desirable position. By fixing the
adjustable axis and releasing the adjusting-apparatus, a rotation of the
plant perpendicular to the horizontal axis may be obtained. This
arrangement is shown in fig. 2; the adjustable axis is fastened with
the screw A, the adjusting-apparatus with the handle 5.

Fig. 3 gives a backview of the whole apparatus, in which the
arrangement of fig. 2 has not yet been fitted on. This figure shows,
that the apparatus is comparatively small and may easily be removed
by one person. The position of the axis too may be modified
without any difficulty during the experiment.

To the simple construction it is owing that the costs of purchase
are considerably lower than of any other satisfactory clinostat. An
objection is, that the motor keeps running throughout the experiment
and therefore constantly uses current. But then the axis revolves
with great power, so that considerable weights can be carried, while
excentric loading that is rather considerable, does not cause any
alteration in the regular running of the clinostat. .

In order to check the running of this clinostat and compare it
with Prerrer’s and vAN HAarREVELD’s clinostats, the recording-
apparatus of the auxanometer of KONINGSBERGER*) was used.

For this purpose electrodes were fixed to the axis of the
clinostat either right opposite to each other or at an angle of 90°,
in such a way, that after each full rotation of the axis, the top of
such an electrode once made contact in a mercurydish and in this
way a circuit was closed for a short moment. Closing that circuit
caused a writing glass-pen to be stopped in its course and to be

1) V. J. KONINGSBERGER, A method of recording growth under various external
influences. Proceedings Kon. Ak. v. Wet. Amsterdam. W. en Nat. Afd. XXX,
6/7. 1921.

478

sent back to its starting-point, while a drum with paper, on which
the recording occurred, was moved on 1.5 mm.

SSID

Les
EZ

Fig. 2. Top of the clinostat-axis with conical wheels, as described
in the text.

The pen moves along the paper .with a velocity of 1 mm. a
second, writing a straight line. A number of parallel lines arises
in this way, as shown in fig. 4, drawn for so many seconds as the
period amounts to, needed by the clinostat-axis to make a half or
a quarter of a rotation.

If therefore the clinostat runs regularly, these lines must be of
equal length, or may differ one second at most, with respect to the
point of time at which the contact with the mercury is made.

In the figure something else has been recorded: every 6 minutes

479

a time-signal is given on a continuous line T. Of course the distance
covered by the circumference of the clinostat-axis in successive 6

Fig. 3. Backview of the whole clinostat.

minutes must always be the same; so the distance between the
time-signals must not vary with a good clinostat.

Now the various clinostats were tested in two ways; partly
without load, partly with an excentric load on the axis. This latter
was done, because that very unequal load causes the greatest diffi-
culties in practice, especially when in the dark plants have to be
fixed on a clinostat, or when we have to try several times in order
to get an exact centering, when meanwhile the plants have already
been exposed to the unilateral influence of gravitation for a long
time. Fig. 4 shows the results of those experiments.

In I the behaviour of a clinostat of Prerrer is shown with an
excentric load, amounting to 0,26 KG. when calculated on the axis.

31

Proceedings Royal Acad. Amsterdam. Vol. XXV.

480

Fig. 4. I. Clinostat of Prrrrer. Records of half rotations.

this load

Clinostat of VAN HARREVELD. Record of 1/4

B as above. At t this load was increased to 2 KG. at

Il.

B is the excentric overload converted on the axis. At ij

was removed.

rotations.

which the clinostat stopped; next the overload was removed. III.

Clinostat of pe Bourer. Record of half rotations. B.

load as above.
6 minutes.

excentric Over-

In all 3 figures T is the time-line, checked every

481

It may be noticed how great the difference is between the two
halves of the revolution, while this difference disappears beyond the
arrow, indicating the moment at which the excentric load is removed.

II refers to the clinostat of van Harrrvurp; here the excentric
load was larger, 1.6 KG., calculated on the axis and there too
irregularities appear, which are sometimes very considerable. The
arrow indicates the moment at which the excentric load was
increased to 2 KG. The clinostat had come to a stop; this happened
with a clock-weight of 13 KG. If a heavier weight had been
chosen, the movement would of course have continued. After
removing every excentrie load, the running was perfectly regular,
as appears from the rest of the figure.

III shows the working of the clinostat px Bourrr with an excentric
load of 26 KG. calculated on the axis. We see that notwithstanding
this, it runs quite regularly, so that the superiority of this clinostat
is perfectly clear from the figure.

A contemplation of the time-signals T in the three parts of the
figure will necessarily lead to the same conclusion; these time-
signals gave a sign after every six minutes.

Summarizing I arrive at the conclusion, that this clinostat is a
great improvement on those hitherto used. Now that plant-physiology
is developing more and more into an exact science, the old “a peu
pres” methods will have to be left and therefore care should be
taken that the instruments used come up to high requirements of
precision. |

Utrecht, Botanical Laboratory, December 1922.

Biochemistry. — ,,Concerning the Synthetic Action of Bacteria in
the Paunch of the Cow’. By Prof. B. Ssontuma and J. E. van
DER ZANDE. (Communicated by Prof. H. ZwaarDEMAKER).

(Communicated at the meeting of December 30, 1922).

The question whether bacterial processes occurring in the paunch
of ruminants are significant for the metabolism of these amimals’),
should be given more attention to than here to fore, since, by way of
trial, ruminants are fed with urea, made from the nitrogen in the
air. For the significance of the substitution of urea for protein in
the animal’s diet depends to a great extent on the capacity of the
bacteria of the paunch to synthesize from urea, in the presence of
non-nitrogenous substances, the amino-acids which the higher animals
are not able to build up.

Tryptophane is one of the amino-acids indispensable to man and
to the higher animals. It is highly improbable that mammals can
synthesize tyrosine from non-aromatic substances.

We have tried to ascertain whether these two substances can be
built up by the bacteria occurring in the cow’s paunch, when,
beyond ammonia no other source of nitrogen is present than urea,
asparagin or aspartic acid.

Our procedure was as follows: *)

Directly when the animal was killed, part of the contents of the
paunch was brought to our Laboratory in a sterile bottle, fitted
with a glass stopper’).

With the help of a sterile wire a little of the paunch contents
(i.e. of the turbid fluid after removal of the coarser particles) was
transmitted to sterile nutrient soltitions, contained in Erlenmeyer-
flasks plugged with cotton-cool, and which were of a depth of 1

i

1) Here we refer to the development of volatile acids in the paunch from sugar,
as demonstrated before by one of us (B. S.). See Bericht II] 5th International.
Congres für “angewandte Chemie” Berlin 1903, p. 825.

*) It was adopted because bacterial growth could not easily be recognized
directly in the turbid juice of the paunch (even when much diluted), and also
because we wanted quantitative data regarding tryptophane-formation.

3) We would here gratefully acknowledge our thanks to Mr. HorernaceL and to
Mr. pe Graar, respectively director and sub-director of the Utrecht abattoir, for
their kind assistance in obtaining the material required for these experiments.

483

to 1'/, em. The flasks were then left standing in an incubator
at 36° C. Duplicate cultures were made for each experiment.

When the bacteria were fairly developed (which was the case
after two days) one of the cultures was examined for the presence
of the amino-acids, alluded to above; the other remained in the
neubator. Moreover a new culture-medium was inoculated with it.
We used Uscuinsky’s solution, unmodified or modified as indicated
below. *)

Since the py of the- paunch contents was about 7,4, we took
care to let the py of our culture media be the same.

In order to demonstrate the presence of tryptophane we applied
the reactions of Voisenwr (with HCI, formaldehyde and nitrite) and
of Horkins-Corr (with H,SO, and glyoxylic acid). Mition’s reagent
was used for ascertaining the presence of tyrosine. VoIsENET’s rea-
gent stains differently with indole and with tryptophane. Indole after
shaking out with ether was reacted on with dimethylpara amidoben-
zaldehy de.

Uscuinski’s solution, whether modified or not, but invariably
without an aromatic or heterocyclic compound, inoculated with a
small quantum of the paunch-contents, always gave in the sediment
(obtained by centrifugation after the addition of alcohol) after a
sojourn at 36° C. in an incubator, a very distinct tryptophane, and
tyrosine-reaction, whereas initially the reactions were negative.

A better growth and more powerful reactions were obtained by
mixing 10 ¢.c. of the fresh paunch fluid with 25 e.c. of Uscninskr's
solution.

Whereas the reactions in the sediment were invariably positive,
the supernatant fluid displayed negative reactions.

In order to make sure that the tryptophane and the tyrosine
reactions were not due to other indole or phenol-derivatives, the
sediment was, in a few cases, centrifuged anew with diluted alcohol
and once more with ether (indole). The reactions of the sediment
were as distinct as before. The cultures themselves were also shaken
out with ether some times. With the above-named aromatic
aldehyde the ether gave a negative indole-reaction. It was evident,
therefore, that neither free tryptophane, nor other free indole-deriva-
tives, nor free phenol-like bodies were present. The positive reactions
may, therefore, be attributed to the body-protein of the bacteria.

On inoculation of new Uscuinsky solutions with the cultures an

1) The ordinary Uscuinsxy-solution contains K, Na, Ca, Mg, PO,, Cl and SO,;
besides glycerol, ammonium-lactate and sodium aspartate.

484

excellent growth could be noted, and after a couple of days positive
tryptophane, and tyrosine-reactions of the sediment.

The present investigation, therefore, shows clearly that there are
bacteria in the paunch of the cow, capable of building up trypto-
phane and tyrosine’ with an aliphatic nitrogen-compound and with
ammonia. With every one of the six paunches we succeeded in
obtaining this result.

We consider the presence of tyrosine to be established when
bacterial bodies show a phenol-reaction (MiLLon’s) The non-specificity
of the tryptophane reactions is of no importance in our experiments.
They are only needed to show the presence of an indole-derivative so
long as tryptophane is considered as sole indole-derivative in the
protein-molecule *).

Positive results were also obtained in the experiments in which
asparagin (or sodium-aspartate) had been replaced by urea. The
bacterial growth was, however, decidedly slower. The ammonium-
lactate had been substituted in these experiments by potassium
lactate, so that urea was the sole source of nitrogen.

After 2 X 24 hours the tryptophane-reactions were as a rule weak
in the turbid culture solution and very clear in the sediment, which
had been obtained through centrifugation.

A couple of times we added tryptophane to the Uscninsky solution
which resulted in the formation of indole contrary to the other
experiments.

Direct addition of indole inhibited bacterial growth considerably ;
it was arrested completely by 50 mgms per 100 c.c.

Whether tryptophane can be developed from indole, as assumed
by Loar, is not borne out by the present experiments, for, where
addition of a small quantity of indole caused some bacterial growth,
the formation of tryptophane may have resulted from the presence
of ammonium-nitrogen or asparagine-nitrogen.

When substituting glucose for the glycerol and the lactic acid of
the Uscuinsky-solution a tryptophane synthesis takes place which is
almost equal to that in the ordinary Uscninsky-solution.

In experiments under approximately anaérobic conditions the growth
was inferior to that obtained in the manner above-described. An
experiment, in which air was drawn through the fluid by suction,
did not yield a larger growth than usual.

1) Since gelatine does not yield Vorsenet’s, nor Mition’s reaction and proline
and oxyproline are contained in it, it follows that these two’ amino-acids do not
give these reactions.

485

The histidine reactions thus far obtained, were still somewhat
doubtful.

Several microscopic preparations were made of the cultures. Some-
times different species were present, i.e. diplococci, rod-shaped bac-
teria; sometimes staphylococci and streptococci; in one case the
predominance of one species was such as to render it difficult to
find another. These almost pure cultures were not always made up
of the same bacteria; sometimes they were small ovoid, at other
times rod-shaped bacteria.

It being known that even various stocks of one and the same
species may differ largely as to the chemical changes they engender,
we did not ascertain whether the developing species were in any
way concerned in the result of the reaction.

According to an approximate quantitative determination in a
culture, three days old, the sediment of 100 ce. contained about
3 mgms of tryptophane, i.e. per Liter 30 mgms, or 3 grms per
100 L. (putting the paunch contents at 100 L.).

A man of 70 k.g. weight requires per day about 2'/,—3 grms
of tryptophane. Assuming the same ratio for a cow, this animal
would require per day about 17'/,—20 grms. The quantity necessary
for the producton of milk has not been taken into account here.

Putting the tryptophane content of milk per L. at about 750 mgms,
and putting the daily flow of milk at, say, 12 Liters, the animal
would have to take in another quantum of 9 grms of tryptophane.

As far as we are aware tryptophane synthesis by bacteria (B.
coli and B. FrrepLANDER) from ammoniae and aliphatic nitrogen-
compounds, has been demonstrated only once, viz. by Login’).

From the publication of Braun and Cann—Bronner’), which came
to our notice when our experiments had nearly come to an end,
it may be inferred that their experiments also pointed to trypto-
phane synthesis, for they could grow coli, paratyphoid-, and Friep-
LANDER-bacteria when ammonia nitrogen was the only source of
nitrogen present. Where they report, that under perfectly anaérobic
conditions ammoniac-assimilation is impossible, even after the supply
of more energy, the question rises (granting their theory to hold
generally) whether in the rumination process an aérobic condition
exists which allows any synthesis worth mentioning.

It may rationally be supposed that, wherever micro-organisms
manage to live on inorganic or aliphatic nitrogen-sources, they them-

1) J. of Pathol. and Bact. Bd. 23, 224 (1919/1920).
2) Biochem. Zeitschrift Bd. 131, 272 (1922).

486

selves derive the cyclic amino-acids from these sources, it being a
fact that protein, containing these amino-acids, is always present in
these organisms.

In how far the amino-acids, formed in the paunch, are of use
to the metabolism of ruminants, will have to be made out by food-
experiments, which will also have to show whether the bacterial
protein, formed in the paunch, is resorbed.

Let it be observed that we have never succeeded in demonstrating
tryptophane (or tyrosine) in the fresh turbid paunch-fluid (after the
removal of the solid particles) and also that we were not more
successful in this respect after cultivating for some days in the
incubator, either under aérobic or anaérobie conditions.

Meanwhile we should not omit stating that reactions in a fluid
like the paunch-fluid, are far less sensitive than those in unstained
solutions. Only when 7 mgms of tryptophane per 100 cc. was added
in the form of protein (bloodplasma) a perfectly distinct try ptopbane-
reaction was recognizable.

Still, the phenomenon, just alluded to, does not point to an abund-
ant tryptophane formation in the paunch, which is the more
striking since the paunch fluid with Uscninsky’s solution (10: 25)
yields negative results at starting, but exhibits distinct reactions
after 2 24 hrs.

The above experiments show: 1°. that various bacteria present in
the paunch of cows can build up the amino-acids tryptophane and
tyrosine from ammonia nitrogen plus asparagine (or aspartic) nitrogen,
and also from urea as nitrogen-source.

2°. that these bacteria can form quantities of tryptophane in the
culture-medium of Uscuinsky, which may be of some significance
for the metabolism in cows; however it is not quite certain whether
this synthesis is equally intense in the paunch.

(From the Chem. Labor. of the Utrecht Veterinary Univ.)

CONTENTS.

ALPHA-AUTOMATICITY (On the) of the autonomous organs. 152.
AMYLASE of Aspergillus niger (The influence of hydrogen ion concentration
upon the action of the). 6.
ANAPHYLAXIS (Experiments on) with azoproteins. 34.
ANTHLES (Cuba, the) and the Southern Moluccas. 263.
ANTIPHOTOTROPIC CURVATURES (Further researches on the) occurring in the
coleoptiles of Avena. 158.
ARGON (A connection between the spectra of ionized potassium and). I. 67.
— (On the mean free path of slow electrons in neon and). 90.
— (On the excitation and ionization potentials of neon and). 179. Appen-
dix. 442.
ARSENIC (Determination of the vapour pressure of metallic). 387.
ASPERGILLUS NIGER (The influence of hydrogen ion concentration upon the
action of the amylase of). 6.
Atom (On WHIT7AKER’S quantum mechanism in the). 414.
AXES OF ROTATION of quadratic surfaces through 4 given points. 52.
— and planes of symmetry of quadratic surfaces of revolution through 5,
6 and 7 given points. 61.
AZOPROTEINS (Experiments on anaphylaxis with). 34.
BACILLUS POLYMYXA (On)279.
BACKER (H. J.). The dissociation constants of sulphonacetic and x sul-
phonpropionic acids. 359.
BACTERIA (Concerning the synthetic action of) in the paunch of the cow. 482.
BACTERIOPHAGUS of D'HERELLE (Studies on the). 31. II. 87. [IL 171.
BAUMSTAMM (Ueber einen fossilen) von Bolang (Java), ein Beitrag zur Kennt-
nis der fossilen Flora Niederländisch-Indiens. 9.
BENDING-POINTS (Abnormal strikes near the) of the horizontal projection of
the geanticlinal axis. 327.
BEWERINCK (M. W.) and L. E. DEN DOOREN DE JONG. On bacillus poly-
myxa. 279.
BISCOUMARIC ACIDS (The). 175.
Broop (An objective method for determining the coagulation-time of). 127.
BLOODVESSELS (On the significance of calcium- and potassiumions for the
artificial oedema and for the lumen of the). 145.
BOEKE (J.). On the regeneration of sensitive end-corpuscles after section

of the nerve. 319.
32
Proceedings Royal Acad. Amsterdam. Vol. XXV.

Il COUN Tee N TS

BoËSEKEN (J.). The dislocation theory of catalysis. 210.
Bork (L.). On the significance of the supra-orbital ridges in the primates. 16.
— The problem of orthognathism. 371.

BouTER (DE) (On a new clinostat after). 475.

BRAIN (Phylogenetic and ontogenetic increase of the volume of the) in
vertebrata. 230.

Breit (G.) and P. EHRENFEST. A remarkable case of quantization. 2.

— Calculations of the effective permeability and dielectric constant of a
powder. 293.

BREMEKAMP (C. E. B). Further researches on the antiphototropic curva-
tures occurring in the coleoptiles of Avena. 158.

BROUWER (H.A.). Fractures and faults near the surface of moving geanti-
clines. II]. Abnormal strikes near the bendingpoints of the horizontal
projection of the geanticlinal axis. 327.

Bure (J. H. N. vAN DER) and P. vAN RoMBURGH. Cyclic derivatives of
mannitol. 335.

BUIJTENDIJK (F. J. J.). A contribution to the physiology of the electrical
organ of Torpedo. 131.

BiuvoeT (J. M.) and A. KARSSEN: Research by means of Röntgen-rays on
the structure of the crystals of lithium and some of its compounds
with light elements. II. Lithium-hydride. 27.

CALCIUM- and potassiumions (On the significance of) for the artificial oedema
and for the lumen of the bloodvessels. 145.

CALCIUM OUTPUT (On the influence of the compositon of the food on the). 395.

CaraLysis (The dislocation theory of). 210.

— (Heterogeneous) and the orientation of adsorbed molecules. 324.

CaTALyst (The influence of a) on the thermodynamic quantities regulating
the velocity of a reaction. 199.

CLINOSTAT (On a new) after DE BOUTER. 475.

COAGULATION-TIME of blood (An objective method for determining the). 127.

COLEOPTILES of Avena (Further researches on the antiphototropic curva-
tures occurring in the). 158.

CONGRUENCE OF RAYS (Representation of a bilinear congruence of twisted
cubics on a bilinear). 22.

CrysraLs (Research by means of Röntgen-rays on the structure of the) of
lithium and some of its compounds with light elements. II. Lithium-
hydride. 27.

— (Explanation of some interference-curves of uni-axial and bi-axial) by
superposition of elliptic pencils. III. 81.
CRYSTAL STRUCTURE (The) of germanium. 125.
Cusa, the Antilles and the Southern Moluccas. 263.

GIOEN ZT EL-N Tes Ill

CURVATURES (Further researches on the antiphototropic) occurring in the
coleoptiles of Avena. 158.

CYCLIC DERIVATIVES of mannitol. 335.

Dik (H. W. J.) and P. ZEEMAN. A connection between the spectra of
ionized potassium and argon. [. 67.

DINGEMANSE (ELISABETH) and J. P. Wipaut. The action of sodium-
amide on pyridine, and some properties of x-aminopyridine. 458.

DISLOCATION THEORY (The) of catalysis. 210.

DissOCcIATION CONSTANTS (The) of sulphonacetic and z-sulphonpropionic
acids. 359.

DOOREN DE JONG (L. E. DEN) v. Jone (L. E. DEN DOOREN DE).

DuBors (EuG.). Phylogenetic and ontogenetic increase of the volume of
the brain in vertebrata. 230.

Duin (C. F. van) and H. R. Kruwr. Heterogeneous catalysis and the
orientation of adsorbed molecules. 324.

EHRENFEST (P.) and G. Breir. A remarkable case of quantization. 2.

ELECTRIC RESISTANCE (On the) of pure metals etc. X. Measurements con-
cerning the electric resistance of thallium in the temperature field of
liquid helium. 443. XI. Measurements concerning the electric resistance
of ordinary lead and of uranium lead below 14° K. 451.

ELECTRONS (On the mean free path of slow) in neon and argon. 90.

ELLIPTIC PENCILS (Explanation of some interference-curves of uni-axial and
bi-axial crystals by superposition of). III. 81.

EMIGRATION (On the causes of the) of leukocytes. 36.

END-CORPUSCLES (On the regeneration of sensitive) after section of the
nerve. 319.

EQuILiBRiA (In-, mono- and divariant). XXII. 341.

EXCITATION POTENTIALS (On the) and ionization potentials of neon and
argon. 179. Appendix. 442.

FERINGA (K.J.). On the causes of the emigration of leukocytes. 36.

Frora (Ueber einen fossilen Baumstamm von Bolang (Java), ein Beitrag zur
Kenntnis der fossilen) Niederländisch-Indiens. 9. -

FORMENKOEFFIZIENTEN (Ueber Determinanten aus). 354.

FROG-MUSCLE (On the progress of the veratrin-poisoning of the striated). 364.

FuNKE (G. L.). The influence of hydrogen ion concentration upon the
action of the amylase of Aspergillus niger. 6.

GALVANOGRAM of man (On respiratory oscillations in the). 225.

Gas MIXTURES (On the separation of) by diffusion in a flowing gas. 434.

GAS PRESSURE (On centres of luminescence and variations of the) in spectrum
tubes at electrical discharges. II. 463.

IV CAO WN VOL EN Sis,

GEANTICLINES (Fractures and faults near the surface of moving). Il. Abnor-
mal strikes near the bending-points of the horizontal projection of the
geahticlinal axis. 327.

Geometry (A new method for the solution of the problem of the character-
istics in the enumerative). 113.

GERMANIUM (The crystal structure of). 125.

Griaas (R. F.). Observations on the incandescent sand flow of the valley
of ten thousand smokes. 42.

HAMBURGER (L.). On centres of luminescence and variations of the gas
pressure in spectrum tubes at electrical discharges. II. 463.

HAMBURGER (R. J.). On the significance of calcium- and potassiumions
for the artificial oedema and for the lumen of the bloodvessels. 145.

Hevium (Further experiments with liquid). Q. On the electric resistance of
pure metals etc. X. Measurements concerning the electric resistance of
thallium in the temperature field of liquid helium. 443. XI. Measure-
ments concerning the electric resistance of ordinary lead and of
uranium lead below 14° K. 451.

HERELLE (p’) (Studies on the bacteriophagus of). 31. II. 87. HI. 171.

HerTz (G.). On the mean free path of slow electrons in neon and argon. 90.

— On the excitation and ionization potentials of neon and argon. 179.
Appendix. 442.
— On the separation of gas mixtures by diffusion in a flowing gas. 434.

Heux (J. W. N. re). Explanation of some interference-curves of uni-axial
and bi-axial crystals by superposition of elliptic pencils. III. 81.

HOLLEMAN (A. F.). Monochloro-trinitrobenzenes. 223.

HoRrIBA (SHINKICH}1). Determination of the vapour pressure of metallic
arsenic. 387.

HYDROGEN ION CONCENTRATION (The influence of) upon the action of. the
amylase of Aspergillus niger. 6.

HUMANS VAN DEN BERGH (A. A.) v. BERGH (A. A. HIJMANS VAN DEN).

INFLAMMATION of the udder (Changes in milk due to sterile). 275.

IONIZATION POTENTIALS (On the excitation and) of neon and argon. 179.

» Appendix. 442.

JANZEN (J. W.) and L.K. Wo rr. Studies on the bacteriophagus of D’HERELLE.
Sie ZE Al:

Jona (A. W. K. pe). The biscoumaric acids. 175.

Jona (L. E. DEN DOOREN DE) and M. W. BEIJERINCK. On bacillus poly-
myxa. 279, ;

KAMERLINGH ONNES (H.) v. ONNES (H. KAMERLINGH).

KARSSEN (A.) and J. M. Buvort. Research by means of Röntgen-rays on

the structure of the crystals of lithium and some of its compounds with
light elements. II, Lithium-hydride. 27.

C..OCN TT. Be Nr: Ss Vv

KEESOM (W. H.) and J. DE SMEDT. On the diffraction of Röntgen-ravs in
liquids. 118.

KLEIN (A. DE) and R. MAGNus. A further contribution concerning the function
of the otolithic apparatus. 256.

KOLKMEIJER (N. H.). The crystal structure of germanium. 125.
Kräuser (R.). Ueber einen fossilen Baumstamm von Bolang (Java), ein
Beitrag zur Kenntnis der fossilen Flora Niederlandisch-Indiens. 9.
KruutT (H. R.) and C.F. van Duin. Heterogeneous catalysis and the orient-

ation of adsorbed molecules. 324.

KUENEN (J. P.). The magneto-thermic effect according to thermodynamics.384.

KiihrR (C. A. H. vON WoOLZOGEN). On the occurrence of sulphate-
reduction in the deeper layers of the earth. 188.

LAAR (J. J. VAN). On the heat of mixing of normal and associating liquids.
309. 399.

LANDSTEINER (K.). Experiments on anaphylaxis with azoproteins. 34.

LEAD (Measurements concerning the electric resistance of ordinary) and
of uranium lead below 14° K. 451.

LEUKOCYTES (On the causes of the emigration of). 36.

LIGHT PATH (On the) in the general theory of relativity. 288.

Liguips (On the diffraction of Röntgen-rays in). 118.

— (On the heat of mixing of normal and associating). 309. 399.

LitHium (Research by means of Röntgen-rays on the structure of the crystals
of) and some of its compounds with light elements. II. Lithium-hydride. 27.

LORENTZ (H. A). On WuiITTAKER’sS quantum mechanism in the atom. 414.

LUMINESCENCE (On centres of) and variations of the gas pressure in spec-
trum tubes at electrical discharges. II. 463.

MaaNus (R.) and A. DE KreEIJN. A further contribution concerning the
function of the otolithic apparatus. 256.

MANNITOL (Cyclic derivatives of). 335.

Mirk (Changes in) due to sterile inflammation of the udder. 275.

Mor (W. E. pe). The disappearance of the diploid and triploid magnico-
ronate narcissi from the larger cultures and the appearance in their
place of tetraploid forms. 216.

MOLECULES (Heterogeneous catalysis and the orientation of adsorbed). 324.

Mo.uccas (Cuba, the Antilles and the Southern). 263.

MONOCHLORO-TRINITROBENZENES. 223.

MorpuHo.ocy (On the) of the testis of Rana fusca Rösel. 99.

Narcissit (The disappearance of the diploid and triploid magnicoronate)
from the larger cultures and the appearance in their place of tetraploid
forms. 216.

NEON AND ARGON (On the mean free path of slow electrons in). 90.

— (On the excitation and ionization potentials of). 179. Appendix. 442.

VI GaOpN) TEE NPL Ss

Nerve (On the regeneration of sensitive end-corpuscles after section of
the). 319.

ONNES (H. KAMERLINGH) and W. Tuijn. Further experiments with liquid
helium. QO. On the electric resistance of pure metals etc. X. Measure-
ments concerning the electric resistance of thallium in the temperature
field of liquid helium. 443.

— and W. Tuin. Further experiments with liquid helium. R. On the
electric resistance of pure metals etc. XI. Measurements concerning the
electric resistance of ordinary lead and of uranium lead below 14°
Ke dale

OorptT (G. J. van). On the morphology of the testis of Rana fusca
Rosel. 99.

ORTHOGNATHISM (The problem of). 371.

OTOLITHIC APPARATUS (A further contribution concerning the function of
the). 256.

PERMEABILITY (Calculations of the effective) and dielectric constant of a
powder. 293.

PHYLOGENETIC and ontogenetic increase of the volume of the brain in
vertebrata. 230.

PLANES OF SYMMETRY (Axes of rotation and) of quadratic surfaces of revolution
through 5, 6 and 7 given points. 61.

Point SPACE (Numbers of circles touching plane curves defined by represent-
ation on). 221.

PorassiuM (A connection between the spectra of ionized) and argon. I. 67.

POTASSIUMIONS (On the significance of calcium- and) for the artificial oedema
and for the lumen of the bloodvessels. 145.

Powpber (Calculations of the effective permeability and dielectric constant
of a). 203.

PRIMATES (On the significance of the supraorbital ridges in the). 16.

PsYCHOLOGICAL and physiological phenomena (Concordance of the laws of
some). 423.

PYRIDINE (The action of sodiumamide on), and some properties of x-ami-
nopyridine. 458.

QUANTIZATION (A remarkable case of). 2.

QUANTUM MECHANISM (On WHITTAKER’S) in the atom. 414.

OVERIDO (ARIE). On the progress of the veratrin-poisoning of the striated
frog-muscle. 364.

RANA FUSCA (On the morphology of the testis of) Rösel. 99.

Rays (Representation of a bilinear congruence of twisted cubics on a bilinear
congruence of). 22.

RELATIVITY (On the light path in the general theory of). 288.

RESPIRATORY OSCILLATIONS (On) in the galvanogram of man. 225.

ClOLNS TEEN T's VII

ROMBURGH (P VAN) and J. H. N. vaN DER Bura. Cyclic derivatives of
mannitol. 335.

RÖöNTGEN-RAYs (Research by means of) on the structure of the crystals of
lithium and some of its compounds with light elements. II. Lithium-
hydride. 27.

— (On the diffraction of) in liquids. 118.

RUTTEN (L.). Cuba, the Antilles and the Southern Moluccas. 263.

SAND FLOW (Observations on the incandescent) of the valley of ten thousand
smokes. 42.

SCHAAKE (G.). A new method for the solution of the problem of the
characteristics in the enumerative geometry. 113.

SCHREINEMAKERS (F. A. H.). In-, mono- and divariant equilibria. XXII. 341.

SJOLLEMA (B.). On the influence of the composition of the food on the
calcium output. 395.

.— and J. E. VAN DER ZANDE. Changes in milk due to sterile inflam-
mation of the udder. 275.

— and J. E.vAN DER ZANDE. Concerning the synthetic action of bacteria
in the paunch of the cow. 482.

SMEDT (J. DE) and W. H. Keresom. On the diffraction of Röntgen-rays in
liquids. 118.

SmMip Jr. (L. J.). Numbers of circles touching plane curves defined by
representation on point space. 221.

SODIUMAMIDE (The action of) on pyridine, and some properties of x-amino-
pyridine. 458.

SULPHATE-REDUCTION (On the occurrence of) in the deeper layers of the
earth. 188.

SULPHONACETIC and x-sulphongropionic acids (The dissociation constants
of). 359.

SUPERPOSITION (Explanation of some interference-curves of uni-axial and
bi-axial crystals by) of elliptic pencils. Il. 81.

SUPRA-ORBITAL RIDGES (On the significance of the) in the primates. 16.

SYNTHETIC ACTION of bacteria (Concerning the) in the paunch of the cow. 482.

TEN THOUSAND SMOKES (Observations on the incandescent sand flow of the
valley of). 42.

THALLIUM (Measurements concerning the electric resistance of) in the temper-
ature field of liquid helium. 443.

THERMODYNAMIC QUANTITIES (The influence of a catalyst on the) regulating
the velocity of a reaction. 199.

THERMODYNaMiIcs (The magneto-thermic effect according to). 384.

THIEL (E. vaN). The influence of a catalyst on the thermodynamic quanti-
ties regulating the velocity of a reaction. 199.

ToRrPEDO (A contribution to the physiology of the electrical organ of). 131.

Vill GO Ne TIE NES

Tuur (W.) and H. KAMERLINGH ONNEs. Further experiments with liquid
helium. O. On the electric resistance of pure metals etc. X. Measure-
ments concerning the electric resistance of thallium in the temperature
field of liquid helium. 443.

— and H. KAMERLINGH ONNEs. Further experiments with liquid helium.
R. On the electric resistance of pure metals etc. XI. Measurements
concerning the electric resistance of ordinary lead and of uranium
lead below 14° K. 451.

TwIsTED CUBICS (Representation of a bilinear congruence of) on a bilinear
congruence of rays. 22.

VEEN (H.J. vAN). Axes of rotation of quadratic surfaces through 4 given points.52.

— Axes of rotation and planes of symmetry of quadratic surfaces of
revolution through 5, 6 and 7 given points. 61.

VERATRIN-POISONING (On the progress of the) cf the striated frog-muscle. 364.

VERTEBRATA (Phylogenetic and ontogenetic increase of the volume of the
brain in). 230. |

WAERDEN (B. L. VAN DER). Ueber Determinanten aus Formenkoefh-
zienten. 354.

WEINBERG (A. A). On respiratory oscillations in the galvanogram of man. 225.

W EITZENBOCK (R.). Ueber Wirkungsfunktionen. 166. .

WenrT (F. A. F. C.). On a new clinostat after DE BOUTER. 475.

WHITTAKER’S quantum mechanism in the atom (On). 414.

WisautT (J. P.) and ELisABETH DINGEMANSE. The action of sodiumamide
on pyridine, and some properties of x-aminopyridine. 458.

WieERSMA (E. D.). Concordance of the laws of some psychological and
physiological phenomena. 423.

Wormer (Ere) and .J: W.. JANZEN. Studies on the bacteriophagus of
DPEREnEE ol. IL. 87. TT. Vii.

Worvius (R. J.). An objective method for determining the coagulation-
time of blood. 127.

WOLzZOGEN Künr (C. A. H. von) v. Künr (C. A. H. von WOLZOGEN).

W ouDE(W. VAN DER). On the light path in the general theory of relativity. 288.

ZANDE (J. E. VAN DER) and B. SJOLLEMA. Changes in milk due to sterile
inflammation of the udder. 275.

— and B. SJOLLEMA. Concerning the synthetic action of bacteria in the
paunch of the cow. 482.

ZEEMAN (P.) and H. W. J. Dik. A connection between the spectra of
ionized potassium and argon. I. 67.

ZW AARDEMAKER (H.). On the alpha-automaticity of the autonomous organs. 152.

KONINKLIJKE AKADEMIE
VAN WETENSCHAPPEN
-- TE AMSTERDAM -:-

PROCEEDINGS OF THE
SECTION OF SCIENCES

VOLUME XXV
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PUBLISHED BY
“KONINKLIJKE AKADEMIE VAN WETENSCHAPPEN”, AMSTERDAM
MARCH 1923

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